============================== Prover9 =============================== Prover9 (64) version 2009-02A, February 2009. Process 3230 was started by veroff on proof, Mon Feb 20 11:45:55 2012 The command was "prover9 -f first_sketch.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file first_sketch.in assign(order,kbo). set(lex_order_vars). lex([LEX_1,1,a,K,L,R,T,*,\,/]). set(para_units_only). % set(para_units_only) -> assign(para_lit_limit, 1). assign(max_megs,8000). assign(max_weight,35). assign(sos_limit,-1). list(actions). given = 30 -> assign(max_weight,25). end_of_list. list(given_selection). part(H,high,weight,hint) = 1. part(Wf,low,weight,false) = 3. part(W0w,low,weight,weight <= 20) = 16. part(W0a,low,age,weight <= 20) = 2. part(W0r,low,random,weight <= 20) = 5. part(W1w,low,weight,weight > 20 & weight <= 30) = 8. part(W1a,low,age,weight > 20 & weight <= 30) = 2. part(W1r,low,random,weight > 20 & weight <= 30) = 5. part(W2w,low,weight,weight > 30) = 4. part(W2a,low,age,weight > 30) = 2. part(W2r,low,random,weight > 30) = 5. end_of_list. formulas(assumptions). 1 * x = x. x * 1 = x. x \ (x * y) = y. x * (x \ y) = y. (x * y) / y = x. (x / y) * y = x. (x * (y * z)) \ ((x * y) * z) = a(x,y,z). (x * y) \ (y * x) = K(y,x). (y * x) \ (y * (x * u)) = L(u,x,y). ((u * x) * y) / (x * y) = R(u,x,y). x \ (u * x) = T(u,x). a(x,y,z) = 1 -> L(z,y,x) = z. L(x,y,z) = x -> a(z,y,x) = 1. T(x,y) = x -> T(y,x) = y. T(x,y) = x -> K(x,y) = 1. K(x,y) = 1 -> T(x,y) = x. T(T(u,x),y) = T(T(u,y),x). T(L(u,x,y),z) = L(T(u,z),x,y). T(R(u,x,y),z) = R(T(u,z),x,y). L(R(u,x,y),z,w) = R(L(u,z,w),x,y). L(L(u,x,y),z,w) = L(L(u,z,w),x,y). R(R(u,x,y),z,w) = R(R(u,z,w),x,y). end_of_list. formulas(goals). a(K(x,y),z,u) = 1 # label("aK1"). a(x,K(y,z),u) = 1 # label("aK2"). a(x,y,K(z,u)) = 1 # label("aK3"). K(a(x,y,z),u) = 1 # label("Ka"). a(a(x,y,z),u,w) = 1 # label("aa1"). a(x,a(y,z,u),w) = 1 # label("aa2"). a(x,y,a(z,u,w)) = 1 # label("aa3"). end_of_list. formulas(assumptions). ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang (M1)"). (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). end_of_list. WARNING, function symbols in function_order (lex) command not found in formulas: LEX_1. WARNING, function symbols in function_order (lex) command not found in formulas: LEX_1. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: 1 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 2 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 3 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 4 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 5 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 6 a(K(x,y),z,u) = 1 # label("aK1") # label(non_clause) # label(goal). [goal]. 7 a(x,K(y,z),u) = 1 # label("aK2") # label(non_clause) # label(goal). [goal]. 8 a(x,y,K(z,u)) = 1 # label("aK3") # label(non_clause) # label(goal). [goal]. 9 K(a(x,y,z),u) = 1 # label("Ka") # label(non_clause) # label(goal). [goal]. 10 a(a(x,y,z),u,w) = 1 # label("aa1") # label(non_clause) # label(goal). [goal]. 11 a(x,a(y,z,u),w) = 1 # label("aa2") # label(non_clause) # label(goal). [goal]. 12 a(x,y,a(z,u,w)) = 1 # label("aa3") # label(non_clause) # label(goal). [goal]. ============================== end of process non-clausal formulas === ============================== PROCESS INITIAL CLAUSES =============== % Clauses before input processing: formulas(usable). end_of_list. formulas(sos). 1 * x = x. [assumption]. x * 1 = x. [assumption]. x \ (x * y) = y. [assumption]. x * (x \ y) = y. [assumption]. (x * y) / y = x. [assumption]. (x / y) * y = x. [assumption]. (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. (x * y) \ (y * x) = K(y,x). [assumption]. (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. x \ (y * x) = T(y,x). [assumption]. a(x,y,z) != 1 | L(z,y,x) = z. [clausify(1)]. L(x,y,z) != x | a(z,y,x) = 1. [clausify(2)]. T(x,y) != x | T(y,x) = y. [clausify(3)]. T(x,y) != x | K(x,y) = 1. [clausify(4)]. K(x,y) != 1 | T(x,y) = x. [clausify(5)]. T(T(x,y),z) = T(T(x,z),y). [assumption]. T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang (M1)"). [assumption]. (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. a(K(c1,c2),c3,c4) != 1 # label("aK1"). [deny(6)]. a(c5,K(c6,c7),c8) != 1 # label("aK2"). [deny(7)]. a(c9,c10,K(c11,c12)) != 1 # label("aK3"). [deny(8)]. K(a(c13,c14,c15),c16) != 1 # label("Ka"). [deny(9)]. a(a(c17,c18,c19),c20,c21) != 1 # label("aa1"). [deny(10)]. a(c22,a(c23,c24,c25),c26) != 1 # label("aa2"). [deny(11)]. a(c27,c28,a(c29,c30,c31)) != 1 # label("aa3"). [deny(12)]. end_of_list. formulas(demodulators). end_of_list. ============================== PREDICATE ELIMINATION ================= No predicates eliminated. ============================== end predicate elimination =============  WARNING: denials share constants (see output). Auto_denials: % copying label "aK1" to answer in negative clause % copying label "aK2" to answer in negative clause % copying label "aK3" to answer in negative clause % copying label "Ka" to answer in negative clause % copying label "aa1" to answer in negative clause % copying label "aa2" to answer in negative clause % copying label "aa3" to answer in negative clause % assign(max_proofs, 7). % (Horn set with more than one neg. clause) WARNING, because some of the denials share constants, some of the denials or their descendents may be subsumed, preventing the target number of proofs from being found. The shared constants are: 1. Term ordering decisions: Function symbol KB weights: 1=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. c25=1. c26=1. c27=1. c28=1. c29=1. c30=1. c31=1. a=1. K=1. L=1. R=1. T=1. *=1. \=1. /=1. Predicate symbol precedence: predicate_order([ = ]). Function symbol precedence: function_order([ 1, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, a, K, L, R, T, *, \, / ]). Skipping inverse_order, because there is a function_order (lex) command. Skipping unfold_eq, because there is a function_order (lex) command. Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(hyper_resolution). % (nonunit Horn with equality) % set(hyper_resolution) -> set(pos_hyper_resolution). % set(neg_ur_resolution). % (nonunit Horn with equality) Auto_process settings: (no changes). kept: 13 1 * x = x. [assumption]. kept: 14 x * 1 = x. [assumption]. kept: 15 x \ (x * y) = y. [assumption]. kept: 16 x * (x \ y) = y. [assumption]. kept: 17 (x * y) / y = x. [assumption]. kept: 18 (x / y) * y = x. [assumption]. kept: 19 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. kept: 20 (x * y) \ (y * x) = K(y,x). [assumption]. kept: 21 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. kept: 22 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. kept: 23 x \ (y * x) = T(y,x). [assumption]. kept: 24 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(1)]. kept: 25 L(x,y,z) != x | a(z,y,x) = 1. [clausify(2)]. kept: 26 T(x,y) != x | T(y,x) = y. [clausify(3)]. kept: 27 T(x,y) != x | K(x,y) = 1. [clausify(4)]. kept: 28 K(x,y) != 1 | T(x,y) = x. [clausify(5)]. kept: 29 T(T(x,y),z) = T(T(x,z),y). [assumption]. kept: 30 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. kept: 31 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 32 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. kept: 33 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(32),flip(a)]. kept: 34 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. kept: 35 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. kept: 36 ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang (M1)"). [assumption]. kept: 37 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. kept: 38 a(K(c1,c2),c3,c4) != 1 # label("aK1") # answer("aK1"). [deny(6)]. kept: 39 a(c5,K(c6,c7),c8) != 1 # label("aK2") # answer("aK2"). [deny(7)]. kept: 40 a(c9,c10,K(c11,c12)) != 1 # label("aK3") # answer("aK3"). [deny(8)]. kept: 41 K(a(c13,c14,c15),c16) != 1 # label("Ka") # answer("Ka"). [deny(9)]. kept: 42 a(a(c17,c18,c19),c20,c21) != 1 # label("aa1") # answer("aa1"). [deny(10)]. kept: 43 a(c22,a(c23,c24,c25),c26) != 1 # label("aa2") # answer("aa2"). [deny(11)]. kept: 44 a(c27,c28,a(c29,c30,c31)) != 1 # label("aa3") # answer("aa3"). [deny(12)]. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). end_of_list. formulas(sos). 13 1 * x = x. [assumption]. 14 x * 1 = x. [assumption]. 15 x \ (x * y) = y. [assumption]. 16 x * (x \ y) = y. [assumption]. 17 (x * y) / y = x. [assumption]. 18 (x / y) * y = x. [assumption]. 19 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 20 (x * y) \ (y * x) = K(y,x). [assumption]. 21 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 22 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 23 x \ (y * x) = T(y,x). [assumption]. 24 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(1)]. 25 L(x,y,z) != x | a(z,y,x) = 1. [clausify(2)]. 26 T(x,y) != x | T(y,x) = y. [clausify(3)]. 27 T(x,y) != x | K(x,y) = 1. [clausify(4)]. 28 K(x,y) != 1 | T(x,y) = x. [clausify(5)]. 29 T(T(x,y),z) = T(T(x,z),y). [assumption]. 30 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 31 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 33 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(32),flip(a)]. 34 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 35 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 36 ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang (M1)"). [assumption]. 37 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 38 a(K(c1,c2),c3,c4) != 1 # label("aK1") # answer("aK1"). [deny(6)]. 39 a(c5,K(c6,c7),c8) != 1 # label("aK2") # answer("aK2"). [deny(7)]. 40 a(c9,c10,K(c11,c12)) != 1 # label("aK3") # answer("aK3"). [deny(8)]. 41 K(a(c13,c14,c15),c16) != 1 # label("Ka") # answer("Ka"). [deny(9)]. 42 a(a(c17,c18,c19),c20,c21) != 1 # label("aa1") # answer("aa1"). [deny(10)]. 43 a(c22,a(c23,c24,c25),c26) != 1 # label("aa2") # answer("aa2"). [deny(11)]. 44 a(c27,c28,a(c29,c30,c31)) != 1 # label("aa3") # answer("aa3"). [deny(12)]. end_of_list. formulas(demodulators). 13 1 * x = x. [assumption]. 14 x * 1 = x. [assumption]. 15 x \ (x * y) = y. [assumption]. 16 x * (x \ y) = y. [assumption]. 17 (x * y) / y = x. [assumption]. 18 (x / y) * y = x. [assumption]. 19 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 20 (x * y) \ (y * x) = K(y,x). [assumption]. 21 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 22 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 23 x \ (y * x) = T(y,x). [assumption]. 29 T(T(x,y),z) = T(T(x,z),y). [assumption]. % (lex-dep) 30 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 31 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 33 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(32),flip(a)]. 36 ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang (M1)"). [assumption]. 37 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.00 seconds. given #1 (I,wt=5): 13 1 * x = x. [assumption]. given #2 (I,wt=5): 14 x * 1 = x. [assumption]. given #3 (I,wt=7): 15 x \ (x * y) = y. [assumption]. given #4 (I,wt=7): 16 x * (x \ y) = y. [assumption]. given #5 (I,wt=7): 17 (x * y) / y = x. [assumption]. given #6 (I,wt=7): 18 (x / y) * y = x. [assumption]. given #7 (I,wt=16): 19 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. given #8 (I,wt=11): 20 (x * y) \ (y * x) = K(y,x). [assumption]. given #9 (I,wt=14): 21 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. given #10 (I,wt=14): 22 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. given #11 (I,wt=9): 23 x \ (y * x) = T(y,x). [assumption]. given #12 (I,wt=12): 24 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(1)]. given #13 (I,wt=12): 25 L(x,y,z) != x | a(z,y,x) = 1. [clausify(2)]. given #14 (I,wt=10): 26 T(x,y) != x | T(y,x) = y. [clausify(3)]. given #15 (I,wt=10): 27 T(x,y) != x | K(x,y) = 1. [clausify(4)]. given #16 (I,wt=10): 28 K(x,y) != 1 | T(x,y) = x. [clausify(5)]. given #17 (I,wt=11): 29 T(T(x,y),z) = T(T(x,z),y). [assumption]. given #18 (I,wt=13): 30 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. given #19 (I,wt=13): 31 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. given #20 (I,wt=15): 33 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(32),flip(a)]. given #21 (I,wt=15): 34 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. given #22 (I,wt=15): 35 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. given #23 (I,wt=15): 36 ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang (M1)"). [assumption]. given #24 (I,wt=15): 37 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. given #25 (I,wt=8): 38 a(K(c1,c2),c3,c4) != 1 # label("aK1") # answer("aK1"). [deny(6)]. given #26 (I,wt=8): 39 a(c5,K(c6,c7),c8) != 1 # label("aK2") # answer("aK2"). [deny(7)]. given #27 (I,wt=8): 40 a(c9,c10,K(c11,c12)) != 1 # label("aK3") # answer("aK3"). [deny(8)]. given #28 (I,wt=8): 41 K(a(c13,c14,c15),c16) != 1 # label("Ka") # answer("Ka"). [deny(9)]. given #29 (I,wt=9): 42 a(a(c17,c18,c19),c20,c21) != 1 # label("aa1") # answer("aa1"). [deny(10)]. given #30 (I,wt=9): 43 a(c22,a(c23,c24,c25),c26) != 1 # label("aa2") # answer("aa2"). [deny(11)]. % Applying rule: given = 30 -> assign(max_weight,25). given #31 (I,wt=9): 44 a(c27,c28,a(c29,c30,c31)) != 1 # label("aa3") # answer("aa3"). [deny(12)]. given #32 (Wf,wt=8): 151 L(c4,c3,K(c1,c2)) != c4 # answer("aK1"). [ur(25,b,38,a)]. given #33 (Wf,wt=8): 152 L(c8,K(c6,c7),c5) != c8 # answer("aK2"). [ur(25,b,39,a)]. given #34 (Wf,wt=9): 155 L(c21,c20,a(c17,c18,c19)) != c21 # answer("aa1"). [ur(25,b,42,a)]. given #35 (W0w,wt=5): 45 1 \ x = x. [para(13(a,1),15(a,1,2))]. given #36 (W0w,wt=5): 46 x \ x = 1. [para(14(a,1),15(a,1,2))]. given #37 (W0w,wt=5): 47 x / x = 1. [para(13(a,1),17(a,1,1))]. given #38 (W0w,wt=5): 48 x / 1 = x. [para(14(a,1),17(a,1,1))]. given #39 (W0w,wt=5): 61 K(x,1) = 1. [para(13(a,1),20(a,1,1)),rewrite([14(2),46(1)]),flip(a)]. given #40 (W0w,wt=5): 62 K(1,x) = 1. [para(13(a,1),20(a,1,2)),rewrite([14(2),46(1)]),flip(a)]. given #41 (W0w,wt=5): 87 T(1,x) = 1. [para(13(a,1),23(a,1,2)),rewrite([46(1)]),flip(a)]. given #42 (W0w,wt=5): 88 T(x,1) = x. [para(14(a,1),23(a,1,2)),rewrite([45(2)]),flip(a)]. given #43 (W0w,wt=5): 89 T(x,x) = x. [para(23(a,1),15(a,1))]. given #44 (W0w,wt=5): 158 K(x,x) = 1. [para(46(a,1),20(a,1)),flip(a)]. given #45 (W0w,wt=6): 51 a(x,1,y) = 1. [para(13(a,1),19(a,1,1,2)),rewrite([14(3),46(3)]),flip(a)]. given #46 (W0w,wt=6): 52 a(1,x,y) = 1. [para(13(a,1),19(a,1,1)),rewrite([13(3),46(3)]),flip(a)]. given #47 (W0w,wt=6): 53 a(x,y,1) = 1. [para(14(a,1),19(a,1,1,2)),rewrite([14(4),46(3)]),flip(a)]. given #48 (W0w,wt=6): 69 L(x,y,1) = x. [para(13(a,1),21(a,1,1)),rewrite([13(3),15(2)]),flip(a)]. given #49 (W0w,wt=6): 70 L(x,1,y) = x. [para(13(a,1),21(a,1,2,2)),rewrite([14(2),15(2)]),flip(a)]. given #50 (W0w,wt=6): 71 L(1,x,y) = 1. [para(14(a,1),21(a,1,2,2)),rewrite([46(3)]),flip(a)]. given #51 (W0a,wt=7): 49 x / (y \ x) = y. [para(16(a,1),17(a,1,1))]. given #52 (W0a,wt=7): 50 (x / y) \ x = y. [para(18(a,1),15(a,1,2))]. given #53 (W0r,wt=15): 104 x * ((x \ y) * (x * z)) = (y * x) * z. [para(16(a,1),36(a,1,1,1)),flip(a)]. given #54 (W0r,wt=16): 191 (x * ((x \ y) * z)) / z = R(y,x,x \ z). [back_rewrite(83),rewrite([169(3)])]. given #55 (W0r,wt=11): 91 T(x,x \ y) = (x \ y) \ y. [para(16(a,1),23(a,1,2)),flip(a)]. given #56 (W0r,wt=10): 93 T(x,x * x) = L(x,x,x). [para(23(a,1),21(a,1))]. given #57 (W0r,wt=6): 79 R(x,1,y) = x. [para(13(a,1),22(a,1,2)),rewrite([14(2),17(2)]),flip(a)]. given #58 (W1w,wt=21): 97 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,v5,v6),y,z),u,w). [para(34(a,1),34(a,1,1)),flip(a)]. given #59 (W1w,wt=21): 98 L(R(R(x,y,z),u,w),v5,v6) = L(R(R(x,u,w),y,z),v5,v6). [para(35(a,1),33(a,2,1)),rewrite([33(3)])]. given #60 (W1w,wt=21): 99 R(R(R(x,y,z),u,w),v5,v6) = R(R(R(x,v5,v6),y,z),u,w). [para(35(a,1),35(a,1,1)),flip(a)]. given #61 (W1w,wt=21): 209 a(x,y,z) \ ((x * y) * z) = T(x * (y * z),a(x,y,z)). [para(19(a,1),91(a,1,2)),rewrite([19(9)]),flip(a)]. given #62 (W1w,wt=21): 220 R(x,y \ z,T(y,y \ z)) = R(x,y \ z,(y \ z) \ z). [para(91(a,2),191(a,2,3)),rewrite([191(6)]),flip(a)]. given #63 (W1w,wt=21): 228 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,u,w),y,z),v5,v6). [para(97(a,1),34(a,1))]. given #64 (W1w,wt=21): 230 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,v5,v6),u,w),y,z). [para(97(a,2),34(a,1))]. given #65 (W1w,wt=21): 245 R(R(R(x,y,z),u,w),v5,v6) = R(R(R(x,u,w),y,z),v5,v6). [para(99(a,1),35(a,1))]. given #66 (W1a,wt=28): 110 (x * (y * (z * (y * u)))) \ ((x * (y * (z * y))) * u) = a(x,y * (z * y),u). [para(36(a,1),19(a,1,1,2)),rewrite([101(6),101(11)])]. given #67 (W1a,wt=23): 114 (x * (y * (x * z))) \ (z * (x * (y * x))) = K(z,x * (y * x)). [para(36(a,1),20(a,1,1)),rewrite([101(5),101(9)])]. given #68 (W1r,wt=26): 148 ((x * (y * (y * z))) * u) / (y * (y * (z * u))) = R(x,y * (y * z),u). [para(37(a,1),22(a,1,2))]. given #69 (W1r,wt=25): 176 ((x * y) * z) \ (((y \ x) * (y * z)) * y) = K((y \ x) * (y * z),y). [para(104(a,1),20(a,1,1))]. given #70 (W1r,wt=28): 312 (x * (y * (z * (y * u)))) * a(x,y * (z * y),u) = (x * (y * (z * y))) * u. [para(110(a,1),16(a,1,2))]. given #71 (W1r,wt=25): 248 R(R(R(x,y,y \ z),u,w),v5,v6) = R(R(R(x,u,w),v5,v6),y,y \ z). [para(99(a,1),191(a,2)),rewrite([191(6)]),flip(a)]. given #72 (W1r,wt=26): 341 R(x,y * (y * z),u) * (y * (y * (z * u))) = (x * (y * (y * z))) * u. [para(148(a,1),18(a,1,1))]. given #73 (W2w,wt=31): 129 (x * (y * (x * (z * (x * (y * x)))))) * u = x * (y * (x * (z * (x * (y * (x * u)))))). [back_rewrite(125),rewrite([128(6),128(14)])]. given #74 (W2w,wt=31): 150 x * (x * ((y * (x * (x * (y * z)))) * u)) = x * (x * (y * (x * (x * (y * (z * u)))))). [para(37(a,1),37(a,1,1,2)),rewrite([37(6),37(7),37(13),37(14)])]. given #75 (W2w,wt=31): 188 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * (y * u)))))) = (z * (x * (x * y))) * u. [para(104(a,1),37(a,1)),rewrite([37(10)]),flip(a)]. given #76 (W2w,wt=31): 194 (x * (((y * (x * z)) * x) * (y * x))) * u = x * (y * (x * (z * (x * (y * (x * u)))))). [back_rewrite(131),rewrite([189(6)])]. given #77 (W2a,wt=32): 175 (x * (y * z)) * (a(x,y,z) * ((x * (y * z)) * u)) = (((x * y) * z) * (x * (y * z))) * u. [para(19(a,1),104(a,1,2,1))]. given #78 (W2a,wt=33): 201 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) = ((x * (y * z)) * (a(x,y,z) * u)) / u. [para(19(a,1),191(a,1,1,2,1)),flip(a)]. given #79 (W2r,wt=33): 308 R(R(R(x,y \ z,(y \ z) \ z),u,w),v5,v6) = R(R(R(x,u,w),y \ z,T(y,y \ z)),v5,v6). [para(220(a,1),245(a,1,1,1))]. given #80 (W2r,wt=33): 295 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v5,v6),y,z),v9,v10),v7,v8),u,w). [para(97(a,2),230(a,1,1,1))]. given #81 (W2r,wt=31): 393 x * (x * ((x * (y * (x * (x * x)))) * z)) = x * (x * (x * (y * (x * (x * (x * z)))))). [para(129(a,1),37(a,1)),flip(a)]. given #82 (W2r,wt=33): 307 R(R(R(x,y,z),u,w),v5 \ v6,T(v5,v5 \ v6)) = R(R(R(x,u,w),y,z),v5 \ v6,(v5 \ v6) \ v6). [para(245(a,1),220(a,1))]. given #83 (W2r,wt=33): 249 L(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(R(R(R(R(x,v7,v8),y,z),u,w),v5,v6),v9,v10). [para(99(a,1),98(a,1,1,1)),flip(a)]. given #84 (Wf,wt=9): 156 L(c26,a(c23,c24,c25),c22) != c26 # answer("aa2"). [ur(25,b,43,a)]. given #85 (Wf,wt=10): 153 L(K(c11,c12),c10,c9) != K(c11,c12) # answer("aK3"). [ur(25,b,40,a)]. given #86 (Wf,wt=11): 154 T(a(c13,c14,c15),c16) != a(c13,c14,c15) # answer("Ka"). [ur(27,b,41,a)]. given #87 (W0w,wt=6): 78 R(1,x,y) = 1. [para(13(a,1),22(a,1,1,1)),rewrite([47(3)]),flip(a)]. given #88 (W0w,wt=6): 80 R(x,y,1) = x. [para(14(a,1),22(a,1,1)),rewrite([14(3),17(2)]),flip(a)]. given #89 (W0w,wt=8): 197 R(x,y,y \ 1) = x. [para(14(a,1),191(a,1,1,2)),rewrite([16(2),48(2)]),flip(a)]. given #90 (W0w,wt=8): 206 R(x,x,x \ y) = x. [para(46(a,1),191(a,1,1,2,1)),rewrite([13(2),17(2)]),flip(a)]. given #91 (W0w,wt=6): 480 R(x,x,y) = x. [para(15(a,1),206(a,1,3))]. given #92 (W0w,wt=8): 477 T(c16,a(c13,c14,c15)) != c16 # answer("Ka"). [ur(26,b,154,a)]. given #93 (W0w,wt=8): 478 R(x,1 / y,y) = x. [para(50(a,1),197(a,1,3))]. given #94 (W0w,wt=8): 505 K(c16,a(c13,c14,c15)) != 1 # answer("Ka"). [ur(28,b,477,a)]. given #95 (W0w,wt=9): 90 x * T(y,x) = y * x. [para(23(a,1),16(a,1,2))]. given #96 (W0w,wt=9): 92 T(x / y,y) = y \ x. [para(18(a,1),23(a,1,2)),flip(a)]. given #97 (W0w,wt=9): 159 T(T(x,y),x) = T(x,y). [para(89(a,1),29(a,1,1)),flip(a)]. given #98 (W0w,wt=7): 540 K(T(x,y),x) = 1. [hyper(27,a,159,a)]. given #99 (W0w,wt=7): 541 T(x,T(x,y)) = x. [hyper(26,a,159,a)]. given #100 (W0w,wt=7): 555 K(x,T(x,y)) = 1. [hyper(27,a,541,a)]. given #101 (W0w,wt=8): 553 K(L(x,x,x),x) = 1. [para(93(a,1),540(a,1,1))]. given #102 (W0w,wt=8): 561 T(x,L(x,x,x)) = x. [para(93(a,1),541(a,1,2))]. given #103 (W0a,wt=16): 54 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(19(a,1),16(a,1,2))]. given #104 (W0a,wt=18): 56 (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z). [para(16(a,1),19(a,1,2,1))]. given #105 (W0r,wt=18): 318 K(x * (x * (x * x)),x) = a(x,x * (x * x),x). [para(110(a,1),20(a,1)),flip(a)]. given #106 (W0r,wt=13): 537 T(T(x / y,z),y) = T(y \ x,z). [para(92(a,1),29(a,1,1)),flip(a)]. given #107 (W0r,wt=14): 74 L(x \ y,x,z) = (z * x) \ (z * y). [para(16(a,1),21(a,1,2,2)),flip(a)]. given #108 (W0r,wt=17): 186 x * (T(y,x) * (x * z)) = ((y * x) * x) * z. [para(23(a,1),104(a,1,2,1))]. given #109 (W0r,wt=11): 563 K(T(x,y),T(T(x,z),y)) = 1. [para(29(a,1),555(a,1,2))]. given #110 (W1w,wt=21): 247 R(R(R(x,y,z),u,w),v5,v6) = R(R(R(x,v5,v6),u,w),y,z). [para(99(a,2),35(a,1))]. given #111 (W1w,wt=21): 265 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(209(a,1),49(a,1,2))]. given #112 (W1w,wt=21): 328 (x * ((y / x) * (x * z))) \ (z * (x * y)) = K(z,x * y). [para(18(a,1),114(a,1,2,2,2)),rewrite([18(9)])]. given #113 (W1w,wt=21): 497 R(R(R(x,y,z),u,w),R(x,u,w),v5) = R(R(x,u,w),y,z). [para(480(a,1),99(a,1,1)),flip(a)]. given #114 (W1w,wt=21): 500 R(R(R(x,R(x,y,z),u),w,v5),y,z) = R(R(x,y,z),w,v5). [para(480(a,1),99(a,2,1))]. given #115 (W1w,wt=21): 521 x * (x * (y * T(z,x * (x * y)))) = z * (x * (x * y)). [para(90(a,1),37(a,1)),flip(a)]. given #116 (W1w,wt=21): 604 L(a(x,y,y * (x * y)),x * (y * (y * (x * y))),y) = 1. [back_rewrite(334),rewrite([589(11)])]. given #117 (W1w,wt=21): 616 a(x \ y,T(x,x \ y),z) = a(x \ y,(x \ y) \ y,z). [para(91(a,2),56(a,2,2)),rewrite([56(7)]),flip(a)]. given #118 (W1a,wt=23): 115 (x * (y * (z * y))) \ (y * (z * (y * x))) = K(y * (z * y),x). [para(36(a,1),20(a,1,2)),rewrite([101(2),101(9)])]. given #119 (W1a,wt=26): 117 (x * (y * (z * y))) \ (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(36(a,1),21(a,1,2,2)),rewrite([101(2),101(10)])]. given #120 (W1r,wt=27): 675 ((T(x,y) * (y * z)) * y) \ (((x * y) * y) * z) = K(y,T(x,y) * (y * z)). [para(186(a,1),20(a,1,2))]. given #121 (W1r,wt=23): 697 ((x * T(x,y)) * T(x,y)) * z = T(x,y) * (x * (T(x,y) * z)). [para(541(a,1),186(a,1,2,1)),flip(a)]. given #122 (W1r,wt=27): 843 (((x * y) * y) * z) / K(y,T(x,y) * (y * z)) = (T(x,y) * (y * z)) * y. [para(675(a,1),49(a,1,2))]. given #123 (W1r,wt=25): 729 ((x * (y / z)) * z) / T(x * y,a(x,y / z,z)) = a(x,y / z,z). [para(18(a,1),265(a,1,2,1,2))]. given #124 (W1r,wt=25): 350 ((x * y) * z) * K((y \ x) * (y * z),y) = ((y \ x) * (y * z)) * y. [para(176(a,1),16(a,1,2))]. given #125 (W2w,wt=31): 273 R(x,(y \ z) \ z,T(y \ z,T(y,y \ z))) = R(x,(y \ z) \ z,((y \ z) \ z) \ z). [para(91(a,2),220(a,1,3,2))]. given #126 (W2w,wt=31): 326 ((x / y) * (z * x)) \ (y * ((x / y) * (z * (x / y)))) = K(y,(x / y) * (z * (x / y))). [para(18(a,1),114(a,1,1,2,2))]. given #127 (W2w,wt=31): 354 ((x * (y / z)) * z) \ ((((y / z) \ x) * y) * (y / z)) = K(((y / z) \ x) * y,y / z). [para(18(a,1),176(a,1,2,1,2)),rewrite([18(13)])]. given #128 (W2w,wt=31): 357 ((x * (x / y)) * z) \ ((y * ((x / y) * z)) * (x / y)) = K(y * ((x / y) * z),x / y). [para(50(a,1),176(a,1,2,1,1)),rewrite([50(11)])]. given #129 (W2a,wt=32): 205 (x * (x * (y * (((x * (x * y)) \ z) * u)))) / u = R(z,x * (x * y),(x * (x * y)) \ u). [para(37(a,1),191(a,1,1))]. given #130 (W2a,wt=34): 226 T(x * (x * y),x * (x * (y * (x * (x * y))))) = L(x * (x * y),x * (x * y),x * (x * y)). [para(37(a,1),93(a,1,2))]. given #131 (W2r,wt=32): 267 T(x * (y * z),a(x,y,z)) \ ((x * y) * z) = T(a(x,y,z),T(x * (y * z),a(x,y,z))). [para(209(a,1),91(a,1,2)),rewrite([209(10)]),flip(a)]. given #132 (W2r,wt=31): 372 R(R(R(R(x,y,y \ z),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v7,v8),y,y \ z),v5,v6). [para(248(a,1),35(a,1,1)),flip(a)]. given #133 (W2r,wt=33): 720 R(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = R(R(R(R(R(x,v9,v10),y,z),u,w),v7,v8),v5,v6). [para(99(a,1),247(a,1,1,1)),flip(a)]. given #134 (W2r,wt=33): 448 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),y,z),v9,v10),v5,v6),u,w). [para(34(a,1),295(a,1,1))]. given #135 (W2r,wt=31): 662 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,(x * y) \ (x * z),u). [para(74(a,2),56(a,1,1,2,1))]. given #136 (Wf,wt=12): 157 L(a(c29,c30,c31),c28,c27) != a(c29,c30,c31) # answer("aa3"). [ur(25,b,44,a)]. given #137 (W0w,wt=8): 567 K(x,L(x,x,x)) = 1. [para(93(a,1),555(a,1,2))]. given #138 (W0w,wt=9): 165 (x * y) / T(x,y) = y. [para(23(a,1),49(a,1,2))]. given #139 (W0w,wt=9): 333 K(x,x * (x * x)) = 1. [para(114(a,1),46(a,1))]. given #140 (W0w,wt=9): 506 (x * (1 / y)) * y = x. [para(478(a,1),22(a,2)),rewrite([18(7),48(6)])]. given #141 (W0w,wt=7): 982 K(x,1 / x) = 1. [para(506(a,1),357(a,1,1)),rewrite([18(4),14(3),974(4),47(2),46(3),18(4),14(3)]),flip(a)]. given #142 (W0w,wt=7): 986 T(x,1 / x) = x. [hyper(28,a,982,a)]. given #143 (W0w,wt=7): 987 K(x \ 1,x) = 1. [para(49(a,1),982(a,1,2))]. given #144 (W0w,wt=7): 989 1 / x = x \ 1. [hyper(26,a,986,a),rewrite([92(3)]),flip(a)]. given #145 (W0w,wt=7): 990 (x \ 1) \ 1 = x. [para(986(a,1),23(a,2)),rewrite([989(2),989(4),16(5)])]. given #146 (W0w,wt=7): 997 (x \ 1) * x = 1. [para(986(a,1),90(a,1,2)),rewrite([989(2),989(5),16(6)])]. given #147 (W0w,wt=7): 998 T(x,x \ 1) = x. [para(986(a,1),159(a,1,1)),rewrite([89(1),989(2)]),flip(a)]. given #148 (W0w,wt=7): 1007 K(x,x \ 1) = 1. [back_rewrite(982),rewrite([989(2)])]. given #149 (W0w,wt=8): 1012 a(x,y \ 1,y) = 1. [back_rewrite(976),rewrite([989(2)])]. given #150 (W0w,wt=8): 1015 R(x,y \ 1,y) = x. [back_rewrite(478),rewrite([989(2)])]. given #151 (W0w,wt=8): 1022 L(x,x \ 1,y) = x. [para(990(a,1),74(a,1,1)),rewrite([1014(6),14(6),50(5)])]. given #152 (W0w,wt=8): 1072 a(x,y,y \ 1) = 1. [para(50(a,1),1012(a,1,2)),rewrite([989(2)])]. given #153 (W0a,wt=20): 57 (x * (y * ((x * y) \ z))) \ z = a(x,y,(x * y) \ z). [para(16(a,1),19(a,1,2))]. given #154 (W0a,wt=18): 58 (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z). [para(18(a,1),19(a,1,1,2))]. given #155 (W0r,wt=18): 1026 L(x,y,(y * x) \ 1) = (((y * x) \ 1) * y) \ 1. [para(997(a,1),21(a,1,2)),flip(a)]. given #156 (W0r,wt=13): 67 (x * (y / x)) \ y = K(y / x,x). [para(18(a,1),20(a,1,2))]. given #157 (W0r,wt=16): 181 L(x * y,x \ z,x) = z \ ((z * x) * y). [para(104(a,1),21(a,1,2)),rewrite([16(2)]),flip(a)]. given #158 (W0r,wt=14): 223 T(T(x,y),x * x) = L(T(x,y),x,x). [para(93(a,1),29(a,1,1)),rewrite([30(2)]),flip(a)]. given #159 (W0r,wt=17): 961 (x * (x * (y * z))) / T(x * (x * y),z) = z. [para(37(a,1),165(a,1,1))]. given #160 (W1w,wt=21): 682 x * (T(T(y,x),z) * (x * u)) = ((T(y,z) * x) * x) * u. [para(29(a,1),186(a,1,2,1))]. given #161 (W1w,wt=21): 690 a((x * y) * y,T(x,y),z) = a(y,T(x,y) * (x * y),z). [para(186(a,1),110(a,1,2,1)),rewrite([186(6),19(11),90(7)])]. given #162 (W1w,wt=21): 726 R(R(R(x,y,z),R(x,u,w),v5),u,w) = R(R(x,u,w),y,z). [para(480(a,1),247(a,1,1)),flip(a)]. given #163 (W1w,wt=21): 778 x * (y * T(z,x * (x * y))) = x \ (z * (x * (x * y))). [para(521(a,1),15(a,1,2)),flip(a)]. given #164 (W1w,wt=21): 788 x * (y * (x * T(z,x * (y * x)))) = z * (x * (y * x)). [para(90(a,1),521(a,1,2,2,2,2,2)),rewrite([520(7),90(8)])]. given #165 (W1w,wt=21): 791 L(a(x / y,y,y * x),(x / y) * (y * (y * x)),y) = 1. [para(18(a,1),604(a,1,1,3,2)),rewrite([18(6)])]. given #166 (W1w,wt=21): 838 ((T(x,y) * y) * y) \ ((x * y) * y) = K(y,T(x,y) * y). [para(14(a,1),675(a,1,1,1,2)),rewrite([14(7),14(9)])]. given #167 (W1w,wt=21): 858 ((x * y) * y) / K(y,T(x,y) * y) = (T(x,y) * y) * y. [para(14(a,1),843(a,1,1)),rewrite([14(5),14(9)])]. given #168 (W1a,wt=22): 119 ((x * (y * (x * z))) * u) / (z * u) = R(x * (y * x),z,u). [para(36(a,1),22(a,1,1,1)),rewrite([101(8)])]. given #169 (W1a,wt=26): 121 ((x * (y * (z * y))) * u) / (y * (z * (y * u))) = R(x,y * (z * y),u). [para(36(a,1),22(a,1,2)),rewrite([101(2),101(10)])]. given #170 (W1r,wt=24): 268 ((x * (y \ z)) * T(y,y \ z)) / z = R(x,y \ z,(y \ z) \ z). [para(220(a,1),22(a,2)),rewrite([90(9),16(7)])]. given #171 (W1r,wt=23): 863 (T(T(x,y),z) * (z * u)) * z = (T(T(x,z),y) * (z * u)) * z. [para(29(a,1),843(a,2,1,1)),rewrite([843(10)])]. given #172 (W1r,wt=23): 1470 K(T(T(x,y),z) * (z * u),z) = K(T(T(x,z),y) * (z * u),z). [para(863(a,1),20(a,1,2)),rewrite([186(5),1269(10)]),flip(a)]. given #173 (W1r,wt=29): 732 (x * (y * z)) / T((x * y) * z,a(y,y \ x,y * z)) = a(y,y \ x,y * z). [para(104(a,1),265(a,1,2,1)),rewrite([16(2)])]. given #174 (W1r,wt=24): 780 L(x * T(y,z * (z * x)),z,z) = (z * z) \ (y * (z * (z * x))). [para(521(a,1),21(a,1,2)),flip(a)]. given #175 (W2w,wt=31): 358 K(T(x,x \ y) * ((x \ y) * z),x \ y) = K(((x \ y) \ y) * ((x \ y) * z),x \ y). [para(91(a,2),176(a,2,1,1)),rewrite([176(11)]),flip(a)]. given #176 (W2w,wt=31): 369 R(R(R(x,y * z,L(u,z,y)),w,v5),v6,v7) = R(R(R(x,w,v5),v6,v7),y * z,L(u,z,y)). [para(21(a,1),248(a,1,1,1,3)),rewrite([21(12)])]. given #177 (W2w,wt=31): 371 L(R(R(R(x,y,y \ z),u,w),v5,v6),v7,v8) = L(R(R(R(x,u,w),v5,v6),y,y \ z),v7,v8). [para(248(a,1),33(a,2,1)),rewrite([33(5)])]. given #178 (W2w,wt=31): 373 R(R(R(R(x,y,y \ z),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v5,v6),v7,v8),y,y \ z). [para(248(a,2),35(a,1,1))]. given #179 (W2a,wt=33): 231 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),y,z),u,w),v9,v10),v5,v6). [para(97(a,1),97(a,1,1,1)),flip(a)]. given #180 (W2a,wt=33): 233 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),y,z),u,w),v5,v6),v7,v8). [para(97(a,1),97(a,2,1,1))]. given #181 (W2r,wt=31): 844 K(x \ y,T(x,x \ y) * ((x \ y) * z)) = K(x \ y,((x \ y) \ y) * ((x \ y) * z)). [para(91(a,1),675(a,1,1,1,1)),rewrite([16(9),177(11)]),flip(a)]. given #182 (W2r,wt=31): 1295 (((T(x,y) * z) * z) * u) / T(z,T(T(x,z),y) * (z * u)) = T(T(x,z),y) * (z * u). [para(682(a,1),165(a,1,1))]. given #183 (W2r,wt=33): 1556 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),v5,v6),y,z),u,w),v9,v10). [para(231(a,1),295(a,2))]. given #184 (W2r,wt=33): 868 (x * y) / T((x / (z / y)) * z,a(x / (z / y),z / y,y)) = a(x / (z / y),z / y,y). [para(18(a,1),729(a,1,1,1))]. given #185 (W2r,wt=31): 1479 x * (x * ((T(T(y,z),u) * (u * w)) * u)) = x * (x * ((T(T(y,u),z) * (u * w)) * u)). [para(863(a,1),37(a,2,2,2)),rewrite([37(7)])]. given #186 (W0w,wt=6): 1300 a(x,x,y) = 1. [para(13(a,1),690(a,1,1,1)),rewrite([87(3),51(3),87(3),13(4),13(3)]),flip(a)]. given #187 (W0w,wt=6): 1607 L(x,y,y) = x. [hyper(24,a,1300,a)]. given #188 (W0w,wt=7): 1316 K(x * x,x) = 1. [back_rewrite(68),rewrite([1300(3)])]. given #189 (W0w,wt=7): 1392 K(x,x * x) = 1. [para(89(a,1),838(a,1,1,1,1)),rewrite([100(2),100(4),46(5),89(2)]),flip(a)]. given #190 (W0w,wt=7): 1648 T(x,x * x) = x. [back_rewrite(93),rewrite([1607(3)])]. given #191 (W0w,wt=8): 1180 L(x,x \ y,x) = x. [para(14(a,1),181(a,1,1)),rewrite([14(5),15(4)])]. given #192 (W0w,wt=6): 1667 L(x,y,x) = x. [para(15(a,1),1180(a,1,2))]. given #193 (W0w,wt=6): 1684 a(x,y,x) = 1. [hyper(25,a,1667,a)]. given #194 (W0w,wt=9): 552 K((x \ y) \ y,x) = 1. [para(91(a,1),540(a,1,1))]. given #195 (W0w,wt=9): 554 K(x \ y,y / x) = 1. [para(92(a,1),540(a,1,1))]. given #196 (W0w,wt=9): 560 T(x,(x \ y) \ y) = x. [para(91(a,1),541(a,1,2))]. given #197 (W0w,wt=9): 566 K(x,(x \ y) \ y) = 1. [para(91(a,1),555(a,1,2))]. given #198 (W0w,wt=9): 568 K(x / y,y \ x) = 1. [para(92(a,1),555(a,1,2))]. given #199 (W0w,wt=9): 996 T(x \ 1,x) = x \ 1. [para(49(a,1),986(a,1,2))]. given #200 (W0w,wt=9): 1013 x / (y \ 1) = x * y. [back_rewrite(975),rewrite([989(2)])]. given #201 (W0w,wt=9): 1014 x * (y \ 1) = x / y. [back_rewrite(974),rewrite([989(2)])]. given #202 (W0a,wt=20): 59 x \ (((x / (y * z)) * y) * z) = a(x / (y * z),y,z). [para(18(a,1),19(a,1,1))]. given #203 (W0a,wt=18): 60 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(18(a,1),19(a,1,2,1))]. given #204 (W0r,wt=20): 208 R(x,x / y,(x / y) \ z) = ((x / y) * (y * z)) / z. [para(50(a,1),191(a,1,1,2,1)),flip(a)]. given #205 (W0r,wt=17): 1885 x * (x * ((y * z) / T(x * (x * y),z))) = z. [para(961(a,1),1014(a,2)),rewrite([1014(9),1839(7)])]. given #206 (W0r,wt=19): 1660 K(x * (x * (y * (x * (x * y)))),x * (x * y)) = 1. [para(37(a,1),1316(a,1,1))]. given #207 (W0r,wt=20): 1771 K(x * ((x \ y) * z),a(x,x \ y,z) \ (y * z)) = 1. [para(56(a,1),566(a,1,2,1))]. given #208 (W0r,wt=18): 1109 K(a(x,y,(x * y) \ 1),x * (y / (x * y))) = 1. [para(57(a,1),987(a,1,1)),rewrite([1014(8)])]. given #209 (W1w,wt=21): 1009 (x / y) / K(y \ 1,T(x,y \ 1)) = T(x,y \ 1) / y. [back_rewrite(980),rewrite([989(3),989(5),989(10)])]. given #210 (W1w,wt=21): 1010 (T(x,y \ 1) / y) \ (x / y) = K(y \ 1,T(x,y \ 1)). [back_rewrite(979),rewrite([989(2),989(8),989(10)])]. given #211 (W1w,wt=21): 1058 (L(x,y,y \ 1) * y) \ (y * x) = K(y,L(x,y,y \ 1)). [para(997(a,1),675(a,1,2,1,1)),rewrite([996(3),1025(4),13(6),996(9),1025(10)])]. given #212 (W1w,wt=21): 1059 (x * y) / K(x,L(y,x,x \ 1)) = L(y,x,x \ 1) * x. [para(997(a,1),843(a,1,1,1,1)),rewrite([13(2),996(4),1025(5),996(9),1025(10)])]. given #213 (W1w,wt=21): 1069 (x * y) * K(L(y,x,x \ 1),x) = L(y,x,x \ 1) * x. [back_rewrite(871),rewrite([1025(5),1025(10)])]. given #214 (W1w,wt=21): 1266 (((T(x,y) * z) * z) * u) / (T(T(x,z),y) * (z * u)) = z. [para(682(a,1),17(a,1,1))]. given #215 (W1w,wt=21): 1268 a(x,T(T(y,z),x),x * u) = a(x,T(T(y,x),z),x * u). [para(682(a,1),19(a,1,1)),rewrite([517(7),673(9)])]. given #216 (W1w,wt=21): 1271 L(x * y,T(T(z,u),x),x) = L(x * y,T(T(z,x),u),x). [para(682(a,1),21(a,1,2)),rewrite([517(3),678(7)])]. given #217 (W1a,wt=23): 130 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [back_rewrite(126),rewrite([128(3)])]. given #218 (W1a,wt=26): 132 (x * (y * (x * z))) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [back_rewrite(118),rewrite([128(3)])]. given #219 (W1r,wt=30): 1230 L((x * (y / x)) * z,K(y / x,x),x * (y / x)) = y \ ((y * (x * (y / x))) * z). [para(67(a,1),181(a,1,2))]. given #220 (W1r,wt=27): 1920 x * (x * ((y * T(x * (x * y),z)) / (x * (x * y)))) = T(x * (x * y),z). [back_rewrite(1255),rewrite([1839(9)])]. given #221 (W1r,wt=27): 422 x * (((y * (x * z)) * x) * (y * x)) = x * (y * (x * (z * (x * (y * x))))). [para(194(a,1),14(a,1)),rewrite([14(2)]),flip(a)]. given #222 (W1r,wt=24): 501 R(R(R(x,y,z),R(R(x,u,w),y,z),v5),u,w) = R(R(x,u,w),y,z). [para(480(a,1),99(a,2))]. given #223 (W1r,wt=23): 1078 L(L(L(x,y,z),u,w),L(x,u,w) \ 1,v5) = L(L(x,u,w),y,z). [para(1022(a,1),97(a,1,1)),flip(a)]. given #224 (W2w,wt=31): 375 R(R(R(R(x,y,y \ z),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v7,v8),v5,v6),y,y \ z). [para(248(a,2),99(a,1,1))]. given #225 (W2w,wt=31): 376 R(R(R(R(x,y,y \ z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v5,v6),u,w),v7,v8),y,y \ z). [para(99(a,2),248(a,1,1))]. given #226 (W2w,wt=31): 384 (R(R(x,y,z),u,w) * (v5 * (v5 * v6))) * v7 = (R(R(x,u,w),y,z) * (v5 * (v5 * v6))) * v7. [para(99(a,2),341(a,1,1)),rewrite([382(9)])]. given #227 (W2w,wt=31): 387 (x * (y * (x * (z * (x * (y * x)))))) \ (x * (y * (x * (z * (x * (y * (x * u))))))) = u. [para(129(a,1),15(a,1,2))]. given #228 (W2a,wt=33): 235 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v5,v6),y,z),v9,v10),u,w),v7,v8). [para(97(a,2),97(a,1,1,1))]. given #229 (W2a,wt=33): 237 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v5,v6),y,z),v7,v8),v9,v10),u,w). [para(97(a,2),97(a,2,1,1)),flip(a)]. given #230 (W2r,wt=32): 1929 R(x * (x * (y * z)),x * (x * y),(x * (x * y)) \ u) = x * (x * ((y * (z * u)) / u)). [back_rewrite(899),rewrite([1839(14)])]. given #231 (W2r,wt=32): 314 (x * ((y \ z) * (y * ((y \ z) * u)))) \ ((x * ((y \ z) * z)) * u) = a(x,(y \ z) * z,u). [para(16(a,1),110(a,1,2,1,2,2)),rewrite([16(14)])]. given #232 (W2r,wt=34): 1446 (x * (y * (x * z))) \ ((u * (x * (y * x))) * z) = R(T(u,x * (y * (x * z))),x * (y * x),z). [para(121(a,1),92(a,1,1)),rewrite([31(7)]),flip(a)]. given #233 (W2r,wt=33): 454 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),v5,v6),y,z),v7,v8),u,w). [para(97(a,1),295(a,2,1,1))]. given #234 (W2r,wt=35): 1508 K(T(T(x,y),x \ z) * ((x \ z) * u),x \ z) = K(T((x \ z) \ z,y) * ((x \ z) * u),x \ z). [para(91(a,1),1470(a,2,1,1,1))]. given #235 (W0w,wt=8): 2044 R(x,y * y,z) = x. [back_rewrite(338),rewrite([2040(3),17(6)]),flip(a)]. given #236 (W0w,wt=8): 2045 a(x,y * y,z) = 1. [back_rewrite(311),rewrite([2040(6),46(7)]),flip(a)]. given #237 (W0w,wt=8): 2254 L(x,y,z * z) = x. [para(13(a,1),132(a,1,1,2)),rewrite([13(6),638(6),667(3),13(2)]),flip(a)]. given #238 (W0w,wt=8): 2485 L(x,y * y,z) = x. [hyper(24,a,2045,a)]. given #239 (W0w,wt=8): 2492 a(x * x,y,z) = 1. [hyper(25,a,2254,a)]. given #240 (W0w,wt=9): 1091 (x * y) \ x = y \ 1. [back_rewrite(632),rewrite([1077(3)]),flip(a)]. given #241 (W0w,wt=9): 1397 K(x,x * T(x,y)) = 1. [para(159(a,1),838(a,1,1,1,1)),rewrite([547(2),101(3),547(2),547(5),101(6),547(5),46(7),159(3),547(3)]),flip(a)]. given #242 (W0w,wt=9): 1649 x / (x * x) = x \ 1. [back_rewrite(1353),rewrite([1609(3),1014(4)])]. given #243 (W0w,wt=8): 2593 L(x,x,x \ 1) = x. [para(1649(a,1),18(a,1,1)),rewrite([1025(4)])]. given #244 (W0w,wt=8): 2607 a(x \ 1,x,x) = 1. [para(1649(a,1),59(a,1,2,1,1)),rewrite([997(3),13(2),46(1),1649(3)]),flip(a)]. given #245 (W0w,wt=9): 1659 T(x * x,x) = x * x. [hyper(28,a,1316,a)]. given #246 (W0w,wt=9): 1708 T(x,x * y) = T(x,y). [back_rewrite(639),rewrite([1685(2)]),flip(a)]. given #247 (W0w,wt=9): 1723 K(x,(y * x) / y) = 1. [para(15(a,1),554(a,1,1))]. given #248 (W0w,wt=9): 1727 K(x,y / (y / x)) = 1. [para(50(a,1),554(a,1,1))]. given #249 (W0w,wt=9): 1780 K((x * y) / x,y) = 1. [para(15(a,1),568(a,1,2))]. given #250 (W0w,wt=9): 1784 K(x / (x / y),y) = 1. [para(50(a,1),568(a,1,2))]. given #251 (W0a,wt=11): 63 (x * y) * K(y,x) = y * x. [para(20(a,1),16(a,1,2))]. given #252 (W0a,wt=13): 64 x \ ((y \ x) * y) = K(y \ x,y). [para(16(a,1),20(a,1,1))]. given #253 (W0r,wt=15): 189 (x * y) * (x * z) = x * ((y * x) * z). [para(104(a,1),37(a,2,2)),rewrite([16(2)])]. given #254 (W0r,wt=15): 103 x * (y * (x * ((x * (y * x)) \ z))) = z. [para(36(a,1),16(a,1)),rewrite([101(2)])]. given #255 (W0r,wt=15): 2495 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(2254(a,1),74(a,1)),rewrite([100(3),100(5)]),flip(a)]. given #256 (W0r,wt=11): 2918 T(x * y,K(y,x)) = x * y. [para(63(a,1),1708(a,1,2)),rewrite([2759(3)]),flip(a)]. given #257 (W0r,wt=15): 94 T(T(T(x,y),z),u) = T(T(T(x,u),y),z). [para(29(a,1),29(a,1,1)),flip(a)]. given #258 (W1w,wt=21): 1287 ((T(x,T(T(x,y),z)) * y) * y) * u = ((x * y) * y) * u. [para(541(a,1),682(a,1,2,1)),rewrite([186(4)]),flip(a)]. given #259 (W1w,wt=21): 1324 x \ (x \ (y * (x * (x * z)))) = z * T(y,x * (x * z)). [para(778(a,1),15(a,1,2))]. given #260 (W1w,wt=21): 1326 (x \ (y * (x * (x * z)))) / (z * T(y,x * (x * z))) = x. [para(778(a,1),17(a,1,1))]. given #261 (W1w,wt=21): 1359 x * (y * T(z,y * (x * y))) = y \ (z * (y * (x * y))). [para(788(a,1),15(a,1,2)),flip(a)]. given #262 (W1w,wt=21): 1689 L(L(L(x,y,z),u,w),v5,L(x,u,w)) = L(L(x,u,w),y,z). [para(1667(a,1),97(a,1,1)),flip(a)]. given #263 (W1w,wt=21): 1692 L(L(L(x,y,L(x,z,u)),w,v5),z,u) = L(L(x,z,u),w,v5). [para(1667(a,1),97(a,2,1))]. given #264 (W1w,wt=21): 1696 L(L(L(x,y,z),u,L(x,w,v5)),w,v5) = L(L(x,w,v5),y,z). [para(1667(a,1),230(a,1,1)),flip(a)]. given #265 (W1w,wt=21): 1884 x * (x * ((y / z) / T(x * (x * y),z \ 1))) = z \ 1. [para(1014(a,1),961(a,1,1,2,2)),rewrite([1839(9)])]. given #266 (W1a,wt=28): 133 (x * (y * (x * (z * u)))) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [back_rewrite(112),rewrite([128(4)])]. given #267 (W1a,wt=28): 139 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(37(a,1),19(a,1,1,2))]. given #268 (W1r,wt=23): 3382 T(T(T(x,y \ 1),z),u) / y = T(T(T(x,z),u),y \ 1) / y. [para(94(a,1),1009(a,2,1)),rewrite([1009(12)]),flip(a)]. given #269 (W1r,wt=27): 227 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v7,v8),y,z),u,w),v5,v6). [para(97(a,1),34(a,1,1)),flip(a)]. given #270 (W1r,wt=21): 3352 T(T(T(T(x / y,z),u),w),y) = T(T(T(y \ x,z),u),w). [para(537(a,1),94(a,2,1,1))]. given #271 (W1r,wt=27): 327 (x * y) \ (z * (x * ((y / (x * z)) * x))) = K(z,x * ((y / (x * z)) * x)). [para(18(a,1),114(a,1,1,2))]. given #272 (W1r,wt=25): 3784 K(T(T(T(x,y \ 1),z),u) / y,y \ T(T(T(x,z),u),y \ 1)) = 1. [para(3382(a,2),568(a,1,1))]. given #273 (W2w,wt=31): 389 (x * (y * (x * (z * (x * (y * (x * u))))))) / u = x * (y * (x * (z * (x * (y * x))))). [para(129(a,1),17(a,1,1))]. given #274 (W2w,wt=31): 391 x * (y * (x * ((z / (x * (y * x))) * (x * (y * (x * u)))))) = (x * (y * (x * z))) * u. [para(18(a,1),129(a,1,1,2,2,2)),flip(a)]. given #275 (W2w,wt=31): 397 x * (x * (y * (x * (x * (y * ((y \ z) * u)))))) = x * (x * ((y * (x * (x * z))) * u)). [para(16(a,1),150(a,1,2,2,1,2,2,2)),flip(a)]. given #276 (W2w,wt=31): 398 x * (x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u))))))) = x * (x * u). [para(16(a,1),150(a,1,2,2)),flip(a)]. given #277 (W2a,wt=33): 243 L(L(L(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(R(R(x,u,w),y,z),v9,v10),v5,v6),v7,v8). [para(98(a,1),97(a,1,1,1))]. given #278 (W2a,wt=33): 250 L(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(R(R(R(R(x,v5,v6),y,z),v7,v8),u,w),v9,v10). [para(99(a,2),98(a,1,1,1))]. given #279 (W2r,wt=35): 1599 (x * y) * (y * ((T(T(z,u),w) * (w * v5)) * w)) = (x * y) * (y * ((T(T(z,w),u) * (w * v5)) * w)). [para(1479(a,1),104(a,1,2,2)),rewrite([104(10)]),flip(a)]. given #280 (W2r,wt=31): 2372 R(R(R(R(x,y / z,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v5,v6),u,w),v7,v8),y / z,z). [para(50(a,1),376(a,1,1,1,1,3)),rewrite([50(11)])]. given #281 (W2r,wt=31): 4049 R(R(R(R(x,y / z,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v7,v8),v5,v6),u,w),y / z,z). [para(2372(a,1),99(a,1)),flip(a)]. given #282 (W2r,wt=31): 3794 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,w),y),z),v5),u \ 1) / u. [para(94(a,1),3382(a,2,1,1,1))]. given #283 (W2r,wt=33): 2880 ((x * (y * z)) * K(z,y)) / T(x * (z * y),a(x,y * z,K(z,y))) = a(x,y * z,K(z,y)). [para(63(a,1),265(a,1,2,1,2))]. given #284 (W0w,wt=8): 3266 L(x,y,y \ 1) = x. [back_rewrite(1025),rewrite([3143(4),15(2)]),flip(a)]. given #285 (W0w,wt=8): 3301 a(x \ 1,x,y) = 1. [back_rewrite(1066),rewrite([3266(3),46(1)]),flip(a)]. given #286 (W0w,wt=8): 4111 L(x,y \ 1,y) = x. [para(50(a,1),3266(a,1,3)),rewrite([989(2)])]. given #287 (W0w,wt=9): 1829 x \ (x / y) = y \ 1. [para(1014(a,1),15(a,1,2))]. given #288 (W0w,wt=9): 2538 (x \ y) \ 1 = y \ x. [para(16(a,1),1091(a,1,1)),flip(a)]. given #289 (W0w,wt=9): 2606 K(x \ 1,x * x) = 1. [para(1649(a,1),67(a,1,1,2)),rewrite([1014(4),17(2),46(1),1649(3)]),flip(a)]. given #290 (W0w,wt=9): 2642 T(x,x \ y) = T(x,y). [para(16(a,1),1708(a,1,2)),flip(a)]. given #291 (W0w,wt=9): 2643 T(x / y,x) = y \ x. [para(18(a,1),1708(a,1,2)),rewrite([92(4)])]. given #292 (W0w,wt=9): 2649 (x \ y) \ y = T(x,y). [para(91(a,1),1708(a,2)),rewrite([16(2)]),flip(a)]. given #293 (W0w,wt=9): 2690 (x \ y) * T(x,y) = y. [back_rewrite(1457),rewrite([2649(3),2642(7),166(8)])]. given #294 (W0w,wt=9): 2711 x / T(y,x) = y \ x. [back_rewrite(218),rewrite([2642(2)])]. given #295 (W0w,wt=9): 2755 (x \ 1) \ y = x * y. [back_rewrite(1227),rewrite([2747(5)]),flip(a)]. given #296 (W0w,wt=9): 2772 K(x * y,y * x) = 1. [back_rewrite(1826),rewrite([2755(4)])]. given #297 (W0w,wt=9): 2810 T(x,(y * x) / y) = x. [hyper(28,a,1723,a)]. given #298 (W0w,wt=9): 2825 T(x,y / (y / x)) = x. [hyper(28,a,1727,a)]. given #299 (W0w,wt=9): 2917 K(x,y) \ 1 = K(y,x). [para(63(a,1),1091(a,1,1)),rewrite([20(3)]),flip(a)]. given #300 (W0a,wt=13): 66 x \ (y * (x / y)) = K(y,x / y). [para(18(a,1),20(a,1,1))]. given #301 (W0a,wt=14): 72 (x * y) * L(z,y,x) = x * (y * z). [para(21(a,1),16(a,1,2))]. given #302 (W0r,wt=16): 3940 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(398(a,1),74(a,2,1)),rewrite([3936(10),3936(12),3136(8)])]. given #303 (W0r,wt=10): 4151 a(x,y \ z,z \ y) = 1. [para(2538(a,1),1012(a,1,2))]. given #304 (W0r,wt=13): 4357 (x \ (x \ y)) * T(x,y) = x \ y. [para(2642(a,1),2690(a,1,2))]. given #305 (W0r,wt=17): 2812 K((x \ y) * (x * z),((y * x) * z) / x) = 1. [para(104(a,1),1723(a,1,2,1))]. given #306 (W0r,wt=20): 507 (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z)). [para(90(a,1),19(a,1,1,2))]. given #307 (W1w,wt=21): 1921 x * (x * ((y * z) / T(x * (x * z),T(y,z)))) = T(y,z). [back_rewrite(1252),rewrite([1839(8)])]. given #308 (W1w,wt=21): 2445 ((x \ y) * (x * ((x \ y) * z))) \ (((x \ y) * y) * z) = 1. [para(13(a,1),314(a,1,1)),rewrite([13(9),52(13)])]. given #309 (W1w,wt=21): 2588 K(x * (x * y),x * (x * (y * T(x * (x * y),z)))) = 1. [para(37(a,1),1397(a,1,2))]. given #310 (W1w,wt=21): 2640 x * (x * (y * (y * (z / (T(x * x,y) * (y * z)))))) = y. [para(1659(a,1),1266(a,1,1,1,1,1)),rewrite([100(2),37(3),37(4),100(2),2635(7),1839(9),1839(7)])]. given #311 (W1w,wt=21): 2647 T(x * (x * y),x * (x * (y * z))) = T(x * (x * y),z). [para(37(a,1),1708(a,1,2))]. given #312 (W1w,wt=21): 2664 T(x,y * T(z,x * (x * y))) = T(x,z * (x * (x * y))). [para(778(a,1),1708(a,1,2)),rewrite([2642(5)]),flip(a)]. given #313 (W1w,wt=21): 2697 a(x * (y \ x),T(y,x),z) = a(y \ x,T(y,x) * x,z). [back_rewrite(1301),rewrite([2642(4),2642(7)])]. given #314 (W1w,wt=21): 2713 ((x \ y) * (x * z)) \ ((y * x) * z) = T(x,(y * x) * z). [back_rewrite(185),rewrite([2648(10)])]. given #315 (W1a,wt=23): 143 (x * (y * (y * z))) \ (y * (y * (z * x))) = K(y * (y * z),x). [para(37(a,1),20(a,1,2))]. given #316 (W1a,wt=26): 145 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(37(a,1),21(a,1,2,2))]. given #317 (W1r,wt=29): 806 x \ (y * (z * (y * (x / (y * (z * y)))))) = K(y * (z * y),x / (y * (z * y))). [para(18(a,1),115(a,1,1))]. given #318 (W1r,wt=23): 2215 x * (y * (z * (y * (x * ((x * (y * (z * (y * x)))) \ u))))) = u. [para(130(a,1),16(a,1))]. given #319 (W1r,wt=24): 5575 a(x,T(y,(z * y) * u),((z * y) * u) \ ((y \ z) * (y * u))) = 1. [para(2713(a,1),4151(a,1,2))]. given #320 (W1r,wt=23): 2934 (x * (y * z)) \ (L(z,y,x) * (x * y)) = K(L(z,y,x),x * y). [para(21(a,1),64(a,1,2,1)),rewrite([21(10)])]. given #321 (W1r,wt=25): 2051 K(x * (y * (y * ((z * x) * (y * (y * z))))),x * (y * (y * z))) = 1. [para(778(a,1),1660(a,1,1,2,2,2,2)),rewrite([16(9),785(10),189(7),37(3),189(6),101(3),189(5),420(6),778(12),16(12)])]. given #322 (W2w,wt=31): 405 x * ((y * x) * (x * ((x \ y) * (z * u)))) = x * (x * (((x \ y) * ((x * y) * z)) * u)). [para(104(a,1),150(a,2,2)),rewrite([136(5)]),flip(a)]. given #323 (W2w,wt=31): 435 R(x * ((x \ y) * z),y * z,(y * z) \ u) = ((y * z) * (a(y,x,x \ z) * u)) / u. [para(16(a,1),201(a,1,2,2)),rewrite([169(3),16(6),16(9)])]. given #324 (W2w,wt=31): 436 R((x * (y / z)) * z,x * y,(x * y) \ u) = ((x * y) * (a(x,y / z,z) * u)) / u. [para(18(a,1),201(a,1,2,2)),rewrite([18(6),18(9)])]. given #325 (W2w,wt=31): 463 x * (x * (x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))))) = x * (x * z). [para(16(a,1),393(a,1,2,2)),flip(a)]. given #326 (W2a,wt=33): 252 R(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = R(R(R(R(R(x,v7,v8),y,z),u,w),v9,v10),v5,v6). [para(99(a,1),99(a,1,1,1)),flip(a)]. given #327 (W2a,wt=33): 254 R(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = R(R(R(R(R(x,v9,v10),y,z),u,w),v5,v6),v7,v8). [para(99(a,1),99(a,2,1,1))]. given #328 (W2r,wt=33): 3604 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,L(x,v8,v9)),v8,v9) = L(L(L(L(x,v8,v9),u,w),y,z),v5,v6). [para(1689(a,1),448(a,1,1,1)),flip(a)]. given #329 (W2r,wt=32): 4778 (x * ((T(y,x) * (x * z)) * u)) \ ((y * (x * (x * z))) * u) = a(x,T(y,x) * (x * z),u). [back_rewrite(674),rewrite([4578(7),2040(8)])]. given #330 (W2r,wt=31): 654 L(T(x * (y * z),a(x,y,z)),a(x,y,z),u) = (u * a(x,y,z)) \ (u * ((x * y) * z)). [para(209(a,1),74(a,1,1))]. given #331 (W2r,wt=31): 4092 T(T(T(T(T(x,y),z),u),w \ 1),v5) / w = T(T(T(T(T(x,v5),y),z),u),w \ 1) / w. [para(94(a,1),3794(a,1,1))]. given #332 (W2r,wt=33): 5752 (x * ((y * x) * z)) \ (L(z,x,x * y) * (x * (y * x))) = K(L(z,x,x * y),x * (y * x)). [para(189(a,1),2934(a,1,1)),rewrite([101(7),101(13)])]. given #333 (W0w,wt=6): 5332 a(x,y,y) = 1. [para(89(a,1),507(a,1,2,2)),rewrite([4578(4),46(5),89(2)]),flip(a)]. given #334 (W0w,wt=6): 6018 L(x,x,y) = x. [hyper(24,a,5332,a)]. given #335 (W0w,wt=8): 5462 a(x,y,T(x,y)) = 1. [para(2640(a,1),507(a,1,1)),rewrite([5428(7),16(3),5428(8),2642(4),2642(3),2690(3),46(1),5428(8),5428(10),2642(6),2642(5),3954(5),16(3)]),flip(a)]. given #336 (W0w,wt=9): 3143 (x \ 1) * y = x \ y. [para(997(a,1),2495(a,1,1,2)),rewrite([14(4),15(9)])]. given #337 (W0w,wt=8): 6233 a(x,x / y,y) = 1. [back_rewrite(4419),rewrite([6132(4),46(5)]),flip(a)]. given #338 (W0w,wt=8): 6257 L(x,y / x,y) = x. [hyper(24,a,6233,a)]. given #339 (W0w,wt=8): 6258 a(x * y,x,y) = 1. [para(17(a,1),6233(a,1,2))]. given #340 (W0w,wt=8): 6279 L(x,y,y * x) = x. [para(17(a,1),6257(a,1,2))]. given #341 (W0w,wt=8): 6335 a(x,y,y \ x) = 1. [para(16(a,1),6258(a,1,1))]. given #342 (W0w,wt=9): 3302 K(x * y,K(y,x)) = 1. [hyper(27,a,2918,a)]. given #343 (W0w,wt=9): 3304 T(x,K(y \ x,y)) = x. [para(16(a,1),2918(a,1,1)),rewrite([16(5)])]. given #344 (W0w,wt=9): 3305 T(x,K(y,x / y)) = x. [para(18(a,1),2918(a,1,1)),rewrite([18(5)])]. given #345 (W0w,wt=9): 3317 K(K(x,y),x * y) = 1. [para(2918(a,1),838(a,1,1,1,1)),rewrite([63(3),63(6),46(7),2918(5),63(5)]),flip(a)]. given #346 (W0w,wt=9): 3327 K(K(x,y),y * x) = 1. [back_rewrite(2855),rewrite([3308(4),46(3)]),flip(a)]. given #347 (W0w,wt=9): 3500 K(x \ (x \ 1),x) = 1. [back_rewrite(2611),rewrite([3436(3),2642(4),2642(3),88(2),1649(2),46(5),3436(4),3436(7),2642(8),2642(7),88(6)]),flip(a)]. given #348 (W0w,wt=9): 3666 (x \ y) / y = x \ 1. [para(1884(a,1),201(a,1,2)),rewrite([3645(8),100(6),16(5),16(4),3645(11),16(9),16(8),2755(7),480(6),3645(9),16(7),16(6),3645(11),1300(9),13(6),3143(5)]),flip(a)]. given #349 (W0a,wt=16): 73 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(16(a,1),21(a,1,1))]. given #350 (W0a,wt=16): 76 L(x,y / x,z) = (z * (y / x)) \ (z * y). [para(18(a,1),21(a,1,2,2)),flip(a)]. given #351 (W0r,wt=14): 2893 L(x * K(x,y),x \ y,x) = T(x,y). [para(63(a,1),181(a,2,2)),rewrite([23(6)])]. given #352 (W0r,wt=16): 6557 K(K(L(x,y,z),z * y),z * (y * x)) = 1. [para(72(a,1),3327(a,1,2))]. given #353 (W0r,wt=16): 4445 L(L(x,y,z),u,x \ (u \ 1)) = L(x,y,z). [back_rewrite(3192),rewrite([4407(4)])]. given #354 (W0r,wt=19): 5505 T(x,y * (x * (x * x))) = T(x,T(y,x * (x * x))). [para(2664(a,1),1708(a,1))]. given #355 (W0r,wt=18): 2587 K(R(x,y,z),R(x,y,z) * R(T(x,u),y,z)) = 1. [para(31(a,1),1397(a,1,2,2))]. given #356 (W1w,wt=21): 2757 ((x / y) * (y * y)) \ (y * x) = K(y * (x * y),y \ 1). [back_rewrite(2601),rewrite([2755(6),2755(8),101(7)])]. given #357 (W1w,wt=21): 2778 K(T(a(x,y,z),x * (y * z)) \ 1,a(x,y,z) \ 1) = 1. [back_rewrite(2578),rewrite([2758(6),2547(7,R)])]. given #358 (W1w,wt=21): 2779 K(a(x,y,z) \ 1,T(a(x,y,z),x * (y * z)) \ 1) = 1. [back_rewrite(2577),rewrite([2758(9),2547(10,R)])]. given #359 (W1w,wt=21): 3139 T(x * (x * (y / (x * (x * z)))),x * (x * z)) = z \ y. [para(2495(a,1),92(a,2)),rewrite([1839(5)])]. given #360 (W1w,wt=21): 3218 x * (y \ T(z,x * (x / y))) = x \ (z * (x * (x / y))). [back_rewrite(1888),rewrite([3143(6)])]. given #361 (W1w,wt=21): 3307 T((x * y) * z,K((y \ x) * (y * z),y)) = (x * y) * z. [para(104(a,1),2918(a,1,1)),rewrite([104(11)])]. given #362 (W1w,wt=21): 3322 T((x * y) * z,((y \ x) * (y * z)) * y) = (x * y) * z. [back_rewrite(2659),rewrite([3307(14)])]. given #363 (W1w,wt=21): 3337 L(T(T(T(x,y),z),u),w,v5) = L(T(T(T(x,u),y),z),w,v5). [para(94(a,1),30(a,2,1)),rewrite([30(4)])]. given #364 (W1a,wt=30): 174 (x * (((x \ y) * (x * z)) * u)) \ (((y * x) * z) * u) = a(x,(x \ y) * (x * z),u). [para(104(a,1),19(a,1,2,1))]. given #365 (W1a,wt=25): 177 (((x \ y) * (x * z)) * x) \ ((y * x) * z) = K(x,(x \ y) * (x * z)). [para(104(a,1),20(a,1,2))]. given #366 (W1r,wt=23): 3715 x * (x * (((x \ (y \ 1)) / z) / T(x / y,z \ 1))) = z \ 1. [para(1884(a,1),1884(a,1,2,2,2,1,2)),rewrite([3645(7),16(5),1014(7)])]. given #367 (W1r,wt=27): 4559 (T(x,y) * (y * (z * (x * y)))) * u = T(x,y) * (y * (z * (x * (y * u)))). [back_rewrite(2234),rewrite([4525(4)]),flip(a)]. given #368 (W1r,wt=23): 6375 L(L(L(x,y,z),u,w),v5,v5 * L(x,u,w)) = L(L(x,u,w),y,z). [para(6279(a,1),97(a,1,1)),flip(a)]. given #369 (W1r,wt=23): 4770 x * (R(T(y,x),z,u) * (x * w)) = R(y,z,u) * (x * (x * w)). [back_rewrite(684),rewrite([4578(8),2040(9)])]. given #370 (W1r,wt=27): 7262 T(x,y) * (y * ((z / (x * y)) * (x * (y * u)))) = (T(x,y) * (y * z)) * u. [para(18(a,1),4559(a,1,1,2,2)),flip(a)]. given #371 (W2w,wt=31): 759 R(R(R(R(x,y,y \ z),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v5,v6),y,y \ z),v7,v8). [para(248(a,1),497(a,2,1)),rewrite([497(10)])]. given #372 (W2w,wt=31): 807 (x * ((y / x) * (z * (y / x)))) \ ((y / x) * (z * y)) = K((y / x) * (z * (y / x)),x). [para(18(a,1),115(a,1,2,2,2))]. given #373 (W2w,wt=31): 870 ((x * (T(y,x) / z)) * z) / T(y * x,a(x,T(y,x) / z,z)) = a(x,T(y,x) / z,z). [para(90(a,1),729(a,1,2,1))]. given #374 (W2w,wt=31): 876 ((x * (y / z)) * z) * K(((y / z) \ x) * y,y / z) = (((y / z) \ x) * y) * (y / z). [para(18(a,1),350(a,1,2,1,2)),rewrite([18(13)])]. given #375 (W2a,wt=33): 256 R(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = R(R(R(R(R(x,v5,v6),y,z),v9,v10),u,w),v7,v8). [para(99(a,2),99(a,1,1,1))]. given #376 (W2a,wt=33): 258 R(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = R(R(R(R(R(x,v5,v6),y,z),v7,v8),v9,v10),u,w). [para(99(a,2),99(a,2,1,1)),flip(a)]. given #377 (W2r,wt=33): 7114 L(L(L(T(T(T(x,y),z),u),w,v5),v6,v7),v8,v9) = L(L(L(T(T(T(x,u),y),z),v6,v7),v8,v9),w,v5). [para(3337(a,1),97(a,1,1,1)),flip(a)]. given #378 (W2r,wt=35): 5452 x * (x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u))))))) = y * z. [para(189(a,1),2640(a,1,2,2,2,2,2,2))]. given #379 (W2r,wt=33): 6505 T((x * (y / z)) * z,K(T(x * y,a(x,y / z,z)),a(x,y / z,z))) = (x * (y / z)) * z. [para(729(a,1),3305(a,1,2,2))]. given #380 (W2r,wt=33): 7052 T(x * (x * ((y * z) * u)),K((z \ (x * (x * y))) * (z * u),z)) = x * (x * ((y * z) * u)). [para(37(a,1),3307(a,1,1,1)),rewrite([37(4),37(14),37(15)])]. given #381 (W2r,wt=34): 1226 R(x,y * (y * z),L(u * w,u \ (y * (y * z)),u)) = R(x,y * (y * z),z \ ((z * u) * w)). [para(181(a,2),205(a,2,3)),rewrite([37(6),37(7),411(11),37(10),37(11),340(12)]),flip(a)]. given #382 (W0w,wt=9): 3691 x / (y * x) = y \ 1. [para(1884(a,1),1013(a,2)),rewrite([3645(7),16(5),2538(5),2755(3)])]. given #383 (W0w,wt=9): 4108 K(x * y,K(x,y)) = 1. [para(1684(a,1),2880(a,1,2,2)),rewrite([3308(3),88(8),2925(7),1684(7)])]. given #384 (W0w,wt=9): 4137 (x \ y) * (y \ x) = 1. [para(2538(a,1),16(a,1,2))]. given #385 (W0w,wt=9): 4150 K(x \ y,y \ x) = 1. [para(2538(a,1),987(a,1,1))]. given #386 (W0w,wt=9): 4192 K(x,x \ (x \ 1)) = 1. [para(50(a,1),2606(a,1,1)),rewrite([989(2),989(4),1014(5),2712(3)])]. given #387 (W0w,wt=9): 4209 T(x * y,x) = y * x. [para(1091(a,1),2642(a,1,2)),rewrite([2774(4)]),flip(a)]. given #388 (W0w,wt=9): 4358 K(K(x \ y,x),y) = 1. [back_rewrite(2963),rewrite([4342(5),46(5)]),flip(a)]. given #389 (W0w,wt=9): 4505 (x \ y) * x = T(y,x). [back_rewrite(2649),rewrite([4408(2)])]. given #390 (W0w,wt=8): 8054 a(x \ y,y,x) = 1. [para(4505(a,1),6258(a,1,1)),rewrite([4537(3)])]. given #391 (W0w,wt=8): 8105 L(x,y,x \ y) = x. [hyper(24,a,8054,a)]. given #392 (W0w,wt=8): 8106 a(x,y * x,y) = 1. [para(15(a,1),8054(a,1,1))]. given #393 (W0w,wt=8): 8111 a(x,y,y / x) = 1. [para(50(a,1),8054(a,1,1))]. given #394 (W0w,wt=9): 4915 K(x,y * (x / y)) = 1. [para(18(a,1),2772(a,1,1))]. given #395 (W0w,wt=9): 4916 K(x * (y / x),y) = 1. [para(18(a,1),2772(a,1,2))]. given #396 (W0w,wt=9): 4993 K(x,y) * K(y,x) = 1. [para(2917(a,1),16(a,1,2))]. given #397 (W0w,wt=9): 5002 K(K(x,y),K(y,x)) = 1. [para(2917(a,1),987(a,1,1))]. given #398 (W0a,wt=16): 81 R(x,x \ y,z) = (y * z) / ((x \ y) * z). [para(16(a,1),22(a,1,1,1)),flip(a)]. given #399 (W0a,wt=18): 82 R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z)). [para(16(a,1),22(a,1,1)),flip(a)]. given #400 (W0r,wt=11): 4539 K(x,x \ y) = T(y,x) \ y. [back_rewrite(65),rewrite([4505(2)]),flip(a)]. given #401 (W0r,wt=18): 8061 T(x * ((x \ y) * z),y) = L(z,x \ y,x) * y. [para(73(a,1),4505(a,1,1)),flip(a)]. given #402 (W0r,wt=16): 6062 a(T(T(x,y),z),u,T(T(T(x,u),y),z)) = 1. [para(94(a,1),5462(a,1,3))]. given #403 (W0r,wt=13): 3199 L(x,y,z / (y * x)) = L(x,y,z). [back_rewrite(2278),rewrite([3143(5),1091(3),1014(4),3143(9),2538(9),21(7)])]. given #404 (W0r,wt=17): 6603 x * K(y * (z * y),(z * y) \ (y \ 1)) = x. [back_rewrite(5679),rewrite([6567(5),16(6),5641(7)])]. given #405 (W1w,wt=21): 3338 R(T(T(T(x,y),z),u),w,v5) = R(T(T(T(x,u),y),z),w,v5). [para(94(a,1),31(a,2,1)),rewrite([31(4)])]. given #406 (W1w,wt=21): 3341 T(T(T(T(x,y),z),u),T(T(x,z),u)) = T(T(T(x,z),u),y). [para(94(a,1),159(a,1,1))]. given #407 (W1w,wt=21): 3342 T(T(T(T(x,y),z),u),T(T(x,u),y)) = T(T(T(x,u),y),z). [para(94(a,2),159(a,1,1))]. given #408 (W1w,wt=21): 3395 K(T(T(x,y),z),T(T(x,y),z) * T(T(T(x,u),y),z)) = 1. [para(94(a,1),1397(a,1,2,2))]. given #409 (W1w,wt=21): 3396 K(T(T(x,y),z),T(T(x,y),z) * T(T(T(x,z),u),y)) = 1. [para(94(a,2),1397(a,1,2,2))]. given #410 (W1w,wt=21): 3398 T(T(T(x,y),z),T(T(x,z),y) * u) = T(T(T(x,z),y),u). [para(94(a,2),1708(a,1)),rewrite([29(6)])]. given #411 (W1w,wt=21): 3476 x * T(y * z,y * (y * x)) = (y \ z) * (y * (y * x)). [para(181(a,2),1324(a,1,2)),rewrite([3018(5),168(4)]),flip(a)]. given #412 (W1w,wt=21): 3541 x \ (y \ (z * (y * (x * y)))) = y * T(z,y * (x * y)). [para(1359(a,1),15(a,1,2))]. given #413 (W1a,wt=23): 178 (x * y) * (K(y,x) * ((x * y) * z)) = ((y * x) * (x * y)) * z. [para(20(a,1),104(a,1,2,1))]. given #414 (W1a,wt=28): 179 ((x * y) * z) \ (y * (((y \ x) * (y * z)) * u)) = L(u,(y \ x) * (y * z),y). [para(104(a,1),21(a,1,1))]. given #415 (W1r,wt=25): 3835 T(T(T(x \ y,z),u),T(T(T(y / x,z),u),w)) = T(T(x \ y,z),u). [para(541(a,1),3352(a,1,1)),rewrite([622(4)]),flip(a)]. given #416 (W1r,wt=30): 5708 a(x,T(y / z,(u * (y / z)) * z),((u * (y / z)) * z) \ (((y / z) \ u) * y)) = 1. [para(18(a,1),5575(a,1,3,2,2))]. given #417 (W1r,wt=27): 8758 R(R(T(T(T(x,y),z),u),w,v5),v6,v7) = R(R(T(T(T(x,u),y),z),v6,v7),w,v5). [para(3338(a,1),35(a,1,1)),flip(a)]. given #418 (W1r,wt=22): 4325 L(x * y,x \ z,x) * T(z,(z * x) * y) = (z * x) * y. [para(181(a,2),2690(a,1,1))]. given #419 (W1r,wt=25): 8795 T(T(T(T(x,y),z),u),T(T(x,T(x,y) * z),u)) = T(T(T(x,y),z),u). [para(1708(a,1),3341(a,1,1,1)),rewrite([3401(13)])]. given #420 (W2w,wt=31): 889 ((x / y) * (z * x)) * K(y,(x / y) * (z * (x / y))) = y * ((x / y) * (z * (x / y))). [para(326(a,1),16(a,1,2))]. given #421 (W2w,wt=31): 909 R(R(R(R(x,y,T(z,y)),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v7,v8),y,T(z,y)),v5,v6). [para(23(a,1),372(a,1,1,1,1,3)),rewrite([23(9)])]. given #422 (W2w,wt=31): 910 R(R(R(R(x,y / z,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v7,v8),y / z,z),v5,v6). [para(50(a,1),372(a,1,1,1,1,3)),rewrite([50(10)])]. given #423 (W2w,wt=31): 911 R(R(R(R(x,y,z),u,u \ w),v5,v6),v7,v8) = R(R(R(R(x,v5,v6),v7,v8),u,u \ w),y,z). [para(99(a,1),372(a,1,1))]. given #424 (W2a,wt=33): 284 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,u,w),y,z),v9,v10),v5,v6),v7,v8). [para(228(a,1),97(a,1,1,1))]. given #425 (W2a,wt=33): 285 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),y,z),u,w),v5,v6),v9,v10). [para(97(a,1),228(a,1,1,1)),flip(a)]. given #426 (W2r,wt=32): 4025 (x * ((x \ y) * ((y \ z) * (y * u)))) \ ((z * y) * u) = a(x,x * y,(y \ z) * (y * u)). [back_rewrite(614),rewrite([3954(14)])]. given #427 (W2r,wt=31): 2377 (R(R(x,y,z),u,w) * (v5 * (v5 * v6))) * ((R(R(x,u,w),y,z) * (v5 * (v5 * v6))) \ v7) = v7. [para(384(a,1),16(a,1))]. given #428 (W2r,wt=34): 2836 K(((((x * y) * z) * (x * (y * z))) * u) / (x * (y * z)),a(x,y,z) * ((x * (y * z)) * u)) = 1. [para(175(a,1),1780(a,1,1,1))]. given #429 (W2r,wt=33): 1907 x * (x * (((T(T(y,z),u) * (u * w)) * u) / (x * (x * ((T(T(y,u),z) * (u * w)) * u))))) = 1. [back_rewrite(1603),rewrite([1839(15)])]. given #430 (W2r,wt=31): 3947 x * (x * (y * (x * (x * (y * (z \ ((y * (x * (x * (y / z)))) \ u))))))) = x * (x * u). [para(1014(a,1),398(a,1,2,2,2,2,2,2,2,1,2,2,2)),rewrite([3143(8)])]. given #431 (W0w,wt=8): 8327 R(x,x \ 1,y) = x. [para(13(a,1),81(a,2,1)),rewrite([3143(6),4155(5),16(5)])]. given #432 (W0w,wt=8): 8415 R(x,x \ y,x) = x. [para(4505(a,1),81(a,2,2)),rewrite([165(5)])]. given #433 (W0w,wt=6): 9874 R(x,y,x) = x. [para(15(a,1),8415(a,1,2))]. given #434 (W0w,wt=9): 5006 K(x * T(x,y),x) = 1. [para(1397(a,1),2917(a,1,1)),rewrite([46(3)]),flip(a)]. given #435 (W0w,wt=9): 5014 K(x * x,x \ 1) = 1. [para(2606(a,1),2917(a,1,1)),rewrite([46(3)]),flip(a)]. given #436 (W0w,wt=9): 5067 T(x,y * (x / y)) = x. [para(66(a,1),2642(a,1,2)),rewrite([3305(3)]),flip(a)]. given #437 (W0w,wt=9): 5359 (x / y) * (y / x) = 1. [back_rewrite(4813),rewrite([5358(6),88(4),3691(3),1014(4),5358(7)])]. given #438 (W0w,wt=9): 6445 K(x,K(y \ x,y)) = 1. [para(16(a,1),3302(a,1,1))]. given #439 (W0w,wt=9): 6446 K(x,K(y,x / y)) = 1. [para(18(a,1),3302(a,1,1))]. given #440 (W0w,wt=9): 6523 K(K(x,x \ y),y) = 1. [para(16(a,1),3317(a,1,2))]. given #441 (W0w,wt=9): 6524 K(K(x / y,y),x) = 1. [para(18(a,1),3317(a,1,2))]. given #442 (W0w,wt=9): 6543 K(K(x,y / x),y) = 1. [para(18(a,1),3327(a,1,2))]. given #443 (W0w,wt=9): 6565 (x / y) \ 1 = y / x. [para(50(a,1),3666(a,1,1)),flip(a)]. given #444 (W0w,wt=9): 7616 T(x,y) / y = y \ x. [para(2690(a,1),3691(a,1,2)),rewrite([4408(5),14(5)])]. given #445 (W0w,wt=9): 7635 K(x,K(y,y \ x)) = 1. [para(16(a,1),4108(a,1,1))]. given #446 (W0w,wt=9): 7636 K(x,K(x / y,y)) = 1. [para(18(a,1),4108(a,1,1))]. given #447 (W0a,wt=14): 84 R(x,y,z) * (y * z) = (x * y) * z. [para(22(a,1),18(a,1,1))]. given #448 (W0a,wt=14): 85 R(x / y,y,z) = (x * z) / (y * z). [para(18(a,1),22(a,1,1,1)),flip(a)]. given #449 (W0r,wt=14): 8701 L(x \ y,x,z) = ((z / y) * x) \ z. [para(3199(a,1),74(a,1)),rewrite([16(4),16(6),18(6)])]. given #450 (W0r,wt=19): 4213 T(T(T(x,T(x,y) \ z),u),y) = T(T(T(x,y),z),u). [para(2642(a,1),94(a,2,1))]. given #451 (W0r,wt=20): 3064 a(K(x,y),y * x,K(x,y) * (K(x,y) * (x * y))) = 1. [back_rewrite(2881),rewrite([2971(15)])]. given #452 (W0r,wt=11): 7967 x \ T(y,x) = T(x \ y,x). [para(4505(a,1),23(a,1,2))]. given #453 (W0r,wt=18): 2705 L(x \ y,x,z) \ (z * y) = T(z * x,z * y). [back_rewrite(650),rewrite([2642(5)]),flip(a)]. given #454 (W1w,wt=21): 3544 (x \ (y * (x * (z * x)))) / (x * T(y,x * (z * x))) = z. [para(1359(a,1),17(a,1,1))]. given #455 (W1w,wt=21): 3575 x * (y \ T(z,y \ (x / y))) = y * (z * (y \ (x / y))). [para(1014(a,1),1359(a,1,2,2,2,2)),rewrite([3143(6),3143(6),1014(12),3143(11),2755(11)])]. given #456 (W1w,wt=21): 3640 x * (x * (((x \ y) / z) / T(x * y,z \ 1))) = z \ 1. [para(16(a,1),1884(a,1,2,2,2,1,2))]. given #457 (W1w,wt=21): 3641 x * (x * (y / T(x * (x * (y * z)),z \ 1))) = z \ 1. [para(17(a,1),1884(a,1,2,2,1))]. given #458 (W1w,wt=21): 3645 (x / y) / T(z * (z * x),y \ 1) = z \ (z \ (y \ 1)). [para(1884(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. given #459 (W1w,wt=21): 3683 x * ((x \ (y \ 1)) * T(z,x / y)) = x \ (z * (x / y)). [para(1884(a,1),778(a,1,2,2,2,2)),rewrite([3645(7),16(5),1014(6),3645(14),16(12),16(11),1014(10)])]. given #460 (W1w,wt=21): 3710 (x \ (x \ (y \ 1))) * T(z,y \ 1) = x \ (x \ (z / y)). [para(1884(a,1),1324(a,1,2,2,2)),rewrite([1014(3),3645(10),3645(14),16(12),16(11)]),flip(a)]. given #461 (W1w,wt=21): 3712 (x \ (y * (x / z))) / ((x \ (z \ 1)) * T(y,x / z)) = x. [para(1884(a,1),1326(a,1,1,2,2,2)),rewrite([1014(3),3645(10),16(8),3645(13),16(11),16(10),1014(9)])]. given #462 (W1a,wt=22): 180 L((x \ y) * (x * z),x,u) = (u * x) \ (u * ((y * x) * z)). [para(104(a,1),21(a,1,2,2)),flip(a)]. given #463 (W1a,wt=28): 183 (((x * y) * z) * u) / (((y \ x) * (y * z)) * u) = R(y,(y \ x) * (y * z),u). [para(104(a,1),22(a,1,1,1))]. given #464 (W1r,wt=24): 9159 a(K(x,y) * ((y * x) * z),((x * y) * (y * x)) * z,y * x) = 1. [para(178(a,1),8106(a,1,2))]. given #465 (W1r,wt=23): 10700 a(x / y,z,(x * z) \ (x * y)) = a(x,z,(x * z) \ (x * y)). [para(8701(a,2),57(a,1,1,2,2)),rewrite([10690(6),1105(6),10690(8)]),flip(a)]. given #466 (W1r,wt=21): 5469 T(x * (y \ x),x * (y \ (x * z))) = T(x * (y \ x),z). [para(18(a,1),2647(a,1,1,2)),rewrite([4230(2),4136(7),18(9),4230(8)])]. given #467 (W1r,wt=26): 3141 L(x \ y,z * (z * x),u) = (u * (z * (z * x))) \ (u * (z * (z * y))). [para(2495(a,1),74(a,1,1))]. given #468 (W1r,wt=21): 7679 L(x,y \ z,(z \ y) * (u * (z \ y))) = L(x,u,z \ y). [para(4137(a,1),132(a,1,1,2,2)),rewrite([14(3),6353(7),7656(6),21(6)]),flip(a)]. given #469 (W2w,wt=31): 978 (x * (y * (x * (z * (x * (y * (x / u))))))) * u = x * (y * (x * (z * (x * (y * x))))). [para(129(a,1),506(a,1,1)),rewrite([974(3)])]. given #470 (W2w,wt=31): 1187 (x * (y * z)) \ ((x * (((y * z) * x) * y)) * u) = L((x * y) * u,L(z,y,x),x * y). [para(21(a,1),181(a,1,2)),rewrite([189(11)]),flip(a)]. given #471 (W2w,wt=31): 1487 K(x,y * ((T(T(z,u),y) * (y * w)) * y)) = K(x,y * ((T(T(z,y),u) * (y * w)) * y)). [para(863(a,1),114(a,2,2,2)),rewrite([114(15)])]. given #472 (W2w,wt=31): 1492 K(x * ((T(T(y,z),x) * (x * u)) * x),w) = K(x * ((T(T(y,x),z) * (x * u)) * x),w). [para(863(a,1),115(a,2,1,2)),rewrite([115(15)])]. given #473 (W2a,wt=33): 287 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v5,v6),y,z),v7,v8),u,w),v9,v10). [para(97(a,2),228(a,1,1,1))]. given #474 (W2a,wt=33): 289 L(L(L(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(R(R(x,u,w),y,z),v7,v8),v5,v6),v9,v10). [para(98(a,1),228(a,1,1,1))]. given #475 (W2r,wt=33): 8883 K(T(T(T(T(x,y),z),u),w),T(T(T(T(x,u),y),z),w) * T(T(T(T(T(x,u),y),v5),z),w)) = 1. [para(94(a,2),3395(a,1,1,1))]. given #476 (W2r,wt=34): 6663 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,u,w),y,z))) \ (v6 * v5). [para(76(a,1),228(a,1)),flip(a)]. given #477 (W2r,wt=35): 1598 x * (x * (x * ((T(T(y,z),u) * (u * w)) * u))) = x * (x * (x * ((T(T(y,u),z) * (u * w)) * u))). [para(1479(a,1),37(a,2,2)),rewrite([37(8)])]. given #478 (W2r,wt=31): 10784 T(T(T(T(T(x,y),z),u),w),T(T(T(x,T(x,y) \ z),w),u)) = T(T(T(T(x,y),z),w),u). [para(4213(a,1),3342(a,1,1,1)),rewrite([10750(16)])]. given #479 (W2r,wt=33): 8967 T(T(T(T(T(T(x,y),z),u),w),v5),T(T(T(T(x,z),y),w),v5)) = T(T(T(T(T(x,y),z),u),w),v5). [para(3398(a,1),3341(a,1,1,1,1)),rewrite([8947(18)])]. given #480 (W0w,wt=9): 7722 K(x,K(x,y \ x)) = 1. [back_rewrite(6460),rewrite([7716(3)])]. given #481 (W0w,wt=9): 7723 T(x,K(x,y \ x)) = x. [back_rewrite(4345),rewrite([7716(3)])]. given #482 (W0w,wt=9): 7726 K(K(x,y \ z),x) = 1. [back_rewrite(7707),rewrite([7719(4)])]. given #483 (W0w,wt=7): 12303 K(K(x,y),x) = 1. [para(15(a,1),7726(a,1,1,2))]. given #484 (W0w,wt=7): 12309 K(x,K(x,y)) = 1. [para(12303(a,1),4993(a,1,1)),rewrite([13(4)])]. given #485 (W0w,wt=7): 12312 T(x,K(x,y)) = x. [hyper(28,a,12309,a)]. given #486 (W0w,wt=9): 7769 T(T(x,y),y \ x) = x. [para(16(a,1),4209(a,2)),rewrite([4505(2)])]. given #487 (W0w,wt=7): 12432 T(x,K(y,x)) = x. [para(12312(a,1),7769(a,1,1)),rewrite([6144(2),12349(2),1708(3)])]. given #488 (W0w,wt=7): 12456 K(x,K(y,x)) = 1. [hyper(27,a,12432,a)]. given #489 (W0w,wt=7): 12497 K(K(x,y),y) = 1. [para(12456(a,1),4993(a,1,1)),rewrite([13(4)])]. given #490 (W0w,wt=9): 7925 T(x,K(y * x,y)) = x. [back_rewrite(7047),rewrite([7820(6),16(4)])]. given #491 (W0w,wt=9): 8513 K(x,x \ T(x,y)) = 1. [para(159(a,1),4539(a,2,1)),rewrite([46(6)])]. given #492 (W0w,wt=9): 9999 K(x / y,y / x) = 1. [para(5359(a,1),20(a,1,1)),rewrite([5359(4),46(3)]),flip(a)]. given #493 (W0w,wt=9): 10442 T(x,K(y,y \ x)) = x. [hyper(28,a,7635,a)]. given #494 (W0w,wt=9): 10461 T(x,K(x / y,y)) = x. [hyper(28,a,7636,a)]. given #495 (W0w,wt=9): 12307 T(K(x,y),x) = K(x,y). [hyper(28,a,12303,a)]. given #496 (W0a,wt=16): 86 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(18(a,1),22(a,1,2))]. given #497 (W0a,wt=17): 95 L(T(T(x,y),z),u,w) = L(T(T(x,z),y),u,w). [para(30(a,1),29(a,1,1)),rewrite([30(3),30(5),30(6)])]. given #498 (W0r,wt=16): 6071 ((x \ y) * z) / (y * z) = R(x \ 1,y,z). [para(3143(a,1),22(a,1,1,1))]. given #499 (W0r,wt=18): 12506 L(T(x,K(y * L(x,z,u),y)),z,u) = L(x,z,u). [para(7925(a,1),30(a,1)),flip(a)]. NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 34 (0.00 of 3.24 sec). given #500 (W0r,wt=20): 10094 R(x,y,(x * y) \ z) * ((y * ((x * y) \ z)) / z) = 1. [para(82(a,2),5359(a,1,1))]. given #501 (W0r,wt=17): 8260 K(x * (x * y),z * (x * (x * (y / z)))) = 1. [para(4915(a,1),143(a,2)),rewrite([1839(3),1839(10),143(15)])]. given #502 (W0r,wt=16): 10144 K(K(x * y,L(y \ z,y,x)),x * z) = 1. [para(74(a,2),6523(a,1,1,2))]. given #503 (W1w,wt=21): 3825 T(T(T(T(x,y),z),u),x \ w) = T(T(T(T(x,w),y),z),u). [para(49(a,1),3352(a,1,1,1,1,1)),rewrite([2649(7)])]. given #504 (W1w,wt=21): 3831 T(T(T(x \ y,z),u),T(y / x,z)) = T(T(x \ y,z),u). [para(159(a,1),3352(a,1,1)),rewrite([622(4)]),flip(a)]. given #505 (W1w,wt=21): 3832 K(T(T(T(x \ y,z),u),w),T(T(T(y / x,z),u),w)) = 1. [para(3352(a,1),540(a,1,1))]. given #506 (W1w,wt=21): 3836 K(T(T(T(x / y,z),u),w),T(T(T(y \ x,z),u),w)) = 1. [para(3352(a,1),555(a,1,2))]. given #507 (W1w,wt=21): 3840 T(T(T(T(x \ 1,y),z),u),x) = T(T(T(x \ 1,y),z),u). [para(989(a,1),3352(a,1,1,1,1,1))]. given #508 (W1w,wt=21): 3968 a(x / y,y,T(z,y * x)) = a(y,y * x,T(z,y * x)). [back_rewrite(3576),rewrite([3954(8)])]. given #509 (W1w,wt=21): 4173 (x \ (y * (x * (x / z)))) * (T(y,x * (x / z)) \ z) = x. [back_rewrite(3536),rewrite([4155(9)])]. given #510 (W1w,wt=21): 4214 T(T(T(x,y),z),T(T(x,z),y) \ u) = T(T(T(x,z),y),u). [para(2642(a,1),94(a,2)),rewrite([29(6)])]. given #511 (W1a,wt=23): 187 x * (x * (((x \ y) * (x * z)) * u)) = (x * ((y * x) * z)) * u. [para(104(a,1),37(a,1,1,2)),flip(a)]. given #512 (W1a,wt=23): 190 (x * y) * ((y \ z) * (y * u)) = y * ((y \ x) * ((z * y) * u)). [para(104(a,1),104(a,1,2,2)),flip(a)]. given #513 (W1r,wt=21): 11295 x * (x * (x / T(x / y,y * (x * x)))) = y * (x * x). [para(3641(a,1),3641(a,1,2,2,2,1,2)),rewrite([1014(3),11276(8),4408(7),4408(5),4408(4),45(3),4578(3),14(5),11276(14),4408(13),4408(11),4408(10),45(9),4578(9),14(11)])]. given #514 (W1r,wt=27): 13210 K(T(T(x \ y,z),u),T(T(T(y / x,z),K(w * T(x \ y,z),w)),u)) = 1. [para(7925(a,1),3832(a,1,1,1))]. given #515 (W1r,wt=24): 9729 x * (L(y,z * x,z) * (x * u)) = ((z * ((z \ x) * y)) * x) * u. [back_rewrite(6606),rewrite([9559(2)])]. given #516 (W1r,wt=30): 13523 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,y * ((z * y) * x),y). [back_rewrite(9186),rewrite([13457(14)])]. given #517 (W1r,wt=25): 4440 L(L(L(x,y,z),u,L(x,w,v5) \ (u \ 1)),w,v5) = L(L(x,w,v5),y,z). [back_rewrite(3247),rewrite([4407(5)])]. given #518 (W2w,wt=31): 1545 L(R(R(R(x,y,T(z,y)),u,w),v5,v6),v7,v8) = L(R(R(R(x,u,w),v5,v6),y,T(z,y)),v7,v8). [para(23(a,1),371(a,1,1,1,1,3)),rewrite([23(9)])]. given #519 (W2w,wt=31): 1546 L(R(R(R(x,y / z,z),u,w),v5,v6),v7,v8) = L(R(R(R(x,u,w),v5,v6),y / z,z),v7,v8). [para(50(a,1),371(a,1,1,1,1,3)),rewrite([50(10)])]. given #520 (W2w,wt=31): 1548 R(R(R(R(x,y,T(z,y)),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v5,v6),v7,v8),y,T(z,y)). [para(23(a,1),373(a,1,1,1,1,3)),rewrite([23(10)])]. given #521 (W2w,wt=31): 1549 R(R(R(R(x,y / z,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v5,v6),v7,v8),y / z,z). [para(50(a,1),373(a,1,1,1,1,3)),rewrite([50(11)])]. given #522 (W2a,wt=33): 290 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,u,w),y,z),v7,v8),v5,v6),v9,v10). [para(228(a,1),228(a,1,1,1))]. given #523 (W2a,wt=33): 291 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),u,w),y,z),v9,v10),v5,v6). [para(230(a,1),97(a,1,1,1)),flip(a)]. given #524 (W2r,wt=34): 9423 (x * ((x \ (y \ 1)) * ((y * z) * (y \ u)))) \ ((z / y) * u) = a(x,x / y,(y * z) * (y \ u)). [para(1014(a,1),4025(a,1,2,1)),rewrite([4408(6),45(5),3143(7),1014(14),4408(15),45(14),3143(16)])]. given #525 (W2r,wt=34): 13951 L(L(L(L(x,y,z),u,L(L(x,w,v5),v6,v7) \ (u \ 1)),w,v5),v6,v7) = L(L(L(x,w,v5),v6,v7),y,z). [para(97(a,2),4440(a,1,1))]. given #526 (W2r,wt=34): 13952 L(L(L(L(x,y,L(L(x,z,u),w,v5) \ (y \ 1)),v6,v7),z,u),w,v5) = L(L(L(x,z,u),w,v5),v6,v7). [para(230(a,1),4440(a,1,1))]. given #527 (W2r,wt=35): 5750 (x * (y * z)) \ (L(K(y,z),z * y,x) * (x * (z * y))) = K(L(K(y,z),z * y,x),x * (z * y)). [para(63(a,1),2934(a,1,1,2))]. given #528 (W2r,wt=32): 13687 ((x / y) * (z * (y * y))) \ (x * (y * T(z,y * y))) = a(x / y,y,y * T(z,y * y)). [para(11295(a,1),60(a,1,1,2)),rewrite([13663(9),13663(15)])]. given #529 (W0w,wt=9): 12372 T(T(x,y),y \ 1) = x. [para(1091(a,1),7769(a,1,2)),rewrite([1708(2)])]. given #530 (W0w,wt=9): 12386 T(x,y / (y * x)) = x. [para(2810(a,1),7769(a,1,1)),rewrite([10229(3),10408(3),1708(4)])]. given #531 (W0w,wt=9): 12457 T(K(x,y),y) = K(x,y). [hyper(26,a,12432,a)]. given #532 (W0w,wt=9): 12500 K(x,K(y * x,y)) = 1. [hyper(27,a,7925,a)]. given #533 (W0w,wt=9): 12503 T(x,K(y,y / x)) = x. [para(18(a,1),7925(a,1,2,1))]. given #534 (W0w,wt=9): 12563 T(x,K(y,y * x)) = x. [para(7925(a,1),7769(a,1,1)),rewrite([6144(3),12554(3),1708(4)])]. given #535 (W0w,wt=9): 12571 K(x \ T(x,y),x) = 1. [para(8513(a,1),4993(a,1,1)),rewrite([13(5)])]. given #536 (W0w,wt=9): 14102 T(x,T(x,y) \ 1) = x. [para(541(a,1),12372(a,1,1))]. given #537 (W0w,wt=9): 14123 T(x,(y / x) / y) = x. [para(5067(a,1),12372(a,1,1)),rewrite([4407(4),10229(4),1014(4)])]. given #538 (W0w,wt=9): 14154 K(x,y / (y * x)) = 1. [hyper(27,a,12386,a)]. given #539 (W0w,wt=9): 14186 T(x,y \ (x \ y)) = x. [para(3143(a,1),12386(a,1,2,2)),rewrite([4155(4),3143(4)])]. given #540 (W0w,wt=9): 14246 K(x \ y,K(y,x)) = 1. [para(16(a,1),12500(a,1,2,1))]. given #541 (W0w,wt=9): 14247 K(x,K(y,y / x)) = 1. [para(18(a,1),12500(a,1,2,1))]. given #542 (W0w,wt=9): 14268 K(K(x * y,x),y) = 1. [para(12500(a,1),4993(a,1,1)),rewrite([13(5)])]. given #543 (W0w,wt=9): 14333 T(x,K(y / x,y)) = x. [para(12503(a,1),7769(a,1,1)),rewrite([6144(3),14327(3),1708(4)])]. given #544 (W0w,wt=9): 14347 K(x,K(y,y * x)) = 1. [hyper(27,a,12563,a)]. given #545 (W0a,wt=17): 96 R(T(T(x,y),z),u,w) = R(T(T(x,z),y),u,w). [para(31(a,1),29(a,1,1)),rewrite([31(3),31(5),31(6)])]. given #546 (W0a,wt=11): 100 (x * x) * y = x * (x * y). [para(13(a,1),36(a,2,2)),rewrite([14(2)])]. given #547 (W0r,wt=19): 14083 (x / y) * (y * (x * T(x \ (x \ 1),x * x))) = 1. [para(996(a,1),13687(a,2,3,2)),rewrite([3436(4),8972(6),16(4),87(4),14(3),3436(4),10229(9),3436(13),16(14),1072(13)])]. given #548 (W0r,wt=16): 15045 L(x,y * (z * (z * y)),u * (z * z)) = x. [back_rewrite(2522),rewrite([14874(6)])]. given #549 (W0r,wt=15): 10702 K(x * (y / x),x / y) = K(x \ 1,y). [para(8701(a,2),67(a,1)),rewrite([10215(2),67(3),10215(4),666(5),5152(3),10215(5)]),flip(a)]. given #550 (W0r,wt=19): 12519 T(x * y,K(x * ((z * x) * y),x * z)) = x * y. [para(189(a,1),7925(a,1,2,1))]. given #551 (W0r,wt=18): 8418 K(((x \ y) * z) * R(x,x \ y,z),y * z) = 1. [para(81(a,2),4916(a,1,1,2))]. given #552 (W1w,wt=21): 4254 (x / y) * ((x / y) * ((y * z) / T(x * (y \ x),z))) = z. [back_rewrite(2009),rewrite([4230(5)])]. given #553 (W1w,wt=21): 4314 T(x,y) * (T(x \ y,y) * (T(x,y) * z)) = (x * y) * z. [para(2690(a,1),186(a,2,1,1)),rewrite([4281(4),90(9)])]. given #554 (W1w,wt=21): 4338 K(x \ 1,T(y,x \ 1)) * (T(y,x \ 1) / x) = y / x. [para(1010(a,1),2690(a,1,1)),rewrite([4207(12)])]. given #555 (W1w,wt=21): 4344 (x \ y) * ((z * (x \ y)) * T(x,y)) = ((x \ y) * z) * y. [para(2690(a,1),189(a,1,2)),flip(a)]. given #556 (W1w,wt=21): 4397 x \ (y * T(z,x \ (x \ y))) = x * (z * (x \ (x \ y))). [para(2755(a,1),778(a,2)),rewrite([3143(7),3143(6),3143(7),3143(10),3143(9)])]. given #557 (W1w,wt=21): 4404 x * T(y,z \ (z \ x)) = z * (z * (y * (z \ (z \ x)))). [para(2755(a,1),1324(a,1,2)),rewrite([3143(7),3143(6),2755(7),3143(10),3143(9)]),flip(a)]. given #558 (W1w,wt=21): 4414 K((x * y) \ (x \ 1),x * (x * (y * (x * (x * y))))) = 1. [back_rewrite(4191),rewrite([4407(4)])]. given #559 (W1w,wt=21): 4504 (x \ y) * (((y \ x) * z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(2692),rewrite([4408(3)])]. given #560 (W1a,wt=26): 193 (x * y) * (L(z,y,x) * ((x * y) * u)) = (x * (((y * z) * x) * y)) * u. [back_rewrite(182),rewrite([189(10)])]. given #561 (W1a,wt=23): 195 (x * (y * (x * (x * y)))) * z = x * ((y * x) * ((x * y) * z)). [back_rewrite(124),rewrite([189(10)])]. given #562 (W1r,wt=23): 11449 x \ (x \ (T(T(y,z),u) / w)) = x \ (x \ (T(T(y,u),z) / w)). [para(94(a,2),3710(a,1,2)),rewrite([11428(10)])]. given #563 (W1r,wt=28): 4499 R(T(x,y * (x * z)),x * (y * x),z) = ((y * (x * z)) \ x) * ((y * x) * z). [back_rewrite(3161),rewrite([4408(12)])]. given #564 (W1r,wt=27): 4809 ((T(x,y) * (y / z)) * y) \ (x * (y * (y / z))) = K(y,T(x,y) * (y / z)). [back_rewrite(4596),rewrite([4613(7)])]. given #565 (W1r,wt=27): 5166 L(L(x \ (y \ z),u,L((y * x) \ z,w,v5)),w,v5) = L(x \ (y \ z),w,v5). [para(3940(a,1),1696(a,1,1,1)),rewrite([5141(12)])]. given #566 (W1r,wt=26): 13709 L((x * (y * y)) \ z,x * (y * y),y) = (y * T(x,y * y)) \ (y \ z). [para(11295(a,1),3940(a,1,1,1)),rewrite([13663(8),777(7),13663(11)])]. given #567 (W2w,wt=31): 1550 R(R(R(R(x,y,y \ z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v5,v6),v7,v8),u,w),y,y \ z). [para(373(a,1),99(a,1)),flip(a)]. given #568 (W2w,wt=31): 1551 R(R(R(R(x,y,y \ z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v7,v8),u,w),v5,v6),y,y \ z). [para(373(a,1),99(a,2))]. given #569 (W2w,wt=31): 1584 (x * T(y,z)) / T((x / z) * (y * z),a(x / z,z,T(y,z))) = a(x / z,z,T(y,z)). [para(165(a,1),868(a,1,2,1,1,2)),rewrite([165(8),165(9),165(13),165(14)])]. given #570 (W2w,wt=31): 1606 x * (((T(T(y,z),u) * (u * w)) * u) * v5) = x * (((T(T(y,u),z) * (u * w)) * u) * v5). [para(1479(a,1),181(a,2,2,1)),rewrite([1091(14),1194(21),37(15),15(16)])]. given #571 (W2a,wt=33): 293 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),u,w),y,z),v5,v6),v7,v8). [para(230(a,1),97(a,2,1,1))]. given #572 (W2a,wt=33): 294 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),y,z),u,w),v7,v8),v5,v6). [para(97(a,1),230(a,1,1,1)),flip(a)]. given #573 (W2r,wt=33): 10474 K((x * y) * (a(x,z,z \ y) * u),K(R(z * ((z \ x) * y),x * y,(x * y) \ u),u)) = 1. [para(435(a,2),7636(a,1,2,1))]. given #574 (W2r,wt=31): 13569 (x / y) * (((y / x) * z) * ((u * (x / y)) * y)) = (z * (x / y)) * (((y / x) * u) * x). [para(18(a,1),190(a,1,2,2)),rewrite([10229(4),10229(9)]),flip(a)]. given #575 (W2r,wt=34): 13950 L(L(L(L(x,y,L(L(x,z,u),w,v5) \ (y \ 1)),z,u),v6,v7),w,v5) = L(L(L(x,z,u),w,v5),v6,v7). [para(97(a,1),4440(a,1,1))]. given #576 (W2r,wt=35): 5824 R(x * ((x \ y) * T(z,y)),z * y,(z * y) \ u) = ((z * y) * (a(y,x,x \ T(z,y)) * u)) / u. [para(90(a,1),435(a,1,2)),rewrite([90(7),90(10)])]. given #577 (W2r,wt=35): 12078 (L(L(x,y,z),u,w) * (v5 / L(L(x,u,w),y,z))) \ (L(L(x,y,z),u,w) * v5) = L(L(x,y,z),u,w). [para(6663(a,1),1667(a,1))]. given #578 (W0w,wt=8): 16567 R(x,y,K(y,x)) = x. [back_rewrite(4290),rewrite([16343(2)])]. given #579 (W0w,wt=8): 16999 a(x,y,K(y,x)) = 1. [back_rewrite(1097),rewrite([16716(2),90(2),46(3)]),flip(a)]. given #580 (W0w,wt=9): 14429 K(x,T(x,y) \ 1) = 1. [hyper(27,a,14102,a)]. given #581 (W0w,wt=9): 14479 K(x,(y / x) / y) = 1. [hyper(27,a,14123,a)]. given #582 (W0w,wt=9): 14546 K(x \ y,x / y) = 1. [para(16(a,1),14154(a,1,2,2))]. given #583 (W0w,wt=9): 14560 K(x,y \ (x \ y)) = 1. [para(3143(a,1),14154(a,1,2,2)),rewrite([4155(4),3143(4)])]. given #584 (W0w,wt=9): 14564 K(x / (x * y),y) = 1. [para(14154(a,1),4993(a,1,1)),rewrite([13(5)])]. given #585 (W0w,wt=9): 14577 T(x,(x * y) \ y) = x. [para(15(a,1),14186(a,1,2,2))]. given #586 (W0w,wt=9): 14670 K(K(x,y),y \ x) = 1. [para(14246(a,1),4993(a,1,1)),rewrite([13(5)])]. given #587 (W0w,wt=9): 14733 K(x,K(y / x,y)) = 1. [hyper(27,a,14333,a)]. given #588 (W0w,wt=9): 14802 K(x \ y,K(x,y)) = 1. [para(16(a,1),14347(a,1,2,2))]. given #589 (W0w,wt=9): 16343 x \ T(x,y) = K(x,y). [back_rewrite(10321),rewrite([16103(6),2254(4)]),flip(a)]. given #590 (W0w,wt=9): 16487 L(L(x,y,z),z,y) = x. [back_rewrite(667),rewrite([16103(3)])]. given #591 (W0w,wt=8): 18454 L(x,y,x \ 1) = x. [para(1022(a,1),16487(a,1,1))]. given #592 (W0w,wt=8): 18466 L(x,y,y / x) = x. [para(6257(a,1),16487(a,1,1))]. given #593 (W0w,wt=8): 18472 L(x,x \ y,y) = x. [para(8105(a,1),16487(a,1,1))]. given #594 (W0a,wt=11): 101 (x * y) * x = x * (y * x). [para(36(a,1),14(a,1)),rewrite([14(2)]),flip(a)]. given #595 (W0a,wt=15): 106 (x * (y * (x * z))) / z = x * (y * x). [para(36(a,1),17(a,1,1)),rewrite([101(6)])]. given #596 (W0r,wt=17): 10927 T(x * (x * y),y \ z) = T(y * (x * x),z). [back_rewrite(5468),rewrite([10888(9),101(6),4209(7),4578(6)])]. given #597 (W0r,wt=15): 11221 x * (x / T(x * y,y \ x)) = y \ x. [para(47(a,1),3640(a,1,2,2,1)),rewrite([4408(5),14(5),989(5),1014(6),4408(8),14(8)])]. given #598 (W0r,wt=18): 15056 L(x * T(x \ (x \ 1),x * x),y,x) = x \ 1. [para(14083(a,1),21(a,1,2)),rewrite([18(2),3200(10)]),flip(a)]. given #599 (W0r,wt=16): 7696 (x * (a(y,x,x \ (y \ x)) * z)) / z = x. [para(4137(a,1),435(a,1,1,2)),rewrite([14(2),16(2),16(2),480(2),16(2)]),flip(a)]. given #600 (W0r,wt=11): 18399 K(T(x \ y,x),K(x,y)) = 1. [para(7967(a,1),14802(a,1,1)),rewrite([17771(4)])]. given #601 (W1w,wt=21): 4636 a(x * (y * (x * x)),z,u) = a(x * y,x * (x * z),u). [back_rewrite(3762),rewrite([4578(2)])]. given #602 (W1w,wt=21): 4638 a(T(x,y) * (x * y),y,z) = a(T(x,y),x * (y * y),z). [back_rewrite(3739),rewrite([4578(7)])]. given #603 (W1w,wt=21): 4658 T(x,T(T(x,y),z)) * (z * (z * u)) = x * (z * (z * u)). [back_rewrite(3416),rewrite([4578(5),2040(6),4578(8),2040(9)])]. given #604 (W1w,wt=21): 4678 x * (y * (x * (y * ((T(x,y) * (x * y)) \ z)))) = y * z. [back_rewrite(3096),rewrite([4578(2),2040(9),4525(7)])]. given #605 (W1w,wt=21): 4707 L(x,y * (z * z),T(y,z)) = L(x,z,T(y,z) * (y * z)). [back_rewrite(2274),rewrite([4578(2)])]. given #606 (W1w,wt=21): 4713 x / (T(T(y,z),u) * (z * ((T(y,u) * (z * z)) \ x))) = z. [back_rewrite(2166),rewrite([4578(5)])]. given #607 (W1w,wt=21): 4907 L(x * y,x,T(T(z,u),w)) = L(x * y,x,T(T(z,w),u)). [back_rewrite(4791),rewrite([4793(5)])]. given #608 (W1w,wt=21): 4908 a(T(T(x,y),z),u,u * w) = a(T(T(x,z),y),u,u * w). [back_rewrite(4797),rewrite([4799(5)])]. given #609 (W1a,wt=22): 196 (x * ((y * x) * z)) \ (x * (y * (x * z))) = a(x * y,x,z). [back_rewrite(113),rewrite([189(3)])]. given #610 (W1a,wt=24): 202 R(x * y,y * x,(y * x) \ z) = ((y * x) * (K(x,y) * z)) / z. [para(20(a,1),191(a,1,1,2,1)),flip(a)]. given #611 (W1r,wt=21): 10900 T((x \ y) * (z * z),T(y,x)) = T(z * (z * (x \ y)),x). [back_rewrite(8036),rewrite([10888(7),101(3),4209(4),4578(3)])]. given #612 (W1r,wt=23): 19786 T((x \ y) * (z \ (z \ 1)),T(y,x)) = T(z \ (z \ (x \ y)),x). [para(1014(a,1),10900(a,1,1,2)),rewrite([10400(4),989(3),3143(13),3143(12)])]. given #613 (W1r,wt=23): 6459 K(x \ (y * (x * (z * x))),K(x * T(y,x * (z * x)),z)) = 1. [para(1359(a,1),3302(a,1,1))]. given #614 (W1r,wt=29): 9450 (R(R(x,y,z),u,w) * (v5 * (v5 * v6))) / (R(R(x,u,w),y,z) * (v5 * (v5 * v6))) = 1. [para(2377(a,1),1014(a,1)),flip(a)]. given #615 (W1r,wt=29): 13055 T(T(T(T(T(T(x,y),z),u),w),v5),x \ v6) = T(T(T(T(T(T(x,v6),y),z),u),w),v5). [para(3825(a,1),94(a,2,1,1))]. given #616 (W2w,wt=31): 1851 (x * (y * (x * (z * (x * (y * x)))))) / u = x * (y * (x * (z * (x * (y * (x / u)))))). [para(1014(a,1),129(a,1)),rewrite([1014(10)])]. given #617 (W2w,wt=31): 1908 x * (x * (((T(T(y,z),u) * (u * w)) * u) / (x * ((T(T(y,u),z) * (u * w)) * u)))) = x. [back_rewrite(1589),rewrite([1839(14)])]. given #618 (W2w,wt=31): 1909 x * (x * (((T(T(y,z),u) * (z * w)) * z) / (x * ((T(T(y,u),z) * (z * w)) * z)))) = x. [back_rewrite(1588),rewrite([1839(14)])]. given #619 (W2w,wt=31): 1961 L(a(x / y,y,z),(x / y) * (y * z),u) = (u * ((x / y) * (y * z))) \ (u * (x * z)). [para(60(a,1),74(a,1,1))]. given #620 (W2a,wt=33): 296 L(L(L(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(R(R(x,u,w),y,z),v9,v10),v7,v8),v5,v6). [para(98(a,1),230(a,1,1,1))]. given #621 (W2a,wt=33): 297 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),u,w),y,z),v5,v6),v9,v10). [para(230(a,1),228(a,1,1,1)),flip(a)]. given #622 (W2r,wt=31): 5980 T(T(T(T(T(x,y),z),u),w \ 1),v5) / w = T(T(T(T(T(x,z),v5),y),u),w \ 1) / w. [para(94(a,1),4092(a,2,1,1,1))]. given #623 (W2r,wt=33): 461 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),v5,v6),u,w),v7,v8),y,z). [para(295(a,1),295(a,2))]. given #624 (W2r,wt=31): 4063 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,w),y),z),u \ 1),v5) / u. [para(29(a,1),3794(a,2,1))]. given #625 (W2r,wt=31): 18321 T(x \ (y * (x * (x / z))),x \ (T(y,x * (x / z)) \ z)) = x \ (y * (x * (x / z))). [para(4173(a,1),14577(a,1,2,1))]. given #626 (W2r,wt=33): 10082 (x / T(T(T(T(T(y,z),u),w),x \ 1),v5)) * (T(T(T(T(T(y,v5),z),u),w),x \ 1) / x) = 1. [para(4092(a,1),5359(a,1,2))]. given #627 (W0w,wt=8): 18483 a(x \ 1,y,x) = 1. [hyper(25,a,18454,a)]. given #628 (W0w,wt=8): 18604 a(x,y \ x,y) = 1. [hyper(25,a,18472,a)]. given #629 (W0w,wt=8): 18742 a(x,y,y * x) = 1. [para(101(a,1),8106(a,1,2)),rewrite([3982(4),4795(4)])]. given #630 (W0w,wt=8): 20341 a(x * y,y,x) = 1. [para(15(a,1),18604(a,1,2))]. given #631 (W0w,wt=8): 20386 a(x \ y,x,y) = 1. [para(16(a,1),18742(a,1,3))]. given #632 (W0w,wt=8): 20387 a(x,y / x,y) = 1. [para(18(a,1),18742(a,1,3))]. given #633 (W0w,wt=8): 20541 a(x,y,x / y) = 1. [para(18(a,1),20341(a,1,1))]. given #634 (W0w,wt=8): 20551 a(x,y,x \ y) = 1. [para(2690(a,1),20341(a,1,1)),rewrite([4582(3)])]. given #635 (W0w,wt=8): 20573 L(x,y,y \ x) = x. [hyper(24,a,20386,a)]. given #636 (W0w,wt=8): 20613 L(x,x / y,y) = x. [hyper(24,a,20387,a)]. given #637 (W0w,wt=8): 20691 a(x,x * y,y) = 1. [para(15(a,1),20551(a,1,3))]. given #638 (W0w,wt=9): 16564 K(x \ y,x) = K(y,x). [back_rewrite(4516),rewrite([16343(4)])]. given #639 (W0w,wt=9): 16566 T(x,y) / x = K(x,y). [back_rewrite(4366),rewrite([16343(4)])]. given #640 (W0w,wt=9): 16568 K(x * y,x) = K(y,x). [back_rewrite(3934),rewrite([16343(4)])]. given #641 (W0w,wt=9): 16604 K(T(x \ 1,y),x) = 1. [back_rewrite(15133),rewrite([16564(5)])]. given #642 (W0w,wt=9): 16623 T(x,y) * K(y,x) = x. [back_rewrite(14430),rewrite([16564(3)])]. given #643 (W0a,wt=18): 120 (x * (y * (x * z))) / (x * z) = R(x * y,x,z). [para(36(a,1),22(a,1,1))]. given #644 (W0a,wt=17): 122 x \ (y * (z * (y * x))) = T(y * (z * y),x). [para(36(a,1),23(a,1,2)),rewrite([101(6)])]. given #645 (W0r,wt=18): 12363 R(T(T(x,y),y \ R(x,z,u)),z,u) = R(x,z,u). [para(31(a,1),7769(a,1,1)),rewrite([31(5)])]. given #646 (W0r,wt=16): 10347 L((x / y) * z,y / x,y) = x * (y \ z). [back_rewrite(5155),rewrite([10229(2)])]. given #647 (W0r,wt=20): 21291 ((x * y) / (x * (z * (x * y)))) * R(x * z,x,y) = 1. [para(120(a,1),5359(a,1,2))]. given #648 (W0r,wt=18): 17761 K(((x * (y / z)) * z) \ y,R(x,y / z,z)) = 1. [para(86(a,1),14546(a,1,2))]. given #649 (W0r,wt=15): 10379 T(x \ y,(x / y) * z) = T(x \ y,z). [back_rewrite(2732),rewrite([10229(3)])]. given #650 (W1w,wt=21): 4950 T(a(x,y,z),((x * y) * z) / (x * (y * z))) = a(x,y,z). [para(54(a,1),2810(a,1,2,1))]. given #651 (W1w,wt=21): 5194 R(x,y * (y * z),z \ (y \ (y \ u))) = R(x,z,z \ u). [back_rewrite(1870),rewrite([5162(3),191(6),1935(6),16(3),16(2),5162(7)]),flip(a)]. given #652 (W1w,wt=21): 5226 (T(x,y) \ (T(x,y) \ z)) * T(T(x,z),y) = T(x,y) \ z. [para(29(a,1),4357(a,1,2))]. given #653 (W1w,wt=21): 5290 K((x \ y) * (x * z),y * (y * ((x * z) / (y * x)))) = 1. [para(37(a,1),2812(a,1,2,1)),rewrite([1091(2),3143(5),168(3),1839(8)])]. given #654 (W1w,wt=21): 5299 K(((x * y) \ z) * ((x * y) * a(z,x,y)),R(z,x,y)) = 1. [para(54(a,1),2812(a,1,2,1)),rewrite([22(10)])]. given #655 (W1w,wt=21): 5316 K((x \ y) * (x * (y * z)),(y * ((x * y) * z)) / x) = 1. [para(189(a,1),2812(a,1,2,1))]. given #656 (W1w,wt=21): 5347 a(x,y,T(T(T(z,u),w),y)) = a(x,y,T(T(T(z,y),u),w)). [para(94(a,1),507(a,2,3)),rewrite([507(10)])]. given #657 (W1w,wt=21): 5349 a(x,y,T(T(T(z,u),w),y)) = a(x,y,T(T(T(z,w),y),u)). [para(94(a,2),507(a,2,3)),rewrite([507(10)])]. given #658 (W1a,wt=27): 203 R(x * (y * z),x * y,(x * y) \ u) = ((x * y) * (L(z,y,x) * u)) / u. [para(21(a,1),191(a,1,1,2,1)),flip(a)]. given #659 (W1a,wt=27): 229 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v5,v6),y,z),v7,v8),u,w). [para(97(a,2),34(a,1,1))]. given #660 (W1r,wt=26): 20336 (T(x * y,y) * K(y,x)) / T(x * y,a(K(x,y),x * y,K(y,x))) = 1. [para(18483(a,1),2880(a,2)),rewrite([6144(3),14(3),18062(3),6144(7),14(7),3308(7),6144(8),14(8)])]. given #661 (W1r,wt=27): 17093 (x \ y) * (((y \ x) * z) * ((z * (x \ y)) * u)) = z * (z * ((x \ y) * u)). [para(4137(a,1),193(a,2,1,2,1,1)),rewrite([4145(5),13639(8),13(10),37(12)])]. given #662 (W1r,wt=22): 6694 T(x * (y / z),L(z,y / z,x)) = T(x * (y / z),x * y). [para(76(a,2),2642(a,1,2))]. given #663 (W1r,wt=27): 11720 a(x \ (y \ 1),z,(z \ x) * (x \ y)) = a(x \ 1,z,(z \ x) * (x \ y)). [para(3143(a,1),10700(a,1,3,1)),rewrite([6120(3),3143(7),4408(6),3143(12),3143(13),4408(12)])]. given #664 (W1r,wt=27): 16722 ((x * T(x,y)) * z) * K(K(x,y) * (x * z),x) = (K(x,y) * (x * z)) * x. [back_rewrite(4529),rewrite([16564(5),16564(10)])]. given #665 (W2w,wt=31): 2049 K(x * (x * (y * (y * (z * (x * (x * (y * (y * z)))))))),x * (x * (y * (y * z)))) = 1. [para(37(a,1),1660(a,1,1,2,2))]. given #666 (W2w,wt=31): 2226 (x * (y * (z * (z * (u * (y * x)))))) * w = x * (y * (z * (z * (u * (y * (x * w)))))). [para(37(a,1),130(a,1,1,2,2)),rewrite([37(12)])]. given #667 (W2w,wt=31): 2249 K(x * (y * (z * (y * x))),x * (y * (z * (y * (x * (x * (y * (z * (y * x))))))))) = 1. [para(130(a,1),1392(a,1,2))]. given #668 (W2w,wt=31): 2365 L(L(L(x,y,z),u,w),L(L(x,u,w),L(x,y,z) \ 1,v5) \ 1,v6) = L(L(x,y,z),u,w). [para(1078(a,1),1078(a,1,1)),rewrite([1085(16)])]. given #669 (W2a,wt=33): 298 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,u,w),y,z),v9,v10),v7,v8),v5,v6). [para(228(a,1),230(a,1,1,1))]. given #670 (W2a,wt=33): 299 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),u,w),y,z),v7,v8),v5,v6). [para(230(a,1),230(a,1,1,1)),flip(a)]. given #671 (W2r,wt=33): 6160 R((x \ (y / z)) * z,x \ y,(y \ x) * u) = ((x \ y) * (a(x \ 1,y / z,z) * u)) / u. [para(3143(a,1),436(a,1,1,1)),rewrite([3143(6),3143(7),4408(6),3143(10)])]. given #672 (W2r,wt=31): 16286 L(x,(y * ((y \ z) * u)) * z,L(u,y,z)) = L(x,z,L(u,y,z) * (y * ((y \ z) * u))). [back_rewrite(13845),rewrite([16103(6),16103(8)])]. given #673 (W2r,wt=35): 15976 L(((x \ y) * z) * x,y \ x,u / ((z * (y \ x)) * T(y,x))) = L(((x \ y) * z) * x,y \ x,u). [para(4504(a,1),3199(a,1,3,2))]. given #674 (W2r,wt=35): 15026 (x * (y * (y * (z * u)))) \ (x * (y * (y * (z * (u * w))))) = L(L(w,u,z),z * u,x * (y * y)). [back_rewrite(5629),rewrite([14874(15)])]. given #675 (W2r,wt=33): 7474 R(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = R(R(R(R(R(x,v7,v8),v5,v6),y,z),u,w),v9,v10). [para(256(a,2),720(a,1))]. given #676 (W0w,wt=9): 16686 K(x,x * y) = K(x,y). [back_rewrite(8594),rewrite([16564(2)]),flip(a)]. given #677 (W0w,wt=9): 16687 x / T(x,y) = K(y,x). [back_rewrite(8593),rewrite([16564(4)])]. given #678 (W0w,wt=9): 16705 K(K(x,y),T(y,x)) = 1. [back_rewrite(8551),rewrite([16564(2)])]. given #679 (W0w,wt=9): 16706 K(T(x,y),K(y,x)) = 1. [back_rewrite(8547),rewrite([16564(3)])]. given #680 (W0w,wt=9): 16710 K(x,x \ y) = K(x,y). [back_rewrite(8534),rewrite([16564(2)]),flip(a)]. given #681 (W0w,wt=9): 16711 T(x,y) \ x = K(y,x). [back_rewrite(8532),rewrite([16564(4)])]. given #682 (W0w,wt=9): 16712 K(T(x,y),K(x,y)) = 1. [back_rewrite(8078),rewrite([16564(3)])]. given #683 (W0w,wt=9): 16713 K(K(x,y),T(x,y)) = 1. [back_rewrite(8059),rewrite([16564(2)])]. given #684 (W0w,wt=9): 16716 x * K(x,y) = T(x,y). [back_rewrite(4535),rewrite([16564(2)])]. given #685 (W0w,wt=9): 16875 K(x,y) * T(y,x) = y. [back_rewrite(12504),rewrite([16686(2)])]. given #686 (W0w,wt=9): 16985 K(x,y) * x = T(x,y). [back_rewrite(12308),rewrite([16716(4)])]. given #687 (W0w,wt=9): 17671 K(x / y,x \ y) = 1. [para(92(a,1),14429(a,1,2,1)),rewrite([4408(4),14(4)])]. given #688 (W0w,wt=9): 17702 K((x / y) / x,y) = 1. [para(14479(a,1),4993(a,1,1)),rewrite([13(5)])]. given #689 (W0w,wt=9): 17712 K((x * y) \ y,x) = 1. [para(17(a,1),14546(a,1,2))]. given #690 (W0w,wt=9): 17771 K(x,T(y,x)) = K(x,y). [back_rewrite(17019),rewrite([17730(5),4407(4),15144(5)]),flip(a)]. given #691 (W0w,wt=9): 17781 K(x,y \ 1) = K(y,x). [back_rewrite(16569),rewrite([17730(4),4407(3),16710(4)])]. given #692 (W0a,wt=15): 128 (x * (y * x)) * z = x * (y * (x * z)). [back_rewrite(36),rewrite([101(2)])]. given #693 (W0a,wt=15): 136 x * (x * ((x \ y) * z)) = (x * y) * z. [para(16(a,1),37(a,1,1,2)),flip(a)]. given #694 (W0r,wt=19): 8485 a(x,R(y,z,(y * z) \ x),z * ((y * z) \ x)) = 1. [para(82(a,2),6233(a,1,2))]. given #695 (W0r,wt=17): 20620 (x * (y * (x / y))) / (y * (x * (y \ x))) = 1. [para(20387(a,1),265(a,1,2,2)),rewrite([8255(3),4230(5),88(8),20387(9)])]. given #696 (W0r,wt=17): 19486 x / (T(K(y,z),u) * (u \ (K(z,y) * x))) = u. [para(12307(a,1),4713(a,1,2,2,2,1,1)),rewrite([12698(3),19474(6),6144(4),6073(6),7550(7)])]. given #697 (W0r,wt=13): 3951 K(x * (x * (y / x)),x * y) = 1. [para(398(a,1),1780(a,1,1,1)),rewrite([1839(3),3936(13)])]. given #698 (W0r,wt=20): 5120 T(x * (y * z),K(L(z,y,x),x * y)) = x * (y * z). [para(72(a,1),2918(a,1,1)),rewrite([72(9)])]. given #699 (W1w,wt=21): 5364 (x * y) / T(z * (z * y),T(x,y)) = z \ (z \ T(x,y)). [para(1921(a,1),21(a,1,2)),rewrite([3436(3),1607(10)]),flip(a)]. given #700 (W1w,wt=21): 5409 (x * ((x \ y) * z)) \ ((y \ x) * (((x \ y) * y) * z)) = 1. [para(2445(a,1),3940(a,1,1)),rewrite([5392(6),71(6),4408(9)]),flip(a)]. given #701 (W1w,wt=21): 5416 K(x * (y \ x),x * (y \ (x * T(x * (y \ x),z)))) = 1. [para(18(a,1),2588(a,1,1,2)),rewrite([4230(2),18(7),4230(6),4136(10)])]. given #702 (W1w,wt=21): 5421 K(x * (x / y),x * (x * (y \ T(x * (x / y),z)))) = 1. [para(1014(a,1),2588(a,1,1,2)),rewrite([1014(7),3143(8)])]. given #703 (W1w,wt=21): 5428 x * (x * (y / (T(z * z,x) * (x * y)))) = z \ (z \ x). [para(2640(a,1),21(a,1,2)),rewrite([3436(2),1607(10)]),flip(a)]. given #704 (W1w,wt=21): 5475 T(x * (y * x),x * (y * (x * z))) = T(x * (y * x),z). [para(90(a,1),2647(a,1,1,2)),rewrite([4525(5),90(8)])]. given #705 (W1w,wt=21): 5504 T(x,y \ T(z,x * (x / y))) = T(x,z * (x * (x / y))). [para(1014(a,1),2664(a,1,2,2,2,2)),rewrite([3143(6),1014(8)])]. given #706 (W1w,wt=21): 5524 a((x * y) * L(z \ y,z,x),T(x * z,x * y),u) = 1. [para(74(a,2),2697(a,1,1,2)),rewrite([5515(17)])]. given #707 (W1a,wt=27): 232 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v7,v8),y,z),v5,v6),u,w). [para(97(a,1),97(a,1,1)),flip(a)]. given #708 (W1a,wt=27): 234 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,u,w),y,z),v7,v8),v5,v6). [para(97(a,1),97(a,2,1))]. given #709 (W1r,wt=30): 22957 (((x * y) * K(y,z)) * u) / (((y \ x) * T(y,z)) * u) = R(y,(y \ x) * T(y,z),u). [para(16716(a,1),183(a,1,2,1,2)),rewrite([16716(12)])]. given #710 (W1r,wt=21): 22239 (x * y) * (T(x,y) \ (y * (x * z))) = y * ((y * x) * z). [para(17093(a,1),190(a,2,2)),rewrite([16(5),6968(6),136(10)])]. given #711 (W1r,wt=25): 25317 T(x,y \ T(T(z,x * (x / y)),u)) = T(x,T(z,u) * (x * (x / y))). [para(29(a,1),5504(a,1,2,2))]. given #712 (W1r,wt=23): 11340 K(x / y,K(T(z * (z * x),y \ 1),z \ (z \ (y \ 1)))) = 1. [para(3645(a,1),6446(a,1,2,2))]. given #713 (W1r,wt=29): 17175 (x * ((y \ z) * T(x,z \ y))) * T(z,y) = x * ((y \ z) * ((y \ z) * (x * y))). [para(195(a,1),4504(a,1,2)),rewrite([17151(9),7715(10),2213(13),7681(11)]),flip(a)]. given #714 (W2w,wt=31): 2367 R(R(R(R(x,y,T(z,y)),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v7,v8),v5,v6),y,T(z,y)). [para(23(a,1),375(a,1,1,1,1,3)),rewrite([23(10)])]. given #715 (W2w,wt=31): 2368 R(R(R(R(x,y / z,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v7,v8),v5,v6),y / z,z). [para(50(a,1),375(a,1,1,1,1,3)),rewrite([50(11)])]. given #716 (W2w,wt=31): 2369 R(R(R(R(x,y,z),u,w),v5,v5 \ v6),v7,v8) = R(R(R(R(x,u,w),v7,v8),y,z),v5,v5 \ v6). [para(247(a,1),375(a,1,1))]. given #717 (W2w,wt=31): 2371 R(R(R(R(x,y,T(z,y)),u,w),v5,v6),v7,v8) = R(R(R(R(x,v5,v6),u,w),v7,v8),y,T(z,y)). [para(23(a,1),376(a,1,1,1,1,3)),rewrite([23(10)])]. given #718 (W2a,wt=33): 301 L(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(R(R(R(R(x,u,w),y,z),v7,v8),v5,v6),v9,v10). [para(245(a,1),98(a,1,1,1))]. given #719 (W2a,wt=33): 302 R(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = R(R(R(R(R(x,u,w),y,z),v9,v10),v5,v6),v7,v8). [para(245(a,1),99(a,1,1,1))]. given #720 (W2r,wt=35): 17251 x * ((x \ y) * (T(T(T(z,u),w) / v5,x) * v6)) = x * ((x \ y) * (T(T(T(z,w),u) / v5,x) * v6)). [para(11449(a,1),190(a,1,2,1)),rewrite([190(9),4505(6),4505(14)])]. given #721 (W2r,wt=32): 17271 R(T(x \ 1,y * (x \ z)),x \ (y / x),z) = ((y * (x \ z)) \ (x \ 1)) * ((y / x) * z). [para(1014(a,1),4499(a,1,2,2)),rewrite([3143(5),3143(9),3143(11),1014(16)])]. given #722 (W2r,wt=31): 25112 (x * T(y,z)) / T(y * K(z,y),T(x,T(y,z))) = K(y,z) * (K(y,z) * T(x,T(y,z))). [para(16875(a,1),5364(a,1,2,1,2)),rewrite([12349(4),6144(13),6144(14)])]. given #723 (W2r,wt=33): 12178 T(T(T(T(T(T(x,y),z),u),w),v5),T(T(T(T(x,z),y),u),v5)) = T(T(T(T(T(x,y),z),w),u),v5). [para(29(a,1),8967(a,1,1,1))]. given #724 (W2r,wt=35): 809 (x * (y * (z * (z * (u * y))))) \ (y * (z * (z * (u * (y * x))))) = K(y * (z * (z * (u * y))),x). [para(37(a,1),115(a,1,1,2,2)),rewrite([37(9),37(14)])]. given #725 (W0w,wt=8): 24597 a(x,y,K(x,y)) = 1. [back_rewrite(23464),rewrite([24189(4)])]. given #726 (W0w,wt=8): 24678 a(x,T(x,y),y) = 1. [back_rewrite(19218),rewrite([24596(6),16(4),14(3),22980(2)])]. given #727 (W0w,wt=8): 26041 L(x,T(y,x),y) = x. [hyper(24,a,24678,a)]. given #728 (W0w,wt=8): 26139 L(x,y,T(y,x)) = x. [para(26041(a,1),16487(a,1,1))]. given #729 (W0w,wt=9): 17814 K(K(x,y),y / x) = 1. [back_rewrite(15178),rewrite([17730(3),17781(3)])]. given #730 (W0w,wt=9): 17815 K(x / y,K(y,x)) = 1. [back_rewrite(15176),rewrite([17730(4),17781(4)])]. given #731 (W0w,wt=9): 17822 K(x / y,y) = K(x,y). [back_rewrite(15148),rewrite([17730(4),4408(3),14(3),16710(2)]),flip(a)]. given #732 (W0w,wt=9): 17860 K(K(x,y),x / y) = 1. [back_rewrite(6552),rewrite([17730(3),17781(3)])]. given #733 (W0w,wt=9): 17861 K(x / y,K(x,y)) = 1. [back_rewrite(6456),rewrite([17730(4),17781(4)])]. given #734 (W0w,wt=9): 17884 K(x,y * x) = K(x,y). [back_rewrite(16909),rewrite([17771(4)])]. given #735 (W0w,wt=9): 17910 K(T(x,y),y) = K(x,y). [back_rewrite(17772),rewrite([17781(4)])]. given #736 (W0w,wt=9): 17913 K(x \ 1,y) = K(y,x). [back_rewrite(17730),rewrite([17781(6)])]. given #737 (W0w,wt=9): 17914 K(x,x / y) = K(y,x). [back_rewrite(17291),rewrite([17781(3)]),flip(a)]. given #738 (W0w,wt=9): 17924 K(x,y / x) = K(x,y). [back_rewrite(16967),rewrite([17781(3)]),flip(a)]. given #739 (W0w,wt=9): 17937 K(x,T(x \ 1,y)) = 1. [back_rewrite(9948),rewrite([17781(7),16710(5)])]. given #740 (W0w,wt=9): 17944 K(x,(x * y) \ y) = 1. [back_rewrite(7608),rewrite([17781(5)])]. given #741 (W0a,wt=14): 160 L(T(x,L(x,y,z)),y,z) = L(x,y,z). [para(89(a,1),30(a,1)),flip(a)]. given #742 (W0a,wt=14): 161 R(T(x,R(x,y,z)),y,z) = R(x,y,z). [para(89(a,1),31(a,1)),flip(a)]. given #743 (W0r,wt=17): 16920 x \ ((y \ (y \ K(y,x))) * (y * (x * y))) = 1. [back_rewrite(6789),rewrite([16686(2)])]. given #744 (W0r,wt=17): 1925 x * (x * (y / T(x * (x * (y / z)),z))) = z. [back_rewrite(1246),rewrite([1839(7)])]. given #745 (W0r,wt=10): 26047 a(x / y,y \ x,y) = 1. [para(92(a,1),24678(a,1,2))]. given #746 (W0r,wt=19): 10393 (x / y) * (((y / x) * z) * x) = (z * (x / y)) * y. [back_rewrite(171),rewrite([10229(3)])]. given #747 (W0r,wt=17): 18553 (x * ((y \ x) * x)) \ (x * T(x,y)) = x \ y. [para(18466(a,1),74(a,1)),rewrite([4155(3),101(4),4155(6),4247(7),23(6)]),flip(a)]. given #748 (W1w,wt=21): 5543 ((x \ y) * (x * z)) * T(x,(y * x) * z) = (y * x) * z. [para(2713(a,1),16(a,1,2))]. given #749 (W1w,wt=21): 5557 T(T(x,y),(x \ z) * (x * u)) = T(T(x,(z * x) * u),y). [para(2713(a,1),537(a,2,1)),rewrite([170(6)])]. given #750 (W1w,wt=21): 5560 ((x \ y) * (x / z)) \ ((y * x) / z) = T(x,(y * x) / z). [para(1014(a,1),2713(a,1,1,2)),rewrite([1014(7),1014(10)])]. given #751 (W1w,wt=21): 5600 ((x * (y * (y * (y * x)))) \ y) * (x * (y * (x * y))) = 1. [para(2772(a,1),143(a,2)),rewrite([101(2),189(5),4578(2),2040(4),101(7),4501(11)])]. given #752 (W1w,wt=21): 5674 x * (y * (z * (y * (x / (x * (y * (z * (y * x)))))))) = 1. [para(1014(a,1),2215(a,1,2,2,2,2))]. given #753 (W1w,wt=21): 5817 (x * (a(x / y,z,z \ y) * u)) / u = R(x,y \ 1,z). [para(18(a,1),435(a,1,2)),rewrite([4180(4),18(5),495(5),18(5)]),flip(a)]. given #754 (W1w,wt=21): 5926 x \ ((y * (x * (x * z))) * ((x * z) \ (T(y,x) \ 1))) = 1. [para(1072(a,1),4778(a,2)),rewrite([4407(8),169(9),1014(8),3666(6),4407(4),169(5),1014(4),3666(2),16(3),14(2),4407(8)])]. given #755 (W1w,wt=21): 6024 L(L(L(x,y,z),u,w),L(x,u,w),v5) = L(L(x,u,w),y,z). [para(6018(a,1),97(a,1,1)),flip(a)]. given #756 (W1a,wt=27): 236 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v5,v6),v7,v8),y,z),u,w). [para(97(a,2),97(a,1,1))]. given #757 (W1a,wt=27): 238 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v7,v8),u,w),y,z),v5,v6). [para(97(a,2),97(a,2,1))]. given #758 (W1r,wt=25): 14116 x * (y \ (z * (T(x,y) * (y \ u)))) = x * ((y \ (z / y)) * (x * u)). [para(12372(a,1),4559(a,1,1,1)),rewrite([1014(6),7616(4),3143(5),9490(3),128(5),12372(9),3143(11),3143(12)]),flip(a)]. given #759 (W1r,wt=28): 6697 L(x,L(y,z,u) / x,u * z) = ((u * z) * (L(y,z,u) / x)) \ (u * (z * y)). [para(72(a,1),76(a,2,2))]. given #760 (W1r,wt=24): 23673 a(x,y * x,x * (y * (x * (x * (y * (x * (x * (y * x)))))))) = 1. [back_rewrite(3077),rewrite([23494(10)])]. given #761 (W1r,wt=28): 17092 K((x * (((y * z) * x) * y)) * u,K(x * y,L(z,y,x) * ((x * y) * u))) = 1. [para(193(a,1),4108(a,1,1))]. given #762 (W1r,wt=29): 16237 a(L(x,y,(z * y) * u),u \ (y \ (z \ 1)),y * (((y \ z) * (y * u)) * x)) = 1. [back_rewrite(13923),rewrite([16103(4)])]. given #763 (W2w,wt=31): 2376 (R(R(x,y,z),u,w) * (v5 * (v5 * v6))) \ ((R(R(x,u,w),y,z) * (v5 * (v5 * v6))) * v7) = v7. [para(384(a,1),15(a,1,2))]. given #764 (W2w,wt=31): 2379 T(R(R(x,y,z),u,w) * (v5 * (v5 * v6)),v7) = T(R(R(x,u,w),y,z) * (v5 * (v5 * v6)),v7). [para(384(a,1),23(a,1,2)),rewrite([23(7)])]. given #765 (W2w,wt=31): 2383 (R(R(x,y,z),u,w) * (v5 * (v5 * v6))) / v7 = (R(R(x,u,w),y,z) * (v5 * (v5 * v6))) / v7. [para(384(a,1),1014(a,1)),rewrite([1014(8)])]. given #766 (W2w,wt=31): 2384 (x * (y * (x * (z * (x * (y * x)))))) \ (x * (y * (x * (z * (x * (y * u)))))) = x \ u. [para(16(a,1),387(a,1,2,2,2,2,2,2,2))]. given #767 (W2a,wt=33): 303 R(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = R(R(R(R(R(x,v7,v8),y,z),u,w),v5,v6),v9,v10). [para(99(a,1),245(a,1,1,1)),flip(a)]. given #768 (W2a,wt=33): 305 R(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = R(R(R(R(R(x,v5,v6),y,z),v7,v8),u,w),v9,v10). [para(99(a,2),245(a,1,1,1))]. given #769 (W2r,wt=32): 24354 a(L(a(x,x * y,z),x * ((x \ y) * z),u),u * (y * z),u * (x * ((x \ y) * z))) = 1. [back_rewrite(23881),rewrite([24057(2)])]. given #770 (W2r,wt=31): 28029 L(x,((y * z) \ (y * u)) / x,y * z) = ((y * z) * (L(z \ u,z,y) / x)) \ (y * u). [para(74(a,1),6697(a,1,2,1)),rewrite([16(13)])]. given #771 (W2r,wt=33): 7498 (x * (y * z)) \ (((x \ (x \ y)) * z) * (x * (x * x))) = K((x \ (x \ y)) * z,x * (x * x)). [para(5452(a,1),114(a,1,1,2)),rewrite([7490(15),7490(22)])]. given #772 (W2r,wt=33): 17572 K(K(((x / y) * z) * ((u * (y / x)) * x),y / x),(z * (y / x)) * (((x / y) * u) * y)) = 1. [para(13569(a,1),3327(a,1,2))]. given #773 (W2r,wt=32): 11534 R(x,y * z,L((z \ u) * (z * w),z,y)) = R(x,y * z,(y * z) \ (y * ((u * z) * w))). [para(180(a,2),191(a,2,3)),rewrite([191(12)]),flip(a)]. given #774 (W0w,wt=8): 26839 T(x,L(x,y,z)) = x. [para(160(a,1),16487(a,1,1)),rewrite([16487(2)]),flip(a)]. given #775 (W0w,wt=8): 28463 K(x,L(x,y,z)) = 1. [hyper(27,a,26839,a)]. given #776 (W0w,wt=8): 28532 K(L(x,y,z),x) = 1. [para(26839(a,1),16687(a,1,2)),rewrite([47(1)]),flip(a)]. given #777 (W0w,wt=9): 17949 K(K(x,y),x \ y) = 1. [back_rewrite(6559),rewrite([17781(3)])]. given #778 (W0w,wt=9): 18043 K(x * y,y) = K(x,y). [back_rewrite(16827),rewrite([17910(4)])]. given #779 (W0w,wt=9): 18225 K(x \ (y \ x),y) = 1. [para(14560(a,1),4993(a,1,1)),rewrite([13(5)])]. given #780 (W0w,wt=9): 18412 K(x / y,x) = K(x,y). [para(2643(a,1),16343(a,1,2)),rewrite([10229(3),17843(3)]),flip(a)]. given #781 (W0w,wt=9): 18461 L(x,y,L(x,z,u)) = x. [para(16487(a,1),1689(a,1,1)),rewrite([16487(4)])]. given #782 (W0w,wt=9): 19257 T(x,T(T(x,y),z)) = x. [para(4658(a,1),17(a,1,1)),rewrite([17(6)]),flip(a)]. given #783 (W0w,wt=9): 19567 K(x,y \ x) = K(y,x). [back_rewrite(17919),rewrite([19474(7),4408(5),4408(3),45(2),3032(3),19074(2),15(4),18156(3)]),flip(a)]. given #784 (W0w,wt=9): 21133 T(x,T(x \ 1,y)) = x. [para(16604(a,1),16623(a,1,2)),rewrite([14(6)])]. given #785 (W0w,wt=9): 23360 K(x \ y,y) = K(y,x). [para(2642(a,1),17771(a,1,2)),rewrite([16691(3),16564(4)])]. given #786 (W0w,wt=9): 23380 T(x,T(y,x)) = T(x,y). [para(17771(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. given #787 (W0w,wt=8): 29215 a(x,y,T(y,x)) = 1. [para(23380(a,1),5462(a,1,3)),rewrite([4582(3)])]. given #788 (W0w,wt=9): 23443 T(x,y * x) = T(x,y). [back_rewrite(2652),rewrite([23380(4)])]. given #789 (W0w,wt=9): 26764 T(x,y / x) = T(x,y). [para(17924(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. given #790 (W0a,wt=16): 162 ((x * y) * z) / a(x,y,z) = x * (y * z). [para(19(a,1),49(a,1,2))]. given #791 (W0a,wt=14): 164 (x * (y * z)) / L(z,y,x) = x * y. [para(21(a,1),49(a,1,2))]. given #792 (W0r,wt=18): 27248 R(x,(x \ y) * (x * z),T(x,(y * x) * z)) = x. [para(5543(a,1),183(a,1,2)),rewrite([90(6),17(6)]),flip(a)]. given #793 (W0r,wt=18): 13019 K(K(x \ y,L(y \ z,y,x \ 1)),x \ z) = 1. [para(3143(a,1),10144(a,1,1,1)),rewrite([3143(9)])]. given #794 (W0r,wt=17): 14557 K(x * y,(x * z) / (x * ((z * x) * y))) = 1. [para(189(a,1),14154(a,1,2,2))]. given #795 (W0r,wt=18): 6067 a(x,y * (y * (x * z)),T(y * (y * x),z)) = 1. [para(2647(a,1),5462(a,1,3)),rewrite([2508(9)])]. given #796 (W0r,wt=20): 29771 R(x,K(x,y) * (x * z),T(x,(x * T(x,y)) * z)) = x. [para(16343(a,1),27248(a,1,2,1)),rewrite([547(5)])]. given #797 (W1w,wt=21): 6031 L(L(L(x,y,z),L(x,u,w),v5),u,w) = L(L(x,u,w),y,z). [para(6018(a,1),230(a,1,1)),flip(a)]. given #798 (W1w,wt=21): 6137 x \ (y * T(z,y * (x \ y))) = y \ (z * (y * (x \ y))). [para(3143(a,1),1359(a,1,2,2,2,2)),rewrite([3143(7),3143(8)])]. given #799 (W1w,wt=21): 6152 ((x * y) \ (z \ x)) * ((z * x) * y) = T(x,(z * x) * y). [para(2713(a,1),3143(a,2)),rewrite([4407(5),4408(4),14(4)])]. given #800 (W1w,wt=21): 6177 (x \ (y * z)) * ((z \ (z \ x)) * (z / y)) = K(x,z / y). [back_rewrite(5182),rewrite([6073(6)])]. given #801 (W1w,wt=21): 6185 (x \ (y \ 1)) * T(z,x / y) = (x \ (x \ z)) * (x / y). [back_rewrite(3709),rewrite([6073(4)]),flip(a)]. given #802 (W1w,wt=21): 6188 x \ T(y,z * (z / x)) = (z \ (z \ y)) * (z * (z / x)). [back_rewrite(3482),rewrite([6073(9)])]. given #803 (W1w,wt=21): 6209 K(T(T(T(x,y),z \ 1),u) / z,T(T(x,u),y) / z) = 1. [back_rewrite(3883),rewrite([6095(12)])]. given #804 (W1w,wt=21): 6212 K(T(T(x * y,z),u) / x,T(T(y * x,z),u) / x) = 1. [back_rewrite(3878),rewrite([6095(11)])]. given #805 (W1a,wt=27): 239 L(R(R(R(x,y,z),u,w),v5,v6),v7,v8) = L(R(R(R(x,u,w),y,z),v5,v6),v7,v8). [para(98(a,1),33(a,1,1)),rewrite([33(4)])]. given #806 (W1a,wt=27): 240 L(L(R(R(x,y,z),u,w),v5,v6),v7,v8) = L(L(R(R(x,u,w),y,z),v5,v6),v7,v8). [para(33(a,1),98(a,1,1,1)),rewrite([33(3),33(6),33(7)])]. given #807 (W1r,wt=27): 31086 T(T(T(x,y * (x * (x * z))),u),w) = T(T(T(x,u),w),T(y,x * x) * z). [back_rewrite(10947),rewrite([30703(10)])]. given #808 (W1r,wt=29): 20537 K(x,y) * (x * (y * (x * (y * (x * y))))) = T(x * y,y) * (x * (y * (x * y))). [back_rewrite(18189),rewrite([20449(6),189(6),189(5),189(4),101(3)])]. given #809 (W1r,wt=28): 10214 (x * (y * (x * z))) / ((u * (x * (y * x))) * z) = R(u,x * (y * x),z) \ 1. [para(121(a,1),6565(a,1,1)),flip(a)]. given #810 (W1r,wt=29): 18855 (x * (y * (z * (u * (z \ (x / z)))))) * (T(u,z \ (x / z)) \ z) = x * (y * x). [para(3575(a,1),106(a,1,1,2,2)),rewrite([4155(11)])]. given #811 (W1r,wt=28): 29782 R(K(x,y),(K(y,x) * z) * y,T(K(x,y),(z * K(x,y)) * T(y,x))) = K(x,y). [para(16875(a,1),27248(a,1,2,2)),rewrite([6144(3)])]. given #812 (W2w,wt=31): 2404 L(x * ((y * (z * u)) / u),x,w) = (w * x) \ (w * R(x * (x * (y * z)),y,y \ u)). [para(1929(a,2),21(a,1,2,2)),rewrite([2395(10)]),flip(a)]. given #813 (W2w,wt=31): 2455 ((x * y) * ((x \ z) * ((z * x) * y))) * u = (x * y) * (((x \ z) * z) * ((x * y) * u)). [back_rewrite(2227),rewrite([2446(9)]),flip(a)]. given #814 (W2w,wt=31): 2957 (((x / (y * z)) * y) * z) \ (a(x / (y * z),y,z) * x) = K(a(x / (y * z),y,z),x). [para(59(a,1),64(a,1,2,1)),rewrite([59(14)])]. given #815 (W2w,wt=31): 2979 x * (x * ((y * z) * (x * (x * (y * u))))) = x * (x * (y * ((z * (x * (x * y))) * u))). [para(37(a,1),189(a,1,1)),rewrite([37(6),189(7),101(3),189(6),420(7),37(14)])]. given #816 (W2a,wt=33): 310 R(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = R(R(R(R(R(x,u,w),y,z),v7,v8),v5,v6),v9,v10). [para(245(a,1),245(a,1,1,1))]. given #817 (W2a,wt=35): 331 (x * (y * (y * (z * (x * u))))) \ (u * (x * (y * (y * (z * x))))) = K(u,x * (y * (y * (z * x)))). [para(37(a,1),114(a,1,1,2)),rewrite([37(8),37(14)])]. given #818 (W2r,wt=32): 6278 a(T(T(T(T(T(x,y),z),u),w),v5 \ 1),T(T(T(T(T(x,z),u),w),v5 \ 1),y) / v5,v5) = 1. [para(4092(a,2),6233(a,1,2))]. given #819 (W2r,wt=34): 27070 R(x * (y / z),z / y,((y / z) * u) * z) = (x * (((y / z) * u) * z)) / ((u * (z / y)) * y). [para(10393(a,1),85(a,2,2)),rewrite([10215(2)])]. given #820 (W2r,wt=35): 22545 ((x * (y * (y * (z * (x * (u \ w)))))) * (w \ u)) * T(w,u) = x * (y * (y * (z * (x * T(w,u))))). [para(2226(a,1),4504(a,1,2)),rewrite([4505(4),7715(10)]),flip(a)]. given #821 (W2r,wt=35): 29536 T(T(T(T(T(x,y),z),u),w \ 1),v5 / T(x,z)) / w = T(T(T(T(T(x,z),v5),y),u),w \ 1) / w. [para(26764(a,1),5980(a,2,1,1,1,1))]. given #822 (W2r,wt=33): 28298 K(x \ y,K(x * (z * (x * (u * (x * (z * y))))),x * (z * (x * (u * (x * (z * x))))))) = 1. [para(2384(a,1),14246(a,1,1))]. given #823 (W0w,wt=8): 29715 R(x,y,T(x,y)) = x. [para(13(a,1),27248(a,1,3,2,1)),rewrite([3143(4),15(2),1708(2)])]. given #824 (W0w,wt=9): 27871 L(x,L(x,y,z),u) = x. [para(16487(a,1),6024(a,1,1)),rewrite([16487(4)])]. given #825 (W0w,wt=9): 28813 a(L(x,y,z),u,x) = 1. [hyper(25,a,18461,a)]. given #826 (W0w,wt=9): 28868 K(x,T(T(x,y),z)) = 1. [hyper(27,a,19257,a)]. given #827 (W0w,wt=9): 28929 K(T(T(x,y),z),x) = 1. [para(19257(a,1),16687(a,1,2)),rewrite([47(1)]),flip(a)]. given #828 (W0w,wt=9): 29529 T(T(x,y),x / y) = x. [para(26764(a,1),12372(a,1,1)),rewrite([10229(4),14(4)])]. given #829 (W0w,wt=9): 32156 a(x,L(y,z,u),y) = 1. [hyper(25,a,27871,a)]. given #830 (W0w,wt=9): 32269 a(x,y,L(x,z,u)) = 1. [para(16487(a,1),28813(a,1,1))]. given #831 (W0w,wt=9): 32304 K(T(x,y),T(x,z)) = 1. [para(7769(a,1),28868(a,1,2,1))]. given #832 (W0w,wt=9): 32506 a(x,y,L(y,z,u)) = 1. [para(16487(a,1),32156(a,1,2))]. given #833 (W0w,wt=10): 493 R(T(x,y),x,z) = T(x,y). [para(480(a,1),31(a,1,1)),flip(a)]. given #834 (W0w,wt=8): 32750 R(x,T(x,y),z) = x. [para(7769(a,1),493(a,1,1)),rewrite([7769(5)])]. given #835 (W0w,wt=10): 1077 L(x \ 1,x,y) = x \ 1. [para(50(a,1),1022(a,1,2)),rewrite([989(2),989(5)])]. given #836 (W0w,wt=10): 1685 L(T(x,y),z,x) = T(x,y). [para(1667(a,1),30(a,1,1)),flip(a)]. given #837 (W0w,wt=8): 33049 a(x,y,T(x,z)) = 1. [hyper(25,a,1685,a)]. given #838 (W0w,wt=8): 33075 L(x,y,T(x,z)) = x. [para(7769(a,1),1685(a,1,1)),rewrite([7769(5)])]. given #839 (W0a,wt=14): 166 R(x,y,z) \ ((x * y) * z) = y * z. [para(22(a,1),50(a,1,1))]. given #840 (W0a,wt=15): 168 x \ ((y * x) * z) = (x \ y) * (x * z). [para(104(a,1),15(a,1,2))]. given #841 (W0r,wt=20): 16122 T(T(x * ((x \ y) * z),u),y) = T(L(z,x,y) * y,u). [back_rewrite(9647),rewrite([16103(7)])]. given #842 (W0r,wt=17): 6280 L(x * y,R(z,x,y),(z * x) * y) = x * y. [para(22(a,1),6257(a,1,2))]. given #843 (W0r,wt=17): 30627 x * ((y * x) \ T(z,x / y)) = T(z,x) / y. [back_rewrite(7622),rewrite([30455(8)])]. given #844 (W0r,wt=12): 3260 L(x \ y,x,y \ 1) = x \ y. [back_rewrite(1053),rewrite([3143(7),2538(7)])]. given #845 (W0r,wt=18): 33300 R(x,K(x,y),z) \ (T(x,y) * z) = K(x,y) * z. [para(16716(a,1),166(a,1,2,1))]. given #846 (W1w,wt=21): 6215 K(T(T(T(x,y \ 1),z),u) / y,T(T(x,u),z) / y) = 1. [back_rewrite(3871),rewrite([6095(12)])]. given #847 (W1w,wt=21): 6219 K(T(T(T(x,y \ 1),z),u) / y,T(T(x,z),u) / y) = 1. [back_rewrite(3784),rewrite([6095(12)])]. given #848 (W1w,wt=21): 6220 K(T(T(x,y),z) / u,T(T(T(x,u \ 1),y),z) / u) = 1. [back_rewrite(3782),rewrite([6095(6)])]. given #849 (W1w,wt=21): 6422 a(x,y * (z * ((y * z) \ x)),a(y,z,(y * z) \ x)) = 1. [para(57(a,1),6335(a,1,3))]. given #850 (W1w,wt=21): 6426 a(((x / (y * z)) * y) * z,x,a(x / (y * z),y,z)) = 1. [para(59(a,1),6335(a,1,3))]. given #851 (W1w,wt=21): 6438 a((x * y) * T(z,y),x * (z * y),a(x,y,T(z,y))) = 1. [para(507(a,1),6335(a,1,3))]. given #852 (W1w,wt=21): 6520 T(x * (x * y),K(z,x * (x * (y / z)))) = x * (x * y). [para(3305(a,1),2647(a,2)),rewrite([1839(5),2647(10)])]. given #853 (W1w,wt=21): 6953 (x \ ((y * z) \ (y \ 1))) * u = (z * x) \ (y \ (y \ u)). [para(341(a,1),3139(a,1,1,2,2,2,2)),rewrite([341(27),6946(26),4417(8),4407(4),5162(10)])]. given #854 (W1a,wt=27): 241 L(L(R(R(x,y,z),u,w),v5,v6),v7,v8) = L(L(R(R(x,u,w),y,z),v7,v8),v5,v6). [para(98(a,1),34(a,1,1))]. given #855 (W1a,wt=27): 242 L(R(R(R(x,y,z),u,w),v5,v6),v7,v8) = L(R(R(R(x,v5,v6),y,z),u,w),v7,v8). [para(35(a,1),98(a,1,1,1)),flip(a)]. given #856 (W1r,wt=28): 1828 R(x,y,y \ (z \ 1)) / T(x,a(y,(y \ x) / z,z)) = a(y,(y \ x) / z,z). [back_rewrite(867),rewrite([1810(4)])]. given #857 (W1r,wt=29): 4677 T(x,y) * (z * (T(x,y) * (z * ((T(T(x,z),y) * (T(x,y) * z)) \ u)))) = z * u. [back_rewrite(3106),rewrite([4578(3),2040(13),4567(11)])]. given #858 (W1r,wt=26): 18655 L(T(T(T(x,y),z),u),T(T(T(x,u),y),z) \ w,w) = T(T(T(x,u),y),z). [para(18472(a,1),3337(a,2))]. given #859 (W1r,wt=25): 35637 T((x * y) * z,K(u,x * (x * (((x \ y) * z) / u)))) = (x * y) * z. [para(136(a,1),6520(a,1,1)),rewrite([136(13)])]. given #860 (W1r,wt=25): 4747 x * (T(T(T(y,x),z),u) * (x * w)) = T(T(y,z),u) * (x * (x * w)). [back_rewrite(1273),rewrite([4578(10),2040(11)])]. given #861 (W2w,wt=31): 3043 (x * ((y * x) * (z * (x * (x * y))))) * u = x * ((y * x) * (z * (x * ((x * y) * u)))). [para(189(a,1),130(a,1,1)),rewrite([189(14)])]. given #862 (W2w,wt=31): 3045 (x * ((x * y) * (z * (x * (y * x))))) * u = x * ((x * y) * (z * (x * ((y * x) * u)))). [para(189(a,1),130(a,2,2,2,2)),rewrite([101(3)])]. given #863 (W2w,wt=31): 3115 x * (y * (z * (u * (z * (y * (x * ((x * (y * (z * (u * (z * (y * x)))))) \ w))))))) = w. [para(130(a,1),103(a,1,2,2,2,1,2)),rewrite([130(13)])]. given #864 (W2w,wt=31): 3184 x * (x * ((y * z) * K((y \ x) * (y * z),x * y))) = ((y \ x) * (y * z)) * (x * y). [back_rewrite(2551),rewrite([3143(6),168(4),3143(14),168(12)])]. given #865 (W2a,wt=34): 339 R(x,y * (y * z),(x * (y * (y * z))) \ u) = u / (y * (y * (z * ((x * (y * (y * z))) \ u)))). [para(16(a,1),148(a,1,1)),flip(a)]. given #866 (W2a,wt=34): 365 (x * ((y \ z) * ((z * y) * u))) * a(x,(y \ z) * z,y * u) = (x * ((y \ z) * z)) * (y * u). [para(104(a,1),312(a,1,1,2,2)),rewrite([16(8),16(13)])]. given #867 (W2r,wt=32): 8192 L(L(L(L(x,y,z),u,w),v5,v6),v7,L(L(x,u,w),v5,v6) \ v7) = L(L(L(x,u,w),v5,v6),y,z). [para(8105(a,1),227(a,1,1)),flip(a)]. given #868 (W2r,wt=33): 20245 K(x,(T(T(T(T(T(y,z),u),w),x \ 1),v5) / x) / T(T(T(T(T(y,u),w),x \ 1),z),v5)) = 1. [para(4063(a,1),14479(a,1,2,1))]. given #869 (W2r,wt=31): 5946 T(T(T(T(T(x,y),z),u),w \ 1),v5) / w = T(T(T(T(T(x,v5),y),u),z),w \ 1) / w. [para(29(a,1),4092(a,1,1,1,1))]. given #870 (W2r,wt=35): 36208 L(R(R(R(x,y,z),u,w),v5,v6),v7,R(R(R(T(x,v8),v5,v6),y,z),u,w)) = R(R(R(x,v5,v6),y,z),u,w). [para(242(a,2),33075(a,1)),rewrite([31(7),31(6),31(5)])]. given #871 (W2r,wt=35): 36377 (x * (T(T(y,z),u) * (w * w))) \ (T(T(y,z),u) * (w * (w * x))) = K(T(T(y,z),u) * (w * w),x). [para(4747(a,1),115(a,1,2)),rewrite([7867(4),90(5),4578(4),7867(15),90(16),4578(15)])]. given #872 (W0w,wt=8): 33128 a(T(x,y),z,x) = 1. [para(7769(a,1),33049(a,1,3))]. given #873 (W0w,wt=8): 33194 L(x,T(x,y),z) = x. [para(33075(a,1),16487(a,1,1))]. given #874 (W0w,wt=8): 33734 L(x,y,K(y,z)) = x. [back_rewrite(23108),rewrite([33497(4),15(4)]),flip(a)]. given #875 (W0w,wt=8): 33753 a(K(x,y),x,z) = 1. [back_rewrite(20946),rewrite([33497(3),46(5)]),flip(a)]. given #876 (W0w,wt=8): 37006 a(x,T(y,z),y) = 1. [hyper(25,a,33194,a)]. given #877 (W0w,wt=8): 37107 L(x,K(y,z),y) = x. [para(33734(a,1),16487(a,1,1))]. given #878 (W0w,wt=8): 37111 L(x,y,K(z,y)) = x. [para(17781(a,1),33734(a,1,3))]. given #879 (W0w,wt=8): 37155 a(x,K(x,y),z) = 1. [back_rewrite(16720),rewrite([37125(3),46(5)]),flip(a)]. given #880 (W0w,wt=8): 37180 a(K(x,y),y,z) = 1. [para(17781(a,1),33753(a,1,1))]. given #881 (W0w,wt=8): 37199 a(x,y,T(y,z)) = 1. [para(7769(a,1),37006(a,1,2))]. given #882 (W0w,wt=8): 37216 L(x,K(y,z),z) = x. [para(17781(a,1),37107(a,1,2))]. given #883 (W0w,wt=8): 38147 a(x,K(y,x),z) = 1. [para(17781(a,1),37155(a,1,2))]. given #884 (W0w,wt=10): 1916 R(x * x,y,z) = x * x. [back_rewrite(1412),rewrite([1839(5),47(3),14(2)]),flip(a)]. given #885 (W0w,wt=10): 2693 R(x,x \ y,T(x,y)) = x. [back_rewrite(1451),rewrite([2649(3),2642(5),90(5),17(5)])]. given #886 (W0w,wt=10): 2746 a(x \ (x \ 1),y,z) = 1. [back_rewrite(2536),rewrite([2712(3)])]. given #887 (W0w,wt=10): 2747 L(x,y \ (y \ 1),z) = x. [back_rewrite(2528),rewrite([2712(3)])]. given #888 (W0a,wt=15): 169 (x * y) * (y \ z) = y * ((y \ x) * z). [para(16(a,1),104(a,1,2,2)),flip(a)]. given #889 (W0a,wt=15): 170 ((x * y) * z) / ((y \ x) * (y * z)) = y. [para(104(a,1),17(a,1,1))]. given #890 (W0r,wt=17): 26074 x * (y * T(y * x,x)) = y * (x * (y * x)). [back_rewrite(24777),rewrite([26045(3)])]. given #891 (W0r,wt=18): 28478 T(T(T(x,y),z),L(T(x,z),u,w)) = T(T(x,z),y). [para(26839(a,1),94(a,1,1)),flip(a)]. given #892 (W0r,wt=15): 33450 (x \ (y / x)) * (x * z) = x \ (y * z). [para(18(a,1),168(a,1,2,1)),flip(a)]. given #893 (W0r,wt=18): 6591 L(x,y,z) \ (y \ (z \ 1)) = (y * x) \ (z \ 1). [para(2934(a,1),3666(a,1,1)),rewrite([6562(7),4407(4),4407(9)])]. given #894 (W0r,wt=20): 21579 K((x / (y * (z * x))) * z,R(y,z * x,x \ 1)) = 1. [para(1014(a,1),17761(a,1,1,1)),rewrite([4155(3),45(2),10229(4),4155(7),45(6)])]. given #895 (W1w,wt=21): 6970 T((x \ (x \ y)) * ((z \ x) * x),x \ (x \ z)) = z \ y. [para(3143(a,1),3139(a,1,1,2,2,2,2)),rewrite([3143(8),4155(7),4408(6),3143(8),3143(7),6073(5),3143(10),3143(9)])]. given #896 (W1w,wt=21): 6973 ((x * y) \ (z * x)) * ((z \ x) * y) = T(x,(z \ x) * y). [back_rewrite(6151),rewrite([6951(8),4408(4),45(3)])]. given #897 (W1w,wt=21): 7021 T(x,y * (y / z)) \ z = ((x * (y * (y / z))) \ y) * y. [para(3218(a,1),1091(a,1,1)),rewrite([4408(5),4408(11),14(11)]),flip(a)]. given #898 (W1w,wt=21): 7107 L(T(T(T(x,y),z),u),w,v5) = L(T(T(T(x,u),z),y),w,v5). [para(29(a,1),3337(a,1,1,1))]. given #899 (W1w,wt=21): 7108 L(T(T(T(x,y),z),u),w,v5) = L(T(T(T(x,z),y),u),w,v5). [para(29(a,1),3337(a,1,1))]. given #900 (W1w,wt=21): 7251 T(x \ y,K(x * ((z / x) * y),z \ (x \ 1))) = x \ y. [para(3715(a,1),3307(a,1,1,1)),rewrite([3143(3),7194(10),16(6),4408(5),4408(4),45(3),4578(3),7194(12),16(8),2040(8),136(7),1014(4),7194(13),16(9),7194(18),16(14),16(13),3143(12)])]. given #901 (W1w,wt=21): 7252 T(x \ y,(x * ((z / x) * y)) * (z \ (x \ 1))) = x \ y. [para(3715(a,1),3322(a,1,1,1)),rewrite([3143(3),7194(10),16(6),4408(5),4408(4),45(3),4578(3),7194(12),16(8),2040(8),136(7),1014(4),7194(13),16(9),7194(18),16(14),16(13),3143(12)])]. given #902 (W1w,wt=21): 7347 a(x,R(T(y,x),z,u),x * w) = a(R(y,z,u),x,x * w). [para(4770(a,1),19(a,1,1)),rewrite([519(7),19(9)]),flip(a)]. given #903 (W1a,wt=27): 244 R(R(R(R(x,y,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v7,v8),y,z),u,w),v5,v6). [para(99(a,1),35(a,1,1)),flip(a)]. given #904 (W1a,wt=27): 246 R(R(R(R(x,y,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v5,v6),y,z),v7,v8),u,w). [para(99(a,2),35(a,1,1))]. given #905 (W1r,wt=27): 2466 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v7,v8),u,w),v5,v6),y,z). [para(69(a,1),454(a,1,1,1,1,1)),rewrite([69(8)])]. given #906 (W1r,wt=26): 17065 (x * y) * (L(z,y,x) * ((x * y) / u)) = (x * (((y * z) * x) * y)) / u. [para(1014(a,1),193(a,1,2,2)),rewrite([1014(13)])]. given #907 (W1r,wt=22): 26628 K((x \ y) * z,R(x \ 1,y,z)) = K(y * z,(x \ y) * z). [para(6071(a,1),17914(a,1,2))]. given #908 (W1r,wt=23): 37014 L(L(L(x,y,z),u,w),L(T(x,v5),u,w),v6) = L(L(x,u,w),y,z). [para(33194(a,1),97(a,1,1)),rewrite([30(6)]),flip(a)]. given #909 (W1r,wt=23): 33415 x * (y * (y * (x * T(z,y * x)))) = (x * y) * (z * (y * x)). [back_rewrite(20509),rewrite([33346(6)]),flip(a)]. given #910 (W2w,wt=31): 3284 x * (x * ((y \ z) * K(y * ((x / y) * z),x / y))) = (y * ((x / y) * z)) * (x / y). [back_rewrite(878),rewrite([3228(3),37(9)])]. given #911 (W2w,wt=31): 3792 T(T(T(T(T(x,y \ 1),z),u),w),v5) / y = T(T(T(T(T(x,z),u),w),v5),y \ 1) / y. [para(94(a,1),3382(a,1,1,1,1))]. given #912 (W2w,wt=31): 3796 T(T(T(T(T(x,y),z \ 1),u),w),v5) / z = T(T(T(T(T(x,u),y),w),v5),z \ 1) / z. [para(94(a,2),3382(a,1,1,1,1))]. given #913 (W2w,wt=31): 3798 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,z),w),y),v5),u \ 1) / u. [para(94(a,2),3382(a,2,1,1,1))]. given #914 (W2a,wt=35): 367 R(R(R(x,y * (z * u),a(y,z,u)),w,v5),v6,v7) = R(R(R(x,w,v5),v6,v7),y * (z * u),a(y,z,u)). [para(19(a,1),248(a,1,1,1,3)),rewrite([19(15)])]. given #915 (W2a,wt=32): 381 L(R(x,y * (y * z),u),w,v5) * (y * (y * (z * u))) = (L(x,w,v5) * (y * (y * z))) * u. [para(33(a,1),341(a,1,1))]. given #916 (W2r,wt=33): 13939 (x / y) * (((x * y) * T(z,y)) \ (y * (z * y))) = K(T(z,y) \ (y \ (x \ 1)),y * (z * y)). [back_rewrite(10316),rewrite([13888(9)])]. given #917 (W2r,wt=31): 32886 ((x * (y * (x / y))) * (y * (x * (y \ x)))) * z = y * (x * (x * (((y \ x) * x) * z))). [back_rewrite(24640),rewrite([32749(12),7617(11),37(13)])]. given #918 (W2r,wt=33): 32658 a(x,L(L(L(L(y,z,u),w,v5),v6,v7),v8,v9),L(L(L(L(L(y,v10,v11),z,u),w,v5),v6,v7),v8,v9)) = 1. [para(233(a,1),32506(a,1,3))]. given #919 (W2r,wt=33): 28849 L(L(L(L(x,y,L(L(L(x,z,u),w,v5),v6,v7)),z,u),v8,v9),w,v5) = L(L(L(x,z,u),w,v5),v8,v9). [para(18461(a,1),229(a,1,1)),flip(a)]. given #920 (W2r,wt=32): 11803 (x * ((y \ z) * z)) \ (x * ((y \ z) * ((y \ z) * u))) = L(T(y,z) \ u,(y \ z) * z,x). [para(2690(a,1),3141(a,1,2,2)),rewrite([2690(9)]),flip(a)]. given #921 (W0w,wt=8): 38713 R(x,K(x,y),z) = x. [para(16985(a,1),170(a,1,1,1)),rewrite([38223(6),18422(5)])]. given #922 (W0w,wt=8): 41732 R(x,K(y,x),z) = x. [para(17781(a,1),38713(a,1,2))]. given #923 (W0w,wt=10): 2748 L(x,y,z \ (z \ 1)) = x. [back_rewrite(2497),rewrite([2712(3)])]. given #924 (W0w,wt=10): 2749 a(x,y \ (y \ 1),z) = 1. [back_rewrite(2489),rewrite([2712(3)])]. given #925 (W0w,wt=10): 2750 R(x,y \ (y \ 1),z) = x. [back_rewrite(2483),rewrite([2712(3)])]. given #926 (W0w,wt=10): 3717 L(x,y \ 1,x \ y) = x. [back_rewrite(3220),rewrite([3666(6),2649(8),88(6)])]. given #927 (W0w,wt=10): 3723 R(x \ 1,x,y) = x \ 1. [back_rewrite(1027),rewrite([3691(5)])]. given #928 (W0w,wt=10): 4141 R(x,y \ z,z \ y) = x. [para(2538(a,1),191(a,2,3)),rewrite([14(5),16(4),48(2)]),flip(a)]. given #929 (W0w,wt=10): 4165 L(x,y \ z,z \ y) = x. [para(2538(a,1),3266(a,1,3))]. given #930 (W0w,wt=10): 4166 a(x \ y,y \ x,z) = 1. [para(2538(a,1),3301(a,1,1))]. given #931 (W0w,wt=10): 4422 a(x,y,y \ (x \ 1)) = 1. [back_rewrite(3722),rewrite([4407(3)])]. given #932 (W0w,wt=10): 4996 R(x,K(y,z),K(z,y)) = x. [para(2917(a,1),191(a,2,3)),rewrite([14(5),16(4),48(2)]),flip(a)]. given #933 (W0w,wt=10): 5003 a(x,K(y,z),K(z,y)) = 1. [para(2917(a,1),1012(a,1,2))]. given #934 (W0w,wt=10): 5011 L(x,K(y,z),K(z,y)) = x. [para(2917(a,1),3266(a,1,3))]. given #935 (W0w,wt=10): 5012 a(K(x,y),K(y,x),z) = 1. [para(2917(a,1),3301(a,1,1))]. given #936 (W0w,wt=10): 5407 a(x \ y,y,T(x,y)) = 1. [para(2690(a,1),2445(a,1,1,2,2)),rewrite([507(8)])]. given #937 (W0a,wt=18): 192 (x * y) \ (z * ((z \ x) * y)) = a(x,z,z \ y). [back_rewrite(55),rewrite([169(4)])]. given #938 (W0a,wt=16): 198 R(x * y,x,x \ z) = (x * (y * z)) / z. [para(15(a,1),191(a,1,1,2,1)),flip(a)]. given #939 (W0r,wt=19): 37860 K(x * (x * y),T(x \ (x \ (y \ 1)),z \ 1)) = 1. [back_rewrite(17706),rewrite([37242(10)])]. given #940 (W0r,wt=17): 33984 T(x,y * (x * (x / y))) = T(x,K(y,x * x)). [back_rewrite(25347),rewrite([33665(7)])]. given #941 (W0r,wt=10): 38164 a(x,y / z,z \ y) = 1. [para(92(a,1),37199(a,1,3))]. given #942 (W0r,wt=19): 20994 K((x * y) * z,R(x,y,z)) = K(y * z,R(x,y,z)). [para(84(a,1),16568(a,1,1))]. given #943 (W0r,wt=19): 22782 K(K(x \ y,z * (z * x)),T(x * (z * z),y)) = 1. [para(10927(a,1),16705(a,1,2))]. given #944 (W1w,wt=21): 7348 L(x * y,R(T(z,x),u,w),x) = L(x * y,x,R(z,u,w)). [para(4770(a,1),21(a,1,2)),rewrite([519(3),21(7)]),flip(a)]. given #945 (W1w,wt=21): 7353 R(x,y,z) * (x * (x * u)) = x * (R(x,y,z) * (x * u)). [para(89(a,1),4770(a,1,2,1,1)),flip(a)]. given #946 (W1w,wt=21): 7682 a((x \ y) * (z * (x \ y)),y \ x,u) = a(x \ y,z,u). [para(4137(a,1),133(a,1,2,1,2,2)),rewrite([6353(5),7656(4),14(6),19(7)]),flip(a)]. given #947 (W1w,wt=21): 7773 T(T((x * y) * z,y),(y \ x) * (y * z)) = (x * y) * z. [para(104(a,1),4209(a,2)),rewrite([7772(4)])]. given #948 (W1w,wt=21): 7822 (x \ y) * (x * (z * (y * x))) = T((y * x) * (z * y),x). [back_rewrite(2240),rewrite([7772(5)]),flip(a)]. given #949 (W1w,wt=21): 7839 a(L(x \ y,x,z),T(z * ((x * z) * y),z * y),u) = 1. [back_rewrite(5525),rewrite([7775(7),189(5)])]. given #950 (W1w,wt=21): 7968 (x \ y) * ((x \ y) * (x * z)) = ((x \ y) * T(y,x)) * z. [para(4505(a,1),37(a,1,1,2)),flip(a)]. given #951 (W1w,wt=21): 7969 (x \ y) * (((y \ x) * z) * T(y,x)) = (z * (x \ y)) * x. [para(4505(a,1),104(a,1,2,2)),rewrite([4408(3)])]. given #952 (W1a,wt=27): 251 L(R(R(R(x,y,z),u,w),v5,v6),v7,v8) = L(R(R(R(x,v5,v6),u,w),y,z),v7,v8). [para(99(a,2),98(a,1,1))]. given #953 (W1a,wt=27): 253 R(R(R(R(x,y,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v7,v8),y,z),v5,v6),u,w). [para(99(a,1),99(a,1,1)),flip(a)]. given #954 (W1r,wt=29): 5866 R((x * (y / z)) * z,x * y,y \ 1) = ((x * y) * (a(x,y / z,z) * x)) / x. [para(1091(a,1),436(a,1,3))]. given #955 (W1r,wt=23): 19765 T(K(x,y) * (z * z),x * y) = T(z * (z * K(x,y)),y * x). [para(20(a,1),10900(a,1,1,1)),rewrite([2759(6),20(8)])]. given #956 (W1r,wt=25): 29520 T(T(T(x \ y,z),u),T(y / x,z * (y \ x))) = T(T(x \ y,z),u). [para(26764(a,1),3831(a,1,1,1)),rewrite([4155(6),4155(11),29470(12)])]. given #957 (W1r,wt=25): 14495 T(x,(T(T(T(y,z),u),x \ 1) / x) / T(T(T(y,x \ 1),z),u)) = x. [para(3382(a,1),14123(a,1,2,1))]. given #958 (W1r,wt=21): 31324 K(T(T(x * y,z),u) / y,y / T(T(y * x,z),u)) = 1. [para(6212(a,1),17781(a,2)),rewrite([10229(10),14(10)])]. given #959 (W2w,wt=31): 3847 T(T(T(T(x / y,z),u),w),y * T(T(T(y \ x,z),u),w)) = T(T(T(y \ x,z),u),w). [para(3352(a,1),1708(a,2)),rewrite([3828(9)])]. given #960 (W2w,wt=31): 3894 x * (y * (x * ((z / (x * (y * (x * u)))) * (x * (y * x))))) = (x * (y * (x * z))) / u. [para(18(a,1),389(a,1,1,2,2,2)),flip(a)]. given #961 (W2w,wt=31): 3925 x * (x * (y * (x * (x * (y * ((y \ z) / u)))))) = x * (x * ((y * (x * (x * z))) / u)). [para(1014(a,1),397(a,1,2,2,2,2,2,2)),rewrite([1014(14)])]. given #962 (W2w,wt=31): 4007 (x * (y * z)) / T((x * z) * T(y,z),a(z,z * x,y * z)) = a(z,z * x,y * z). [back_rewrite(1517),rewrite([3954(8),3954(13)])]. given #963 (W2a,wt=32): 382 R(R(x,y * (y * z),u),w,v5) * (y * (y * (z * u))) = (R(x,w,v5) * (y * (y * z))) * u. [para(35(a,1),341(a,1,1))]. given #964 (W2a,wt=32): 429 ((((x * y) * z) * (x * (y * z))) * u) / (a(x,y,z) * ((x * (y * z)) * u)) = x * (y * z). [para(175(a,1),17(a,1,1))]. given #965 (W2r,wt=35): 29604 T(x * (y * (z * u)),L(a(y,z,u),y * (z * u),x)) = T(x * (y * (z * u)),x * ((y * z) * u)). [para(162(a,1),6694(a,1,1,2)),rewrite([162(8),162(12)])]. given #966 (W2r,wt=31): 4047 R(R(R(R(x,y / z,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v7,v8),u,w),v5,v6),y / z,z). [para(2372(a,1),35(a,1)),flip(a)]. given #967 (W2r,wt=35): 43773 T(T(x \ y,z),u) / T(y / x,z * (y \ x)) = T(y / x,z * (y \ x)) \ T(T(x \ y,z),u). [para(29520(a,1),7616(a,1,1))]. given #968 (W2r,wt=33): 13056 T(T(T(T(T(T(x,y),z),u),w),v5),T(T(x,z),u) \ v6) = T(T(T(T(T(T(x,z),u),v6),y),w),v5). [para(94(a,1),3825(a,1,1,1,1))]. given #969 (W2r,wt=35): 38669 (((x * (y * (x * z))) * (z * (x * (y * x)))) * u) / ((x * (y * (x * z))) * u) = z * (x * (y * x)). [para(115(a,1),170(a,1,2,1)),rewrite([33342(16),128(11)])]. given #970 (W0w,wt=8): 42144 a(x,y,x * y) = 1. [para(1091(a,1),5407(a,1,1)),rewrite([4209(4),24189(4)])]. given #971 (W0w,wt=10): 6020 L(T(x,y),x,z) = T(x,y). [para(6018(a,1),30(a,1,1)),flip(a)]. given #972 (W0w,wt=10): 6265 a(x * y,y,T(x,y)) = 1. [para(165(a,1),6233(a,1,2))]. given #973 (W0w,wt=10): 6274 a(x,y \ x,T(y,x)) = 1. [para(2711(a,1),6233(a,1,2))]. given #974 (W0w,wt=10): 6352 a(x \ y,x \ 1,y) = 1. [para(3143(a,1),6258(a,1,1))]. given #975 (W0w,wt=10): 6368 L(x \ y,x,y) = x \ y. [para(16(a,1),6279(a,1,3))]. given #976 (W0w,wt=10): 6416 L(x,y \ 1,y \ x) = x. [para(3143(a,1),6279(a,1,3))]. given #977 (W0w,wt=10): 6432 a(x,x * y,y \ 1) = 1. [para(1091(a,1),6335(a,1,3))]. given #978 (W0w,wt=10): 6596 L(x \ 1,y,x) = x \ 1. [back_rewrite(3221),rewrite([6565(5),3200(4)])]. given #979 (W0w,wt=8): 44870 a(x,y,x \ 1) = 1. [hyper(25,a,6596,a)]. given #980 (W0w,wt=10): 7659 R(x,y,y \ (x \ y)) = x. [para(4137(a,1),191(a,1,1,2)),rewrite([14(2),4155(2),16(2)]),flip(a)]. given #981 (W0w,wt=10): 8110 a(T(x,y),x * y,y) = 1. [para(23(a,1),8054(a,1,1))]. given #982 (W0w,wt=10): 8150 L(x,y * x,T(y,x)) = x. [para(23(a,1),8105(a,1,3))]. given #983 (W0w,wt=10): 8155 L(x / y,x,y) = x / y. [para(50(a,1),8105(a,1,3))]. given #984 (W0w,wt=10): 8199 L(x,x / y,y \ 1) = x. [para(1829(a,1),8105(a,1,3))]. given #985 (W0w,wt=10): 8221 a(T(x,y),y,x \ y) = 1. [para(2690(a,1),8106(a,1,2))]. given #986 (W0a,wt=16): 200 R(x,y,y \ z) * z = y * ((y \ x) * z). [para(191(a,1),18(a,1,1))]. given #987 (W0a,wt=16): 207 R(x,y,y \ z) \ (y * ((y \ x) * z)) = z. [para(191(a,1),50(a,1,1))]. given #988 (W0r,wt=17): 37774 K(K(x,T(T(y,z),u)),T(T(T(x,y),u),z)) = 1. [back_rewrite(22881),rewrite([37242(3),37242(3)])]. given #989 (W0r,wt=17): 25093 (x \ y) / T(z * (z / x),y) = z \ (z \ y). [para(12372(a,1),5364(a,1,2,2)),rewrite([1014(4),7616(2),1014(4),12372(9)])]. given #990 (W0r,wt=19): 24859 (x * (y * (z * (y \ z)))) / (z * (y * (z / y))) = x. [para(20620(a,1),86(a,1,1,1,2)),rewrite([14(2),20620(15),79(13)])]. given #991 (W0r,wt=20): 6377 L(L(L(x,y,z),u,w),v5,v5 * x) = L(L(x,y,z),u,w). [para(6279(a,1),97(a,2,1,1))]. given #992 (W0r,wt=11): 26497 K(x,T(y,x \ 1)) = K(x,y). [para(17910(a,1),17781(a,1)),rewrite([17781(3)]),flip(a)]. given #993 (W1w,wt=21): 8020 (x \ y) * ((z * (x \ y)) * x) = ((x \ y) * z) * T(y,x). [para(4505(a,1),189(a,1,2)),flip(a)]. given #994 (W1w,wt=21): 8101 K(L(x * y,z,x),a(z \ x,T(z,x),y) \ (x * y)) = 1. [back_rewrite(2678),rewrite([7997(4)])]. given #995 (W1w,wt=21): 8125 a(a(x / (y * z),y,z),((x / (y * z)) * y) * z,x) = 1. [para(59(a,1),8054(a,1,1))]. given #996 (W1w,wt=21): 8137 a(a(x,y,T(z,y)),(x * y) * T(z,y),x * (z * y)) = 1. [para(507(a,1),8054(a,1,1))]. given #997 (W1w,wt=21): 8147 L(x * (y * z),(x * y) * z,a(x,y,z)) = x * (y * z). [para(19(a,1),8105(a,1,3))]. given #998 (W1w,wt=21): 8173 L(x * y,(x * (y / z)) * z,a(x,y / z,z)) = x * y. [para(58(a,1),8105(a,1,3))]. given #999 (W1w,wt=21): 8181 L(x,((x / (y * z)) * y) * z,a(x / (y * z),y,z)) = x. [para(59(a,1),8105(a,1,3))]. given #1000 (W1w,wt=21): 8208 L(x * (y / z),x * y,L(z,y / z,x)) = x * (y / z). [para(76(a,2),8105(a,1,3))]. given #1001 (W1a,wt=27): 255 R(R(R(R(x,y,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),y,z),v7,v8),v5,v6). [para(99(a,1),99(a,2,1))]. given #1002 (W1a,wt=27): 257 R(R(R(R(x,y,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v5,v6),v7,v8),y,z),u,w). [para(99(a,2),99(a,1,1))]. given #1003 (W1r,wt=27): 19616 a(L(T(T(x,y),z),u,w),v5,v5 * v6) = a(L(T(T(x,z),y),u,w),v5,v5 * v6). [para(30(a,1),4908(a,1,1,1)),rewrite([30(3),30(7),30(8)])]. given #1004 (W1r,wt=26): 24428 ((x / (y * z)) * (y * (z * y))) \ (x * y) = a(y * z,(y * z) * x,y). [back_rewrite(18703),rewrite([24057(11)])]. given #1005 (W1r,wt=25): 33549 K(((x \ y) * y) * ((z * x) * u),y * (y * (((z * x) * u) / x))) = 1. [back_rewrite(15510),rewrite([33451(5)])]. given #1006 (W1r,wt=27): 20356 a(x * (y * (x * (z * u))),L(u,z,x * (y * x)),x * (y * (x * z))) = 1. [para(132(a,1),18604(a,1,2))]. given #1007 (W1r,wt=29): 13583 (x * ((y * x) * (x * z))) \ (z * (x * (y * (x * x)))) = K(z,x * (y * (x * x))). [para(190(a,1),114(a,1,2,2)),rewrite([100(4),10809(5),100(5),4525(4),46(5),4578(7),13(8),8972(13),90(14),189(12),4578(11)])]. given #1008 (W2w,wt=31): 4017 ((x * y) * (L(y \ z,y,x) * u)) * a(x * y,x * ((y * x) * z),u) = (x * z) * u. [back_rewrite(945),rewrite([3954(10),189(9)])]. given #1009 (W2w,wt=31): 4019 L(a(x,x * y,z),x * ((x \ y) * z),u) = (u * (x * ((x \ y) * z))) \ (u * (y * z)). [back_rewrite(664),rewrite([3954(2)])]. given #1010 (W2w,wt=31): 4021 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,x * ((y * x) * z),u). [back_rewrite(662),rewrite([3954(13),189(12)])]. given #1011 (W2w,wt=31): 4039 (x * y) * (y * ((T(T(z,u),w) * v5) * w)) = (x * y) * (y * ((T(T(z,w),u) * v5) * w)). [para(16(a,1),1599(a,1,2,2,1,2)),rewrite([16(12)])]. given #1012 (W2a,wt=35): 432 a(((x * y) * z) * (x * (y * z)),a(x,y,z),u) = a(x * (y * z),a(x,y,z) * ((x * y) * z),u). [para(175(a,1),110(a,1,2,1)),rewrite([175(10),19(17),54(14)])]. given #1013 (W2a,wt=33): 433 K(((x * y) * z) * (x * (y * z)),a(x,y,z)) = K(x * (y * z),a(x,y,z) * ((x * y) * z)). [para(175(a,1),114(a,1,2)),rewrite([427(8),20(15),54(14)])]. given #1014 (W2r,wt=34): 36747 L(L(L(x,y,z),u,w),v5,L(L(x,u,w),v6,T(v6,L(L(x,y,z),u,w))) \ v5) = L(L(x,y,z),u,w). [para(26139(a,1),8192(a,1,1)),rewrite([26174(15)])]. given #1015 (W2r,wt=31): 44709 L(L(L(L(x,y,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(L(x,u,w),y,z),v5,v6). [para(6416(a,1),229(a,1,1,1)),flip(a)]. given #1016 (W2r,wt=35): 4046 T(x * y,y * ((T(T(z,u),w) * (w * v5)) * w)) = T(x * y,y * ((T(T(z,w),u) * (w * v5)) * w)). [para(1599(a,1),1708(a,1,2)),rewrite([1708(10)]),flip(a)]. given #1017 (W2r,wt=35): 9282 R(R(T(T(T(T(T(x,y),z),u),w),v5),v6,v7),v8,v9) = R(R(T(T(T(T(T(x,v5),y),z),u),w),v8,v9),v6,v7). [para(94(a,1),8758(a,2,1,1,1,1))]. given #1018 (W2r,wt=33): 39702 K((x * y) \ (y \ (x \ (y \ 1))),y * (x * (y * (x * (y * (y * (x * (y * (x * y))))))))) = 1. [back_rewrite(38938),rewrite([39506(5)])]. given #1019 (W0w,wt=10): 8223 a(x,y \ x,y \ 1) = 1. [para(3143(a,1),8106(a,1,2))]. given #1020 (W0w,wt=10): 8245 a(x * y,y,x \ 1) = 1. [para(3691(a,1),8111(a,1,3))]. given #1021 (W0w,wt=10): 8451 R(x,y,y \ (x \ 1)) = x. [para(82(a,2),989(a,1)),rewrite([4407(3),4407(7),16(8),4408(8),45(6),14(6)])]. given #1022 (W0w,wt=10): 9896 R(T(x,y),z,x) = T(x,y). [para(9874(a,1),31(a,1,1)),flip(a)]. given #1023 (W0w,wt=8): 47248 R(x,y,T(x,z)) = x. [para(7769(a,1),9896(a,1,1)),rewrite([7769(5)])]. given #1024 (W0w,wt=10): 10008 R(x,y / z,z / y) = x. [para(5359(a,1),104(a,1,2,2)),rewrite([14(5),16(4),10003(4)]),flip(a)]. given #1025 (W0w,wt=10): 10045 a(x,y / z,z / y) = 1. [para(5359(a,1),59(a,1,2,1,1,2)),rewrite([48(2),10003(4),10008(3),46(1),5359(4),48(3)]),flip(a)]. given #1026 (W0w,wt=10): 10221 L(x,y / z,z / y) = x. [para(6565(a,1),3266(a,1,3))]. given #1027 (W0w,wt=10): 10222 a(x / y,y / x,z) = 1. [para(6565(a,1),3301(a,1,1))]. given #1028 (W0w,wt=10): 12825 R(x \ 1,y,x) = x \ 1. [para(4505(a,1),6071(a,1,1)),rewrite([6564(3)]),flip(a)]. given #1029 (W0w,wt=10): 14869 a(x * (x / y),y,z) = 1. [para(100(a,1),60(a,1,2)),rewrite([14868(2),3228(4),15(2),46(5),14868(3)]),flip(a)]. given #1030 (W0w,wt=10): 15035 L(x,y,y * (z * z)) = x. [back_rewrite(5614),rewrite([14874(3)])]. given #1031 (W0w,wt=10): 16731 L(K(x,y),y,x) = K(x,y). [back_rewrite(16488),rewrite([16568(4)])]. given #1032 (W0w,wt=10): 16954 a(x,T(x,y),K(y,x)) = 1. [back_rewrite(8546),rewrite([16710(3)])]. given #1033 (W0w,wt=10): 16990 L(x * y,y,x) = x * y. [back_rewrite(6905),rewrite([16716(3),16202(4)])]. given #1034 (W0w,wt=10): 17666 L(K(x,y),x,y) = K(x,y). [hyper(24,a,16999,a)]. given #1035 (W0a,wt=19): 211 L(x,y,z) \ (z * (y * x)) = T(z * y,L(x,y,z)). [para(21(a,1),91(a,1,2)),rewrite([21(7)]),flip(a)]. given #1036 (W0a,wt=15): 494 L(R(x,L(x,y,z),u),y,z) = L(x,y,z). [para(480(a,1),33(a,1)),flip(a)]. given #1037 (W0r,wt=20): 8029 L(T(x,y) \ z,T(x,y),y \ x) = y \ ((x \ y) * z). [para(4505(a,1),3940(a,1,1,1)),rewrite([4505(4),4408(7)])]. given #1038 (W0r,wt=15): 960 (R(x,y,z) * u) / R(T(x,u),y,z) = u. [para(31(a,1),165(a,1,2))]. given #1039 (W0r,wt=16): 38503 L((x \ y) * z,y \ x,x) = x \ (y * z). [back_rewrite(21472),rewrite([38356(7)])]. given #1040 (W0r,wt=19): 20921 K(T(T(x,y),z) / u,w) = K(T(T(x,z),y) / u,w). [para(11449(a,1),16564(a,1,1)),rewrite([16564(6),16564(5),16564(9)])]. given #1041 (W0r,wt=12): 20850 L(x \ y,x \ 1,y) = x \ y. [para(3666(a,1),20613(a,1,2))]. given #1042 (W1w,wt=21): 8308 L(x,K(y,z),K(z,y) * (u * K(z,y))) = L(x,u,K(z,y)). [para(4993(a,1),132(a,1,1,2,2)),rewrite([14(3),8296(7),21(6)]),flip(a)]. given #1043 (W1w,wt=21): 8311 a(K(x,y) * (z * K(x,y)),K(y,x),u) = a(K(x,y),z,u). [para(4993(a,1),133(a,1,2,1,2,2)),rewrite([8296(5),14(6),19(7)]),flip(a)]. given #1044 (W1w,wt=21): 8403 L((x \ y) * z,R(x,x \ y,z),y * z) = (x \ y) * z. [para(81(a,2),6257(a,1,2))]. given #1045 (W1w,wt=21): 8706 L(K(x,y),y * x,z / (x * y)) = L(K(x,y),y * x,z). [para(63(a,1),3199(a,1,3,2))]. given #1046 (W1w,wt=21): 8753 R(T(T(T(x,y),z),u),w,v5) = R(T(T(T(x,u),z),y),w,v5). [para(29(a,1),3338(a,1,1,1))]. given #1047 (W1w,wt=21): 8754 R(T(T(T(x,y),z),u),w,v5) = R(T(T(T(x,z),y),u),w,v5). [para(29(a,1),3338(a,1,1))]. given #1048 (W1w,wt=21): 8781 T(T(T(T(x,y),z),u),T(T(x,u),z)) = T(T(T(x,u),z),y). [para(29(a,1),3341(a,1,1))]. given #1049 (W1w,wt=21): 8832 T(T(T(T(x,y),z),u),T(T(x,z),y)) = T(T(T(x,z),y),u). [para(29(a,1),3342(a,1,1))]. given #1050 (W1a,wt=27): 259 R(R(R(R(x,y,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v7,v8),u,w),y,z),v5,v6). [para(99(a,2),99(a,2,1))]. given #1051 (W1a,wt=25): 262 a(x,y,y \ z) \ (y * ((y \ x) * z)) = T(x * z,a(x,y,y \ z)). [para(16(a,1),209(a,2,1,2)),rewrite([169(5)])]. given #1052 (W1r,wt=25): 33965 T(x,R(T(y,x * x),z,u) / w) = T(x,R(y,z,u) * (x * (x / w))). [back_rewrite(25319),rewrite([33640(5)])]. given #1053 (W1r,wt=28): 15109 L(x,y * ((z * y) * (u * (y * (u * (y * z))))),w * (y * (u * (y * u)))) = x. [para(189(a,1),15045(a,1,2,2,2)),rewrite([189(6),404(6),189(7),189(10),101(9)])]. given #1054 (W1r,wt=29): 21880 K(T(x,y * z) * ((y * z) * a(x * (y * z),y,z)),R(x * (y * z),y,z)) = 1. [para(23(a,1),5299(a,1,1,1))]. given #1055 (W1r,wt=22): 10595 R(T(T(x / y,z),y * u),y,u) = T((y * u) \ (x * u),z). [para(85(a,2),537(a,1,1,1)),rewrite([31(3),31(5)])]. given #1056 (W1r,wt=23): 43648 T(K(x,y) * (z * z),y / x) = T(z * (z * K(x,y)),x \ y). [para(1014(a,1),19765(a,1,2)),rewrite([17781(3),17781(8),3143(11)])]. given #1057 (W2w,wt=31): 4042 x * (y * ((T(T(z,u),w) * (w * v5)) * w)) = x * (y * ((T(T(z,w),u) * (w * v5)) * w)). [para(18(a,1),1599(a,1,1)),rewrite([18(9)])]. given #1058 (W2w,wt=31): 4048 R(R(R(R(x,y / z,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v5,v6),v7,v8),u,w),y / z,z). [para(35(a,1),2372(a,2,1))]. given #1059 (W2w,wt=31): 4057 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,w),z),y),v5),u \ 1) / u. [para(29(a,1),3794(a,1,1,1,1,1))]. given #1060 (W2w,wt=31): 4058 T(T(T(T(T(x,y),z \ 1),u),w),v5) / z = T(T(T(T(T(x,w),y),u),v5),z \ 1) / z. [para(29(a,1),3794(a,1,1,1,1))]. given #1061 (W2a,wt=33): 439 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) \ ((x * (y * z)) * (a(x,y,z) * u)) = u. [para(201(a,2),50(a,1,1))]. given #1062 (W2a,wt=33): 449 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v5,v6),v9,v10),y,z),v7,v8),u,w). [para(34(a,1),295(a,2,1,1))]. given #1063 (W2r,wt=32): 47331 R(R(R(R(x,y,z),u,w),v5,v6),v7,R(R(T(x,v8),u,w),v5,v6)) = R(R(R(x,u,w),v5,v6),y,z). [para(47248(a,1),244(a,1,1)),rewrite([31(9),31(8)]),flip(a)]. given #1064 (W2r,wt=33): 20330 (x / T(T(T(T(T(T(x,y),z),u),w),v5),v6)) * (T(T(T(T(T(T(x,y),z),v6),u),w),v5) / x) = 1. [para(13055(a,1),10082(a,1,1,2,1)),rewrite([88(2),19929(16),88(9)])]. given #1065 (W2r,wt=31): 43986 T(T(T(T(x / y,K(z,y \ x)),u),w),y * T(T(y \ x,u),w)) = T(T(y \ x,u),w). [para(12432(a,1),3847(a,1,2,2,1,1)),rewrite([12432(15)])]. given #1066 (W2r,wt=32): 18582 L(x,T(T(T(T(T(y,z),u),w),x \ 1),v5),T(T(T(T(T(y,v5),z),u),w),x \ 1) / x) = x. [para(4092(a,1),18466(a,1,3))]. given #1067 (W2r,wt=35): 47034 L(L(L(R(x,y \ 1,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(R(x,y \ 1,z),v5,v6),u,w). [para(76(a,1),44709(a,1,1)),rewrite([24261(6),24016(16)])]. given #1068 (W0w,wt=8): 49860 L(x,T(y,z),y) = x. [para(18604(a,1),439(a,1,2,2,1)),rewrite([4247(3),23(2),4505(4),4505(6),480(8),4505(4),13(6),32749(5),21(6)])]. given #1069 (W0w,wt=8): 50347 a(x,T(x,y),z) = 1. [hyper(25,a,49860,a)]. given #1070 (W0w,wt=8): 50365 L(x,y,T(y,z)) = x. [para(7769(a,1),49860(a,1,2))]. given #1071 (W0w,wt=8): 50401 a(T(x,y),x,z) = 1. [back_rewrite(22980),rewrite([50347(4)])]. given #1072 (W0w,wt=9): 48138 R(x,L(x,y,z),u) = x. [para(494(a,1),16487(a,1,1)),rewrite([16487(2)]),flip(a)]. given #1073 (W0w,wt=10): 18468 L(x,x \ (y \ 1),y) = x. [para(16487(a,1),4445(a,1)),flip(a)]. given #1074 (W0w,wt=10): 18592 L(x,T(y,x),x \ y) = x. [para(7616(a,1),18466(a,1,3))]. given #1075 (W0w,wt=10): 18608 L(x,T(y,x),y * x) = x. [para(23(a,1),18472(a,1,2))]. given #1076 (W0w,wt=10): 18650 L(x,y \ 1,x / y) = x. [para(1829(a,1),18472(a,1,2))]. given #1077 (W0w,wt=10): 19175 a(x,y * (y * x),z) = 1. [para(1300(a,1),4636(a,2)),rewrite([189(3),4578(2),2508(5),14882(3)])]. given #1078 (W0w,wt=10): 20345 a(x * y,T(x,y),y) = 1. [para(23(a,1),18604(a,1,2))]. given #1079 (W0w,wt=10): 20358 a(x,y \ 1,x * y) = 1. [para(1091(a,1),18604(a,1,2))]. given #1080 (W0w,wt=10): 20361 a(x / y,y \ 1,x) = 1. [para(1829(a,1),18604(a,1,2))]. given #1081 (W0w,wt=10): 20385 L(x * y,x,y) = x * y. [hyper(24,a,18742,a)]. given #1082 (W0w,wt=10): 20397 a(T(x,y),y,x * y) = 1. [para(90(a,1),18742(a,1,3))]. given #1083 (W0w,wt=10): 20404 a(T(x,y),x \ y,y) = 1. [para(2690(a,1),18742(a,1,3))]. given #1084 (W0a,wt=12): 495 R(R(x,y,z),x,u) = R(x,y,z). [para(480(a,1),35(a,1,1)),flip(a)]. given #1085 (W0a,wt=15): 496 R(R(x,R(x,y,z),u),y,z) = R(x,y,z). [para(480(a,1),35(a,1)),flip(a)]. given #1086 (W0r,wt=15): 25011 T(x * (y * y),K(y,x)) = x * (y * y). [para(6018(a,1),5120(a,1,2,1)),rewrite([17884(4)])]. given #1087 (W0r,wt=20): 47290 R(T(T(x,y),z),u,T(T(T(x,w),y),z)) = T(T(x,y),z). [para(94(a,1),47248(a,1,3))]. given #1088 (W0r,wt=15): 10718 a(x,(x / y) * z,L(z \ y,z,x)) = 1. [para(8701(a,2),6335(a,1,3))]. given #1089 (W0r,wt=19): 22354 T(T(x * (y * y),y),T(x * y,y)) = x * (y * y). [back_rewrite(13735),rewrite([22270(6)])]. given #1090 (W0r,wt=16): 10707 ((x * (y / z)) * z) \ x = L(y \ 1,z,x). [para(1829(a,1),8701(a,1,1)),rewrite([10215(5)]),flip(a)]. given #1091 (W1w,wt=21): 8961 T(T(T(x,y),z),u * (T(T(x,z),y) / u)) = T(T(x,z),y). [para(3305(a,1),3398(a,2)),rewrite([2853(9)])]. given #1092 (W1w,wt=21): 9018 (x * y) * T(z * (z * x),y) = x * (z * (z * (x * y))). [para(2647(a,1),3476(a,1,2)),rewrite([15(7)])]. given #1093 (W1w,wt=21): 9061 x \ (y * (z * (y \ (x / y)))) = y \ T(z,y \ (x / y)). [para(1014(a,1),3541(a,1,2,2,2,2)),rewrite([3143(6),4408(6),45(2),1014(12),3143(11),3143(11)])]. given #1094 (W1w,wt=21): 9223 T(T(x \ y,z),T(y / x,z) * u) = T(T(x \ y,z),u). [para(1708(a,1),3835(a,1,2,1)),rewrite([3848(11),3835(8)]),flip(a)]. given #1095 (W1w,wt=21): 9232 T(T(x \ y,z),T(y / x,z) \ u) = T(T(x \ y,z),u). [para(2642(a,1),3835(a,1,2,1)),rewrite([4215(11),3835(8)]),flip(a)]. given #1096 (W1w,wt=21): 9477 K(x * (x * (x * (x * (y / (x * x))))),x * (x * y)) = 1. [para(6233(a,1),2836(a,1,2,1)),rewrite([3228(3),46(1),14(2),18(3),100(3),37(4),100(2),18(6),1839(6),1839(4),18(9),100(9),13(10)])]. given #1097 (W1w,wt=21): 9556 (T(x * y,y * y) \ y) * x = K(y * (y * y),y \ x). [para(3947(a,1),115(a,1,2)),rewrite([5162(5),7004(7),16(4),16(3),9080(4),4501(7),5162(12),7004(14),16(11),16(10)])]. given #1098 (W1w,wt=21): 9901 R(R(R(x,y,z),u,w),v5,R(x,u,w)) = R(R(x,u,w),y,z). [para(9874(a,1),99(a,1,1)),flip(a)]. given #1099 (W1a,wt=27): 283 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v5,v6),y,z),u,w),v7,v8). [para(34(a,1),228(a,1,1,1)),flip(a)]. given #1100 (W1a,wt=27): 286 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,u,w),y,z),v5,v6),v7,v8). [para(97(a,1),228(a,1,1))]. given #1101 (W1r,wt=21): 24267 (x * (a(y,z,z \ (y \ x)) * u)) / u = L(x,y \ 1,z). [back_rewrite(5816),rewrite([24021(4),33(5),480(2)]),flip(a)]. given #1102 (W1r,wt=24): 33249 R(x,y * z,a(x,y,z)) \ ((x * y) * z) = (y * z) * a(x,y,z). [para(54(a,1),166(a,1,2))]. given #1103 (W1r,wt=23): 38815 (T(x,y) * (z * x)) \ (x * (T(x,y) * z)) = K(x,K(x,y) * z). [back_rewrite(33181),rewrite([38752(10)])]. given #1104 (W1r,wt=25): 37955 K(x \ y,T(T(T(y / x,z / (z * (x \ y))),u),w * (w * u))) = 1. [back_rewrite(14217),rewrite([37242(11),30703(10),37242(11),26921(10)])]. given #1105 (W1r,wt=24): 7120 L(T(T(T(x,y),z),u),w,T(T(T(x,z),u),y)) = T(T(T(x,z),u),y). [para(3337(a,1),1667(a,1))]. given #1106 (W2w,wt=31): 4059 T(T(T(T(T(x,y),z),u),w \ 1),v5) / w = T(T(T(T(T(x,u),y),z),v5),w \ 1) / w. [para(29(a,1),3794(a,1,1,1))]. given #1107 (W2w,wt=31): 4060 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,v5),y),z),w),u \ 1) / u. [para(29(a,1),3794(a,1,1))]. given #1108 (W2w,wt=31): 4062 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,w),y),v5),z),u \ 1) / u. [para(29(a,1),3794(a,2,1,1))]. given #1109 (W2w,wt=31): 4073 T(T(T(T(T(x,y),z),u \ 1),T(x,w)),v5) / u = T(T(T(T(x,y),z),v5),u \ 1) / u. [para(541(a,1),3794(a,2,1,1,1,1,1))]. given #1110 (W2a,wt=33): 450 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),y,z),v5,v6),v9,v10),u,w). [para(295(a,1),97(a,1)),flip(a)]. given #1111 (W2a,wt=33): 451 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),y,z),v7,v8),v5,v6),u,w). [para(295(a,1),97(a,2))]. given #1112 (W2r,wt=35): 18842 (x * (T(y,z) * (z * (u * (y * (z * (x * w))))))) / w = x * (T(y,z) * (z * (u * (y * (z * x))))). [para(4559(a,1),106(a,1,1,2)),rewrite([4559(15)])]. given #1113 (W2r,wt=31): 40228 (x * T(x,T(y \ 1,z * z))) / (T(y,z * (z / x)) * (x * (x / T(y,z * z)))) = 1. [para(7021(a,1),20620(a,1,2,2,2)),rewrite([2771(8,R),11265(5),33627(6),40139(14)])]. given #1114 (W2r,wt=35): 45637 K(K((x * y) * z,K(u,T(T(x * (x * (((x \ y) * z) / u)),w),v5))),T(T((x * y) * z,v5),w)) = 1. [para(35637(a,1),37774(a,1,2,1,1)),rewrite([37429(9),37429(10)])]. given #1115 (W2r,wt=34): 47368 R(x,T(T(T(T(T(y,z),u),w),v5 \ 1),v6) / v5,v5 / T(T(T(T(T(y,v6),z),u),w),v5 \ 1)) = x. [para(4092(a,2),10008(a,1,2))]. given #1116 (W2r,wt=35): 52445 T(x * (y * y),y) * (T(x * y,y * y) \ x) = T(x * y,y * y) * K(y * (y * y),y \ x). [para(9556(a,1),169(a,2,2)),rewrite([22270(4),4578(2)])]. given #1117 (Wf,wt=8): 56239 L(c8,c5,K(c6,c7)) != c8 # answer("aK2"). [back_rewrite(152),rewrite([52858(6)])]. given #1118 (Wf,wt=9): 56237 L(c26,c22,a(c23,c24,c25)) != c26 # answer("aa2"). [back_rewrite(156),rewrite([52858(7)])]. given #1119 (Wf,wt=10): 56238 L(K(c11,c12),c9,c10) != K(c11,c12) # answer("aK3"). [back_rewrite(153),rewrite([52858(6)])]. given #1120 (W0w,wt=8): 56858 R(x,x / y,y) = x. [back_rewrite(24303),rewrite([52953(4),52858(3),6018(3)])]. given #1121 (W0w,wt=8): 58833 L(x,1,y \ z) = x. [para(37955(a,1),33734(a,1,3)),rewrite([52858(3)])]. given #1122 (W0w,wt=8): 59418 L(x,1,T(y,z)) = x. [para(23(a,1),58833(a,1,3))]. given #1123 (W0w,wt=8): 59426 L(x,1,K(y,z)) = x. [para(16343(a,1),58833(a,1,3))]. given #1124 (W0w,wt=8): 59427 L(x,1,y * z) = x. [para(166(a,1),58833(a,1,3))]. given #1125 (W0w,wt=8): 59434 L(x,1,y / z) = x. [para(1014(a,1),59427(a,1,3))]. given #1126 (W0w,wt=9): 52858 L(x,y,z) = L(x,z,y). [back_rewrite(16398),rewrite([52573(4),4407(3),26903(4),52573(3),52596(3)])]. given #1127 (W0w,wt=9): 55660 L(L(x,y,z),y,z) = x. [back_rewrite(18473),rewrite([52858(4),8684(4)])]. given #1128 (W0w,wt=9): 57649 L(x,y,R(y,z,z)) = x. [back_rewrite(47741),rewrite([55819(4),52858(2)])]. given #1129 (W0w,wt=9): 59432 L(x,1,a(y,z,u)) = x. [para(4950(a,1),59418(a,1,3))]. given #1130 (W0w,wt=9): 59436 L(x,1,R(y,z,u)) = x. [para(22(a,1),59434(a,1,3))]. given #1131 (W0w,wt=9): 59443 a(R(x,y,y),x,z) = 1. [hyper(25,a,57649,a)]. given #1132 (W0w,wt=9): 59560 a(x,R(x,y,y),z) = 1. [para(161(a,1),59443(a,1,1)),rewrite([4582(4)])]. given #1133 (W0w,wt=10): 20407 a(x,y \ 1,y \ x) = 1. [para(3143(a,1),18742(a,1,3))]. given #1134 (W0w,wt=10): 20410 a(x,x * y,T(y,x)) = 1. [para(4505(a,1),18742(a,1,3)),rewrite([3954(3)])]. given #1135 (W0w,wt=10): 20555 a(x \ y,y,x \ 1) = 1. [para(3143(a,1),20341(a,1,1))]. given #1136 (W0a,wt=18): 499 R(R(R(x,y,z),u,w),x,v5) = R(R(x,y,z),u,w). [para(480(a,1),99(a,2,1,1))]. given #1137 (W0a,wt=18): 514 ((x * y) * z) / (T(x,y) * z) = R(y,T(x,y),z). [para(90(a,1),22(a,1,1,1))]. given #1138 (W0r,wt=17): 34025 (K(x / y,z) * x) \ (y * T(y \ x,z)) = 1. [back_rewrite(23126),rewrite([33753(11)])]. given #1139 (W0r,wt=13): 42471 K(K(x,y),K(y,T(x,z \ 1))) = 1. [para(4993(a,1),37860(a,1,1,2)),rewrite([14(3),6144(6),14(6),46(5),6144(4),14(4),37429(5)])]. given #1140 (W0r,wt=20): 51302 L(x \ (y * z),x \ (y / x),x * z) = x \ (y * z). [para(33450(a,1),20385(a,1,1)),rewrite([33450(10)])]. given #1141 (W0r,wt=18): 53738 K(x / ((x * (y / z)) * z),L(y \ 1,x,z)) = 1. [back_rewrite(51779),rewrite([52858(7)])]. given #1142 (W0r,wt=20): 40205 a(x / T(y,z * z),z,(y * (z * (z / x))) \ z) = 1. [para(7021(a,2),20341(a,1,1)),rewrite([40152(4)])]. given #1143 (W1w,wt=21): 9904 R(R(R(x,y,R(x,z,u)),w,v5),z,u) = R(R(x,z,u),w,v5). [para(9874(a,1),99(a,2,1))]. given #1144 (W1w,wt=21): 9909 R(R(R(x,y,z),u,R(x,w,v5)),w,v5) = R(R(x,w,v5),y,z). [para(9874(a,1),247(a,1,1)),flip(a)]. given #1145 (W1w,wt=21): 9978 T(x * (x * y),z * (x * (x * (y / z)))) = x * (x * y). [para(5067(a,1),2647(a,2)),rewrite([1839(5),2647(10)])]. given #1146 (W1w,wt=21): 9992 T(T(x \ y,z),u * (T(y / x,z) / u)) = T(x \ y,z). [para(5067(a,1),3835(a,1,2,1)),rewrite([9973(11),9209(6)]),flip(a)]. given #1147 (W1w,wt=21): 10258 K(x * ((y / x) * z),y * (y * ((x \ z) * (x / y)))) = 1. [back_rewrite(5291),rewrite([10215(6)])]. given #1148 (W1w,wt=21): 10259 K(((x / y) * z) * y,((z * (y / x)) * x) * (x / y)) = 1. [back_rewrite(5284),rewrite([10229(2),10215(8)])]. given #1149 (W1w,wt=21): 10314 K((x * (y / z)) * z,K(((z / y) * x) * y,y / z)) = 1. [back_rewrite(7466),rewrite([10229(5)])]. given #1150 (W1w,wt=21): 10315 K(K(((x / y) * z) * y,y / x),(z * (y / x)) * x) = 1. [back_rewrite(7465),rewrite([10229(2)])]. given #1151 (W1a,wt=27): 288 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v5,v6),u,w),y,z),v7,v8). [para(97(a,2),228(a,1,1))]. given #1152 (W1a,wt=27): 292 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v7,v8),v5,v6),y,z),u,w). [para(230(a,1),97(a,1,1)),flip(a)]. given #1153 (W1r,wt=21): 45471 K(K(x * y,K(y,T(T(x,z),u))),T(T(x * y,u),z)) = 1. [para(2918(a,1),37774(a,1,2,1,1)),rewrite([37429(3),37429(4)])]. given #1154 (W1r,wt=28): 59707 a(x * y,y * ((y \ x) * ((z * y) * u)),T((y \ z) * (y * u),x * y)) = 1. [para(190(a,1),20410(a,1,2))]. given #1155 (W1r,wt=26): 36148 K(L(R(R(x,y,z),u,w),v5,v6),L(L(R(R(x,u,w),y,z),v7,v8),v5,v6)) = 1. [para(241(a,1),28463(a,1,2))]. given #1156 (W1r,wt=30): 59812 ((T(T(x,y),z) * u) * w) / (T(T(T(x,z),u),y) * w) = R(u,T(T(T(x,y),z),u),w). [para(94(a,2),514(a,1,2,1))]. given #1157 (W1r,wt=29): 46232 a(a(K(x * y,z),y,T(x,y)),(K(x * y,z) * y) * T(x,y),T(x * y,z)) = 1. [para(16985(a,1),8137(a,1,3))]. given #1158 (W2w,wt=31): 4090 T(T(T(T(T(x,y \ 1),z),u),w),v5) / y = T(T(T(T(T(x,w),z),u),v5),y \ 1) / y. [para(94(a,1),3794(a,1,1,1,1))]. given #1159 (W2w,wt=31): 4091 T(T(T(T(T(x,y),z),u),w \ 1),v5) / w = T(T(T(T(T(x,z),y),u),v5),w \ 1) / w. [para(94(a,1),3794(a,1,1,1))]. given #1160 (W2w,wt=31): 4094 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,w),v5),y),z),u \ 1) / u. [para(94(a,1),3794(a,2,1,1))]. given #1161 (W2w,wt=31): 4095 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,w),y),u \ 1),z),v5) / u. [para(94(a,1),3794(a,2,1))]. given #1162 (W2a,wt=33): 452 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v5,v6),y,z),u,w),v9,v10),v7,v8). [para(295(a,2),97(a,1))]. given #1163 (W2a,wt=33): 453 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),y,z),v9,v10),u,w),v5,v6). [para(97(a,1),295(a,1,1))]. given #1164 (W2r,wt=31): 15743 (((T(x,y \ (y \ z)) * z) \ y) * y) * (x * (y \ (y \ z))) = K(z,T(x,y \ (y \ z))). [para(4404(a,1),20(a,1,2)),rewrite([15452(10)])]. given #1165 (W2r,wt=31): 13636 (T(x \ y,x) * ((x * z) * (y * x))) * u = T(x \ y,x) * ((x * z) * ((y * x) * u)). [para(190(a,1),4559(a,2,2,2)),rewrite([4505(5),2994(6),136(15)])]. given #1166 (W2r,wt=35): 31981 a((x * (y / z)) * z,u * (((z / y) * x) * y),R(u * (z / y),y / z,((z / y) * x) * y)) = 1. [para(27070(a,2),8111(a,1,3))]. given #1167 (W2r,wt=33): 50584 R(R(R(R(x,L(R(R(x,y,z),u,w),v5,v6),v7),u,w),v8,v9),y,z) = R(R(R(x,y,z),u,w),v8,v9). [para(48138(a,1),259(a,2,1))]. given #1168 (W2r,wt=31): 27188 T((x \ y) * (z * z),x * T(x,y \ x)) = T(z * (z * (x \ y)),x * ((y \ x) * x)). [para(18553(a,1),10900(a,1,1,1)),rewrite([27154(9),18553(13)])]. given #1169 (Wf,wt=12): 56236 L(a(c29,c30,c31),c27,c28) != a(c29,c30,c31) # answer("aa3"). [back_rewrite(157),rewrite([52858(7)])]. given #1170 (W0w,wt=8): 59838 R(x,T(y,x),y) = x. [para(101(a,1),514(a,1,1)),rewrite([547(4),19991(5),23407(5)]),flip(a)]. given #1171 (W0w,wt=10): 20558 a(T(x,y),y,y \ x) = 1. [para(4505(a,1),20341(a,1,1))]. given #1172 (W0w,wt=10): 20635 a(x * y,x \ 1,y) = 1. [para(3691(a,1),20387(a,1,2))]. given #1173 (W0w,wt=10): 20670 a(x,y * x,y \ 1) = 1. [para(3691(a,1),20541(a,1,3))]. given #1174 (W0w,wt=10): 20695 a(x,y * x,T(y,x)) = 1. [para(23(a,1),20551(a,1,3))]. given #1175 (W0w,wt=10): 20714 a(x,x / y,y \ 1) = 1. [para(1829(a,1),20551(a,1,3))]. given #1176 (W0w,wt=10): 20724 a(x,y,T(y \ x,y)) = 1. [para(7967(a,1),20551(a,1,3)),rewrite([4582(4)])]. given #1177 (W0w,wt=10): 20882 a(x \ y,T(y,x),x) = 1. [para(4505(a,1),20691(a,1,2))]. given #1178 (W0w,wt=10): 20924 a(x,x * y,K(y,x)) = 1. [para(16564(a,1),16999(a,1,3)),rewrite([3954(3)])]. given #1179 (W0w,wt=10): 21916 K(x,R(x,y \ x,y)) = 1. [para(18604(a,1),5299(a,1,1,2,2)),rewrite([4505(2),16711(2),4505(3),14(4),16875(3)])]. given #1180 (W0w,wt=10): 21920 K(x,R(x,y,x / y)) = 1. [para(20541(a,1),5299(a,1,1,2,2)),rewrite([18023(3),14(5),21063(4),17791(3),16(2)])]. given #1181 (W0w,wt=10): 22438 R(x,(x \ y) * y,z) = x. [back_rewrite(14904),rewrite([22398(2)])]. given #1182 (W0w,wt=10): 22816 a(x \ y,x,K(x,y)) = 1. [para(16710(a,1),16999(a,1,3))]. given #1183 (W0w,wt=10): 23365 a(T(x,y),y,K(y,x)) = 1. [para(17771(a,1),16999(a,1,3))]. given #1184 (W0w,wt=10): 24058 a(x,(x \ y) * y,z) = 1. [back_rewrite(15500),rewrite([23698(4),1091(3),4407(3),6132(4),4505(3),87(2)]),flip(a)]. given #1185 (W0w,wt=10): 24469 a(x,x * y,x \ y) = 1. [back_rewrite(6059),rewrite([24057(3)])]. given #1186 (W0a,wt=18): 516 ((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,y)). [para(90(a,1),22(a,1,2))]. given #1187 (W0a,wt=13): 517 x * T(T(y,x),z) = T(y,z) * x. [para(29(a,1),90(a,1,2))]. given #1188 (W0r,wt=17): 60466 K(x * ((x \ y) * z),K(x,y * (z * x))) = 1. [para(17(a,1),10314(a,1,2,1,1,1)),rewrite([3691(2),1014(3),23697(3),3691(7),17781(8),56584(6)])]. given #1189 (W0r,wt=14): 38761 L(x,K(x,y) * z,T(x,y) * z) = x. [back_rewrite(35265),rewrite([38713(2),38713(7)])]. given #1190 (W0r,wt=14): 61611 a(T(x,y * y),y,T(y \ x,y)) = 1. [para(7967(a,1),20558(a,1,3)),rewrite([30703(2)])]. given #1191 (W0r,wt=20): 34971 a(T(x,y / z),y \ (T(x,y) / z),y \ (z \ 1)) = 1. [back_rewrite(30438),rewrite([34858(6)])]. given #1192 (W0r,wt=18): 56854 L(T(x \ (x \ y),y),y,z) = T(x \ (x \ y),y). [back_rewrite(25263),rewrite([52953(5)])]. given #1193 (W1w,wt=21): 10684 T(x * (x * y),y) = x * (x * (x * (x * (y / (x * x))))). [back_rewrite(2301),rewrite([10624(4)]),flip(a)]. given #1194 (W1w,wt=21): 10824 K(T(x \ y,x) * (x * z),(T(y * x,x) * z) / x) = 1. [para(7967(a,1),2812(a,1,1,1)),rewrite([7775(6)])]. given #1195 (W1w,wt=21): 10905 T((x / (y * (y * z))) * (y * y),z * (x \ z)) = z \ x. [back_rewrite(6967),rewrite([10888(10),101(5),4209(6),4578(5)])]. given #1196 (W1w,wt=21): 10916 T(x * (x * (y \ z)),T(y,z)) = T((y \ z) * (x * x),z). [back_rewrite(5488),rewrite([10888(11),101(8),4209(9),4578(8)])]. given #1197 (W1w,wt=21): 10985 T(x * (x * y),x * (x / z)) = T(y * (x * x),z \ 1). [back_rewrite(7227),rewrite([10927(6)]),flip(a)]. given #1198 (W1w,wt=21): 11138 (x * (y * (x \ (z / x)))) * (T(y,x \ (z / x)) \ x) = z. [para(1014(a,1),3544(a,1,1,2,2,2)),rewrite([3143(6),4408(6),45(2),1014(11),3143(10),3143(10),4155(9)])]. given #1199 (W1w,wt=21): 11174 (x * (y * (x \ (z / x)))) \ z = T(y,x \ (z / x)) \ x. [para(3575(a,1),1091(a,1,1)),rewrite([4408(11),14(11)])]. given #1200 (W1w,wt=21): 11219 ((x \ y) / z) / T(x * y,z \ 1) = x \ (x \ (z \ 1)). [para(3640(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. given #1201 (W1a,wt=27): 300 R(R(R(R(x,y,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v5,v6),y,z),u,w),v7,v8). [para(35(a,1),245(a,1,1,1)),flip(a)]. given #1202 (W1a,wt=27): 304 R(R(R(R(x,y,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),y,z),v5,v6),v7,v8). [para(99(a,1),245(a,1,1))]. given #1203 (W1r,wt=27): 8836 T(T(T(x,y),z),u) * T(T(x,u),y) = T(T(x,u),y) * T(T(T(x,u),y),z). [para(3342(a,1),90(a,1,2)),flip(a)]. given #1204 (W1r,wt=30): 55954 L(T(x * y,x * z),u,L(y \ z,x,y)) = (u * L(y \ z,x,y)) \ (u * (x * z)). [back_rewrite(11076),rewrite([52858(5),52858(6),52858(8)])]. given #1205 (W1r,wt=21): 18481 L(x \ (y \ z),u,L((y * x) \ z,w,v5)) = x \ (y \ z). [para(5166(a,1),16487(a,1,1)),rewrite([16487(4)]),flip(a)]. given #1206 (W1r,wt=27): 19049 T(T(x,y) \ z,K(T(x,y) \ ((x \ y) * z),T(x \ y,y))) = T(x,y) \ z. [para(11221(a,1),12519(a,1,2,1,2,1)),rewrite([18962(4),6968(3),18962(6),6968(7),18962(10),4505(9),18962(14),6968(13)])]. given #1207 (W1r,wt=22): 32739 R(T(T(T(x,y),z),u),T(T(x,u),y),w) = T(T(T(x,u),y),z). [para(94(a,2),493(a,1,1))]. given #1208 (W2w,wt=31): 4097 T(T(T(T(T(x,y),z \ 1),u),w),v5) / z = T(T(T(T(T(x,w),u),y),v5),z \ 1) / z. [para(94(a,2),3794(a,1,1,1,1))]. given #1209 (W2w,wt=31): 4098 T(T(T(T(T(x,y),z),u),w),v5 \ 1) / v5 = T(T(T(T(T(x,u),y),z),w),v5 \ 1) / v5. [para(94(a,2),3794(a,1,1))]. given #1210 (W2w,wt=31): 4100 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,w),z),v5),y),u \ 1) / u. [para(94(a,2),3794(a,2,1,1))]. given #1211 (W2w,wt=31): 4101 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,w),y),v5),u \ 1),z) / u. [para(94(a,2),3794(a,2,1))]. given #1212 (W2a,wt=33): 455 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v5,v6),v9,v10),y,z),u,w),v7,v8). [para(97(a,1),295(a,2,1)),flip(a)]. given #1213 (W2a,wt=33): 457 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),v9,v10),y,z),v5,v6),u,w). [para(97(a,2),295(a,2,1)),flip(a)]. given #1214 (W2r,wt=33): 63349 a(x,y,T(T(T(z * (z * u),z \ (z \ 1)),w),y)) = a(x,y,T(T(T(z * (z * u),y),u),w)). [back_rewrite(63174),rewrite([63205(12)]),flip(a)]. given #1215 (W2r,wt=31): 12493 R(R(R(R(x,K(y,z),z),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v7,v8),K(y,z),z),v5,v6). [para(12432(a,1),909(a,1,1,1,1,3)),rewrite([12432(10)])]. given #1216 (W2r,wt=32): 33221 L(L(L(L(x,y,L(L(T(x,z),u,w),v5,v6)),v5,v6),v7,v8),u,w) = L(L(L(x,u,w),v5,v6),v7,v8). [para(33075(a,1),238(a,2,1)),rewrite([30(3),30(2)])]. given #1217 (W2r,wt=33): 24578 R((x \ (y / z)) * z,x \ y,(y \ x) * u) * (u / ((x \ y) * (a(x,y / z,z) * u))) = 1. [back_rewrite(22598),rewrite([24189(12)])]. given #1218 (W2r,wt=32): 28660 K(L(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10),R(R(R(R(x,v5,v6),y,z),v7,v8),u,w)) = 1. [para(250(a,2),28532(a,1,1))]. given #1219 (W0w,wt=6): 62296 R(x,y,y) = x. [para(89(a,1),516(a,1,1,2)),rewrite([4578(2),17(4),89(1)]),flip(a)]. given #1220 (W0w,wt=8): 62298 R(x,y,T(y,z)) = x. [para(159(a,1),516(a,1,1,2)),rewrite([38163(3),547(5),17(6),159(2)]),flip(a)]. given #1221 (W0w,wt=8): 62299 R(x,T(y,z),y) = x. [para(541(a,1),516(a,1,1,2)),rewrite([37045(3),17(6),541(3)]),flip(a)]. given #1222 (W0w,wt=9): 62359 R(x,L(y,z,u),y) = x. [para(26839(a,1),516(a,1,1,2)),rewrite([32180(3),17(6),26839(3)]),flip(a)]. given #1223 (W0w,wt=9): 64977 R(x,y,L(y,z,u)) = x. [para(55660(a,1),62359(a,1,2))]. given #1224 (W0w,wt=10): 24484 a(x * y,y \ x,z) = 1. [back_rewrite(1302),rewrite([24058(6)])]. given #1225 (W0w,wt=10): 24687 a(x / y,y * x,z) = 1. [back_rewrite(5529),rewrite([24596(6),1300(6)])]. given #1226 (W0w,wt=10): 25357 a(x,y * (x * y),z) = 1. [para(14(a,1),5524(a,1,2,1)),rewrite([45(3),70(3),4578(2),1708(4),14882(4),90(2)])]. given #1227 (W0w,wt=10): 25410 a(x * (y * x),y,z) = 1. [back_rewrite(3735),rewrite([25357(6)])]. given #1228 (W0w,wt=10): 26036 a(x \ y,x,K(y,x)) = 1. [para(16564(a,1),24597(a,1,3))]. given #1229 (W0w,wt=10): 26037 a(x,y * x,K(y,x)) = 1. [para(16568(a,1),24597(a,1,3)),rewrite([23494(3)])]. given #1230 (W0w,wt=10): 26039 a(x,x * y,K(x,y)) = 1. [para(16686(a,1),24597(a,1,3))]. given #1231 (W0w,wt=10): 26040 a(x,y \ 1,K(y,x)) = 1. [para(17781(a,1),24597(a,1,3))]. given #1232 (W0w,wt=10): 26352 R(x,y / x,K(y,x)) = x. [para(17822(a,1),16567(a,1,3))]. given #1233 (W0w,wt=10): 26353 a(x,y / x,K(y,x)) = 1. [para(17822(a,1),16999(a,1,3))]. given #1234 (W0w,wt=10): 26461 a(x * y,y,K(y,x)) = 1. [para(17884(a,1),16999(a,1,3))]. given #1235 (W0a,wt=15): 518 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(30(a,1),90(a,1,2))]. given #1236 (W0a,wt=15): 519 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(31(a,1),90(a,1,2))]. given #1237 (W0r,wt=15): 8011 T(x / y,T(x,y \ 1) / y) = x / y. [para(1010(a,1),4505(a,1,1)),rewrite([4338(11)]),flip(a)]. given #1238 (W0r,wt=13): 62818 K(x * (y / z),K(z / y,x)) = 1. [para(5359(a,1),60466(a,1,2,2,2)),rewrite([10229(3),101(5),10287(6),14(5)])]. given #1239 (W0r,wt=18): 25408 a(x,R(T(y,x),z,u) * (R(y,z,u) * x),w) = 1. [back_rewrite(7357),rewrite([25357(11)])]. given #1240 (W0r,wt=10): 62033 K(R(x,y,x / y),x) = 1. [para(21920(a,1),4993(a,1,1)),rewrite([13(5)])]. given #1241 (W0r,wt=14): 50437 a(x / y,T(x,z),T(x,z) \ y) = 1. [para(50347(a,1),10700(a,2)),rewrite([50353(6)])]. given #1242 (W1w,wt=21): 11445 K((x \ (x \ (y / z))) * (z * (x * x)),T(y,z \ 1)) = 1. [para(3710(a,1),1780(a,1,1,1)),rewrite([4155(8),4408(7),4408(6),45(5),4578(5)])]. given #1243 (W1w,wt=21): 11692 a(x * (y \ x),z,(x * z) \ y) = a(x,z,(x * z) \ y). [para(16(a,1),10700(a,1,3,2)),rewrite([4155(2),16(8)])]. given #1244 (W1w,wt=21): 11739 T(x * (y \ x),x * (y \ z)) = T(x * (y \ x),x \ z). [para(16(a,1),5469(a,1,2,2,2))]. given #1245 (W1w,wt=21): 11791 (x \ (y \ (y \ (x \ 1)))) * (x * (y * (y * z))) = x \ z. [para(3141(a,1),1607(a,1)),rewrite([189(5),101(2),189(4),4578(2),101(3),100(2),189(10),101(7),189(9),4578(7),2040(8),4501(11),1091(5),4407(5),5162(5)])]. given #1246 (W1w,wt=21): 11792 T(x * (y * y),z) \ ((z \ x) * (y * (y * x))) = z \ x. [para(3141(a,1),1667(a,1)),rewrite([11083(4)])]. given #1247 (W1w,wt=21): 11810 (x \ (y \ (y \ (z \ 1)))) * (z * (y * (y * z))) = x \ z. [para(3141(a,1),6279(a,1)),rewrite([37(4),16(2),189(5),101(2),189(4),4578(2),2040(3),37(9),16(7),189(10),101(7),189(9),4578(7),101(8),100(7),4501(11),1091(5),4407(5),5162(5)])]. given #1248 (W1w,wt=21): 12376 T(T(T(T(x,y),z),u),y \ T(T(x,z),u)) = T(T(x,z),u). [para(94(a,1),7769(a,1,1))]. given #1249 (W1w,wt=21): 12377 T(T(T(T(x,y),z),u),z \ T(T(x,u),y)) = T(T(x,u),y). [para(94(a,2),7769(a,1,1))]. given #1250 (W1a,wt=27): 306 R(R(R(R(x,y,z),u,w),v5,v6),v7,v8) = R(R(R(R(x,v5,v6),u,w),y,z),v7,v8). [para(99(a,2),245(a,1,1))]. given #1251 (W1a,wt=23): 323 (x * (y * (x * z))) * K(z,x * (y * x)) = z * (x * (y * x)). [para(114(a,1),16(a,1,2))]. given #1252 (W1r,wt=25): 24204 a((x / y) / y,T(x,y \ 1),z) = a(y,T(x,y \ 1) * (x / y),z). [back_rewrite(1887),rewrite([24189(8)]),flip(a)]. given #1253 (W1r,wt=30): 54342 L(R(x * (y * x),z,u),z * u,(x * (y * (x * z))) * u) = R(x * (y * x),z,u). [back_rewrite(45112),rewrite([52858(9)])]. given #1254 (W1r,wt=26): 15271 ((x / y) * (((y / x) * z) * u)) \ (z * u) = a(x / y,(y / x) * z,u). [para(4254(a,1),19(a,1,2,1)),rewrite([15266(8),15266(15)])]. given #1255 (W1r,wt=29): 63384 T(T(x \ y,x) * (x * z),(T(y * x,x) * z) / x) = T(x \ y,x) * (x * z). [hyper(28,a,10824,a)]. given #1256 (W1r,wt=28): 42170 a(T(x,(y * x) / z),(y * x) / z,T((x \ y) * (x / z),(y * x) / z)) = 1. [para(5560(a,1),5407(a,1,1))]. given #1257 (W2w,wt=31): 4122 R(R(R(R(x,y,z \ 1),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v7,v8),y,z \ 1),v5,v6). [para(1829(a,1),372(a,1,1,1,1,3)),rewrite([1829(10)])]. given #1258 (W2w,wt=31): 4125 L(R(R(R(x,y,z \ 1),u,w),v5,v6),v7,v8) = L(R(R(R(x,u,w),v5,v6),y,z \ 1),v7,v8). [para(1829(a,1),371(a,1,1,1,1,3)),rewrite([1829(10)])]. given #1259 (W2w,wt=31): 4126 R(R(R(R(x,y,z \ 1),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v5,v6),v7,v8),y,z \ 1). [para(1829(a,1),373(a,1,1,1,1,3)),rewrite([1829(11)])]. given #1260 (W2w,wt=31): 4129 R(R(R(R(x,y,z \ 1),u,w),v5,v6),v7,v8) = R(R(R(R(x,u,w),v7,v8),v5,v6),y,z \ 1). [para(1829(a,1),375(a,1,1,1,1,3)),rewrite([1829(11)])]. given #1261 (W2a,wt=33): 458 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),y,z),v5,v6),v7,v8),u,w). [para(295(a,1),230(a,1)),flip(a)]. given #1262 (W2a,wt=33): 459 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v5,v6),y,z),u,w),v7,v8),v9,v10). [para(295(a,2),230(a,1))]. given #1263 (W2r,wt=35): 36655 x * (T(x,y * y) * ((x * z) * K(T(x,y) * z,x * T(x,y)))) = (T(x,y) * z) * (x * T(x,y)). [para(16343(a,1),3184(a,1,2,2,2,1,1)),rewrite([33497(6),547(7),33992(11),16343(13),33497(14),547(15)])]. given #1264 (W2r,wt=35): 49808 T(T(T(T(T(x,y * T(x,z)),u \ 1),w),z),v5) / u = T(T(T(T(T(x,z),y),w),v5),u \ 1) / u. [para(23443(a,1),4058(a,2,1,1,1,1))]. given #1265 (W2r,wt=31): 39205 ((x * (y * (z * (y * z)))) * K(y,z * T(z,y))) / (x * T(y * (z * (y * z)),z)) = 1. [back_rewrite(39009),rewrite([39111(7)])]. given #1266 (W2r,wt=35): 22710 K(x / y,((y / x) * z) * ((u * (x / y)) * y)) = K(x / y,(z * (x / y)) * (((y / x) * u) * x)). [para(13569(a,1),16686(a,1,2)),flip(a)]. given #1267 (W2r,wt=33): 31902 x * (x * (y * ((z * (x * (x * y))) * K(y,u)))) = x * (x * ((y * z) * (x * (x * T(y,u))))). [para(16716(a,1),2979(a,1,2,2,2,2,2)),flip(a)]. given #1268 (W0w,wt=10): 26482 R(x,T(y,x),K(y,x)) = x. [para(17910(a,1),16567(a,1,3))]. given #1269 (W0w,wt=10): 26501 a(T(x,y),y,K(x,y)) = 1. [para(17910(a,1),24597(a,1,3))]. given #1270 (W0w,wt=10): 26595 a(x,y \ 1,K(x,y)) = 1. [para(17913(a,1),16999(a,1,3))]. given #1271 (W0w,wt=10): 26631 a(x,y \ x,K(y,x)) = 1. [para(17914(a,1),16999(a,1,3)),rewrite([19659(3)])]. given #1272 (W0w,wt=10): 26647 a(x,x / y,K(y,x)) = 1. [para(17914(a,1),24597(a,1,3))]. given #1273 (W0w,wt=10): 26768 a(x,y / x,K(x,y)) = 1. [para(17924(a,1),24597(a,1,3))]. given #1274 (W0w,wt=10): 26987 a(x * (y / x),y,x) = 1. [para(15(a,1),26047(a,1,2)),rewrite([19074(2)])]. given #1275 (W0w,wt=10): 27009 a(x,y \ (x \ y),y) = 1. [para(3666(a,1),26047(a,1,1)),rewrite([24189(5)])]. given #1276 (W0w,wt=10): 27459 L(x,y,z * (y * z)) = x. [para(5600(a,1),21(a,1,1)),rewrite([27454(6),24558(10),6600(11),45(5),27454(11),3050(12)])]. given #1277 (W0w,wt=10): 28511 T(x,L(x,y,z) \ x) = x. [para(26839(a,1),7769(a,1,1))]. given #1278 (W0w,wt=10): 28622 K(L(x \ 1,y,z),x) = 1. [para(28463(a,1),17913(a,1)),flip(a)]. given #1279 (W0w,wt=10): 28697 K(x,L(x \ 1,y,z)) = 1. [para(28532(a,1),17781(a,1)),flip(a)]. given #1280 (W0w,wt=10): 28737 R(x,y * x,K(y,x)) = x. [para(18043(a,1),16567(a,1,3))]. given #1281 (W0w,wt=10): 28747 a(x * y,y,K(x,y)) = 1. [para(18043(a,1),24597(a,1,3))]. given #1282 (W0w,wt=10): 28795 R(x,x / y,K(x,y)) = x. [para(18412(a,1),16567(a,1,3))]. given #1283 (W0w,wt=10): 28796 a(x,x / y,K(x,y)) = 1. [para(18412(a,1),16999(a,1,3))]. given #1284 (W0a,wt=17): 522 x * ((x \ y) * (z * x)) = (y * x) * T(z,x). [para(90(a,1),104(a,1,2,2))]. given #1285 (W0a,wt=18): 536 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(22(a,1),92(a,1,1)),rewrite([31(3)]),flip(a)]. given #1286 (W0r,wt=13): 37775 K(K(x,T(y,z)),T(T(x,y),z)) = 1. [back_rewrite(22877),rewrite([37242(2)])]. given #1287 (W0r,wt=17): 33996 T(x,y) * (K(x,y) * z) = T(x,y * y) * z. [back_rewrite(22926),rewrite([33705(8)])]. given #1288 (W0r,wt=13): 13425 T(T(T(x,y),z),y \ 1) = T(x,z). [para(7769(a,1),4214(a,2)),rewrite([8018(7)])]. given #1289 (W0r,wt=18): 44572 a(x,T(T(y,z),u) \ x,T(T(T(y,x),z),u)) = 1. [para(94(a,1),6274(a,1,3))]. given #1290 (W0r,wt=12): 6022 L(L(x,y,z),x,u) = L(x,y,z). [para(6018(a,1),34(a,1,1)),flip(a)]. given #1291 (W1w,wt=21): 12380 T(T(T(x \ y,z),u),u \ T(y / x,z)) = T(x \ y,z). [para(7769(a,1),3352(a,1,1)),rewrite([537(3)]),flip(a)]. given #1292 (W1w,wt=21): 12406 T(x \ y,T(T(T(y / x,z),z \ (x \ y)),u)) = x \ y. [para(7769(a,1),3835(a,1,1)),rewrite([7769(13)])]. given #1293 (W1w,wt=21): 12937 K(x * (y \ x),z * ((x / y) * ((x / y) * (y / z)))) = 1. [para(18(a,1),8260(a,1,1,2)),rewrite([4230(2)])]. given #1294 (W1w,wt=21): 12957 K(x * (x * y),x * ((z * x) * (x * (y / (x * z))))) = 1. [para(189(a,1),8260(a,1,2))]. given #1295 (W1w,wt=21): 13017 K(K((x \ (x \ y)) * z,(y * z) \ (x * y)),x \ y) = 1. [para(4357(a,1),10144(a,1,2)),rewrite([7552(8)])]. given #1296 (W1w,wt=21): 13051 T(T(T(x \ 1,y),z),x * u) = T(T(T(x \ 1,u),y),z). [para(996(a,1),3825(a,1,1,1,1)),rewrite([4408(7),45(6),1018(10)])]. given #1297 (W1w,wt=21): 13104 T(T(T(T(T(x,y),z),u),w),y \ 1) = T(T(T(x,z),u),w). [para(7769(a,1),3825(a,2,1,1,1)),rewrite([8018(7)])]. given #1298 (W1w,wt=21): 13123 T(T(T(x \ y,z),u),T(y / x,u)) = T(T(x \ y,u),z). [para(29(a,1),3831(a,1,1))]. given #1299 (W1a,wt=25): 324 (x * (y * z)) \ ((x \ z) * (x * (y * x))) = K(x \ z,x * (y * x)). [para(16(a,1),114(a,1,1,2,2))]. given #1300 (W1a,wt=26): 342 R(x / (y * (y * z)),y * (y * z),u) = (x * u) / (y * (y * (z * u))). [para(18(a,1),148(a,1,1,1)),flip(a)]. given #1301 (W1r,wt=24): 59863 T(T((x * y) * z,T(x,y) * z),R(y,T(x,y),z)) = (x * y) * z. [para(514(a,1),29529(a,1,2))]. given #1302 (W1r,wt=24): 54885 T(x \ T(y * ((y \ x) * z),u),x) = x \ T(L(z,x,y) * x,u). [back_rewrite(34610),rewrite([52858(7)])]. given #1303 (W1r,wt=23): 2214 (x * (y * (z * (y * x)))) \ (x * (y * (z * (y * (x * u))))) = u. [para(130(a,1),15(a,1,2))]. given #1304 (W1r,wt=23): 16868 K((x * ((y * x) * z)) * u,K(x,((x \ y) * (x * z)) * u)) = 1. [back_rewrite(13486),rewrite([16686(10)])]. given #1305 (W1r,wt=28): 64741 a(T(T(x * (x * y),y) \ z,z),z,T(x * (x * y),z * ((z / x) / x))) = 1. [para(63349(a,2),5407(a,1)),rewrite([57104(5),30703(13),38975(13),50886(11)])]. given #1306 (W2w,wt=31): 4130 R(R(R(R(x,y,z \ 1),u,w),v5,v6),v7,v8) = R(R(R(R(x,v5,v6),u,w),v7,v8),y,z \ 1). [para(1829(a,1),376(a,1,1,1,1,3)),rewrite([1829(11)])]. given #1307 (W2w,wt=31): 4168 x * (x * ((x * (y * (x * (x * z)))) * (z \ x))) = x * (x * (x * (y * (x * (x * x))))). [back_rewrite(3956),rewrite([4155(6)])]. given #1308 (W2w,wt=31): 4170 (x * (y * (x * (z * (x * (y * u)))))) * (u \ x) = x * (y * (x * (z * (x * (y * x))))). [back_rewrite(3893),rewrite([4155(8)])]. given #1309 (W2w,wt=31): 4237 R(T(x * (y * x),(x * (y * (x * z))) * u),z,u) = R(T(x * (y * x),z * u),z,u). [para(119(a,1),2643(a,1,1)),rewrite([31(8),1426(14)])]. given #1310 (W2a,wt=33): 460 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),v9,v10),y,z),u,w),v5,v6). [para(230(a,1),295(a,2,1)),flip(a)]. given #1311 (W2a,wt=33): 470 L(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(R(R(R(R(x,v7,v8),u,w),y,z),v5,v6),v9,v10). [para(35(a,1),249(a,1,1,1,1))]. given #1312 (W2r,wt=31): 67230 K(K(x,T(T(T(y,z),u),w)),T(T(T(x,T(T(T(y,u),v5),z)),w),v5 \ T(T(y,z),u))) = 1. [para(12377(a,1),37774(a,1,1,2,1))]. given #1313 (W2r,wt=31): 66121 K(K((R(x,y,z) * (u / w)) * w,w / u),(R(T(x,u / w),y,z) * (w / u)) * u) = 1. [para(519(a,1),10315(a,1,1,1,1))]. given #1314 (W2r,wt=35): 67347 ((x \ y) * (z * (z * T(x,y)))) * K(x,T((x \ y) * (z * z),y)) = T(x,y) * ((x \ y) * (z * z)). [para(7969(a,1),323(a,1,1,2)),rewrite([22202(6),4505(3),7715(12),4578(9),37242(10),7715(18),4578(15)])]. given #1315 (W2r,wt=32): 61989 K(x * (y * (x * z)),R(x * (y * (x * z)),K(x * (y * x),z),z * (x * (y * x)))) = 1. [para(115(a,1),21916(a,1,2,2))]. given #1316 (W2r,wt=35): 66593 K(T(T((x \ y) * y,y * (x \ z)),u) * (y \ x),T(T(y * (x \ y),y \ z),u) * (y \ x)) = 1. [para(11739(a,1),6212(a,1,2,1,1)),rewrite([4155(8),4155(15)])]. given #1317 (W0w,wt=8): 69001 R(x,y,x / y) = x. [para(5067(a,1),536(a,2,1)),rewrite([3032(5),19074(4),23(6),5067(3)]),flip(a)]. given #1318 (W0w,wt=9): 69551 T(x,K(x * x,y)) = x. [back_rewrite(42539),rewrite([69337(7),16716(4)])]. given #1319 (W0w,wt=9): 69569 T(x,T(x * x,y)) = x. [back_rewrite(42517),rewrite([69551(6)])]. given #1320 (W0w,wt=9): 69586 T(x,K(y,T(x,z))) = x. [para(12432(a,1),13425(a,1,1)),rewrite([12372(4)]),flip(a)]. given #1321 (W0w,wt=9): 71566 K(x,K(x * x,y)) = 1. [hyper(27,a,69551,a)]. given #1322 (W0w,wt=9): 71590 T(x,K(y,x * x)) = x. [para(69551(a,1),7769(a,1,1)),rewrite([6144(3),71587(3),1708(4)])]. given #1323 (W0w,wt=9): 71605 K(K(x * x,y),x) = 1. [para(69551(a,1),16687(a,1,2)),rewrite([47(1)]),flip(a)]. given #1324 (W0w,wt=9): 71672 K(K(x,y * y),y) = 1. [back_rewrite(42542),rewrite([71566(6)])]. given #1325 (W0w,wt=9): 71724 K(x,T(x * x,y)) = 1. [hyper(27,a,69569,a)]. given #1326 (W0w,wt=9): 71768 K(x * x,T(x,y)) = 1. [para(69569(a,1),16687(a,1,2)),rewrite([47(1),37242(4)]),flip(a)]. given #1327 (W0w,wt=9): 71857 K(x,K(y,T(x,z))) = 1. [hyper(27,a,69586,a)]. given #1328 (W0w,wt=9): 71899 K(K(x,T(y,z)),y) = 1. [para(69586(a,1),16687(a,1,2)),rewrite([47(1)]),flip(a)]. given #1329 (W0w,wt=9): 72000 K(x,K(y,x * x)) = 1. [para(17781(a,1),71566(a,1,2))]. given #1330 (W0w,wt=9): 72229 K(K(x,y),T(y,z)) = 1. [para(7769(a,1),71899(a,1,1,2))]. given #1331 (W0w,wt=9): 72271 K(K(x,y),T(x,z)) = 1. [para(17913(a,1),72229(a,1,1))]. given #1332 (W0w,wt=10): 28808 a(x,y \ x,K(x,y)) = 1. [para(18412(a,1),24597(a,1,3)),rewrite([19659(3)])]. given #1333 (W0a,wt=13): 542 T(T(T(x,y),z),x) = T(T(x,y),z). [para(159(a,1),29(a,1,1)),flip(a)]. given #1334 (W0a,wt=18): 545 R(T(T(x,y),R(x,z,u)),z,u) = R(T(x,y),z,u). [para(31(a,1),159(a,1,1)),rewrite([31(4),31(6)])]. given #1335 (W0r,wt=19): 22433 K(x \ (x \ y),(y \ x) * (x * ((y \ x) * x))) = 1. [back_rewrite(15907),rewrite([22398(5)])]. given #1336 (W0r,wt=19): 38903 (x * (y * (x * y))) \ (T(x * y,y) * (y * x)) = 1. [para(26074(a,1),2934(a,1,1)),rewrite([38864(6),38864(11),37242(12),4209(11),158(11)])]. given #1337 (W0r,wt=14): 39254 K(x,L(T(x,y * (y * z)),u,w)) = 1. [para(28478(a,1),16566(a,1,1)),rewrite([15576(5),37242(6),30(5),30703(4),37242(6),30(5),26921(4)]),flip(a)]. given #1338 (W0r,wt=12): 28464 T(T(x,y),L(x,z,u)) = T(x,y). [para(26839(a,1),29(a,1,1)),flip(a)]. given #1339 (W0r,wt=19): 45786 x / (y * (z * (y \ z))) = x / (z * (y * (z / y))). [para(18(a,1),24859(a,1,1)),flip(a)]. given #1340 (W1w,wt=21): 13311 a(x \ y,x,T(z,y * x)) = a(x,y * x,T(z,y * x)). [para(90(a,1),3968(a,1,3,2)),rewrite([7616(2),90(6),90(7)])]. given #1341 (W1w,wt=21): 13466 a(x,(x \ y) * (x * z),u) = a(x,x * ((y * x) * z),u). [para(187(a,1),133(a,1,1,2)),rewrite([104(9),37(10),4501(11),4498(9),2508(10)]),flip(a)]. given #1342 (W1w,wt=21): 13641 T(x,y) * ((y \ z) * (y * u)) = y \ (x * ((z * y) * u)). [para(4505(a,1),190(a,1,1)),rewrite([7550(11)])]. given #1343 (W1w,wt=21): 13712 K(x * (y * y),x * (y * (y * T(x * (y * y),z)))) = 1. [para(11295(a,1),2588(a,1,1)),rewrite([13663(7),13663(9),777(8),13668(10)])]. given #1344 (W1w,wt=21): 13759 K(K(x * y,(y \ x) * T(z,x * x)),z * (x * x)) = 1. [para(11295(a,1),10144(a,1,2)),rewrite([13663(6),4480(6)])]. given #1345 (W1w,wt=21): 13910 (x \ (y \ (y \ (z \ 1)))) * ((z * (y * (y * x))) * u) = u. [para(2254(a,1),13523(a,2)),rewrite([3436(4),3436(8),100(10),10809(11),4505(8),100(11),10981(11)])]. given #1346 (W1w,wt=21): 14132 T(T(T(T(T(x,y),z),u),w),y \ x) = T(T(T(x,z),u),w). [para(3825(a,1),12372(a,1,1)),rewrite([4408(7),14(7)])]. given #1347 (W1w,wt=21): 14164 T(a(x,y,z),(x * (y * z)) / ((x * y) * z)) = a(x,y,z). [para(54(a,1),12386(a,1,2,2))]. given #1348 (W1a,wt=28): 343 ((x * (y * (y * (z / u)))) * u) / (y * (y * z)) = R(x,y * (y * (z / u)),u). [para(18(a,1),148(a,1,2,2,2))]. given #1349 (W1a,wt=26): 346 ((x * (y * z)) * (y * u)) / (y * ((z * y) * u)) = R(x,y * z,y * u). [para(104(a,1),148(a,1,2,2)),rewrite([16(2),16(10)])]. given #1350 (W1r,wt=24): 71504 R(x * y,T(z * (z * y),T(x,y)),z \ (z \ T(x,y))) = x * y. [para(5364(a,1),69001(a,1,3))]. given #1351 (W1r,wt=30): 67433 L(R(x * (y \ x),z,u),z * u,(x * (y \ (x * z))) * u) = R(x * (y \ x),z,u). [para(3143(a,1),54342(a,1,1,1,2)),rewrite([3143(8),3143(12)])]. given #1352 (W1r,wt=29): 25980 T(T(T(T(T(x,y),z),u),w),T(T(T(T(x,u),z),y),w)) = T(T(T(T(x,y),z),u),w). [para(3342(a,1),12178(a,1,1,1)),rewrite([29(15),3342(15)])]. given #1353 (W1r,wt=23): 27447 ((x * (y * (x \ y))) / (x * (y / x))) * K(x,y) = x * (y / x). [para(20620(a,1),5560(a,1,2)),rewrite([18023(3),4407(10),6144(9),14(9),10229(8),20620(17),88(12)])]. given #1354 (W1r,wt=29): 33494 (x \ y) * (z * (z * (u * (z \ (z \ x))))) = (x \ y) * (x * T(u,z \ (z \ x))). [para(4404(a,1),168(a,2,2)),rewrite([168(6)]),flip(a)]. given #1355 (W2w,wt=31): 4253 (x / y) * ((x / y) * ((y * T(x * (y \ x),z)) / (x * (y \ x)))) = T(x * (y \ x),z). [back_rewrite(2297),rewrite([4230(4),4230(8),4230(13)])]. given #1356 (W2w,wt=31): 4315 ((x * (y \ z)) * T(y,z)) / T(x * z,a(x,y \ z,T(y,z))) = a(x,y \ z,T(y,z)). [para(2690(a,1),265(a,1,2,1,2))]. given #1357 (W2w,wt=31): 4418 ((T(T(x,y),z) * (z * u)) * z) \ (w \ 1) = ((T(T(x,z),y) * (z * u)) * z) \ (w \ 1). [back_rewrite(4045),rewrite([4407(8),4407(16)])]. given #1358 (W2w,wt=31): 4607 (x * (y * (z \ y))) \ ((T(x,y / z) * y) * (y / z)) = K(T(x,y / z) * y,y / z). [back_rewrite(893),rewrite([4578(4),2040(5),18(3),4230(2)])]. given #1359 (W2a,wt=33): 471 L(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(R(R(R(R(x,v7,v8),y,z),v5,v6),u,w),v9,v10). [para(35(a,1),249(a,1,1,1))]. given #1360 (W2a,wt=33): 472 L(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(R(R(R(R(x,v5,v6),y,z),u,w),v7,v8),v9,v10). [para(35(a,1),249(a,1,1))]. given #1361 (W2r,wt=33): 35715 ((T(x,y \ (z / y)) \ y) / z) * (u \ (u \ w)) = (y * (x * (y \ (z / y)))) \ (u \ (u \ w)). [para(3575(a,1),6953(a,2,1)),rewrite([4408(9),35675(10)])]. given #1362 (W2r,wt=31): 63529 K(K(x * (x * (y * ((z \ y) * (z \ y)))),x * (x * (z / (x * (x * y))))),y \ z) = 1. [para(10905(a,1),22782(a,1,2)),rewrite([10229(6),1839(3),37(6),3169(4)])]. given #1363 (W2r,wt=31): 67775 T(T(T(T(T(x,T(y \ x,y)),z \ 1),u),y),w) / z = T(T(T(x,u),w),z \ 1) / z. [para(12372(a,1),49808(a,2,1,1,1,1)),rewrite([3143(4),7967(2)])]. given #1364 (W2r,wt=33): 64397 T(x,(T(T(T(T(T(y,z),x \ 1),u),w),v5) / x) / T(T(T(T(T(y,w),u),x \ 1),z),v5)) = x. [para(4097(a,2),14495(a,1,2,1))]. given #1365 (W2r,wt=31): 48016 L(x * (y * z),y,z) \ T((y * z) * (x * y),z) = T(T(y,z),L(x * (y * z),y,z)). [para(7822(a,1),211(a,1,2)),rewrite([26903(4),4505(10),26903(13)])]. given #1366 (W0w,wt=10): 28957 a(x \ y,y,K(x,y)) = 1. [para(19567(a,1),16999(a,1,3))]. given #1367 (W0w,wt=10): 29166 R(x,y \ x,K(x,y)) = x. [para(23360(a,1),16567(a,1,3))]. given #1368 (W0w,wt=10): 29171 a(x \ y,y,K(y,x)) = 1. [para(23360(a,1),24597(a,1,3))]. given #1369 (W0w,wt=10): 29383 a(x * y,y * x,z) = 1. [para(23443(a,1),5524(a,1,2)),rewrite([23(4),1685(4),37(4),90(2),4209(5),2508(5)])]. given #1370 (W0w,wt=10): 32790 R(x * y,x,y) = x * y. [back_rewrite(20536),rewrite([32743(4)]),flip(a)]. given #1371 (W0w,wt=6): 75422 L(x,y,x) = x. [para(16(a,1),32790(a,2)),rewrite([16(2),52953(2)])]. given #1372 (W0w,wt=10): 33091 a(x,y * x,K(x,z)) = 1. [back_rewrite(23589),rewrite([33049(5),46(6)])]. given #1373 (W0w,wt=8): 75476 a(x,y,K(x,z)) = 1. [para(18(a,1),33091(a,1,2))]. given #1374 (W0w,wt=8): 75570 R(x,y,K(y,z)) = x. [back_rewrite(22892),rewrite([75493(3),17(4)]),flip(a)]. given #1375 (W0w,wt=8): 75589 a(x,y,K(z,x)) = 1. [para(17781(a,1),75476(a,1,3))]. given #1376 (W0w,wt=8): 75628 R(x,y,K(z,y)) = x. [para(17781(a,1),75570(a,1,3))]. given #1377 (W0w,wt=10): 33119 a(x / y,z,y \ x) = 1. [para(92(a,1),33049(a,1,3))]. given #1378 (W0w,wt=10): 33124 a(x * y,z,y * x) = 1. [para(4209(a,1),33049(a,1,3))]. given #1379 (W0w,wt=10): 33334 L(x,K(y,z),z * y) = x. [back_rewrite(2857),rewrite([33258(6),8296(4)]),flip(a)]. given #1380 (W0w,wt=10): 33423 a(x * y,K(y,x),z) = 1. [back_rewrite(609),rewrite([33346(4),46(5)]),flip(a)]. given #1381 (W0w,wt=10): 33440 a(x * y,K(x,y),z) = 1. [back_rewrite(19648),rewrite([33403(4),46(7)]),flip(a)]. given #1382 (W0a,wt=11): 547 T(x,y) * x = x * T(x,y). [para(159(a,1),90(a,1,2)),flip(a)]. given #1383 (W0a,wt=11): 548 T(x \ y,y / x) = x \ y. [para(92(a,1),159(a,1,1)),rewrite([92(5)])]. given #1384 (W0r,wt=19): 10920 T(x * (y * y),x / z) = T(y * (y * x),z \ 1). [back_rewrite(5480),rewrite([10888(6),101(2),4209(3),4578(2)])]. given #1385 (W0r,wt=14): 45211 a(T(T(x,y),z),y,T(x,z) \ y) = 1. [para(29(a,1),8221(a,1,1))]. given #1386 (W0r,wt=19): 20986 K(x * ((y * x) * z),x * y) = K(x * z,x * y). [para(189(a,1),16568(a,1,1))]. given #1387 (W0r,wt=17): 59923 K(x * T(x \ y,z),K(y / x,z) * y) = 1. [para(34025(a,1),16564(a,1,1)),rewrite([62(5)]),flip(a)]. given #1388 (W0r,wt=19): 59242 K(K(x,K(y,T(T(x / y,z),u))),T(T(x,u),z)) = 1. [para(5359(a,1),45637(a,1,1,1,1)),rewrite([13(2),10229(5),100(6),1839(7),10287(8),10287(5),5359(8),13(7)])]. given #1389 (W1w,wt=21): 14174 T(T(T(x,y),z),u / (u * T(T(x,z),y))) = T(T(x,z),y). [para(12386(a,1),94(a,2)),rewrite([29(7)])]. given #1390 (W1w,wt=21): 14200 T(T(x \ y,z),u / (u * T(y / x,z))) = T(x \ y,z). [para(12386(a,1),3835(a,1,2,1)),rewrite([14176(11),9209(6)]),flip(a)]. given #1391 (W1w,wt=21): 14601 T(T(T(x,y),z),u \ (T(T(x,z),y) \ u)) = T(T(x,z),y). [para(14186(a,1),94(a,2)),rewrite([29(7)])]. given #1392 (W1w,wt=21): 14627 T(T(x \ y,z),u \ (T(y / x,z) \ u)) = T(x \ y,z). [para(14186(a,1),3835(a,1,2,1)),rewrite([14602(11),9209(6)]),flip(a)]. given #1393 (W1w,wt=21): 14929 K(x * (x * y),z * (z * (x * (x * (y / (z * z)))))) = 1. [para(100(a,1),8260(a,1,2))]. given #1394 (W1w,wt=21): 15079 a((x / y) * (z * (x / y)),y / x,u) = a(x / y,z,u). [para(14083(a,1),133(a,1,2,1,2,2)),rewrite([15052(9),10287(5),14(6),19(7),15052(13)]),flip(a)]. given #1395 (W1w,wt=21): 15276 (x * y) / T(z * (x \ z),y) = (x / z) * ((x / z) * y). [para(4254(a,1),21(a,1,2)),rewrite([3436(4),10229(3),10229(4),1607(12)]),flip(a)]. given #1396 (W1w,wt=21): 15308 a(x / y,(y / x) * ((y / x) * z),u) = a(x / y,z,u). [para(4254(a,1),133(a,1,2,1,2)),rewrite([15276(8),37(8),10287(9),10287(6),19(7),15276(12),2508(12)]),flip(a)]. given #1397 (W1a,wt=29): 347 R(R(R(x,y * (y * z),u),w,v5),v6,v7) = R(R(R(x,w,v5),v6,v7),y * (y * z),u). [para(99(a,1),148(a,2)),rewrite([148(10)]),flip(a)]. given #1398 (W1a,wt=30): 360 (x * (y * (z * u))) * a(x,y * (z * y),y \ u) = (x * (y * (z * y))) * (y \ u). [para(16(a,1),312(a,1,1,2,2,2))]. given #1399 (W1r,wt=29): 44612 a(L(x,y,z * (u * z)),y \ (z \ (u \ (z \ 1))),z * (u * (z * (y * x)))) = 1. [para(132(a,1),6352(a,1,1)),rewrite([4407(8),39789(8)])]. given #1400 (W1r,wt=23): 63683 K(x * (x * y),y \ (z \ 1)) = K(x * (x * y),x * (x / z)). [para(10985(a,1),16343(a,1,2)),rewrite([5162(8),18956(8)])]. given #1401 (W1r,wt=27): 57364 T(x,y \ (z \ (y \ 1))) \ (y * (z * (y * (x * (y \ (z \ (y \ x))))))) = x. [back_rewrite(39772),rewrite([54309(8)])]. given #1402 (W1r,wt=30): 17760 K((((x * y) * z) * u) \ (((y \ x) * (y * z)) * u),R(y,(y \ x) * (y * z),u)) = 1. [para(183(a,1),14546(a,1,2))]. given #1403 (W1r,wt=23): 29547 T(x * (y * (x \ y)),y * (x * (y / x))) = x * (y * (x \ y)). [para(20620(a,1),26764(a,1,2)),rewrite([88(5)]),flip(a)]. given #1404 (W2w,wt=31): 4609 ((T(x,y / z) * y) * (y / z)) \ (x * (y * (z \ y))) = K(y / z,T(x,y / z) * y). [back_rewrite(840),rewrite([4578(9),2040(10),18(8),4230(7)])]. given #1405 (W2w,wt=31): 4640 x * (x * (((T(y,x) * (x * z)) / u) / T(x * (y * (x * (x * z))),u \ 1))) = u \ 1. [back_rewrite(3670),rewrite([4578(6),2040(7)])]. given #1406 (W2w,wt=31): 4652 K(x * (x * ((y * z) * (z * (x * (x * (y * (z * z))))))),x * (x * (y * (z * z)))) = 1. [back_rewrite(3424),rewrite([4578(3),4578(11)])]. given #1407 (W2w,wt=31): 4674 T(T(x,y) * (z * (z * u)),K(T(T(x,z),y) * (z * u),z)) = T(x,y) * (z * (z * u)). [back_rewrite(3315),rewrite([4578(3),2040(4),4578(13),2040(14)])]. given #1408 (W2a,wt=33): 473 L(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(R(R(R(R(x,v7,v8),u,w),v5,v6),y,z),v9,v10). [para(99(a,1),249(a,1,1,1))]. given #1409 (W2a,wt=33): 474 L(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(R(R(R(R(x,u,w),y,z),v5,v6),v7,v8),v9,v10). [para(99(a,1),249(a,1,1))]. given #1410 (W2r,wt=32): 54969 (x * (y * R(R(R(z,u,w),v5,v6),v7,v8))) / L(R(R(R(z,v5,v6),u,w),v7,v8),x,y) = x * y. [back_rewrite(31377),rewrite([52858(9)])]. given #1411 (W2r,wt=33): 78409 T(T(x,y) * T(z,u \ z),K(T(T(x,K(u,z)),y) * z,K(u,z))) = T(x,y) * T(z,u \ z). [para(16875(a,1),4674(a,1,1,2,2)),rewrite([28991(3),16875(10),16875(16),28991(14)])]. given #1412 (W2r,wt=32): 17569 a((x * (y / z)) * (((z / y) * u) * y),y / z,((z / y) * x) * ((u * (y / z)) * z)) = 1. [para(13569(a,1),6258(a,1,1))]. given #1413 (W2r,wt=31): 10351 K(((x / y) * z) * y,y / x) * ((z * (y / x)) * x) = (((x / y) * z) * y) * (y / x). [back_rewrite(4321),rewrite([10229(2),10229(11)])]. given #1414 (W2r,wt=33): 67839 K(K(x / y,(z * (x / y)) * (((y / x) * u) * x)),((y / x) * z) * ((u * (x / y)) * y)) = 1. [para(22710(a,1),12497(a,1,1))]. given #1415 (W0w,wt=10): 33797 a(K(x,y),T(y,x),z) = 1. [back_rewrite(22732),rewrite([33507(4),46(3)]),flip(a)]. given #1416 (W0w,wt=10): 36988 a(x \ y,z,y / x) = 1. [para(92(a,1),33128(a,1,1))]. given #1417 (W0w,wt=10): 37178 a(K(x,y),y \ x,z) = 1. [para(16564(a,1),33753(a,1,1))]. given #1418 (W0w,wt=10): 37179 a(K(x,y),y * x,z) = 1. [para(16568(a,1),33753(a,1,1))]. given #1419 (W0w,wt=10): 37181 a(K(x,y),x / y,z) = 1. [para(17822(a,1),33753(a,1,1))]. given #1420 (W0w,wt=10): 37182 a(K(x,y),T(x,y),z) = 1. [para(17910(a,1),33753(a,1,1))]. given #1421 (W0w,wt=10): 37183 a(K(x,y),y \ 1,z) = 1. [para(17913(a,1),33753(a,1,1))]. given #1422 (W0w,wt=10): 37184 a(K(x,y),x * y,z) = 1. [para(18043(a,1),33753(a,1,1))]. given #1423 (W0w,wt=10): 37187 a(T(x,y),K(x,y),z) = 1. [back_rewrite(23695),rewrite([37182(6)])]. given #1424 (W0w,wt=10): 37192 a(x,y \ z,z / y) = 1. [para(92(a,1),37006(a,1,2))]. given #1425 (W0w,wt=10): 37197 a(x,y * z,z * y) = 1. [para(4209(a,1),37006(a,1,2))]. given #1426 (W0w,wt=10): 37214 L(x,K(y,z),z \ y) = x. [para(16564(a,1),37107(a,1,2))]. given #1427 (W0w,wt=10): 37217 L(x,K(y,z),y / z) = x. [para(17822(a,1),37107(a,1,2))]. given #1428 (W0w,wt=10): 37218 L(x,K(y,z),T(y,z)) = x. [para(17910(a,1),37107(a,1,2))]. given #1429 (W0w,wt=9): 79307 L(x,1,L(y,z,u)) = x. [para(28532(a,1),37218(a,1,2)),rewrite([30(3),89(2)])]. given #1430 (W0w,wt=10): 37221 L(x,K(y,z),y * z) = x. [para(18043(a,1),37107(a,1,2))]. given #1431 (W0a,wt=13): 550 K(L(T(x,y),z,u),L(x,z,u)) = 1. [para(30(a,1),540(a,1,1))]. given #1432 (W0a,wt=13): 551 K(R(T(x,y),z,u),R(x,z,u)) = 1. [para(31(a,1),540(a,1,1))]. given #1433 (W0r,wt=20): 55733 K(K(L(x,y,T(z,x)),y),(y * (z \ x)) * T(z,x)) = 1. [back_rewrite(16506),rewrite([52858(2),52963(2)])]. given #1434 (W0r,wt=16): 10670 L(x,y,R(z / y,y,x)) = L(x,y,z * x). [para(85(a,2),3199(a,1,3))]. given #1435 (W0r,wt=18): 50398 a(x \ (y \ 1),T(x,z),K(z,x) * (x \ y)) = 1. [back_rewrite(24599),rewrite([50347(13)])]. given #1436 (W0r,wt=14): 57033 L(x * y,y,z) = (x * (y * z)) / z. [back_rewrite(4583),rewrite([52953(3)])]. given #1437 (W0r,wt=17): 47125 a((x * y) * z,y * z,R(x,y,z) \ 1) = 1. [para(166(a,1),8223(a,1,2))]. given #1438 (W1w,wt=21): 15338 K(K((x / y) * ((x / y) * z),(y / x) * (y / x)),z) = 1. [para(4254(a,1),6557(a,1,2)),rewrite([15276(5),1607(7)])]. given #1439 (W1w,wt=21): 15408 T(x \ y,y) * (T(x,y) * z) = T(x,y) \ ((x * y) * z). [para(4314(a,1),15(a,1,2)),flip(a)]. given #1440 (W1w,wt=21): 15411 a(T(x,y),T(x \ y,y),T(x,y) * z) = a(x,y,z) \ 1. [para(4314(a,1),19(a,1,1)),rewrite([4304(6),4525(5),2548(5)]),flip(a)]. given #1441 (W1w,wt=21): 15419 T(x * y,y) * (T(x,y) * z) = T(x,y) * ((x * y) * z). [para(4314(a,1),37(a,2,2)),rewrite([4304(5),7775(2)])]. given #1442 (W1w,wt=21): 15533 T(x * (x * (y \ x)),x * y) = (y \ x) * T(x * x,y). [back_rewrite(11112),rewrite([15498(9)])]. given #1443 (W1w,wt=21): 15593 a(x \ y,z * (x \ y),T(x,y)) = a(x \ y,z,y) \ 1. [para(4344(a,1),19(a,1,1)),rewrite([128(9),2690(7),2548(7)]),flip(a)]. given #1444 (W1w,wt=21): 15621 (((x \ y) * z) * y) \ (x \ y) = T(x,y) \ ((y \ x) / z). [para(4344(a,1),1091(a,1,1)),rewrite([4407(11),4407(10),4408(10),1014(10)])]. given #1445 (W1w,wt=21): 15700 T(x,y * T(z,x \ (x \ y))) = T(x,z * (x \ (x \ y))). [para(4397(a,1),2642(a,1,2)),rewrite([1708(5)]),flip(a)]. given #1446 (W1a,wt=25): 370 R(R(R(x,y,T(z,y)),u,w),v5,v6) = R(R(R(x,u,w),v5,v6),y,T(z,y)). [para(23(a,1),248(a,1,1,1,3)),rewrite([23(8)])]. given #1447 (W1a,wt=28): 379 R(x,y * (y * (z / u)),u) * (y * (y * z)) = (x * (y * (y * (z / u)))) * u. [para(18(a,1),341(a,1,2,2,2))]. given #1448 (W1r,wt=27): 42999 T(T(T(x * y,y) * z,y),T(y \ x,y) * (y * z)) = T(x * y,y) * z. [para(7967(a,1),7773(a,1,2,1)),rewrite([7775(2),7775(11)])]. given #1449 (W1r,wt=25): 46479 (((x * y) / (K(y,x) * z)) * (K(y,x) * (z * K(y,x)))) \ (y * x) = 1. [para(63(a,1),24428(a,1,2)),rewrite([37102(19)])]. given #1450 (W1r,wt=26): 55548 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y))))) = x * x. [back_rewrite(21507),rewrite([52858(6)])]. given #1451 (W1r,wt=21): 28122 K(((x \ y) * y) * z,K(x \ y,x * ((x \ y) * z))) = 1. [para(18454(a,1),17092(a,1,2,2,1)),rewrite([1014(6),17(4),3143(4),22398(2),3143(6),3143(7)])]. given #1452 (W1r,wt=25): 35408 K(T(T(T(x,y),z),u) / w,T(T(T(T(x,w \ 1),y),z),u) / w) = 1. [para(29(a,1),6220(a,1,2,1,1,1))]. given #1453 (W2w,wt=31): 4675 T(x * y,z) * (K(y,x) * (K(y,x) * u)) = K(y,x) * (T(x * y,z) * (K(y,x) * u)). [back_rewrite(3314),rewrite([4578(6),2040(7)])]. given #1454 (W2w,wt=31): 4714 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w))) = w. [back_rewrite(2032),rewrite([4578(8),2040(9)])]. given #1455 (W2w,wt=31): 4782 x * (x * (((y * z) * (x * (x * y))) * u)) = x * (x * (y * (z * (x * (x * (y * u)))))). [back_rewrite(410),rewrite([4578(3),2040(4)])]. given #1456 (W2w,wt=31): 4910 (T(T(x,y),z) * (y * u)) \ (T(x,z) * (y * (y * u))) = T(y,T(x,z) * (y * (y * u))). [back_rewrite(4748),rewrite([4814(14)])]. given #1457 (W2a,wt=33): 475 L(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(R(R(R(R(x,v7,v8),v5,v6),y,z),u,w),v9,v10). [para(99(a,1),249(a,2,1))]. given #1458 (W2a,wt=33): 476 L(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(R(R(R(R(x,v5,v6),v7,v8),y,z),u,w),v9,v10). [para(249(a,1),249(a,2))]. given #1459 (W2r,wt=33): 43834 T(x,(T(T(T(T(T(y,z),x \ 1),u),w),v5) / x) / T(T(T(T(T(y,u),z),x \ 1),w),v5)) = x. [para(3796(a,2),14495(a,1,2,1))]. given #1460 (W2r,wt=35): 59235 K(K((x * y) / z,K(u,T(T(x * (x * (((x \ y) / z) / u)),w),v5))),T(T((x * y) / z,v5),w)) = 1. [para(1014(a,1),45637(a,1,1,1)),rewrite([1014(6),1014(15)])]. given #1461 (W2r,wt=31): 79515 K(R(R(R(R(T(x,y),z,u),w,v5),v6,v7),v8,v9),R(R(R(R(x,v8,v9),w,v5),z,u),v6,v7)) = 1. [para(259(a,1),551(a,1,2)),rewrite([31(4),31(3),31(2)])]. given #1462 (W2r,wt=35): 11057 K(x * (y * (y * ((T(z,y * (y * y)) * x) * T(z * (y * y),y)))),x * T(z * (y * y),y)) = 1. [back_rewrite(5779),rewrite([11037(7),11037(14)])]. given #1463 (W2r,wt=34): 82079 a(x * y,R((y \ x) * T(x * x,y),z,u) * (R(x * (x * (y \ x)),z,u) * (x * y)),w) = 1. [para(15533(a,1),25408(a,1,2,1,1))]. given #1464 (Wf,wt=8): 87201 a(c3,K(c1,c2),c4) != 1 # answer("aK1"). [back_rewrite(38),rewrite([84171(6)])]. given #1465 (Wf,wt=9): 87200 a(c20,a(c17,c18,c19),c21) != 1 # answer("aa1"). [back_rewrite(42),rewrite([84171(7)])]. given #1466 (W0w,wt=8): 79981 L(x,y,K(z,x)) = x. [para(16623(a,1),57033(a,1,1)),rewrite([52858(2),38207(6),17(4)])]. given #1467 (W0w,wt=8): 80283 R(x,K(y,z),z) = x. [back_rewrite(62334),rewrite([79991(6),23360(4),8298(4)]),flip(a)]. given #1468 (W0w,wt=8): 80289 R(x,K(y,z),y) = x. [back_rewrite(20967),rewrite([79991(5),8298(4)]),flip(a)]. given #1469 (W0w,wt=8): 82782 R(x,y,y * y) = x. [para(55548(a,1),148(a,1,2,2)),rewrite([46865(13),82774(11),4613(6),18740(4),16(5),1014(4),17(2),82780(12),82774(10)]),flip(a)]. given #1470 (W0w,wt=8): 82978 a(x,K(y,z),y) = 1. [back_rewrite(81262),rewrite([82951(4)])]. given #1471 (W0w,wt=8): 83024 a(x,y,K(y,z)) = 1. [back_rewrite(75560),rewrite([82951(4)])]. given #1472 (W0w,wt=8): 89189 L(x,y,K(x,z)) = x. [para(17913(a,1),79981(a,1,3))]. given #1473 (W0w,wt=8): 89356 a(x,K(y,z),z) = 1. [para(17781(a,1),82978(a,1,2))]. given #1474 (W0w,wt=8): 89371 a(x,y,K(z,y)) = 1. [para(17781(a,1),83024(a,1,3))]. given #1475 (W0w,wt=9): 84171 a(x,y,z) = a(y,x,z). [back_rewrite(42930),rewrite([83255(3)])]. given #1476 (W0w,wt=10): 38154 a(K(x,y),x \ y,z) = 1. [para(16710(a,1),37180(a,1,1))]. given #1477 (W0w,wt=8): 89481 a(1,K(x,y),z) = 1. [para(555(a,1),38154(a,1,1)),rewrite([16343(3)])]. given #1478 (W0w,wt=8): 89485 a(1,x * y,z) = 1. [para(3317(a,1),38154(a,1,1)),rewrite([6144(4),21063(4),16985(3),90(3)])]. given #1479 (W0w,wt=8): 89486 a(1,x \ y,z) = 1. [para(3327(a,1),38154(a,1,1)),rewrite([6144(4),33497(4),7775(3),85250(4)])]. given #1480 (W0w,wt=8): 89488 a(1,T(x,y),z) = 1. [para(12303(a,1),38154(a,1,1)),rewrite([6144(3),28991(3),85241(4)])]. given #1481 (W0w,wt=9): 89508 a(1,a(x,y,z),u) = 1. [para(4950(a,1),89488(a,1,2))]. given #1482 (W0a,wt=11): 556 T(T(x,y),T(x,z)) = T(x,y). [para(541(a,1),29(a,1,1)),flip(a)]. given #1483 (W0a,wt=16): 559 R(T(x,R(T(x,y),z,u)),z,u) = R(x,z,u). [para(541(a,1),31(a,1)),rewrite([31(3)]),flip(a)]. given #1484 (W0r,wt=13): 17882 K(x,T(T(y,x),z)) = K(x,T(y,z)). [back_rewrite(17021),rewrite([17771(4)])]. given #1485 (W0r,wt=18): 14554 K(a(x,y,z),(x * (y * z)) / ((x * y) * z)) = 1. [para(54(a,1),14154(a,1,2,2))]. given #1486 (W0r,wt=17): 36090 (T(x,y) \ T(y,x \ y)) * z = (x \ y) * z. [back_rewrite(18978),rewrite([35978(5),27608(4),4230(3),33957(5),7789(4)])]. given #1487 (W0r,wt=17): 87780 a(x,(y * z) * (u * z),R(u / y,y,z)) = 1. [back_rewrite(47441),rewrite([85263(6)])]. given #1488 (W0r,wt=19): 71733 T(T(T(x,y),z),T(T(x * x,z),u)) = T(T(x,z),y). [para(69569(a,1),94(a,1,1)),rewrite([46094(7)]),flip(a)]. given #1489 (W1w,wt=21): 15737 ((x \ y) * y) * (z * (y \ (y \ x))) = T(z,y \ (y \ x)). [para(4404(a,1),15(a,1,2)),rewrite([15452(6)])]. given #1490 (W1w,wt=21): 15739 (x * T(y,z \ (z \ x))) / (z * (y * (z \ (z \ x)))) = z. [para(4404(a,2),17(a,1,1))]. given #1491 (W1w,wt=21): 15943 (x \ y) * (((y \ x) / z) * y) = (z \ (x \ y)) * T(x,y). [para(1014(a,1),4504(a,1,2,1)),rewrite([3143(9)])]. given #1492 (W1w,wt=21): 16118 (x * ((x \ y) * z)) \ (L(z,x,y) * y) = K(L(z,x,y),y). [back_rewrite(9738),rewrite([16103(5),16103(8)])]. given #1493 (W1w,wt=21): 16121 (L(x,y,z) * z) \ (y * ((y \ z) * x)) = K(z,L(x,y,z)). [back_rewrite(9648),rewrite([16103(2),16103(8)])]. given #1494 (W1w,wt=21): 16129 T(L(x,y,z) * z,y * ((y \ z) * x)) = L(x,y,z) * z. [back_rewrite(9639),rewrite([16103(2),16103(8)])]. given #1495 (W1w,wt=21): 16545 K(x \ (y / x),z * (x * (y \ x))) = K(z,x * (y \ x)). [back_rewrite(9087),rewrite([16343(10)])]. given #1496 (W1w,wt=21): 16575 K(x * T(y,z \ (z \ x)),K(z,y * (z \ (z \ x)))) = 1. [back_rewrite(15721),rewrite([16527(9)])]. given #1497 (W1a,wt=26): 383 R(x,y * z,y * u) * (y * ((z * y) * u)) = (x * (y * z)) * (y * u). [para(104(a,1),341(a,1,2,2)),rewrite([16(2),16(9)])]. given #1498 (W1a,wt=27): 418 (x * y) * (((x * y) \ z) * (x * ((y * x) * u))) = (z * (x * y)) * (x * u). [para(104(a,1),188(a,1,2,2,2,2,2)),rewrite([16(3),136(10),16(10)])]. given #1499 (W1r,wt=29): 21676 T(a(x,x * y,z),x * (x * ((y * z) / (x * ((x * y) * z))))) = a(x,x * y,z). [para(37(a,1),4950(a,1,2,1)),rewrite([1839(9)])]. given #1500 (W1r,wt=21): 27619 (((x * y) * z) * x) * (((z * x) \ ((x * y) \ z)) / z) = 1. [para(5674(a,1),193(a,2)),rewrite([27573(23),4407(9),193(12),169(11),4458(7),1014(10)])]. given #1501 (W1r,wt=26): 80698 (x \ y) * ((z * (y \ x)) * (L(z,x,y) * y)) = z * (T(z,y \ x) * y). [back_rewrite(25805),rewrite([80225(7)])]. given #1502 (W1r,wt=25): 89778 K(a(x,(x * y) * z,y),(x * y) * (z / R((x * y) * z,x,y))) = 1. [para(101(a,1),14554(a,1,2,1)),rewrite([84171(3),19991(12),10206(10),1014(10)])]. given #1503 (W1r,wt=23): 49458 T(x \ y,K(x,y) * (z * z)) = T(x \ y,z * (z * K(x,y))). [para(43648(a,2),23380(a,1,2)),rewrite([29196(7)])]. given #1504 (W2w,wt=31): 4912 K(T(T(x,y),z) * (y * u),T(T(T(x,z),y) * (y * u),T(x,z) * (y * (y * u)))) = 1. [back_rewrite(4720),rewrite([4814(9),4278(14),4753(9)])]. given #1505 (W2w,wt=31): 5027 (x * (y * (z \ y))) * K(T(x,y / z) * y,y / z) = (T(x,y / z) * y) * (y / z). [back_rewrite(4608),rewrite([5005(9)])]. given #1506 (W2w,wt=31): 5188 x * (x * (y * (z * (x * (x * (y * ((y * (z * (x * (x * y)))) \ (x \ (x \ u))))))))) = u. [back_rewrite(3084),rewrite([5162(7)])]. given #1507 (W2w,wt=31): 5310 (((x * y) * z) / y) * ((y \ x) * (y * z)) = ((y \ x) * (y * z)) * (((x * y) * z) / y). [para(2812(a,1),63(a,1,2)),rewrite([14(9)])]. given #1508 (W2a,wt=32): 597 (x * (y * z)) * (((x * (y * z)) \ u) * ((x * y) * z)) = (u * (x * (y * z))) * a(x,y,z). [para(54(a,1),104(a,1,2,2))]. given #1509 (W2a,wt=34): 600 ((x * y) * (y * z)) / (y * (y * (z * a(x,y,y * z)))) = R(x,y * (y * z),a(x,y,y * z)). [para(54(a,1),148(a,1,1))]. given #1510 (W2r,wt=32): 30541 R(T(x,y) \ (T(x,y) \ (z / u)),u,T(T(x,z),y)) = (T(x,y) \ z) / (u * T(T(x,z),y)). [back_rewrite(21797),rewrite([30432(5)])]. given #1511 (W2r,wt=33): 70206 (T(T(T(x * x,y),z),u) * w) * T(T(T(T(x \ 1,y),z),u),w) = T(T(T(x,y),z),u) * w. [para(13051(a,1),5226(a,1,1,2,1)),rewrite([13051(6),70205(11),70205(10),68297(8),46094(5),46094(3),70154(12),13051(18),70205(18)])]. given #1512 (W2r,wt=31): 56793 K(L(x * ((y * (z * u)) / u),x,w),(w * x) / (w * L(x * (x * (y * z)),y,u))) = 1. [back_rewrite(31759),rewrite([52953(11)])]. given #1513 (W2r,wt=31): 47328 L(R(R(x,y,z),u,w),v5,R(R(R(T(x,v6),u,w),v7,T(x,v8)),y,z)) = R(R(x,u,w),y,z). [para(47248(a,1),36208(a,1,1,1,1)),rewrite([47269(11)])]. given #1514 (W2r,wt=33): 82278 (((x * y) \ z) * (u * (u / x))) \ (y \ (x \ 1)) = T(y * (u * u),x \ 1) \ ((x * y) / z). [para(10985(a,1),15621(a,2,1)),rewrite([5162(5),15(3),1829(2),35645(4),5162(10),15(8),1829(7),15452(19),1091(17),10229(17),14(17),18(16)])]. given #1515 (W0w,wt=10): 38195 L(x,K(y,z),y \ z) = x. [para(16710(a,1),37216(a,1,2))]. given #1516 (W0w,wt=10): 38196 L(x,K(y,z),T(z,y)) = x. [para(17771(a,1),37216(a,1,2))]. given #1517 (W0w,wt=10): 38199 L(x,K(y,z),z / y) = x. [para(17914(a,1),37216(a,1,2))]. given #1518 (W0w,wt=10): 38648 R(x,y,(y \ z) * z) = x. [back_rewrite(9487),rewrite([38534(5),14(4)])]. given #1519 (W0w,wt=10): 38710 R(K(x,y),x,z) = K(x,y). [para(16716(a,1),170(a,1,1,1)),rewrite([6144(4),28991(4),33781(7),8296(6),20961(4)])]. given #1520 (W0w,wt=10): 39244 T(x,L(T(x,y),z,u)) = x. [para(7769(a,1),28478(a,2)),rewrite([29(3),7769(3)])]. given #1521 (W0w,wt=10): 44515 a(x,y,T(x \ y,y)) = 1. [para(2690(a,1),6265(a,1,1)),rewrite([4281(4),4582(4)])]. given #1522 (W0w,wt=10): 44713 L(x,y,z \ (z \ y)) = x. [para(6416(a,1),16286(a,1,3)),rewrite([4408(6),45(4),16(4),3143(4),22398(2),101(4),33664(5),547(4),30136(4),16256(4),6416(8),4408(10),45(8),16(8),3143(8),22398(6),27459(8)])]. given #1523 (W0w,wt=10): 47657 L(x,y,z * (z / y)) = x. [hyper(24,a,14869,a)]. given #1524 (W0w,wt=10): 48247 T(x,R(x,y,z) \ 1) = x. [para(89(a,1),960(a,1,2,1)),rewrite([19074(4),2771(4,R)])]. given #1525 (W0w,wt=8): 94651 K(R(x,y,z),x) = 1. [hyper(27,a,48247,a),rewrite([17781(4)])]. given #1526 (W0w,wt=8): 94677 T(x,R(x,y,z)) = x. [para(48247(a,1),7769(a,1,1)),rewrite([4408(4),45(3),65951(2),1708(3)])]. given #1527 (W0w,wt=8): 94684 K(x,R(x,y,z)) = 1. [para(48247(a,1),16687(a,1,2)),rewrite([47(1),17913(5)]),flip(a)]. given #1528 (W0w,wt=9): 94789 a(1,R(x,y,z),u) = 1. [para(94651(a,1),37155(a,1,2)),rewrite([84171(3)])]. given #1529 (W0w,wt=10): 50351 L(x,y \ z,z / y) = x. [para(92(a,1),49860(a,1,2))]. given #1530 (W0w,wt=10): 50359 L(x,y * z,z * y) = x. [para(4209(a,1),49860(a,1,2))]. given #1531 (W0a,wt=11): 562 T(x / y,y \ x) = x / y. [para(92(a,1),541(a,1,2))]. given #1532 (W0a,wt=13): 564 K(L(x,y,z),L(T(x,u),y,z)) = 1. [para(30(a,1),555(a,1,2))]. given #1533 (W0r,wt=17): 69089 K(x,T(T(y,z),T(T(x,y),z))) = K(x,T(y,z)). [hyper(28,a,37775,a),rewrite([37429(5)])]. given #1534 (W0r,wt=19): 35134 K(x / y,(x \ (x \ z)) * ((y / T(z,x)) * x)) = 1. [back_rewrite(30470),rewrite([35052(7),4155(5),10229(4),6073(7)])]. given #1535 (W0r,wt=17): 93030 (T(x,K(y,z)) * K(z,y)) * (x \ K(y,z)) = 1. [para(4993(a,1),27619(a,1,2,1,1)),rewrite([9037(4),45(10),5005(10),12830(10),4407(8),6144(7),14(7)])]. given #1536 (W0r,wt=17): 29202 T(T(T(x,y),z),T(u,x)) = T(T(T(x,u),y),z). [para(23380(a,1),94(a,2,1,1))]. given #1537 (W0r,wt=15): 79394 K(L(x \ y,z,u),L(y / x,z,u)) = 1. [para(92(a,1),550(a,1,1,1))]. given #1538 (W1w,wt=21): 16576 K(K(x,y * (x \ (x \ z))),z * T(y,x \ (x \ z))) = 1. [back_rewrite(15720),rewrite([16527(5)])]. given #1539 (W1w,wt=21): 16682 T(T(T(x,y),z),u) \ T(T(x,u),y) = K(z,T(T(x,u),y)). [back_rewrite(8854),rewrite([16564(12)])]. given #1540 (W1w,wt=21): 16684 T(T(T(x,y),z),u) \ T(T(x,z),u) = K(y,T(T(x,z),u)). [back_rewrite(8811),rewrite([16564(12)])]. given #1541 (W1w,wt=21): 16740 K(x * T(y,z \ (z \ x)),K(y * (z \ (z \ x)),z)) = 1. [back_rewrite(15719),rewrite([16568(9)])]. given #1542 (W1w,wt=21): 16741 K(K(x * (y \ (y \ z)),y),z * T(x,y \ (y \ z))) = 1. [back_rewrite(15712),rewrite([16568(5)])]. given #1543 (W1w,wt=21): 16830 x \ (y \ (y \ T(y * (y * x),z))) = K(y * (y * x),z). [back_rewrite(5602),rewrite([16568(4)]),flip(a)]. given #1544 (W1w,wt=21): 16885 K(R(T(T(x,y),z),u,w),R(T(T(T(x,z),y),v5),u,w)) = 1. [back_rewrite(8963),rewrite([16686(12)])]. given #1545 (W1w,wt=21): 16893 K(L(T(T(x,y),z),u,w),L(T(T(T(x,z),v5),y),u,w)) = 1. [back_rewrite(8910),rewrite([16686(12)])]. given #1546 (W1a,wt=24): 498 R(R(R(x,R(R(x,y,z),u,w),v5),y,z),u,w) = R(R(x,y,z),u,w). [para(480(a,1),99(a,1)),flip(a)]. given #1547 (W1a,wt=24): 502 R(R(R(x,y,z),u,w),R(R(x,u,w),y,z),v5) = R(R(x,u,w),y,z). [para(480(a,1),245(a,1)),flip(a)]. given #1548 (W1r,wt=22): 87133 K((x * y) \ (z \ 1),a(x,z,y) * (y \ (x \ (z \ 1)))) = 1. [back_rewrite(9529),rewrite([84171(5)])]. given #1549 (W1r,wt=25): 66169 R(x / y,z,u) * (x * (y \ x)) = x * ((y \ x) * R(y \ x,z,u)). [back_rewrite(42831),rewrite([65976(9),3169(10)])]. given #1550 (W1r,wt=29): 74070 K(x,(T(T(T(T(y,z),u),w),x \ 1) / x) / T(T(T(T(y,w),u),z),x \ 1)) = 1. [para(25980(a,1),20245(a,1,2,1,1)),rewrite([12184(20)])]. given #1551 (W1r,wt=24): 79360 L(x,T((y * z) * (u * y),z),K(z \ y,z * (u * (y * z)))) = x. [para(7822(a,1),37221(a,1,3)),rewrite([52858(10)])]. given #1552 (W1r,wt=28): 62069 R(R(R(x,(R(R(x,y,z),u,w) \ v5) * v5,v6),u,w),y,z) = R(R(x,y,z),u,w). [para(22438(a,1),247(a,1)),flip(a)]. given #1553 (W2w,wt=31): 5325 K((((x \ y) * y) * z) * (y \ x),((z * (y \ (y \ x))) * T(y,x)) * ((x \ y) * y)) = 1. [para(4357(a,1),2812(a,1,1,2)),rewrite([4408(3),4408(2),4155(13),4408(12)])]. given #1554 (W2w,wt=31): 5457 x * (x * ((x * (y * (x * z))) * ((z \ x) * x))) = x * (x * (x * (y * (x * (x * x))))). [para(2640(a,1),389(a,1,1,2,2,2,2,2)),rewrite([5428(12),4155(8),4408(7),37(8)])]. given #1555 (W2w,wt=31): 5660 x * (y * (z * (z * (u * (y * (x * ((x * (y * (z * (z * (u * (y * x)))))) \ w))))))) = w. [para(37(a,1),2215(a,1,2,2,2,2,2,1,2,2)),rewrite([37(12)])]. given #1556 (W2w,wt=31): 5680 x * ((y * x) * (z * (x * ((x * y) * ((x * ((y * x) * (z * (x * (x * y))))) \ u))))) = u. [para(2215(a,1),189(a,1)),rewrite([189(8)]),flip(a)]. given #1557 (W2a,wt=33): 601 (((x * y) * z) * (x * (y * z))) * a(x,y,z) = (x * (y * z)) * (a(x,y,z) * ((x * y) * z)). [para(54(a,1),175(a,1,2,2)),flip(a)]. given #1558 (W2a,wt=32): 603 (x * ((y * z) * u)) * a(x,y * (z * u),a(y,z,u)) = (x * (y * (z * u))) * a(y,z,u). [para(54(a,1),54(a,1,1,2))]. given #1559 (W2r,wt=31): 74478 K(x,T(T(T(T(T(T(T(T(T(T(x,y),z),u),w),v5 \ (v5 \ 1)),z),v5 \ 1),w),u),y)) = 1. [back_rewrite(64627),rewrite([74284(9)])]. given #1560 (W2r,wt=33): 64174 a(x * (y * z),L(T(y * u,y * z),x,L(u \ z,y,u)),L(u \ z,y,u) \ (x \ 1)) = 1. [para(55954(a,2),8223(a,1,2)),rewrite([4407(13)])]. given #1561 (W2r,wt=31): 92334 K(L(L(R(R(x,y,z),u,w),v5,v6),v7,v8),v8) = K(L(L(R(R(x,u,w),y,z),v5,v6),v7,v8),v8). [para(240(a,1),16118(a,2,1)),rewrite([16118(12)])]. given #1562 (W2r,wt=33): 31881 x * (x * (y * ((T(z,y) * (x * (x * y))) * u))) = x * (x * ((z * y) * (x * (x * (y * u))))). [para(90(a,1),2979(a,1,2,2,1)),flip(a)]. given #1563 (W2r,wt=35): 66489 K((x \ (x \ (y \ (y \ z)))) * (T(y * (y / u),z) * (x * x)),T(u \ z,T((u / y) / y,z))) = 1. [para(25093(a,1),11445(a,1,1,1,2,2)),rewrite([52619(16),4407(15),10229(15),1014(15)])]. given #1564 (W0w,wt=9): 95345 a(1,L(x,y,z),u) = 1. [para(564(a,1),37155(a,1,2)),rewrite([84171(3)])]. given #1565 (W0w,wt=10): 50914 L(x,y,(y / z) / z) = x. [back_rewrite(47730),rewrite([50886(4)])]. given #1566 (W0w,wt=10): 51038 a(x,y * (x \ y),z) = 1. [para(18(a,1),19175(a,1,2,2)),rewrite([4230(2)])]. given #1567 (W0w,wt=10): 51046 a(x,y * (y / x),z) = 1. [para(1014(a,1),19175(a,1,2,2)),rewrite([24189(5)])]. given #1568 (W0w,wt=10): 51052 a(x,y \ (y \ x),z) = 1. [para(3143(a,1),19175(a,1,2,2)),rewrite([3143(4)])]. given #1569 (W0w,wt=10): 51766 a(x,y,T(x * y,y)) = 1. [para(22354(a,1),20404(a,1,1)),rewrite([51714(8),14882(7),16(3),14(2)])]. given #1570 (W0w,wt=10): 52627 L(x,y,T(y \ 1,z)) = x. [para(50347(a,1),24267(a,1,1,2,1)),rewrite([13(2),17(2),52573(4),52619(3)]),flip(a)]. given #1571 (W0w,wt=10): 53837 L(x,y * z,z / y) = x. [back_rewrite(49857),rewrite([52858(3)])]. given #1572 (W0w,wt=10): 57546 L(x,y * z,z \ y) = x. [back_rewrite(2266),rewrite([55410(6),4578(5),53163(6),2254(5)])]. given #1573 (W0w,wt=10): 57670 L(x,y,z * T(z,u)) = x. [back_rewrite(27119),rewrite([55819(7),52858(3)])]. given #1574 (W0w,wt=10): 58301 R(x,y * z,K(z,y)) = x. [back_rewrite(2860),rewrite([57952(4),17(4)]),flip(a)]. given #1575 (W0w,wt=10): 58360 T(x,L(x \ 1,y,z)) = x. [back_rewrite(57274),rewrite([58139(3)])]. given #1576 (W0w,wt=10): 58702 L(x / y,y,x) = x / y. [para(8245(a,1),33249(a,1,1,3)),rewrite([1014(4),80(4),4578(3),1014(6),19074(4),14868(3),56242(5),1014(5),8245(7),14(5)])]. given #1577 (W0w,wt=10): 58703 L(x \ y,y,x) = x \ y. [para(20361(a,1),33249(a,1,1,3)),rewrite([3143(4),80(4),1014(5),50942(4),10229(5),23697(5),38342(4),53598(5),3143(5),20361(7),14(5)])]. given #1578 (W0w,wt=10): 59682 a(x,y,T(x \ y,x)) = 1. [para(16(a,1),20410(a,1,2))]. given #1579 (W0w,wt=10): 59761 a(x,y,x \ (y \ 1)) = 1. [para(1091(a,1),20555(a,1,1)),rewrite([4407(5),24189(6)])]. given #1580 (W0a,wt=13): 565 K(R(x,y,z),R(T(x,u),y,z)) = 1. [para(31(a,1),555(a,1,2))]. given #1581 (W0a,wt=20): 602 (x * (y * z)) * a(x,z,T(y,z)) = (x * z) * T(y,z). [para(90(a,1),54(a,1,1,2))]. given #1582 (W0r,wt=18): 4026 (x * y) / a(z,z * x,y) = z * ((z \ x) * y). [back_rewrite(613),rewrite([3954(3)])]. given #1583 (W0r,wt=19): 99433 (x * y) * T(z,y * x) = K(x,y) * (z * (y * x)). [para(37179(a,1),602(a,1,2)),rewrite([14(6),21063(7),16985(6),90(6)]),flip(a)]. given #1584 (W0r,wt=19): 75793 ((x / y) * z) * (y \ x) = (x / y) * (z * (y \ x)). [para(33119(a,1),209(a,1,1)),rewrite([45(6),33119(11),88(10)])]. given #1585 (W0r,wt=20): 96714 K(x \ y,K(L(T(T(z,x) \ y,x),x,z),x \ z)) = 1. [back_rewrite(57475),rewrite([96031(8)])]. given #1586 (W0r,wt=19): 98170 L(x \ 1,y,z * (u * z)) = L(x \ 1,y,T(u,z)). [para(5660(a,1),10214(a,1,2)),rewrite([98147(22),56705(8),98147(28),57210(11),58434(9)]),flip(a)]. given #1587 (W1w,wt=21): 16897 K(L(T(T(x,y),z),u,w),L(T(T(T(x,v5),y),z),u,w)) = 1. [back_rewrite(8871),rewrite([16686(12)])]. given #1588 (W1w,wt=21): 16914 K(R(T(T(x,y),z),u,w),R(T(T(T(x,z),v5),y),u,w)) = 1. [back_rewrite(6861),rewrite([16686(12)])]. given #1589 (W1w,wt=21): 16915 K(R(T(T(x,y),z),u,w),R(T(T(T(x,v5),y),z),u,w)) = 1. [back_rewrite(6860),rewrite([16686(12)])]. given #1590 (W1w,wt=21): 16981 x * (y \ K(y \ (x / y),z)) = y * T(y \ (x / y),z). [back_rewrite(12705),rewrite([16716(6)]),flip(a)]. given #1591 (W1w,wt=21): 17885 K(a(x,y,z),(x * y) * z) = K(a(x,y,z),x * (y * z)). [back_rewrite(16900),rewrite([17771(6)]),flip(a)]. given #1592 (W1w,wt=21): 17941 K(x \ (y \ (y \ z)),y * (y * x)) = K(z,y * (y * x)). [back_rewrite(8543),rewrite([17781(12),17883(10)])]. given #1593 (W1w,wt=21): 18235 K(x,L(L(y,z,u),w,v5) * (x / L(L(y,w,v5),z,u))) = 1. [para(12078(a,1),14560(a,1,2,2)),rewrite([1091(12),17781(9)])]. given #1594 (W1w,wt=21): 18271 T(x * (x * y),(y * z) \ (x \ (x \ z))) = x * (x * y). [para(37(a,1),14577(a,1,2,1)),rewrite([5162(6)])]. given #1595 (W1a,wt=22): 515 (x * (y * z)) / (z * T(x,y * z)) = R(y,z,T(x,y * z)). [para(90(a,1),22(a,1,1))]. given #1596 (W1a,wt=30): 530 ((x * (y * (y * z))) * T(u,z)) / (y * (y * (u * z))) = R(x,y * (y * z),T(u,z)). [para(90(a,1),148(a,1,2,2,2))]. given #1597 (W1r,wt=30): 79239 L(x,K(y,T(T(T(T(z,u),w),v5),v6)),T(T(T(T(T(y,v5),w),u),z \ 1),v6) / z) = x. [para(4092(a,2),37217(a,1,3)),rewrite([37242(8),2642(7),88(6),37242(5),37242(5),37242(5),37242(5)])]. given #1598 (W1r,wt=25): 101760 x * T(x \ (y / x),x * (x * (y \ z))) = x * T(x \ (y / x),z). [para(10379(a,1),16981(a,2,2)),rewrite([10215(4),3228(5),16981(8)])]. given #1599 (W1r,wt=28): 70633 K(R(x / (y * (y * z)),y * (y * z),u),(z * u) \ ((y \ (y \ x)) * u)) = 1. [para(342(a,2),568(a,1,1)),rewrite([5162(11),6073(10)])]. given #1600 (W1r,wt=27): 24045 x * ((y / x) * (z * (x * ((x \ y) * u)))) = (x * ((y / x) * (z * y))) * u. [back_rewrite(2218),rewrite([23697(4)])]. given #1601 (W1r,wt=24): 97403 a(T(T(T(x,y),z),u),T(T(T(x \ 1,u),y),z),T(T(x,u),y)) = 1. [para(16682(a,1),27009(a,1,2,2)),rewrite([22940(9,R),52619(7),52619(6)])]. given #1602 (W2w,wt=31): 5681 x * ((y * x) * (z * ((y * x) * (x * ((x * ((y * x) * (z * (y * (x * x))))) \ u))))) = u. [para(2215(a,1),189(a,2)),rewrite([4578(5),189(14)])]. given #1603 (W2w,wt=31): 5688 (x * (y * z)) * (z \ (x * (y * (x * (y * x))))) = x * (y * (x * (y * (x * (y * x))))). [para(2215(a,1),389(a,1,1,2,2)),rewrite([4155(8)])]. given #1604 (W2w,wt=31): 5778 K(x * ((y * x) * (x * ((z * (x * y)) * (x * (x * z))))),x * ((y * x) * (x * z))) = 1. [para(189(a,1),2051(a,1,1)),rewrite([189(13)])]. given #1605 (W2w,wt=31): 5780 K(T(x,y) * (z * (z * (y * (z * (z * (x \ y)))))),T(x,y) * (z * (z * (x \ y)))) = 1. [para(2690(a,1),2051(a,1,1,2,2,2,1))]. given #1606 (W2a,wt=33): 717 R(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = R(R(R(R(R(x,v7,v8),u,w),y,z),v9,v10),v5,v6). [para(247(a,1),99(a,1,1,1)),flip(a)]. given #1607 (W2a,wt=33): 719 R(R(R(R(R(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = R(R(R(R(R(x,v9,v10),u,w),y,z),v5,v6),v7,v8). [para(247(a,1),99(a,2,1,1))]. given #1608 (W2r,wt=35): 73004 K((T(x,y) \ z) * (y \ (x * ((u * y) * w))),((z * T(x,y)) * ((y \ u) * (y * w))) / T(x,y)) = 1. [para(13641(a,1),2812(a,1,1,2))]. given #1609 (W2r,wt=34): 7380 T(R(x,y,z) * (u * (u * w)),K(R(T(x,u),y,z) * (u * w),u)) = R(x,y,z) * (u * (u * w)). [para(4770(a,1),2918(a,1,1)),rewrite([7345(15)])]. given #1610 (W2r,wt=34): 101369 K((x * y) * (z * (x * z)),K(z * x,L(y,x,z) * (z * (x * K(((x * y) * z) * x,z))))) = 1. [back_rewrite(75673),rewrite([101264(4)])]. given #1611 (W2r,wt=33): 90806 a(x,y \ ((y / (z * u)) * L(w \ u,z,w)),L(T(z * w,z * u),y,L(w \ u,z,w))) = 1. [back_rewrite(64119),rewrite([90470(6)])]. given #1612 (W2r,wt=31): 15866 K(x * (y * T(z,x \ (x \ y))),u * (x * (x * ((x * (z * (x \ (x \ y)))) / u)))) = 1. [para(4404(a,2),8260(a,1,1,2))]. given #1613 (W0w,wt=8): 102189 R(x,y,x * y) = x. [para(89(a,1),515(a,1,2,2)),rewrite([189(3),101(2),17(6),89(3)]),flip(a)]. given #1614 (W0w,wt=10): 59835 R(x,T(y * y,x),z) = x. [para(100(a,1),514(a,1,1,1)),rewrite([37(3),1839(7),25193(5),16(3),16(2)]),flip(a)]. given #1615 (W0w,wt=10): 62053 R(x,y * (x * y),z) = x. [para(15(a,1),22438(a,1,2,1))]. given #1616 (W0w,wt=10): 62078 R(x,y \ (x / y),z) = x. [para(1829(a,1),22438(a,1,2,1)),rewrite([3143(4)])]. given #1617 (W0w,wt=10): 64162 L(x * x,x,y) = x * x. [para(1077(a,1),55954(a,1,3)),rewrite([14(3),4209(2),52596(4),52858(2),1607(5),1014(5),14(5),10229(5),23697(5),6351(5)])]. given #1618 (W0w,wt=10): 64186 R(x,y * z,y * y) = x. [back_rewrite(58601),rewrite([64162(3)])]. -------- Proof 1 -------- "aK2". ============================== PROOF ================================= % Proof 1 at 43.67 (+ 0.24) seconds: "aK2". % Length of proof is 662. % Level of proof is 46. % Maximum clause weight is 35. % Given clauses 1618. 1 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 2 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 3 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 5 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 7 a(x,K(y,z),u) = 1 # label("aK2") # label(non_clause) # label(goal). [goal]. 13 1 * x = x. [assumption]. 14 x * 1 = x. [assumption]. 15 x \ (x * y) = y. [assumption]. 16 x * (x \ y) = y. [assumption]. 17 (x * y) / y = x. [assumption]. 18 (x / y) * y = x. [assumption]. 19 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 20 (x * y) \ (y * x) = K(y,x). [assumption]. 21 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 22 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 23 x \ (y * x) = T(y,x). [assumption]. 24 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(1)]. 25 L(x,y,z) != x | a(z,y,x) = 1. [clausify(2)]. 26 T(x,y) != x | T(y,x) = y. [clausify(3)]. 28 K(x,y) != 1 | T(x,y) = x. [clausify(5)]. 29 T(T(x,y),z) = T(T(x,z),y). [assumption]. 30 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 31 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 32 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 33 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(32),flip(a)]. 34 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 36 ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang (M1)"). [assumption]. 37 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 39 a(c5,K(c6,c7),c8) != 1 # label("aK2") # answer("aK2"). [deny(7)]. 45 1 \ x = x. [para(13(a,1),15(a,1,2))]. 46 x \ x = 1. [para(14(a,1),15(a,1,2))]. 47 x / x = 1. [para(13(a,1),17(a,1,1))]. 48 x / 1 = x. [para(14(a,1),17(a,1,1))]. 49 x / (y \ x) = y. [para(16(a,1),17(a,1,1))]. 50 (x / y) \ x = y. [para(18(a,1),15(a,1,2))]. 51 a(x,1,y) = 1. [para(13(a,1),19(a,1,1,2)),rewrite([14(3),46(3)]),flip(a)]. 54 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(19(a,1),16(a,1,2))]. 55 (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y). [para(16(a,1),19(a,1,1,2))]. 56 (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z). [para(16(a,1),19(a,1,2,1))]. 58 (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z). [para(18(a,1),19(a,1,1,2))]. 60 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(18(a,1),19(a,1,2,1))]. 63 (x * y) * K(y,x) = y * x. [para(20(a,1),16(a,1,2))]. 64 x \ ((y \ x) * y) = K(y \ x,y). [para(16(a,1),20(a,1,1))]. 65 ((x \ y) * x) \ y = K(x,x \ y). [para(16(a,1),20(a,1,2))]. 68 K(x * x,x) = a(x,x,x). [para(20(a,1),19(a,1))]. 73 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(16(a,1),21(a,1,1))]. 74 L(x \ y,x,z) = (z * x) \ (z * y). [para(16(a,1),21(a,1,2,2)),flip(a)]. 75 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(18(a,1),21(a,1,1))]. 76 L(x,y / x,z) = (z * (y / x)) \ (z * y). [para(18(a,1),21(a,1,2,2)),flip(a)]. 81 R(x,x \ y,z) = (y * z) / ((x \ y) * z). [para(16(a,1),22(a,1,1,1)),flip(a)]. 82 R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z)). [para(16(a,1),22(a,1,1)),flip(a)]. 83 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(16(a,1),22(a,1,2))]. 84 R(x,y,z) * (y * z) = (x * y) * z. [para(22(a,1),18(a,1,1))]. 85 R(x / y,y,z) = (x * z) / (y * z). [para(18(a,1),22(a,1,1,1)),flip(a)]. 87 T(1,x) = 1. [para(13(a,1),23(a,1,2)),rewrite([46(1)]),flip(a)]. 88 T(x,1) = x. [para(14(a,1),23(a,1,2)),rewrite([45(2)]),flip(a)]. 89 T(x,x) = x. [para(23(a,1),15(a,1))]. 90 x * T(y,x) = y * x. [para(23(a,1),16(a,1,2))]. 91 T(x,x \ y) = (x \ y) \ y. [para(16(a,1),23(a,1,2)),flip(a)]. 92 T(x / y,y) = y \ x. [para(18(a,1),23(a,1,2)),flip(a)]. 97 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,v5,v6),y,z),u,w). [para(34(a,1),34(a,1,1)),flip(a)]. 100 (x * x) * y = x * (x * y). [para(13(a,1),36(a,2,2)),rewrite([14(2)])]. 101 (x * y) * x = x * (y * x). [para(36(a,1),14(a,1)),rewrite([14(2)]),flip(a)]. 103 x * (y * (x * ((x * (y * x)) \ z))) = z. [para(36(a,1),16(a,1)),rewrite([101(2)])]. 104 x * ((x \ y) * (x * z)) = (y * x) * z. [para(16(a,1),36(a,1,1,1)),flip(a)]. 106 (x * (y * (x * z))) / z = x * (y * x). [para(36(a,1),17(a,1,1)),rewrite([101(6)])]. 110 (x * (y * (z * (y * u)))) \ ((x * (y * (z * y))) * u) = a(x,y * (z * y),u). [para(36(a,1),19(a,1,1,2)),rewrite([101(6),101(11)])]. 112 ((x * (y * x)) * (z * u)) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [para(36(a,1),19(a,1,2,1)),rewrite([101(2),101(11)])]. 117 (x * (y * (z * y))) \ (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(36(a,1),21(a,1,2,2)),rewrite([101(2),101(10)])]. 118 ((x * (y * x)) * z) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(36(a,1),21(a,1,2)),rewrite([101(2),101(10)])]. 121 ((x * (y * (z * y))) * u) / (y * (z * (y * u))) = R(x,y * (z * y),u). [para(36(a,1),22(a,1,2)),rewrite([101(2),101(10)])]. 125 ((x * (y * x)) * (z * (x * (y * x)))) * u = (x * (y * x)) * (z * (x * (y * (x * u)))). [para(36(a,1),36(a,2,2,2)),rewrite([101(2),101(5),101(6),101(9)])]. 126 (x * ((y * (z * y)) * x)) * u = x * (y * (z * (y * (x * u)))). [para(36(a,1),36(a,2,2)),rewrite([101(2),101(4)])]. 128 (x * (y * x)) * z = x * (y * (x * z)). [back_rewrite(36),rewrite([101(2)])]. 129 (x * (y * (x * (z * (x * (y * x)))))) * u = x * (y * (x * (z * (x * (y * (x * u)))))). [back_rewrite(125),rewrite([128(6),128(14)])]. 130 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [back_rewrite(126),rewrite([128(3)])]. 132 (x * (y * (x * z))) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [back_rewrite(118),rewrite([128(3)])]. 133 (x * (y * (x * (z * u)))) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [back_rewrite(112),rewrite([128(4)])]. 134 (x * (x * y)) \ (x * (x * (y * z))) = z. [para(37(a,1),15(a,1,2))]. 136 x * (x * ((x \ y) * z)) = (x * y) * z. [para(16(a,1),37(a,1,1,2)),flip(a)]. 139 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(37(a,1),19(a,1,1,2))]. 140 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(37(a,1),19(a,1,1)),rewrite([37(7),37(8)])]. 141 (x * ((x * y) * z)) \ (x * (x * (y * z))) = a(x,x * y,z). [para(37(a,1),19(a,1,2))]. 144 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(37(a,1),21(a,1,1)),rewrite([37(7)])]. 145 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(37(a,1),21(a,1,2,2))]. 146 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(37(a,1),22(a,1,1,1)),rewrite([37(4)])]. 148 ((x * (y * (y * z))) * u) / (y * (y * (z * u))) = R(x,y * (y * z),u). [para(37(a,1),22(a,1,2))]. 150 x * (x * ((y * (x * (x * (y * z)))) * u)) = x * (x * (y * (x * (x * (y * (z * u)))))). [para(37(a,1),37(a,1,1,2)),rewrite([37(6),37(7),37(13),37(14)])]. 152 L(c8,K(c6,c7),c5) != c8 # answer("aK2"). [ur(25,b,39,a)]. 159 T(T(x,y),x) = T(x,y). [para(89(a,1),29(a,1,1)),flip(a)]. 165 (x * y) / T(x,y) = y. [para(23(a,1),49(a,1,2))]. 166 R(x,y,z) \ ((x * y) * z) = y * z. [para(22(a,1),50(a,1,1))]. 168 x \ ((y * x) * z) = (x \ y) * (x * z). [para(104(a,1),15(a,1,2))]. 169 (x * y) * (y \ z) = y * ((y \ x) * z). [para(16(a,1),104(a,1,2,2)),flip(a)]. 173 a(x,x \ y,x * z) = ((y * x) * z) \ (y * (x * z)). [para(104(a,1),19(a,1,1)),rewrite([16(4)]),flip(a)]. 176 ((x * y) * z) \ (((y \ x) * (y * z)) * y) = K((y \ x) * (y * z),y). [para(104(a,1),20(a,1,1))]. 177 (((x \ y) * (x * z)) * x) \ ((y * x) * z) = K(x,(x \ y) * (x * z)). [para(104(a,1),20(a,1,2))]. 178 (x * y) * (K(y,x) * ((x * y) * z)) = ((y * x) * (x * y)) * z. [para(20(a,1),104(a,1,2,1))]. 179 ((x * y) * z) \ (y * (((y \ x) * (y * z)) * u)) = L(u,(y \ x) * (y * z),y). [para(104(a,1),21(a,1,1))]. 181 L(x * y,x \ z,x) = z \ ((z * x) * y). [para(104(a,1),21(a,1,2)),rewrite([16(2)]),flip(a)]. 182 (x * y) * (L(z,y,x) * ((x * y) * u)) = ((x * (y * z)) * (x * y)) * u. [para(21(a,1),104(a,1,2,1))]. 183 (((x * y) * z) * u) / (((y \ x) * (y * z)) * u) = R(y,(y \ x) * (y * z),u). [para(104(a,1),22(a,1,1,1))]. 186 x * (T(y,x) * (x * z)) = ((y * x) * x) * z. [para(23(a,1),104(a,1,2,1))]. 187 x * (x * (((x \ y) * (x * z)) * u)) = (x * ((y * x) * z)) * u. [para(104(a,1),37(a,1,1,2)),flip(a)]. 188 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * (y * u)))))) = (z * (x * (x * y))) * u. [para(104(a,1),37(a,1)),rewrite([37(10)]),flip(a)]. 189 (x * y) * (x * z) = x * ((y * x) * z). [para(104(a,1),37(a,2,2)),rewrite([16(2)])]. 190 (x * y) * ((y \ z) * (y * u)) = y * ((y \ x) * ((z * y) * u)). [para(104(a,1),104(a,1,2,2)),flip(a)]. 191 (x * ((x \ y) * z)) / z = R(y,x,x \ z). [back_rewrite(83),rewrite([169(3)])]. 192 (x * y) \ (z * ((z \ x) * y)) = a(x,z,z \ y). [back_rewrite(55),rewrite([169(4)])]. 193 (x * y) * (L(z,y,x) * ((x * y) * u)) = (x * (((y * z) * x) * y)) * u. [back_rewrite(182),rewrite([189(10)])]. 197 R(x,y,y \ 1) = x. [para(14(a,1),191(a,1,1,2)),rewrite([16(2),48(2)]),flip(a)]. 199 R(x,y,y \ ((y \ x) \ z)) = (y * z) / ((y \ x) \ z). [para(16(a,1),191(a,1,1,2)),flip(a)]. 200 R(x,y,y \ z) * z = y * ((y \ x) * z). [para(191(a,1),18(a,1,1))]. 201 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) = ((x * (y * z)) * (a(x,y,z) * u)) / u. [para(19(a,1),191(a,1,1,2,1)),flip(a)]. 205 (x * (x * (y * (((x * (x * y)) \ z) * u)))) / u = R(z,x * (x * y),(x * (x * y)) \ u). [para(37(a,1),191(a,1,1))]. 206 R(x,x,x \ y) = x. [para(46(a,1),191(a,1,1,2,1)),rewrite([13(2),17(2)]),flip(a)]. 208 R(x,x / y,(x / y) \ z) = ((x / y) * (y * z)) / z. [para(50(a,1),191(a,1,1,2,1)),flip(a)]. 209 a(x,y,z) \ ((x * y) * z) = T(x * (y * z),a(x,y,z)). [para(19(a,1),91(a,1,2)),rewrite([19(9)]),flip(a)]. 218 x / T(y,y \ x) = y \ x. [para(91(a,2),49(a,1,2))]. 220 R(x,y \ z,T(y,y \ z)) = R(x,y \ z,(y \ z) \ z). [para(91(a,2),191(a,2,3)),rewrite([191(6)]),flip(a)]. 221 T(x \ y,T(x,x \ y)) = ((x \ y) \ y) \ y. [para(91(a,2),91(a,1,2))]. 228 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,u,w),y,z),v5,v6). [para(97(a,1),34(a,1))]. 229 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v5,v6),y,z),v7,v8),u,w). [para(97(a,2),34(a,1,1))]. 265 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(209(a,1),49(a,1,2))]. 268 ((x * (y \ z)) * T(y,y \ z)) / z = R(x,y \ z,(y \ z) \ z). [para(220(a,1),22(a,2)),rewrite([90(9),16(7)])]. 311 (x * (y * (y * z))) \ ((x * (y * y)) * z) = a(x,y * y,z). [para(13(a,1),110(a,1,1,2,2)),rewrite([13(5),13(9)])]. 312 (x * (y * (z * (y * u)))) * a(x,y * (z * y),u) = (x * (y * (z * y))) * u. [para(110(a,1),16(a,1,2))]. 338 ((x * (y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(13(a,1),148(a,1,2,2,2)),rewrite([14(2),14(8)])]. 340 ((x * (y * (y * z))) * (z \ u)) / (y * (y * u)) = R(x,y * (y * z),z \ u). [para(16(a,1),148(a,1,2,2,2))]. 341 R(x,y * (y * z),u) * (y * (y * (z * u))) = (x * (y * (y * z))) * u. [para(148(a,1),18(a,1,1))]. 342 R(x / (y * (y * z)),y * (y * z),u) = (x * u) / (y * (y * (z * u))). [para(18(a,1),148(a,1,1,1)),flip(a)]. 350 ((x * y) * z) * K((y \ x) * (y * z),y) = ((y \ x) * (y * z)) * y. [para(176(a,1),16(a,1,2))]. 354 ((x * (y / z)) * z) \ ((((y / z) \ x) * y) * (y / z)) = K(((y / z) \ x) * y,y / z). [para(18(a,1),176(a,1,2,1,2)),rewrite([18(13)])]. 357 ((x * (x / y)) * z) \ ((y * ((x / y) * z)) * (x / y)) = K(y * ((x / y) * z),x / y). [para(50(a,1),176(a,1,2,1,1)),rewrite([50(11)])]. 393 x * (x * ((x * (y * (x * (x * x)))) * z)) = x * (x * (x * (y * (x * (x * (x * z)))))). [para(129(a,1),37(a,1)),flip(a)]. 398 x * (x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u))))))) = x * (x * u). [para(16(a,1),150(a,1,2,2)),flip(a)]. 407 x * (x * (((x * x) \ y) * (x * (x * z)))) = (y * (x * x)) * z. [para(13(a,1),188(a,1,2,2,2,2,2,2)),rewrite([14(3),13(7),14(9)])]. 411 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [para(16(a,1),188(a,1,2,2,2,2,2,2))]. 435 R(x * ((x \ y) * z),y * z,(y * z) \ u) = ((y * z) * (a(y,x,x \ z) * u)) / u. [para(16(a,1),201(a,1,2,2)),rewrite([169(3),16(6),16(9)])]. 439 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) \ ((x * (y * z)) * (a(x,y,z) * u)) = u. [para(201(a,2),50(a,1,1))]. 463 x * (x * (x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))))) = x * (x * z). [para(16(a,1),393(a,1,2,2)),flip(a)]. 478 R(x,1 / y,y) = x. [para(50(a,1),197(a,1,3))]. 480 R(x,x,y) = x. [para(15(a,1),206(a,1,3))]. 493 R(T(x,y),x,z) = T(x,y). [para(480(a,1),31(a,1,1)),flip(a)]. 506 (x * (1 / y)) * y = x. [para(478(a,1),22(a,2)),rewrite([18(7),48(6)])]. 507 (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z)). [para(90(a,1),19(a,1,1,2))]. 508 (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z). [para(90(a,1),19(a,1,2,1))]. 520 x * (x * (T(y,x) * z)) = x * (y * (x * z)). [para(90(a,1),37(a,1,1,2)),rewrite([128(3)]),flip(a)]. 521 x * (x * (y * T(z,x * (x * y)))) = z * (x * (x * y)). [para(90(a,1),37(a,1)),flip(a)]. 541 T(x,T(x,y)) = x. [hyper(26,a,159,a)]. 547 T(x,y) * x = x * T(x,y). [para(159(a,1),90(a,1,2)),flip(a)]. 560 T(x,(x \ y) \ y) = x. [para(91(a,1),541(a,1,2))]. 632 L(x \ 1,x,y) = (y * x) \ y. [para(14(a,1),74(a,2,2))]. 638 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(21(a,1),74(a,1,1)),flip(a)]. 639 L(T(x,y),y,x) = T(x,x * y). [para(74(a,2),23(a,1)),rewrite([23(2)])]. 648 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(y * z) \ (y * u)). [para(74(a,2),191(a,2,3)),rewrite([191(8)]),flip(a)]. 650 T(x * y,(x * y) \ (x * z)) = L(y \ z,y,x) \ (x * z). [para(74(a,2),91(a,2,1))]. 662 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,(x * y) \ (x * z),u). [para(74(a,2),56(a,1,1,2,1))]. 667 L(L(x,y,z),z * y,z) = x. [back_rewrite(134),rewrite([638(6)])]. 669 x * (T(y,x) * x) = (y * x) * x. [para(14(a,1),186(a,1,2,2)),rewrite([14(7)])]. 673 (((x * y) * y) * z) \ ((x * y) * (y * z)) = a(y,T(x,y),y * z). [para(186(a,1),19(a,1,1)),rewrite([90(5)])]. 682 x * (T(T(y,x),z) * (x * u)) = ((T(y,z) * x) * x) * u. [para(29(a,1),186(a,1,2,1))]. 690 a((x * y) * y,T(x,y),z) = a(y,T(x,y) * (x * y),z). [para(186(a,1),110(a,1,2,1)),rewrite([186(6),19(11),90(7)])]. 729 ((x * (y / z)) * z) / T(x * y,a(x,y / z,z)) = a(x,y / z,z). [para(18(a,1),265(a,1,2,1,2))]. 778 x * (y * T(z,x * (x * y))) = x \ (z * (x * (x * y))). [para(521(a,1),15(a,1,2)),flip(a)]. 780 L(x * T(y,z * (z * x)),z,z) = (z * z) \ (y * (z * (z * x))). [para(521(a,1),21(a,1,2)),flip(a)]. 788 x * (y * (x * T(z,x * (y * x)))) = z * (x * (y * x)). [para(90(a,1),521(a,1,2,2,2,2,2)),rewrite([520(7),90(8)])]. 831 (x * ((x \ y) * y)) \ ((y * x) * ((x \ y) * z)) = L(z,(x \ y) * y,x). [para(104(a,1),117(a,1,1)),rewrite([169(3),104(9),16(11)])]. 874 x * K((y \ z) * (y * ((z * y) \ x)),y) = ((y \ z) * (y * ((z * y) \ x))) * y. [para(16(a,1),350(a,1,1))]. 961 (x * (x * (y * z))) / T(x * (x * y),z) = z. [para(37(a,1),165(a,1,1))]. 965 (x * y) / T(y,T(x,y)) = T(x,y). [para(90(a,1),165(a,1,1))]. 969 (((x \ y) * (x * z)) * x) / T((y * x) * z,K((x \ y) * (x * z),x)) = K((x \ y) * (x * z),x). [para(350(a,1),165(a,1,1))]. 974 x * (1 / y) = x / y. [para(506(a,1),17(a,1,1)),flip(a)]. 975 x / (1 / y) = x * y. [para(18(a,1),506(a,1,1)),flip(a)]. 976 a(x,1 / y,y) = 1. [para(506(a,1),19(a,1,2)),rewrite([18(3),14(2),46(1)]),flip(a)]. 982 K(x,1 / x) = 1. [para(506(a,1),357(a,1,1)),rewrite([18(4),14(3),974(4),47(2),46(3),18(4),14(3)]),flip(a)]. 986 T(x,1 / x) = x. [hyper(28,a,982,a)]. 989 1 / x = x \ 1. [hyper(26,a,986,a),rewrite([92(3)]),flip(a)]. 990 (x \ 1) \ 1 = x. [para(986(a,1),23(a,2)),rewrite([989(2),989(4),16(5)])]. 996 T(x \ 1,x) = x \ 1. [para(49(a,1),986(a,1,2))]. 997 (x \ 1) * x = 1. [para(986(a,1),90(a,1,2)),rewrite([989(2),989(5),16(6)])]. 1012 a(x,y \ 1,y) = 1. [back_rewrite(976),rewrite([989(2)])]. 1013 x / (y \ 1) = x * y. [back_rewrite(975),rewrite([989(2)])]. 1014 x * (y \ 1) = x / y. [back_rewrite(974),rewrite([989(2)])]. 1022 L(x,x \ 1,y) = x. [para(990(a,1),74(a,1,1)),rewrite([1014(6),14(6),50(5)])]. 1025 (x \ 1) * (x * y) = L(y,x,x \ 1). [para(997(a,1),21(a,1,1)),rewrite([45(6)])]. 1026 L(x,y,(y * x) \ 1) = (((y * x) \ 1) * y) \ 1. [para(997(a,1),21(a,1,2)),flip(a)]. 1027 R(x \ 1,x,y) = y / (x * y). [para(997(a,1),22(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1039 R((x * (x * y)) \ 1,x * (x * y),z) = z / (x * (x * (y * z))). [para(997(a,1),148(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1051 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x \ (y \ 1),y). [para(997(a,1),56(a,1,2))]. 1077 L(x \ 1,x,y) = x \ 1. [para(50(a,1),1022(a,1,2)),rewrite([989(2),989(5)])]. 1078 L(L(L(x,y,z),u,w),L(x,u,w) \ 1,v5) = L(L(x,u,w),y,z). [para(1022(a,1),97(a,1,1)),flip(a)]. 1080 L(L(L(x,y,z),u,w),x \ 1,v5) = L(L(x,y,z),u,w). [para(1022(a,1),97(a,2,1,1))]. 1091 (x * y) \ x = y \ 1. [back_rewrite(632),rewrite([1077(3)]),flip(a)]. 1141 L(x,y,(y * x) \ 1) \ 1 = ((y * x) \ 1) * y. [para(1026(a,2),49(a,1,2)),rewrite([989(6)])]. 1180 L(x,x \ y,x) = x. [para(14(a,1),181(a,1,1)),rewrite([14(5),15(4)])]. 1227 L(x * y,x \ (x \ 1),x) = (x \ 1) \ y. [para(997(a,1),181(a,2,2,1)),rewrite([13(9)])]. 1246 (x * (x * y)) / T(x * (x * (y / z)),z) = z. [para(18(a,1),961(a,1,1,2,2))]. 1266 (((T(x,y) * z) * z) * u) / (T(T(x,z),y) * (z * u)) = z. [para(682(a,1),17(a,1,1))]. 1300 a(x,x,y) = 1. [para(13(a,1),690(a,1,1,1)),rewrite([87(3),51(3),87(3),13(4),13(3)]),flip(a)]. 1316 K(x * x,x) = 1. [back_rewrite(68),rewrite([1300(3)])]. 1324 x \ (x \ (y * (x * (x * z)))) = z * T(y,x * (x * z)). [para(778(a,1),15(a,1,2))]. 1353 x * (y / (x * (x * y))) = x \ 1. [para(997(a,1),778(a,2,2)),rewrite([996(7),1014(5)])]. 1359 x * (y * T(z,y * (x * y))) = y \ (z * (y * (x * y))). [para(788(a,1),15(a,1,2)),flip(a)]. 1448 R((x * (y * x)) \ 1,x * (y * x),z) = z / (x * (y * (x * z))). [para(997(a,1),121(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1452 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,x \ y). [para(268(a,1),18(a,1,1)),rewrite([200(5)])]. 1457 R(x,y \ z,(y \ z) \ z) \ ((x * (y \ z)) * T(y,y \ z)) = z. [para(268(a,1),50(a,1,1))]. 1524 L(x * ((y * (y * x)) \ z),y,y) = (y * y) \ z. [para(18(a,1),780(a,2,2)),rewrite([92(6)])]. 1534 L(x / (y * (y * x)),y,y) = (y * y) \ 1. [para(997(a,1),780(a,2,2)),rewrite([996(7),1014(5)])]. 1607 L(x,y,y) = x. [hyper(24,a,1300,a)]. 1609 x / (y * (y * x)) = (y * y) \ 1. [back_rewrite(1534),rewrite([1607(4)])]. 1619 x * ((y * (y * x)) \ z) = (y * y) \ z. [back_rewrite(1524),rewrite([1607(5)])]. 1649 x / (x * x) = x \ 1. [back_rewrite(1353),rewrite([1609(3),1014(4)])]. 1659 T(x * x,x) = x * x. [hyper(28,a,1316,a)]. 1667 L(x,y,x) = x. [para(15(a,1),1180(a,1,2))]. 1685 L(T(x,y),z,x) = T(x,y). [para(1667(a,1),30(a,1,1)),flip(a)]. 1699 ((x \ y) * x) \ ((x \ y) * y) = x \ y. [para(1667(a,1),74(a,1)),flip(a)]. 1702 a((x \ y) * x,x \ y,z) = a(x \ y,y,z). [para(1667(a,1),662(a,1,1,2,1)),rewrite([189(5),16(3),19(7),1699(9)]),flip(a)]. 1708 T(x,x * y) = T(x,y). [back_rewrite(639),rewrite([1685(2)]),flip(a)]. 1812 T(x * y,y \ 1) = (y \ 1) \ x. [para(1013(a,1),92(a,1,1))]. 1829 x \ (x / y) = y \ 1. [para(1014(a,1),15(a,1,2))]. 1834 (x / y) \ (x * ((y \ 1) * z)) = L(z,y \ 1,x). [para(1014(a,1),21(a,1,1))]. 1836 ((x * y) / z) / (y / z) = R(x,y,z \ 1). [para(1014(a,1),22(a,1,1)),rewrite([1014(5)])]. 1839 (x * (x * y)) / z = x * (x * (y / z)). [para(1014(a,1),37(a,1)),rewrite([1014(6)])]. 1859 x * (T(y,x) * (x / z)) = ((y * x) * x) / z. [para(1014(a,1),186(a,1,2,2)),rewrite([1014(9)])]. 1870 x * (x * ((y * (((x * (x * y)) \ z) * u)) / u)) = R(z,x * (x * y),(x * (x * y)) \ u). [para(205(a,1),1014(a,2)),rewrite([1014(10),1839(8)])]. 1884 x * (x * ((y / z) / T(x * (x * y),z \ 1))) = z \ 1. [para(1014(a,1),961(a,1,1,2,2)),rewrite([1839(9)])]. 1885 x * (x * ((y * z) / T(x * (x * y),z))) = z. [para(961(a,1),1014(a,2)),rewrite([1014(9),1839(7)])]. 1888 x * ((y \ 1) * T(z,x * (x / y))) = x \ (z * (x * (x / y))). [para(1014(a,1),778(a,1,2,2,2,2)),rewrite([1014(10)])]. 1925 x * (x * (y / T(x * (x * (y / z)),z))) = z. [back_rewrite(1246),rewrite([1839(7)])]. 1935 x * (x * R(y,z,u)) = R(x * (x * y),z,u). [back_rewrite(146),rewrite([1839(6),22(4)])]. 1952 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(x / (y * (y * z)),y * (y * z),u). [para(37(a,1),60(a,1,1,2))]. 1972 R(x,x / y,(x / y) \ (y \ z)) = ((x / y) * z) / (y \ z). [para(16(a,1),208(a,2,1,2))]. 2004 R(x,x * y,(x * y) \ z) = ((x * y) * ((y \ 1) * z)) / z. [para(1013(a,1),208(a,1,2)),rewrite([1013(4),1013(7)])]. 2009 (x / y) * ((x / y) * ((y * z) / T((x / y) * x,z))) = z. [para(18(a,1),1885(a,1,2,2,2,1,2))]. 2010 (x * y) / T(z * (z * x),y) = (z * z) \ y. [para(1885(a,1),21(a,1,2)),rewrite([1607(8)]),flip(a)]. 2012 x * (x * (((x * x) \ y) * z)) = y * z. [para(1885(a,1),37(a,1,1)),rewrite([2010(6)]),flip(a)]. 2032 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (((T(y,z) * x) * x) * u),w))) = w. [para(682(a,1),1885(a,1,2,2,2,1,2))]. 2040 (x * (y * y)) * z = x * (y * (y * z)). [back_rewrite(407),rewrite([2012(7)]),flip(a)]. 2044 R(x,y * y,z) = x. [back_rewrite(338),rewrite([2040(3),17(6)]),flip(a)]. 2045 a(x,y * y,z) = 1. [back_rewrite(311),rewrite([2040(6),46(7)]),flip(a)]. 2166 x / (T(T(y,z),u) * (z * (((T(y,u) * z) * z) \ x))) = z. [para(16(a,1),1266(a,1,1))]. 2213 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(13(a,1),130(a,1,1,2,2)),rewrite([13(8)])]. 2215 x * (y * (z * (y * (x * ((x * (y * (z * (y * x)))) \ u))))) = u. [para(130(a,1),16(a,1))]. 2254 L(x,y,z * z) = x. [para(13(a,1),132(a,1,1,2)),rewrite([13(6),638(6),667(3),13(2)]),flip(a)]. 2276 L(x,y,z * (((z * y) \ 1) * z)) = ((z * y) \ 1) * (z * (y * x)). [para(997(a,1),132(a,1,1,2)),rewrite([14(2),15(8)]),flip(a)]. 2278 L(x,y,z * (((z * (y * x)) \ 1) * z)) = (((z * (y * x)) \ 1) * (z * y)) \ 1. [para(997(a,1),132(a,1,2,2)),rewrite([14(9),1091(8)]),flip(a)]. 2356 L(L(L(x,y,z),u,(u * x) \ 1),((u * x) \ 1) * u,w) = L(L(x,u,(u * x) \ 1),y,z). [para(1026(a,1),1078(a,1,2,1)),rewrite([990(13)])]. 2357 L(L(x,y,(y * x) \ 1),z,u) = L((((y * x) \ 1) * y) \ 1,z,u). [para(1026(a,1),1078(a,2,1)),rewrite([1141(11),2356(10)])]. 2485 L(x,y * y,z) = x. [hyper(24,a,2045,a)]. 2486 a(x,y * (y * (z * (y * (y * z)))),u) = 1. [para(37(a,1),2045(a,1,2))]. 2495 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(2254(a,1),74(a,1)),rewrite([100(3),100(5)]),flip(a)]. 2507 L(x,y,z * (z * u)) = L(x,y,u). [back_rewrite(144),rewrite([2495(8),21(4)]),flip(a)]. 2508 a(x * (x * y),z,u) = a(y,z,u). [back_rewrite(140),rewrite([2495(9),19(5)]),flip(a)]. 2528 L(x,(y \ 1) / y,z) = x. [para(1014(a,1),2485(a,1,2))]. 2538 (x \ y) \ 1 = y \ x. [para(16(a,1),1091(a,1,1)),flip(a)]. 2540 ((x \ y) * (x * z)) \ 1 = ((y * x) * z) \ x. [para(104(a,1),1091(a,1,1)),flip(a)]. 2548 ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. [para(54(a,1),1091(a,1,1))]. 2556 ((x / y) * ((y \ 1) \ z)) / z = R(x,y \ 1,(y \ 1) \ z). [para(1091(a,1),268(a,1,1,1,2)),rewrite([1014(3),1091(4),1812(5),1091(8),1091(10)])]. 2560 T(x * y,(y \ 1) \ x) = x * y. [para(1091(a,1),560(a,1,2,1))]. 2574 a(x,T(y,x),x * z) = a(y * x,x,z) \ 1. [back_rewrite(673),rewrite([2548(7)]),flip(a)]. 2575 a(x,x \ y,x * z) = a(y,x,z) \ 1. [back_rewrite(173),rewrite([2548(8)])]. 2599 ((x / y) * (y * y)) / T(x * y,a(x,y \ 1,y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),729(a,1,1,1,2)),rewrite([1014(3),1649(6),1649(12)])]. 2601 ((x / y) * (y * y)) \ ((y \ 1) \ x) = K(((y \ 1) \ x) * y,y \ 1). [para(1649(a,1),354(a,1,1,1,2)),rewrite([1014(3),1649(5),1649(9),1014(10),17(8),1649(9),1649(13)])]. 2604 (x * y) \ ((x / y) * (y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),58(a,1,2,1,2)),rewrite([1014(4),1649(7)])]. 2635 T(T(x * x,y),x) = T(x * x,y). [para(1659(a,1),29(a,1,1)),flip(a)]. 2639 T((x \ 1) / x,x \ 1) = (x \ 1) / x. [para(1014(a,1),1659(a,1,1)),rewrite([1014(11)])]. 2640 x * (x * (y * (y * (z / (T(x * x,y) * (y * z)))))) = y. [para(1659(a,1),1266(a,1,1,1,1,1)),rewrite([100(2),37(3),37(4),100(2),2635(7),1839(9),1839(7)])]. 2642 T(x,x \ y) = T(x,y). [para(16(a,1),1708(a,1,2)),flip(a)]. 2643 T(x / y,x) = y \ x. [para(18(a,1),1708(a,1,2)),rewrite([92(4)])]. 2647 T(x * (x * y),x * (x * (y * z))) = T(x * (x * y),z). [para(37(a,1),1708(a,1,2))]. 2649 (x \ y) \ y = T(x,y). [para(91(a,1),1708(a,2)),rewrite([16(2)]),flip(a)]. 2652 T(x,y * x) = T(x,T(y,x)). [para(90(a,1),1708(a,1,2))]. 2690 (x \ y) * T(x,y) = y. [back_rewrite(1457),rewrite([2649(3),2642(7),166(8)])]. 2692 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(1452),rewrite([2642(9)])]. 2705 L(x \ y,x,z) \ (z * y) = T(z * x,z * y). [back_rewrite(650),rewrite([2642(5)]),flip(a)]. 2709 T(x \ y,T(x,y)) = T(x,y) \ y. [back_rewrite(221),rewrite([2642(3),2649(5)])]. 2711 x / T(y,x) = y \ x. [back_rewrite(218),rewrite([2642(2)])]. 2712 (x \ 1) / x = x \ (x \ 1). [back_rewrite(2639),rewrite([2643(6)]),flip(a)]. 2747 L(x,y \ (y \ 1),z) = x. [back_rewrite(2528),rewrite([2712(3)])]. 2755 (x \ 1) \ y = x * y. [back_rewrite(1227),rewrite([2747(5)]),flip(a)]. 2757 ((x / y) * (y * y)) \ (y * x) = K(y * (x * y),y \ 1). [back_rewrite(2601),rewrite([2755(6),2755(8),101(7)])]. 2759 T(x * y,y * x) = x * y. [back_rewrite(2560),rewrite([2755(4)])]. 2760 ((x / y) * (y * z)) / z = R(x,y \ 1,y * z). [back_rewrite(2556),rewrite([2755(4),2755(9)])]. 2774 T(x * y,y \ 1) = y * x. [back_rewrite(1812),rewrite([2755(7)])]. 2796 R(x,x / y,(x / y) \ z) = R(x,y \ 1,y * z). [back_rewrite(208),rewrite([2760(8)])]. 2806 ((x / y) * z) / (y \ z) = R(x,y \ 1,z). [back_rewrite(1972),rewrite([2796(5),16(4)]),flip(a)]. 2917 K(x,y) \ 1 = K(y,x). [para(63(a,1),1091(a,1,1)),rewrite([20(3)]),flip(a)]. 2918 T(x * y,K(y,x)) = x * y. [para(63(a,1),1708(a,1,2)),rewrite([2759(3)]),flip(a)]. 2934 (x * (y * z)) \ (L(z,y,x) * (x * y)) = K(L(z,y,x),x * y). [para(21(a,1),64(a,1,2,1)),rewrite([21(10)])]. 2965 x * (((x \ y) * x) * z) = y * (x * z). [para(16(a,1),189(a,1,1)),flip(a)]. 3018 L(x * (y * z),x \ y,x) = (x * y) * z. [para(189(a,1),181(a,2,2)),rewrite([15(8)])]. 3031 x * (((y \ 1) * x) * z) = (x / y) * (x * z). [para(1014(a,1),189(a,1,1)),flip(a)]. 3093 x * a(y,z,y * ((y * (z * y)) \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [para(103(a,1),54(a,1,1)),rewrite([189(12)])]. 3135 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(16(a,1),2495(a,1,1,2))]. 3136 (x * (x * y)) \ (x * z) = y \ (x \ z). [para(16(a,1),2495(a,1,2,2))]. 3139 T(x * (x * (y / (x * (x * z)))),x * (x * z)) = z \ y. [para(2495(a,1),92(a,2)),rewrite([1839(5)])]. 3143 (x \ 1) * y = x \ y. [para(997(a,1),2495(a,1,1,2)),rewrite([14(4),15(9)])]. 3162 (x \ ((x * y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(141),rewrite([3135(7)])]. 3169 (x / y) * (x * z) = x * ((y \ x) * z). [back_rewrite(3031),rewrite([3143(3)]),flip(a)]. 3191 L(L(x,y,(y * x) \ 1),z,u) = L(x,z,u). [back_rewrite(2357),rewrite([3143(9),1091(7),2649(9),88(7)])]. 3192 L(L(x,y,z),u,(u * x) \ 1) = L(x,y,z). [back_rewrite(2356),rewrite([3143(9),1091(7),1080(8),3191(10)])]. 3199 L(x,y,z / (y * x)) = L(x,y,z). [back_rewrite(2278),rewrite([3143(5),1091(3),1014(4),3143(9),2538(9),21(7)])]. 3200 L(x,y,z / y) = L(x,y,z). [back_rewrite(2276),rewrite([3143(4),1091(2),1014(3),3143(8),21(6)])]. 3213 R(x,x * y,(x * y) \ z) = R(x,y,y \ z). [back_rewrite(2004),rewrite([3143(8),169(7),191(8)])]. 3218 x * (y \ T(z,x * (x / y))) = x \ (z * (x * (x / y))). [back_rewrite(1888),rewrite([3143(6)])]. 3229 (x / y) \ (x * (y \ z)) = L(z,y \ 1,x). [back_rewrite(1834),rewrite([3143(4)])]. 3266 L(x,y,y \ 1) = x. [back_rewrite(1025),rewrite([3143(4),15(2)]),flip(a)]. 3276 x \ ((x / y) * (y * z)) = L(z,y,x). [back_rewrite(75),rewrite([3200(6)])]. 3304 T(x,K(y \ x,y)) = x. [para(16(a,1),2918(a,1,1)),rewrite([16(5)])]. 3307 T((x * y) * z,K((y \ x) * (y * z),y)) = (x * y) * z. [para(104(a,1),2918(a,1,1)),rewrite([104(11)])]. 3308 K(x,y) * (y * x) = x * y. [para(2918(a,1),90(a,1,2)),rewrite([63(6)])]. 3323 (((x \ y) * (x * z)) * x) / ((y * x) * z) = K((x \ y) * (x * z),x). [back_rewrite(969),rewrite([3307(11)])]. 3436 (x * x) \ y = x \ (x \ y). [para(18(a,1),1324(a,1,2,2)),rewrite([92(8),1619(6)]),flip(a)]. 3476 x * T(y * z,y * (y * x)) = (y \ z) * (y * (y * x)). [para(181(a,2),1324(a,1,2)),rewrite([3018(5),168(4)]),flip(a)]. 3541 x \ (y \ (z * (y * (x * y)))) = y * T(z,y * (x * y)). [para(1359(a,1),15(a,1,2))]. 3640 x * (x * (((x \ y) / z) / T(x * y,z \ 1))) = z \ 1. [para(16(a,1),1884(a,1,2,2,2,1,2))]. 3645 (x / y) / T(z * (z * x),y \ 1) = z \ (z \ (y \ 1)). [para(1884(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 3646 R(x,x \ (y \ 1),z) = (y \ z) / ((x \ (y \ 1)) * z). [para(1884(a,1),22(a,1,1,1)),rewrite([3143(3),3645(8),16(6),3645(13),16(11)]),flip(a)]. 3666 (x \ y) / y = x \ 1. [para(1884(a,1),201(a,1,2)),rewrite([3645(8),100(6),16(5),16(4),3645(11),16(9),16(8),2755(7),480(6),3645(9),16(7),16(6),3645(11),1300(9),13(6),3143(5)]),flip(a)]. 3691 x / (y * x) = y \ 1. [para(1884(a,1),1013(a,2)),rewrite([3645(7),16(5),2538(5),2755(3)])]. 3723 R(x \ 1,x,y) = x \ 1. [back_rewrite(1027),rewrite([3691(5)])]. 3724 x / (y * (z * (y * x))) = (y * (z * y)) \ 1. [back_rewrite(1448),rewrite([3723(7)]),flip(a)]. 3725 x / (y * (y * (z * x))) = (y * (y * z)) \ 1. [back_rewrite(1039),rewrite([3723(7)]),flip(a)]. 3933 x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u)))))) = x * u. [para(398(a,1),15(a,1,2)),rewrite([15(3)]),flip(a)]. 3934 K(x * y,x) = y \ T(y,x). [para(398(a,1),20(a,1,1)),rewrite([3933(13),101(4),3136(5),23(2),3933(13)]),flip(a)]. 3935 K(x,x * y) = T(y,x) \ y. [para(398(a,1),20(a,1,2)),rewrite([3933(11),101(2),3135(5),23(2),3933(13)]),flip(a)]. 3936 x * (y * (y * (x * (z * ((x * (y * (y * (x * z)))) \ u))))) = u. [para(398(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 3940 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(398(a,1),74(a,2,1)),rewrite([3936(10),3936(12),3136(8)])]. 3941 L(x \ (y * z),x,y) = (y \ x) \ z. [para(398(a,1),74(a,2,2)),rewrite([3936(10),3135(7)])]. 3947 x * (x * (y * (x * (x * (y * (z \ ((y * (x * (x * (y / z)))) \ u))))))) = x * (x * u). [para(1014(a,1),398(a,1,2,2,2,2,2,2,2,1,2,2,2)),rewrite([3143(8)])]. 3949 x * (x * (y * ((x * (x * (x * (x * y)))) \ z))) = x \ (x \ z). [para(398(a,1),132(a,1,2)),rewrite([3135(6),15(3),3436(2),2507(13),1607(11)]),flip(a)]. 3954 a(x,x \ y,z) = a(x,x * y,z). [para(398(a,1),133(a,1,2,1)),rewrite([3949(8),16(3),136(4),37(6),3135(7),3162(5),3949(12),16(7),2508(6)]),flip(a)]. 3982 a(x,x * y,x * z) = a(y,x,z) \ 1. [back_rewrite(2575),rewrite([3954(3)])]. 4013 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x / y,y). [back_rewrite(1051),rewrite([3954(11),1014(10)])]. 4021 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,x * ((y * x) * z),u). [back_rewrite(662),rewrite([3954(13),189(12)])]. 4032 (x * ((x \ y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(56),rewrite([3954(7)])]. 4114 ((x * y) * z) \ R(x,y,z) = (y * z) \ 1. [para(22(a,1),1829(a,1,2))]. 4115 ((x / y) * x) * z = x * (y \ (x * z)). [para(1829(a,1),104(a,1,2,1)),rewrite([3143(4)]),flip(a)]. 4137 (x \ y) * (y \ x) = 1. [para(2538(a,1),16(a,1,2))]. 4145 L(x \ y,y \ x,z) = x \ y. [para(2538(a,1),74(a,1,1)),rewrite([14(7),1091(6),2538(6)])]. 4151 a(x,y \ z,z \ y) = 1. [para(2538(a,1),1012(a,1,2))]. 4155 x / (y \ z) = x * (z \ y). [para(2538(a,1),1013(a,1,2))]. 4157 (x * y) \ ((x / z) * (z * y)) = a(x / z,z,y) \ 1. [para(60(a,1),2538(a,1,1)),flip(a)]. 4165 L(x,y \ z,z \ y) = x. [para(2538(a,1),3266(a,1,3))]. 4180 x * ((x \ (y / z)) * z) = R(y,z \ 1,x). [back_rewrite(2806),rewrite([4155(4),169(4)])]. 4186 R(x,y,y \ ((y \ x) \ z)) = z * ((z \ y) * (y \ x)). [back_rewrite(199),rewrite([4155(8),169(8)])]. 4187 a(x / y,y,y) \ 1 = a(x,y \ 1,y * y). [back_rewrite(2604),rewrite([4157(5)])]. 4209 T(x * y,x) = y * x. [para(1091(a,1),2642(a,1,2)),rewrite([2774(4)]),flip(a)]. 4210 T(x,(y \ x) * y) = x. [para(64(a,1),2642(a,1,2)),rewrite([3304(3)]),flip(a)]. 4230 (x / y) * x = x * (y \ x). [para(2643(a,1),90(a,1,2)),flip(a)]. 4247 (x * (y \ x)) * z = x * (y \ (x * z)). [back_rewrite(4115),rewrite([4230(2)])]. 4254 (x / y) * ((x / y) * ((y * z) / T(x * (y \ x),z))) = z. [back_rewrite(2009),rewrite([4230(5)])]. 4278 T(x,y) \ y = T(x \ y,y). [para(2649(a,1),2642(a,1,2)),rewrite([2709(3)])]. 4281 T(x \ y,T(x,y)) = T(x \ y,y). [back_rewrite(2709),rewrite([4278(5)])]. 4314 T(x,y) * (T(x \ y,y) * (T(x,y) * z)) = (x * y) * z. [para(2690(a,1),186(a,2,1,1)),rewrite([4281(4),90(9)])]. 4357 (x \ (x \ y)) * T(x,y) = x \ y. [para(2642(a,1),2690(a,1,2))]. 4365 x / T(x,y) = T(x,y) \ x. [para(159(a,1),2711(a,1,2))]. 4366 T(x,y) / x = x \ T(x,y). [para(541(a,1),2711(a,1,2))]. 4379 ((x \ y) * x) / y = K(x \ y,x). [para(64(a,1),2711(a,2)),rewrite([4210(5)])]. 4407 (x * y) \ 1 = y \ (x \ 1). [para(2755(a,1),2538(a,1,1))]. 4408 (x \ y) \ z = (y \ x) * z. [para(2538(a,1),2755(a,1,1))]. 4417 ((x * y) * z) \ R(x,y,z) = z \ (y \ 1). [back_rewrite(4114),rewrite([4407(7)])]. 4419 ((x \ (y \ 1)) * y) \ (x \ 1) = a(x,x / y,y). [back_rewrite(4013),rewrite([4407(7)])]. 4420 x / (y * (y * (z * x))) = (y * z) \ (y \ 1). [back_rewrite(3725),rewrite([4407(8)])]. 4421 x / (y * (z * (y * x))) = (z * y) \ (y \ 1). [back_rewrite(3724),rewrite([4407(8)])]. 4445 L(L(x,y,z),u,x \ (u \ 1)) = L(x,y,z). [back_rewrite(3192),rewrite([4407(4)])]. 4458 ((x * y) * z) \ y = (y * z) \ (x \ y). [back_rewrite(2540),rewrite([4407(5),4408(4),14(4)]),flip(a)]. 4470 R(x,y,y \ ((x \ y) * z)) = z * ((z \ y) * (y \ x)). [back_rewrite(4186),rewrite([4408(2)])]. 4480 L(x \ (y * z),x,y) = (x \ y) * z. [back_rewrite(3941),rewrite([4408(5)])]. 4498 (((x * y) * z) \ x) * (y * z) = a(x,x * y,z). [back_rewrite(3162),rewrite([4408(5)])]. 4501 (x * y) \ (x * (x * z)) = (y \ x) * z. [back_rewrite(3135),rewrite([4408(6)])]. 4504 (x \ y) * (((y \ x) * z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(2692),rewrite([4408(3)])]. 4505 (x \ y) * x = T(y,x). [back_rewrite(2649),rewrite([4408(2)])]. 4516 K(x \ y,x) = y \ T(y,x). [back_rewrite(4379),rewrite([4505(2),4366(2)]),flip(a)]. 4525 x * (T(y,x) * z) = y * (x * z). [back_rewrite(2965),rewrite([4505(2)])]. 4537 a(T(x,y),y \ x,z) = a(y \ x,x,z). [back_rewrite(1702),rewrite([4505(2)])]. 4539 K(x,x \ y) = T(y,x) \ y. [back_rewrite(65),rewrite([4505(2)]),flip(a)]. 4562 ((x * y) * y) / z = x * (y * (y / z)). [back_rewrite(1859),rewrite([4525(4)]),flip(a)]. 4578 (x * y) * y = x * (y * y). [back_rewrite(669),rewrite([4525(3)]),flip(a)]. 4582 a(x,T(y,x),z) = a(y,x,z). [back_rewrite(508),rewrite([4525(3),19(5)]),flip(a)]. 4613 (x * (y * y)) / z = x * (y * (y / z)). [back_rewrite(4562),rewrite([4578(2)])]. 4713 x / (T(T(y,z),u) * (z * ((T(y,u) * (z * z)) \ x))) = z. [back_rewrite(2166),rewrite([4578(5)])]. 4714 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w))) = w. [back_rewrite(2032),rewrite([4578(8),2040(9)])]. 4795 a(x * y,y,z) \ 1 = a(x,y,y * z). [back_rewrite(2574),rewrite([4582(3)]),flip(a)]. 4813 (x / y) * (y * (y / T(x * y,a(x,y \ 1,y * y)))) = a(x,y \ 1,y * y). [back_rewrite(2599),rewrite([4613(10)])]. 4993 K(x,y) * K(y,x) = 1. [para(2917(a,1),16(a,1,2))]. 4996 R(x,K(y,z),K(z,y)) = x. [para(2917(a,1),191(a,2,3)),rewrite([14(5),16(4),48(2)]),flip(a)]. 5005 x / K(y,z) = x * K(z,y). [para(2917(a,1),1014(a,1,2)),flip(a)]. 5011 L(x,K(y,z),K(z,y)) = x. [para(2917(a,1),3266(a,1,3))]. 5134 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(15(a,1),3940(a,1,1)),flip(a)]. 5155 L((x / y) \ z,x / y,x) = y * (x \ z). [para(1014(a,1),3940(a,1,1,1)),rewrite([1014(5),4408(8),45(6)])]. 5162 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(3940(a,1),2254(a,1)),rewrite([3436(2),100(5)]),flip(a)]. 5163 L((x * y) \ z,x * y,y * x) = K(x,y) \ ((y * x) \ z). [para(63(a,1),3940(a,1,1,1)),rewrite([63(5)])]. 5194 R(x,y * (y * z),z \ (y \ (y \ u))) = R(x,z,z \ u). [back_rewrite(1870),rewrite([5162(3),191(6),1935(6),16(3),16(2),5162(7)]),flip(a)]. 5200 x * (x * (y * ((y \ (x \ (x \ z))) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [back_rewrite(411),rewrite([5162(3)])]. 5208 (x * (y \ z)) * (z \ y) = x. [para(4151(a,1),209(a,1,1)),rewrite([45(6),4137(7),14(6),4151(7),88(6)])]. 5332 a(x,y,y) = 1. [para(89(a,1),507(a,1,2,2)),rewrite([4578(4),46(5),89(2)]),flip(a)]. 5358 a(x,y \ 1,y * y) = 1. [back_rewrite(4187),rewrite([5332(2),46(3)]),flip(a)]. 5359 (x / y) * (y / x) = 1. [back_rewrite(4813),rewrite([5358(6),88(4),3691(3),1014(4),5358(7)])]. 5452 x * (x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u))))))) = y * z. [para(189(a,1),2640(a,1,2,2,2,2,2,2))]. 5468 T(x * (x * y),y \ z) = T(x * (x * y),x * (x * z)). [para(16(a,1),2647(a,1,2,2,2)),flip(a)]. 5480 T(x * (x * y),x * (x * (y / z))) = T(x * (x * y),z \ 1). [para(1014(a,1),2647(a,1,2,2,2))]. 5610 (x \ (y \ (y \ (z \ 1)))) * (z * (y * (y * (x * u)))) = L(u,y * (y * x),z). [para(37(a,1),145(a,1,1)),rewrite([37(11),4501(12),1091(5),4407(5),5162(5),2507(15)])]. 5614 L(x,y * (y * z),z) = x. [para(1607(a,1),145(a,2)),rewrite([189(5),101(2),189(4),4578(2),101(3),100(2),189(11),101(7),189(10),4578(7),189(9),100(7),37(8),4501(12),1091(5),4407(5),5162(5),5610(10)])]. 5657 x * (y * (x * (z * ((z * (x * (y * (x * z)))) \ u)))) = z \ u. [para(2215(a,1),15(a,1,2)),flip(a)]. 5665 R(x,y,y \ ((x \ y) * z)) = (y * z) / ((x \ y) * z). [para(2215(a,1),191(a,1,1,2)),rewrite([5657(13),4408(3),5657(16),4408(6)]),flip(a)]. 5816 R(x * ((x \ y) * (y \ z)),z,z \ u) = (z * (a(y,x,x \ (y \ z)) * u)) / u. [para(16(a,1),435(a,1,2)),rewrite([16(6),16(8)])]. 5879 x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))) = z. [para(463(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 5885 (x \ (y \ 1)) * (y * (x * z)) = L(z,x,y). [para(463(a,1),132(a,1,1,2)),rewrite([5879(13),4501(8),1091(3),4407(3),5879(16),2507(9)])]. 6069 (x \ (y \ 1)) * (x * y) = K(x,y). [para(20(a,1),3143(a,2)),rewrite([4407(3)])]. 6070 (x \ y) * (y \ (x * z)) = L(z,x,y \ 1). [para(3143(a,1),21(a,1,1)),rewrite([3143(5),4408(4)])]. 6073 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [para(3143(a,1),37(a,1,1,2)),rewrite([3143(4),3143(9),3143(8)]),flip(a)]. 6120 (x \ 1) / y = x \ (y \ 1). [para(3143(a,1),1014(a,1)),flip(a)]. 6132 (x \ (y \ 1)) * y = x \ 1. [para(1091(a,1),3143(a,2)),rewrite([4407(3)])]. 6134 T(x \ 1,x \ y) = T(x \ 1,y). [para(3143(a,1),1708(a,1,2))]. 6141 ((x * y) \ (z \ (z \ (u \ 1)))) * ((u * (z * (z * x))) * y) = a(u,z * (z * x),y). [para(139(a,1),3143(a,2)),rewrite([4407(6),5162(6)])]. 6144 K(x,y) \ z = K(y,x) * z. [para(2917(a,1),3143(a,1,1)),flip(a)]. 6233 a(x,x / y,y) = 1. [back_rewrite(4419),rewrite([6132(4),46(5)]),flip(a)]. 6238 L((x * y) \ z,x * y,y * x) = K(y,x) * ((y * x) \ z). [back_rewrite(5163),rewrite([6144(9)])]. 6257 L(x,y / x,y) = x. [hyper(24,a,6233,a)]. 6258 a(x * y,x,y) = 1. [para(17(a,1),6233(a,1,2))]. 6279 L(x,y,y * x) = x. [para(17(a,1),6257(a,1,2))]. 6351 x * ((x \ y) * y) = y * y. [para(6258(a,1),435(a,2,1,2,1)),rewrite([16(2),16(5),16(6),3436(6),2044(7),16(5),13(6),100(5),1839(6),47(4),14(5)])]. 6353 (x \ y) * ((y \ x) * z) = L(z,(y \ x) * x,y). [back_rewrite(831),rewrite([6351(3),3436(6),6073(6),15(2)])]. 6416 L(x,y \ 1,y \ x) = x. [para(3143(a,1),6279(a,1,3))]. 6562 K(x,y) / (x * y) = x \ (y \ 1). [para(20(a,1),3666(a,1,1)),rewrite([4407(6)])]. 6565 (x / y) \ 1 = y / x. [para(50(a,1),3666(a,1,1)),flip(a)]. 6591 L(x,y,z) \ (y \ (z \ 1)) = (y * x) \ (z \ 1). [para(2934(a,1),3666(a,1,1)),rewrite([6562(7),4407(4),4407(9)])]. 6618 L(x,y \ 1,z * y) = L(x,y \ z,y). [para(73(a,1),181(a,2)),rewrite([1091(2),3143(3),16(2),1091(4)]),flip(a)]. 6663 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,u,w),y,z))) \ (v6 * v5). [para(76(a,1),228(a,1)),flip(a)]. 6676 L(x,y \ (x \ 1),z) = (z * (y \ (x \ 1))) \ (z / y). [para(1014(a,1),76(a,2,2)),rewrite([6120(3),6120(7)])]. 6793 L(L(R(x,y,z),u,w),v5,x \ (v5 \ 1)) = L(R(x,y,z),u,w). [para(4445(a,1),33(a,1,1)),rewrite([33(2),33(4)]),flip(a)]. 6887 L(K(x * (y * x),x \ 1),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [para(2757(a,1),3940(a,1,1)),rewrite([3436(15)])]. 6890 K(x * (y * x),x \ 1) = K(x,y). [para(2757(a,1),3143(a,2)),rewrite([4407(5),6565(4),3436(3),1829(2),6069(5)]),flip(a)]. 6897 L(K(x,y),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [back_rewrite(6887),rewrite([6890(5)])]. 6946 T(x * (x * (y / (x * z))),x * z) = (z \ x) * y. [para(16(a,1),3139(a,1,1,2,2,2,2)),rewrite([16(6),4408(8)])]. 6953 (x \ ((y * z) \ (y \ 1))) * u = (z * x) \ (y \ (y \ u)). [para(341(a,1),3139(a,1,1,2,2,2,2)),rewrite([341(27),6946(26),4417(8),4407(4),5162(10)])]. 7004 x * (y \ ((x * (x / y)) \ z)) = x \ z. [para(18(a,1),3218(a,2,2)),rewrite([92(6)])]. 7047 T(x,K((y \ z) * (y * ((z * y) \ x)),y)) = x. [para(16(a,1),3307(a,1,1)),rewrite([16(11)])]. 7488 x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u)))))) = x \ (y * z). [para(5452(a,1),15(a,1,2)),flip(a)]. 7490 (x * y) * ((x * y) * ((x * z) / (T(u * u,x * y) * (x * ((y * x) * z))))) = (u \ (u \ x)) * y. [para(5452(a,1),21(a,1,2)),rewrite([3436(3),6073(3),1607(17)]),flip(a)]. 7550 x * ((x \ (x \ y)) * z) = x \ (y * z). [back_rewrite(7488),rewrite([7490(13)])]. 7616 T(x,y) / y = y \ x. [para(2690(a,1),3691(a,1,2)),rewrite([4408(5),14(5)])]. 7617 T(x,y) * (y \ x) = (y \ x) * x. [para(4357(a,1),3691(a,1,2)),rewrite([4155(3),4408(7),4408(5),14(7)])]. 7656 L(x,(y \ z) * z,y) = x. [para(4137(a,1),21(a,1,1)),rewrite([6353(5),45(5),4165(6)])]. 7679 L(x,y \ z,(z \ y) * (u * (z \ y))) = L(x,u,z \ y). [para(4137(a,1),132(a,1,1,2,2)),rewrite([14(3),6353(7),7656(6),21(6)]),flip(a)]. 7713 K(x \ y,(y \ x) * z) = K(x \ y,z). [para(4137(a,1),177(a,1,1,1,2)),rewrite([4408(2),14(4),5208(8),4458(5),4408(4),20(5),4408(5),4137(8),14(7)]),flip(a)]. 7715 (x \ y) * ((y \ x) * z) = z. [back_rewrite(6353),rewrite([7656(7)])]. 7769 T(T(x,y),y \ x) = x. [para(16(a,1),4209(a,2)),rewrite([4505(2)])]. 7772 ((x \ y) * (x * z)) * x = T((y * x) * z,x). [para(104(a,1),4209(a,1,1)),flip(a)]. 7775 T(x,y) * y = T(x * y,y). [para(90(a,1),4209(a,1,1)),flip(a)]. 7820 K((x \ y) * (x * z),x) = K(x * ((y * x) * z),x). [back_rewrite(3323),rewrite([7772(4),4366(6),3934(6,R)]),flip(a)]. 7826 x * K(y * x,y) = T(x,y). [back_rewrite(874),rewrite([7820(6),16(4),7772(9),16(7)])]. 7925 T(x,K(y * x,y)) = x. [back_rewrite(7047),rewrite([7820(6),16(4)])]. 7967 x \ T(y,x) = T(x \ y,x). [para(4505(a,1),23(a,1,2))]. 8018 T(x,y) \ (y \ x) = y \ 1. [para(4505(a,1),1091(a,1,1))]. 8054 a(x \ y,y,x) = 1. [para(4505(a,1),6258(a,1,1)),rewrite([4537(3)])]. 8105 L(x,y,x \ y) = x. [hyper(24,a,8054,a)]. 8106 a(x,y * x,y) = 1. [para(15(a,1),8054(a,1,1))]. 8296 K(x,y) * (K(y,x) * z) = z. [para(4993(a,1),21(a,1,1)),rewrite([45(6),5011(7)])]. 8298 (x * K(y,z)) * K(z,y) = x. [para(4993(a,1),22(a,1,2)),rewrite([48(6),4996(7)])]. 8308 L(x,K(y,z),K(z,y) * (u * K(z,y))) = L(x,u,K(z,y)). [para(4993(a,1),132(a,1,1,2,2)),rewrite([14(3),8296(7),21(6)]),flip(a)]. 8379 R(x,x \ y,z) = z * ((z \ y) * (y \ x)). [para(81(a,2),1014(a,2)),rewrite([4407(5),4408(4),14(4),169(4)]),flip(a)]. 8463 R(x,y \ 1,(x / y) \ z) = R(x,y \ 1,z). [para(1014(a,1),82(a,1,3,1)),rewrite([1014(10),3143(10),4155(9),4408(8),4180(9)])]. 8532 T(x,y) \ x = K(x \ y,x). [para(2642(a,1),4539(a,2,1)),rewrite([4408(3),7713(4)]),flip(a)]. 8593 x / T(x,y) = K(x \ y,x). [back_rewrite(4365),rewrite([8532(4)])]. 8594 K(x \ y,x) = K(y,y * x). [back_rewrite(3935),rewrite([8532(4)]),flip(a)]. 8701 L(x \ y,x,z) = ((z / y) * x) \ z. [para(3199(a,1),74(a,1)),rewrite([16(4),16(6),18(6)])]. 8992 ((x \ y) * (x * (x * z))) / T(z,T(x * y,x * (x * z))) = T(x * y,x * (x * z)). [para(3476(a,1),165(a,1,1))]. 9001 T(x,(y \ z) * (y * (y * x))) = T(x,T(y * z,y * (y * x))). [para(3476(a,1),1708(a,1,2))]. 9050 x * ((x * (y * x)) \ z) = y \ (x \ z). [para(18(a,1),3541(a,1,2,2)),rewrite([92(8)]),flip(a)]. 9085 x * a(y,z,z \ (y \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [back_rewrite(3093),rewrite([9050(4)])]. 9101 (x * (((y * z) * (z * y)) * u)) * a(x,(z * y) * (y * z),u) = (x * ((z * y) * (y * z))) * u. [para(178(a,1),312(a,1,1,2)),rewrite([3308(9),3308(14)])]. 9114 ((x * ((y * z) * (z * y))) * u) / (((z * y) * (y * z)) * u) = R(x,(y * z) * (z * y),u). [para(178(a,1),121(a,1,2)),rewrite([3308(4),3308(14)])]. 9186 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,(y \ z) * (y * x),y). [para(179(a,1),3143(a,2)),rewrite([4407(4),4407(3)])]. 9198 x \ (K(y,z) * ((K(z,y) * x) * u)) = L(u,K(z,y) * x,K(y,z)). [para(4993(a,1),179(a,1,1,1)),rewrite([13(2),6144(4),100(7),8296(6),6144(9),100(12),8296(11)])]. 9548 x * (x * (y * (x * (x * (y * (z \ ((y / z) \ (x \ (x \ (y \ 1)))))))))) = x * x. [para(14(a,1),3947(a,2,2)),rewrite([4407(6),5162(6)])]. 9559 L(x,y \ z,y) = L(x,y * z,y). [para(3947(a,1),132(a,1,1)),rewrite([5162(7),7004(9),16(6),16(5),136(6),21(6),5162(7),7004(9),16(6),16(5),2507(6)]),flip(a)]. 9719 L(x,y \ 1,z * y) = L(x,y * z,y). [back_rewrite(6618),rewrite([9559(6)])]. 10000 (x / y) * ((y / x) * z) = L(z,y / x,x / y). [para(5359(a,1),21(a,1,1)),rewrite([45(6)])]. 10215 x / (y / z) = x * (z / y). [para(6565(a,1),1014(a,1,2)),flip(a)]. 10221 L(x,y / z,z / y) = x. [para(6565(a,1),3266(a,1,3))]. 10229 (x / y) \ z = (y / x) * z. [para(6565(a,1),3143(a,1,1)),flip(a)]. 10279 ((x * y) / z) * (z / y) = R(x,y,z \ 1). [back_rewrite(1836),rewrite([10215(4)])]. 10287 (x / y) * ((y / x) * z) = z. [back_rewrite(10000),rewrite([10221(7)])]. 10296 x * (x * (y * (x * (x * (y * (z \ ((z / y) * (x \ (x \ (y \ 1)))))))))) = x * x. [back_rewrite(9548),rewrite([10229(6)])]. 10305 R(x,y \ 1,(y / x) * z) = R(x,y \ 1,z). [back_rewrite(8463),rewrite([10229(4)])]. 10321 L(K(x,y),(y / x) * (x * x),y / x) = x \ T(x,y). [back_rewrite(6897),rewrite([10229(9),3169(9),4505(8),15(9)])]. 10347 L((x / y) * z,y / x,y) = x * (y \ z). [back_rewrite(5155),rewrite([10229(2)])]. 10367 (x / y) * (y * (x \ z)) = L(z,x \ 1,y). [back_rewrite(3229),rewrite([10229(4)])]. 10690 ((x / y) * z) \ x = (x * z) \ (x * y). [para(8701(a,1),21(a,2)),rewrite([16(3)]),flip(a)]. 10809 (x \ y) * (x * (x * z)) = T(y * x,x) * z. [para(7967(a,1),104(a,1,2,1)),rewrite([4525(5),7775(6)])]. 10885 T(x,T(y * z,y * (y * x))) = T(x,T(T(z * y,y),x)). [back_rewrite(9001),rewrite([10809(4),2652(4)]),flip(a)]. 10888 T(x * y,x * (x * z)) = T(T(y * x,x),z). [back_rewrite(8992),rewrite([10809(4),10885(8),965(8)]),flip(a)]. 10920 T(x * (y * y),x / z) = T(y * (y * x),z \ 1). [back_rewrite(5480),rewrite([10888(6),101(2),4209(3),4578(2)])]. 10927 T(x * (x * y),y \ z) = T(y * (x * x),z). [back_rewrite(5468),rewrite([10888(9),101(6),4209(7),4578(6)])]. 11076 L(T(x * y,x * z),L(y \ z,y,x),u) = (u * L(y \ z,y,x)) \ (u * (x * z)). [para(2705(a,1),74(a,1,1))]. 11083 (x \ y) * (z * (z * x)) = T(y * (z * z),x). [para(2254(a,1),2705(a,1,1)),rewrite([100(3),4408(4),100(6),100(8),10888(9),101(6),4209(7),4578(6)])]. 11219 ((x \ y) / z) / T(x * y,z \ 1) = x \ (x \ (z \ 1)). [para(3640(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 11253 R(x,x \ (y \ 1),y * z) = z / ((x \ (y \ 1)) * (y * z)). [para(3640(a,1),82(a,1,3,1)),rewrite([11219(7),16(5),4408(6),45(5),11219(12),16(10),11219(15),16(13),16(12),4408(11),45(10)])]. 11645 (((x \ y) * z) * u) / (((y \ (x \ 1)) * (y * z)) * u) = R(y,(y \ (x \ 1)) * (y * z),u). [para(3143(a,1),183(a,1,1,1,1))]. 12076 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,y,z),u,w))) \ (v6 * v5). [para(34(a,1),6663(a,2,1,2,2))]. 12077 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = ((L(L(x,u,w),y,z) / v5) / v6) * (v6 * v5). [para(37(a,1),6663(a,2,1)),rewrite([2507(8),37(15),4501(16),1091(12),4407(12),10229(12),1014(12)])]. 12372 T(T(x,y),y \ 1) = x. [para(1091(a,1),7769(a,1,2)),rewrite([1708(2)])]. 12504 K(x,x * y) * T(y,x) = y. [para(7925(a,1),23(a,2)),rewrite([7826(5),6144(4)])]. 13457 L(x,(y \ z) * (y * u),y) = L(x,y * ((z * y) * u),y). [para(187(a,1),132(a,1,2,2)),rewrite([104(4),21(10),2507(10)]),flip(a)]. 13523 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,y * ((z * y) * x),y). [back_rewrite(9186),rewrite([13457(14)])]. 13639 (x * (y \ z)) * ((z \ y) * u) = (y \ z) * (((z \ y) * x) * u). [para(4137(a,1),190(a,1,2,2)),rewrite([4408(4),14(6),4408(8),5208(12)])]. 13884 L(x,y * (z * y),y) = L(x,y,z). [para(14(a,1),13523(a,1,2,2,1,2)),rewrite([45(5),4505(5),4525(6),5885(6),14(4)]),flip(a)]. 13932 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y) * u,K(z,y)). [para(4993(a,1),13523(a,1,2,2,1,2)),rewrite([6144(5),1014(5),1829(4),6144(5),14(7),3143(8),9198(6),8298(9)])]. 14102 T(x,T(x,y) \ 1) = x. [para(541(a,1),12372(a,1,1))]. 14430 T(x,y) * K(x \ y,x) = x. [para(14102(a,1),23(a,2)),rewrite([1014(7),8593(5),4408(6),45(3)])]. 14868 (x * x) / y = x * (x / y). [para(100(a,1),1014(a,1)),rewrite([1014(3)]),flip(a)]. 14874 L(x,y * (y * z),u) = L(x,z,u * (y * y)). [para(100(a,1),132(a,1,1,2,2)),rewrite([100(5),100(9),100(11),4501(12),1091(5),4407(5),5162(5),5610(10),100(7),2507(8)])]. 14882 a(x * (y * y),z,u) = a(x,y * (y * z),u). [para(100(a,1),133(a,1,1,2,2)),rewrite([100(6),100(9),100(11),37(12),4501(13),1091(6),4407(6),5162(6),6141(11),100(7),2508(8)]),flip(a)]. 15035 L(x,y,y * (z * z)) = x. [back_rewrite(5614),rewrite([14874(3)])]. 15276 (x * y) / T(z * (x \ z),y) = (x / z) * ((x / z) * y). [para(4254(a,1),21(a,1,2)),rewrite([3436(4),10229(3),10229(4),1607(12)]),flip(a)]. 15308 a(x / y,(y / x) * ((y / x) * z),u) = a(x / y,z,u). [para(4254(a,1),133(a,1,2,1,2)),rewrite([15276(8),37(8),10287(9),10287(6),19(7),15276(12),2508(12)]),flip(a)]. 15452 x \ (y * (y * z)) = ((x \ y) * y) * z. [para(7769(a,1),4314(a,1,1)),rewrite([8018(3),6134(4),7769(6),4525(6),3143(5),7617(6)])]. 15916 x \ ((x * y) * z) = (y / x) * (x * z). [para(15(a,1),4504(a,1,2,1,1)),rewrite([1091(2),3143(5),1091(5),1014(6),4209(6)])]. 16103 L(x,y * z,y) = L(x,y,z). [back_rewrite(5134),rewrite([15916(3),3276(4)]),flip(a)]. 16229 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y),u). [back_rewrite(13932),rewrite([16103(8)])]. 16256 L(x,y,z * y) = L(x,y,z). [back_rewrite(13884),rewrite([16103(3)])]. 16343 x \ T(x,y) = K(x,y). [back_rewrite(10321),rewrite([16103(6),2254(4)]),flip(a)]. 16398 L(x,y \ 1,z * y) = L(x,y,z). [back_rewrite(9719),rewrite([16103(6)])]. 16465 L(x,y \ z,y) = L(x,y,z). [back_rewrite(9559),rewrite([16103(4)])]. 16485 L((x * y) \ z,x,y) = y \ (x \ z). [back_rewrite(3940),rewrite([16103(4)])]. 16487 L(L(x,y,z),z,y) = x. [back_rewrite(667),rewrite([16103(3)])]. 16564 K(x \ y,x) = K(y,x). [back_rewrite(4516),rewrite([16343(4)])]. 16623 T(x,y) * K(y,x) = x. [back_rewrite(14430),rewrite([16564(3)])]. 16686 K(x,x * y) = K(x,y). [back_rewrite(8594),rewrite([16564(2)]),flip(a)]. 16875 K(x,y) * T(y,x) = y. [back_rewrite(12504),rewrite([16686(2)])]. 17093 (x \ y) * (((y \ x) * z) * ((z * (x \ y)) * u)) = z * (z * ((x \ y) * u)). [para(4137(a,1),193(a,2,1,2,1,1)),rewrite([4145(5),13639(8),13(10),37(12)])]. 18454 L(x,y,x \ 1) = x. [para(1022(a,1),16487(a,1,1))]. 18472 L(x,x \ y,y) = x. [para(8105(a,1),16487(a,1,1))]. 18485 L(R(x,y,z),u,x \ 1) = R(x,y,z). [para(18454(a,1),33(a,1,1)),flip(a)]. 18604 a(x,y \ x,y) = 1. [hyper(25,a,18472,a)]. 18742 a(x,y,y * x) = 1. [para(101(a,1),8106(a,1,2)),rewrite([3982(4),4795(4)])]. 18870 (((x \ y) * z) * ((z * (y \ x)) * T(y,x))) / x = (x \ y) * (z * z). [para(4504(a,1),106(a,1,1,2)),rewrite([7715(14),4578(11)])]. 19450 (x * ((T(y,z) * (x * x)) \ u)) \ (T(T(y,x),z) \ 1) = u \ x. [para(4713(a,1),1829(a,1,2)),rewrite([4407(11)]),flip(a)]. 19474 (x * (y * y)) \ z = y \ (y \ (x \ z)). [para(4713(a,1),3645(a,1,1)),rewrite([4407(12),19450(12),10927(4),2711(4),4407(13),19450(13)])]. 20390 (x * y) * (y * x) = x * (y * (y * x)). [para(18742(a,1),209(a,1,1)),rewrite([45(5),18742(8),88(8)])]. 20504 ((x * (y * (z * (z * y)))) * u) / (z * (y * (y * (z * u)))) = R(x,y * (z * (z * y)),u). [back_rewrite(9114),rewrite([20390(3),20390(8),2213(9),20390(13)])]. 20510 (x * (y * (z * (z * (y * u))))) * a(x,z * (y * (y * z)),u) = (x * (z * (y * (y * z)))) * u. [back_rewrite(9101),rewrite([20390(3),2213(4),20390(8),20390(13)])]. 21062 T(x,y) * (x * z) = x * (T(x,y) * z). [para(16623(a,1),189(a,1,1)),rewrite([16875(7)]),flip(a)]. 21447 x * (y \ ((y / x) * z)) = L(z,y / x,y). [para(16(a,1),10347(a,1,1)),rewrite([10229(4)]),flip(a)]. 21507 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z / y,z))))) = x * x. [back_rewrite(10296),rewrite([21447(8)])]. 21704 R(x,y * (y * z),z \ ((y \ (y \ z)) * u)) = R(x,z,u). [para(15(a,1),5194(a,2,3)),rewrite([6073(5)])]. 21708 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * (u * w))) = R(x,z * u,L(w,u,z)). [para(21(a,1),5194(a,2,3)),rewrite([6073(8)])]. 21713 (x * (y * (y * z))) * (z \ (y \ (y \ u))) = z * ((z \ x) * u). [para(5194(a,1),341(a,1,1)),rewrite([16(6),16(5),16(4),200(3)]),flip(a)]. 21715 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * w)) = R(x,z * u,L(u \ w,u,z)). [para(74(a,2),5194(a,2,3)),rewrite([6073(7)])]. 21721 R(x,(y \ (y \ z)) * u,((y \ (y \ z)) * u) \ z) = R(x,z * u,u \ 1). [para(1091(a,1),5194(a,1,3)),rewrite([7550(4),16(3)]),flip(a)]. 21722 R(x,y * (z * (z * y)),K(y,z) * ((y * z) \ ((y * z) \ u))) = R(x,K(z,y),K(y,z) * u). [para(63(a,1),5194(a,1,2,2)),rewrite([20390(3),6144(9),6144(13)])]. 22202 ((x \ y) * z) * ((z * (y \ x)) * u) = (x \ y) * (z * (z * ((y \ x) * u))). [para(17093(a,1),15(a,1,2)),rewrite([15452(6),4408(2),4578(3),2040(6)]),flip(a)]. 22250 x \ (y * (z * z)) = (x \ y) * (z * z). [back_rewrite(18870),rewrite([22202(7),2690(4),11083(4),7616(4)])]. 23697 (x / y) * (y * z) = y * ((y \ x) * z). [para(136(a,1),15(a,1,2)),rewrite([15916(3)])]. 23717 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(136(a,1),74(a,2,1)),rewrite([16103(8),16485(7)])]. 23718 (x * y) \ ((x * z) * u) = (y \ x) * ((x \ z) * u). [para(136(a,1),74(a,2,2)),rewrite([4480(5)]),flip(a)]. 24016 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = L(L(R(x,v5 \ 1,v6),u,w),y,z). [back_rewrite(12077),rewrite([23697(12),4180(12),33(11),33(10)])]. 24021 x * ((x \ y) * (y \ z)) = L(z,y \ 1,x). [back_rewrite(10367),rewrite([23697(4)])]. 24043 R(x,y \ 1,y * z) = R(x,y,y \ z). [back_rewrite(2760),rewrite([23697(3),191(4)]),flip(a)]. 24057 a(x / y,y,z) = a(y,y * x,z). [back_rewrite(60),rewrite([23697(3),4032(5)]),flip(a)]. 24261 (x * (y / L(L(z,u,w),v5,v6))) \ (x * y) = L(L(R(z,y \ 1,x),v5,v6),u,w). [back_rewrite(12076),rewrite([24016(6)]),flip(a)]. 24264 R(x,x \ y,z) = L(x,y \ 1,z). [back_rewrite(8379),rewrite([24021(6)])]. 24267 (x * (a(y,z,z \ (y \ x)) * u)) / u = L(x,y \ 1,z). [back_rewrite(5816),rewrite([24021(4),33(5),480(2)]),flip(a)]. 24268 R(x,y,y \ ((x \ y) * z)) = L(x,y \ 1,z). [back_rewrite(4470),rewrite([24021(8)])]. 24479 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(z,y * (y * (z * x)),u). [back_rewrite(1952),rewrite([24057(15),37(14),2508(15)])]. 24638 (x * y) / ((z \ x) * y) = L(z,x \ 1,y). [back_rewrite(5665),rewrite([24268(4)]),flip(a)]. 26897 x / T(y * (y * (x / z)),z) = y \ (y \ z). [para(1925(a,1),21(a,1,2)),rewrite([3436(2),1607(8)]),flip(a)]. 26903 L(x,y,y \ z) = L(x,z,y). [para(1925(a,1),132(a,1,1,2)),rewrite([26897(6),7550(5),16(4),21(4),26897(6),2507(6),16465(4)]),flip(a)]. 32749 (x * T(x,y)) * z = x * (T(x,y) * z). [para(493(a,1),84(a,1,1)),rewrite([21062(3),547(5)]),flip(a)]. 33472 (x \ (y \ 1)) * (x * z) = x \ ((y \ x) * z). [para(3143(a,1),168(a,1,2,1)),flip(a)]. 33575 R(x,x \ ((y \ x) * z),u) = L(x,z \ (x \ y),u). [back_rewrite(11645),rewrite([33472(8),24638(8),4407(4),4408(3),14(3),33472(8)]),flip(a)]. 35645 (x \ (y \ 1)) * z = (y * x) \ z. [para(13(a,1),6953(a,1,1,2,1)),rewrite([46(3),45(8),45(7)])]. 35648 (x \ (y \ (z \ 1))) * u = ((z * y) * x) \ u. [para(16(a,1),6953(a,1,1,2,1)),rewrite([23717(10),16(9)])]. 35675 (x * ((y * z) \ (y \ 1))) * u = (x / z) * (y \ (y \ u)). [para(1014(a,1),6953(a,2,1)),rewrite([4408(7),45(2),10229(10)])]. 35905 R(x,x \ (y \ 1),y * z) = z * ((y * z) \ (y * x)). [back_rewrite(11253),rewrite([35645(10),4155(9)])]. 35922 R(x,x \ (y \ 1),z) = L(x,y,z \ 1). [back_rewrite(3646),rewrite([35645(9),4155(8),6070(8)])]. 36021 x * ((y * x) \ (y * z)) = L(z,y,x \ (y \ 1)). [back_rewrite(35905),rewrite([35922(5),4407(3)]),flip(a)]. 38314 x * (x * (y * ((y \ (x \ (x \ z))) * u))) = y * ((y \ z) * u). [para(37(a,1),169(a,2)),rewrite([5162(6),21713(7),5162(6)]),flip(a)]. 38342 (x \ y) * (y \ z) = y * ((x * y) \ z). [para(3143(a,1),169(a,1,1)),rewrite([35645(7)])]. 38445 (x * (y * (y * z))) * (z \ u) = z * ((z \ x) * (y * (y * u))). [back_rewrite(5200),rewrite([38314(9)]),flip(a)]. 38475 x * (y * ((x * y) \ z)) = L(z,y \ 1,x). [back_rewrite(24021),rewrite([38342(3)])]. 38488 L(x,y,z \ (y \ 1)) = L(x,y,z \ 1). [back_rewrite(6070),rewrite([38342(4),36021(4)])]. 38534 R(x,y * (y * z),z \ u) = R(x,z,((z \ y) * y) * u). [back_rewrite(340),rewrite([38445(5),191(8),15452(3)]),flip(a)]. 38568 x * a(y,z,z \ (y \ x)) = L(x,y,z \ 1). [back_rewrite(9085),rewrite([38475(10),4407(7),16465(8)])]. 38590 x * ((y * x) \ (y * z)) = L(z,y,x \ 1). [back_rewrite(36021),rewrite([38488(8)])]. 38623 L(L(R(x,y,z),u,w),v5,x \ 1) = L(R(x,y,z),u,w). [back_rewrite(6793),rewrite([38488(6)])]. 38642 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(21715),rewrite([38534(9)]),flip(a)]. 38643 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,z,y)). [back_rewrite(21708),rewrite([38534(10)])]. 38644 R(x,y,((y \ z) * z) * ((z \ (z \ y)) * u)) = R(x,y,u). [back_rewrite(21704),rewrite([38534(7)])]. 39505 (x * y) \ (x \ 1) = y \ (x \ (x \ 1)). [para(1607(a,1),6591(a,1,1)),flip(a)]. 39506 (x * y) \ (y \ 1) = y \ (x \ (y \ 1)). [para(1667(a,1),6591(a,1,1)),flip(a)]. 39650 (x * (y \ (z \ (z \ 1)))) * u = (x / y) * (z \ (z \ u)). [back_rewrite(35675),rewrite([39505(4)])]. 39699 x / (y * (y * (z * x))) = z \ (y \ (y \ 1)). [back_rewrite(4420),rewrite([39505(8)])]. 39792 x / (y * (z * (y * x))) = y \ (z \ (y \ 1)). [back_rewrite(4421),rewrite([39506(8)])]. 42198 a(x,x * y,(x * y) \ z) = a(x,y,y \ z). [para(1091(a,1),192(a,1,2,2,1)),rewrite([3143(5),169(4),192(5)]),flip(a)]. 44671 L(L(L(x,y,z),u,w),v5 \ 1,v5 \ x) = L(L(x,y,z),u,w). [para(6416(a,1),97(a,2,1,1))]. 44709 L(L(L(L(x,y,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(L(x,u,w),y,z),v5,v6). [para(6416(a,1),229(a,1,1,1)),flip(a)]. 46815 a(x,y * (y * (x * (y * z))),u) = a(x,x * (y \ z),u). [para(37(a,1),4021(a,1,1)),rewrite([16103(4),16485(3),23718(9),1091(6),4407(6),23717(6),14(5),4498(7),101(7),128(8),2508(10)]),flip(a)]. 47034 L(L(L(R(x,y \ 1,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(R(x,y \ 1,z),v5,v6),u,w). [para(76(a,1),44709(a,1,1)),rewrite([24261(6),24016(16)])]. 47036 L(L(x,y,z),u \ 1,u \ L(x,w,v5)) = L(x,y,z). [para(16487(a,1),44709(a,1,1,1)),rewrite([16487(8)])]. 47734 L(x,y * z,y * (z * (y * y))) = x. [para(189(a,1),15035(a,1,3)),rewrite([4578(3)])]. 48721 L(x,y * K(z,u),K(u,z)) = L(x,K(z,u),K(u,z) * y). [para(18(a,1),8308(a,1,3,2)),rewrite([5005(6)]),flip(a)]. 48733 L(x,K(y,z),u * K(z,y)) = L(x,K(z,y),u). [para(4505(a,1),8308(a,1,3,2)),rewrite([90(5),6144(6),16229(8)])]. 49860 L(x,T(y,z),y) = x. [para(18604(a,1),439(a,1,2,2,1)),rewrite([4247(3),23(2),4505(4),4505(6),480(8),4505(4),13(6),32749(5),21(6)])]. 50186 L(L(R(x,y \ 1,z),u,w),v5,v6) = L(L(L(x,y,z \ 1),u,w),v5,v6). [para(82(a,1),47034(a,2,1,1)),rewrite([1014(5),10229(4),10305(5),47034(10),1014(10),10229(9),3143(10),4155(9),10690(8),38590(9)])]. 50188 L(R(x,y \ 1,z),u \ 1,u \ L(x,w,v5)) = R(x,y \ 1,z). [para(16487(a,1),47034(a,1,1)),rewrite([16487(13)])]. 50190 L(R(x,y \ 1,z),u,w) = L(L(x,y,z \ 1),u,w). [para(18454(a,1),47034(a,1,3,2)),rewrite([18485(6),50186(8),44671(8),38623(11)]),flip(a)]. 50224 R(x,y \ 1,z) = L(x,y,z \ 1). [back_rewrite(50188),rewrite([50190(8),47036(8)]),flip(a)]. 50308 R(x,y,y \ z) = L(x,y,z \ 1). [back_rewrite(24043),rewrite([50224(4),4407(3),38488(4)]),flip(a)]. 50359 L(x,y * z,z * y) = x. [para(4209(a,1),49860(a,1,2))]. 50404 K(x,y) * ((x * y) \ z) = (y * x) \ z. [back_rewrite(6238),rewrite([50359(5)]),flip(a)]. 50423 R(x,y * (z * (z * y)),(z * y) \ ((y * z) \ u)) = R(x,K(z,y),K(y,z) * u). [back_rewrite(21722),rewrite([50404(9)])]. 52573 L(x,y \ 1,z) = L(x,y,z \ 1). [para(14(a,1),24267(a,1,1,2)),rewrite([38568(4),48(5)]),flip(a)]. 52576 x * (a(y,z,z \ (y \ x)) * u) = L(x,y,z \ 1) * u. [para(24267(a,1),18(a,1,1)),rewrite([52573(3)]),flip(a)]. 52596 L(x,y,z \ 1) = L(x,y,z). [para(7679(a,1),24267(a,2)),rewrite([45(2),45(2),45(4),45(4),42198(7),52576(7),4407(3),26903(4),52573(3),17(5),45(5)])]. 52843 R(x,x \ y,z) = L(x,y,z). [back_rewrite(24264),rewrite([52573(5),52596(5)])]. 52858 L(x,y,z) = L(x,z,y). [back_rewrite(16398),rewrite([52573(4),4407(3),26903(4),52573(3),52596(3)])]. 52953 R(x,y,y \ z) = L(x,y,z). [back_rewrite(50308),rewrite([52596(5)])]. 53483 L(x,y,z \ (x \ u)) = L(x,y,(u \ x) * z). [back_rewrite(33575),rewrite([52843(4),52858(3),52858(6)]),flip(a)]. 53894 L(x,K(y,z),u * K(z,y)) = L(x,u,K(z,y)). [back_rewrite(48733),rewrite([52858(6)])]. 53895 L(x,K(y,z),K(z,y) * u) = L(x,u,K(y,z)). [back_rewrite(48721),rewrite([52858(4),53894(4)]),flip(a)]. 54757 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,y,z)). [back_rewrite(38643),rewrite([52858(12)])]. 54758 R(x,y * z,L(z \ u,y,z)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(38642),rewrite([52858(3)])]. 55548 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y))))) = x * x. [back_rewrite(21507),rewrite([52858(6)])]. 55954 L(T(x * y,x * z),u,L(y \ z,x,y)) = (u * L(y \ z,x,y)) \ (u * (x * z)). [back_rewrite(11076),rewrite([52858(5),52858(6),52858(8)])]. 56084 L(x,y,x * z) = (y * (z \ (x \ 1))) \ (y / z). [back_rewrite(6676),rewrite([52858(4),53483(4),45(2)])]. 56223 R(x,y * z,L(z \ u,y,z)) = L(x,y * z,y * u). [back_rewrite(648),rewrite([52858(3),52953(9)])]. 56239 L(c8,c5,K(c6,c7)) != c8 # answer("aK2"). [back_rewrite(152),rewrite([52858(6)])]. 56903 R(x,y * z,z \ 1) = L(x,y,(u \ (u \ y)) * z). [back_rewrite(21721),rewrite([52953(8),52858(4)]),flip(a)]. 57044 L(x,y,x * z) = L(x,z,y). [back_rewrite(3213),rewrite([52953(4),52858(2),52953(4)])]. 57097 (x * ((x \ y) * z)) / z = L(y,x,z). [back_rewrite(191),rewrite([52953(6)])]. 57908 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * w)) = L(x,y * z,y * w). [back_rewrite(54758),rewrite([56223(4)]),flip(a)]. 58091 (x * (y \ (z \ 1))) \ (x / y) = L(z,x,y). [back_rewrite(56084),rewrite([57044(2),52858(1)]),flip(a)]. 58275 L(x,y * z,y * (z * u)) = R(x,y * z,L(u,y,z)). [back_rewrite(54757),rewrite([57908(10)])]. 58601 R(x,y * z,L(y * y,y,z)) = x. [back_rewrite(47734),rewrite([58275(5)])]. 64162 L(x * x,x,y) = x * x. [para(1077(a,1),55954(a,1,3)),rewrite([14(3),4209(2),52596(4),52858(2),1607(5),1014(5),14(5),10229(5),23697(5),6351(5)])]. 64186 R(x,y * z,y * y) = x. [back_rewrite(58601),rewrite([64162(3)])]. 76377 T(x * (x * y),z \ 1) * (z / y) = z * (x * x). [para(10920(a,1),7616(a,1,1)),rewrite([10215(7),22250(11),10229(9),18(9)])]. 77479 a(x,x * (y \ (y \ (x \ z))),u) = a(x,y * (y * z),u). [para(3645(a,1),15308(a,1,2,1)),rewrite([10215(7),76377(7),3645(13),35648(11),4578(8),19474(9),35648(10),4578(4),19474(8),14882(9),16(7),16(6),3954(5),10215(12),76377(12),14882(8)])]. 82774 x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y)))) = x. [para(55548(a,1),15(a,1,2)),rewrite([15(2)]),flip(a)]. 82800 R(x / y,y,x) = x / y. [para(55548(a,1),85(a,2,1)),rewrite([82774(11),82774(13),14868(5),3691(4),1014(5)])]. 82841 x * (y \ (z \ (z \ 1))) = x / (z * (z * y)). [para(55548(a,1),342(a,2,1)),rewrite([82774(15),82800(6),82774(14),14868(8),39699(7)]),flip(a)]. 82892 (x / (y * (y * z))) * u = (x / z) * (y \ (y \ u)). [back_rewrite(39650),rewrite([82841(5)])]. 82924 a(x,y * (y * (x * z)),u) = a(x,x * z,u). [back_rewrite(24479),rewrite([82892(7),15(5),15(4),23697(3),4032(5)]),flip(a)]. 82939 a(x,x * (y \ z),u) = a(x,x * (y * z),u). [back_rewrite(46815),rewrite([82924(5)]),flip(a)]. 82951 a(x,y * (y * z),u) = a(x,z,u). [back_rewrite(77479),rewrite([82939(5),16(3),16(2)]),flip(a)]. 83285 a(x,y * (z * (z * y)),u) = 1. [back_rewrite(2486),rewrite([82951(6)])]. 84200 (x * (y * (z * (z * y)))) * u = x * (z * (y * (y * (z * u)))). [back_rewrite(20510),rewrite([83285(9),14(7)]),flip(a)]. 87206 R(x,y * (z * (z * y)),u) = x. [back_rewrite(20504),rewrite([84200(5),17(10)]),flip(a)]. 88170 R(x,K(y,z),K(z,y) * u) = x. [back_rewrite(50423),rewrite([87206(8)]),flip(a)]. 88394 x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w)) = x \ w. [para(4714(a,1),15(a,1,2)),flip(a)]. 88400 R(x,y,((y \ z) * z) * u) = L(x,y,u). [para(4714(a,1),148(a,1,2,2,2)),rewrite([88394(16),38445(5),57097(8),2507(3),88394(16),38534(5)]),flip(a)]. 88449 L(x,y,(z \ (z \ y)) * u) = R(x,y,u). [back_rewrite(38644),rewrite([88400(7)])]. 88465 R(x,y * z,z \ 1) = R(x,y,z). [back_rewrite(56903),rewrite([88449(8)])]. 103664 x * (y \ (z \ 1)) = x / (z * y). [para(64186(a,1),85(a,1)),rewrite([189(7),4578(6),4613(8),39792(6),16(7)]),flip(a)]. 103820 R(x,y,z \ 1) = L(x,z,y). [back_rewrite(58091),rewrite([103664(4),10229(4),10279(4)])]. 104117 R(x,y,z) = L(x,y,z). [back_rewrite(88465),rewrite([103820(4),16256(2),52858(1)]),flip(a)]. 105864 L(x,y,K(z,u)) = x. [back_rewrite(88170),rewrite([104117(4),53895(4)])]. 105865 $F # answer("aK2"). [resolve(105864,a,56239,a)]. ============================== end of proof ========================== -------- Proof 2 -------- "aK1". ============================== PROOF ================================= % Proof 2 at 43.68 (+ 0.24) seconds: "aK1". % Length of proof is 661. % Level of proof is 46. % Maximum clause weight is 35. % Given clauses 1618. 1 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 2 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 3 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 5 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 6 a(K(x,y),z,u) = 1 # label("aK1") # label(non_clause) # label(goal). [goal]. 13 1 * x = x. [assumption]. 14 x * 1 = x. [assumption]. 15 x \ (x * y) = y. [assumption]. 16 x * (x \ y) = y. [assumption]. 17 (x * y) / y = x. [assumption]. 18 (x / y) * y = x. [assumption]. 19 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 20 (x * y) \ (y * x) = K(y,x). [assumption]. 21 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 22 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 23 x \ (y * x) = T(y,x). [assumption]. 24 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(1)]. 25 L(x,y,z) != x | a(z,y,x) = 1. [clausify(2)]. 26 T(x,y) != x | T(y,x) = y. [clausify(3)]. 28 K(x,y) != 1 | T(x,y) = x. [clausify(5)]. 29 T(T(x,y),z) = T(T(x,z),y). [assumption]. 30 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 31 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 32 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 33 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(32),flip(a)]. 34 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 36 ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang (M1)"). [assumption]. 37 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 38 a(K(c1,c2),c3,c4) != 1 # label("aK1") # answer("aK1"). [deny(6)]. 45 1 \ x = x. [para(13(a,1),15(a,1,2))]. 46 x \ x = 1. [para(14(a,1),15(a,1,2))]. 47 x / x = 1. [para(13(a,1),17(a,1,1))]. 48 x / 1 = x. [para(14(a,1),17(a,1,1))]. 49 x / (y \ x) = y. [para(16(a,1),17(a,1,1))]. 50 (x / y) \ x = y. [para(18(a,1),15(a,1,2))]. 51 a(x,1,y) = 1. [para(13(a,1),19(a,1,1,2)),rewrite([14(3),46(3)]),flip(a)]. 54 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(19(a,1),16(a,1,2))]. 55 (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y). [para(16(a,1),19(a,1,1,2))]. 56 (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z). [para(16(a,1),19(a,1,2,1))]. 58 (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z). [para(18(a,1),19(a,1,1,2))]. 60 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(18(a,1),19(a,1,2,1))]. 63 (x * y) * K(y,x) = y * x. [para(20(a,1),16(a,1,2))]. 64 x \ ((y \ x) * y) = K(y \ x,y). [para(16(a,1),20(a,1,1))]. 65 ((x \ y) * x) \ y = K(x,x \ y). [para(16(a,1),20(a,1,2))]. 68 K(x * x,x) = a(x,x,x). [para(20(a,1),19(a,1))]. 73 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(16(a,1),21(a,1,1))]. 74 L(x \ y,x,z) = (z * x) \ (z * y). [para(16(a,1),21(a,1,2,2)),flip(a)]. 75 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(18(a,1),21(a,1,1))]. 76 L(x,y / x,z) = (z * (y / x)) \ (z * y). [para(18(a,1),21(a,1,2,2)),flip(a)]. 81 R(x,x \ y,z) = (y * z) / ((x \ y) * z). [para(16(a,1),22(a,1,1,1)),flip(a)]. 82 R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z)). [para(16(a,1),22(a,1,1)),flip(a)]. 83 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(16(a,1),22(a,1,2))]. 84 R(x,y,z) * (y * z) = (x * y) * z. [para(22(a,1),18(a,1,1))]. 85 R(x / y,y,z) = (x * z) / (y * z). [para(18(a,1),22(a,1,1,1)),flip(a)]. 87 T(1,x) = 1. [para(13(a,1),23(a,1,2)),rewrite([46(1)]),flip(a)]. 88 T(x,1) = x. [para(14(a,1),23(a,1,2)),rewrite([45(2)]),flip(a)]. 89 T(x,x) = x. [para(23(a,1),15(a,1))]. 90 x * T(y,x) = y * x. [para(23(a,1),16(a,1,2))]. 91 T(x,x \ y) = (x \ y) \ y. [para(16(a,1),23(a,1,2)),flip(a)]. 92 T(x / y,y) = y \ x. [para(18(a,1),23(a,1,2)),flip(a)]. 97 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,v5,v6),y,z),u,w). [para(34(a,1),34(a,1,1)),flip(a)]. 100 (x * x) * y = x * (x * y). [para(13(a,1),36(a,2,2)),rewrite([14(2)])]. 101 (x * y) * x = x * (y * x). [para(36(a,1),14(a,1)),rewrite([14(2)]),flip(a)]. 103 x * (y * (x * ((x * (y * x)) \ z))) = z. [para(36(a,1),16(a,1)),rewrite([101(2)])]. 104 x * ((x \ y) * (x * z)) = (y * x) * z. [para(16(a,1),36(a,1,1,1)),flip(a)]. 106 (x * (y * (x * z))) / z = x * (y * x). [para(36(a,1),17(a,1,1)),rewrite([101(6)])]. 110 (x * (y * (z * (y * u)))) \ ((x * (y * (z * y))) * u) = a(x,y * (z * y),u). [para(36(a,1),19(a,1,1,2)),rewrite([101(6),101(11)])]. 112 ((x * (y * x)) * (z * u)) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [para(36(a,1),19(a,1,2,1)),rewrite([101(2),101(11)])]. 117 (x * (y * (z * y))) \ (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(36(a,1),21(a,1,2,2)),rewrite([101(2),101(10)])]. 118 ((x * (y * x)) * z) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(36(a,1),21(a,1,2)),rewrite([101(2),101(10)])]. 121 ((x * (y * (z * y))) * u) / (y * (z * (y * u))) = R(x,y * (z * y),u). [para(36(a,1),22(a,1,2)),rewrite([101(2),101(10)])]. 125 ((x * (y * x)) * (z * (x * (y * x)))) * u = (x * (y * x)) * (z * (x * (y * (x * u)))). [para(36(a,1),36(a,2,2,2)),rewrite([101(2),101(5),101(6),101(9)])]. 126 (x * ((y * (z * y)) * x)) * u = x * (y * (z * (y * (x * u)))). [para(36(a,1),36(a,2,2)),rewrite([101(2),101(4)])]. 128 (x * (y * x)) * z = x * (y * (x * z)). [back_rewrite(36),rewrite([101(2)])]. 129 (x * (y * (x * (z * (x * (y * x)))))) * u = x * (y * (x * (z * (x * (y * (x * u)))))). [back_rewrite(125),rewrite([128(6),128(14)])]. 130 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [back_rewrite(126),rewrite([128(3)])]. 132 (x * (y * (x * z))) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [back_rewrite(118),rewrite([128(3)])]. 133 (x * (y * (x * (z * u)))) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [back_rewrite(112),rewrite([128(4)])]. 134 (x * (x * y)) \ (x * (x * (y * z))) = z. [para(37(a,1),15(a,1,2))]. 136 x * (x * ((x \ y) * z)) = (x * y) * z. [para(16(a,1),37(a,1,1,2)),flip(a)]. 139 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(37(a,1),19(a,1,1,2))]. 140 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(37(a,1),19(a,1,1)),rewrite([37(7),37(8)])]. 141 (x * ((x * y) * z)) \ (x * (x * (y * z))) = a(x,x * y,z). [para(37(a,1),19(a,1,2))]. 144 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(37(a,1),21(a,1,1)),rewrite([37(7)])]. 145 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(37(a,1),21(a,1,2,2))]. 146 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(37(a,1),22(a,1,1,1)),rewrite([37(4)])]. 148 ((x * (y * (y * z))) * u) / (y * (y * (z * u))) = R(x,y * (y * z),u). [para(37(a,1),22(a,1,2))]. 150 x * (x * ((y * (x * (x * (y * z)))) * u)) = x * (x * (y * (x * (x * (y * (z * u)))))). [para(37(a,1),37(a,1,1,2)),rewrite([37(6),37(7),37(13),37(14)])]. 151 L(c4,c3,K(c1,c2)) != c4 # answer("aK1"). [ur(25,b,38,a)]. 159 T(T(x,y),x) = T(x,y). [para(89(a,1),29(a,1,1)),flip(a)]. 165 (x * y) / T(x,y) = y. [para(23(a,1),49(a,1,2))]. 166 R(x,y,z) \ ((x * y) * z) = y * z. [para(22(a,1),50(a,1,1))]. 168 x \ ((y * x) * z) = (x \ y) * (x * z). [para(104(a,1),15(a,1,2))]. 169 (x * y) * (y \ z) = y * ((y \ x) * z). [para(16(a,1),104(a,1,2,2)),flip(a)]. 173 a(x,x \ y,x * z) = ((y * x) * z) \ (y * (x * z)). [para(104(a,1),19(a,1,1)),rewrite([16(4)]),flip(a)]. 176 ((x * y) * z) \ (((y \ x) * (y * z)) * y) = K((y \ x) * (y * z),y). [para(104(a,1),20(a,1,1))]. 177 (((x \ y) * (x * z)) * x) \ ((y * x) * z) = K(x,(x \ y) * (x * z)). [para(104(a,1),20(a,1,2))]. 178 (x * y) * (K(y,x) * ((x * y) * z)) = ((y * x) * (x * y)) * z. [para(20(a,1),104(a,1,2,1))]. 179 ((x * y) * z) \ (y * (((y \ x) * (y * z)) * u)) = L(u,(y \ x) * (y * z),y). [para(104(a,1),21(a,1,1))]. 181 L(x * y,x \ z,x) = z \ ((z * x) * y). [para(104(a,1),21(a,1,2)),rewrite([16(2)]),flip(a)]. 182 (x * y) * (L(z,y,x) * ((x * y) * u)) = ((x * (y * z)) * (x * y)) * u. [para(21(a,1),104(a,1,2,1))]. 183 (((x * y) * z) * u) / (((y \ x) * (y * z)) * u) = R(y,(y \ x) * (y * z),u). [para(104(a,1),22(a,1,1,1))]. 186 x * (T(y,x) * (x * z)) = ((y * x) * x) * z. [para(23(a,1),104(a,1,2,1))]. 187 x * (x * (((x \ y) * (x * z)) * u)) = (x * ((y * x) * z)) * u. [para(104(a,1),37(a,1,1,2)),flip(a)]. 188 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * (y * u)))))) = (z * (x * (x * y))) * u. [para(104(a,1),37(a,1)),rewrite([37(10)]),flip(a)]. 189 (x * y) * (x * z) = x * ((y * x) * z). [para(104(a,1),37(a,2,2)),rewrite([16(2)])]. 190 (x * y) * ((y \ z) * (y * u)) = y * ((y \ x) * ((z * y) * u)). [para(104(a,1),104(a,1,2,2)),flip(a)]. 191 (x * ((x \ y) * z)) / z = R(y,x,x \ z). [back_rewrite(83),rewrite([169(3)])]. 192 (x * y) \ (z * ((z \ x) * y)) = a(x,z,z \ y). [back_rewrite(55),rewrite([169(4)])]. 193 (x * y) * (L(z,y,x) * ((x * y) * u)) = (x * (((y * z) * x) * y)) * u. [back_rewrite(182),rewrite([189(10)])]. 197 R(x,y,y \ 1) = x. [para(14(a,1),191(a,1,1,2)),rewrite([16(2),48(2)]),flip(a)]. 199 R(x,y,y \ ((y \ x) \ z)) = (y * z) / ((y \ x) \ z). [para(16(a,1),191(a,1,1,2)),flip(a)]. 200 R(x,y,y \ z) * z = y * ((y \ x) * z). [para(191(a,1),18(a,1,1))]. 201 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) = ((x * (y * z)) * (a(x,y,z) * u)) / u. [para(19(a,1),191(a,1,1,2,1)),flip(a)]. 205 (x * (x * (y * (((x * (x * y)) \ z) * u)))) / u = R(z,x * (x * y),(x * (x * y)) \ u). [para(37(a,1),191(a,1,1))]. 206 R(x,x,x \ y) = x. [para(46(a,1),191(a,1,1,2,1)),rewrite([13(2),17(2)]),flip(a)]. 208 R(x,x / y,(x / y) \ z) = ((x / y) * (y * z)) / z. [para(50(a,1),191(a,1,1,2,1)),flip(a)]. 209 a(x,y,z) \ ((x * y) * z) = T(x * (y * z),a(x,y,z)). [para(19(a,1),91(a,1,2)),rewrite([19(9)]),flip(a)]. 218 x / T(y,y \ x) = y \ x. [para(91(a,2),49(a,1,2))]. 220 R(x,y \ z,T(y,y \ z)) = R(x,y \ z,(y \ z) \ z). [para(91(a,2),191(a,2,3)),rewrite([191(6)]),flip(a)]. 221 T(x \ y,T(x,x \ y)) = ((x \ y) \ y) \ y. [para(91(a,2),91(a,1,2))]. 228 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,u,w),y,z),v5,v6). [para(97(a,1),34(a,1))]. 229 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v5,v6),y,z),v7,v8),u,w). [para(97(a,2),34(a,1,1))]. 265 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(209(a,1),49(a,1,2))]. 268 ((x * (y \ z)) * T(y,y \ z)) / z = R(x,y \ z,(y \ z) \ z). [para(220(a,1),22(a,2)),rewrite([90(9),16(7)])]. 311 (x * (y * (y * z))) \ ((x * (y * y)) * z) = a(x,y * y,z). [para(13(a,1),110(a,1,1,2,2)),rewrite([13(5),13(9)])]. 312 (x * (y * (z * (y * u)))) * a(x,y * (z * y),u) = (x * (y * (z * y))) * u. [para(110(a,1),16(a,1,2))]. 338 ((x * (y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(13(a,1),148(a,1,2,2,2)),rewrite([14(2),14(8)])]. 340 ((x * (y * (y * z))) * (z \ u)) / (y * (y * u)) = R(x,y * (y * z),z \ u). [para(16(a,1),148(a,1,2,2,2))]. 341 R(x,y * (y * z),u) * (y * (y * (z * u))) = (x * (y * (y * z))) * u. [para(148(a,1),18(a,1,1))]. 342 R(x / (y * (y * z)),y * (y * z),u) = (x * u) / (y * (y * (z * u))). [para(18(a,1),148(a,1,1,1)),flip(a)]. 350 ((x * y) * z) * K((y \ x) * (y * z),y) = ((y \ x) * (y * z)) * y. [para(176(a,1),16(a,1,2))]. 354 ((x * (y / z)) * z) \ ((((y / z) \ x) * y) * (y / z)) = K(((y / z) \ x) * y,y / z). [para(18(a,1),176(a,1,2,1,2)),rewrite([18(13)])]. 357 ((x * (x / y)) * z) \ ((y * ((x / y) * z)) * (x / y)) = K(y * ((x / y) * z),x / y). [para(50(a,1),176(a,1,2,1,1)),rewrite([50(11)])]. 393 x * (x * ((x * (y * (x * (x * x)))) * z)) = x * (x * (x * (y * (x * (x * (x * z)))))). [para(129(a,1),37(a,1)),flip(a)]. 398 x * (x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u))))))) = x * (x * u). [para(16(a,1),150(a,1,2,2)),flip(a)]. 407 x * (x * (((x * x) \ y) * (x * (x * z)))) = (y * (x * x)) * z. [para(13(a,1),188(a,1,2,2,2,2,2,2)),rewrite([14(3),13(7),14(9)])]. 411 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [para(16(a,1),188(a,1,2,2,2,2,2,2))]. 435 R(x * ((x \ y) * z),y * z,(y * z) \ u) = ((y * z) * (a(y,x,x \ z) * u)) / u. [para(16(a,1),201(a,1,2,2)),rewrite([169(3),16(6),16(9)])]. 439 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) \ ((x * (y * z)) * (a(x,y,z) * u)) = u. [para(201(a,2),50(a,1,1))]. 463 x * (x * (x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))))) = x * (x * z). [para(16(a,1),393(a,1,2,2)),flip(a)]. 478 R(x,1 / y,y) = x. [para(50(a,1),197(a,1,3))]. 480 R(x,x,y) = x. [para(15(a,1),206(a,1,3))]. 493 R(T(x,y),x,z) = T(x,y). [para(480(a,1),31(a,1,1)),flip(a)]. 506 (x * (1 / y)) * y = x. [para(478(a,1),22(a,2)),rewrite([18(7),48(6)])]. 507 (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z)). [para(90(a,1),19(a,1,1,2))]. 508 (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z). [para(90(a,1),19(a,1,2,1))]. 520 x * (x * (T(y,x) * z)) = x * (y * (x * z)). [para(90(a,1),37(a,1,1,2)),rewrite([128(3)]),flip(a)]. 521 x * (x * (y * T(z,x * (x * y)))) = z * (x * (x * y)). [para(90(a,1),37(a,1)),flip(a)]. 541 T(x,T(x,y)) = x. [hyper(26,a,159,a)]. 547 T(x,y) * x = x * T(x,y). [para(159(a,1),90(a,1,2)),flip(a)]. 560 T(x,(x \ y) \ y) = x. [para(91(a,1),541(a,1,2))]. 632 L(x \ 1,x,y) = (y * x) \ y. [para(14(a,1),74(a,2,2))]. 638 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(21(a,1),74(a,1,1)),flip(a)]. 639 L(T(x,y),y,x) = T(x,x * y). [para(74(a,2),23(a,1)),rewrite([23(2)])]. 648 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(y * z) \ (y * u)). [para(74(a,2),191(a,2,3)),rewrite([191(8)]),flip(a)]. 650 T(x * y,(x * y) \ (x * z)) = L(y \ z,y,x) \ (x * z). [para(74(a,2),91(a,2,1))]. 662 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,(x * y) \ (x * z),u). [para(74(a,2),56(a,1,1,2,1))]. 667 L(L(x,y,z),z * y,z) = x. [back_rewrite(134),rewrite([638(6)])]. 669 x * (T(y,x) * x) = (y * x) * x. [para(14(a,1),186(a,1,2,2)),rewrite([14(7)])]. 673 (((x * y) * y) * z) \ ((x * y) * (y * z)) = a(y,T(x,y),y * z). [para(186(a,1),19(a,1,1)),rewrite([90(5)])]. 682 x * (T(T(y,x),z) * (x * u)) = ((T(y,z) * x) * x) * u. [para(29(a,1),186(a,1,2,1))]. 690 a((x * y) * y,T(x,y),z) = a(y,T(x,y) * (x * y),z). [para(186(a,1),110(a,1,2,1)),rewrite([186(6),19(11),90(7)])]. 729 ((x * (y / z)) * z) / T(x * y,a(x,y / z,z)) = a(x,y / z,z). [para(18(a,1),265(a,1,2,1,2))]. 778 x * (y * T(z,x * (x * y))) = x \ (z * (x * (x * y))). [para(521(a,1),15(a,1,2)),flip(a)]. 780 L(x * T(y,z * (z * x)),z,z) = (z * z) \ (y * (z * (z * x))). [para(521(a,1),21(a,1,2)),flip(a)]. 788 x * (y * (x * T(z,x * (y * x)))) = z * (x * (y * x)). [para(90(a,1),521(a,1,2,2,2,2,2)),rewrite([520(7),90(8)])]. 831 (x * ((x \ y) * y)) \ ((y * x) * ((x \ y) * z)) = L(z,(x \ y) * y,x). [para(104(a,1),117(a,1,1)),rewrite([169(3),104(9),16(11)])]. 874 x * K((y \ z) * (y * ((z * y) \ x)),y) = ((y \ z) * (y * ((z * y) \ x))) * y. [para(16(a,1),350(a,1,1))]. 961 (x * (x * (y * z))) / T(x * (x * y),z) = z. [para(37(a,1),165(a,1,1))]. 965 (x * y) / T(y,T(x,y)) = T(x,y). [para(90(a,1),165(a,1,1))]. 969 (((x \ y) * (x * z)) * x) / T((y * x) * z,K((x \ y) * (x * z),x)) = K((x \ y) * (x * z),x). [para(350(a,1),165(a,1,1))]. 974 x * (1 / y) = x / y. [para(506(a,1),17(a,1,1)),flip(a)]. 975 x / (1 / y) = x * y. [para(18(a,1),506(a,1,1)),flip(a)]. 976 a(x,1 / y,y) = 1. [para(506(a,1),19(a,1,2)),rewrite([18(3),14(2),46(1)]),flip(a)]. 982 K(x,1 / x) = 1. [para(506(a,1),357(a,1,1)),rewrite([18(4),14(3),974(4),47(2),46(3),18(4),14(3)]),flip(a)]. 986 T(x,1 / x) = x. [hyper(28,a,982,a)]. 989 1 / x = x \ 1. [hyper(26,a,986,a),rewrite([92(3)]),flip(a)]. 990 (x \ 1) \ 1 = x. [para(986(a,1),23(a,2)),rewrite([989(2),989(4),16(5)])]. 996 T(x \ 1,x) = x \ 1. [para(49(a,1),986(a,1,2))]. 997 (x \ 1) * x = 1. [para(986(a,1),90(a,1,2)),rewrite([989(2),989(5),16(6)])]. 1012 a(x,y \ 1,y) = 1. [back_rewrite(976),rewrite([989(2)])]. 1013 x / (y \ 1) = x * y. [back_rewrite(975),rewrite([989(2)])]. 1014 x * (y \ 1) = x / y. [back_rewrite(974),rewrite([989(2)])]. 1022 L(x,x \ 1,y) = x. [para(990(a,1),74(a,1,1)),rewrite([1014(6),14(6),50(5)])]. 1025 (x \ 1) * (x * y) = L(y,x,x \ 1). [para(997(a,1),21(a,1,1)),rewrite([45(6)])]. 1026 L(x,y,(y * x) \ 1) = (((y * x) \ 1) * y) \ 1. [para(997(a,1),21(a,1,2)),flip(a)]. 1027 R(x \ 1,x,y) = y / (x * y). [para(997(a,1),22(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1039 R((x * (x * y)) \ 1,x * (x * y),z) = z / (x * (x * (y * z))). [para(997(a,1),148(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1051 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x \ (y \ 1),y). [para(997(a,1),56(a,1,2))]. 1077 L(x \ 1,x,y) = x \ 1. [para(50(a,1),1022(a,1,2)),rewrite([989(2),989(5)])]. 1078 L(L(L(x,y,z),u,w),L(x,u,w) \ 1,v5) = L(L(x,u,w),y,z). [para(1022(a,1),97(a,1,1)),flip(a)]. 1080 L(L(L(x,y,z),u,w),x \ 1,v5) = L(L(x,y,z),u,w). [para(1022(a,1),97(a,2,1,1))]. 1091 (x * y) \ x = y \ 1. [back_rewrite(632),rewrite([1077(3)]),flip(a)]. 1141 L(x,y,(y * x) \ 1) \ 1 = ((y * x) \ 1) * y. [para(1026(a,2),49(a,1,2)),rewrite([989(6)])]. 1180 L(x,x \ y,x) = x. [para(14(a,1),181(a,1,1)),rewrite([14(5),15(4)])]. 1227 L(x * y,x \ (x \ 1),x) = (x \ 1) \ y. [para(997(a,1),181(a,2,2,1)),rewrite([13(9)])]. 1246 (x * (x * y)) / T(x * (x * (y / z)),z) = z. [para(18(a,1),961(a,1,1,2,2))]. 1266 (((T(x,y) * z) * z) * u) / (T(T(x,z),y) * (z * u)) = z. [para(682(a,1),17(a,1,1))]. 1300 a(x,x,y) = 1. [para(13(a,1),690(a,1,1,1)),rewrite([87(3),51(3),87(3),13(4),13(3)]),flip(a)]. 1316 K(x * x,x) = 1. [back_rewrite(68),rewrite([1300(3)])]. 1324 x \ (x \ (y * (x * (x * z)))) = z * T(y,x * (x * z)). [para(778(a,1),15(a,1,2))]. 1353 x * (y / (x * (x * y))) = x \ 1. [para(997(a,1),778(a,2,2)),rewrite([996(7),1014(5)])]. 1359 x * (y * T(z,y * (x * y))) = y \ (z * (y * (x * y))). [para(788(a,1),15(a,1,2)),flip(a)]. 1448 R((x * (y * x)) \ 1,x * (y * x),z) = z / (x * (y * (x * z))). [para(997(a,1),121(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1452 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,x \ y). [para(268(a,1),18(a,1,1)),rewrite([200(5)])]. 1457 R(x,y \ z,(y \ z) \ z) \ ((x * (y \ z)) * T(y,y \ z)) = z. [para(268(a,1),50(a,1,1))]. 1524 L(x * ((y * (y * x)) \ z),y,y) = (y * y) \ z. [para(18(a,1),780(a,2,2)),rewrite([92(6)])]. 1534 L(x / (y * (y * x)),y,y) = (y * y) \ 1. [para(997(a,1),780(a,2,2)),rewrite([996(7),1014(5)])]. 1607 L(x,y,y) = x. [hyper(24,a,1300,a)]. 1609 x / (y * (y * x)) = (y * y) \ 1. [back_rewrite(1534),rewrite([1607(4)])]. 1619 x * ((y * (y * x)) \ z) = (y * y) \ z. [back_rewrite(1524),rewrite([1607(5)])]. 1649 x / (x * x) = x \ 1. [back_rewrite(1353),rewrite([1609(3),1014(4)])]. 1659 T(x * x,x) = x * x. [hyper(28,a,1316,a)]. 1667 L(x,y,x) = x. [para(15(a,1),1180(a,1,2))]. 1685 L(T(x,y),z,x) = T(x,y). [para(1667(a,1),30(a,1,1)),flip(a)]. 1699 ((x \ y) * x) \ ((x \ y) * y) = x \ y. [para(1667(a,1),74(a,1)),flip(a)]. 1702 a((x \ y) * x,x \ y,z) = a(x \ y,y,z). [para(1667(a,1),662(a,1,1,2,1)),rewrite([189(5),16(3),19(7),1699(9)]),flip(a)]. 1708 T(x,x * y) = T(x,y). [back_rewrite(639),rewrite([1685(2)]),flip(a)]. 1812 T(x * y,y \ 1) = (y \ 1) \ x. [para(1013(a,1),92(a,1,1))]. 1829 x \ (x / y) = y \ 1. [para(1014(a,1),15(a,1,2))]. 1834 (x / y) \ (x * ((y \ 1) * z)) = L(z,y \ 1,x). [para(1014(a,1),21(a,1,1))]. 1836 ((x * y) / z) / (y / z) = R(x,y,z \ 1). [para(1014(a,1),22(a,1,1)),rewrite([1014(5)])]. 1839 (x * (x * y)) / z = x * (x * (y / z)). [para(1014(a,1),37(a,1)),rewrite([1014(6)])]. 1859 x * (T(y,x) * (x / z)) = ((y * x) * x) / z. [para(1014(a,1),186(a,1,2,2)),rewrite([1014(9)])]. 1870 x * (x * ((y * (((x * (x * y)) \ z) * u)) / u)) = R(z,x * (x * y),(x * (x * y)) \ u). [para(205(a,1),1014(a,2)),rewrite([1014(10),1839(8)])]. 1884 x * (x * ((y / z) / T(x * (x * y),z \ 1))) = z \ 1. [para(1014(a,1),961(a,1,1,2,2)),rewrite([1839(9)])]. 1885 x * (x * ((y * z) / T(x * (x * y),z))) = z. [para(961(a,1),1014(a,2)),rewrite([1014(9),1839(7)])]. 1888 x * ((y \ 1) * T(z,x * (x / y))) = x \ (z * (x * (x / y))). [para(1014(a,1),778(a,1,2,2,2,2)),rewrite([1014(10)])]. 1925 x * (x * (y / T(x * (x * (y / z)),z))) = z. [back_rewrite(1246),rewrite([1839(7)])]. 1935 x * (x * R(y,z,u)) = R(x * (x * y),z,u). [back_rewrite(146),rewrite([1839(6),22(4)])]. 1952 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(x / (y * (y * z)),y * (y * z),u). [para(37(a,1),60(a,1,1,2))]. 1972 R(x,x / y,(x / y) \ (y \ z)) = ((x / y) * z) / (y \ z). [para(16(a,1),208(a,2,1,2))]. 2004 R(x,x * y,(x * y) \ z) = ((x * y) * ((y \ 1) * z)) / z. [para(1013(a,1),208(a,1,2)),rewrite([1013(4),1013(7)])]. 2009 (x / y) * ((x / y) * ((y * z) / T((x / y) * x,z))) = z. [para(18(a,1),1885(a,1,2,2,2,1,2))]. 2010 (x * y) / T(z * (z * x),y) = (z * z) \ y. [para(1885(a,1),21(a,1,2)),rewrite([1607(8)]),flip(a)]. 2012 x * (x * (((x * x) \ y) * z)) = y * z. [para(1885(a,1),37(a,1,1)),rewrite([2010(6)]),flip(a)]. 2032 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (((T(y,z) * x) * x) * u),w))) = w. [para(682(a,1),1885(a,1,2,2,2,1,2))]. 2040 (x * (y * y)) * z = x * (y * (y * z)). [back_rewrite(407),rewrite([2012(7)]),flip(a)]. 2044 R(x,y * y,z) = x. [back_rewrite(338),rewrite([2040(3),17(6)]),flip(a)]. 2045 a(x,y * y,z) = 1. [back_rewrite(311),rewrite([2040(6),46(7)]),flip(a)]. 2166 x / (T(T(y,z),u) * (z * (((T(y,u) * z) * z) \ x))) = z. [para(16(a,1),1266(a,1,1))]. 2213 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(13(a,1),130(a,1,1,2,2)),rewrite([13(8)])]. 2215 x * (y * (z * (y * (x * ((x * (y * (z * (y * x)))) \ u))))) = u. [para(130(a,1),16(a,1))]. 2254 L(x,y,z * z) = x. [para(13(a,1),132(a,1,1,2)),rewrite([13(6),638(6),667(3),13(2)]),flip(a)]. 2276 L(x,y,z * (((z * y) \ 1) * z)) = ((z * y) \ 1) * (z * (y * x)). [para(997(a,1),132(a,1,1,2)),rewrite([14(2),15(8)]),flip(a)]. 2278 L(x,y,z * (((z * (y * x)) \ 1) * z)) = (((z * (y * x)) \ 1) * (z * y)) \ 1. [para(997(a,1),132(a,1,2,2)),rewrite([14(9),1091(8)]),flip(a)]. 2356 L(L(L(x,y,z),u,(u * x) \ 1),((u * x) \ 1) * u,w) = L(L(x,u,(u * x) \ 1),y,z). [para(1026(a,1),1078(a,1,2,1)),rewrite([990(13)])]. 2357 L(L(x,y,(y * x) \ 1),z,u) = L((((y * x) \ 1) * y) \ 1,z,u). [para(1026(a,1),1078(a,2,1)),rewrite([1141(11),2356(10)])]. 2485 L(x,y * y,z) = x. [hyper(24,a,2045,a)]. 2486 a(x,y * (y * (z * (y * (y * z)))),u) = 1. [para(37(a,1),2045(a,1,2))]. 2495 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(2254(a,1),74(a,1)),rewrite([100(3),100(5)]),flip(a)]. 2507 L(x,y,z * (z * u)) = L(x,y,u). [back_rewrite(144),rewrite([2495(8),21(4)]),flip(a)]. 2508 a(x * (x * y),z,u) = a(y,z,u). [back_rewrite(140),rewrite([2495(9),19(5)]),flip(a)]. 2528 L(x,(y \ 1) / y,z) = x. [para(1014(a,1),2485(a,1,2))]. 2538 (x \ y) \ 1 = y \ x. [para(16(a,1),1091(a,1,1)),flip(a)]. 2540 ((x \ y) * (x * z)) \ 1 = ((y * x) * z) \ x. [para(104(a,1),1091(a,1,1)),flip(a)]. 2548 ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. [para(54(a,1),1091(a,1,1))]. 2556 ((x / y) * ((y \ 1) \ z)) / z = R(x,y \ 1,(y \ 1) \ z). [para(1091(a,1),268(a,1,1,1,2)),rewrite([1014(3),1091(4),1812(5),1091(8),1091(10)])]. 2560 T(x * y,(y \ 1) \ x) = x * y. [para(1091(a,1),560(a,1,2,1))]. 2574 a(x,T(y,x),x * z) = a(y * x,x,z) \ 1. [back_rewrite(673),rewrite([2548(7)]),flip(a)]. 2575 a(x,x \ y,x * z) = a(y,x,z) \ 1. [back_rewrite(173),rewrite([2548(8)])]. 2599 ((x / y) * (y * y)) / T(x * y,a(x,y \ 1,y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),729(a,1,1,1,2)),rewrite([1014(3),1649(6),1649(12)])]. 2601 ((x / y) * (y * y)) \ ((y \ 1) \ x) = K(((y \ 1) \ x) * y,y \ 1). [para(1649(a,1),354(a,1,1,1,2)),rewrite([1014(3),1649(5),1649(9),1014(10),17(8),1649(9),1649(13)])]. 2604 (x * y) \ ((x / y) * (y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),58(a,1,2,1,2)),rewrite([1014(4),1649(7)])]. 2635 T(T(x * x,y),x) = T(x * x,y). [para(1659(a,1),29(a,1,1)),flip(a)]. 2639 T((x \ 1) / x,x \ 1) = (x \ 1) / x. [para(1014(a,1),1659(a,1,1)),rewrite([1014(11)])]. 2640 x * (x * (y * (y * (z / (T(x * x,y) * (y * z)))))) = y. [para(1659(a,1),1266(a,1,1,1,1,1)),rewrite([100(2),37(3),37(4),100(2),2635(7),1839(9),1839(7)])]. 2642 T(x,x \ y) = T(x,y). [para(16(a,1),1708(a,1,2)),flip(a)]. 2643 T(x / y,x) = y \ x. [para(18(a,1),1708(a,1,2)),rewrite([92(4)])]. 2647 T(x * (x * y),x * (x * (y * z))) = T(x * (x * y),z). [para(37(a,1),1708(a,1,2))]. 2649 (x \ y) \ y = T(x,y). [para(91(a,1),1708(a,2)),rewrite([16(2)]),flip(a)]. 2652 T(x,y * x) = T(x,T(y,x)). [para(90(a,1),1708(a,1,2))]. 2690 (x \ y) * T(x,y) = y. [back_rewrite(1457),rewrite([2649(3),2642(7),166(8)])]. 2692 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(1452),rewrite([2642(9)])]. 2705 L(x \ y,x,z) \ (z * y) = T(z * x,z * y). [back_rewrite(650),rewrite([2642(5)]),flip(a)]. 2709 T(x \ y,T(x,y)) = T(x,y) \ y. [back_rewrite(221),rewrite([2642(3),2649(5)])]. 2711 x / T(y,x) = y \ x. [back_rewrite(218),rewrite([2642(2)])]. 2712 (x \ 1) / x = x \ (x \ 1). [back_rewrite(2639),rewrite([2643(6)]),flip(a)]. 2747 L(x,y \ (y \ 1),z) = x. [back_rewrite(2528),rewrite([2712(3)])]. 2755 (x \ 1) \ y = x * y. [back_rewrite(1227),rewrite([2747(5)]),flip(a)]. 2757 ((x / y) * (y * y)) \ (y * x) = K(y * (x * y),y \ 1). [back_rewrite(2601),rewrite([2755(6),2755(8),101(7)])]. 2759 T(x * y,y * x) = x * y. [back_rewrite(2560),rewrite([2755(4)])]. 2760 ((x / y) * (y * z)) / z = R(x,y \ 1,y * z). [back_rewrite(2556),rewrite([2755(4),2755(9)])]. 2774 T(x * y,y \ 1) = y * x. [back_rewrite(1812),rewrite([2755(7)])]. 2796 R(x,x / y,(x / y) \ z) = R(x,y \ 1,y * z). [back_rewrite(208),rewrite([2760(8)])]. 2806 ((x / y) * z) / (y \ z) = R(x,y \ 1,z). [back_rewrite(1972),rewrite([2796(5),16(4)]),flip(a)]. 2917 K(x,y) \ 1 = K(y,x). [para(63(a,1),1091(a,1,1)),rewrite([20(3)]),flip(a)]. 2918 T(x * y,K(y,x)) = x * y. [para(63(a,1),1708(a,1,2)),rewrite([2759(3)]),flip(a)]. 2934 (x * (y * z)) \ (L(z,y,x) * (x * y)) = K(L(z,y,x),x * y). [para(21(a,1),64(a,1,2,1)),rewrite([21(10)])]. 2965 x * (((x \ y) * x) * z) = y * (x * z). [para(16(a,1),189(a,1,1)),flip(a)]. 3018 L(x * (y * z),x \ y,x) = (x * y) * z. [para(189(a,1),181(a,2,2)),rewrite([15(8)])]. 3031 x * (((y \ 1) * x) * z) = (x / y) * (x * z). [para(1014(a,1),189(a,1,1)),flip(a)]. 3093 x * a(y,z,y * ((y * (z * y)) \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [para(103(a,1),54(a,1,1)),rewrite([189(12)])]. 3135 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(16(a,1),2495(a,1,1,2))]. 3136 (x * (x * y)) \ (x * z) = y \ (x \ z). [para(16(a,1),2495(a,1,2,2))]. 3139 T(x * (x * (y / (x * (x * z)))),x * (x * z)) = z \ y. [para(2495(a,1),92(a,2)),rewrite([1839(5)])]. 3143 (x \ 1) * y = x \ y. [para(997(a,1),2495(a,1,1,2)),rewrite([14(4),15(9)])]. 3162 (x \ ((x * y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(141),rewrite([3135(7)])]. 3169 (x / y) * (x * z) = x * ((y \ x) * z). [back_rewrite(3031),rewrite([3143(3)]),flip(a)]. 3191 L(L(x,y,(y * x) \ 1),z,u) = L(x,z,u). [back_rewrite(2357),rewrite([3143(9),1091(7),2649(9),88(7)])]. 3192 L(L(x,y,z),u,(u * x) \ 1) = L(x,y,z). [back_rewrite(2356),rewrite([3143(9),1091(7),1080(8),3191(10)])]. 3199 L(x,y,z / (y * x)) = L(x,y,z). [back_rewrite(2278),rewrite([3143(5),1091(3),1014(4),3143(9),2538(9),21(7)])]. 3200 L(x,y,z / y) = L(x,y,z). [back_rewrite(2276),rewrite([3143(4),1091(2),1014(3),3143(8),21(6)])]. 3213 R(x,x * y,(x * y) \ z) = R(x,y,y \ z). [back_rewrite(2004),rewrite([3143(8),169(7),191(8)])]. 3218 x * (y \ T(z,x * (x / y))) = x \ (z * (x * (x / y))). [back_rewrite(1888),rewrite([3143(6)])]. 3229 (x / y) \ (x * (y \ z)) = L(z,y \ 1,x). [back_rewrite(1834),rewrite([3143(4)])]. 3266 L(x,y,y \ 1) = x. [back_rewrite(1025),rewrite([3143(4),15(2)]),flip(a)]. 3276 x \ ((x / y) * (y * z)) = L(z,y,x). [back_rewrite(75),rewrite([3200(6)])]. 3304 T(x,K(y \ x,y)) = x. [para(16(a,1),2918(a,1,1)),rewrite([16(5)])]. 3307 T((x * y) * z,K((y \ x) * (y * z),y)) = (x * y) * z. [para(104(a,1),2918(a,1,1)),rewrite([104(11)])]. 3308 K(x,y) * (y * x) = x * y. [para(2918(a,1),90(a,1,2)),rewrite([63(6)])]. 3323 (((x \ y) * (x * z)) * x) / ((y * x) * z) = K((x \ y) * (x * z),x). [back_rewrite(969),rewrite([3307(11)])]. 3436 (x * x) \ y = x \ (x \ y). [para(18(a,1),1324(a,1,2,2)),rewrite([92(8),1619(6)]),flip(a)]. 3476 x * T(y * z,y * (y * x)) = (y \ z) * (y * (y * x)). [para(181(a,2),1324(a,1,2)),rewrite([3018(5),168(4)]),flip(a)]. 3541 x \ (y \ (z * (y * (x * y)))) = y * T(z,y * (x * y)). [para(1359(a,1),15(a,1,2))]. 3640 x * (x * (((x \ y) / z) / T(x * y,z \ 1))) = z \ 1. [para(16(a,1),1884(a,1,2,2,2,1,2))]. 3645 (x / y) / T(z * (z * x),y \ 1) = z \ (z \ (y \ 1)). [para(1884(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 3646 R(x,x \ (y \ 1),z) = (y \ z) / ((x \ (y \ 1)) * z). [para(1884(a,1),22(a,1,1,1)),rewrite([3143(3),3645(8),16(6),3645(13),16(11)]),flip(a)]. 3666 (x \ y) / y = x \ 1. [para(1884(a,1),201(a,1,2)),rewrite([3645(8),100(6),16(5),16(4),3645(11),16(9),16(8),2755(7),480(6),3645(9),16(7),16(6),3645(11),1300(9),13(6),3143(5)]),flip(a)]. 3691 x / (y * x) = y \ 1. [para(1884(a,1),1013(a,2)),rewrite([3645(7),16(5),2538(5),2755(3)])]. 3723 R(x \ 1,x,y) = x \ 1. [back_rewrite(1027),rewrite([3691(5)])]. 3724 x / (y * (z * (y * x))) = (y * (z * y)) \ 1. [back_rewrite(1448),rewrite([3723(7)]),flip(a)]. 3725 x / (y * (y * (z * x))) = (y * (y * z)) \ 1. [back_rewrite(1039),rewrite([3723(7)]),flip(a)]. 3933 x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u)))))) = x * u. [para(398(a,1),15(a,1,2)),rewrite([15(3)]),flip(a)]. 3934 K(x * y,x) = y \ T(y,x). [para(398(a,1),20(a,1,1)),rewrite([3933(13),101(4),3136(5),23(2),3933(13)]),flip(a)]. 3935 K(x,x * y) = T(y,x) \ y. [para(398(a,1),20(a,1,2)),rewrite([3933(11),101(2),3135(5),23(2),3933(13)]),flip(a)]. 3936 x * (y * (y * (x * (z * ((x * (y * (y * (x * z)))) \ u))))) = u. [para(398(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 3940 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(398(a,1),74(a,2,1)),rewrite([3936(10),3936(12),3136(8)])]. 3941 L(x \ (y * z),x,y) = (y \ x) \ z. [para(398(a,1),74(a,2,2)),rewrite([3936(10),3135(7)])]. 3947 x * (x * (y * (x * (x * (y * (z \ ((y * (x * (x * (y / z)))) \ u))))))) = x * (x * u). [para(1014(a,1),398(a,1,2,2,2,2,2,2,2,1,2,2,2)),rewrite([3143(8)])]. 3949 x * (x * (y * ((x * (x * (x * (x * y)))) \ z))) = x \ (x \ z). [para(398(a,1),132(a,1,2)),rewrite([3135(6),15(3),3436(2),2507(13),1607(11)]),flip(a)]. 3954 a(x,x \ y,z) = a(x,x * y,z). [para(398(a,1),133(a,1,2,1)),rewrite([3949(8),16(3),136(4),37(6),3135(7),3162(5),3949(12),16(7),2508(6)]),flip(a)]. 3982 a(x,x * y,x * z) = a(y,x,z) \ 1. [back_rewrite(2575),rewrite([3954(3)])]. 4013 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x / y,y). [back_rewrite(1051),rewrite([3954(11),1014(10)])]. 4021 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,x * ((y * x) * z),u). [back_rewrite(662),rewrite([3954(13),189(12)])]. 4032 (x * ((x \ y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(56),rewrite([3954(7)])]. 4114 ((x * y) * z) \ R(x,y,z) = (y * z) \ 1. [para(22(a,1),1829(a,1,2))]. 4115 ((x / y) * x) * z = x * (y \ (x * z)). [para(1829(a,1),104(a,1,2,1)),rewrite([3143(4)]),flip(a)]. 4137 (x \ y) * (y \ x) = 1. [para(2538(a,1),16(a,1,2))]. 4145 L(x \ y,y \ x,z) = x \ y. [para(2538(a,1),74(a,1,1)),rewrite([14(7),1091(6),2538(6)])]. 4151 a(x,y \ z,z \ y) = 1. [para(2538(a,1),1012(a,1,2))]. 4155 x / (y \ z) = x * (z \ y). [para(2538(a,1),1013(a,1,2))]. 4157 (x * y) \ ((x / z) * (z * y)) = a(x / z,z,y) \ 1. [para(60(a,1),2538(a,1,1)),flip(a)]. 4165 L(x,y \ z,z \ y) = x. [para(2538(a,1),3266(a,1,3))]. 4180 x * ((x \ (y / z)) * z) = R(y,z \ 1,x). [back_rewrite(2806),rewrite([4155(4),169(4)])]. 4186 R(x,y,y \ ((y \ x) \ z)) = z * ((z \ y) * (y \ x)). [back_rewrite(199),rewrite([4155(8),169(8)])]. 4187 a(x / y,y,y) \ 1 = a(x,y \ 1,y * y). [back_rewrite(2604),rewrite([4157(5)])]. 4209 T(x * y,x) = y * x. [para(1091(a,1),2642(a,1,2)),rewrite([2774(4)]),flip(a)]. 4210 T(x,(y \ x) * y) = x. [para(64(a,1),2642(a,1,2)),rewrite([3304(3)]),flip(a)]. 4230 (x / y) * x = x * (y \ x). [para(2643(a,1),90(a,1,2)),flip(a)]. 4247 (x * (y \ x)) * z = x * (y \ (x * z)). [back_rewrite(4115),rewrite([4230(2)])]. 4254 (x / y) * ((x / y) * ((y * z) / T(x * (y \ x),z))) = z. [back_rewrite(2009),rewrite([4230(5)])]. 4278 T(x,y) \ y = T(x \ y,y). [para(2649(a,1),2642(a,1,2)),rewrite([2709(3)])]. 4281 T(x \ y,T(x,y)) = T(x \ y,y). [back_rewrite(2709),rewrite([4278(5)])]. 4314 T(x,y) * (T(x \ y,y) * (T(x,y) * z)) = (x * y) * z. [para(2690(a,1),186(a,2,1,1)),rewrite([4281(4),90(9)])]. 4357 (x \ (x \ y)) * T(x,y) = x \ y. [para(2642(a,1),2690(a,1,2))]. 4365 x / T(x,y) = T(x,y) \ x. [para(159(a,1),2711(a,1,2))]. 4366 T(x,y) / x = x \ T(x,y). [para(541(a,1),2711(a,1,2))]. 4379 ((x \ y) * x) / y = K(x \ y,x). [para(64(a,1),2711(a,2)),rewrite([4210(5)])]. 4407 (x * y) \ 1 = y \ (x \ 1). [para(2755(a,1),2538(a,1,1))]. 4408 (x \ y) \ z = (y \ x) * z. [para(2538(a,1),2755(a,1,1))]. 4417 ((x * y) * z) \ R(x,y,z) = z \ (y \ 1). [back_rewrite(4114),rewrite([4407(7)])]. 4419 ((x \ (y \ 1)) * y) \ (x \ 1) = a(x,x / y,y). [back_rewrite(4013),rewrite([4407(7)])]. 4420 x / (y * (y * (z * x))) = (y * z) \ (y \ 1). [back_rewrite(3725),rewrite([4407(8)])]. 4421 x / (y * (z * (y * x))) = (z * y) \ (y \ 1). [back_rewrite(3724),rewrite([4407(8)])]. 4445 L(L(x,y,z),u,x \ (u \ 1)) = L(x,y,z). [back_rewrite(3192),rewrite([4407(4)])]. 4458 ((x * y) * z) \ y = (y * z) \ (x \ y). [back_rewrite(2540),rewrite([4407(5),4408(4),14(4)]),flip(a)]. 4470 R(x,y,y \ ((x \ y) * z)) = z * ((z \ y) * (y \ x)). [back_rewrite(4186),rewrite([4408(2)])]. 4480 L(x \ (y * z),x,y) = (x \ y) * z. [back_rewrite(3941),rewrite([4408(5)])]. 4498 (((x * y) * z) \ x) * (y * z) = a(x,x * y,z). [back_rewrite(3162),rewrite([4408(5)])]. 4501 (x * y) \ (x * (x * z)) = (y \ x) * z. [back_rewrite(3135),rewrite([4408(6)])]. 4504 (x \ y) * (((y \ x) * z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(2692),rewrite([4408(3)])]. 4505 (x \ y) * x = T(y,x). [back_rewrite(2649),rewrite([4408(2)])]. 4516 K(x \ y,x) = y \ T(y,x). [back_rewrite(4379),rewrite([4505(2),4366(2)]),flip(a)]. 4525 x * (T(y,x) * z) = y * (x * z). [back_rewrite(2965),rewrite([4505(2)])]. 4537 a(T(x,y),y \ x,z) = a(y \ x,x,z). [back_rewrite(1702),rewrite([4505(2)])]. 4539 K(x,x \ y) = T(y,x) \ y. [back_rewrite(65),rewrite([4505(2)]),flip(a)]. 4562 ((x * y) * y) / z = x * (y * (y / z)). [back_rewrite(1859),rewrite([4525(4)]),flip(a)]. 4578 (x * y) * y = x * (y * y). [back_rewrite(669),rewrite([4525(3)]),flip(a)]. 4582 a(x,T(y,x),z) = a(y,x,z). [back_rewrite(508),rewrite([4525(3),19(5)]),flip(a)]. 4613 (x * (y * y)) / z = x * (y * (y / z)). [back_rewrite(4562),rewrite([4578(2)])]. 4713 x / (T(T(y,z),u) * (z * ((T(y,u) * (z * z)) \ x))) = z. [back_rewrite(2166),rewrite([4578(5)])]. 4714 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w))) = w. [back_rewrite(2032),rewrite([4578(8),2040(9)])]. 4795 a(x * y,y,z) \ 1 = a(x,y,y * z). [back_rewrite(2574),rewrite([4582(3)]),flip(a)]. 4813 (x / y) * (y * (y / T(x * y,a(x,y \ 1,y * y)))) = a(x,y \ 1,y * y). [back_rewrite(2599),rewrite([4613(10)])]. 4993 K(x,y) * K(y,x) = 1. [para(2917(a,1),16(a,1,2))]. 4996 R(x,K(y,z),K(z,y)) = x. [para(2917(a,1),191(a,2,3)),rewrite([14(5),16(4),48(2)]),flip(a)]. 5005 x / K(y,z) = x * K(z,y). [para(2917(a,1),1014(a,1,2)),flip(a)]. 5011 L(x,K(y,z),K(z,y)) = x. [para(2917(a,1),3266(a,1,3))]. 5134 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(15(a,1),3940(a,1,1)),flip(a)]. 5155 L((x / y) \ z,x / y,x) = y * (x \ z). [para(1014(a,1),3940(a,1,1,1)),rewrite([1014(5),4408(8),45(6)])]. 5162 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(3940(a,1),2254(a,1)),rewrite([3436(2),100(5)]),flip(a)]. 5163 L((x * y) \ z,x * y,y * x) = K(x,y) \ ((y * x) \ z). [para(63(a,1),3940(a,1,1,1)),rewrite([63(5)])]. 5194 R(x,y * (y * z),z \ (y \ (y \ u))) = R(x,z,z \ u). [back_rewrite(1870),rewrite([5162(3),191(6),1935(6),16(3),16(2),5162(7)]),flip(a)]. 5200 x * (x * (y * ((y \ (x \ (x \ z))) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [back_rewrite(411),rewrite([5162(3)])]. 5208 (x * (y \ z)) * (z \ y) = x. [para(4151(a,1),209(a,1,1)),rewrite([45(6),4137(7),14(6),4151(7),88(6)])]. 5332 a(x,y,y) = 1. [para(89(a,1),507(a,1,2,2)),rewrite([4578(4),46(5),89(2)]),flip(a)]. 5358 a(x,y \ 1,y * y) = 1. [back_rewrite(4187),rewrite([5332(2),46(3)]),flip(a)]. 5359 (x / y) * (y / x) = 1. [back_rewrite(4813),rewrite([5358(6),88(4),3691(3),1014(4),5358(7)])]. 5452 x * (x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u))))))) = y * z. [para(189(a,1),2640(a,1,2,2,2,2,2,2))]. 5468 T(x * (x * y),y \ z) = T(x * (x * y),x * (x * z)). [para(16(a,1),2647(a,1,2,2,2)),flip(a)]. 5480 T(x * (x * y),x * (x * (y / z))) = T(x * (x * y),z \ 1). [para(1014(a,1),2647(a,1,2,2,2))]. 5610 (x \ (y \ (y \ (z \ 1)))) * (z * (y * (y * (x * u)))) = L(u,y * (y * x),z). [para(37(a,1),145(a,1,1)),rewrite([37(11),4501(12),1091(5),4407(5),5162(5),2507(15)])]. 5614 L(x,y * (y * z),z) = x. [para(1607(a,1),145(a,2)),rewrite([189(5),101(2),189(4),4578(2),101(3),100(2),189(11),101(7),189(10),4578(7),189(9),100(7),37(8),4501(12),1091(5),4407(5),5162(5),5610(10)])]. 5657 x * (y * (x * (z * ((z * (x * (y * (x * z)))) \ u)))) = z \ u. [para(2215(a,1),15(a,1,2)),flip(a)]. 5665 R(x,y,y \ ((x \ y) * z)) = (y * z) / ((x \ y) * z). [para(2215(a,1),191(a,1,1,2)),rewrite([5657(13),4408(3),5657(16),4408(6)]),flip(a)]. 5816 R(x * ((x \ y) * (y \ z)),z,z \ u) = (z * (a(y,x,x \ (y \ z)) * u)) / u. [para(16(a,1),435(a,1,2)),rewrite([16(6),16(8)])]. 5879 x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))) = z. [para(463(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 5885 (x \ (y \ 1)) * (y * (x * z)) = L(z,x,y). [para(463(a,1),132(a,1,1,2)),rewrite([5879(13),4501(8),1091(3),4407(3),5879(16),2507(9)])]. 6069 (x \ (y \ 1)) * (x * y) = K(x,y). [para(20(a,1),3143(a,2)),rewrite([4407(3)])]. 6070 (x \ y) * (y \ (x * z)) = L(z,x,y \ 1). [para(3143(a,1),21(a,1,1)),rewrite([3143(5),4408(4)])]. 6073 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [para(3143(a,1),37(a,1,1,2)),rewrite([3143(4),3143(9),3143(8)]),flip(a)]. 6120 (x \ 1) / y = x \ (y \ 1). [para(3143(a,1),1014(a,1)),flip(a)]. 6132 (x \ (y \ 1)) * y = x \ 1. [para(1091(a,1),3143(a,2)),rewrite([4407(3)])]. 6134 T(x \ 1,x \ y) = T(x \ 1,y). [para(3143(a,1),1708(a,1,2))]. 6141 ((x * y) \ (z \ (z \ (u \ 1)))) * ((u * (z * (z * x))) * y) = a(u,z * (z * x),y). [para(139(a,1),3143(a,2)),rewrite([4407(6),5162(6)])]. 6144 K(x,y) \ z = K(y,x) * z. [para(2917(a,1),3143(a,1,1)),flip(a)]. 6233 a(x,x / y,y) = 1. [back_rewrite(4419),rewrite([6132(4),46(5)]),flip(a)]. 6238 L((x * y) \ z,x * y,y * x) = K(y,x) * ((y * x) \ z). [back_rewrite(5163),rewrite([6144(9)])]. 6257 L(x,y / x,y) = x. [hyper(24,a,6233,a)]. 6258 a(x * y,x,y) = 1. [para(17(a,1),6233(a,1,2))]. 6279 L(x,y,y * x) = x. [para(17(a,1),6257(a,1,2))]. 6351 x * ((x \ y) * y) = y * y. [para(6258(a,1),435(a,2,1,2,1)),rewrite([16(2),16(5),16(6),3436(6),2044(7),16(5),13(6),100(5),1839(6),47(4),14(5)])]. 6353 (x \ y) * ((y \ x) * z) = L(z,(y \ x) * x,y). [back_rewrite(831),rewrite([6351(3),3436(6),6073(6),15(2)])]. 6416 L(x,y \ 1,y \ x) = x. [para(3143(a,1),6279(a,1,3))]. 6562 K(x,y) / (x * y) = x \ (y \ 1). [para(20(a,1),3666(a,1,1)),rewrite([4407(6)])]. 6565 (x / y) \ 1 = y / x. [para(50(a,1),3666(a,1,1)),flip(a)]. 6591 L(x,y,z) \ (y \ (z \ 1)) = (y * x) \ (z \ 1). [para(2934(a,1),3666(a,1,1)),rewrite([6562(7),4407(4),4407(9)])]. 6618 L(x,y \ 1,z * y) = L(x,y \ z,y). [para(73(a,1),181(a,2)),rewrite([1091(2),3143(3),16(2),1091(4)]),flip(a)]. 6663 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,u,w),y,z))) \ (v6 * v5). [para(76(a,1),228(a,1)),flip(a)]. 6676 L(x,y \ (x \ 1),z) = (z * (y \ (x \ 1))) \ (z / y). [para(1014(a,1),76(a,2,2)),rewrite([6120(3),6120(7)])]. 6793 L(L(R(x,y,z),u,w),v5,x \ (v5 \ 1)) = L(R(x,y,z),u,w). [para(4445(a,1),33(a,1,1)),rewrite([33(2),33(4)]),flip(a)]. 6887 L(K(x * (y * x),x \ 1),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [para(2757(a,1),3940(a,1,1)),rewrite([3436(15)])]. 6890 K(x * (y * x),x \ 1) = K(x,y). [para(2757(a,1),3143(a,2)),rewrite([4407(5),6565(4),3436(3),1829(2),6069(5)]),flip(a)]. 6897 L(K(x,y),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [back_rewrite(6887),rewrite([6890(5)])]. 6946 T(x * (x * (y / (x * z))),x * z) = (z \ x) * y. [para(16(a,1),3139(a,1,1,2,2,2,2)),rewrite([16(6),4408(8)])]. 6953 (x \ ((y * z) \ (y \ 1))) * u = (z * x) \ (y \ (y \ u)). [para(341(a,1),3139(a,1,1,2,2,2,2)),rewrite([341(27),6946(26),4417(8),4407(4),5162(10)])]. 7004 x * (y \ ((x * (x / y)) \ z)) = x \ z. [para(18(a,1),3218(a,2,2)),rewrite([92(6)])]. 7047 T(x,K((y \ z) * (y * ((z * y) \ x)),y)) = x. [para(16(a,1),3307(a,1,1)),rewrite([16(11)])]. 7488 x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u)))))) = x \ (y * z). [para(5452(a,1),15(a,1,2)),flip(a)]. 7490 (x * y) * ((x * y) * ((x * z) / (T(u * u,x * y) * (x * ((y * x) * z))))) = (u \ (u \ x)) * y. [para(5452(a,1),21(a,1,2)),rewrite([3436(3),6073(3),1607(17)]),flip(a)]. 7550 x * ((x \ (x \ y)) * z) = x \ (y * z). [back_rewrite(7488),rewrite([7490(13)])]. 7616 T(x,y) / y = y \ x. [para(2690(a,1),3691(a,1,2)),rewrite([4408(5),14(5)])]. 7617 T(x,y) * (y \ x) = (y \ x) * x. [para(4357(a,1),3691(a,1,2)),rewrite([4155(3),4408(7),4408(5),14(7)])]. 7656 L(x,(y \ z) * z,y) = x. [para(4137(a,1),21(a,1,1)),rewrite([6353(5),45(5),4165(6)])]. 7679 L(x,y \ z,(z \ y) * (u * (z \ y))) = L(x,u,z \ y). [para(4137(a,1),132(a,1,1,2,2)),rewrite([14(3),6353(7),7656(6),21(6)]),flip(a)]. 7713 K(x \ y,(y \ x) * z) = K(x \ y,z). [para(4137(a,1),177(a,1,1,1,2)),rewrite([4408(2),14(4),5208(8),4458(5),4408(4),20(5),4408(5),4137(8),14(7)]),flip(a)]. 7715 (x \ y) * ((y \ x) * z) = z. [back_rewrite(6353),rewrite([7656(7)])]. 7769 T(T(x,y),y \ x) = x. [para(16(a,1),4209(a,2)),rewrite([4505(2)])]. 7772 ((x \ y) * (x * z)) * x = T((y * x) * z,x). [para(104(a,1),4209(a,1,1)),flip(a)]. 7775 T(x,y) * y = T(x * y,y). [para(90(a,1),4209(a,1,1)),flip(a)]. 7820 K((x \ y) * (x * z),x) = K(x * ((y * x) * z),x). [back_rewrite(3323),rewrite([7772(4),4366(6),3934(6,R)]),flip(a)]. 7826 x * K(y * x,y) = T(x,y). [back_rewrite(874),rewrite([7820(6),16(4),7772(9),16(7)])]. 7925 T(x,K(y * x,y)) = x. [back_rewrite(7047),rewrite([7820(6),16(4)])]. 7967 x \ T(y,x) = T(x \ y,x). [para(4505(a,1),23(a,1,2))]. 8018 T(x,y) \ (y \ x) = y \ 1. [para(4505(a,1),1091(a,1,1))]. 8054 a(x \ y,y,x) = 1. [para(4505(a,1),6258(a,1,1)),rewrite([4537(3)])]. 8105 L(x,y,x \ y) = x. [hyper(24,a,8054,a)]. 8106 a(x,y * x,y) = 1. [para(15(a,1),8054(a,1,1))]. 8296 K(x,y) * (K(y,x) * z) = z. [para(4993(a,1),21(a,1,1)),rewrite([45(6),5011(7)])]. 8298 (x * K(y,z)) * K(z,y) = x. [para(4993(a,1),22(a,1,2)),rewrite([48(6),4996(7)])]. 8308 L(x,K(y,z),K(z,y) * (u * K(z,y))) = L(x,u,K(z,y)). [para(4993(a,1),132(a,1,1,2,2)),rewrite([14(3),8296(7),21(6)]),flip(a)]. 8379 R(x,x \ y,z) = z * ((z \ y) * (y \ x)). [para(81(a,2),1014(a,2)),rewrite([4407(5),4408(4),14(4),169(4)]),flip(a)]. 8463 R(x,y \ 1,(x / y) \ z) = R(x,y \ 1,z). [para(1014(a,1),82(a,1,3,1)),rewrite([1014(10),3143(10),4155(9),4408(8),4180(9)])]. 8532 T(x,y) \ x = K(x \ y,x). [para(2642(a,1),4539(a,2,1)),rewrite([4408(3),7713(4)]),flip(a)]. 8593 x / T(x,y) = K(x \ y,x). [back_rewrite(4365),rewrite([8532(4)])]. 8594 K(x \ y,x) = K(y,y * x). [back_rewrite(3935),rewrite([8532(4)]),flip(a)]. 8701 L(x \ y,x,z) = ((z / y) * x) \ z. [para(3199(a,1),74(a,1)),rewrite([16(4),16(6),18(6)])]. 8992 ((x \ y) * (x * (x * z))) / T(z,T(x * y,x * (x * z))) = T(x * y,x * (x * z)). [para(3476(a,1),165(a,1,1))]. 9001 T(x,(y \ z) * (y * (y * x))) = T(x,T(y * z,y * (y * x))). [para(3476(a,1),1708(a,1,2))]. 9050 x * ((x * (y * x)) \ z) = y \ (x \ z). [para(18(a,1),3541(a,1,2,2)),rewrite([92(8)]),flip(a)]. 9085 x * a(y,z,z \ (y \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [back_rewrite(3093),rewrite([9050(4)])]. 9101 (x * (((y * z) * (z * y)) * u)) * a(x,(z * y) * (y * z),u) = (x * ((z * y) * (y * z))) * u. [para(178(a,1),312(a,1,1,2)),rewrite([3308(9),3308(14)])]. 9114 ((x * ((y * z) * (z * y))) * u) / (((z * y) * (y * z)) * u) = R(x,(y * z) * (z * y),u). [para(178(a,1),121(a,1,2)),rewrite([3308(4),3308(14)])]. 9186 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,(y \ z) * (y * x),y). [para(179(a,1),3143(a,2)),rewrite([4407(4),4407(3)])]. 9198 x \ (K(y,z) * ((K(z,y) * x) * u)) = L(u,K(z,y) * x,K(y,z)). [para(4993(a,1),179(a,1,1,1)),rewrite([13(2),6144(4),100(7),8296(6),6144(9),100(12),8296(11)])]. 9548 x * (x * (y * (x * (x * (y * (z \ ((y / z) \ (x \ (x \ (y \ 1)))))))))) = x * x. [para(14(a,1),3947(a,2,2)),rewrite([4407(6),5162(6)])]. 9559 L(x,y \ z,y) = L(x,y * z,y). [para(3947(a,1),132(a,1,1)),rewrite([5162(7),7004(9),16(6),16(5),136(6),21(6),5162(7),7004(9),16(6),16(5),2507(6)]),flip(a)]. 9719 L(x,y \ 1,z * y) = L(x,y * z,y). [back_rewrite(6618),rewrite([9559(6)])]. 10000 (x / y) * ((y / x) * z) = L(z,y / x,x / y). [para(5359(a,1),21(a,1,1)),rewrite([45(6)])]. 10215 x / (y / z) = x * (z / y). [para(6565(a,1),1014(a,1,2)),flip(a)]. 10221 L(x,y / z,z / y) = x. [para(6565(a,1),3266(a,1,3))]. 10229 (x / y) \ z = (y / x) * z. [para(6565(a,1),3143(a,1,1)),flip(a)]. 10279 ((x * y) / z) * (z / y) = R(x,y,z \ 1). [back_rewrite(1836),rewrite([10215(4)])]. 10287 (x / y) * ((y / x) * z) = z. [back_rewrite(10000),rewrite([10221(7)])]. 10296 x * (x * (y * (x * (x * (y * (z \ ((z / y) * (x \ (x \ (y \ 1)))))))))) = x * x. [back_rewrite(9548),rewrite([10229(6)])]. 10305 R(x,y \ 1,(y / x) * z) = R(x,y \ 1,z). [back_rewrite(8463),rewrite([10229(4)])]. 10321 L(K(x,y),(y / x) * (x * x),y / x) = x \ T(x,y). [back_rewrite(6897),rewrite([10229(9),3169(9),4505(8),15(9)])]. 10347 L((x / y) * z,y / x,y) = x * (y \ z). [back_rewrite(5155),rewrite([10229(2)])]. 10367 (x / y) * (y * (x \ z)) = L(z,x \ 1,y). [back_rewrite(3229),rewrite([10229(4)])]. 10690 ((x / y) * z) \ x = (x * z) \ (x * y). [para(8701(a,1),21(a,2)),rewrite([16(3)]),flip(a)]. 10809 (x \ y) * (x * (x * z)) = T(y * x,x) * z. [para(7967(a,1),104(a,1,2,1)),rewrite([4525(5),7775(6)])]. 10885 T(x,T(y * z,y * (y * x))) = T(x,T(T(z * y,y),x)). [back_rewrite(9001),rewrite([10809(4),2652(4)]),flip(a)]. 10888 T(x * y,x * (x * z)) = T(T(y * x,x),z). [back_rewrite(8992),rewrite([10809(4),10885(8),965(8)]),flip(a)]. 10920 T(x * (y * y),x / z) = T(y * (y * x),z \ 1). [back_rewrite(5480),rewrite([10888(6),101(2),4209(3),4578(2)])]. 10927 T(x * (x * y),y \ z) = T(y * (x * x),z). [back_rewrite(5468),rewrite([10888(9),101(6),4209(7),4578(6)])]. 11076 L(T(x * y,x * z),L(y \ z,y,x),u) = (u * L(y \ z,y,x)) \ (u * (x * z)). [para(2705(a,1),74(a,1,1))]. 11083 (x \ y) * (z * (z * x)) = T(y * (z * z),x). [para(2254(a,1),2705(a,1,1)),rewrite([100(3),4408(4),100(6),100(8),10888(9),101(6),4209(7),4578(6)])]. 11219 ((x \ y) / z) / T(x * y,z \ 1) = x \ (x \ (z \ 1)). [para(3640(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 11253 R(x,x \ (y \ 1),y * z) = z / ((x \ (y \ 1)) * (y * z)). [para(3640(a,1),82(a,1,3,1)),rewrite([11219(7),16(5),4408(6),45(5),11219(12),16(10),11219(15),16(13),16(12),4408(11),45(10)])]. 11645 (((x \ y) * z) * u) / (((y \ (x \ 1)) * (y * z)) * u) = R(y,(y \ (x \ 1)) * (y * z),u). [para(3143(a,1),183(a,1,1,1,1))]. 12076 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,y,z),u,w))) \ (v6 * v5). [para(34(a,1),6663(a,2,1,2,2))]. 12077 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = ((L(L(x,u,w),y,z) / v5) / v6) * (v6 * v5). [para(37(a,1),6663(a,2,1)),rewrite([2507(8),37(15),4501(16),1091(12),4407(12),10229(12),1014(12)])]. 12372 T(T(x,y),y \ 1) = x. [para(1091(a,1),7769(a,1,2)),rewrite([1708(2)])]. 12504 K(x,x * y) * T(y,x) = y. [para(7925(a,1),23(a,2)),rewrite([7826(5),6144(4)])]. 13457 L(x,(y \ z) * (y * u),y) = L(x,y * ((z * y) * u),y). [para(187(a,1),132(a,1,2,2)),rewrite([104(4),21(10),2507(10)]),flip(a)]. 13523 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,y * ((z * y) * x),y). [back_rewrite(9186),rewrite([13457(14)])]. 13639 (x * (y \ z)) * ((z \ y) * u) = (y \ z) * (((z \ y) * x) * u). [para(4137(a,1),190(a,1,2,2)),rewrite([4408(4),14(6),4408(8),5208(12)])]. 13884 L(x,y * (z * y),y) = L(x,y,z). [para(14(a,1),13523(a,1,2,2,1,2)),rewrite([45(5),4505(5),4525(6),5885(6),14(4)]),flip(a)]. 13932 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y) * u,K(z,y)). [para(4993(a,1),13523(a,1,2,2,1,2)),rewrite([6144(5),1014(5),1829(4),6144(5),14(7),3143(8),9198(6),8298(9)])]. 14102 T(x,T(x,y) \ 1) = x. [para(541(a,1),12372(a,1,1))]. 14430 T(x,y) * K(x \ y,x) = x. [para(14102(a,1),23(a,2)),rewrite([1014(7),8593(5),4408(6),45(3)])]. 14868 (x * x) / y = x * (x / y). [para(100(a,1),1014(a,1)),rewrite([1014(3)]),flip(a)]. 14874 L(x,y * (y * z),u) = L(x,z,u * (y * y)). [para(100(a,1),132(a,1,1,2,2)),rewrite([100(5),100(9),100(11),4501(12),1091(5),4407(5),5162(5),5610(10),100(7),2507(8)])]. 14882 a(x * (y * y),z,u) = a(x,y * (y * z),u). [para(100(a,1),133(a,1,1,2,2)),rewrite([100(6),100(9),100(11),37(12),4501(13),1091(6),4407(6),5162(6),6141(11),100(7),2508(8)]),flip(a)]. 15035 L(x,y,y * (z * z)) = x. [back_rewrite(5614),rewrite([14874(3)])]. 15276 (x * y) / T(z * (x \ z),y) = (x / z) * ((x / z) * y). [para(4254(a,1),21(a,1,2)),rewrite([3436(4),10229(3),10229(4),1607(12)]),flip(a)]. 15308 a(x / y,(y / x) * ((y / x) * z),u) = a(x / y,z,u). [para(4254(a,1),133(a,1,2,1,2)),rewrite([15276(8),37(8),10287(9),10287(6),19(7),15276(12),2508(12)]),flip(a)]. 15452 x \ (y * (y * z)) = ((x \ y) * y) * z. [para(7769(a,1),4314(a,1,1)),rewrite([8018(3),6134(4),7769(6),4525(6),3143(5),7617(6)])]. 15916 x \ ((x * y) * z) = (y / x) * (x * z). [para(15(a,1),4504(a,1,2,1,1)),rewrite([1091(2),3143(5),1091(5),1014(6),4209(6)])]. 16103 L(x,y * z,y) = L(x,y,z). [back_rewrite(5134),rewrite([15916(3),3276(4)]),flip(a)]. 16229 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y),u). [back_rewrite(13932),rewrite([16103(8)])]. 16256 L(x,y,z * y) = L(x,y,z). [back_rewrite(13884),rewrite([16103(3)])]. 16343 x \ T(x,y) = K(x,y). [back_rewrite(10321),rewrite([16103(6),2254(4)]),flip(a)]. 16398 L(x,y \ 1,z * y) = L(x,y,z). [back_rewrite(9719),rewrite([16103(6)])]. 16465 L(x,y \ z,y) = L(x,y,z). [back_rewrite(9559),rewrite([16103(4)])]. 16485 L((x * y) \ z,x,y) = y \ (x \ z). [back_rewrite(3940),rewrite([16103(4)])]. 16487 L(L(x,y,z),z,y) = x. [back_rewrite(667),rewrite([16103(3)])]. 16564 K(x \ y,x) = K(y,x). [back_rewrite(4516),rewrite([16343(4)])]. 16623 T(x,y) * K(y,x) = x. [back_rewrite(14430),rewrite([16564(3)])]. 16686 K(x,x * y) = K(x,y). [back_rewrite(8594),rewrite([16564(2)]),flip(a)]. 16875 K(x,y) * T(y,x) = y. [back_rewrite(12504),rewrite([16686(2)])]. 17093 (x \ y) * (((y \ x) * z) * ((z * (x \ y)) * u)) = z * (z * ((x \ y) * u)). [para(4137(a,1),193(a,2,1,2,1,1)),rewrite([4145(5),13639(8),13(10),37(12)])]. 18454 L(x,y,x \ 1) = x. [para(1022(a,1),16487(a,1,1))]. 18472 L(x,x \ y,y) = x. [para(8105(a,1),16487(a,1,1))]. 18485 L(R(x,y,z),u,x \ 1) = R(x,y,z). [para(18454(a,1),33(a,1,1)),flip(a)]. 18604 a(x,y \ x,y) = 1. [hyper(25,a,18472,a)]. 18742 a(x,y,y * x) = 1. [para(101(a,1),8106(a,1,2)),rewrite([3982(4),4795(4)])]. 18870 (((x \ y) * z) * ((z * (y \ x)) * T(y,x))) / x = (x \ y) * (z * z). [para(4504(a,1),106(a,1,1,2)),rewrite([7715(14),4578(11)])]. 19450 (x * ((T(y,z) * (x * x)) \ u)) \ (T(T(y,x),z) \ 1) = u \ x. [para(4713(a,1),1829(a,1,2)),rewrite([4407(11)]),flip(a)]. 19474 (x * (y * y)) \ z = y \ (y \ (x \ z)). [para(4713(a,1),3645(a,1,1)),rewrite([4407(12),19450(12),10927(4),2711(4),4407(13),19450(13)])]. 20390 (x * y) * (y * x) = x * (y * (y * x)). [para(18742(a,1),209(a,1,1)),rewrite([45(5),18742(8),88(8)])]. 20504 ((x * (y * (z * (z * y)))) * u) / (z * (y * (y * (z * u)))) = R(x,y * (z * (z * y)),u). [back_rewrite(9114),rewrite([20390(3),20390(8),2213(9),20390(13)])]. 20510 (x * (y * (z * (z * (y * u))))) * a(x,z * (y * (y * z)),u) = (x * (z * (y * (y * z)))) * u. [back_rewrite(9101),rewrite([20390(3),2213(4),20390(8),20390(13)])]. 21062 T(x,y) * (x * z) = x * (T(x,y) * z). [para(16623(a,1),189(a,1,1)),rewrite([16875(7)]),flip(a)]. 21447 x * (y \ ((y / x) * z)) = L(z,y / x,y). [para(16(a,1),10347(a,1,1)),rewrite([10229(4)]),flip(a)]. 21507 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z / y,z))))) = x * x. [back_rewrite(10296),rewrite([21447(8)])]. 21704 R(x,y * (y * z),z \ ((y \ (y \ z)) * u)) = R(x,z,u). [para(15(a,1),5194(a,2,3)),rewrite([6073(5)])]. 21708 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * (u * w))) = R(x,z * u,L(w,u,z)). [para(21(a,1),5194(a,2,3)),rewrite([6073(8)])]. 21713 (x * (y * (y * z))) * (z \ (y \ (y \ u))) = z * ((z \ x) * u). [para(5194(a,1),341(a,1,1)),rewrite([16(6),16(5),16(4),200(3)]),flip(a)]. 21715 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * w)) = R(x,z * u,L(u \ w,u,z)). [para(74(a,2),5194(a,2,3)),rewrite([6073(7)])]. 21721 R(x,(y \ (y \ z)) * u,((y \ (y \ z)) * u) \ z) = R(x,z * u,u \ 1). [para(1091(a,1),5194(a,1,3)),rewrite([7550(4),16(3)]),flip(a)]. 21722 R(x,y * (z * (z * y)),K(y,z) * ((y * z) \ ((y * z) \ u))) = R(x,K(z,y),K(y,z) * u). [para(63(a,1),5194(a,1,2,2)),rewrite([20390(3),6144(9),6144(13)])]. 22202 ((x \ y) * z) * ((z * (y \ x)) * u) = (x \ y) * (z * (z * ((y \ x) * u))). [para(17093(a,1),15(a,1,2)),rewrite([15452(6),4408(2),4578(3),2040(6)]),flip(a)]. 22250 x \ (y * (z * z)) = (x \ y) * (z * z). [back_rewrite(18870),rewrite([22202(7),2690(4),11083(4),7616(4)])]. 23697 (x / y) * (y * z) = y * ((y \ x) * z). [para(136(a,1),15(a,1,2)),rewrite([15916(3)])]. 23717 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(136(a,1),74(a,2,1)),rewrite([16103(8),16485(7)])]. 23718 (x * y) \ ((x * z) * u) = (y \ x) * ((x \ z) * u). [para(136(a,1),74(a,2,2)),rewrite([4480(5)]),flip(a)]. 24016 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = L(L(R(x,v5 \ 1,v6),u,w),y,z). [back_rewrite(12077),rewrite([23697(12),4180(12),33(11),33(10)])]. 24021 x * ((x \ y) * (y \ z)) = L(z,y \ 1,x). [back_rewrite(10367),rewrite([23697(4)])]. 24043 R(x,y \ 1,y * z) = R(x,y,y \ z). [back_rewrite(2760),rewrite([23697(3),191(4)]),flip(a)]. 24057 a(x / y,y,z) = a(y,y * x,z). [back_rewrite(60),rewrite([23697(3),4032(5)]),flip(a)]. 24261 (x * (y / L(L(z,u,w),v5,v6))) \ (x * y) = L(L(R(z,y \ 1,x),v5,v6),u,w). [back_rewrite(12076),rewrite([24016(6)]),flip(a)]. 24264 R(x,x \ y,z) = L(x,y \ 1,z). [back_rewrite(8379),rewrite([24021(6)])]. 24267 (x * (a(y,z,z \ (y \ x)) * u)) / u = L(x,y \ 1,z). [back_rewrite(5816),rewrite([24021(4),33(5),480(2)]),flip(a)]. 24268 R(x,y,y \ ((x \ y) * z)) = L(x,y \ 1,z). [back_rewrite(4470),rewrite([24021(8)])]. 24479 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(z,y * (y * (z * x)),u). [back_rewrite(1952),rewrite([24057(15),37(14),2508(15)])]. 24638 (x * y) / ((z \ x) * y) = L(z,x \ 1,y). [back_rewrite(5665),rewrite([24268(4)]),flip(a)]. 26897 x / T(y * (y * (x / z)),z) = y \ (y \ z). [para(1925(a,1),21(a,1,2)),rewrite([3436(2),1607(8)]),flip(a)]. 26903 L(x,y,y \ z) = L(x,z,y). [para(1925(a,1),132(a,1,1,2)),rewrite([26897(6),7550(5),16(4),21(4),26897(6),2507(6),16465(4)]),flip(a)]. 32749 (x * T(x,y)) * z = x * (T(x,y) * z). [para(493(a,1),84(a,1,1)),rewrite([21062(3),547(5)]),flip(a)]. 33472 (x \ (y \ 1)) * (x * z) = x \ ((y \ x) * z). [para(3143(a,1),168(a,1,2,1)),flip(a)]. 33575 R(x,x \ ((y \ x) * z),u) = L(x,z \ (x \ y),u). [back_rewrite(11645),rewrite([33472(8),24638(8),4407(4),4408(3),14(3),33472(8)]),flip(a)]. 35645 (x \ (y \ 1)) * z = (y * x) \ z. [para(13(a,1),6953(a,1,1,2,1)),rewrite([46(3),45(8),45(7)])]. 35648 (x \ (y \ (z \ 1))) * u = ((z * y) * x) \ u. [para(16(a,1),6953(a,1,1,2,1)),rewrite([23717(10),16(9)])]. 35675 (x * ((y * z) \ (y \ 1))) * u = (x / z) * (y \ (y \ u)). [para(1014(a,1),6953(a,2,1)),rewrite([4408(7),45(2),10229(10)])]. 35905 R(x,x \ (y \ 1),y * z) = z * ((y * z) \ (y * x)). [back_rewrite(11253),rewrite([35645(10),4155(9)])]. 35922 R(x,x \ (y \ 1),z) = L(x,y,z \ 1). [back_rewrite(3646),rewrite([35645(9),4155(8),6070(8)])]. 36021 x * ((y * x) \ (y * z)) = L(z,y,x \ (y \ 1)). [back_rewrite(35905),rewrite([35922(5),4407(3)]),flip(a)]. 38314 x * (x * (y * ((y \ (x \ (x \ z))) * u))) = y * ((y \ z) * u). [para(37(a,1),169(a,2)),rewrite([5162(6),21713(7),5162(6)]),flip(a)]. 38342 (x \ y) * (y \ z) = y * ((x * y) \ z). [para(3143(a,1),169(a,1,1)),rewrite([35645(7)])]. 38445 (x * (y * (y * z))) * (z \ u) = z * ((z \ x) * (y * (y * u))). [back_rewrite(5200),rewrite([38314(9)]),flip(a)]. 38475 x * (y * ((x * y) \ z)) = L(z,y \ 1,x). [back_rewrite(24021),rewrite([38342(3)])]. 38488 L(x,y,z \ (y \ 1)) = L(x,y,z \ 1). [back_rewrite(6070),rewrite([38342(4),36021(4)])]. 38534 R(x,y * (y * z),z \ u) = R(x,z,((z \ y) * y) * u). [back_rewrite(340),rewrite([38445(5),191(8),15452(3)]),flip(a)]. 38568 x * a(y,z,z \ (y \ x)) = L(x,y,z \ 1). [back_rewrite(9085),rewrite([38475(10),4407(7),16465(8)])]. 38590 x * ((y * x) \ (y * z)) = L(z,y,x \ 1). [back_rewrite(36021),rewrite([38488(8)])]. 38623 L(L(R(x,y,z),u,w),v5,x \ 1) = L(R(x,y,z),u,w). [back_rewrite(6793),rewrite([38488(6)])]. 38642 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(21715),rewrite([38534(9)]),flip(a)]. 38643 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,z,y)). [back_rewrite(21708),rewrite([38534(10)])]. 38644 R(x,y,((y \ z) * z) * ((z \ (z \ y)) * u)) = R(x,y,u). [back_rewrite(21704),rewrite([38534(7)])]. 39505 (x * y) \ (x \ 1) = y \ (x \ (x \ 1)). [para(1607(a,1),6591(a,1,1)),flip(a)]. 39506 (x * y) \ (y \ 1) = y \ (x \ (y \ 1)). [para(1667(a,1),6591(a,1,1)),flip(a)]. 39650 (x * (y \ (z \ (z \ 1)))) * u = (x / y) * (z \ (z \ u)). [back_rewrite(35675),rewrite([39505(4)])]. 39699 x / (y * (y * (z * x))) = z \ (y \ (y \ 1)). [back_rewrite(4420),rewrite([39505(8)])]. 39792 x / (y * (z * (y * x))) = y \ (z \ (y \ 1)). [back_rewrite(4421),rewrite([39506(8)])]. 42198 a(x,x * y,(x * y) \ z) = a(x,y,y \ z). [para(1091(a,1),192(a,1,2,2,1)),rewrite([3143(5),169(4),192(5)]),flip(a)]. 44671 L(L(L(x,y,z),u,w),v5 \ 1,v5 \ x) = L(L(x,y,z),u,w). [para(6416(a,1),97(a,2,1,1))]. 44709 L(L(L(L(x,y,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(L(x,u,w),y,z),v5,v6). [para(6416(a,1),229(a,1,1,1)),flip(a)]. 46815 a(x,y * (y * (x * (y * z))),u) = a(x,x * (y \ z),u). [para(37(a,1),4021(a,1,1)),rewrite([16103(4),16485(3),23718(9),1091(6),4407(6),23717(6),14(5),4498(7),101(7),128(8),2508(10)]),flip(a)]. 47034 L(L(L(R(x,y \ 1,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(R(x,y \ 1,z),v5,v6),u,w). [para(76(a,1),44709(a,1,1)),rewrite([24261(6),24016(16)])]. 47036 L(L(x,y,z),u \ 1,u \ L(x,w,v5)) = L(x,y,z). [para(16487(a,1),44709(a,1,1,1)),rewrite([16487(8)])]. 47734 L(x,y * z,y * (z * (y * y))) = x. [para(189(a,1),15035(a,1,3)),rewrite([4578(3)])]. 48721 L(x,y * K(z,u),K(u,z)) = L(x,K(z,u),K(u,z) * y). [para(18(a,1),8308(a,1,3,2)),rewrite([5005(6)]),flip(a)]. 48733 L(x,K(y,z),u * K(z,y)) = L(x,K(z,y),u). [para(4505(a,1),8308(a,1,3,2)),rewrite([90(5),6144(6),16229(8)])]. 49860 L(x,T(y,z),y) = x. [para(18604(a,1),439(a,1,2,2,1)),rewrite([4247(3),23(2),4505(4),4505(6),480(8),4505(4),13(6),32749(5),21(6)])]. 50186 L(L(R(x,y \ 1,z),u,w),v5,v6) = L(L(L(x,y,z \ 1),u,w),v5,v6). [para(82(a,1),47034(a,2,1,1)),rewrite([1014(5),10229(4),10305(5),47034(10),1014(10),10229(9),3143(10),4155(9),10690(8),38590(9)])]. 50188 L(R(x,y \ 1,z),u \ 1,u \ L(x,w,v5)) = R(x,y \ 1,z). [para(16487(a,1),47034(a,1,1)),rewrite([16487(13)])]. 50190 L(R(x,y \ 1,z),u,w) = L(L(x,y,z \ 1),u,w). [para(18454(a,1),47034(a,1,3,2)),rewrite([18485(6),50186(8),44671(8),38623(11)]),flip(a)]. 50224 R(x,y \ 1,z) = L(x,y,z \ 1). [back_rewrite(50188),rewrite([50190(8),47036(8)]),flip(a)]. 50308 R(x,y,y \ z) = L(x,y,z \ 1). [back_rewrite(24043),rewrite([50224(4),4407(3),38488(4)]),flip(a)]. 50359 L(x,y * z,z * y) = x. [para(4209(a,1),49860(a,1,2))]. 50404 K(x,y) * ((x * y) \ z) = (y * x) \ z. [back_rewrite(6238),rewrite([50359(5)]),flip(a)]. 50423 R(x,y * (z * (z * y)),(z * y) \ ((y * z) \ u)) = R(x,K(z,y),K(y,z) * u). [back_rewrite(21722),rewrite([50404(9)])]. 52573 L(x,y \ 1,z) = L(x,y,z \ 1). [para(14(a,1),24267(a,1,1,2)),rewrite([38568(4),48(5)]),flip(a)]. 52576 x * (a(y,z,z \ (y \ x)) * u) = L(x,y,z \ 1) * u. [para(24267(a,1),18(a,1,1)),rewrite([52573(3)]),flip(a)]. 52596 L(x,y,z \ 1) = L(x,y,z). [para(7679(a,1),24267(a,2)),rewrite([45(2),45(2),45(4),45(4),42198(7),52576(7),4407(3),26903(4),52573(3),17(5),45(5)])]. 52843 R(x,x \ y,z) = L(x,y,z). [back_rewrite(24264),rewrite([52573(5),52596(5)])]. 52858 L(x,y,z) = L(x,z,y). [back_rewrite(16398),rewrite([52573(4),4407(3),26903(4),52573(3),52596(3)])]. 52953 R(x,y,y \ z) = L(x,y,z). [back_rewrite(50308),rewrite([52596(5)])]. 53483 L(x,y,z \ (x \ u)) = L(x,y,(u \ x) * z). [back_rewrite(33575),rewrite([52843(4),52858(3),52858(6)]),flip(a)]. 53894 L(x,K(y,z),u * K(z,y)) = L(x,u,K(z,y)). [back_rewrite(48733),rewrite([52858(6)])]. 53895 L(x,K(y,z),K(z,y) * u) = L(x,u,K(y,z)). [back_rewrite(48721),rewrite([52858(4),53894(4)]),flip(a)]. 54757 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,y,z)). [back_rewrite(38643),rewrite([52858(12)])]. 54758 R(x,y * z,L(z \ u,y,z)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(38642),rewrite([52858(3)])]. 55548 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y))))) = x * x. [back_rewrite(21507),rewrite([52858(6)])]. 55954 L(T(x * y,x * z),u,L(y \ z,x,y)) = (u * L(y \ z,x,y)) \ (u * (x * z)). [back_rewrite(11076),rewrite([52858(5),52858(6),52858(8)])]. 56084 L(x,y,x * z) = (y * (z \ (x \ 1))) \ (y / z). [back_rewrite(6676),rewrite([52858(4),53483(4),45(2)])]. 56223 R(x,y * z,L(z \ u,y,z)) = L(x,y * z,y * u). [back_rewrite(648),rewrite([52858(3),52953(9)])]. 56903 R(x,y * z,z \ 1) = L(x,y,(u \ (u \ y)) * z). [back_rewrite(21721),rewrite([52953(8),52858(4)]),flip(a)]. 57044 L(x,y,x * z) = L(x,z,y). [back_rewrite(3213),rewrite([52953(4),52858(2),52953(4)])]. 57097 (x * ((x \ y) * z)) / z = L(y,x,z). [back_rewrite(191),rewrite([52953(6)])]. 57908 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * w)) = L(x,y * z,y * w). [back_rewrite(54758),rewrite([56223(4)]),flip(a)]. 58091 (x * (y \ (z \ 1))) \ (x / y) = L(z,x,y). [back_rewrite(56084),rewrite([57044(2),52858(1)]),flip(a)]. 58275 L(x,y * z,y * (z * u)) = R(x,y * z,L(u,y,z)). [back_rewrite(54757),rewrite([57908(10)])]. 58601 R(x,y * z,L(y * y,y,z)) = x. [back_rewrite(47734),rewrite([58275(5)])]. 64162 L(x * x,x,y) = x * x. [para(1077(a,1),55954(a,1,3)),rewrite([14(3),4209(2),52596(4),52858(2),1607(5),1014(5),14(5),10229(5),23697(5),6351(5)])]. 64186 R(x,y * z,y * y) = x. [back_rewrite(58601),rewrite([64162(3)])]. 76377 T(x * (x * y),z \ 1) * (z / y) = z * (x * x). [para(10920(a,1),7616(a,1,1)),rewrite([10215(7),22250(11),10229(9),18(9)])]. 77479 a(x,x * (y \ (y \ (x \ z))),u) = a(x,y * (y * z),u). [para(3645(a,1),15308(a,1,2,1)),rewrite([10215(7),76377(7),3645(13),35648(11),4578(8),19474(9),35648(10),4578(4),19474(8),14882(9),16(7),16(6),3954(5),10215(12),76377(12),14882(8)])]. 82774 x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y)))) = x. [para(55548(a,1),15(a,1,2)),rewrite([15(2)]),flip(a)]. 82800 R(x / y,y,x) = x / y. [para(55548(a,1),85(a,2,1)),rewrite([82774(11),82774(13),14868(5),3691(4),1014(5)])]. 82841 x * (y \ (z \ (z \ 1))) = x / (z * (z * y)). [para(55548(a,1),342(a,2,1)),rewrite([82774(15),82800(6),82774(14),14868(8),39699(7)]),flip(a)]. 82892 (x / (y * (y * z))) * u = (x / z) * (y \ (y \ u)). [back_rewrite(39650),rewrite([82841(5)])]. 82924 a(x,y * (y * (x * z)),u) = a(x,x * z,u). [back_rewrite(24479),rewrite([82892(7),15(5),15(4),23697(3),4032(5)]),flip(a)]. 82939 a(x,x * (y \ z),u) = a(x,x * (y * z),u). [back_rewrite(46815),rewrite([82924(5)]),flip(a)]. 82951 a(x,y * (y * z),u) = a(x,z,u). [back_rewrite(77479),rewrite([82939(5),16(3),16(2)]),flip(a)]. 83285 a(x,y * (z * (z * y)),u) = 1. [back_rewrite(2486),rewrite([82951(6)])]. 84200 (x * (y * (z * (z * y)))) * u = x * (z * (y * (y * (z * u)))). [back_rewrite(20510),rewrite([83285(9),14(7)]),flip(a)]. 87206 R(x,y * (z * (z * y)),u) = x. [back_rewrite(20504),rewrite([84200(5),17(10)]),flip(a)]. 88170 R(x,K(y,z),K(z,y) * u) = x. [back_rewrite(50423),rewrite([87206(8)]),flip(a)]. 88394 x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w)) = x \ w. [para(4714(a,1),15(a,1,2)),flip(a)]. 88400 R(x,y,((y \ z) * z) * u) = L(x,y,u). [para(4714(a,1),148(a,1,2,2,2)),rewrite([88394(16),38445(5),57097(8),2507(3),88394(16),38534(5)]),flip(a)]. 88449 L(x,y,(z \ (z \ y)) * u) = R(x,y,u). [back_rewrite(38644),rewrite([88400(7)])]. 88465 R(x,y * z,z \ 1) = R(x,y,z). [back_rewrite(56903),rewrite([88449(8)])]. 103664 x * (y \ (z \ 1)) = x / (z * y). [para(64186(a,1),85(a,1)),rewrite([189(7),4578(6),4613(8),39792(6),16(7)]),flip(a)]. 103820 R(x,y,z \ 1) = L(x,z,y). [back_rewrite(58091),rewrite([103664(4),10229(4),10279(4)])]. 104117 R(x,y,z) = L(x,y,z). [back_rewrite(88465),rewrite([103820(4),16256(2),52858(1)]),flip(a)]. 105864 L(x,y,K(z,u)) = x. [back_rewrite(88170),rewrite([104117(4),53895(4)])]. 105866 $F # answer("aK1"). [resolve(105864,a,151,a)]. ============================== end of proof ========================== % Redundant proof: 110412 $F # answer("aK2"). [back_rewrite(56239),rewrite([105864(6)]),xx(a)]. % Redundant proof: 110427 $F # answer("aK1"). [back_rewrite(151),rewrite([105864(6)]),xx(a)]. % Disable descendants (x means already disabled): 38x 151x 87201 39 152x 56239x given #1619 (W0w,wt=8): 105864 L(x,y,K(z,u)) = x. [back_rewrite(88170),rewrite([104117(4),53895(4)])]. given #1620 (W0w,wt=9): 104117 R(x,y,z) = L(x,y,z). [back_rewrite(88465),rewrite([103820(4),16256(2),52858(1)]),flip(a)]. given #1621 (W0w,wt=9): 105379 L(x,y,L(y,z,u)) = x. [back_rewrite(94910),rewrite([104117(1),32180(3),104117(4),17(6),104117(1),104117(2),52858(2)]),flip(a)]. given #1622 (W0w,wt=10): 65699 a(x,y,x * T(x,y)) = 1. [para(101(a,1),26461(a,1,1)),rewrite([16686(4),23494(4),4578(2),24596(4),16716(2)])]. given #1623 (W0w,wt=10): 72513 K(x,L(T(x,y),z,u)) = 1. [para(13(a,1),39254(a,1,2,1,2,2)),rewrite([13(2)])]. given #1624 (W0w,wt=10): 72562 K(L(x,y,z),T(x,u)) = 1. [para(28464(a,1),16687(a,1,2)),rewrite([47(3)]),flip(a)]. given #1625 (W0w,wt=10): 72910 a(x,y * T(y,x),z) = 1. [para(101(a,1),13466(a,2,2,2)),rewrite([15590(3),3048(7)])]. given #1626 (W0w,wt=10): 74464 L(x,y,z * (x / z)) = x. [back_rewrite(56927),rewrite([74236(5),17(2)]),flip(a)]. given #1627 (W0w,wt=10): 75769 L(T(x,y),z,x) = T(x,y). [back_rewrite(38705),rewrite([75751(4),52837(5)])]. given #1628 (W0w,wt=10): 75784 L(x,y,T(y \ x,z)) = x. [back_rewrite(52606),rewrite([75765(6),17(2)]),flip(a)]. given #1629 (W0a,wt=17): 622 T(T(T(x / y,z),u),y) = T(T(y \ x,z),u). [para(537(a,1),29(a,1,1)),flip(a)]. given #1630 (W0a,wt=15): 625 T(x / y,z) * y = y * T(y \ x,z). [para(537(a,1),90(a,1,2)),flip(a)]. given #1631 (W0r,wt=17): 112153 a(x,x * y,z * y) = a(z,x,(x \ z) * y). [back_rewrite(90849),rewrite([110982(3)]),flip(a)]. given #1632 (W0r,wt=19): 62444 (x * y) * T(T(z,u),y) = (x * y) * T(T(z,y),u). [para(517(a,1),104(a,1,2,2)),rewrite([522(5)])]. given #1633 (W0r,wt=20): 79867 a(x \ T(x \ 1,y),T(x,z),K(z,x) * K(x,y)) = 1. [para(16343(a,1),50398(a,1,3,2)),rewrite([52619(3)])]. given #1634 (W0r,wt=19): 33619 (T(x,y * y) / z) / T(x,y * (y / z)) = z \ 1. [back_rewrite(30754),rewrite([33476(5),30455(4),30703(2)])]. given #1635 (W0r,wt=15): 112983 K(x \ y,x * x) * K(x,y) = K(y,x). [back_rewrite(89251),rewrite([112870(5)])]. given #1636 (W1w,wt=21): 18294 T(T(T(T(x,y),z),u),w) / T(T(T(T(x,w),y),z),u) = 1. [para(14577(a,1),4092(a,2,1)),rewrite([14(9),14470(10),14(10),14(19),47(18)])]. given #1637 (W1w,wt=21): 18464 L(L(L(x,y,z),u,w),v5,L(x,v6,v7)) = L(L(x,y,z),u,w). [para(16487(a,1),3604(a,2,1,1)),rewrite([18452(6)])]. given #1638 (W1w,wt=21): 18579 (x * T(x,y)) \ (y * (x * (y \ x))) = K(y,x * (y \ x)). [para(18466(a,1),2934(a,1,2,1)),rewrite([3169(3),4505(2),4230(4),18466(8),4230(8)])]. given #1639 (W1w,wt=21): 18681 K(x * (y * (x * z)),x * (y * x)) = K(z,x * (y * x)). [para(101(a,1),114(a,1,2)),rewrite([128(3),128(12),5158(13),23(6),16343(4),128(6)]),flip(a)]. given #1640 (W1w,wt=21): 18775 x * ((x \ y) * (z * (x * z))) = (y * x) * (z * T(z,x)). [para(101(a,1),190(a,2,2,2)),rewrite([15590(4)]),flip(a)]. given #1641 (W1w,wt=21): 18832 ((x \ y) * (z * y)) / T(x,y) = (x \ y) * (z * (x \ y)). [para(2690(a,1),106(a,1,1,2,2))]. given #1642 (W1w,wt=21): 18843 ((x \ y) * (z * T(y,x))) / x = (x \ y) * (z * (x \ y)). [para(4505(a,1),106(a,1,1,2,2))]. given #1643 (W1w,wt=21): 18848 L(x,y,z * (u * (z * (y * x)))) = L(x,y,z * (u * z)). [para(106(a,1),3199(a,1,3)),flip(a)]. given #1644 (W1a,wt=27): 586 ((x * y) * z) \ (a(x,y,z) * (x * (y * z))) = K(a(x,y,z),x * (y * z)). [para(54(a,1),20(a,1,1))]. given #1645 (W1a,wt=27): 587 (a(x,y,z) * (x * (y * z))) \ ((x * y) * z) = K(x * (y * z),a(x,y,z)). [para(54(a,1),20(a,1,2))]. given #1646 (W1r,wt=30): 105684 T((x * y) * z,T(T((x * y) * (z * ((x * y) * z)),L(y,x,z)),u)) = (x * y) * z. [back_rewrite(90239),rewrite([104117(9),52858(9),79714(9),52858(8)])]. given #1647 (W1r,wt=24): 109358 K(((((x * (y * (y * z))) * u) \ y) * y) * (z * u),L(x,z,u)) = 1. [back_rewrite(17716),rewrite([104117(11),52858(11),2507(11),52858(9)])]. given #1648 (W1r,wt=23): 117850 x * (x * (y * (z * T(z,x * y)))) = x * (z * ((x * y) * z)). [back_rewrite(117689),rewrite([117706(11)])]. given #1649 (W1r,wt=30): 88621 a(x,T(T(y,z) * (u * (u * w)),u) * x,u \ ((u * w) \ T(T(y \ 1,z),u))) = 1. [back_rewrite(85794),rewrite([88602(5)])]. given #1650 (W1r,wt=24): 54785 L(L(x,y,T(z,u)),z,y * T(z,u)) = L(x,K(z,u),z * (y * z)). [back_rewrite(37146),rewrite([52858(2),52858(5)])]. given #1651 (W2w,wt=31): 5781 K(x * ((y \ z) * ((y \ z) * ((T(y,z) * x) * ((y \ z) * z)))),x * ((y \ z) * z)) = 1. [para(2690(a,1),2051(a,1,1,2,2,2,2,2)),rewrite([2690(14)])]. given #1652 (W2w,wt=31): 5791 (x * (y * (x * (x * (y * (x * z)))))) * u = x * (y * (x * (x * (y * (x * (z * u)))))). [para(23(a,1),405(a,1,2,2,2,1)),rewrite([4578(2),4525(6),189(6),100(2),189(5),101(2),128(4),23(9),128(11),4769(15)]),flip(a)]. given #1653 (W2w,wt=31): 5945 T(T(T(T(T(x,y),z),u),w \ 1),v5) / w = T(T(T(T(T(x,v5),z),y),u),w \ 1) / w. [para(29(a,1),4092(a,1,1,1,1,1))]. given #1654 (W2w,wt=31): 5947 T(T(T(T(T(x,y),z),u),w),v5 \ 1) / v5 = T(T(T(T(T(x,w),y),z),u),v5 \ 1) / v5. [para(29(a,1),4092(a,1,1))]. given #1655 (W2a,wt=35): 745 (x * ((y / x) * ((z * x) * u))) \ (((x \ z) * (x * u)) * (x * y)) = K((x \ z) * (x * u),x * y). [para(104(a,1),328(a,1,1,2,2))]. given #1656 (W2a,wt=33): 930 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),u,w),v7,v8),y,z),v5,v6). [para(34(a,1),448(a,1,1,1,1)),flip(a)]. given #1657 (W2r,wt=32): 107917 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = L(y \ (z \ (y \ x)),u,y * (z * y)). [back_rewrite(57428),rewrite([104117(14),52858(14)])]. given #1658 (W2r,wt=34): 111458 L(x,K(y,T(T(T(z,u),w),v5)),T(z,v6) * T(T(T(T(T(y,w),u),v6 \ z),T(z \ 1,v6)),v5)) = x. [back_rewrite(102434),rewrite([110290(16)])]. given #1659 (W2r,wt=31): 111075 T(T(x \ y,z),u) / T(y / x,u * (y \ x)) = T(x / y,u) * T(T(x \ y,u),z). [back_rewrite(109818),rewrite([109821(14)])]. given #1660 (W2r,wt=32): 84067 ((x / y) * ((y * z) * a(y,y * x,z))) \ (x * z) = a(x * y,y * z,a(y,y * x,z)). [back_rewrite(24476),rewrite([83180(13)])]. given #1661 (W2r,wt=34): 98351 (x * (y * z)) * a(x,x * ((x \ y) * z),a(x,x * y,z)) = ((x * y) * z) * a(x,x * y,z). [para(136(a,1),603(a,2,1)),rewrite([16(2),3954(7),3954(13)])]. given #1662 (W0w,wt=9): 117222 K(K(x,y),x * x) = 1. [para(555(a,1),112983(a,1,2)),rewrite([16343(2),14(5),37242(5),555(5)])]. given #1663 (W0w,wt=9): 117245 K(K(x,y),y * y) = 1. [para(4915(a,1),112983(a,1,2)),rewrite([30455(3),16566(2),14(5),4916(6)])]. given #1664 (W0w,wt=9): 119272 K(x * x,K(y,x)) = 1. [para(1014(a,1),117222(a,1,2)),rewrite([17913(3),10400(4),989(3),24628(5)])]. given #1665 (W0w,wt=9): 119275 K(x * x,K(x,y)) = 1. [para(117222(a,1),4993(a,1,1)),rewrite([13(5)])]. given #1666 (W0w,wt=10): 75804 a(x,y,z \ (x \ z)) = 1. [para(3666(a,1),33119(a,1,1)),rewrite([24189(5)])]. given #1667 (W0w,wt=10): 75861 a(x,y,z * (x / z)) = 1. [para(18(a,1),33124(a,1,1))]. given #1668 (W0w,wt=10): 75883 a(x,y,x * (z * z)) = 1. [para(100(a,1),33124(a,1,1)),rewrite([2508(5)])]. given #1669 (W0w,wt=10): 75898 a(x,y,z * (x * z)) = 1. [para(101(a,1),33124(a,1,3)),rewrite([2508(5)])]. given #1670 (W0w,wt=10): 78629 a(x,y,z / (z * x)) = 1. [para(1091(a,1),36988(a,1,1)),rewrite([24189(5)])]. given #1671 (W0w,wt=10): 79040 a(x,y,z * (y / z)) = 1. [para(15(a,1),37192(a,1,2)),rewrite([19074(2)])]. given #1672 (W0w,wt=10): 82977 a(x,K(y,z),T(z,y)) = 1. [back_rewrite(81295),rewrite([82951(5)])]. given #1673 (W0w,wt=10): 82987 a(x,y,z * (y * z)) = 1. [back_rewrite(79149),rewrite([82951(5)])]. given #1674 (W0w,wt=10): 82989 a(x,y,y * (z * z)) = 1. [back_rewrite(79134),rewrite([82951(5)])]. given #1675 (W0w,wt=10): 83021 a(x,T(y,z),K(z,y)) = 1. [back_rewrite(75773),rewrite([82951(5)])]. given #1676 (W0w,wt=10): 84913 a(x,y * z,z \ y) = 1. [back_rewrite(84052),rewrite([84171(3)])]. given #1677 (W0w,wt=10): 85149 a(x,y * z,z / y) = 1. [back_rewrite(83458),rewrite([84171(3)])]. given #1678 (W0a,wt=17): 628 T(T(x / y,z),T(y \ x,z)) = T(x / y,z). [para(537(a,1),541(a,1,2))]. given #1679 (W0a,wt=13): 629 T(x \ y,T(y / x,z)) = x \ y. [para(541(a,1),537(a,1,1)),rewrite([92(2)]),flip(a)]. given #1680 (W0r,wt=19): 72638 x / (y * (z * (y / z))) = x * (y \ (z / (z * y))). [para(45786(a,1),1014(a,2)),rewrite([4407(5),27201(5)]),flip(a)]. given #1681 (W0r,wt=19): 116727 (T(x,y) * (y * T(y,x))) * z = x * (y * (y * z)). [back_rewrite(115519),rewrite([116243(10)])]. given #1682 (W0r,wt=14): 99082 L(x,y,T(T(z * T(z,u),w),v5)) = x. [para(94(a,1),57670(a,1,3,2)),rewrite([73290(6)])]. given #1683 (W0r,wt=19): 23802 (T(T(x,y),z) / u) * w = (T(T(x,z),y) / u) * w. [para(11449(a,1),136(a,1,2,2,1)),rewrite([7550(7),16(6),16(9)])]. given #1684 (W0r,wt=17): 55976 a(x,y \ ((y / z) * u),L(u \ z,y,u)) = 1. [back_rewrite(10713),rewrite([52858(5)])]. given #1685 (W1w,wt=21): 18893 T(x * ((y / x) * (y / x)),z) = T(y * (x \ y),x \ z). [para(18(a,1),10927(a,1,1,2)),rewrite([4230(2)]),flip(a)]. given #1686 (W1w,wt=21): 18894 T(T(x * (x * y),z),y \ u) = T(T(y * (x * x),u),z). [para(10927(a,1),29(a,1,1)),flip(a)]. given #1687 (W1w,wt=21): 18899 T(x * (y * x),T(y,x) \ z) = T(T(y * (x * x),x),z). [para(90(a,1),10927(a,1,1,2)),rewrite([11037(8)])]. given #1688 (W1w,wt=21): 18900 T(T(x * (y * y),z),y * (y * x)) = T(x * (y * y),z). [para(10927(a,1),159(a,1,1)),rewrite([10927(10)])]. given #1689 (W1w,wt=21): 18916 (x \ (y \ (y \ (x \ z)))) * T(x * (y * y),z) = x \ z. [para(10927(a,1),2690(a,1,2)),rewrite([5162(4)])]. given #1690 (W1w,wt=21): 18918 (x \ y) / T(x * (z * z),y) = x \ (z \ (z \ (x \ y))). [para(10927(a,1),2711(a,1,2)),rewrite([5162(9)])]. given #1691 (W1w,wt=21): 18932 T(x * (y * y),z * (x * (y * (y / z)))) = x * (y * y). [para(5067(a,1),10927(a,2)),rewrite([4613(5),10927(8)])]. given #1692 (W1w,wt=21): 18937 T(x * (x * y),T(y \ z,y)) = T(y * (x * x),T(z,y)). [para(7967(a,1),10927(a,1,2))]. given #1693 (W1a,wt=30): 588 ((x * y) * z) \ ((x * (y * z)) * (a(x,y,z) * u)) = L(u,a(x,y,z),x * (y * z)). [para(54(a,1),21(a,1,1))]. given #1694 (W1a,wt=30): 598 (x * ((y * z) * u)) * a(x,z,(z \ y) * (z * u)) = z * ((z \ x) * ((y * z) * u)). [para(104(a,1),54(a,1,1,2)),rewrite([190(13)])]. given #1695 (W1r,wt=30): 116435 a(x * (x * (y * ((z * x) * (y * x)))),(y * ((z * x) * (y * x))) * u,u \ 1) = 1. [back_rewrite(92877),rewrite([115491(3),128(4),115491(9),128(10)])]. given #1696 (W1r,wt=22): 90323 a((x \ y) * y,z * (y \ (y \ x)),T(z,y \ (y \ x))) = 1. [para(15737(a,1),18742(a,1,3)),rewrite([84171(9)])]. given #1697 (W1r,wt=30): 113238 K((L(x \ 1,y,z) * u) * L(y * ((y \ z) * x),u,L(x \ 1,y,z)),z * u) = 1. [back_rewrite(108208),rewrite([112951(7)])]. given #1698 (W1r,wt=27): 35057 K(x * T(T(T(y,z),u),x \ (x \ 1)),x * T(T(T(y,x \ 1),z),u)) = 1. [back_rewrite(24957),rewrite([34869(7)])]. given #1699 (W1r,wt=25): 71394 K(K(x,T((x \ y) * (z * z),y)),(x \ y) * (z * (z * T(x,y)))) = 1. [para(67347(a,1),17884(a,1,2)),rewrite([62476(11)]),flip(a)]. given #1700 (W2w,wt=31): 5949 T(T(T(T(T(x,y),z),u),w \ 1),v5) / w = T(T(T(T(T(x,v5),y),z),w \ 1),u) / w. [para(29(a,1),4092(a,2,1))]. given #1701 (W2w,wt=31): 5959 T(T(T(T(T(x,y),z),u),w \ 1),T(x,v5)) / w = T(T(T(T(x,y),z),u),w \ 1) / w. [para(541(a,1),4092(a,2,1,1,1,1,1))]. given #1702 (W2w,wt=31): 5977 T(T(T(T(T(x,y),z),u),w \ 1),v5) / w = T(T(T(T(T(x,v5),z),u),y),w \ 1) / w. [para(94(a,1),4092(a,1,1,1,1))]. given #1703 (W2w,wt=31): 5978 T(T(T(T(T(x,y),z \ 1),u),w),v5) / z = T(T(T(T(T(x,v5),y),u),w),z \ 1) / z. [para(94(a,1),4092(a,1,1,1))]. given #1704 (W2a,wt=33): 931 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),y,z),v5,v6),u,w),v9,v10). [para(448(a,2),97(a,2)),flip(a)]. given #1705 (W2a,wt=33): 932 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),u,w),v9,v10),y,z),v5,v6). [para(97(a,1),448(a,1,1,1))]. given #1706 (W2r,wt=33): 104817 (((x * y) * (y * z)) * T(u,z)) / (y * (y * (u * z))) = L(L(x,y,z),y * (y * z),T(u,z)). [back_rewrite(102334),rewrite([104117(11),53163(11),104117(14)])]. given #1707 (W2r,wt=32): 74628 a((x \ y) * (z * (z * (u * (z \ (z \ x))))),(x * T(u,z \ (z \ x))) \ (x \ y),w) = 1. [para(33494(a,2),24484(a,1,1))]. given #1708 (W2r,wt=31): 72489 T(T(x * (y * (x * (y * z))),u),x * (y * (x * y))) = T(z * (x * (y * (x * y))),u). [para(38903(a,1),16122(a,1,1,1,2,1)),rewrite([13(5),24558(4),72465(9),72465(16),1607(16),72465(13)])]. given #1709 (W2r,wt=33): 121839 (x \ (x \ y)) * (T(x * x,y) * ((z * (x \ (x \ y))) * u)) = y * ((z * (x \ (x \ y))) * u). [para(51052(a,1),598(a,1,2)),rewrite([14(7),4408(10),4408(9),99656(10),46094(10)]),flip(a)]. given #1710 (W2r,wt=33): 119119 K(T(x / y,z * (x \ y)) * (T(y / x,z) * T(T(y \ x,z),u)),T(T(y \ x,u),z)) = 1. [para(111075(a,1),4916(a,1,1,2))]. given #1711 (W0w,wt=10): 85161 a(x,y * z,y \ z) = 1. [back_rewrite(83440),rewrite([84171(3)])]. given #1712 (W0w,wt=10): 85773 a(x,y \ z,K(y,z)) = 1. [back_rewrite(75654),rewrite([84171(3)])]. given #1713 (W0w,wt=10): 85776 a(x,y * z,K(y,z)) = 1. [back_rewrite(75591),rewrite([84171(3)])]. given #1714 (W0w,wt=10): 85777 a(x,y * z,K(z,y)) = 1. [back_rewrite(75588),rewrite([84171(3)])]. given #1715 (W0w,wt=10): 85778 a(x,y \ z,K(z,y)) = 1. [back_rewrite(75587),rewrite([84171(3)])]. given #1716 (W0w,wt=10): 86568 a(x * y,x \ y,z) = 1. [back_rewrite(51037),rewrite([84171(3)])]. given #1717 (W0w,wt=10): 86615 a(x,T(x \ 1,y),z) = 1. [back_rewrite(48081),rewrite([85298(6),84171(8),4582(8),84171(7),62200(7)])]. given #1718 (W0w,wt=10): 87997 a(x,y,z \ (z \ y)) = 1. [back_rewrite(66538),rewrite([85298(7),82939(5),85230(5),87185(4)])]. given #1719 (W0w,wt=10): 88126 a(x,y,z / (z * y)) = 1. [back_rewrite(79045),rewrite([86999(5),84171(3)])]. given #1720 (W0w,wt=10): 88146 a(x,y,z \ (y \ z)) = 1. [back_rewrite(42583),rewrite([86999(5),84171(3)])]. given #1721 (W0w,wt=10): 89354 a(x,K(y,z),z \ y) = 1. [para(16564(a,1),82978(a,1,2))]. given #1722 (W0w,wt=10): 89355 a(x,K(y,z),z * y) = 1. [para(16568(a,1),82978(a,1,2))]. given #1723 (W0w,wt=10): 89357 a(x,K(y,z),y / z) = 1. [para(17822(a,1),82978(a,1,2))]. given #1724 (W0w,wt=10): 89358 a(x,K(y,z),z \ 1) = 1. [para(17913(a,1),82978(a,1,2))]. given #1725 (W0w,wt=10): 89359 a(x,K(y,z),y * z) = 1. [para(18043(a,1),82978(a,1,2))]. given #1726 (W0w,wt=10): 89462 a(x,K(y,z),y \ z) = 1. [para(16710(a,1),89356(a,1,2))]. given #1727 (W0a,wt=14): 634 L(x \ (y \ z),x,y) = (y * x) \ z. [para(16(a,1),74(a,2,2))]. given #1728 (W0a,wt=16): 659 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(90(a,1),74(a,2,2))]. given #1729 (W0r,wt=10): 89463 a(x,K(y,z),y \ 1) = 1. [para(17781(a,1),89356(a,1,2))]. given #1730 (W0r,wt=19): 115966 K(x * (y * z),K(x * (y * (z * (u * u))),u)) = 1. [back_rewrite(115302),rewrite([115458(4),37242(9),37429(8),89(7)])]. given #1731 (W0r,wt=17): 96688 K(K(x,T(y * z,u)),K(z * y,T(x,u))) = 1. [back_rewrite(59969),rewrite([96031(7),37242(6),96031(7),37242(6)])]. given #1732 (W0r,wt=18): 59438 L(x,y,z) \ (z \ (y \ 1)) = (z * x) \ (y \ 1). [para(52858(a,1),6591(a,1,1))]. given #1733 (W0r,wt=14): 120299 a(x,y,x * (z * (z * (u * u)))) = 1. [para(116727(a,1),75883(a,1,3)),rewrite([120045(4),84171(7),87253(7),84171(5)])]. given #1734 (W1w,wt=21): 18955 T(x * (y * y),(x * (y * (y * z))) \ z) = x * (y * y). [para(14577(a,1),10927(a,2)),rewrite([2040(5),10927(8)])]. given #1735 (W1w,wt=21): 18965 (x / y) * ((x / y) / T(x,y \ (x / y))) = y \ (x / y). [para(18(a,1),11221(a,1,2,2,1))]. given #1736 (W1w,wt=21): 18975 (x * y) * ((x * y) / T(x * (y * y),T(x,y))) = T(x,y). [para(23(a,1),11221(a,1,2,2,2)),rewrite([4578(4),23(10)])]. given #1737 (W1w,wt=21): 19002 T(x \ y,y) * (T(x,y) \ z) = T(x,y) \ ((x \ y) * z). [para(11221(a,1),189(a,2,2,1)),rewrite([18962(4),4505(3),18962(6),6968(5),18962(9),6968(10)])]. given #1738 (W1w,wt=21): 19004 (x / y) * ((x / y) / T(x * (y \ x),y \ 1)) = y \ 1. [para(1829(a,1),11221(a,1,2,2,2)),rewrite([4230(4),1829(11)])]. given #1739 (W1w,wt=21): 19023 L(x \ (y \ x),x,z * (x \ y)) = L(x \ (y \ x),x,z). [para(11221(a,1),3199(a,1,3,2)),rewrite([18962(4),4155(4),18962(9)])]. given #1740 (W1w,wt=21): 19058 T(x,y) * (T(x,y) / T(x * T(x,y),K(x,y))) = K(x,y). [para(16343(a,1),11221(a,1,2,2,2)),rewrite([547(4),16343(10)])]. given #1741 (W1w,wt=21): 19060 T(x * (y \ x),T(y,x) * z) = T(T((y \ x) * x,x),z). [para(11221(a,1),10927(a,1,1,2)),rewrite([18962(6),4408(5),4408(4),4505(4),18962(9),18809(9)])]. given #1742 (W1a,wt=22): 646 L(x \ ((y \ z) * (y * u)),x,y) = (y * x) \ ((z * y) * u). [para(104(a,1),74(a,2,2))]. given #1743 (W1a,wt=27): 661 L(x \ a(y,z,u),x,y * (z * u)) = ((y * (z * u)) * x) \ ((y * z) * u). [para(54(a,1),74(a,2,2))]. given #1744 (W1r,wt=27): 91370 (x \ y) * (((y \ x) * z) * (u * (z * (x \ y)))) = z * ((u * z) * (x \ y)). [back_rewrite(22214),rewrite([90726(14)])]. given #1745 (W1r,wt=27): 118336 a((x * y) * z,T((x * (y * z)) \ (a(x,y,z) \ 1),x * (y * z)),u) = 1. [para(587(a,1),51052(a,1,2,2)),rewrite([113933(11),22940(10,R),7967(11)])]. given #1746 (W1r,wt=26): 106689 L(x * (y \ x),z \ (z \ x),T(z * (z * (x / y)),x)) = x * (y \ x). [back_rewrite(74013),rewrite([104117(9),52858(9)])]. given #1747 (W1r,wt=27): 61432 (x \ (x \ y)) * ((z \ y) * T(z * (x * x),y * y)) = y * T(y,z \ y). [para(27188(a,1),2690(a,1,2)),rewrite([19474(7),4408(5),18677(5),6073(5),38279(13),34336(11),7888(8),2040(7),11083(7),30703(7)])]. given #1748 (W1r,wt=29): 29857 K(x * (((y * x) \ z) * ((y * x) * u)),(x * y) / (x * ((z * (y * x)) * u))) = 1. [para(104(a,1),14557(a,1,2,2,2))]. given #1749 (W2w,wt=31): 5981 T(T(T(T(T(x,y),z),u),w \ 1),v5) / w = T(T(T(T(T(x,v5),u),y),z),w \ 1) / w. [para(94(a,1),4092(a,2,1,1))]. given #1750 (W2w,wt=31): 5982 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,z),w),v5),u \ 1),y) / u. [para(94(a,1),4092(a,2,1)),flip(a)]. given #1751 (W2w,wt=31): 5984 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,v5),y),w),z),u \ 1) / u. [para(94(a,2),4092(a,1,1,1))]. given #1752 (W2w,wt=31): 5986 T(T(T(T(T(x,y),z),u),w \ 1),v5) / w = T(T(T(T(T(x,v5),y),u),w \ 1),z) / w. [para(94(a,2),4092(a,2,1))]. given #1753 (W2a,wt=33): 933 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),v7,v8),y,z),v5,v6),u,w). [para(97(a,1),448(a,2,1,1))]. given #1754 (W2a,wt=33): 934 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),v5,v6),y,z),v9,v10),u,w). [para(97(a,1),448(a,2,1))]. given #1755 (W2r,wt=31): 53343 T(x,y) * (y * (y * (z * (y * (x * ((z * (y * x)) \ T(y \ (y \ (x \ 1)),y))))))) = 1. [back_rewrite(27839),rewrite([52619(6),7967(7),7967(8)])]. given #1756 (W2r,wt=35): 115933 T(x \ y,z * (y * (y * (x \ (x \ (x \ y)))))) = T(x \ y,T(z,y * (y * (x \ (x \ (x \ y)))))). [back_rewrite(6828),rewrite([115377(6),95305(5),115377(14),95305(13)])]. given #1757 (W2r,wt=33): 118849 K(x,(T(T(T(y,z),u),x \ (x \ w)) / x) / T(T(T(T(T(y,z),x \ 1),u),w),x \ 1)) = 1. [para(5945(a,1),74070(a,1,2,1)),rewrite([11038(10)])]. given #1758 (W2r,wt=34): 106331 L(x \ y,z,(u / x) * (y * x)) \ ((((x \ y) * u) * T(y,x)) * z) = ((u / x) * (y * x)) * z. [back_rewrite(80928),rewrite([104117(5),52858(5)])]. given #1759 (W2r,wt=31): 89570 T(x,y) \ (T(x,z) * ((u * T(x,y)) * w)) = T(x,z) * ((T(x,y) \ u) * (T(x,y) * w)). [para(556(a,1),13641(a,1,1)),flip(a)]. given #1760 (W0w,wt=10): 89464 a(x,K(y,z),z / y) = 1. [para(17914(a,1),89356(a,1,2))]. given #1761 (W0w,wt=10): 90048 a(x,y * z,y / z) = 1. [para(100(a,1),87780(a,1,2)),rewrite([62296(5),82951(5)])]. given #1762 (W0w,wt=10): 90871 L(x,y,z * (z / x)) = x. [back_rewrite(57671),rewrite([90470(13),82892(12),15(10),15(9),22250(9),1829(7),4407(7),10229(7),1014(7),23697(7),4505(6),92(5),16(5)])]. given #1763 (W0w,wt=10): 90964 L(K(x,y),z,x) = K(x,y). [back_rewrite(55720),rewrite([90470(4),80819(3),15(3)]),flip(a)]. given #1764 (W0w,wt=10): 92371 a(x,x * K(y,z),y) = 1. [para(89189(a,1),16118(a,1,2,1)),rewrite([16716(6),24373(6),89189(5),12309(5)])]. given #1765 (W0w,wt=10): 92473 a(x,K(y,z),x \ y) = 1. [para(89189(a,1),16121(a,1,1,1)),rewrite([16716(2),84679(6),89189(6),12303(5)])]. given #1766 (W0w,wt=10): 94381 L(K(x,y),y,z) = K(x,y). [para(17913(a,1),38710(a,1,1)),rewrite([53002(4),17913(5)])]. given #1767 (W0w,wt=10): 94436 K(L(T(x,y),z,u),x) = 1. [para(39244(a,1),16687(a,1,2)),rewrite([47(1)]),flip(a)]. given #1768 (W0w,wt=10): 95020 L(x,y,z * (y / z)) = x. [para(15(a,1),50351(a,1,2)),rewrite([19074(2)])]. given #1769 (W0w,wt=10): 96000 a(x,y,y * K(x,z)) = 1. [back_rewrite(84682),rewrite([95811(5),46(3)]),flip(a)]. given #1770 (W0w,wt=10): 96001 a(x,x * y,K(y,z)) = 1. [back_rewrite(24371),rewrite([95811(4),46(3)]),flip(a)]. given #1771 (W0w,wt=10): 99079 L(x,y,T(z * z,u)) = x. [para(159(a,1),57670(a,1,3,2)),rewrite([46094(3)])]. given #1772 (W0w,wt=10): 99259 L(x \ 1,y,x) = x \ 1. [para(3691(a,1),58702(a,2)),rewrite([3691(2),52858(4),16256(4)])]. given #1773 (W0w,wt=10): 99959 a(x * x,y * z,u) = 1. [back_rewrite(83405),rewrite([99399(6),88125(7)])]. given #1774 (W0w,wt=10): 107615 L(x,y,z * (x * z)) = x. [back_rewrite(62053),rewrite([104117(3),52858(3)])]. given #1775 (W0w,wt=10): 108769 L(K(x,y),x,z) = K(x,y). [back_rewrite(38710),rewrite([104117(2)])]. given #1776 (W0a,wt=17): 707 K(L(T(x,y),z,u),L(T(T(x,w),y),z,u)) = 1. [para(30(a,1),563(a,1,1)),rewrite([30(4),30(5)])]. given #1777 (W0a,wt=13): 958 (T(x,y) * z) / T(T(x,z),y) = z. [para(29(a,1),165(a,1,2))]. given #1778 (W0r,wt=20): 72899 a(x,x * ((y * x) * z),((x \ y) * (x * z)) / x) = 1. [para(13466(a,1),8111(a,1))]. given #1779 (W0r,wt=16): 123621 L(x,y \ T(z,u),u * ((y * z) * u)) = x. [para(659(a,1),105379(a,1,3)),rewrite([105587(6),115491(5)])]. given #1780 (W0r,wt=17): 96951 K(x \ y,K(K(z,x) * y,x \ K(x,z))) = 1. [back_rewrite(38201),rewrite([96031(7)])]. given #1781 (W0r,wt=19): 118038 (x \ y) * (x * ((x \ z) * y)) = ((x \ y) * z) * y. [para(169(a,1),18843(a,2,2)),rewrite([114936(4),115458(4),7616(4),99651(3)]),flip(a)]. given #1782 (W0r,wt=13): 27652 T(x \ 1,y \ 1) = y / (y * x). [para(5674(a,1),5560(a,1,2,1)),rewrite([27573(8),4408(3),45(2),27573(9),6120(4),100(5),16(4),1014(3),989(3),10229(4),1014(4),24645(2),27573(10),27573(12),16(7),989(6)]),flip(a)]. given #1783 (W1w,wt=21): 19110 T(x * (y * (x / y)),y / (y * x)) = x * (y * (x / y)). [back_rewrite(14206),rewrite([19074(2),19074(8)])]. given #1784 (W1w,wt=21): 19307 T(x \ (x \ (y \ x)),x) * (x * y) = K(x * (x * x),y). [back_rewrite(8079),rewrite([19285(11)])]. given #1785 (W1w,wt=21): 19355 T(x,y) * ((y \ (y \ x)) * ((x * (y \ x)) \ z)) = y \ z. [para(12372(a,1),4678(a,1,2,2,2,2,1,1)),rewrite([1014(10),7616(8),3143(10),3143(10),9490(8),7616(3),3143(11)])]. given #1786 (W1w,wt=21): 19479 x / (T(y,z) * ((y \ u) * (T(T(y,u),z) \ x))) = u \ y. [para(7769(a,1),4713(a,1,2,1,1)),rewrite([19474(9),4408(8),4408(9),7715(10)])]. given #1787 (W1w,wt=21): 19536 x / (T(T(y,z),u) * ((z \ y) * (T(y,u) \ x))) = y \ z. [back_rewrite(19451),rewrite([19474(9),4408(8),4408(9),7715(10)])]. given #1788 (W1w,wt=21): 19541 x / (T(T(T(y,z),u),w) * (z \ (T(T(y,w),u) \ x))) = z. [back_rewrite(19446),rewrite([19474(8),16(9)])]. given #1789 (W1w,wt=21): 19568 (x * (y * (x * x))) \ (z * x) = T(x \ (y \ (x \ z)),x). [back_rewrite(17413),rewrite([19474(9),4505(10)])]. given #1790 (W1w,wt=21): 19778 T(x * (x * K(y,z)),T(z,y)) = T(K(y,z) * (x * x),z). [para(541(a,1),10900(a,1,2)),rewrite([16711(2),16711(6)]),flip(a)]. given #1791 (W1a,wt=23): 737 (x * ((y / x) * z)) \ ((x \ z) * (x * y)) = K(x \ z,x * y). [para(16(a,1),328(a,1,1,2,2))]. given #1792 (W1a,wt=27): 819 (T(x,y) * (y * (z * y))) \ (y * (z * (x * y))) = K(y * (z * y),T(x,y)). [para(90(a,1),115(a,1,2,2,2))]. given #1793 (W1r,wt=26): 127018 L(x,y,z * (u * (w * (u * (z * (y / (z * (u * (w * (u * z)))))))))) = x. [para(130(a,1),95020(a,1,3))]. given #1794 (W1r,wt=30): 121922 K(L(x * (y * ((y \ z) * u)),x,L(u \ 1,y,z)),z * (L(u \ 1,y,z) \ x)) = 1. [para(16(a,1),113238(a,1,1,1)),rewrite([52858(11),105587(11),53163(11),52858(7),56040(8)])]. given #1795 (W1r,wt=25): 100398 K(x * T(y,x * (z \ x)),T((y * x) / z,x)) = K(z,T(y * x,x)). [back_rewrite(34419),rewrite([100314(7),100314(11),41832(12)])]. given #1796 (W1r,wt=29): 43913 K(T(T(x * (y * (x * z)),u),w) / z,z / T(T(z * (x * (y * x)),u),w)) = 1. [para(128(a,1),31324(a,1,1,1,1,1))]. given #1797 (W1r,wt=24): 104492 K(((x * y) \ (x / z)) * (u \ (u \ y)),L(u * (u * z),x,y)) = 1. [back_rewrite(103945),rewrite([104117(9),52858(9)])]. given #1798 (W2w,wt=31): 5988 T(T(T(T(T(x * y,z),u),w),v5),y \ 1) / y = T(T(T(T(y * x,u),w),v5),z) / y. [para(3352(a,1),4092(a,1,1,1)),rewrite([4408(3),45(2),4155(9),45(8)]),flip(a)]. given #1799 (W2w,wt=31): 6175 x * (x * (x * (x * (y * ((y \ ((x \ (x \ y)) * z)) * u))))) = x * (x * (y * (z * u))). [back_rewrite(5191),rewrite([6073(3)])]. given #1800 (W2w,wt=31): 6180 (x \ y) * (((z \ (z \ y)) * ((z / y) * x)) * (z / y)) = K(y * ((z / y) * x),z / y). [back_rewrite(5179),rewrite([6073(8),6073(6)])]. given #1801 (W2w,wt=31): 6217 T(T(T(T(x,y \ 1),z),u) / y,T(T(x,z),u) / y) = T(T(T(x,y \ 1),z),u) / y. [back_rewrite(3868),rewrite([6095(12)])]. given #1802 (W2a,wt=33): 935 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),v7,v8),u,w),y,z),v5,v6). [para(97(a,2),448(a,1,1,1)),flip(a)]. given #1803 (W2a,wt=33): 937 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),v9,v10),v5,v6),y,z),u,w). [para(97(a,2),448(a,2,1))]. given #1804 (W2r,wt=31): 25890 x * (y * (T(T(T(z,u),w) / v5,x) * v6)) = x * (y * (T(T(T(z,w),u) / v5,x) * v6)). [para(15(a,1),17251(a,1,2,1)),rewrite([15(9)])]. given #1805 (W2r,wt=33): 100318 ((x \ y) * (z * (z * T(u,x \ y)))) * T(x,y) = (x \ y) * (z * (z * (T(x,y) * T(u,y)))). [back_rewrite(22241),rewrite([99656(12)])]. given #1806 (W2r,wt=35): 113004 (x * (y * ((x \ K(x * ((x \ y) * z),u)) * y))) * z = x * ((y / x) * T(x * ((x \ y) * z),u)). [back_rewrite(102725),rewrite([112886(8)])]. given #1807 (W2r,wt=35): 40504 K(x \ (y \ 1),y * ((x / y) * z)) * (y \ z) = (y \ z) * K(x \ (y \ 1),y * ((x / y) * z)). [para(7251(a,1),7616(a,1,1)),rewrite([5005(9),6144(18)]),flip(a)]. given #1808 (W2r,wt=32): 105519 L((x \ y) * ((x \ y) * (z / u)),u,T(y \ x,z)) = ((x \ y) * z) / (u * T(y \ x,z)). [back_rewrite(93889),rewrite([104117(8)])]. given #1809 (W0w,wt=10): 109746 L(x * x,y,z) = x * x. [back_rewrite(1916),rewrite([104117(2)])]. given #1810 (W0w,wt=10): 110426 L(x,y,T(y * x,z)) = x. [back_rewrite(20956),rewrite([105864(6)])]. given #1811 (W0w,wt=10): 111060 a(x,x * y,z * z) = 1. [back_rewrite(82938),rewrite([109746(5),3436(5),46(4),4505(6),87(5)])]. given #1812 (W0w,wt=8): 130577 a(x,y,z * z) = 1. [para(16(a,1),111060(a,1,2))]. given #1813 (W0w,wt=10): 111927 a(x,y,y * K(z,x)) = 1. [back_rewrite(84408),rewrite([110378(6),29084(4),25131(5)]),flip(a)]. given #1814 (W0w,wt=10): 111937 a(x,y,x \ T(y,z)) = 1. [back_rewrite(95886),rewrite([110392(4),96004(4),110392(4)]),flip(a)]. given #1815 (W0w,wt=10): 112217 L(x,y,z * (y \ z)) = x. [back_rewrite(57444),rewrite([111116(4)])]. given #1816 (W0w,wt=10): 112438 a(x \ 1,y * x,y) = 1. [back_rewrite(61870),rewrite([112164(5)])]. given #1817 (W0w,wt=10): 113665 a(x,K(y,z),x * y) = 1. [back_rewrite(113375),rewrite([113434(3),84171(3)])]. given #1818 (W0w,wt=10): 113887 a(x,T(y,z),x * y) = 1. [back_rewrite(92429),rewrite([113661(3)])]. given #1819 (W0w,wt=10): 114256 a(x,T(x * x,y),z) = 1. [para(159(a,1),72910(a,1,2,2)),rewrite([46094(3)])]. given #1820 (W0w,wt=10): 114371 L(x,x * y,T(y,z)) = x. [para(1091(a,1),75784(a,1,3,1)),rewrite([106383(5)])]. given #1821 (W0w,wt=10): 116321 a(x,y \ (y \ z),z) = 1. [back_rewrite(63032),rewrite([115485(4)])]. given #1822 (W0w,wt=10): 116330 a(x,y,x * T(x,z)) = 1. [back_rewrite(34028),rewrite([115485(6)])]. given #1823 (W0w,wt=10): 116872 T(x,a(x,y,z * x)) = x. [back_rewrite(28511),rewrite([116274(2)])]. given #1824 (W0w,wt=8): 131120 T(x,a(x,y,z)) = x. [para(18(a,1),116872(a,1,2,3))]. given #1825 (W0a,wt=15): 959 (L(x,y,z) * u) / L(T(x,u),y,z) = u. [para(30(a,1),165(a,1,2))]. given #1826 (W0a,wt=13): 1018 T(T(x \ 1,y),x) = T(x \ 1,y). [para(989(a,1),537(a,1,1,1))]. given #1827 (W0r,wt=12): 84325 a(x,K(y,x) * z,x \ z) = 1. [back_rewrite(84026),rewrite([84171(4)])]. given #1828 (W0r,wt=15): 104454 K(T(x,y) * (y / x),T(y,x \ 1)) = 1. [back_rewrite(78726),rewrite([103878(4)])]. given #1829 (W0r,wt=18): 127499 L(x,K(y,z) * T(T(y,z),u),u * (y * u)) = x. [para(16875(a,1),123621(a,1,3,2,1)),rewrite([6144(4)])]. given #1830 (W0r,wt=17): 71677 K(x,T(y,K(x,K(y * x,x \ y)))) = K(x,y). [back_rewrite(69452),rewrite([71590(9)])]. given #1831 (W0r,wt=18): 83060 a(x \ y,y * (x \ y),T(y * (z * z),x)) = 1. [back_rewrite(66833),rewrite([82951(9)])]. given #1832 (W1w,wt=21): 19807 T(x * (x * T(y,z)),K(z,y)) = T(T(y,z) * (x * x),y). [para(12432(a,1),10900(a,1,2)),rewrite([6144(2),16985(2),6144(6),16985(6)]),flip(a)]. given #1833 (W1w,wt=21): 19846 T(x \ (y \ (y \ 1)),x \ z) = T(y \ (y \ (x \ 1)),z). [para(1829(a,1),19786(a,1,1,1)),rewrite([3143(6),2643(6),1829(8)])]. given #1834 (W1w,wt=21): 19971 T(T(T(T(T(x,y),z),u),w),x) = T(T(T(T(x,y),z),u),w). [para(13055(a,1),7769(a,1)),rewrite([29(6),29(7),19257(7)])]. given #1835 (W1w,wt=21): 20282 T(T(T(T(x,y),z),u),w) \ T(T(T(T(x,w),y),z),u) = 1. [para(45(a,1),10082(a,1,1,2,1,2)),rewrite([88(6),989(6),46(13),88(12),48(12),3143(11)])]. given #1836 (W1w,wt=21): 20300 T(T(T(T(x,y),z),u),w) / T(T(T(T(x,z),u),w),y) = 1. [para(2642(a,1),10082(a,1,2,1)),rewrite([14470(14),88(15),47(18),14(11)])]. given #1837 (W1w,wt=21): 20322 (x / T(T(T(y,z),u),w)) * (T(T(T(y,w),z),u) / x) = 1. [para(12372(a,1),10082(a,1,1,2,1)),rewrite([12372(11)])]. given #1838 (W1w,wt=21): 20528 (x * (y * (z * (z * y)))) / (x * (z * (y * (y * z)))) = 1. [back_rewrite(4939),rewrite([20390(3),20390(7)])]. given #1839 (W1w,wt=21): 20899 K((x * y) * z,a(x,y,z)) = K(x * (y * z),a(x,y,z)). [para(209(a,1),16564(a,1,1)),rewrite([17910(6)]),flip(a)]. given #1840 (W1a,wt=25): 1270 L(T(T(x,y),z) * (z * u),z,w) = L(T(T(x,z),y) * (z * u),z,w). [para(682(a,1),21(a,1,2,2)),rewrite([677(7)])]. given #1841 (W1a,wt=27): 1278 (x * y) * (T(T(z,u),y) * (y * w)) = (x * y) * (T(T(z,y),u) * (y * w)). [para(682(a,1),104(a,1,2,2)),rewrite([686(7)])]. given #1842 (W1r,wt=30): 111646 L(x,K(y,T(T(T(T(z,u),w),v5),v6)),y * T(T(T(T(T(z,y \ 1),u),w),v5),v6)) = x. [back_rewrite(94283),rewrite([110290(14)])]. given #1843 (W1r,wt=24): 109881 L(T(x,y),(y \ z) * (y * u),y * (x * ((z * y) * u))) = T(x,y). [back_rewrite(104718),rewrite([105587(9)])]. given #1844 (W1r,wt=22): 128944 K(x \ (y \ (z \ (y \ x))),L(T(y * (z * y),u),x,u)) = 1. [back_rewrite(110875),rewrite([128846(4)])]. given #1845 (W1r,wt=28): 106941 (x * T(y * z,z)) / (z * (z * (y * (z * z)))) = L(x / (z * (z * z)),z,y). [back_rewrite(70695),rewrite([104117(7),53163(7),55819(6)]),flip(a)]. given #1846 (W1r,wt=29): 84525 L(a(x,x * y,z),u,x * ((x \ y) * z)) * L(a(x,y,x \ z),u,y * z) = 1. [back_rewrite(54493),rewrite([84171(8)])]. given #1847 (W2w,wt=31): 6765 K(K(L(L(x,y,z),u,w),v5 / L(x,y,z)),v5 * (L(x,y,z) \ L(L(x,u,w),y,z))) = 1. [para(1078(a,1),6557(a,1,1,1)),rewrite([1014(6),3143(11)])]. given #1848 (W2w,wt=31): 6774 K(K(L(L(x,y,z),u,w),L(x,y,z) * v5),L(x,y,z) * (v5 * L(L(x,u,w),y,z))) = 1. [para(1689(a,1),6557(a,1,1,1))]. given #1849 (W2w,wt=31): 7217 x * (x * ((x * (y * (x / z))) * (z * (x * x)))) = x * (x * (x * (y * (x * (x * x))))). [para(3715(a,1),389(a,1,1,2,2,2,2,2)),rewrite([1014(3),7194(14),4155(10),4408(9),4408(8),45(7),4578(7),37(8)])]. given #1850 (W2w,wt=31): 7259 T(x,y) * ((x \ y) * (z * (x * ((x \ y) * u)))) = (T(x,y) * ((x \ y) * (z * y))) * u. [para(16(a,1),4559(a,1,1,2,2,2)),rewrite([2642(2),2642(8)]),flip(a)]. given #1851 (W2a,wt=33): 938 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),v9,v10),u,w),y,z),v5,v6). [para(230(a,1),448(a,1,1,1)),flip(a)]. given #1852 (W2a,wt=33): 939 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),u,w),v5,v6),y,z),v9,v10). [para(448(a,1),295(a,1))]. given #1853 (W2r,wt=33): 62777 K(T(x,y * y) * z,T((z * y) * ((x * (z * (y * (y * (z * z))))) \ (y * z)),z * z)) = 1. [back_rewrite(37503),rewrite([62676(4),37242(15),30703(14)])]. given #1854 (W2r,wt=35): 108539 L(x * y,L(L(L(L(z,u,w),x,y),v5,v6),v7,v8),(L(L(L(z,v7,v8),u,w),v5,v6) * x) * y) = x * y. [back_rewrite(43564),rewrite([104117(2),104117(3),104117(4),104117(5),104117(6),104117(7),104117(8)])]. given #1855 (W2r,wt=35): 45733 (T(x * (x * y),T(z,y)) \ u) / T((z * y) * (x \ (x \ T(z,y))),u) = (z * y) \ ((z * y) \ u). [para(5364(a,1),25093(a,1,2,1,2))]. given #1856 (W2r,wt=32): 122871 a(x,K(T(y,z \ (u / z)) \ z,u * (w * (z * (y * (z \ (u / z)))))),u * (w * u)) = 1. [para(18855(a,1),89355(a,1,3))]. given #1857 (W2r,wt=34): 126750 L(x,y,T(T(T(T(T(z,u),w),v5),x \ 1),v6) * (T(T(T(T(T(z,v6),u),w),v5),x \ 1) / x)) = x. [para(4092(a,1),90871(a,1,3,2))]. given #1858 (W0w,wt=8): 131133 T(x,a(y,z,x)) = x. [para(4505(a,1),116872(a,1,2,3)),rewrite([112164(2),84171(1)])]. given #1859 (W0w,wt=8): 131211 K(x,a(x,y,z)) = 1. [hyper(27,a,131120,a)]. given #1860 (W0w,wt=8): 131246 K(a(x,y,z),x) = 1. [para(131120(a,1),16687(a,1,2)),rewrite([47(1)]),flip(a)]. given #1861 (W0w,wt=8): 133561 K(x,a(y,z,x)) = 1. [hyper(27,a,131133,a)]. given #1862 (W0w,wt=8): 133591 K(a(x,y,z),z) = 1. [para(131133(a,1),16687(a,1,2)),rewrite([47(1)]),flip(a)]. given #1863 (W0w,wt=8): 133716 K(a(x,y,z),y) = 1. [para(84171(a,1),131246(a,1,1))]. given #1864 (W0w,wt=10): 117292 K(L(x,y,z),x * x) = 1. [para(28463(a,1),112983(a,1,2)),rewrite([117216(4),14(5),28532(5)])]. given #1865 (W0w,wt=10): 117338 K(x * x,L(x,y,z)) = 1. [para(28697(a,1),112983(a,1,2)),rewrite([117216(6),68499(5),14(5),68499(7),28463(5)])]. given #1866 (W0w,wt=10): 118611 L(x,y * y,T(z,u)) = x. [para(100(a,1),54785(a,1,3)),rewrite([2507(7),50365(5),100(6),2509(8)])]. given #1867 (W0w,wt=10): 118619 L(x,y,T(T(y,z),u)) = x. [para(16985(a,1),54785(a,1,3)),rewrite([37242(2),52858(4),105864(4),37242(6),16985(7),57670(8)])]. given #1868 (W0w,wt=10): 118644 L(x,K(y,z),T(y,u)) = x. [para(547(a,1),54785(a,2,3,2)),rewrite([118636(7),55660(6),2507(5)]),flip(a)]. given #1869 (W0w,wt=10): 119223 a(x,y,K(x * y,z)) = 1. [back_rewrite(16723),rewrite([119203(4),46(5)]),flip(a)]. given #1870 (W0w,wt=10): 119325 a(x,y,x \ K(z,x)) = 1. [para(23(a,1),75804(a,1,3,2)),rewrite([98840(3)])]. given #1871 (W0w,wt=10): 119423 a(x,y,x / (z * z)) = 1. [para(1014(a,1),75883(a,1,3,2)),rewrite([10400(3),989(2),103664(4)])]. given #1872 (W0w,wt=10): 119427 a(x,y,(x \ z) * z) = 1. [para(3143(a,1),75883(a,1,3)),rewrite([22398(4),84171(5),86999(5)])]. given #1873 (W0w,wt=10): 119443 a(x,y,z \ (z \ x)) = 1. [para(15737(a,1),75883(a,1,3)),rewrite([89(7),84171(5),85298(5)])]. given #1874 (W0a,wt=19): 1251 (x * ((y * x) * z)) / T(x * y,x * z) = x * z. [para(104(a,1),961(a,1,1,2)),rewrite([16(5)])]. given #1875 (W0a,wt=17): 1253 (x * (y * (x * z))) / T(x * (y * x),z) = z. [para(90(a,1),961(a,1,2,1,2)),rewrite([520(4)])]. given #1876 (W0r,wt=19): 72135 T(x \ y,z * ((y / x) * ((y / x) / z))) = x \ y. [back_rewrite(42505),rewrite([72009(13)])]. given #1877 (W0r,wt=16): 114636 a(x,T(y / x,z),T(x \ y,z) * x) = 1. [para(625(a,1),51766(a,1,3,1)),rewrite([4209(6),84171(6)])]. given #1878 (W0r,wt=19): 126256 T(x \ y,y * (y * (x \ (x \ (x \ y))))) = x \ y. [para(13(a,1),115933(a,1,2)),rewrite([87(15),88(10)])]. given #1879 (W0r,wt=18): 127455 L(x,y \ T(z \ 1,u),u * ((y / z) * u)) = x. [para(1014(a,1),123621(a,1,3,2,1))]. given #1880 (W0r,wt=15): 98212 L(x,y,T(z,u \ (u \ y))) = L(x,y,z). [back_rewrite(55803),rewrite([98150(7),52858(5)])]. given #1881 (W1w,wt=21): 20902 K(x * ((y / x) * (z * (y / x))),(y / x) * (z * y)) = 1. [para(326(a,1),16564(a,1,1)),rewrite([9377(9)]),flip(a)]. given #1882 (W1w,wt=21): 20911 K((x / y) * (z * x),y * ((x / y) * (z * (x / y)))) = 1. [para(807(a,1),16564(a,1,1)),rewrite([3327(11)]),flip(a)]. given #1883 (W1w,wt=21): 20920 K(x * T(y,z \ (z \ x)),z) = K(y * (z \ (z \ x)),z). [para(4397(a,1),16564(a,1,1)),rewrite([16568(5)]),flip(a)]. given #1884 (W1w,wt=21): 20983 K(x * (x * (y * z)),x * (x * y)) = K(z,x * (x * y)). [para(37(a,1),16568(a,1,1))]. given #1885 (W1w,wt=21): 21064 T(T(T(x,y),z),u) * K(y,T(T(x,z),u)) = T(T(x,z),u). [para(94(a,1),16623(a,1,1))]. given #1886 (W1w,wt=21): 21065 T(T(T(x,y),z),u) * K(z,T(T(x,u),y)) = T(T(x,u),y). [para(94(a,2),16623(a,1,1))]. given #1887 (W1w,wt=21): 21316 T((x / y) * (z * (x / y)),y) = (y \ x) * (y \ (z * x)). [para(18(a,1),122(a,1,2,2,2)),rewrite([6135(4)]),flip(a)]. given #1888 (W1w,wt=21): 21324 T(x,y) \ (y * (z * (x * y))) = T(y * (z * y),T(x,y)). [para(90(a,1),122(a,1,2,2,2))]. given #1889 (W1a,wt=27): 1467 (T(T(x,y / z),u) * y) * (y / z) = (T(T(x,u),y / z) * y) * (y / z). [para(18(a,1),863(a,1,1,2)),rewrite([18(11)]),flip(a)]. given #1890 (W1a,wt=23): 1474 T(T(T(x,y),z) * (z * u),z) = T(T(T(x,z),y) * (z * u),z). [para(863(a,1),23(a,1,2)),rewrite([23(6)]),flip(a)]. given #1891 (W1r,wt=29): 74564 x * (x * ((y * (x \ (x \ z))) / ((z \ u) * (z * T(y,x \ (x \ z)))))) = u \ z. [para(33494(a,1),3691(a,1,2)),rewrite([1839(12),4408(15),14(15)])]. given #1892 (W1r,wt=25): 133938 K(x \ (y * (K(z,u) * ((K(u,z) * T(z,w)) * x))),T(z,w) * y) = 1. [para(118644(a,1),113238(a,1,1,1,1)),rewrite([3143(3),6144(5),118644(12),105587(10),14(9),52858(8),53170(9)])]. given #1893 (W1r,wt=23): 31656 (x * (y * (x * (z \ (x / z))))) * (z * (x \ z)) = x * (y * x). [para(7769(a,1),18855(a,1,2,1)),rewrite([92(2),12418(5),10229(7),4230(7)])]. given #1894 (W1r,wt=21): 87019 a(x \ y,z * (x \ y),x) = a(z,x \ y,T(y,x)) \ 1. [back_rewrite(23629),rewrite([84171(7)])]. given #1895 (W1r,wt=25): 120097 T(x \ y,x) * (y * (T(y,x) * z)) = (x \ y) * (T(y * y,x) * z). [para(7769(a,1),116727(a,1,1,2,2)),rewrite([8019(3),547(4),92058(6),68297(11)])]. given #1896 (W2w,wt=31): 7268 (T(x,y) * ((x \ y) * (z * y))) * (x * u) = T(x,y) * ((x \ y) * (z * ((y * x) * u))). [para(104(a,1),4559(a,2,2,2,2)),rewrite([2642(2),16(4),2642(9)])]. given #1897 (W2w,wt=31): 7272 (x * (T(x,y) * (z * (x * T(x,y))))) * u = x * (T(x,y) * (z * (x * (T(x,y) * u)))). [para(541(a,1),4559(a,1,1,1)),rewrite([541(9)])]. given #1898 (W2w,wt=31): 7279 (T(x,y \ 1) * (y \ (z * (x / y)))) * u = T(x,y \ 1) * (y \ (z * (x * (y \ u)))). [para(1014(a,1),4559(a,1,1,2,2,2)),rewrite([3143(8),3143(16),3143(17)])]. given #1899 (W2w,wt=31): 7411 T(x,y) * ((x \ y) * ((z / y) * ((y * x) * u))) = (T(x,y) * ((x \ y) * z)) * (x * u). [para(104(a,1),7262(a,1,2,2,2)),rewrite([2642(2),16(4),2642(10)])]. given #1900 (W2a,wt=33): 940 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),v5,v6),u,w),y,z),v7,v8). [para(448(a,1),295(a,2)),flip(a)]. given #1901 (W2a,wt=33): 941 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),v7,v8),u,w),v5,v6),y,z). [para(448(a,2),295(a,1))]. given #1902 (W2r,wt=31): 73485 T((x * (y * (y * z))) * u,(z \ (y \ (y \ (x \ 1)))) / u) = (x * (y * (y * z))) * u. [para(13910(a,1),12386(a,1,2,2))]. given #1903 (W2r,wt=35): 135486 T(T(x,T(T(y,z) * (x * (u \ x)),x / u)),w) = T(T(x,w),T(T(T(y,z),x / u) * x,x) / u). [para(1467(a,2),5557(a,2,1,2)),rewrite([33950(8),135466(14)]),flip(a)]. given #1904 (W2r,wt=31): 99459 (x * (y * (y * (z * (x * K(u,w)))))) * (w * u) = x * (y * (y * (z * (x * (u * w))))). [back_rewrite(31995),rewrite([99351(10)])]. given #1905 (W2r,wt=31): 120863 T(T((x \ y) * (z * (x * (z * x))),u),w) = T(T(z * (x * (z * y)),w),(y \ x) * u). [para(169(a,1),18894(a,1,1,1,2)),rewrite([23711(5),115135(4),65408(4),4408(6),189(11),101(10)]),flip(a)]. given #1906 (W2r,wt=33): 17182 x * ((x * y) * T(z,x * (y * (x * (x * y))))) = (x * y) \ (z * (x * (y * (x * (x * y))))). [back_rewrite(3586),rewrite([17109(5),17109(13)])]. given #1907 (W0w,wt=10): 119452 a(x,y,z \ (x / z)) = 1. [para(1014(a,1),75898(a,1,3,2)),rewrite([3143(4)])]. given #1908 (W0w,wt=10): 119457 a(x,y,z * (x \ z)) = 1. [para(3143(a,1),75898(a,1,3,2)),rewrite([84171(5),86999(5)])]. given #1909 (W0w,wt=10): 119460 a(x,y \ z,z * y) = 1. [para(4505(a,1),75898(a,1,3,2)),rewrite([90(3),84171(3)])]. given #1910 (W0w,wt=10): 119511 a(x,y \ z,y / z) = 1. [para(16(a,1),78629(a,1,3,2)),rewrite([84171(3)])]. given #1911 (W0w,wt=10): 119516 a(x,T(y,z),y \ 1) = 1. [para(90(a,1),78629(a,1,3,2)),rewrite([3691(3),84171(4)])]. given #1912 (W0w,wt=10): 119528 a(x,y,x \ K(x,z)) = 1. [para(101(a,1),78629(a,1,3,2)),rewrite([25101(4)])]. given #1913 (W0w,wt=10): 119607 a(x,y,(y \ z) * z) = 1. [para(16(a,1),82987(a,1,3,2))]. given #1914 (W0w,wt=10): 119612 a(x,y,z \ (y / z)) = 1. [para(1014(a,1),82987(a,1,3,2)),rewrite([3143(4)])]. given #1915 (W0w,wt=10): 119615 a(x,y,z * (y \ z)) = 1. [para(3143(a,1),82987(a,1,3,2)),rewrite([86999(5),84171(3)])]. given #1916 (W0w,wt=10): 119707 a(x,y,y / (z * z)) = 1. [para(1014(a,1),82989(a,1,3,2)),rewrite([10400(3),989(2),103664(4)])]. given #1917 (W0w,wt=10): 119728 a(x,T(y,z),K(y,z)) = 1. [para(18412(a,1),83021(a,1,3)),rewrite([28965(2),85241(4)])]. given #1918 (W0w,wt=10): 119818 a(x,y,z * (z / y)) = 1. [para(18(a,1),85149(a,1,2)),rewrite([10215(2)])]. given #1919 (W0w,wt=10): 122541 a(x,y \ z,y * z) = 1. [para(3143(a,1),85161(a,1,2)),rewrite([4408(4),45(3)])]. given #1920 (W0w,wt=10): 122711 a(x \ 1,T(x,y),z) = 1. [para(1091(a,1),86568(a,1,2)),rewrite([101(2),84171(5),85230(5)])]. given #1921 (W0w,wt=10): 122831 a(x,K(y,z),T(y,z)) = 1. [para(23(a,1),89354(a,1,3)),rewrite([18043(2)])]. given #1922 (W0w,wt=10): 123649 a(x,x * K(y,z),z) = 1. [back_rewrite(114695),rewrite([123541(5),113661(3),113887(3)]),flip(a)]. given #1923 (W0a,wt=15): 1431 (x * (y * (x / z))) * z = x * (y * x). [para(997(a,1),119(a,1,2)),rewrite([1014(3),48(6),1015(9)])]. given #1924 (W0a,wt=19): 1466 (T(T(x,y),z) * u) * z = (T(T(x,z),y) * u) * z. [para(16(a,1),863(a,1,1,2)),rewrite([16(8)])]. given #1925 (W0r,wt=11): 29099 T(x,y \ 1) = T(x,y \ x). [back_rewrite(2667),rewrite([28965(5)])]. given #1926 (W0r,wt=14): 86655 a(x,y * (z * (z * (y / x))),u) = 1. [back_rewrite(47659),rewrite([84171(5)])]. given #1927 (W0r,wt=17): 105846 L(x * ((x \ y) * z),y,z) = L(y * z,x,z). [back_rewrite(88479),rewrite([104117(4)])]. given #1928 (W0r,wt=15): 133073 a(x,y * x,z) * a(x,y,x \ z) = 1. [para(1607(a,1),84525(a,1,2)),rewrite([133057(7),1607(5)])]. given #1929 (W0r,wt=14): 77509 a(x,T(y,x \ 1) * (y / x),z) = 1. [para(24204(a,1),15308(a,2)),rewrite([10215(4),10215(6),3228(10),16343(8),17781(7),16716(6),189(7),4230(4),33065(6),39396(8),18(2),72886(4),38163(3),18677(3),25357(3)]),flip(a)]. given #1930 (W1w,wt=21): 21353 T(x * (((x * y) \ z) * x),y) = y \ (x * T(z,x * y)). [para(4505(a,1),122(a,1,2,2)),flip(a)]. given #1931 (W1w,wt=21): 21360 T(x * (y * x),z * (x * (y * (x / z)))) = x * (y * x). [para(5067(a,1),122(a,2)),rewrite([19991(3),19991(7),122(12)])]. given #1932 (W1w,wt=21): 21377 x \ (y * (z * (z * (y * x)))) = T(y * (z * (z * y)),x). [para(100(a,1),122(a,1,2,2)),rewrite([100(7)])]. given #1933 (W1w,wt=21): 21754 (T(x,y) \ z) / T(T(x,z),y) = T(x,y) \ (T(x,y) \ z). [para(5226(a,1),17(a,1,1))]. given #1934 (W1w,wt=21): 21789 T(T(x,y),z) * (y \ T(x,z)) = (y \ T(x,z)) * T(x,z). [para(5226(a,1),3691(a,1,2)),rewrite([4155(5),4408(11),4408(9),14(11)])]. given #1935 (W1w,wt=21): 21829 K((x \ y) * (x * z),y * (y * (((y \ x) * z) / x))) = 1. [para(16(a,1),5290(a,1,2,2,2,2)),rewrite([4408(2),11586(5),16(3)])]. given #1936 (W1w,wt=21): 21850 K(x * (x * ((y * z) / (x * y))),(y \ x) * (y * z)) = 1. [para(5290(a,1),4993(a,1,1)),rewrite([13(11)])]. given #1937 (W1w,wt=21): 21929 K(x * ((y \ x) * (y * z)),x * (((y * z) * x) / y)) = 1. [para(18(a,1),5316(a,1,2,1,2,1)),rewrite([10229(2),4230(2),4247(6),744(4),168(3),10215(8),3032(8)])]. given #1938 (W1a,wt=29): 1477 (L(T(T(x,y),z),u,w) * (z * v5)) * z = (L(T(T(x,z),y),u,w) * (z * v5)) * z. [para(30(a,1),863(a,1,1,1,1)),rewrite([30(3),30(8),30(9)])]. given #1939 (W1a,wt=29): 1514 (x * ((y * x) * z)) / T(x * (y * (x * z)),a(x,y,x * z)) = a(x,y,x * z). [para(15(a,1),732(a,1,2,2,2)),rewrite([189(3),101(5),128(6),15(12)])]. given #1940 (W1r,wt=26): 119425 a(x,y * (z * (u * (z * y))),y * (z * (u * (z * (y * (w * w)))))) = 1. [para(130(a,1),75883(a,1,3)),rewrite([84171(11)])]. given #1941 (W1r,wt=27): 110023 a(x * (y * (y * z)),L(T(u * (y * y),z),x,u * z),(z \ u) / x) = 1. [back_rewrite(98495),rewrite([105587(8)])]. given #1942 (W1r,wt=27): 70246 K(K(x,T(T(T(y \ 1,z),u),w)),T(T(T(x,T(y \ 1,u)),y * z),w)) = 1. [para(13051(a,1),37774(a,1,1,2))]. given #1943 (W1r,wt=28): 125743 L(x * (x * y),(z \ (z \ x)) * y,T(z * (z * x),x * y)) = x * (x * y). [para(17(a,1),106689(a,1,3,1,2,2)),rewrite([23(3),33065(3),90(2),6073(5),23(13),33065(13),90(12)])]. given #1944 (W1r,wt=21): 128680 K(x \ (y * z),u * (u * (x \ (y * (z / (u * u)))))) = 1. [para(19355(a,1),14929(a,1,1,2)),rewrite([38356(3),128552(10),104328(8),104328(7),38356(9),16(7),38356(7)])]. given #1945 (W2w,wt=31): 7416 x * (T(x,y) * ((z / (x * T(x,y))) * (x * (T(x,y) * u)))) = (x * (T(x,y) * z)) * u. [para(541(a,1),7262(a,1,1)),rewrite([541(12)])]. given #1946 (W2w,wt=31): 7447 T(x * ((y / x) * (z * (y / x))),(y / x) * (z * y)) = x * ((y / x) * (z * (y / x))). [para(807(a,1),2642(a,1,2)),rewrite([2918(11)]),flip(a)]. given #1947 (W2w,wt=31): 7448 ((x / y) * (z * x)) / (y * ((x / y) * (z * (x / y)))) = K((x / y) * (z * (x / y)),y). [para(807(a,1),2711(a,2)),rewrite([7447(12)])]. given #1948 (W2w,wt=31): 7451 (x * ((y / x) * (z \ (y / x)))) \ ((y / x) * (z \ y)) = K((y / x) * (z \ (y / x)),x). [para(3143(a,1),807(a,1,1,2,2)),rewrite([3143(9),3143(14)])]. given #1949 (W2a,wt=33): 943 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),v5,v6),y,z),u,w),v7,v8). [para(448(a,1),448(a,2)),flip(a)]. given #1950 (W2a,wt=33): 1554 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),u,w),v5,v6),y,z),v7,v8). [para(97(a,1),231(a,1,1,1)),flip(a)]. given #1951 (W2r,wt=35): 38415 T(T(x * y,z),((x * y) \ u) * (y * ((y \ x) * w))) = T(T(x * y,(u * (x * y)) * (y \ w)),z). [para(169(a,1),5557(a,1,2,2))]. given #1952 (W2r,wt=31): 62625 (x \ y) * T(T(K(x,y) * (z * z),y / x),u) = T(z * (z * K(x,y)),u) * (x \ y). [para(43648(a,2),517(a,1,2,1))]. given #1953 (W2r,wt=34): 133490 a(x,K(y * T(z * (z * y),u / y),u * (w * (z \ (z \ (y \ (u / y)))))),u * (w * u)) = 1. [para(19846(a,1),122871(a,1,2,1,1)),rewrite([60306(7),4408(4),4408(3),45(2),4578(2),62480(5),100(2),35648(12),100(7),5162(10),16(11)])]. given #1954 (W2r,wt=33): 77876 T(x,y \ (T(x \ y,z) / y)) \ (y * (T(y \ x,z) * (y * (x * (y \ K(z,y \ x)))))) = x. [para(16711(a,1),57364(a,1,2,2,2,2,2,2)),rewrite([60306(5),1014(5)])]. given #1955 (W2r,wt=32): 80094 T(T(T(x,y) * T(z,y),u),w * (L(T(x * z,u),y,z) / w)) = T(T(x,y) * T(z,y),u). [para(57033(a,2),9992(a,1,2,2,1,1)),rewrite([72954(3),52858(6),30(7),72954(13)])]. given #1956 (W0w,wt=10): 124389 a(x,T(y \ 1,z),y) = 1. [para(18965(a,1),78629(a,1,3,2)),rewrite([124276(5),4155(7),10229(6),4230(6),23697(7),38342(6),1091(5),16(6),14(5),84171(4)])]. given #1957 (W0w,wt=10): 124523 a(T(x,y),x * y,x) = 1. [para(18975(a,1),24428(a,2,2)),rewrite([124433(6),124121(4),6562(3),35648(7),101(2),99651(5),54309(3),4505(4),14576(3),4505(3),124433(8),123132(5),4278(4),46(5),84171(4)]),flip(a)]. given #1958 (W0w,wt=10): 124592 a(x,y \ K(z,y),y) = 1. [para(18975(a,1),78629(a,1,3,2)),rewrite([124433(6),91628(5),47(3),13(4),84171(3)])]. given #1959 (W0w,wt=10): 126902 a(x,K(x * y,z),y) = 1. [para(15(a,1),92473(a,1,3))]. given #1960 (W0w,wt=10): 126954 a(x,x * T(y,z),y) = 1. [back_rewrite(114705),rewrite([126918(6)])]. given #1961 (W0w,wt=10): 127096 a(x,y * K(z,x),y) = 1. [para(18(a,1),96000(a,1,3)),rewrite([5005(2)])]. given #1962 (W0w,wt=10): 127111 a(x,y,x * K(y,z)) = 1. [para(96000(a,1),84171(a,1)),flip(a)]. given #1963 (W0w,wt=10): 127119 a(x,y,K(x \ y,z)) = 1. [para(16(a,1),96001(a,1,2))]. given #1964 (W0w,wt=10): 127124 a(x,x * y,K(z,y)) = 1. [para(1014(a,1),96001(a,1,2)),rewrite([17913(4),85263(3)])]. given #1965 (W0w,wt=10): 127129 a(x,y * x,K(y,z)) = 1. [para(4505(a,1),96001(a,1,2)),rewrite([84171(4),87186(4)])]. given #1966 (W0w,wt=10): 127197 a(x * x,y \ z,u) = 1. [para(3143(a,1),99959(a,1,2))]. given #1967 (W0w,wt=10): 127199 a(x * x,T(y,z),u) = 1. [para(4505(a,1),99959(a,1,2))]. given #1968 (W0w,wt=10): 127356 a(x,K(y,T(z,u)),z) = 1. [para(958(a,1),89464(a,1,3)),rewrite([37242(5),37242(5),62536(5)])]. given #1969 (W0w,wt=10): 128267 a(x,y,K(z,x * y)) = 1. [back_rewrite(119263),rewrite([128008(8)]),flip(a)]. given #1970 (W0w,wt=10): 130479 L(x,y / x,T(y,z)) = x. [para(18(a,1),110426(a,1,3,1))]. given #1971 (W0w,wt=10): 130507 L(x,x \ y,T(y,z)) = x. [para(4505(a,1),110426(a,1,3,1)),rewrite([107774(4)])]. given #1972 (W0a,wt=19): 1495 T(T(x,y \ 1),z) / y = T(T(x,z),y \ 1) / y. [para(997(a,1),863(a,1,1,2)),rewrite([14(6),1014(7),997(12),14(11),1014(12)]),flip(a)]. given #1973 (W0a,wt=17): 1635 K(L(L(x,y,z),u,w),L(L(x,u,w),y,z)) = 1. [back_rewrite(957),rewrite([1607(7)])]. given #1974 (W0r,wt=16): 113625 L(x,L(x * y,y,z),L(y * x,y,z)) = x. [back_rewrite(113425),rewrite([113434(5),84564(7),65770(5),57044(6),52858(5)])]. given #1975 (W0r,wt=20): 112056 a(x * y,T(z,y * x),T(z * (x * y),K(y,x))) = 1. [back_rewrite(100881),rewrite([110591(7)])]. given #1976 (W0r,wt=18): 5436 (x * ((x \ y) * z)) * a(x,x * y,z) = y * z. [para(2640(a,1),54(a,2,1)),rewrite([5428(7),16(3),5428(10),16(6),3954(5)])]. given #1977 (W0r,wt=18): 131779 a(x,T(y,K(z,K(y * z,z \ y))),K(z,y)) = 1. [para(71677(a,1),75589(a,1,3)),rewrite([84171(7)])]. given #1978 (W0r,wt=19): 120653 T(x * (y \ x),y \ 1) = y * ((x / y) * (x / y)). [para(18893(a,1),88(a,1))]. given #1979 (W1w,wt=21): 21937 K((x \ y) * (x * (y / z)),(y * ((x * y) / z)) / x) = 1. [para(1014(a,1),5316(a,1,1,2,2)),rewrite([1014(8)])]. given #1980 (W1w,wt=21): 21949 K((x * ((y * x) * z)) / y,(y \ x) * (y * (x * z))) = 1. [para(5316(a,1),4993(a,1,1)),rewrite([13(11)])]. given #1981 (W1w,wt=21): 22011 a(x,y,T(T(y \ z,u),w)) = a(x,y,T(T(y \ z,w),u)). [para(537(a,1),5349(a,2,3,1)),rewrite([622(4)])]. given #1982 (W1w,wt=21): 22278 T(T(x * y,y),y \ T(x \ 1,y * y)) = T(x * y,y). [back_rewrite(20263),rewrite([22270(3),22270(11)])]. given #1983 (W1w,wt=21): 22414 T(x * (y / z),T((z / y) / x,x * y)) = x * (y / z). [para(6694(a,1),14102(a,1,2,1)),rewrite([11265(8),4407(6),10229(6),1014(6)])]. given #1984 (W1w,wt=21): 22685 K(x * (x * y),x * (x * (y * z))) = K(x * (x * y),z). [para(37(a,1),16686(a,1,2))]. given #1985 (W1w,wt=21): 22705 K(x,y * T(z,x \ (x \ y))) = K(x,z * (x \ (x \ y))). [para(4404(a,2),16686(a,1,2)),rewrite([16686(10)])]. given #1986 (W1w,wt=21): 22734 T(T(x,y),z) / T(T(T(x,z),u),y) = K(u,T(T(x,y),z)). [para(94(a,2),16687(a,1,2))]. given #1987 (W1a,wt=23): 1569 T(T(T(x,y),z),u) * (z * w) = T(T(T(x,z),y),u) * (z * w). [para(29(a,1),1295(a,2,1,1)),rewrite([1295(12)])]. given #1988 (W1a,wt=27): 1605 x * (x * (T(T(y,z \ 1),u) / z)) = x * (x * (T(T(y,u),z \ 1) / z)). [para(997(a,1),1479(a,1,2,2,1,2)),rewrite([14(6),1014(7),997(14),14(13),1014(14)]),flip(a)]. given #1989 (W1r,wt=28): 105271 K(L(x,y,z) * ((y * z) * u),K((x * y) * z,L(u,y * z,L(x,y,z)))) = 1. [back_rewrite(97040),rewrite([104117(1),104117(8)])]. given #1990 (W1r,wt=29): 100862 T(T(x,T(T(y,z),u)) * T(T(y * y,z),u),x) = x * T(T(y * T(y,x),z),u). [para(3398(a,1),99433(a,1,2)),rewrite([38163(7),73225(6),73225(4),93225(14),47992(13)]),flip(a)]. given #1991 (W1r,wt=24): 31079 L(x \ (T(y,z * z) * u),x,z) = (z * x) \ (T(y,z) * (z * u)). [back_rewrite(10956),rewrite([30703(2)])]. given #1992 (W1r,wt=27): 103867 T((x * ((y / x) * z)) / (x * y),z \ x) = (x * ((y / x) * z)) / (x * y). [back_rewrite(40540),rewrite([103664(7),103664(14)])]. given #1993 (W1r,wt=27): 140568 K((T(x,y) \ z) / (u * T(T(x,z),y)),(y \ (x \ (x \ y))) * (z / u)) = 1. [back_rewrite(94817),rewrite([140353(11)])]. given #1994 (W2w,wt=31): 7512 (((x \ (x \ y)) * z) * (x * (y * z))) * u = ((x \ (x \ y)) * z) * (x * ((y * z) * u)). [para(5452(a,1),130(a,1,1,2,2)),rewrite([7490(13),7490(20),7490(23),7495(16)])]. given #1995 (W2w,wt=31): 7584 K(x * (x * ((y * z) * u)),x * (x * ((y * z) * (u * (x * (x * ((y * z) * u))))))) = 1. [para(7052(a,1),1397(a,1,2,2)),rewrite([189(13),101(8),189(12),4578(8),101(11),100(10),2979(13),101(10),37(9)])]. given #1996 (W2w,wt=31): 7987 (x * (y * (((y * x) \ z) * y))) \ (y * T(z,y * x)) = K(y * (((y * x) \ z) * y),x). [para(4505(a,1),115(a,1,2,2))]. given #1997 (W2w,wt=31): 8075 T(x,y) * (y * (((x * y) \ z) * (x * (y * u)))) = (T(x,y) * (y * T(z,x * y))) * u. [para(4505(a,1),4559(a,1,1,2,2)),flip(a)]. given #1998 (W2a,wt=33): 1555 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,u,w),y,z),v5,v6),v9,v10),v7,v8). [para(97(a,1),231(a,1,1))]. given #1999 (W2a,wt=33): 1557 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),y,z),v5,v6),u,w),v7,v8). [para(231(a,2),295(a,1)),flip(a)]. given #2000 (W2r,wt=33): 108389 T((L(x,y,z) * u) \ L(T(x,u),y,z),u * w) = T((L(x,y,z) * u) \ L(T(x,u),y,z),w). [back_rewrite(48317),rewrite([104117(1),104117(4),104117(8),104117(11)])]. given #2001 (W2r,wt=35): 54617 L(L(L(T(T(x,y),z),u,w),v5,v6),v7,L(T(T(T(x,z),y),v8),v5,v6)) = L(L(T(T(x,y),z),v5,v6),u,w). [back_rewrite(40924),rewrite([52858(9)])]. given #2002 (W2r,wt=33): 136052 K(x \ (T(T(y,T(z,u)),w) * (K(z,v5) * ((K(v5,z) * T(z,u)) * x))),T(y,w) * T(z,u)) = 1. [para(517(a,1),133938(a,1,2))]. given #2003 (W2r,wt=31): 139595 T(a(x,y,x * z),(a(x,y * x,z) \ a(x,y,x * z)) * u) = T(a(x,y,x * z),u). [para(133073(a,1),6973(a,1,1,2)),rewrite([139543(2),4407(5),136169(4),139543(7),115458(10),16(8),139543(5),139543(9)]),flip(a)]. given #2004 (W2r,wt=32): 108146 L(x,y / z,L(z * ((u / z) * w),y,z)) = L(x,y / z,y * ((y \ z) * ((u / z) * w))). [back_rewrite(53594),rewrite([104117(6),104117(13)])]. given #2005 (W0w,wt=10): 130590 a(x,y,z \ (z \ 1)) = 1. [para(1014(a,1),130577(a,1,3)),rewrite([10400(3),989(2)])]. given #2006 (W0w,wt=10): 130601 a(x,y * K(x,z),y) = 1. [para(18(a,1),111927(a,1,3)),rewrite([5005(2)])]. given #2007 (W0w,wt=10): 130616 a(x,y,x * K(z,y)) = 1. [para(111927(a,1),84171(a,1)),flip(a)]. given #2008 (W0w,wt=10): 130653 a(x,y,y * T(x,z)) = 1. [para(111937(a,1),84171(a,1)),rewrite([84069(4)]),flip(a)]. given #2009 (W0w,wt=10): 130766 a(x,K(x \ y,z),y) = 1. [para(16(a,1),113665(a,1,3))]. given #2010 (W0w,wt=10): 130767 a(x / y,K(y,z),x) = 1. [para(18(a,1),113665(a,1,3))]. given #2011 (W0w,wt=10): 130772 a(x,K(y,z),x / z) = 1. [para(1014(a,1),113665(a,1,3)),rewrite([17913(3)])]. given #2012 (W0w,wt=10): 130790 a(x,K(y,z),x * z) = 1. [para(17781(a,1),113665(a,1,2))]. given #2013 (W0w,wt=10): 130835 a(x,T(x \ y,z),y) = 1. [para(16(a,1),113887(a,1,3))]. given #2014 (W0w,wt=10): 130836 a(x / y,T(y,z),x) = 1. [para(18(a,1),113887(a,1,3))]. given #2015 (W0w,wt=10): 130840 a(x,T(y,z),y * x) = 1. [para(90(a,1),113887(a,1,3)),rewrite([87183(4)])]. given #2016 (W0w,wt=10): 130855 a(x,y,x * T(y,z)) = 1. [para(7769(a,1),113887(a,1,2))]. given #2017 (W0w,wt=10): 130919 L(x,y,T(x \ y,z)) = x. [para(16(a,1),114371(a,1,2))]. given #2018 (W0w,wt=10): 130935 L(x,y * x,T(y,z)) = x. [para(90(a,1),114371(a,1,2)),rewrite([107774(4)])]. given #2019 (W0w,wt=10): 130939 L(x,x / y,T(y,z)) = x. [para(1014(a,1),114371(a,1,2)),rewrite([106383(5)])]. given #2020 (W0w,wt=10): 131106 a(x,y,y * T(y,z)) = 1. [para(116330(a,1),84171(a,1)),flip(a)]. given #2021 (W0a,wt=18): 1724 K(a(x,y,z),((x * y) * z) / (x * (y * z))) = 1. [para(19(a,1),554(a,1,1))]. given #2022 (W0a,wt=16): 1726 K(L(x,y,z),(z * (y * x)) / (z * y)) = 1. [para(21(a,1),554(a,1,1))]. given #2023 (W0r,wt=17): 10402 T(T(T(x,y),z),u) / y = y \ T(T(x,z),u). [para(94(a,1),7616(a,1,1))]. given #2024 (W0r,wt=18): 134066 a(x,y,x / (z * (u * (z * (z * (u * z)))))) = 1. [para(128(a,1),119423(a,1,3,2))]. given #2025 (W0r,wt=19): 18092 T(T(T(T(x,y),z),u),K(w,x)) = T(T(T(x,y),z),u). [back_rewrite(13067),rewrite([17924(5)])]. given #2026 (W0r,wt=15): 116794 a(x,y,(y / x) * z) = a(y,z,x * z). [back_rewrite(91409),rewrite([116274(5),84171(5)])]. given #2027 (W0r,wt=20): 125688 a(((x * y) * z) * u,u \ (z \ (y \ (x \ 1))),w) = 1. [para(54(a,1),118336(a,1,1,1)),rewrite([121576(8),84171(10),121635(10),46(9),4407(8),4407(7),4407(6),121576(13),87185(13)])]. given #2028 (W1w,wt=21): 22894 x * (x * (y * K(x * (x * y),z))) = T(x * (x * y),z). [para(16716(a,1),37(a,1)),flip(a)]. given #2029 (W1w,wt=21): 23012 T(x \ T(T(T(x,y),z),u),x) = x \ T(T(T(x,y),z),u). [back_rewrite(17787),rewrite([22984(9)])]. given #2030 (W1w,wt=21): 23046 K(x,T(T(y,z),u)) * T(T(T(y,u),x),z) = T(T(y,z),u). [para(94(a,2),16875(a,1,2))]. given #2031 (W1w,wt=21): 23093 (K(x,y) * (z * y)) / T(y,x) = K(x,y) * (z * K(x,y)). [para(16875(a,1),106(a,1,1,2,2))]. given #2032 (W1w,wt=21): 23142 x * (y * K(y * (x * y),z)) = y \ T(y * (x * y),z). [para(16985(a,1),1359(a,2,2)),rewrite([12307(6)])]. given #2033 (W1w,wt=21): 23161 x * (y \ K(x * (x / y),z)) = x \ T(x * (x / y),z). [para(16985(a,1),3218(a,2,2)),rewrite([12307(6)])]. given #2034 (W1w,wt=21): 23170 x \ (y \ T(y * (x * y),z)) = y * K(y * (x * y),z). [para(16985(a,1),3541(a,1,2,2)),rewrite([12307(11)])]. given #2035 (W1w,wt=21): 23192 (x \ T(x * (x / y),z)) * (K(z,x * (x / y)) * y) = x. [para(16985(a,1),4173(a,1,1,2)),rewrite([12307(10),6144(8)])]. given #2036 (W1a,wt=23): 1643 (x * (y * (y * (x * z)))) * u = x * (y * (y * (x * (z * u)))). [back_rewrite(401),rewrite([1607(6),1607(11)])]. given #2037 (W1a,wt=29): 1814 ((x * (y * z)) / z) / T(x * y,a(x,y * z,z \ 1)) = a(x,y * z,z \ 1). [para(1013(a,1),729(a,1,1,1,2)),rewrite([1014(5),1013(7),1013(13)])]. given #2038 (W1r,wt=27): 128576 K((T(x,y) \ z) * (y \ u),((z * T(x,y)) * (y \ (x \ u))) / T(x,y)) = 1. [para(19355(a,1),2812(a,1,1,2)),rewrite([128552(12)])]. given #2039 (W1r,wt=24): 56811 L(x * L(y / z,y,u),x,w) = L(x * ((y * (z \ u)) / u),x,w). [back_rewrite(31718),rewrite([52953(3)])]. given #2040 (W1r,wt=25): 116725 K(((x * y) \ z) * (x * (u * (u * (x * y)))),z * (x * (u * u))) = 1. [back_rewrite(51991),rewrite([116234(13),6019(14),93680(10)])]. given #2041 (W1r,wt=27): 77084 T(T(T(T(x,y),z),u),w \ (T(T(T(x,u),y),z) \ w)) = T(T(T(x,y),u),z). [para(29(a,1),14601(a,1,2,2,1,1))]. given #2042 (W1r,wt=28): 147748 a(x,T(T(T(T(x,y),z),u),w) \ (x \ T(T(T(T(x \ 1,y),z),u),w)),v5) = 1. [back_rewrite(139961),rewrite([147639(11),989(6)])]. given #2043 (W2w,wt=31): 8104 ((x * ((x \ y) * ((x * z) * T(y,x)))) * z) \ (((y * x) * z) * ((x \ y) * (x * z))) = 1. [back_rewrite(7162),rewrite([8012(8)])]. given #2044 (W2w,wt=31): 8956 T(T(T(T(x / y,z),u),w),y * T(T(T(y \ x,z),w),u)) = T(T(T(y \ x,z),w),u). [para(3352(a,1),3398(a,2)),rewrite([3828(9)])]. given #2045 (W2w,wt=31): 9475 K((x * (y * (y * z))) * T(u,z \ (y \ (y \ (x \ 1)))),(x * (y * (y * z))) * u) = 1. [para(2045(a,1),2836(a,1,2,1)),rewrite([2040(3),100(5),189(7),37(3),189(6),101(3),189(5),4578(3),2040(4),787(8),100(10),1839(12),2771(11,R),4407(8),5162(8),100(13),13(16)])]. given #2046 (W2w,wt=31): 9544 (x \ (y / x)) * ((z * (x * (y \ x))) * ((x \ (y / x)) * u)) = ((x \ (y / x)) * z) * u. [back_rewrite(9533),rewrite([9537(10)])]. given #2047 (W2a,wt=33): 1558 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v5,v6),v7,v8),y,z),u,w),v9,v10). [para(231(a,1),448(a,2))]. given #2048 (W2a,wt=33): 1559 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),v7,v8),v5,v6),u,w),y,z). [para(231(a,2),448(a,1))]. given #2049 (W2r,wt=35): 49848 K(T(T(T(T(T(x,y),z \ 1),u),w),v5) / z,v6) = K(T(T(T(T(T(x,w),y),u),z \ 1),v5) / z,v6). [para(4058(a,2),20921(a,1,1))]. given #2050 (W2r,wt=34): 136609 L(x,y,z * (T(z,u) * (w * (z * (T(z,u) * (x / (z * (T(z,u) * (w * (z * T(z,u))))))))))) = x. [para(7272(a,1),74464(a,1,3))]. given #2051 (W2r,wt=33): 144192 K((x * ((((x * y) \ z) * x) * y)) * (z \ (x * y)),((z \ (x * y)) * x) * T(z,x * y)) = 1. [para(4505(a,1),21949(a,1,2,2)),rewrite([4155(8),4408(11)])]. given #2052 (W2r,wt=33): 121500 T(T(x * x,y),T(K(y,x * x) * z,K(x * x,y))) = T(T(x * x,y),T(z,K(x * x,y))). [para(16985(a,1),18937(a,2,1)),rewrite([119203(4),6144(5)])]. given #2053 (W2r,wt=31): 109910 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8 * (L(x,u,w) / v8)) = L(L(L(x,u,w),y,z),v5,v6). [back_rewrite(104580),rewrite([105587(7)])]. given #2054 (W0w,wt=10): 131234 T(x,a(x,y,z) \ x) = x. [para(131120(a,1),7769(a,1,1))]. -------- Proof 3 -------- "aK3". ============================== PROOF ================================= % Proof 3 at 74.76 (+ 0.34) seconds: "aK3". % Length of proof is 1322. % Level of proof is 64. % Maximum clause weight is 35. % Given clauses 2054. 1 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 2 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 3 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 4 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 5 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 8 a(x,y,K(z,u)) = 1 # label("aK3") # label(non_clause) # label(goal). [goal]. 13 1 * x = x. [assumption]. 14 x * 1 = x. [assumption]. 15 x \ (x * y) = y. [assumption]. 16 x * (x \ y) = y. [assumption]. 17 (x * y) / y = x. [assumption]. 18 (x / y) * y = x. [assumption]. 19 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 20 (x * y) \ (y * x) = K(y,x). [assumption]. 21 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 22 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 23 x \ (y * x) = T(y,x). [assumption]. 24 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(1)]. 25 L(x,y,z) != x | a(z,y,x) = 1. [clausify(2)]. 26 T(x,y) != x | T(y,x) = y. [clausify(3)]. 27 T(x,y) != x | K(x,y) = 1. [clausify(4)]. 28 K(x,y) != 1 | T(x,y) = x. [clausify(5)]. 29 T(T(x,y),z) = T(T(x,z),y). [assumption]. 30 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 31 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 32 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 33 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(32),flip(a)]. 34 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 35 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 36 ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang (M1)"). [assumption]. 37 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 40 a(c9,c10,K(c11,c12)) != 1 # label("aK3") # answer("aK3"). [deny(8)]. 45 1 \ x = x. [para(13(a,1),15(a,1,2))]. 46 x \ x = 1. [para(14(a,1),15(a,1,2))]. 47 x / x = 1. [para(13(a,1),17(a,1,1))]. 48 x / 1 = x. [para(14(a,1),17(a,1,1))]. 49 x / (y \ x) = y. [para(16(a,1),17(a,1,1))]. 50 (x / y) \ x = y. [para(18(a,1),15(a,1,2))]. 51 a(x,1,y) = 1. [para(13(a,1),19(a,1,1,2)),rewrite([14(3),46(3)]),flip(a)]. 54 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(19(a,1),16(a,1,2))]. 55 (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y). [para(16(a,1),19(a,1,1,2))]. 56 (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z). [para(16(a,1),19(a,1,2,1))]. 57 (x * (y * ((x * y) \ z))) \ z = a(x,y,(x * y) \ z). [para(16(a,1),19(a,1,2))]. 58 (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z). [para(18(a,1),19(a,1,1,2))]. 60 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(18(a,1),19(a,1,2,1))]. 63 (x * y) * K(y,x) = y * x. [para(20(a,1),16(a,1,2))]. 64 x \ ((y \ x) * y) = K(y \ x,y). [para(16(a,1),20(a,1,1))]. 65 ((x \ y) * x) \ y = K(x,x \ y). [para(16(a,1),20(a,1,2))]. 66 x \ (y * (x / y)) = K(y,x / y). [para(18(a,1),20(a,1,1))]. 67 (x * (y / x)) \ y = K(y / x,x). [para(18(a,1),20(a,1,2))]. 68 K(x * x,x) = a(x,x,x). [para(20(a,1),19(a,1))]. 70 L(x,1,y) = x. [para(13(a,1),21(a,1,2,2)),rewrite([14(2),15(2)]),flip(a)]. 72 (x * y) * L(z,y,x) = x * (y * z). [para(21(a,1),16(a,1,2))]. 73 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(16(a,1),21(a,1,1))]. 74 L(x \ y,x,z) = (z * x) \ (z * y). [para(16(a,1),21(a,1,2,2)),flip(a)]. 75 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(18(a,1),21(a,1,1))]. 76 L(x,y / x,z) = (z * (y / x)) \ (z * y). [para(18(a,1),21(a,1,2,2)),flip(a)]. 81 R(x,x \ y,z) = (y * z) / ((x \ y) * z). [para(16(a,1),22(a,1,1,1)),flip(a)]. 82 R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z)). [para(16(a,1),22(a,1,1)),flip(a)]. 83 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(16(a,1),22(a,1,2))]. 84 R(x,y,z) * (y * z) = (x * y) * z. [para(22(a,1),18(a,1,1))]. 85 R(x / y,y,z) = (x * z) / (y * z). [para(18(a,1),22(a,1,1,1)),flip(a)]. 87 T(1,x) = 1. [para(13(a,1),23(a,1,2)),rewrite([46(1)]),flip(a)]. 88 T(x,1) = x. [para(14(a,1),23(a,1,2)),rewrite([45(2)]),flip(a)]. 89 T(x,x) = x. [para(23(a,1),15(a,1))]. 90 x * T(y,x) = y * x. [para(23(a,1),16(a,1,2))]. 91 T(x,x \ y) = (x \ y) \ y. [para(16(a,1),23(a,1,2)),flip(a)]. 92 T(x / y,y) = y \ x. [para(18(a,1),23(a,1,2)),flip(a)]. 94 T(T(T(x,y),z),u) = T(T(T(x,u),y),z). [para(29(a,1),29(a,1,1)),flip(a)]. 97 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,v5,v6),y,z),u,w). [para(34(a,1),34(a,1,1)),flip(a)]. 100 (x * x) * y = x * (x * y). [para(13(a,1),36(a,2,2)),rewrite([14(2)])]. 101 (x * y) * x = x * (y * x). [para(36(a,1),14(a,1)),rewrite([14(2)]),flip(a)]. 103 x * (y * (x * ((x * (y * x)) \ z))) = z. [para(36(a,1),16(a,1)),rewrite([101(2)])]. 104 x * ((x \ y) * (x * z)) = (y * x) * z. [para(16(a,1),36(a,1,1,1)),flip(a)]. 106 (x * (y * (x * z))) / z = x * (y * x). [para(36(a,1),17(a,1,1)),rewrite([101(6)])]. 107 (x / y) * (y * ((x / y) * z)) = (x * (x / y)) * z. [para(18(a,1),36(a,1,1,1)),flip(a)]. 110 (x * (y * (z * (y * u)))) \ ((x * (y * (z * y))) * u) = a(x,y * (z * y),u). [para(36(a,1),19(a,1,1,2)),rewrite([101(6),101(11)])]. 112 ((x * (y * x)) * (z * u)) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [para(36(a,1),19(a,1,2,1)),rewrite([101(2),101(11)])]. 113 ((x * y) * (x * z)) \ (x * (y * (x * z))) = a(x * y,x,z). [para(36(a,1),19(a,1,2))]. 114 (x * (y * (x * z))) \ (z * (x * (y * x))) = K(z,x * (y * x)). [para(36(a,1),20(a,1,1)),rewrite([101(5),101(9)])]. 117 (x * (y * (z * y))) \ (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(36(a,1),21(a,1,2,2)),rewrite([101(2),101(10)])]. 118 ((x * (y * x)) * z) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(36(a,1),21(a,1,2)),rewrite([101(2),101(10)])]. 121 ((x * (y * (z * y))) * u) / (y * (z * (y * u))) = R(x,y * (z * y),u). [para(36(a,1),22(a,1,2)),rewrite([101(2),101(10)])]. 125 ((x * (y * x)) * (z * (x * (y * x)))) * u = (x * (y * x)) * (z * (x * (y * (x * u)))). [para(36(a,1),36(a,2,2,2)),rewrite([101(2),101(5),101(6),101(9)])]. 126 (x * ((y * (z * y)) * x)) * u = x * (y * (z * (y * (x * u)))). [para(36(a,1),36(a,2,2)),rewrite([101(2),101(4)])]. 128 (x * (y * x)) * z = x * (y * (x * z)). [back_rewrite(36),rewrite([101(2)])]. 129 (x * (y * (x * (z * (x * (y * x)))))) * u = x * (y * (x * (z * (x * (y * (x * u)))))). [back_rewrite(125),rewrite([128(6),128(14)])]. 130 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [back_rewrite(126),rewrite([128(3)])]. 132 (x * (y * (x * z))) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [back_rewrite(118),rewrite([128(3)])]. 133 (x * (y * (x * (z * u)))) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [back_rewrite(112),rewrite([128(4)])]. 134 (x * (x * y)) \ (x * (x * (y * z))) = z. [para(37(a,1),15(a,1,2))]. 136 x * (x * ((x \ y) * z)) = (x * y) * z. [para(16(a,1),37(a,1,1,2)),flip(a)]. 139 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(37(a,1),19(a,1,1,2))]. 140 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(37(a,1),19(a,1,1)),rewrite([37(7),37(8)])]. 141 (x * ((x * y) * z)) \ (x * (x * (y * z))) = a(x,x * y,z). [para(37(a,1),19(a,1,2))]. 144 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(37(a,1),21(a,1,1)),rewrite([37(7)])]. 145 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(37(a,1),21(a,1,2,2))]. 146 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(37(a,1),22(a,1,1,1)),rewrite([37(4)])]. 148 ((x * (y * (y * z))) * u) / (y * (y * (z * u))) = R(x,y * (y * z),u). [para(37(a,1),22(a,1,2))]. 150 x * (x * ((y * (x * (x * (y * z)))) * u)) = x * (x * (y * (x * (x * (y * (z * u)))))). [para(37(a,1),37(a,1,1,2)),rewrite([37(6),37(7),37(13),37(14)])]. 159 T(T(x,y),x) = T(x,y). [para(89(a,1),29(a,1,1)),flip(a)]. 160 L(T(x,L(x,y,z)),y,z) = L(x,y,z). [para(89(a,1),30(a,1)),flip(a)]. 165 (x * y) / T(x,y) = y. [para(23(a,1),49(a,1,2))]. 166 R(x,y,z) \ ((x * y) * z) = y * z. [para(22(a,1),50(a,1,1))]. 168 x \ ((y * x) * z) = (x \ y) * (x * z). [para(104(a,1),15(a,1,2))]. 169 (x * y) * (y \ z) = y * ((y \ x) * z). [para(16(a,1),104(a,1,2,2)),flip(a)]. 171 (x / y) * (((x / y) \ z) * x) = (z * (x / y)) * y. [para(18(a,1),104(a,1,2,2))]. 173 a(x,x \ y,x * z) = ((y * x) * z) \ (y * (x * z)). [para(104(a,1),19(a,1,1)),rewrite([16(4)]),flip(a)]. 175 (x * (y * z)) * (a(x,y,z) * ((x * (y * z)) * u)) = (((x * y) * z) * (x * (y * z))) * u. [para(19(a,1),104(a,1,2,1))]. 176 ((x * y) * z) \ (((y \ x) * (y * z)) * y) = K((y \ x) * (y * z),y). [para(104(a,1),20(a,1,1))]. 177 (((x \ y) * (x * z)) * x) \ ((y * x) * z) = K(x,(x \ y) * (x * z)). [para(104(a,1),20(a,1,2))]. 178 (x * y) * (K(y,x) * ((x * y) * z)) = ((y * x) * (x * y)) * z. [para(20(a,1),104(a,1,2,1))]. 179 ((x * y) * z) \ (y * (((y \ x) * (y * z)) * u)) = L(u,(y \ x) * (y * z),y). [para(104(a,1),21(a,1,1))]. 180 L((x \ y) * (x * z),x,u) = (u * x) \ (u * ((y * x) * z)). [para(104(a,1),21(a,1,2,2)),flip(a)]. 181 L(x * y,x \ z,x) = z \ ((z * x) * y). [para(104(a,1),21(a,1,2)),rewrite([16(2)]),flip(a)]. 182 (x * y) * (L(z,y,x) * ((x * y) * u)) = ((x * (y * z)) * (x * y)) * u. [para(21(a,1),104(a,1,2,1))]. 183 (((x * y) * z) * u) / (((y \ x) * (y * z)) * u) = R(y,(y \ x) * (y * z),u). [para(104(a,1),22(a,1,1,1))]. 185 ((x \ y) * (x * z)) \ ((y * x) * z) = T(x,(x \ y) * (x * z)). [para(104(a,1),23(a,1,2))]. 186 x * (T(y,x) * (x * z)) = ((y * x) * x) * z. [para(23(a,1),104(a,1,2,1))]. 187 x * (x * (((x \ y) * (x * z)) * u)) = (x * ((y * x) * z)) * u. [para(104(a,1),37(a,1,1,2)),flip(a)]. 188 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * (y * u)))))) = (z * (x * (x * y))) * u. [para(104(a,1),37(a,1)),rewrite([37(10)]),flip(a)]. 189 (x * y) * (x * z) = x * ((y * x) * z). [para(104(a,1),37(a,2,2)),rewrite([16(2)])]. 190 (x * y) * ((y \ z) * (y * u)) = y * ((y \ x) * ((z * y) * u)). [para(104(a,1),104(a,1,2,2)),flip(a)]. 191 (x * ((x \ y) * z)) / z = R(y,x,x \ z). [back_rewrite(83),rewrite([169(3)])]. 192 (x * y) \ (z * ((z \ x) * y)) = a(x,z,z \ y). [back_rewrite(55),rewrite([169(4)])]. 193 (x * y) * (L(z,y,x) * ((x * y) * u)) = (x * (((y * z) * x) * y)) * u. [back_rewrite(182),rewrite([189(10)])]. 196 (x * ((y * x) * z)) \ (x * (y * (x * z))) = a(x * y,x,z). [back_rewrite(113),rewrite([189(3)])]. 197 R(x,y,y \ 1) = x. [para(14(a,1),191(a,1,1,2)),rewrite([16(2),48(2)]),flip(a)]. 198 R(x * y,x,x \ z) = (x * (y * z)) / z. [para(15(a,1),191(a,1,1,2,1)),flip(a)]. 199 R(x,y,y \ ((y \ x) \ z)) = (y * z) / ((y \ x) \ z). [para(16(a,1),191(a,1,1,2)),flip(a)]. 200 R(x,y,y \ z) * z = y * ((y \ x) * z). [para(191(a,1),18(a,1,1))]. 201 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) = ((x * (y * z)) * (a(x,y,z) * u)) / u. [para(19(a,1),191(a,1,1,2,1)),flip(a)]. 202 R(x * y,y * x,(y * x) \ z) = ((y * x) * (K(x,y) * z)) / z. [para(20(a,1),191(a,1,1,2,1)),flip(a)]. 204 R(x * y,y,y \ z) = (y * (T(x,y) * z)) / z. [para(23(a,1),191(a,1,1,2,1)),flip(a)]. 205 (x * (x * (y * (((x * (x * y)) \ z) * u)))) / u = R(z,x * (x * y),(x * (x * y)) \ u). [para(37(a,1),191(a,1,1))]. 206 R(x,x,x \ y) = x. [para(46(a,1),191(a,1,1,2,1)),rewrite([13(2),17(2)]),flip(a)]. 208 R(x,x / y,(x / y) \ z) = ((x / y) * (y * z)) / z. [para(50(a,1),191(a,1,1,2,1)),flip(a)]. 209 a(x,y,z) \ ((x * y) * z) = T(x * (y * z),a(x,y,z)). [para(19(a,1),91(a,1,2)),rewrite([19(9)]),flip(a)]. 218 x / T(y,y \ x) = y \ x. [para(91(a,2),49(a,1,2))]. 220 R(x,y \ z,T(y,y \ z)) = R(x,y \ z,(y \ z) \ z). [para(91(a,2),191(a,2,3)),rewrite([191(6)]),flip(a)]. 221 T(x \ y,T(x,x \ y)) = ((x \ y) \ y) \ y. [para(91(a,2),91(a,1,2))]. 228 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,u,w),y,z),v5,v6). [para(97(a,1),34(a,1))]. 229 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v5,v6),y,z),v7,v8),u,w). [para(97(a,2),34(a,1,1))]. 260 T(x * ((x \ y) * z),a(x,x \ y,z)) = a(x,x \ y,z) \ (y * z). [para(16(a,1),209(a,1,2,1)),flip(a)]. 263 T((x / y) * (y * z),a(x / y,y,z)) = a(x / y,y,z) \ (x * z). [para(18(a,1),209(a,1,2,1)),flip(a)]. 265 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(209(a,1),49(a,1,2))]. 268 ((x * (y \ z)) * T(y,y \ z)) / z = R(x,y \ z,(y \ z) \ z). [para(220(a,1),22(a,2)),rewrite([90(9),16(7)])]. 311 (x * (y * (y * z))) \ ((x * (y * y)) * z) = a(x,y * y,z). [para(13(a,1),110(a,1,1,2,2)),rewrite([13(5),13(9)])]. 312 (x * (y * (z * (y * u)))) * a(x,y * (z * y),u) = (x * (y * (z * y))) * u. [para(110(a,1),16(a,1,2))]. 326 ((x / y) * (z * x)) \ (y * ((x / y) * (z * (x / y)))) = K(y,(x / y) * (z * (x / y))). [para(18(a,1),114(a,1,1,2,2))]. 338 ((x * (y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(13(a,1),148(a,1,2,2,2)),rewrite([14(2),14(8)])]. 340 ((x * (y * (y * z))) * (z \ u)) / (y * (y * u)) = R(x,y * (y * z),z \ u). [para(16(a,1),148(a,1,2,2,2))]. 341 R(x,y * (y * z),u) * (y * (y * (z * u))) = (x * (y * (y * z))) * u. [para(148(a,1),18(a,1,1))]. 342 R(x / (y * (y * z)),y * (y * z),u) = (x * u) / (y * (y * (z * u))). [para(18(a,1),148(a,1,1,1)),flip(a)]. 350 ((x * y) * z) * K((y \ x) * (y * z),y) = ((y \ x) * (y * z)) * y. [para(176(a,1),16(a,1,2))]. 354 ((x * (y / z)) * z) \ ((((y / z) \ x) * y) * (y / z)) = K(((y / z) \ x) * y,y / z). [para(18(a,1),176(a,1,2,1,2)),rewrite([18(13)])]. 356 (x * (x * y)) \ (x * (y * x)) = K(x * y,x). [para(46(a,1),176(a,1,2,1,1)),rewrite([100(2),13(5),101(4),46(6),13(8)])]. 357 ((x * (x / y)) * z) \ ((y * ((x / y) * z)) * (x / y)) = K(y * ((x / y) * z),x / y). [para(50(a,1),176(a,1,2,1,1)),rewrite([50(11)])]. 393 x * (x * ((x * (y * (x * (x * x)))) * z)) = x * (x * (x * (y * (x * (x * (x * z)))))). [para(129(a,1),37(a,1)),flip(a)]. 398 x * (x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u))))))) = x * (x * u). [para(16(a,1),150(a,1,2,2)),flip(a)]. 407 x * (x * (((x * x) \ y) * (x * (x * z)))) = (y * (x * x)) * z. [para(13(a,1),188(a,1,2,2,2,2,2,2)),rewrite([14(3),13(7),14(9)])]. 411 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [para(16(a,1),188(a,1,2,2,2,2,2,2))]. 435 R(x * ((x \ y) * z),y * z,(y * z) \ u) = ((y * z) * (a(y,x,x \ z) * u)) / u. [para(16(a,1),201(a,1,2,2)),rewrite([169(3),16(6),16(9)])]. 439 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) \ ((x * (y * z)) * (a(x,y,z) * u)) = u. [para(201(a,2),50(a,1,1))]. 463 x * (x * (x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))))) = x * (x * z). [para(16(a,1),393(a,1,2,2)),flip(a)]. 478 R(x,1 / y,y) = x. [para(50(a,1),197(a,1,3))]. 480 R(x,x,y) = x. [para(15(a,1),206(a,1,3))]. 493 R(T(x,y),x,z) = T(x,y). [para(480(a,1),31(a,1,1)),flip(a)]. 495 R(R(x,y,z),x,u) = R(x,y,z). [para(480(a,1),35(a,1,1)),flip(a)]. 506 (x * (1 / y)) * y = x. [para(478(a,1),22(a,2)),rewrite([18(7),48(6)])]. 507 (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z)). [para(90(a,1),19(a,1,1,2))]. 508 (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z). [para(90(a,1),19(a,1,2,1))]. 511 (T(x,y) * y) \ (x * y) = K(y,T(x,y)). [para(90(a,1),20(a,1,2))]. 512 (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y). [para(90(a,1),21(a,1,1))]. 516 ((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,y)). [para(90(a,1),22(a,1,2))]. 517 x * T(T(y,x),z) = T(y,z) * x. [para(29(a,1),90(a,1,2))]. 518 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(30(a,1),90(a,1,2))]. 520 x * (x * (T(y,x) * z)) = x * (y * (x * z)). [para(90(a,1),37(a,1,1,2)),rewrite([128(3)]),flip(a)]. 521 x * (x * (y * T(z,x * (x * y)))) = z * (x * (x * y)). [para(90(a,1),37(a,1)),flip(a)]. 522 x * ((x \ y) * (z * x)) = (y * x) * T(z,x). [para(90(a,1),104(a,1,2,2))]. 537 T(T(x / y,z),y) = T(y \ x,z). [para(92(a,1),29(a,1,1)),flip(a)]. 540 K(T(x,y),x) = 1. [hyper(27,a,159,a)]. 541 T(x,T(x,y)) = x. [hyper(26,a,159,a)]. 547 T(x,y) * x = x * T(x,y). [para(159(a,1),90(a,1,2)),flip(a)]. 554 K(x \ y,y / x) = 1. [para(92(a,1),540(a,1,1))]. 560 T(x,(x \ y) \ y) = x. [para(91(a,1),541(a,1,2))]. 589 (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),y * (z * u),x). [para(54(a,1),21(a,1,2,2))]. 592 ((x * (y * (z * u))) * a(y,z,u)) / ((y * z) * u) = R(x,y * (z * u),a(y,z,u)). [para(54(a,1),22(a,1,2))]. 597 (x * (y * z)) * (((x * (y * z)) \ u) * ((x * y) * z)) = (u * (x * (y * z))) * a(x,y,z). [para(54(a,1),104(a,1,2,2))]. 601 (((x * y) * z) * (x * (y * z))) * a(x,y,z) = (x * (y * z)) * (a(x,y,z) * ((x * y) * z)). [para(54(a,1),175(a,1,2,2)),flip(a)]. 614 (x * ((x \ y) * ((y \ z) * (y * u)))) \ ((z * y) * u) = a(x,x \ y,(y \ z) * (y * u)). [para(104(a,1),56(a,1,2))]. 632 L(x \ 1,x,y) = (y * x) \ y. [para(14(a,1),74(a,2,2))]. 634 L(x \ (y \ z),x,y) = (y * x) \ z. [para(16(a,1),74(a,2,2))]. 637 (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x). [para(20(a,1),74(a,1,1)),flip(a)]. 638 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(21(a,1),74(a,1,1)),flip(a)]. 639 L(T(x,y),y,x) = T(x,x * y). [para(74(a,2),23(a,1)),rewrite([23(2)])]. 648 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(y * z) \ (y * u)). [para(74(a,2),191(a,2,3)),rewrite([191(8)]),flip(a)]. 650 T(x * y,(x * y) \ (x * z)) = L(y \ z,y,x) \ (x * z). [para(74(a,2),91(a,2,1))]. 659 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(90(a,1),74(a,2,2))]. 662 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,(x * y) \ (x * z),u). [para(74(a,2),56(a,1,1,2,1))]. 666 L(K(x,y),y * x,y) = K(y * x,y). [back_rewrite(356),rewrite([637(5)])]. 667 L(L(x,y,z),z * y,z) = x. [back_rewrite(134),rewrite([638(6)])]. 669 x * (T(y,x) * x) = (y * x) * x. [para(14(a,1),186(a,1,2,2)),rewrite([14(7)])]. 673 (((x * y) * y) * z) \ ((x * y) * (y * z)) = a(y,T(x,y),y * z). [para(186(a,1),19(a,1,1)),rewrite([90(5)])]. 674 (x * ((T(y,x) * (x * z)) * u)) \ ((((y * x) * x) * z) * u) = a(x,T(y,x) * (x * z),u). [para(186(a,1),19(a,1,2,1))]. 675 ((T(x,y) * (y * z)) * y) \ (((x * y) * y) * z) = K(y,T(x,y) * (y * z)). [para(186(a,1),20(a,1,2))]. 682 x * (T(T(y,x),z) * (x * u)) = ((T(y,z) * x) * x) * u. [para(29(a,1),186(a,1,2,1))]. 690 a((x * y) * y,T(x,y),z) = a(y,T(x,y) * (x * y),z). [para(186(a,1),110(a,1,2,1)),rewrite([186(6),19(11),90(7)])]. 729 ((x * (y / z)) * z) / T(x * y,a(x,y / z,z)) = a(x,y / z,z). [para(18(a,1),265(a,1,2,1,2))]. 732 (x * (y * z)) / T((x * y) * z,a(y,y \ x,y * z)) = a(y,y \ x,y * z). [para(104(a,1),265(a,1,2,1)),rewrite([16(2)])]. 777 x * (x * T(y,x * x)) = y * (x * x). [para(13(a,1),521(a,1,2,2)),rewrite([14(2),14(6)])]. 778 x * (y * T(z,x * (x * y))) = x \ (z * (x * (x * y))). [para(521(a,1),15(a,1,2)),flip(a)]. 780 L(x * T(y,z * (z * x)),z,z) = (z * z) \ (y * (z * (z * x))). [para(521(a,1),21(a,1,2)),flip(a)]. 788 x * (y * (x * T(z,x * (y * x)))) = z * (x * (y * x)). [para(90(a,1),521(a,1,2,2,2,2,2)),rewrite([520(7),90(8)])]. 831 (x * ((x \ y) * y)) \ ((y * x) * ((x \ y) * z)) = L(z,(x \ y) * y,x). [para(104(a,1),117(a,1,1)),rewrite([169(3),104(9),16(11)])]. 843 (((x * y) * y) * z) / K(y,T(x,y) * (y * z)) = (T(x,y) * (y * z)) * y. [para(675(a,1),49(a,1,2))]. 863 (T(T(x,y),z) * (z * u)) * z = (T(T(x,z),y) * (z * u)) * z. [para(29(a,1),843(a,2,1,1)),rewrite([843(10)])]. 874 x * K((y \ z) * (y * ((z * y) \ x)),y) = ((y \ z) * (y * ((z * y) \ x))) * y. [para(16(a,1),350(a,1,1))]. 888 ((1 / x) * y) \ (x * ((1 / x) * (y * (1 / x)))) = K(x,(1 / x) * (y * (1 / x))). [para(14(a,1),326(a,1,1,2))]. 961 (x * (x * (y * z))) / T(x * (x * y),z) = z. [para(37(a,1),165(a,1,1))]. 965 (x * y) / T(y,T(x,y)) = T(x,y). [para(90(a,1),165(a,1,1))]. 969 (((x \ y) * (x * z)) * x) / T((y * x) * z,K((x \ y) * (x * z),x)) = K((x \ y) * (x * z),x). [para(350(a,1),165(a,1,1))]. 974 x * (1 / y) = x / y. [para(506(a,1),17(a,1,1)),flip(a)]. 975 x / (1 / y) = x * y. [para(18(a,1),506(a,1,1)),flip(a)]. 976 a(x,1 / y,y) = 1. [para(506(a,1),19(a,1,2)),rewrite([18(3),14(2),46(1)]),flip(a)]. 980 (x / y) / K(1 / y,T(x,1 / y)) = T(x,1 / y) / y. [para(506(a,1),843(a,1,1)),rewrite([974(3),18(9),14(8),18(14),14(13),974(14)])]. 982 K(x,1 / x) = 1. [para(506(a,1),357(a,1,1)),rewrite([18(4),14(3),974(4),47(2),46(3),18(4),14(3)]),flip(a)]. 985 ((1 / x) * y) \ (x * ((1 / x) * (y / x))) = K(x,(1 / x) * (y / x)). [back_rewrite(888),rewrite([974(8),974(14)])]. 986 T(x,1 / x) = x. [hyper(28,a,982,a)]. 989 1 / x = x \ 1. [hyper(26,a,986,a),rewrite([92(3)]),flip(a)]. 990 (x \ 1) \ 1 = x. [para(986(a,1),23(a,2)),rewrite([989(2),989(4),16(5)])]. 996 T(x \ 1,x) = x \ 1. [para(49(a,1),986(a,1,2))]. 997 (x \ 1) * x = 1. [para(986(a,1),90(a,1,2)),rewrite([989(2),989(5),16(6)])]. 1004 ((x \ 1) * y) \ (x * ((x \ 1) * (y / x))) = K(x,(x \ 1) * (y / x)). [back_rewrite(985),rewrite([989(2),989(5),989(11)])]. 1009 (x / y) / K(y \ 1,T(x,y \ 1)) = T(x,y \ 1) / y. [back_rewrite(980),rewrite([989(3),989(5),989(10)])]. 1012 a(x,y \ 1,y) = 1. [back_rewrite(976),rewrite([989(2)])]. 1013 x / (y \ 1) = x * y. [back_rewrite(975),rewrite([989(2)])]. 1014 x * (y \ 1) = x / y. [back_rewrite(974),rewrite([989(2)])]. 1022 L(x,x \ 1,y) = x. [para(990(a,1),74(a,1,1)),rewrite([1014(6),14(6),50(5)])]. 1025 (x \ 1) * (x * y) = L(y,x,x \ 1). [para(997(a,1),21(a,1,1)),rewrite([45(6)])]. 1026 L(x,y,(y * x) \ 1) = (((y * x) \ 1) * y) \ 1. [para(997(a,1),21(a,1,2)),flip(a)]. 1027 R(x \ 1,x,y) = y / (x * y). [para(997(a,1),22(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1039 R((x * (x * y)) \ 1,x * (x * y),z) = z / (x * (x * (y * z))). [para(997(a,1),148(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1051 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x \ (y \ 1),y). [para(997(a,1),56(a,1,2))]. 1072 a(x,y,y \ 1) = 1. [para(50(a,1),1012(a,1,2)),rewrite([989(2)])]. 1077 L(x \ 1,x,y) = x \ 1. [para(50(a,1),1022(a,1,2)),rewrite([989(2),989(5)])]. 1078 L(L(L(x,y,z),u,w),L(x,u,w) \ 1,v5) = L(L(x,u,w),y,z). [para(1022(a,1),97(a,1,1)),flip(a)]. 1080 L(L(L(x,y,z),u,w),x \ 1,v5) = L(L(x,y,z),u,w). [para(1022(a,1),97(a,2,1,1))]. 1091 (x * y) \ x = y \ 1. [back_rewrite(632),rewrite([1077(3)]),flip(a)]. 1098 (x * (y * L(z,y,x))) \ (x * (y * z)) = a(x,y,L(z,y,x)). [para(21(a,1),57(a,1,1,2,2)),rewrite([21(10)])]. 1105 (x * (y * L(y \ z,y,x))) \ (x * z) = a(x,y,(x * y) \ (x * z)). [para(74(a,2),57(a,1,1,2,2))]. 1141 L(x,y,(y * x) \ 1) \ 1 = ((y * x) \ 1) * y. [para(1026(a,2),49(a,1,2)),rewrite([989(6)])]. 1180 L(x,x \ y,x) = x. [para(14(a,1),181(a,1,1)),rewrite([14(5),15(4)])]. 1201 T(x,L(y * z,y \ x,y)) = T(x,x \ ((x * y) * z)). [para(181(a,2),91(a,1,2)),rewrite([91(10,R)])]. 1227 L(x * y,x \ (x \ 1),x) = (x \ 1) \ y. [para(997(a,1),181(a,2,2,1)),rewrite([13(9)])]. 1246 (x * (x * y)) / T(x * (x * (y / z)),z) = z. [para(18(a,1),961(a,1,1,2,2))]. 1252 (x * (x * (y * z))) / T(x * (x * z),T(y,z)) = T(y,z). [para(90(a,1),961(a,1,1,2,2))]. 1266 (((T(x,y) * z) * z) * u) / (T(T(x,z),y) * (z * u)) = z. [para(682(a,1),17(a,1,1))]. 1300 a(x,x,y) = 1. [para(13(a,1),690(a,1,1,1)),rewrite([87(3),51(3),87(3),13(4),13(3)]),flip(a)]. 1316 K(x * x,x) = 1. [back_rewrite(68),rewrite([1300(3)])]. 1323 x \ (y * (x * x)) = x * T(y,x * x). [para(13(a,1),778(a,1,2)),rewrite([14(2),14(5)]),flip(a)]. 1324 x \ (x \ (y * (x * (x * z)))) = z * T(y,x * (x * z)). [para(778(a,1),15(a,1,2))]. 1353 x * (y / (x * (x * y))) = x \ 1. [para(997(a,1),778(a,2,2)),rewrite([996(7),1014(5)])]. 1359 x * (y * T(z,y * (x * y))) = y \ (z * (y * (x * y))). [para(788(a,1),15(a,1,2)),flip(a)]. 1448 R((x * (y * x)) \ 1,x * (y * x),z) = z / (x * (y * (x * z))). [para(997(a,1),121(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1452 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,x \ y). [para(268(a,1),18(a,1,1)),rewrite([200(5)])]. 1457 R(x,y \ z,(y \ z) \ z) \ ((x * (y \ z)) * T(y,y \ z)) = z. [para(268(a,1),50(a,1,1))]. 1479 x * (x * ((T(T(y,z),u) * (u * w)) * u)) = x * (x * ((T(T(y,u),z) * (u * w)) * u)). [para(863(a,1),37(a,2,2,2)),rewrite([37(7)])]. 1517 (x * (y * z)) / T((x * z) * T(y,z),a(z,z \ x,y * z)) = a(z,z \ x,y * z). [para(90(a,1),732(a,1,1,2)),rewrite([90(8),90(13)])]. 1524 L(x * ((y * (y * x)) \ z),y,y) = (y * y) \ z. [para(18(a,1),780(a,2,2)),rewrite([92(6)])]. 1534 L(x / (y * (y * x)),y,y) = (y * y) \ 1. [para(997(a,1),780(a,2,2)),rewrite([996(7),1014(5)])]. 1603 (x * (x * ((T(T(y,z),u) * (u * w)) * u))) / (x * (x * ((T(T(y,u),z) * (u * w)) * u))) = 1. [para(1479(a,1),265(a,1,2,1)),rewrite([100(7),1300(20),88(16),1300(21)])]. 1607 L(x,y,y) = x. [hyper(24,a,1300,a)]. 1609 x / (y * (y * x)) = (y * y) \ 1. [back_rewrite(1534),rewrite([1607(4)])]. 1619 x * ((y * (y * x)) \ z) = (y * y) \ z. [back_rewrite(1524),rewrite([1607(5)])]. 1649 x / (x * x) = x \ 1. [back_rewrite(1353),rewrite([1609(3),1014(4)])]. 1659 T(x * x,x) = x * x. [hyper(28,a,1316,a)]. 1667 L(x,y,x) = x. [para(15(a,1),1180(a,1,2))]. 1685 L(T(x,y),z,x) = T(x,y). [para(1667(a,1),30(a,1,1)),flip(a)]. 1699 ((x \ y) * x) \ ((x \ y) * y) = x \ y. [para(1667(a,1),74(a,1)),flip(a)]. 1702 a((x \ y) * x,x \ y,z) = a(x \ y,y,z). [para(1667(a,1),662(a,1,1,2,1)),rewrite([189(5),16(3),19(7),1699(9)]),flip(a)]. 1708 T(x,x * y) = T(x,y). [back_rewrite(639),rewrite([1685(2)]),flip(a)]. 1723 K(x,(y * x) / y) = 1. [para(15(a,1),554(a,1,1))]. 1812 T(x * y,y \ 1) = (y \ 1) \ x. [para(1013(a,1),92(a,1,1))]. 1829 x \ (x / y) = y \ 1. [para(1014(a,1),15(a,1,2))]. 1832 (x / y) \ ((y \ 1) * x) = K(y \ 1,x). [para(1014(a,1),20(a,1,1))]. 1833 ((x \ 1) * y) \ (y / x) = K(y,x \ 1). [para(1014(a,1),20(a,1,2))]. 1834 (x / y) \ (x * ((y \ 1) * z)) = L(z,y \ 1,x). [para(1014(a,1),21(a,1,1))]. 1836 ((x * y) / z) / (y / z) = R(x,y,z \ 1). [para(1014(a,1),22(a,1,1)),rewrite([1014(5)])]. 1838 x * (x * ((y \ 1) * z)) = (x * (x / y)) * z. [para(1014(a,1),37(a,1,1,2)),flip(a)]. 1839 (x * (x * y)) / z = x * (x * (y / z)). [para(1014(a,1),37(a,1)),rewrite([1014(6)])]. 1840 x * ((x \ y) * (x / z)) = (y * x) / z. [para(1014(a,1),104(a,1,2,2)),rewrite([1014(8)])]. 1851 (x * (y * (x * (z * (x * (y * x)))))) / u = x * (y * (x * (z * (x * (y * (x / u)))))). [para(1014(a,1),129(a,1)),rewrite([1014(10)])]. 1859 x * (T(y,x) * (x / z)) = ((y * x) * x) / z. [para(1014(a,1),186(a,1,2,2)),rewrite([1014(9)])]. 1864 ((T(x,y) * (y / z)) * y) \ (((x * y) * y) / z) = K(y,T(x,y) * (y / z)). [para(1014(a,1),675(a,1,1,1,2)),rewrite([1014(9),1014(12)])]. 1870 x * (x * ((y * (((x * (x * y)) \ z) * u)) / u)) = R(z,x * (x * y),(x * (x * y)) \ u). [para(205(a,1),1014(a,2)),rewrite([1014(10),1839(8)])]. 1884 x * (x * ((y / z) / T(x * (x * y),z \ 1))) = z \ 1. [para(1014(a,1),961(a,1,1,2,2)),rewrite([1839(9)])]. 1885 x * (x * ((y * z) / T(x * (x * y),z))) = z. [para(961(a,1),1014(a,2)),rewrite([1014(9),1839(7)])]. 1888 x * ((y \ 1) * T(z,x * (x / y))) = x \ (z * (x * (x / y))). [para(1014(a,1),778(a,1,2,2,2,2)),rewrite([1014(10)])]. 1907 x * (x * (((T(T(y,z),u) * (u * w)) * u) / (x * (x * ((T(T(y,u),z) * (u * w)) * u))))) = 1. [back_rewrite(1603),rewrite([1839(15)])]. 1921 x * (x * ((y * z) / T(x * (x * z),T(y,z)))) = T(y,z). [back_rewrite(1252),rewrite([1839(8)])]. 1925 x * (x * (y / T(x * (x * (y / z)),z))) = z. [back_rewrite(1246),rewrite([1839(7)])]. 1935 x * (x * R(y,z,u)) = R(x * (x * y),z,u). [back_rewrite(146),rewrite([1839(6),22(4)])]. 1952 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(x / (y * (y * z)),y * (y * z),u). [para(37(a,1),60(a,1,1,2))]. 1958 ((x / y) * (z * y)) \ (x * T(z,y)) = a(x / y,y,T(z,y)). [para(90(a,1),60(a,1,1,2))]. 1972 R(x,x / y,(x / y) \ (y \ z)) = ((x / y) * z) / (y \ z). [para(16(a,1),208(a,2,1,2))]. 1990 R(x,x / y,(x / y) \ T(z,y)) = ((x / y) * (z * y)) / T(z,y). [para(90(a,1),208(a,2,1,2))]. 2004 R(x,x * y,(x * y) \ z) = ((x * y) * ((y \ 1) * z)) / z. [para(1013(a,1),208(a,1,2)),rewrite([1013(4),1013(7)])]. 2009 (x / y) * ((x / y) * ((y * z) / T((x / y) * x,z))) = z. [para(18(a,1),1885(a,1,2,2,2,1,2))]. 2010 (x * y) / T(z * (z * x),y) = (z * z) \ y. [para(1885(a,1),21(a,1,2)),rewrite([1607(8)]),flip(a)]. 2012 x * (x * (((x * x) \ y) * z)) = y * z. [para(1885(a,1),37(a,1,1)),rewrite([2010(6)]),flip(a)]. 2032 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (((T(y,z) * x) * x) * u),w))) = w. [para(682(a,1),1885(a,1,2,2,2,1,2))]. 2040 (x * (y * y)) * z = x * (y * (y * z)). [back_rewrite(407),rewrite([2012(7)]),flip(a)]. 2044 R(x,y * y,z) = x. [back_rewrite(338),rewrite([2040(3),17(6)]),flip(a)]. 2045 a(x,y * y,z) = 1. [back_rewrite(311),rewrite([2040(6),46(7)]),flip(a)]. 2166 x / (T(T(y,z),u) * (z * (((T(y,u) * z) * z) \ x))) = z. [para(16(a,1),1266(a,1,1))]. 2213 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(13(a,1),130(a,1,1,2,2)),rewrite([13(8)])]. 2214 (x * (y * (z * (y * x)))) \ (x * (y * (z * (y * (x * u))))) = u. [para(130(a,1),15(a,1,2))]. 2215 x * (y * (z * (y * (x * ((x * (y * (z * (y * x)))) \ u))))) = u. [para(130(a,1),16(a,1))]. 2234 T(x,y) * (y * (z * (y * (T(x,y) * u)))) = (T(x,y) * (y * (z * (x * y)))) * u. [para(90(a,1),130(a,1,1,2,2,2)),flip(a)]. 2243 x * (y * (((y * x) \ 1) * (y * (x * z)))) = (x * y) * z. [para(997(a,1),130(a,1,1,2,2)),rewrite([14(2)]),flip(a)]. 2254 L(x,y,z * z) = x. [para(13(a,1),132(a,1,1,2)),rewrite([13(6),638(6),667(3),13(2)]),flip(a)]. 2276 L(x,y,z * (((z * y) \ 1) * z)) = ((z * y) \ 1) * (z * (y * x)). [para(997(a,1),132(a,1,1,2)),rewrite([14(2),15(8)]),flip(a)]. 2278 L(x,y,z * (((z * (y * x)) \ 1) * z)) = (((z * (y * x)) \ 1) * (z * y)) \ 1. [para(997(a,1),132(a,1,2,2)),rewrite([14(9),1091(8)]),flip(a)]. 2356 L(L(L(x,y,z),u,(u * x) \ 1),((u * x) \ 1) * u,w) = L(L(x,u,(u * x) \ 1),y,z). [para(1026(a,1),1078(a,1,2,1)),rewrite([990(13)])]. 2357 L(L(x,y,(y * x) \ 1),z,u) = L((((y * x) \ 1) * y) \ 1,z,u). [para(1026(a,1),1078(a,2,1)),rewrite([1141(11),2356(10)])]. 2485 L(x,y * y,z) = x. [hyper(24,a,2045,a)]. 2486 a(x,y * (y * (z * (y * (y * z)))),u) = 1. [para(37(a,1),2045(a,1,2))]. 2495 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(2254(a,1),74(a,1)),rewrite([100(3),100(5)]),flip(a)]. 2497 L(x,y,(z \ 1) / z) = x. [para(1014(a,1),2254(a,1,3))]. 2507 L(x,y,z * (z * u)) = L(x,y,u). [back_rewrite(144),rewrite([2495(8),21(4)]),flip(a)]. 2508 a(x * (x * y),z,u) = a(y,z,u). [back_rewrite(140),rewrite([2495(9),19(5)]),flip(a)]. 2522 L(x,y * (y * (z * (y * (y * z)))),u) = x. [para(37(a,1),2485(a,1,2))]. 2528 L(x,(y \ 1) / y,z) = x. [para(1014(a,1),2485(a,1,2))]. 2538 (x \ y) \ 1 = y \ x. [para(16(a,1),1091(a,1,1)),flip(a)]. 2540 ((x \ y) * (x * z)) \ 1 = ((y * x) * z) \ x. [para(104(a,1),1091(a,1,1)),flip(a)]. 2548 ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. [para(54(a,1),1091(a,1,1))]. 2556 ((x / y) * ((y \ 1) \ z)) / z = R(x,y \ 1,(y \ 1) \ z). [para(1091(a,1),268(a,1,1,1,2)),rewrite([1014(3),1091(4),1812(5),1091(8),1091(10)])]. 2560 T(x * y,(y \ 1) \ x) = x * y. [para(1091(a,1),560(a,1,2,1))]. 2574 a(x,T(y,x),x * z) = a(y * x,x,z) \ 1. [back_rewrite(673),rewrite([2548(7)]),flip(a)]. 2575 a(x,x \ y,x * z) = a(y,x,z) \ 1. [back_rewrite(173),rewrite([2548(8)])]. 2599 ((x / y) * (y * y)) / T(x * y,a(x,y \ 1,y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),729(a,1,1,1,2)),rewrite([1014(3),1649(6),1649(12)])]. 2601 ((x / y) * (y * y)) \ ((y \ 1) \ x) = K(((y \ 1) \ x) * y,y \ 1). [para(1649(a,1),354(a,1,1,1,2)),rewrite([1014(3),1649(5),1649(9),1014(10),17(8),1649(9),1649(13)])]. 2604 (x * y) \ ((x / y) * (y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),58(a,1,2,1,2)),rewrite([1014(4),1649(7)])]. 2635 T(T(x * x,y),x) = T(x * x,y). [para(1659(a,1),29(a,1,1)),flip(a)]. 2639 T((x \ 1) / x,x \ 1) = (x \ 1) / x. [para(1014(a,1),1659(a,1,1)),rewrite([1014(11)])]. 2640 x * (x * (y * (y * (z / (T(x * x,y) * (y * z)))))) = y. [para(1659(a,1),1266(a,1,1,1,1,1)),rewrite([100(2),37(3),37(4),100(2),2635(7),1839(9),1839(7)])]. 2642 T(x,x \ y) = T(x,y). [para(16(a,1),1708(a,1,2)),flip(a)]. 2643 T(x / y,x) = y \ x. [para(18(a,1),1708(a,1,2)),rewrite([92(4)])]. 2647 T(x * (x * y),x * (x * (y * z))) = T(x * (x * y),z). [para(37(a,1),1708(a,1,2))]. 2648 T(x,(x \ y) * (x * z)) = T(x,(y * x) * z). [para(104(a,1),1708(a,1,2)),flip(a)]. 2649 (x \ y) \ y = T(x,y). [para(91(a,1),1708(a,2)),rewrite([16(2)]),flip(a)]. 2652 T(x,y * x) = T(x,T(y,x)). [para(90(a,1),1708(a,1,2))]. 2690 (x \ y) * T(x,y) = y. [back_rewrite(1457),rewrite([2649(3),2642(7),166(8)])]. 2692 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(1452),rewrite([2642(9)])]. 2700 T(x,L(y * z,y \ x,y)) = T(x,(x * y) * z). [back_rewrite(1201),rewrite([2642(8)])]. 2705 L(x \ y,x,z) \ (z * y) = T(z * x,z * y). [back_rewrite(650),rewrite([2642(5)]),flip(a)]. 2708 ((x * (y \ z)) * T(y,z)) / z = R(x,y \ z,T(y,z)). [back_rewrite(268),rewrite([2642(4),2649(8)])]. 2709 T(x \ y,T(x,y)) = T(x,y) \ y. [back_rewrite(221),rewrite([2642(3),2649(5)])]. 2711 x / T(y,x) = y \ x. [back_rewrite(218),rewrite([2642(2)])]. 2712 (x \ 1) / x = x \ (x \ 1). [back_rewrite(2639),rewrite([2643(6)]),flip(a)]. 2713 ((x \ y) * (x * z)) \ ((y * x) * z) = T(x,(y * x) * z). [back_rewrite(185),rewrite([2648(10)])]. 2747 L(x,y \ (y \ 1),z) = x. [back_rewrite(2528),rewrite([2712(3)])]. 2748 L(x,y,z \ (z \ 1)) = x. [back_rewrite(2497),rewrite([2712(3)])]. 2755 (x \ 1) \ y = x * y. [back_rewrite(1227),rewrite([2747(5)]),flip(a)]. 2757 ((x / y) * (y * y)) \ (y * x) = K(y * (x * y),y \ 1). [back_rewrite(2601),rewrite([2755(6),2755(8),101(7)])]. 2759 T(x * y,y * x) = x * y. [back_rewrite(2560),rewrite([2755(4)])]. 2760 ((x / y) * (y * z)) / z = R(x,y \ 1,y * z). [back_rewrite(2556),rewrite([2755(4),2755(9)])]. 2774 T(x * y,y \ 1) = y * x. [back_rewrite(1812),rewrite([2755(7)])]. 2796 R(x,x / y,(x / y) \ z) = R(x,y \ 1,y * z). [back_rewrite(208),rewrite([2760(8)])]. 2802 ((x / y) * (z * y)) / T(z,y) = R(x,y \ 1,z * y). [back_rewrite(1990),rewrite([2796(5),90(4)]),flip(a)]. 2806 ((x / y) * z) / (y \ z) = R(x,y \ 1,z). [back_rewrite(1972),rewrite([2796(5),16(4)]),flip(a)]. 2810 T(x,(y * x) / y) = x. [hyper(28,a,1723,a)]. 2852 x * K(y \ x,y) = (y \ x) * y. [para(16(a,1),63(a,1,1))]. 2855 (x * y) \ (K(x,y) * (y * x)) = K(K(x,y),y * x). [para(63(a,1),20(a,1,1))]. 2857 (x * y) \ ((y * x) * (K(x,y) * z)) = L(z,K(x,y),y * x). [para(63(a,1),21(a,1,1))]. 2858 ((x * y) * z) / (K(x,y) * z) = R(y * x,K(x,y),z). [para(63(a,1),22(a,1,1,1))]. 2917 K(x,y) \ 1 = K(y,x). [para(63(a,1),1091(a,1,1)),rewrite([20(3)]),flip(a)]. 2918 T(x * y,K(y,x)) = x * y. [para(63(a,1),1708(a,1,2)),rewrite([2759(3)]),flip(a)]. 2934 (x * (y * z)) \ (L(z,y,x) * (x * y)) = K(L(z,y,x),x * y). [para(21(a,1),64(a,1,2,1)),rewrite([21(10)])]. 2962 x \ ((y \ 1) * (x * y)) = K(y \ 1,x * y). [para(1091(a,1),64(a,1,2,1)),rewrite([1091(7)])]. 2965 x * (((x \ y) * x) * z) = y * (x * z). [para(16(a,1),189(a,1,1)),flip(a)]. 2971 L(a(x,y,z),x * (y * z),y) = a(y,x,y * z). [para(189(a,1),19(a,1,2)),rewrite([589(7)])]. 2975 L(x,y * z,z) = L(x,z,z * y). [para(189(a,1),21(a,1,2)),rewrite([101(2),21(6)])]. 2993 x * ((T(y,x) * x) * z) = (y * x) * (x * z). [para(90(a,1),189(a,1,1)),flip(a)]. 3018 L(x * (y * z),x \ y,x) = (x * y) * z. [para(189(a,1),181(a,2,2)),rewrite([15(8)])]. 3031 x * (((y \ 1) * x) * z) = (x / y) * (x * z). [para(1014(a,1),189(a,1,1)),flip(a)]. 3032 (x * y) * (x / z) = x * ((y * x) / z). [para(1014(a,1),189(a,1,2)),rewrite([1014(7)])]. 3093 x * a(y,z,y * ((y * (z * y)) \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [para(103(a,1),54(a,1,1)),rewrite([189(12)])]. 3103 x * ((x \ 1) * y) = y. [para(997(a,1),103(a,1,2,2,2,1,2)),rewrite([14(4),16(4)])]. 3130 K(x,(x \ 1) * (y / x)) = K(y,x \ 1). [back_rewrite(1004),rewrite([3103(8),1833(5)]),flip(a)]. 3135 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(16(a,1),2495(a,1,1,2))]. 3136 (x * (x * y)) \ (x * z) = y \ (x \ z). [para(16(a,1),2495(a,1,2,2))]. 3139 T(x * (x * (y / (x * (x * z)))),x * (x * z)) = z \ y. [para(2495(a,1),92(a,2)),rewrite([1839(5)])]. 3143 (x \ 1) * y = x \ y. [para(997(a,1),2495(a,1,1,2)),rewrite([14(4),15(9)])]. 3162 (x \ ((x * y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(141),rewrite([3135(7)])]. 3163 K(x,x \ (y / x)) = K(y,x \ 1). [back_rewrite(3130),rewrite([3143(4)])]. 3169 (x / y) * (x * z) = x * ((y \ x) * z). [back_rewrite(3031),rewrite([3143(3)]),flip(a)]. 3171 K(x \ 1,y * x) = y \ T(y,x). [back_rewrite(2962),rewrite([3143(4),23(2)]),flip(a)]. 3191 L(L(x,y,(y * x) \ 1),z,u) = L(x,z,u). [back_rewrite(2357),rewrite([3143(9),1091(7),2649(9),88(7)])]. 3192 L(L(x,y,z),u,(u * x) \ 1) = L(x,y,z). [back_rewrite(2356),rewrite([3143(9),1091(7),1080(8),3191(10)])]. 3199 L(x,y,z / (y * x)) = L(x,y,z). [back_rewrite(2278),rewrite([3143(5),1091(3),1014(4),3143(9),2538(9),21(7)])]. 3200 L(x,y,z / y) = L(x,y,z). [back_rewrite(2276),rewrite([3143(4),1091(2),1014(3),3143(8),21(6)])]. 3204 x * (y * L(z,x,y)) = (x * y) * z. [back_rewrite(2243),rewrite([3143(6),21(4)])]. 3213 R(x,x * y,(x * y) \ z) = R(x,y,y \ z). [back_rewrite(2004),rewrite([3143(8),169(7),191(8)])]. 3218 x * (y \ T(z,x * (x / y))) = x \ (z * (x * (x / y))). [back_rewrite(1888),rewrite([3143(6)])]. 3228 (x * (x / y)) * z = x * (x * (y \ z)). [back_rewrite(1838),rewrite([3143(3)]),flip(a)]. 3229 (x / y) \ (x * (y \ z)) = L(z,y \ 1,x). [back_rewrite(1834),rewrite([3143(4)])]. 3230 (x \ y) \ (y / x) = K(y,x \ 1). [back_rewrite(1833),rewrite([3143(3)])]. 3231 (x / y) \ (y \ x) = K(y \ 1,x). [back_rewrite(1832),rewrite([3143(4)])]. 3266 L(x,y,y \ 1) = x. [back_rewrite(1025),rewrite([3143(4),15(2)]),flip(a)]. 3276 x \ ((x / y) * (y * z)) = L(z,y,x). [back_rewrite(75),rewrite([3200(6)])]. 3286 (x / y) * (y * ((x / y) * z)) = x * (x * (y \ z)). [back_rewrite(107),rewrite([3228(8)])]. 3304 T(x,K(y \ x,y)) = x. [para(16(a,1),2918(a,1,1)),rewrite([16(5)])]. 3305 T(x,K(y,x / y)) = x. [para(18(a,1),2918(a,1,1)),rewrite([18(5)])]. 3307 T((x * y) * z,K((y \ x) * (y * z),y)) = (x * y) * z. [para(104(a,1),2918(a,1,1)),rewrite([104(11)])]. 3308 K(x,y) * (y * x) = x * y. [para(2918(a,1),90(a,1,2)),rewrite([63(6)])]. 3323 (((x \ y) * (x * z)) * x) / ((y * x) * z) = K((x \ y) * (x * z),x). [back_rewrite(969),rewrite([3307(11)])]. 3327 K(K(x,y),y * x) = 1. [back_rewrite(2855),rewrite([3308(4),46(3)]),flip(a)]. 3382 T(T(T(x,y \ 1),z),u) / y = T(T(T(x,z),u),y \ 1) / y. [para(94(a,1),1009(a,2,1)),rewrite([1009(12)]),flip(a)]. 3436 (x * x) \ y = x \ (x \ y). [para(18(a,1),1324(a,1,2,2)),rewrite([92(8),1619(6)]),flip(a)]. 3476 x * T(y * z,y * (y * x)) = (y \ z) * (y * (y * x)). [para(181(a,2),1324(a,1,2)),rewrite([3018(5),168(4)]),flip(a)]. 3482 x \ T(y,z * (z / x)) = z \ (z \ (y * (z * (z / x)))). [para(1014(a,1),1324(a,1,2,2,2,2)),rewrite([1014(10),3143(11)]),flip(a)]. 3541 x \ (y \ (z * (y * (x * y)))) = y * T(z,y * (x * y)). [para(1359(a,1),15(a,1,2))]. 3640 x * (x * (((x \ y) / z) / T(x * y,z \ 1))) = z \ 1. [para(16(a,1),1884(a,1,2,2,2,1,2))]. 3641 x * (x * (y / T(x * (x * (y * z)),z \ 1))) = z \ 1. [para(17(a,1),1884(a,1,2,2,1))]. 3645 (x / y) / T(z * (z * x),y \ 1) = z \ (z \ (y \ 1)). [para(1884(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 3646 R(x,x \ (y \ 1),z) = (y \ z) / ((x \ (y \ 1)) * z). [para(1884(a,1),22(a,1,1,1)),rewrite([3143(3),3645(8),16(6),3645(13),16(11)]),flip(a)]. 3666 (x \ y) / y = x \ 1. [para(1884(a,1),201(a,1,2)),rewrite([3645(8),100(6),16(5),16(4),3645(11),16(9),16(8),2755(7),480(6),3645(9),16(7),16(6),3645(11),1300(9),13(6),3143(5)]),flip(a)]. 3683 x * ((x \ (y \ 1)) * T(z,x / y)) = x \ (z * (x / y)). [para(1884(a,1),778(a,1,2,2,2,2)),rewrite([3645(7),16(5),1014(6),3645(14),16(12),16(11),1014(10)])]. 3691 x / (y * x) = y \ 1. [para(1884(a,1),1013(a,2)),rewrite([3645(7),16(5),2538(5),2755(3)])]. 3709 x \ (x \ (y * (x / z))) = (x \ (z \ 1)) * T(y,x / z). [para(1884(a,1),1324(a,1,2,2,2,2)),rewrite([1014(3),3645(11),16(9),3645(14),16(12),16(11),1014(10)])]. 3723 R(x \ 1,x,y) = x \ 1. [back_rewrite(1027),rewrite([3691(5)])]. 3724 x / (y * (z * (y * x))) = (y * (z * y)) \ 1. [back_rewrite(1448),rewrite([3723(7)]),flip(a)]. 3725 x / (y * (y * (z * x))) = (y * (y * z)) \ 1. [back_rewrite(1039),rewrite([3723(7)]),flip(a)]. 3752 (x * (y * (y * z))) \ ((x * (y * (y * u))) * (u \ z)) = a(x,y * (y * u),u \ z). [para(16(a,1),139(a,1,1,2,2,2))]. 3753 (x * (y * (y * z))) \ ((x * (y * (y * (z / u)))) * u) = a(x,y * (y * (z / u)),u). [para(18(a,1),139(a,1,1,2,2,2))]. 3762 a(x * ((y * x) * x),z,u) = a(x * y,x * (x * z),u). [para(189(a,1),139(a,1,1)),rewrite([189(9),133(11)])]. 3794 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,w),y),z),v5),u \ 1) / u. [para(94(a,1),3382(a,2,1,1,1))]. 3933 x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u)))))) = x * u. [para(398(a,1),15(a,1,2)),rewrite([15(3)]),flip(a)]. 3934 K(x * y,x) = y \ T(y,x). [para(398(a,1),20(a,1,1)),rewrite([3933(13),101(4),3136(5),23(2),3933(13)]),flip(a)]. 3935 K(x,x * y) = T(y,x) \ y. [para(398(a,1),20(a,1,2)),rewrite([3933(11),101(2),3135(5),23(2),3933(13)]),flip(a)]. 3936 x * (y * (y * (x * (z * ((x * (y * (y * (x * z)))) \ u))))) = u. [para(398(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 3940 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(398(a,1),74(a,2,1)),rewrite([3936(10),3936(12),3136(8)])]. 3941 L(x \ (y * z),x,y) = (y \ x) \ z. [para(398(a,1),74(a,2,2)),rewrite([3936(10),3135(7)])]. 3947 x * (x * (y * (x * (x * (y * (z \ ((y * (x * (x * (y / z)))) \ u))))))) = x * (x * u). [para(1014(a,1),398(a,1,2,2,2,2,2,2,2,1,2,2,2)),rewrite([3143(8)])]. 3949 x * (x * (y * ((x * (x * (x * (x * y)))) \ z))) = x \ (x \ z). [para(398(a,1),132(a,1,2)),rewrite([3135(6),15(3),3436(2),2507(13),1607(11)]),flip(a)]. 3954 a(x,x \ y,z) = a(x,x * y,z). [para(398(a,1),133(a,1,2,1)),rewrite([3949(8),16(3),136(4),37(6),3135(7),3162(5),3949(12),16(7),2508(6)]),flip(a)]. 3982 a(x,x * y,x * z) = a(y,x,z) \ 1. [back_rewrite(2575),rewrite([3954(3)])]. 4007 (x * (y * z)) / T((x * z) * T(y,z),a(z,z * x,y * z)) = a(z,z * x,y * z). [back_rewrite(1517),rewrite([3954(8),3954(13)])]. 4013 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x / y,y). [back_rewrite(1051),rewrite([3954(11),1014(10)])]. 4021 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,x * ((y * x) * z),u). [back_rewrite(662),rewrite([3954(13),189(12)])]. 4025 (x * ((x \ y) * ((y \ z) * (y * u)))) \ ((z * y) * u) = a(x,x * y,(y \ z) * (y * u)). [back_rewrite(614),rewrite([3954(14)])]. 4031 T(x * ((x \ y) * z),a(x,x * y,z)) = a(x,x * y,z) \ (y * z). [back_rewrite(260),rewrite([3954(5),3954(8)])]. 4032 (x * ((x \ y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(56),rewrite([3954(7)])]. 4097 T(T(T(T(T(x,y),z \ 1),u),w),v5) / z = T(T(T(T(T(x,w),u),y),v5),z \ 1) / z. [para(94(a,2),3794(a,1,1,1,1))]. 4114 ((x * y) * z) \ R(x,y,z) = (y * z) \ 1. [para(22(a,1),1829(a,1,2))]. 4115 ((x / y) * x) * z = x * (y \ (x * z)). [para(1829(a,1),104(a,1,2,1)),rewrite([3143(4)]),flip(a)]. 4137 (x \ y) * (y \ x) = 1. [para(2538(a,1),16(a,1,2))]. 4138 (x * (y * z)) \ (x * y) = L(z,y,x) \ 1. [para(21(a,1),2538(a,1,1)),flip(a)]. 4145 L(x \ y,y \ x,z) = x \ y. [para(2538(a,1),74(a,1,1)),rewrite([14(7),1091(6),2538(6)])]. 4151 a(x,y \ z,z \ y) = 1. [para(2538(a,1),1012(a,1,2))]. 4155 x / (y \ z) = x * (z \ y). [para(2538(a,1),1013(a,1,2))]. 4157 (x * y) \ ((x / z) * (z * y)) = a(x / z,z,y) \ 1. [para(60(a,1),2538(a,1,1)),flip(a)]. 4165 L(x,y \ z,z \ y) = x. [para(2538(a,1),3266(a,1,3))]. 4180 x * ((x \ (y / z)) * z) = R(y,z \ 1,x). [back_rewrite(2806),rewrite([4155(4),169(4)])]. 4186 R(x,y,y \ ((y \ x) \ z)) = z * ((z \ y) * (y \ x)). [back_rewrite(199),rewrite([4155(8),169(8)])]. 4187 a(x / y,y,y) \ 1 = a(x,y \ 1,y * y). [back_rewrite(2604),rewrite([4157(5)])]. 4206 T((x / y) * (y * z),x * z) = a(x / y,y,z) \ (x * z). [para(60(a,1),2642(a,1,2)),rewrite([263(6)]),flip(a)]. 4209 T(x * y,x) = y * x. [para(1091(a,1),2642(a,1,2)),rewrite([2774(4)]),flip(a)]. 4210 T(x,(y \ x) * y) = x. [para(64(a,1),2642(a,1,2)),rewrite([3304(3)]),flip(a)]. 4230 (x / y) * x = x * (y \ x). [para(2643(a,1),90(a,1,2)),flip(a)]. 4247 (x * (y \ x)) * z = x * (y \ (x * z)). [back_rewrite(4115),rewrite([4230(2)])]. 4254 (x / y) * ((x / y) * ((y * z) / T(x * (y \ x),z))) = z. [back_rewrite(2009),rewrite([4230(5)])]. 4278 T(x,y) \ y = T(x \ y,y). [para(2649(a,1),2642(a,1,2)),rewrite([2709(3)])]. 4281 T(x \ y,T(x,y)) = T(x \ y,y). [back_rewrite(2709),rewrite([4278(5)])]. 4314 T(x,y) * (T(x \ y,y) * (T(x,y) * z)) = (x * y) * z. [para(2690(a,1),186(a,2,1,1)),rewrite([4281(4),90(9)])]. 4335 a(x * (y \ z),z \ y,T(z,y)) = ((x * (y \ z)) * y) \ (x * T(z,y)). [para(2690(a,1),60(a,1,1,2)),rewrite([4155(2),4155(8)]),flip(a)]. 4344 (x \ y) * ((z * (x \ y)) * T(x,y)) = ((x \ y) * z) * y. [para(2690(a,1),189(a,1,2)),flip(a)]. 4357 (x \ (x \ y)) * T(x,y) = x \ y. [para(2642(a,1),2690(a,1,2))]. 4365 x / T(x,y) = T(x,y) \ x. [para(159(a,1),2711(a,1,2))]. 4366 T(x,y) / x = x \ T(x,y). [para(541(a,1),2711(a,1,2))]. 4379 ((x \ y) * x) / y = K(x \ y,x). [para(64(a,1),2711(a,2)),rewrite([4210(5)])]. 4407 (x * y) \ 1 = y \ (x \ 1). [para(2755(a,1),2538(a,1,1))]. 4408 (x \ y) \ z = (y \ x) * z. [para(2538(a,1),2755(a,1,1))]. 4417 ((x * y) * z) \ R(x,y,z) = z \ (y \ 1). [back_rewrite(4114),rewrite([4407(7)])]. 4419 ((x \ (y \ 1)) * y) \ (x \ 1) = a(x,x / y,y). [back_rewrite(4013),rewrite([4407(7)])]. 4420 x / (y * (y * (z * x))) = (y * z) \ (y \ 1). [back_rewrite(3725),rewrite([4407(8)])]. 4421 x / (y * (z * (y * x))) = (z * y) \ (y \ 1). [back_rewrite(3724),rewrite([4407(8)])]. 4445 L(L(x,y,z),u,x \ (u \ 1)) = L(x,y,z). [back_rewrite(3192),rewrite([4407(4)])]. 4458 ((x * y) * z) \ y = (y * z) \ (x \ y). [back_rewrite(2540),rewrite([4407(5),4408(4),14(4)]),flip(a)]. 4470 R(x,y,y \ ((x \ y) * z)) = z * ((z \ y) * (y \ x)). [back_rewrite(4186),rewrite([4408(2)])]. 4480 L(x \ (y * z),x,y) = (x \ y) * z. [back_rewrite(3941),rewrite([4408(5)])]. 4493 (x \ y) * (x / y) = K(x,y \ 1). [back_rewrite(3230),rewrite([4408(3)])]. 4498 (((x * y) * z) \ x) * (y * z) = a(x,x * y,z). [back_rewrite(3162),rewrite([4408(5)])]. 4501 (x * y) \ (x * (x * z)) = (y \ x) * z. [back_rewrite(3135),rewrite([4408(6)])]. 4504 (x \ y) * (((y \ x) * z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(2692),rewrite([4408(3)])]. 4505 (x \ y) * x = T(y,x). [back_rewrite(2649),rewrite([4408(2)])]. 4516 K(x \ y,x) = y \ T(y,x). [back_rewrite(4379),rewrite([4505(2),4366(2)]),flip(a)]. 4525 x * (T(y,x) * z) = y * (x * z). [back_rewrite(2965),rewrite([4505(2)])]. 4535 x * K(y \ x,y) = T(x,y). [back_rewrite(2852),rewrite([4505(5)])]. 4537 a(T(x,y),y \ x,z) = a(y \ x,x,z). [back_rewrite(1702),rewrite([4505(2)])]. 4539 K(x,x \ y) = T(y,x) \ y. [back_rewrite(65),rewrite([4505(2)]),flip(a)]. 4559 (T(x,y) * (y * (z * (x * y)))) * u = T(x,y) * (y * (z * (x * (y * u)))). [back_rewrite(2234),rewrite([4525(4)]),flip(a)]. 4562 ((x * y) * y) / z = x * (y * (y / z)). [back_rewrite(1859),rewrite([4525(4)]),flip(a)]. 4578 (x * y) * y = x * (y * y). [back_rewrite(669),rewrite([4525(3)]),flip(a)]. 4581 L(x,T(y,z),z) = L(x,z,y). [back_rewrite(512),rewrite([4525(4),21(4)]),flip(a)]. 4582 a(x,T(y,x),z) = a(y,x,z). [back_rewrite(508),rewrite([4525(3),19(5)]),flip(a)]. 4583 R(x * y,y,y \ z) = (x * (y * z)) / z. [back_rewrite(204),rewrite([4525(6)])]. 4596 ((T(x,y) * (y / z)) * y) \ ((x * (y * y)) / z) = K(y,T(x,y) * (y / z)). [back_rewrite(1864),rewrite([4578(6)])]. 4613 (x * (y * y)) / z = x * (y * (y / z)). [back_rewrite(4562),rewrite([4578(2)])]. 4636 a(x * (y * (x * x)),z,u) = a(x * y,x * (x * z),u). [back_rewrite(3762),rewrite([4578(2)])]. 4713 x / (T(T(y,z),u) * (z * ((T(y,u) * (z * z)) \ x))) = z. [back_rewrite(2166),rewrite([4578(5)])]. 4714 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w))) = w. [back_rewrite(2032),rewrite([4578(8),2040(9)])]. 4778 (x * ((T(y,x) * (x * z)) * u)) \ ((y * (x * (x * z))) * u) = a(x,T(y,x) * (x * z),u). [back_rewrite(674),rewrite([4578(7),2040(8)])]. 4795 a(x * y,y,z) \ 1 = a(x,y,y * z). [back_rewrite(2574),rewrite([4582(3)]),flip(a)]. 4809 ((T(x,y) * (y / z)) * y) \ (x * (y * (y / z))) = K(y,T(x,y) * (y / z)). [back_rewrite(4596),rewrite([4613(7)])]. 4813 (x / y) * (y * (y / T(x * y,a(x,y \ 1,y * y)))) = a(x,y \ 1,y * y). [back_rewrite(2599),rewrite([4613(10)])]. 4993 K(x,y) * K(y,x) = 1. [para(2917(a,1),16(a,1,2))]. 4996 R(x,K(y,z),K(z,y)) = x. [para(2917(a,1),191(a,2,3)),rewrite([14(5),16(4),48(2)]),flip(a)]. 5005 x / K(y,z) = x * K(z,y). [para(2917(a,1),1014(a,1,2)),flip(a)]. 5011 L(x,K(y,z),K(z,y)) = x. [para(2917(a,1),3266(a,1,3))]. 5067 T(x,y * (x / y)) = x. [para(66(a,1),2642(a,1,2)),rewrite([3305(3)]),flip(a)]. 5116 (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). [para(63(a,1),72(a,1,1))]. 5129 x * L(y,T(z,x),z \ x) = (z \ x) * (T(z,x) * y). [para(2690(a,1),72(a,1,1))]. 5134 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(15(a,1),3940(a,1,1)),flip(a)]. 5138 L(T(x,y * z),y * z,y) = z \ (y \ (x * (y * z))). [para(23(a,1),3940(a,1,1))]. 5147 L((x * y) \ z,y,y * x) = T(x,y) \ (y \ z). [para(90(a,1),3940(a,1,1,1)),rewrite([90(4),2975(4)])]. 5152 K(x * (y / x),x) = K(x \ 1,y). [para(67(a,1),3940(a,1,1)),rewrite([666(5),3231(6)])]. 5155 L((x / y) \ z,x / y,x) = y * (x \ z). [para(1014(a,1),3940(a,1,1,1)),rewrite([1014(5),4408(8),45(6)])]. 5162 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(3940(a,1),2254(a,1)),rewrite([3436(2),100(5)]),flip(a)]. 5163 L((x * y) \ z,x * y,y * x) = K(x,y) \ ((y * x) \ z). [para(63(a,1),3940(a,1,1,1)),rewrite([63(5)])]. 5194 R(x,y * (y * z),z \ (y \ (y \ u))) = R(x,z,z \ u). [back_rewrite(1870),rewrite([5162(3),191(6),1935(6),16(3),16(2),5162(7)]),flip(a)]. 5200 x * (x * (y * ((y \ (x \ (x \ z))) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [back_rewrite(411),rewrite([5162(3)])]. 5208 (x * (y \ z)) * (z \ y) = x. [para(4151(a,1),209(a,1,1)),rewrite([45(6),4137(7),14(6),4151(7),88(6)])]. 5332 a(x,y,y) = 1. [para(89(a,1),507(a,1,2,2)),rewrite([4578(4),46(5),89(2)]),flip(a)]. 5337 (x * (y * (z * u))) \ (x * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),y * (z * u),x). [para(507(a,1),74(a,1,1)),flip(a)]. 5358 a(x,y \ 1,y * y) = 1. [back_rewrite(4187),rewrite([5332(2),46(3)]),flip(a)]. 5359 (x / y) * (y / x) = 1. [back_rewrite(4813),rewrite([5358(6),88(4),3691(3),1014(4),5358(7)])]. 5364 (x * y) / T(z * (z * y),T(x,y)) = z \ (z \ T(x,y)). [para(1921(a,1),21(a,1,2)),rewrite([3436(3),1607(10)]),flip(a)]. 5428 x * (x * (y / (T(z * z,x) * (x * y)))) = z \ (z \ x). [para(2640(a,1),21(a,1,2)),rewrite([3436(2),1607(10)]),flip(a)]. 5444 L(x,y \ (y \ z),y) = L(x,z,y). [para(2640(a,1),132(a,1,1,2)),rewrite([5428(8),136(6),16(3),21(4),5428(8),2507(6)]),flip(a)]. 5452 x * (x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u))))))) = y * z. [para(189(a,1),2640(a,1,2,2,2,2,2,2))]. 5468 T(x * (x * y),y \ z) = T(x * (x * y),x * (x * z)). [para(16(a,1),2647(a,1,2,2,2)),flip(a)]. 5480 T(x * (x * y),x * (x * (y / z))) = T(x * (x * y),z \ 1). [para(1014(a,1),2647(a,1,2,2,2))]. 5569 (((x \ y) * z) * x) \ ((z * (y \ x)) * T(y,x)) = T(y \ x,(z * (y \ x)) * T(y,x)). [para(2690(a,1),2713(a,1,1,2)),rewrite([4408(2)])]. 5610 (x \ (y \ (y \ (z \ 1)))) * (z * (y * (y * (x * u)))) = L(u,y * (y * x),z). [para(37(a,1),145(a,1,1)),rewrite([37(11),4501(12),1091(5),4407(5),5162(5),2507(15)])]. 5614 L(x,y * (y * z),z) = x. [para(1607(a,1),145(a,2)),rewrite([189(5),101(2),189(4),4578(2),101(3),100(2),189(11),101(7),189(10),4578(7),189(9),100(7),37(8),4501(12),1091(5),4407(5),5162(5),5610(10)])]. 5657 x * (y * (x * (z * ((z * (x * (y * (x * z)))) \ u)))) = z \ u. [para(2215(a,1),15(a,1,2)),flip(a)]. 5665 R(x,y,y \ ((x \ y) * z)) = (y * z) / ((x \ y) * z). [para(2215(a,1),191(a,1,1,2)),rewrite([5657(13),4408(3),5657(16),4408(6)]),flip(a)]. 5816 R(x * ((x \ y) * (y \ z)),z,z \ u) = (z * (a(y,x,x \ (y \ z)) * u)) / u. [para(16(a,1),435(a,1,2)),rewrite([16(6),16(8)])]. 5817 (x * (a(x / y,z,z \ y) * u)) / u = R(x,y \ 1,z). [para(18(a,1),435(a,1,2)),rewrite([4180(4),18(5),495(5),18(5)]),flip(a)]. 5841 R(x * ((x \ (y \ z)) * T(y,z)),z,z \ u) = (z * (a(y \ z,x,x \ T(y,z)) * u)) / u. [para(2690(a,1),435(a,1,2)),rewrite([2690(8),2690(10)])]. 5879 x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))) = z. [para(463(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 5885 (x \ (y \ 1)) * (y * (x * z)) = L(z,x,y). [para(463(a,1),132(a,1,1,2)),rewrite([5879(13),4501(8),1091(3),4407(3),5879(16),2507(9)])]. 5921 a(x,T(y,x) * x,z) = a(y,x,x * z) \ 1. [para(14(a,1),4778(a,1,1,2,1,2)),rewrite([2993(4),14(5),2040(6),2548(7),14(7)]),flip(a)]. 6018 L(x,x,y) = x. [hyper(24,a,5332,a)]. 6022 L(L(x,y,z),x,u) = L(x,y,z). [para(6018(a,1),34(a,1,1)),flip(a)]. 6068 ((x * y) \ z) * ((z \ x) * y) = a(z \ 1,x,y). [para(3143(a,1),19(a,1,1)),rewrite([3143(5),4408(5)])]. 6069 (x \ (y \ 1)) * (x * y) = K(x,y). [para(20(a,1),3143(a,2)),rewrite([4407(3)])]. 6070 (x \ y) * (y \ (x * z)) = L(z,x,y \ 1). [para(3143(a,1),21(a,1,1)),rewrite([3143(5),4408(4)])]. 6071 ((x \ y) * z) / (y * z) = R(x \ 1,y,z). [para(3143(a,1),22(a,1,1,1))]. 6072 T(x \ 1,y) = y \ (x \ y). [para(3143(a,1),23(a,1,2)),flip(a)]. 6073 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [para(3143(a,1),37(a,1,1,2)),rewrite([3143(4),3143(9),3143(8)]),flip(a)]. 6120 (x \ 1) / y = x \ (y \ 1). [para(3143(a,1),1014(a,1)),flip(a)]. 6132 (x \ (y \ 1)) * y = x \ 1. [para(1091(a,1),3143(a,2)),rewrite([4407(3)])]. 6134 T(x \ 1,x \ y) = T(x \ 1,y). [para(3143(a,1),1708(a,1,2))]. 6141 ((x * y) \ (z \ (z \ (u \ 1)))) * ((u * (z * (z * x))) * y) = a(u,z * (z * x),y). [para(139(a,1),3143(a,2)),rewrite([4407(6),5162(6)])]. 6144 K(x,y) \ z = K(y,x) * z. [para(2917(a,1),3143(a,1,1)),flip(a)]. 6145 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(3143(a,1),72(a,1,1)),rewrite([3143(9)])]. 6149 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(z \ 1,y,T(x,y)). [para(3143(a,1),507(a,1,1)),rewrite([3143(5),4408(6)])]. 6185 (x \ (y \ 1)) * T(z,x / y) = (x \ (x \ z)) * (x / y). [back_rewrite(3709),rewrite([6073(4)]),flip(a)]. 6188 x \ T(y,z * (z / x)) = (z \ (z \ y)) * (z * (z / x)). [back_rewrite(3482),rewrite([6073(9)])]. 6233 a(x,x / y,y) = 1. [back_rewrite(4419),rewrite([6132(4),46(5)]),flip(a)]. 6238 L((x * y) \ z,x * y,y * x) = K(y,x) * ((y * x) \ z). [back_rewrite(5163),rewrite([6144(9)])]. 6257 L(x,y / x,y) = x. [hyper(24,a,6233,a)]. 6258 a(x * y,x,y) = 1. [para(17(a,1),6233(a,1,2))]. 6279 L(x,y,y * x) = x. [para(17(a,1),6257(a,1,2))]. 6335 a(x,y,y \ x) = 1. [para(16(a,1),6258(a,1,1))]. 6351 x * ((x \ y) * y) = y * y. [para(6258(a,1),435(a,2,1,2,1)),rewrite([16(2),16(5),16(6),3436(6),2044(7),16(5),13(6),100(5),1839(6),47(4),14(5)])]. 6353 (x \ y) * ((y \ x) * z) = L(z,(y \ x) * x,y). [back_rewrite(831),rewrite([6351(3),3436(6),6073(6),15(2)])]. 6368 L(x \ y,x,y) = x \ y. [para(16(a,1),6279(a,1,3))]. 6416 L(x,y \ 1,y \ x) = x. [para(3143(a,1),6279(a,1,3))]. 6438 a((x * y) * T(z,y),x * (z * y),a(x,y,T(z,y))) = 1. [para(507(a,1),6335(a,1,3))]. 6557 K(K(L(x,y,z),z * y),z * (y * x)) = 1. [para(72(a,1),3327(a,1,2))]. 6562 K(x,y) / (x * y) = x \ (y \ 1). [para(20(a,1),3666(a,1,1)),rewrite([4407(6)])]. 6564 T(x,y) / (x * y) = y \ 1. [para(23(a,1),3666(a,1,1))]. 6565 (x / y) \ 1 = y / x. [para(50(a,1),3666(a,1,1)),flip(a)]. 6591 L(x,y,z) \ (y \ (z \ 1)) = (y * x) \ (z \ 1). [para(2934(a,1),3666(a,1,1)),rewrite([6562(7),4407(4),4407(9)])]. 6618 L(x,y \ 1,z * y) = L(x,y \ z,y). [para(73(a,1),181(a,2)),rewrite([1091(2),3143(3),16(2),1091(4)]),flip(a)]. 6634 L(x,y * z,y \ 1) = L(x,y * z,y). [para(3143(a,1),73(a,1,2)),rewrite([4408(3),45(2),5134(4),4408(5),45(4)]),flip(a)]. 6663 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,u,w),y,z))) \ (v6 * v5). [para(76(a,1),228(a,1)),flip(a)]. 6676 L(x,y \ (x \ 1),z) = (z * (y \ (x \ 1))) \ (z / y). [para(1014(a,1),76(a,2,2)),rewrite([6120(3),6120(7)])]. 6694 T(x * (y / z),L(z,y / z,x)) = T(x * (y / z),x * y). [para(76(a,2),2642(a,1,2))]. 6696 L(x,T(y,z) / x,y \ z) = ((y \ z) * (T(y,z) / x)) \ z. [para(2690(a,1),76(a,2,2))]. 6707 L(x,y / x,z \ 1) = ((y / x) \ z) * (z \ y). [para(3143(a,1),76(a,2,1)),rewrite([3143(9),4408(8)])]. 6793 L(L(R(x,y,z),u,w),v5,x \ (v5 \ 1)) = L(R(x,y,z),u,w). [para(4445(a,1),33(a,1,1)),rewrite([33(2),33(4)]),flip(a)]. 6878 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(y * (x \ y),y \ 1). [para(1014(a,1),2757(a,1,2)),rewrite([6120(3),3143(10)])]. 6887 L(K(x * (y * x),x \ 1),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [para(2757(a,1),3940(a,1,1)),rewrite([3436(15)])]. 6890 K(x * (y * x),x \ 1) = K(x,y). [para(2757(a,1),3143(a,2)),rewrite([4407(5),6565(4),3436(3),1829(2),6069(5)]),flip(a)]. 6897 L(K(x,y),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [back_rewrite(6887),rewrite([6890(5)])]. 6946 T(x * (x * (y / (x * z))),x * z) = (z \ x) * y. [para(16(a,1),3139(a,1,1,2,2,2,2)),rewrite([16(6),4408(8)])]. 6953 (x \ ((y * z) \ (y \ 1))) * u = (z * x) \ (y \ (y \ u)). [para(341(a,1),3139(a,1,1,2,2,2,2)),rewrite([341(27),6946(26),4417(8),4407(4),5162(10)])]. 6955 ((x * y) \ y) * z = T(x,y) \ z. [para(90(a,1),3139(a,1,1,2,2,2,2)),rewrite([90(7),6946(8)])]. 6968 (x \ (y \ x)) * z = T(y,x) \ z. [para(2690(a,1),3139(a,1,1,2,2,2,2)),rewrite([2690(11),6946(10)])]. 7004 x * (y \ ((x * (x / y)) \ z)) = x \ z. [para(18(a,1),3218(a,2,2)),rewrite([92(6)])]. 7047 T(x,K((y \ z) * (y * ((z * y) \ x)),y)) = x. [para(16(a,1),3307(a,1,1)),rewrite([16(11)])]. 7262 T(x,y) * (y * ((z / (x * y)) * (x * (y * u)))) = (T(x,y) * (y * z)) * u. [para(18(a,1),4559(a,1,1,2,2)),flip(a)]. 7412 a(x / (y * y),y,y * z) = (x * z) \ (y \ ((y * x) * z)). [para(7262(a,1),110(a,1,1)),rewrite([89(1),37(3),89(4),189(10),101(8),4578(7),18(7),5162(7),15(5),89(6),3982(11),4795(11)]),flip(a)]. 7488 x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u)))))) = x \ (y * z). [para(5452(a,1),15(a,1,2)),flip(a)]. 7490 (x * y) * ((x * y) * ((x * z) / (T(u * u,x * y) * (x * ((y * x) * z))))) = (u \ (u \ x)) * y. [para(5452(a,1),21(a,1,2)),rewrite([3436(3),6073(3),1607(17)]),flip(a)]. 7495 x * (x * (((x \ (x \ y)) * z) * u)) = (y * z) * u. [para(5452(a,1),37(a,1,1)),rewrite([7490(15)]),flip(a)]. 7513 L(x,(y \ (y \ z)) * u,y) = L(x,z * u,y). [para(5452(a,1),132(a,1,1,2)),rewrite([7490(15),7495(8),21(6),7490(15),2507(8)]),flip(a)]. 7550 x * ((x \ (x \ y)) * z) = x \ (y * z). [back_rewrite(7488),rewrite([7490(13)])]. 7607 a(x / y,y,z) \ 1 = a(x,y \ 1,y * z). [para(3691(a,1),58(a,1,2,1,2)),rewrite([1014(4),4157(5),3691(6)])]. 7616 T(x,y) / y = y \ x. [para(2690(a,1),3691(a,1,2)),rewrite([4408(5),14(5)])]. 7617 T(x,y) * (y \ x) = (y \ x) * x. [para(4357(a,1),3691(a,1,2)),rewrite([4155(3),4408(7),4408(5),14(7)])]. 7622 x * ((y * x) \ T(z,x / y)) = x \ (z * (x / y)). [para(3691(a,1),3218(a,1,2,2,2,2)),rewrite([1014(4),3691(7),1014(8)])]. 7628 (x * y) \ ((x / z) * (z * y)) = a(x,z \ 1,z * y). [back_rewrite(4157),rewrite([7607(9)])]. 7656 L(x,(y \ z) * z,y) = x. [para(4137(a,1),21(a,1,1)),rewrite([6353(5),45(5),4165(6)])]. 7662 K(x \ y,(y \ x) * (z * (y \ x))) = K(z,y \ x). [para(4137(a,1),114(a,1,1,2,2)),rewrite([14(3),6353(8),7656(7),20(5)]),flip(a)]. 7679 L(x,y \ z,(z \ y) * (u * (z \ y))) = L(x,u,z \ y). [para(4137(a,1),132(a,1,1,2,2)),rewrite([14(3),6353(7),7656(6),21(6)]),flip(a)]. 7681 (x \ y) * (z * (y \ x)) = T(z,y \ x). [para(4137(a,1),1359(a,1,2,2,2,2)),rewrite([14(5),90(5),4137(9),14(8),23(8)])]. 7682 a((x \ y) * (z * (x \ y)),y \ x,u) = a(x \ y,z,u). [para(4137(a,1),133(a,1,2,1,2,2)),rewrite([6353(5),7656(4),14(6),19(7)]),flip(a)]. 7707 K(K(x \ y,z * (y \ x)),z) = 1. [para(4137(a,1),6557(a,1,2,2)),rewrite([4145(3),14(6)])]. 7713 K(x \ y,(y \ x) * z) = K(x \ y,z). [para(4137(a,1),177(a,1,1,1,2)),rewrite([4408(2),14(4),5208(8),4458(5),4408(4),20(5),4408(5),4137(8),14(7)]),flip(a)]. 7715 (x \ y) * ((y \ x) * z) = z. [back_rewrite(6353),rewrite([7656(7)])]. 7719 K(x \ y,z * (y \ x)) = K(z,y \ x). [back_rewrite(7662),rewrite([7713(6)])]. 7726 K(K(x,y \ z),x) = 1. [back_rewrite(7707),rewrite([7719(4)])]. 7769 T(T(x,y),y \ x) = x. [para(16(a,1),4209(a,2)),rewrite([4505(2)])]. 7772 ((x \ y) * (x * z)) * x = T((y * x) * z,x). [para(104(a,1),4209(a,1,1)),flip(a)]. 7775 T(x,y) * y = T(x * y,y). [para(90(a,1),4209(a,1,1)),flip(a)]. 7789 T(x,y) * (x \ y) = T(y,x \ y). [para(2690(a,1),4209(a,1,1)),flip(a)]. 7820 K((x \ y) * (x * z),x) = K(x * ((y * x) * z),x). [back_rewrite(3323),rewrite([7772(4),4366(6),3934(6,R)]),flip(a)]. 7826 x * K(y * x,y) = T(x,y). [back_rewrite(874),rewrite([7820(6),16(4),7772(9),16(7)])]. 7836 a(x,y,y * z) \ 1 = a(x * y,y,z). [back_rewrite(5921),rewrite([7775(2),4582(3)]),flip(a)]. 7875 K(x,x * (y * x)) = K(x,T(y,x)). [back_rewrite(511),rewrite([7775(2),3935(4,R)])]. 7925 T(x,K(y * x,y)) = x. [back_rewrite(7047),rewrite([7820(6),16(4)])]. 7966 ((x * (y \ z)) * y) / T(z,y) = R(x,y \ z,y). [para(4505(a,1),22(a,1,2))]. 7967 x \ T(y,x) = T(x \ y,x). [para(4505(a,1),23(a,1,2))]. 7969 (x \ y) * (((y \ x) * z) * T(y,x)) = (z * (x \ y)) * x. [para(4505(a,1),104(a,1,2,2)),rewrite([4408(3)])]. 7981 L(x \ y,x,x \ z) = T(z,x) \ ((x \ z) * y). [para(4505(a,1),74(a,2,1))]. 7997 (x \ y) * (T(x,y) * z) = L(y * z,x,y). [para(4505(a,1),181(a,2,2,1)),rewrite([5444(4),4408(6)]),flip(a)]. 8002 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = R((y * (z * y)) \ x,y * (z * y),u). [para(4505(a,1),121(a,1,1,1))]. 8018 T(x,y) \ (y \ x) = y \ 1. [para(4505(a,1),1091(a,1,1))]. 8020 (x \ y) * ((z * (x \ y)) * x) = ((x \ y) * z) * T(y,x). [para(4505(a,1),189(a,1,2)),flip(a)]. 8036 T(x * (x * (y \ z)),x * (x * T(z,y))) = T(x * (x * (y \ z)),y). [para(4505(a,1),2647(a,1,2,2,2))]. 8054 a(x \ y,y,x) = 1. [para(4505(a,1),6258(a,1,1)),rewrite([4537(3)])]. 8091 x * L(y,T(z,x),z \ x) = L(x * y,z,x). [back_rewrite(5129),rewrite([7997(8)])]. 8105 L(x,y,x \ y) = x. [hyper(24,a,8054,a)]. 8106 a(x,y * x,y) = 1. [para(15(a,1),8054(a,1,1))]. 8296 K(x,y) * (K(y,x) * z) = z. [para(4993(a,1),21(a,1,1)),rewrite([45(6),5011(7)])]. 8298 (x * K(y,z)) * K(z,y) = x. [para(4993(a,1),22(a,1,2)),rewrite([48(6),4996(7)])]. 8308 L(x,K(y,z),K(z,y) * (u * K(z,y))) = L(x,u,K(z,y)). [para(4993(a,1),132(a,1,1,2,2)),rewrite([14(3),8296(7),21(6)]),flip(a)]. 8311 a(K(x,y) * (z * K(x,y)),K(y,x),u) = a(K(x,y),z,u). [para(4993(a,1),133(a,1,2,1,2,2)),rewrite([8296(5),14(6),19(7)]),flip(a)]. 8328 R(x,x \ y,y \ z) = z / ((x \ y) * (y \ z)). [para(16(a,1),81(a,2,1))]. 8379 R(x,x \ y,z) = z * ((z \ y) * (y \ x)). [para(81(a,2),1014(a,2)),rewrite([4407(5),4408(4),14(4),169(4)]),flip(a)]. 8393 (x * y) \ R(z,z \ x,y) = y \ (x \ z). [para(81(a,2),1829(a,1,2)),rewrite([4407(8),4408(7),14(7)])]. 8463 R(x,y \ 1,(x / y) \ z) = R(x,y \ 1,z). [para(1014(a,1),82(a,1,3,1)),rewrite([1014(10),3143(10),4155(9),4408(8),4180(9)])]. 8497 R(x,y,(x * y) \ T(z,y / x)) = T(z,y / x) * ((z * (y / x)) \ y). [para(3218(a,1),82(a,2,2)),rewrite([3691(3),1014(4),3691(7),1014(8),3691(9),1014(10),4155(11)])]. 8532 T(x,y) \ x = K(x \ y,x). [para(2642(a,1),4539(a,2,1)),rewrite([4408(3),7713(4)]),flip(a)]. 8534 K(x \ y,x) = K(y,y \ x). [para(4539(a,2),2711(a,2)),rewrite([159(2),4365(2),8532(2)])]. 8593 x / T(x,y) = K(x \ y,x). [back_rewrite(4365),rewrite([8532(4)])]. 8594 K(x \ y,x) = K(y,y * x). [back_rewrite(3935),rewrite([8532(4)]),flip(a)]. 8681 L(x,y,(z * y) * x) = L(x,y,R(z,y,x)). [para(22(a,1),3199(a,1,3)),flip(a)]. 8701 L(x \ y,x,z) = ((z / y) * x) \ z. [para(3199(a,1),74(a,1)),rewrite([16(4),16(6),18(6)])]. 8972 (x \ y) * (x * x) = T(x * y,x * x). [para(3476(a,1),13(a,1)),rewrite([14(3),14(6)])]. 8992 ((x \ y) * (x * (x * z))) / T(z,T(x * y,x * (x * z))) = T(x * y,x * (x * z)). [para(3476(a,1),165(a,1,1))]. 9001 T(x,(y \ z) * (y * (y * x))) = T(x,T(y * z,y * (y * x))). [para(3476(a,1),1708(a,1,2))]. 9031 ((x \ y) * z) * (y \ x) = T(z,y \ x). [para(4137(a,1),3476(a,1,2,2,2)),rewrite([14(6),4209(5),7681(4),4408(4),4137(8),14(7)]),flip(a)]. 9050 x * ((x * (y * x)) \ z) = y \ (x \ z). [para(18(a,1),3541(a,1,2,2)),rewrite([92(8)]),flip(a)]. 9085 x * a(y,z,z \ (y \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [back_rewrite(3093),rewrite([9050(4)])]. 9101 (x * (((y * z) * (z * y)) * u)) * a(x,(z * y) * (y * z),u) = (x * ((z * y) * (y * z))) * u. [para(178(a,1),312(a,1,1,2)),rewrite([3308(9),3308(14)])]. 9104 ((x * y) * (y * x)) * T(z,y * x) = (y * x) * (K(x,y) * (z * (y * x))). [para(90(a,1),178(a,1,2,2)),flip(a)]. 9114 ((x * ((y * z) * (z * y))) * u) / (((z * y) * (y * z)) * u) = R(x,(y * z) * (z * y),u). [para(178(a,1),121(a,1,2)),rewrite([3308(4),3308(14)])]. 9186 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,(y \ z) * (y * x),y). [para(179(a,1),3143(a,2)),rewrite([4407(4),4407(3)])]. 9191 x \ ((y \ z) * (((z \ y) * x) * u)) = L(u,(z \ y) * x,y \ z). [para(4137(a,1),179(a,1,1,1)),rewrite([13(2),4408(4),100(7),7715(6),4408(9),100(12),7715(11)])]. 9195 (T(x,y) * z) \ (y * (((y \ (y \ x)) * (y * z)) * u)) = L(u,x * (y * z),y). [para(4505(a,1),179(a,1,1,1)),rewrite([7513(14)])]. 9198 x \ (K(y,z) * ((K(z,y) * x) * u)) = L(u,K(z,y) * x,K(y,z)). [para(4993(a,1),179(a,1,1,1)),rewrite([13(2),6144(4),100(7),8296(6),6144(9),100(12),8296(11)])]. 9444 (x * ((x \ K(y,z)) * (K(z,y) * u))) \ u = a(x,x * K(y,z),K(z,y) * u). [para(4993(a,1),4025(a,1,1,2,2,2)),rewrite([6144(4),14(6),8298(10),6144(11),4993(14),14(13)])]. 9484 ((T(T(x,y),z) * (z * u)) * z) / (w * (w * ((T(T(x,z),y) * (z * u)) * z))) = w \ (w \ 1). [para(1907(a,1),21(a,1,2)),rewrite([3436(3),1607(17)]),flip(a)]. 9490 x \ (y * (x \ z)) = (x \ (y / x)) * z. [para(1907(a,1),129(a,1,1,2,2,2,2,2)),rewrite([9484(13),16(4),9484(15),16(6),9484(17),16(8),14(8),1014(7),3143(6),16(5),3143(4),9484(16),16(7),9484(18),16(9),9484(20),16(11),9484(22),16(13),3143(12),16(11),3143(10),3143(10),16(9),3143(8)]),flip(a)]. 9548 x * (x * (y * (x * (x * (y * (z \ ((y / z) \ (x \ (x \ (y \ 1)))))))))) = x * x. [para(14(a,1),3947(a,2,2)),rewrite([4407(6),5162(6)])]. 9559 L(x,y \ z,y) = L(x,y * z,y). [para(3947(a,1),132(a,1,1)),rewrite([5162(7),7004(9),16(6),16(5),136(6),21(6),5162(7),7004(9),16(6),16(5),2507(6)]),flip(a)]. 9719 L(x,y \ 1,z * y) = L(x,y * z,y). [back_rewrite(6618),rewrite([9559(6)])]. 9786 L(x * (y * z),x * y,x) = (x * y) * z. [back_rewrite(3018),rewrite([9559(4)])]. 9791 T(x,L(y * z,y * x,y)) = T(x,(x * y) * z). [back_rewrite(2700),rewrite([9559(3)])]. 9832 x \ (y * ((y \ x) * z)) = L(z,y * x,y). [back_rewrite(73),rewrite([9559(6)])]. 10000 (x / y) * ((y / x) * z) = L(z,y / x,x / y). [para(5359(a,1),21(a,1,1)),rewrite([45(6)])]. 10094 R(x,y,(x * y) \ z) * ((y * ((x * y) \ z)) / z) = 1. [para(82(a,2),5359(a,1,1))]. 10215 x / (y / z) = x * (z / y). [para(6565(a,1),1014(a,1,2)),flip(a)]. 10221 L(x,y / z,z / y) = x. [para(6565(a,1),3266(a,1,3))]. 10229 (x / y) \ z = (y / x) * z. [para(6565(a,1),3143(a,1,1)),flip(a)]. 10233 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(81(a,2),6565(a,1,1)),rewrite([6071(8)])]. 10235 R(x,y,(x * y) \ z) \ 1 = (y * ((x * y) \ z)) / z. [para(82(a,2),6565(a,1,1))]. 10279 ((x * y) / z) * (z / y) = R(x,y,z \ 1). [back_rewrite(1836),rewrite([10215(4)])]. 10287 (x / y) * ((y / x) * z) = z. [back_rewrite(10000),rewrite([10221(7)])]. 10296 x * (x * (y * (x * (x * (y * (z \ ((z / y) * (x \ (x \ (y \ 1)))))))))) = x * x. [back_rewrite(9548),rewrite([10229(6)])]. 10305 R(x,y \ 1,(y / x) * z) = R(x,y \ 1,z). [back_rewrite(8463),rewrite([10229(4)])]. 10321 L(K(x,y),(y / x) * (x * x),y / x) = x \ T(x,y). [back_rewrite(6897),rewrite([10229(9),3169(9),4505(8),15(9)])]. 10323 L(x,y / x,z \ 1) = R(x,y \ 1,z). [back_rewrite(6707),rewrite([10229(6),169(8),4180(8)])]. 10347 L((x / y) * z,y / x,y) = x * (y \ z). [back_rewrite(5155),rewrite([10229(2)])]. 10366 (x / y) * (x \ y) = K(x \ 1,y). [back_rewrite(3231),rewrite([10229(3)])]. 10367 (x / y) * (y * (x \ z)) = L(z,x \ 1,y). [back_rewrite(3229),rewrite([10229(4)])]. 10393 (x / y) * (((y / x) * z) * x) = (z * (x / y)) * y. [back_rewrite(171),rewrite([10229(3)])]. 10400 (x \ y) / x = x \ (y / x). [para(92(a,1),7616(a,1,1))]. 10401 T(x \ y,z) / x = x \ T(y / x,z). [para(537(a,1),7616(a,1,1))]. 10408 (x / (x * y)) * y = y * (x / (x * y)). [para(2810(a,1),7616(a,1,1)),rewrite([10215(3),10229(6)]),flip(a)]. 10537 R(x,y \ z,T(y,z)) * z = (x * (y \ z)) * T(y,z). [para(2690(a,1),84(a,1,2))]. 10562 R(x,y \ z,y) * T(z,y) = (x * (y \ z)) * y. [para(4505(a,1),84(a,1,2))]. 10592 R(T(x / y,y * z),y,z) = (y * z) \ (x * z). [para(85(a,2),92(a,1,1)),rewrite([31(4)])]. 10670 L(x,y,R(z / y,y,x)) = L(x,y,z * x). [para(85(a,2),3199(a,1,3))]. 10690 ((x / y) * z) \ x = (x * z) \ (x * y). [para(8701(a,1),21(a,2)),rewrite([16(3)]),flip(a)]. 10700 a(x / y,z,(x * z) \ (x * y)) = a(x,z,(x * z) \ (x * y)). [para(8701(a,2),57(a,1,1,2,2)),rewrite([10690(6),1105(6),10690(8)]),flip(a)]. 10702 K(x * (y / x),x / y) = K(x \ 1,y). [para(8701(a,2),67(a,1)),rewrite([10215(2),67(3),10215(4),666(5),5152(3),10215(5)]),flip(a)]. 10710 ((x \ y) * z) \ y = (y * z) \ (x * y). [para(2711(a,1),8701(a,2,1,1)),rewrite([659(3)]),flip(a)]. 10725 L(x \ (y * z),x,z) = (x \ y) * z. [para(3691(a,1),8701(a,2,1,1)),rewrite([3143(6),4408(5)])]. 10748 L(x,T(y,z) / x,y \ z) = (z * (T(y,z) / x)) \ (y * z). [back_rewrite(6696),rewrite([10710(9)])]. 10809 (x \ y) * (x * (x * z)) = T(y * x,x) * z. [para(7967(a,1),104(a,1,2,1)),rewrite([4525(5),7775(6)])]. 10885 T(x,T(y * z,y * (y * x))) = T(x,T(T(z * y,y),x)). [back_rewrite(9001),rewrite([10809(4),2652(4)]),flip(a)]. 10888 T(x * y,x * (x * z)) = T(T(y * x,x),z). [back_rewrite(8992),rewrite([10809(4),10885(8),965(8)]),flip(a)]. 10900 T((x \ y) * (z * z),T(y,x)) = T(z * (z * (x \ y)),x). [back_rewrite(8036),rewrite([10888(7),101(3),4209(4),4578(3)])]. 10920 T(x * (y * y),x / z) = T(y * (y * x),z \ 1). [back_rewrite(5480),rewrite([10888(6),101(2),4209(3),4578(2)])]. 10927 T(x * (x * y),y \ z) = T(y * (x * x),z). [back_rewrite(5468),rewrite([10888(9),101(6),4209(7),4578(6)])]. 11076 L(T(x * y,x * z),L(y \ z,y,x),u) = (u * L(y \ z,y,x)) \ (u * (x * z)). [para(2705(a,1),74(a,1,1))]. 11083 (x \ y) * (z * (z * x)) = T(y * (z * z),x). [para(2254(a,1),2705(a,1,1)),rewrite([100(3),4408(4),100(6),100(8),10888(9),101(6),4209(7),4578(6)])]. 11215 x * (((x \ y) / z) / T(x * y,z \ 1)) = x \ (z \ 1). [para(3640(a,1),15(a,1,2)),flip(a)]. 11218 K(x * y,x \ 1) = K(y,y \ (x \ 1)). [para(3640(a,1),20(a,1,2)),rewrite([11215(8),4505(4),8532(6),4408(3),45(2),11215(12)])]. 11219 ((x \ y) / z) / T(x * y,z \ 1) = x \ (x \ (z \ 1)). [para(3640(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 11253 R(x,x \ (y \ 1),y * z) = z / ((x \ (y \ 1)) * (y * z)). [para(3640(a,1),82(a,1,3,1)),rewrite([11219(7),16(5),4408(6),45(5),11219(12),16(10),11219(15),16(13),16(12),4408(11),45(10)])]. 11256 (x \ (K(y \ (x \ 1),y) / x)) * z = (x \ T(x \ 1,y)) * z. [para(3640(a,1),178(a,1,1)),rewrite([11219(9),16(7),11219(13),16(11),16(10),3143(9),3143(9),9490(7),11219(14),16(12),4505(11),11219(17),16(15),16(14),1014(13),10401(11),989(9)])]. 11276 x / T(y * (y * (x * z)),z \ 1) = y \ (y \ (z \ 1)). [para(3641(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 11295 x * (x * (x / T(x / y,y * (x * x)))) = y * (x * x). [para(3641(a,1),3641(a,1,2,2,2,1,2)),rewrite([1014(3),11276(8),4408(7),4408(5),4408(4),45(3),4578(3),14(5),11276(14),4408(13),4408(11),4408(10),45(9),4578(9),14(11)])]. 11597 L(K(x,y) * z,K(y,x),u) = (u * K(y,x)) \ (u * z). [para(4993(a,1),180(a,1,1,2)),rewrite([6144(2),14(4),8298(10)])]. 11625 R(x,(x \ (y / x)) * (x * z),u) = ((y * z) * u) / (((x \ (y / x)) * (x * z)) * u). [para(18(a,1),183(a,1,1,1,1)),flip(a)]. 11645 (((x \ y) * z) * u) / (((y \ (x \ 1)) * (y * z)) * u) = R(y,(y \ (x \ 1)) * (y * z),u). [para(3143(a,1),183(a,1,1,1,1))]. 11726 a((x \ y) / z,x,T(y,x) \ ((x \ y) * z)) = a(x \ y,x,T(y,x) \ ((x \ y) * z)). [para(4505(a,1),10700(a,1,3,1)),rewrite([4505(10)])]. 11853 L(x,(y \ z) * u,z \ y) = L(x,y \ z,u * (z \ y)). [para(4505(a,1),7679(a,1,3,2)),rewrite([90(5),4408(6)]),flip(a)]. 11861 x \ ((y \ z) * (((z \ y) * x) * u)) = L(u,z \ y,x * (y \ z)). [back_rewrite(9191),rewrite([11853(10)])]. 12076 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,y,z),u,w))) \ (v6 * v5). [para(34(a,1),6663(a,2,1,2,2))]. 12077 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = ((L(L(x,u,w),y,z) / v5) / v6) * (v6 * v5). [para(37(a,1),6663(a,2,1)),rewrite([2507(8),37(15),4501(16),1091(12),4407(12),10229(12),1014(12)])]. 12303 K(K(x,y),x) = 1. [para(15(a,1),7726(a,1,1,2))]. 12307 T(K(x,y),x) = K(x,y). [hyper(28,a,12303,a)]. 12308 K(x,y) * x = x * K(x,y). [para(12303(a,1),63(a,1,2)),rewrite([14(4)]),flip(a)]. 12309 K(x,K(x,y)) = 1. [para(12303(a,1),4993(a,1,1)),rewrite([13(4)])]. 12312 T(x,K(x,y)) = x. [hyper(28,a,12309,a)]. 12328 K(x,y) / x = x \ K(x,y). [para(12312(a,1),2711(a,1,2))]. 12349 K(x,y) * y = y * K(x,y). [para(12312(a,1),7616(a,1,1)),rewrite([5005(2),6144(4)]),flip(a)]. 12372 T(T(x,y),y \ 1) = x. [para(1091(a,1),7769(a,1,2)),rewrite([1708(2)])]. 12386 T(x,y / (y * x)) = x. [para(2810(a,1),7769(a,1,1)),rewrite([10229(3),10408(3),1708(4)])]. 12432 T(x,K(y,x)) = x. [para(12312(a,1),7769(a,1,1)),rewrite([6144(2),12349(2),1708(3)])]. 12473 K(x,y) / y = y \ K(x,y). [para(12432(a,1),2711(a,1,2))]. 12504 K(x,x * y) * T(y,x) = y. [para(7925(a,1),23(a,2)),rewrite([7826(5),6144(4)])]. 12698 T(T(K(x,y),z),x) = T(K(x,y),z). [para(12307(a,1),29(a,1,1)),flip(a)]. 12884 (x * R(y,z,(y * z) \ u)) * ((z * ((y * z) \ u)) / u) = x. [para(10094(a,1),104(a,1,2,2)),rewrite([14(9),16(8)]),flip(a)]. 12928 R(x,R(y,z,(y * z) \ u),(z * ((y * z) \ u)) / u) = x. [para(10094(a,1),84(a,1,2)),rewrite([14(10),12884(17)])]. 12931 x / R(y,z,(y * z) \ u) = x * ((z * ((y * z) \ u)) / u). [para(10094(a,1),85(a,2,2)),rewrite([12928(12),48(11)])]. 13457 L(x,(y \ z) * (y * u),y) = L(x,y * ((z * y) * u),y). [para(187(a,1),132(a,1,2,2)),rewrite([104(4),21(10),2507(10)]),flip(a)]. 13466 a(x,(x \ y) * (x * z),u) = a(x,x * ((y * x) * z),u). [para(187(a,1),133(a,1,1,2)),rewrite([104(9),37(10),4501(11),4498(9),2508(10)]),flip(a)]. 13523 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,y * ((z * y) * x),y). [back_rewrite(9186),rewrite([13457(14)])]. 13639 (x * (y \ z)) * ((z \ y) * u) = (y \ z) * (((z \ y) * x) * u). [para(4137(a,1),190(a,1,2,2)),rewrite([4408(4),14(6),4408(8),5208(12)])]. 13641 T(x,y) * ((y \ z) * (y * u)) = y \ (x * ((z * y) * u)). [para(4505(a,1),190(a,1,1)),rewrite([7550(11)])]. 13663 x / T(x / y,y * (x * x)) = T(y,x * x). [para(11295(a,1),21(a,1,2)),rewrite([23(4),1607(8)]),flip(a)]. 13687 ((x / y) * (z * (y * y))) \ (x * (y * T(z,y * y))) = a(x / y,y,y * T(z,y * y)). [para(11295(a,1),60(a,1,1,2)),rewrite([13663(9),13663(15)])]. 13709 L((x * (y * y)) \ z,x * (y * y),y) = (y * T(x,y * y)) \ (y \ z). [para(11295(a,1),3940(a,1,1,1)),rewrite([13663(8),777(7),13663(11)])]. 13734 x * (T(y,x * x) * x) = T(y * (x * x),x). [para(11295(a,1),4209(a,1,1)),rewrite([13663(8),101(7)]),flip(a)]. 13735 T(T(x * (y * y),y),y * T(x,y * y)) = x * (y * y). [para(11295(a,1),4209(a,2)),rewrite([13663(5),101(4),13734(4),13663(8)])]. 13884 L(x,y * (z * y),y) = L(x,y,z). [para(14(a,1),13523(a,1,2,2,1,2)),rewrite([45(5),4505(5),4525(6),5885(6),14(4)]),flip(a)]. 13929 L(x,(y \ z) * u,y \ z) = L(x,z \ y,u * (y \ z)). [para(4137(a,1),13523(a,1,2,2,1,2)),rewrite([4408(5),1014(5),1829(4),4408(5),14(7),3143(8),11861(6),5208(9)]),flip(a)]. 13932 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y) * u,K(z,y)). [para(4993(a,1),13523(a,1,2,2,1,2)),rewrite([6144(5),1014(5),1829(4),6144(5),14(7),3143(8),9198(6),8298(9)])]. 14083 (x / y) * (y * (x * T(x \ (x \ 1),x * x))) = 1. [para(996(a,1),13687(a,2,3,2)),rewrite([3436(4),8972(6),16(4),87(4),14(3),3436(4),10229(9),3436(13),16(14),1072(13)])]. 14102 T(x,T(x,y) \ 1) = x. [para(541(a,1),12372(a,1,1))]. 14123 T(x,(y / x) / y) = x. [para(5067(a,1),12372(a,1,1)),rewrite([4407(4),10229(4),1014(4)])]. 14154 K(x,y / (y * x)) = 1. [hyper(27,a,12386,a)]. 14430 T(x,y) * K(x \ y,x) = x. [para(14102(a,1),23(a,2)),rewrite([1014(7),8593(5),4408(6),45(3)])]. 14495 T(x,(T(T(T(y,z),u),x \ 1) / x) / T(T(T(y,x \ 1),z),u)) = x. [para(3382(a,1),14123(a,1,2,1))]. 14546 K(x \ y,x / y) = 1. [para(16(a,1),14154(a,1,2,2))]. 14868 (x * x) / y = x * (x / y). [para(100(a,1),1014(a,1)),rewrite([1014(3)]),flip(a)]. 14874 L(x,y * (y * z),u) = L(x,z,u * (y * y)). [para(100(a,1),132(a,1,1,2,2)),rewrite([100(5),100(9),100(11),4501(12),1091(5),4407(5),5162(5),5610(10),100(7),2507(8)])]. 14882 a(x * (y * y),z,u) = a(x,y * (y * z),u). [para(100(a,1),133(a,1,1,2,2)),rewrite([100(6),100(9),100(11),37(12),4501(13),1091(6),4407(6),5162(6),6141(11),100(7),2508(8)]),flip(a)]. 15035 L(x,y,y * (z * z)) = x. [back_rewrite(5614),rewrite([14874(3)])]. 15045 L(x,y * (z * (z * y)),u * (z * z)) = x. [back_rewrite(2522),rewrite([14874(6)])]. 15056 L(x * T(x \ (x \ 1),x * x),y,x) = x \ 1. [para(14083(a,1),21(a,1,2)),rewrite([18(2),3200(10)]),flip(a)]. 15120 L(x,y * ((y \ z) * T(z,y)),u * ((y \ z) * (y \ z))) = x. [para(4505(a,1),15045(a,1,2,2,2))]. 15137 K(T(x * y,y),y \ 1) = K(T(x,y) \ 1,x * y). [para(165(a,1),10702(a,1,1,2)),rewrite([7775(2),6564(5)])]. 15144 K(T(x,y),y \ (x \ 1)) = K(y,x). [para(3143(a,1),10702(a,1,1)),rewrite([4155(3),45(2),23(2),6120(4),4408(9),45(7),14(7)])]. 15149 K(T(x,y),y \ 1) = K(x \ y,x). [para(3666(a,1),10702(a,1,2)),rewrite([4155(3),16(3),4505(2),4408(7),14(7)])]. 15276 (x * y) / T(z * (x \ z),y) = (x / z) * ((x / z) * y). [para(4254(a,1),21(a,1,2)),rewrite([3436(4),10229(3),10229(4),1607(12)]),flip(a)]. 15308 a(x / y,(y / x) * ((y / x) * z),u) = a(x / y,z,u). [para(4254(a,1),133(a,1,2,1,2)),rewrite([15276(8),37(8),10287(9),10287(6),19(7),15276(12),2508(12)]),flip(a)]. 15452 x \ (y * (y * z)) = ((x \ y) * y) * z. [para(7769(a,1),4314(a,1,1)),rewrite([8018(3),6134(4),7769(6),4525(6),3143(5),7617(6)])]. 15593 a(x \ y,z * (x \ y),T(x,y)) = a(x \ y,z,y) \ 1. [para(4344(a,1),19(a,1,1)),rewrite([128(9),2690(7),2548(7)]),flip(a)]. 15622 T(x \ y,(z * (x \ y)) * T(x,y)) = T(x \ y,((x \ y) * z) * y). [para(4344(a,1),1708(a,1,2)),flip(a)]. 15674 (((x \ y) * z) * x) \ ((z * (y \ x)) * T(y,x)) = T(y \ x,((y \ x) * z) * x). [back_rewrite(5569),rewrite([15622(14)])]. 15916 x \ ((x * y) * z) = (y / x) * (x * z). [para(15(a,1),4504(a,1,2,1,1)),rewrite([1091(2),3143(5),1091(5),1014(6),4209(6)])]. 15922 L(x,x \ y,z * (y \ x)) = ((y \ x) / z) * (z * T(y,x)). [para(4504(a,1),21(a,1,2)),rewrite([7715(4),15916(5),11853(9)]),flip(a)]. 15924 T(x \ y,((y \ x) * z) * y) = T(x \ y,((x \ y) * z) * y). [para(4504(a,1),23(a,1,2)),rewrite([15674(8)]),flip(a)]. 15928 T(x,y \ z) * T(y,z) = (z \ y) * (x * z). [para(37(a,1),4504(a,1,2)),rewrite([7715(7),9031(7)]),flip(a)]. 15940 ((x * (y \ z)) * T(y,z)) / T(y \ z,((z \ y) * x) * z) = ((z \ y) * x) * z. [para(4504(a,1),165(a,1,1))]. 15943 (x \ y) * (((y \ x) / z) * y) = (z \ (x \ y)) * T(x,y). [para(1014(a,1),4504(a,1,2,1)),rewrite([3143(9)])]. 15957 x * L(y,y \ z,x * (z \ y)) = (x * (z \ y)) * T(z,y). [para(4504(a,1),72(a,2)),rewrite([7715(4),11853(4)])]. 16096 a(x / (y * y),y,y * z) = a(x,y \ 1,y * z). [back_rewrite(7412),rewrite([15916(8),7628(9)])]. 16103 L(x,y * z,y) = L(x,y,z). [back_rewrite(5134),rewrite([15916(3),3276(4)]),flip(a)]. 16229 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y),u). [back_rewrite(13932),rewrite([16103(8)])]. 16231 L(x,y \ z,u * (z \ y)) = L(x,z \ y,u). [back_rewrite(13929),rewrite([16103(4)]),flip(a)]. 16256 L(x,y,z * y) = L(x,y,z). [back_rewrite(13884),rewrite([16103(3)])]. 16343 x \ T(x,y) = K(x,y). [back_rewrite(10321),rewrite([16103(6),2254(4)]),flip(a)]. 16348 x \ (y * ((y \ x) * z)) = L(z,y,x). [back_rewrite(9832),rewrite([16103(6)])]. 16362 T(x,L(y * z,y,x)) = T(x,(x * y) * z). [back_rewrite(9791),rewrite([16103(3)])]. 16364 L(x * (y * z),x,y) = (x * y) * z. [back_rewrite(9786),rewrite([16103(4)])]. 16398 L(x,y \ 1,z * y) = L(x,y,z). [back_rewrite(9719),rewrite([16103(6)])]. 16465 L(x,y \ z,y) = L(x,y,z). [back_rewrite(9559),rewrite([16103(4)])]. 16470 L(x,y * z,y \ 1) = L(x,y,z). [back_rewrite(6634),rewrite([16103(6)])]. 16484 x \ (y \ (z * (y * x))) = L(T(z,y * x),y,x). [back_rewrite(5138),rewrite([16103(4)]),flip(a)]. 16485 L((x * y) \ z,x,y) = y \ (x \ z). [back_rewrite(3940),rewrite([16103(4)])]. 16487 L(L(x,y,z),z,y) = x. [back_rewrite(667),rewrite([16103(3)])]. 16508 (x * (y \ z)) * T(y,z) = x * L(z,y \ z,x). [back_rewrite(15957),rewrite([16231(4)]),flip(a)]. 16509 ((x \ y) / z) * (z * T(x,y)) = L(y,x \ y,z). [back_rewrite(15922),rewrite([16231(4)]),flip(a)]. 16564 K(x \ y,x) = K(y,x). [back_rewrite(4516),rewrite([16343(4)])]. 16566 T(x,y) / x = K(x,y). [back_rewrite(4366),rewrite([16343(4)])]. 16569 K(x \ 1,y * x) = K(y,x). [back_rewrite(3171),rewrite([16343(6)])]. 16603 K(T(x,y),y \ 1) = K(y,x). [back_rewrite(15149),rewrite([16564(6)])]. 16623 T(x,y) * K(y,x) = x. [back_rewrite(14430),rewrite([16564(3)])]. 16660 (x \ (K(x \ 1,y) / x)) * z = (x \ T(x \ 1,y)) * z. [back_rewrite(11256),rewrite([16564(4)])]. 16686 K(x,x * y) = K(x,y). [back_rewrite(8594),rewrite([16564(2)]),flip(a)]. 16687 x / T(x,y) = K(y,x). [back_rewrite(8593),rewrite([16564(4)])]. 16710 K(x,x \ y) = K(x,y). [back_rewrite(8534),rewrite([16564(2)]),flip(a)]. 16711 T(x,y) \ x = K(y,x). [back_rewrite(8532),rewrite([16564(4)])]. 16716 x * K(x,y) = T(x,y). [back_rewrite(4535),rewrite([16564(2)])]. 16839 K(T(x,y) \ 1,x * y) = K(y,x * y). [back_rewrite(15137),rewrite([16603(5)]),flip(a)]. 16875 K(x,y) * T(y,x) = y. [back_rewrite(12504),rewrite([16686(2)])]. 16909 K(x,y * x) = K(x,T(y,x)). [back_rewrite(7875),rewrite([16686(3)])]. 16950 K(x * y,x \ 1) = K(y,x \ 1). [back_rewrite(11218),rewrite([16710(8)])]. 16967 K(x,y \ 1) = K(y,x / y). [back_rewrite(3163),rewrite([16710(3)]),flip(a)]. 16985 K(x,y) * x = T(x,y). [back_rewrite(12308),rewrite([16716(4)])]. 17019 K(T(x,y) \ 1,x * y) = K(y,T(x,y)). [back_rewrite(16839),rewrite([16909(7)])]. 17040 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(x \ y,y \ 1). [back_rewrite(6878),rewrite([16950(12)])]. 17093 (x \ y) * (((y \ x) * z) * ((z * (x \ y)) * u)) = z * (z * ((x \ y) * u)). [para(4137(a,1),193(a,2,1,2,1,1)),rewrite([4145(5),13639(8),13(10),37(12)])]. 17291 K(x,y \ 1) = K(x,x / y). [para(89(a,1),4809(a,1,1,1,1)),rewrite([101(3),4230(2),15452(7),1091(4),4407(4),4408(4),1014(4),10400(2),4505(3),92(2),4493(3),89(4),16686(6)])]. 17387 (x * T(y,x * x)) \ T(z,x) = ((y * (x * x)) \ z) * x. [para(23(a,1),13709(a,2,2)),rewrite([10725(7)]),flip(a)]. 17730 K(x \ 1,y) = K(x,y \ 1). [para(14546(a,1),63(a,1,2)),rewrite([10366(3),14(5),4493(6)])]. 17771 K(x,T(y,x)) = K(x,y). [back_rewrite(17019),rewrite([17730(5),4407(4),15144(5)]),flip(a)]. 17778 (x \ (x \ K(x,y \ 1))) * z = (x \ T(x \ 1,y)) * z. [back_rewrite(16660),rewrite([17730(3),12328(4)])]. 17781 K(x,y \ 1) = K(y,x). [back_rewrite(16569),rewrite([17730(4),4407(3),16710(4)])]. 17906 (x \ T(x \ 1,y)) * z = (x \ (x \ K(y,x))) * z. [back_rewrite(17778),rewrite([17781(3)]),flip(a)]. 17914 K(x,x / y) = K(y,x). [back_rewrite(17291),rewrite([17781(3)]),flip(a)]. 17919 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(y,x \ y). [back_rewrite(17040),rewrite([17781(11)])]. 17924 K(x,y / x) = K(x,y). [back_rewrite(16967),rewrite([17781(3)]),flip(a)]. 18156 x \ (y * (x / y)) = K(y,x). [back_rewrite(66),rewrite([17924(5)])]. 18454 L(x,y,x \ 1) = x. [para(1022(a,1),16487(a,1,1))]. 18472 L(x,x \ y,y) = x. [para(8105(a,1),16487(a,1,1))]. 18485 L(R(x,y,z),u,x \ 1) = R(x,y,z). [para(18454(a,1),33(a,1,1)),flip(a)]. 18604 a(x,y \ x,y) = 1. [hyper(25,a,18472,a)]. 18608 L(x,T(y,x),y * x) = x. [para(23(a,1),18472(a,1,2))]. 18689 (x * (y * x)) \ ((x * y) * z) = L(x \ z,x,x * y). [para(101(a,1),74(a,2,1)),flip(a)]. 18703 ((x / (y * z)) * (y * (z * y))) \ (x * y) = a(x / (y * z),y * z,y). [para(101(a,1),60(a,1,1,2))]. 18718 T(x * y,x * x) = T(y * x,x). [para(2690(a,1),101(a,2,2)),rewrite([7789(3),15928(4),8972(3),7775(5)])]. 18724 a(x * y,x,T(z,x)) = a(x,y,z * x) \ 1. [para(101(a,1),507(a,1,2,1)),rewrite([128(7),90(5),2548(7)]),flip(a)]. 18742 a(x,y,y * x) = 1. [para(101(a,1),8106(a,1,2)),rewrite([3982(4),4795(4)])]. 18750 R(x,y * z,y) * (y * (z * y)) = (x * (y * z)) * y. [para(101(a,1),84(a,1,2))]. 18752 R((x * y) / z,z,x) = (x * (y * x)) / (z * x). [para(101(a,1),85(a,2,1))]. 18763 a((x * y) / z,x,L(x \ z,x,x * y)) = a(x * y,x,L(x \ z,x,x * y)). [para(101(a,1),10700(a,1,3,1)),rewrite([18689(7),101(9),18689(12)])]. 18809 (x \ y) * (x * x) = T(y * x,x). [back_rewrite(8972),rewrite([18718(6)])]. 18870 (((x \ y) * z) * ((z * (y \ x)) * T(y,x))) / x = (x \ y) * (z * z). [para(4504(a,1),106(a,1,1,2)),rewrite([7715(14),4578(11)])]. 19065 x * T(x \ (x \ 1),x * x) = x \ 1. [para(15056(a,1),70(a,1)),flip(a)]. 19074 (x * y) / x = x * (y / x). [para(15056(a,1),72(a,1,2)),rewrite([1014(4),19065(8),1014(5)])]. 19167 a(x,(x / y) * ((x / y) * z),u) = a(y \ (x / y),z,u). [para(18(a,1),4636(a,2,1)),rewrite([3286(6),2508(5)]),flip(a)]. 19450 (x * ((T(y,z) * (x * x)) \ u)) \ (T(T(y,x),z) \ 1) = u \ x. [para(4713(a,1),1829(a,1,2)),rewrite([4407(11)]),flip(a)]. 19451 x / (T(T(y,z),u) * ((y \ z) * ((T(y,u) * ((y \ z) * (y \ z))) \ x))) = y \ z. [para(2642(a,1),4713(a,1,2,1,1))]. 19474 (x * (y * y)) \ z = y \ (y \ (x \ z)). [para(4713(a,1),3645(a,1,1)),rewrite([4407(12),19450(12),10927(4),2711(4),4407(13),19450(13)])]. 19479 x / (T(y,z) * ((y \ u) * (T(T(y,u),z) \ x))) = u \ y. [para(7769(a,1),4713(a,1,2,1,1)),rewrite([19474(9),4408(8),4408(9),7715(10)])]. 19486 x / (T(K(y,z),u) * (u \ (K(z,y) * x))) = u. [para(12307(a,1),4713(a,1,2,2,2,1,1)),rewrite([12698(3),19474(6),6144(4),6073(6),7550(7)])]. 19536 x / (T(T(y,z),u) * ((z \ y) * (T(y,u) \ x))) = y \ z. [back_rewrite(19451),rewrite([19474(9),4408(8),4408(9),7715(10)])]. 19567 K(x,y \ x) = K(y,x). [back_rewrite(17919),rewrite([19474(7),4408(5),4408(3),45(2),3032(3),19074(2),15(4),18156(3)]),flip(a)]. 19570 (x * T(y,x * x)) \ T(z,x) = T(x \ (y \ z),x). [back_rewrite(17387),rewrite([19474(8),4505(9)])]. 19639 (x * (y * (z * x))) \ (x * (z * (x * T(y,z * x)))) = a(x * z,x,T(y,z * x)). [para(90(a,1),196(a,1,1,2))]. 19660 (x * (y * (x * z))) \ (x * (y * (x * L(z,x,y)))) = a(x * y,x,L(z,x,y)). [para(72(a,1),196(a,1,1,2))]. 19674 a((x \ y) * z,x \ y,x) = a(x \ y,z,T(y,x)) \ 1. [para(4505(a,1),196(a,1,2,2,2)),rewrite([8020(5),2548(9)]),flip(a)]. 19707 R(x * y,y * x,(y * x) \ (K(y,x) * z)) = R(x * y,K(y,x),z). [para(16(a,1),202(a,2,1,2)),rewrite([6144(5),6144(11),2858(12)])]. 19771 T(x * (x / y),y) = y \ (x * x). [para(87(a,1),10900(a,1,2)),rewrite([3143(4),88(4),1014(5)]),flip(a)]. 19991 (x * (y * x)) / z = x * (y * (x / z)). [para(13(a,1),1851(a,1,1,2,2,2,2)),rewrite([14(4),13(4),13(4),989(8),1014(9),13(8),13(8),13(8)])]. 20016 R((x * y) / z,z,x) = x * (y / z). [back_rewrite(18752),rewrite([19991(7),3691(5),1014(6)])]. 20341 a(x * y,y,x) = 1. [para(15(a,1),18604(a,1,2))]. 20390 (x * y) * (y * x) = x * (y * (y * x)). [para(18742(a,1),209(a,1,1)),rewrite([45(5),18742(8),88(8)])]. 20504 ((x * (y * (z * (z * y)))) * u) / (z * (y * (y * (z * u)))) = R(x,y * (z * (z * y)),u). [back_rewrite(9114),rewrite([20390(3),20390(8),2213(9),20390(13)])]. 20509 (x * y) * (K(y,x) * (z * (x * y))) = y * (x * (x * (y * T(z,x * y)))). [back_rewrite(9104),rewrite([20390(3),2213(6)]),flip(a)]. 20510 (x * (y * (z * (z * (y * u))))) * a(x,z * (y * (y * z)),u) = (x * (z * (y * (y * z)))) * u. [back_rewrite(9101),rewrite([20390(3),2213(4),20390(8),20390(13)])]. 20551 a(x,y,x \ y) = 1. [para(2690(a,1),20341(a,1,1)),rewrite([4582(3)])]. 20692 a(x * (y * z),(x * y) * z,a(x,y,z)) = 1. [para(19(a,1),20551(a,1,3))]. 21062 T(x,y) * (x * z) = x * (T(x,y) * z). [para(16623(a,1),189(a,1,1)),rewrite([16875(7)]),flip(a)]. 21070 x * L(y,K(z,x),T(x,z)) = T(x,z) * (K(z,x) * y). [para(16623(a,1),72(a,1,1))]. 21447 x * (y \ ((y / x) * z)) = L(z,y / x,y). [para(16(a,1),10347(a,1,1)),rewrite([10229(4)]),flip(a)]. 21463 T(x,y) * ((x * y) \ z) = L(y \ z,y,x). [para(165(a,1),10347(a,1,2)),rewrite([6564(3),3143(3),16256(3)]),flip(a)]. 21472 L((x \ y) * z,y \ x,x) = T(y,x) * (x \ z). [para(2711(a,1),10347(a,1,2)),rewrite([7616(2)])]. 21504 L(K(x,y) * z,K(y,x),x) = T(x,y) * (x \ z). [para(16566(a,1),10347(a,1,1,1)),rewrite([16687(4)])]. 21507 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z / y,z))))) = x * x. [back_rewrite(10296),rewrite([21447(8)])]. 21510 R(x,y,(x * y) \ T(z,y / x)) = L(x,y / x,z). [back_rewrite(8497),rewrite([21463(11),10229(7),18(7)])]. 21704 R(x,y * (y * z),z \ ((y \ (y \ z)) * u)) = R(x,z,u). [para(15(a,1),5194(a,2,3)),rewrite([6073(5)])]. 21708 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * (u * w))) = R(x,z * u,L(w,u,z)). [para(21(a,1),5194(a,2,3)),rewrite([6073(8)])]. 21713 (x * (y * (y * z))) * (z \ (y \ (y \ u))) = z * ((z \ x) * u). [para(5194(a,1),341(a,1,1)),rewrite([16(6),16(5),16(4),200(3)]),flip(a)]. 21715 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * w)) = R(x,z * u,L(u \ w,u,z)). [para(74(a,2),5194(a,2,3)),rewrite([6073(7)])]. 21721 R(x,(y \ (y \ z)) * u,((y \ (y \ z)) * u) \ z) = R(x,z * u,u \ 1). [para(1091(a,1),5194(a,1,3)),rewrite([7550(4),16(3)]),flip(a)]. 21722 R(x,y * (z * (z * y)),K(y,z) * ((y * z) \ ((y * z) \ u))) = R(x,K(z,y),K(y,z) * u). [para(63(a,1),5194(a,1,2,2)),rewrite([20390(3),6144(9),6144(13)])]. 21734 (x * ((x \ ((y \ z) * z)) * (z \ (z \ u)))) / u = R(y \ 1,x,x \ u). [para(5194(a,1),6071(a,2)),rewrite([15452(3),169(7),37(13),16(11),16(10),16(9)])]. 22202 ((x \ y) * z) * ((z * (y \ x)) * u) = (x \ y) * (z * (z * ((y \ x) * u))). [para(17093(a,1),15(a,1,2)),rewrite([15452(6),4408(2),4578(3),2040(6)]),flip(a)]. 22250 x \ (y * (z * z)) = (x \ y) * (z * z). [back_rewrite(18870),rewrite([22202(7),2690(4),11083(4),7616(4)])]. 22270 x * T(y,x * x) = T(y * x,x). [back_rewrite(1323),rewrite([22250(3),18809(3)]),flip(a)]. 22283 T(x * y,y) \ T(z,y) = T(y \ (x \ z),y). [back_rewrite(19570),rewrite([22270(3)])]. 22354 T(T(x * (y * y),y),T(x * y,y)) = x * (y * y). [back_rewrite(13735),rewrite([22270(6)])]. 22398 x \ (y * y) = (x \ y) * y. [para(6257(a,1),6694(a,1,2)),rewrite([19771(3),18718(6),4230(4),4209(5)])]. 22947 R(x,K(x,y),T(x,y) \ z) = z / (K(x,y) * (T(x,y) \ z)). [para(16716(a,1),82(a,1,3,1)),rewrite([16716(7)])]. 23022 x \ (K(y,x) * (T(x,y) * z)) = L(z,T(x,y),K(y,x)). [para(16875(a,1),21(a,1,1))]. 23033 L(T(x,y) \ z,T(x,y),K(y,x)) = x \ (K(y,x) * z). [para(16875(a,1),74(a,2,1))]. 23108 T(x,y) \ (K(x,y) * (x * z)) = L(z,x,K(x,y)). [para(16985(a,1),21(a,1,1))]. 23380 T(x,T(y,x)) = T(x,y). [para(17771(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 23443 T(x,y * x) = T(x,y). [back_rewrite(2652),rewrite([23380(4)])]. 23494 a(x * y,x,z) = a(x,y * x,z). [para(128(a,1),19(a,1,2)),rewrite([196(7)])]. 23629 a(x \ y,z * (x \ y),x) = a(x \ y,z,T(y,x)) \ 1. [back_rewrite(19674),rewrite([23494(4)])]. 23643 (x * (y * (x * z))) \ (x * (y * (x * L(z,x,y)))) = a(x,y * x,L(z,x,y)). [back_rewrite(19660),rewrite([23494(11)])]. 23655 (x * (y * (z * x))) \ (x * (z * (x * T(y,z * x)))) = a(x,z * x,T(y,z * x)). [back_rewrite(19639),rewrite([23494(13)])]. 23662 a((x * y) / z,x,L(x \ z,x,x * y)) = a(x,y * x,L(x \ z,x,x * y)). [back_rewrite(18763),rewrite([23494(11)])]. 23663 a(x,y * x,T(z,x)) = a(x,y,z * x) \ 1. [back_rewrite(18724),rewrite([23494(3)])]. 23697 (x / y) * (y * z) = y * ((y \ x) * z). [para(136(a,1),15(a,1,2)),rewrite([15916(3)])]. 23717 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(136(a,1),74(a,2,1)),rewrite([16103(8),16485(7)])]. 23718 (x * y) \ ((x * z) * u) = (y \ x) * ((x \ z) * u). [para(136(a,1),74(a,2,2)),rewrite([4480(5)]),flip(a)]. 23926 x * ((x \ (y \ z)) * T(y,z)) = L(z,y \ z,x). [back_rewrite(16509),rewrite([23697(5)])]. 24002 x \ ((x * y) * z) = x * ((x \ y) * z). [back_rewrite(15916),rewrite([23697(6)])]. 24016 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = L(L(R(x,v5 \ 1,v6),u,w),y,z). [back_rewrite(12077),rewrite([23697(12),4180(12),33(11),33(10)])]. 24021 x * ((x \ y) * (y \ z)) = L(z,y \ 1,x). [back_rewrite(10367),rewrite([23697(4)])]. 24030 a(x,y \ 1,y * z) = a(x,y,y \ z). [back_rewrite(7628),rewrite([23697(4),192(5)]),flip(a)]. 24034 T(x * ((x \ y) * z),y * z) = a(y / x,x,z) \ (y * z). [back_rewrite(4206),rewrite([23697(3)])]. 24043 R(x,y \ 1,y * z) = R(x,y,y \ z). [back_rewrite(2760),rewrite([23697(3),191(4)]),flip(a)]. 24057 a(x / y,y,z) = a(y,y * x,z). [back_rewrite(60),rewrite([23697(3),4032(5)]),flip(a)]. 24100 L(x \ y,x,x * z) = T(z,x) \ ((x \ z) * y). [back_rewrite(18689),rewrite([23718(5),6955(5)]),flip(a)]. 24163 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,y * (y * (x / u)),u). [back_rewrite(3753),rewrite([23718(9),5162(3),15452(7)])]. 24164 (x \ (y \ (y \ z))) * (u * ((u \ ((z \ y) * y)) * x)) = a(z,y * (y * u),u \ x). [back_rewrite(3752),rewrite([23718(9),5162(3),15452(6),169(8)])]. 24189 a(x \ 1,y,z) = a(x,y,z). [back_rewrite(19),rewrite([23718(5),6068(5)])]. 24229 (x * (a(y \ x,z,z \ T(y,x)) * u)) / u = L(x,y \ x,z). [back_rewrite(5841),rewrite([23926(5),33(4),480(2)]),flip(a)]. 24261 (x * (y / L(L(z,u,w),v5,v6))) \ (x * y) = L(L(R(z,y \ 1,x),v5,v6),u,w). [back_rewrite(12076),rewrite([24016(6)]),flip(a)]. 24264 R(x,x \ y,z) = L(x,y \ 1,z). [back_rewrite(8379),rewrite([24021(6)])]. 24267 (x * (a(y,z,z \ (y \ x)) * u)) / u = L(x,y \ 1,z). [back_rewrite(5816),rewrite([24021(4),33(5),480(2)]),flip(a)]. 24268 R(x,y,y \ ((x \ y) * z)) = L(x,y \ 1,z). [back_rewrite(4470),rewrite([24021(8)])]. 24279 a(x / (y * y),y,y * z) = a(x,y,y \ z). [back_rewrite(16096),rewrite([24030(8)])]. 24305 T(x * ((x \ y) * z),y * z) = a(x,x * y,z) \ (y * z). [back_rewrite(24034),rewrite([24057(7)])]. 24428 ((x / (y * z)) * (y * (z * y))) \ (x * y) = a(y * z,(y * z) * x,y). [back_rewrite(18703),rewrite([24057(11)])]. 24477 ((x / y) * (z * y)) \ (x * T(z,y)) = a(y,y * x,T(z,y)). [back_rewrite(1958),rewrite([24057(9)])]. 24479 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(z,y * (y * (z * x)),u). [back_rewrite(1952),rewrite([24057(15),37(14),2508(15)])]. 24566 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(z,y,T(x,y)). [back_rewrite(6149),rewrite([24189(10)])]. 24624 ((x * y) \ z) * ((z \ x) * y) = a(z,x,y). [back_rewrite(6068),rewrite([24189(8)])]. 24638 (x * y) / ((z \ x) * y) = L(z,x \ 1,y). [back_rewrite(5665),rewrite([24268(4)]),flip(a)]. 24897 x * ((T(K(y,z),u) * (u \ (K(z,y) * x))) \ T(w,x * u)) = x \ (w * (x * u)). [para(19486(a,1),3218(a,1,2,2,2,2)),rewrite([19486(17)])]. 24915 x / (K(y,z) * (y \ (K(z,y) * x))) = y. [para(12307(a,1),19486(a,1,2,1))]. 25093 (x \ y) / T(z * (z / x),y) = z \ (z \ y). [para(12372(a,1),5364(a,1,2,2)),rewrite([1014(4),7616(2),1014(4),12372(9)])]. 26642 x * K(y,x) = T(x,x / y). [para(17914(a,1),16716(a,1,2))]. 26745 K(x,y) * y = T(y,y / x). [back_rewrite(12349),rewrite([26642(4)])]. 26764 T(x,y / x) = T(x,y). [para(17924(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 26839 T(x,L(x,y,z)) = x. [para(160(a,1),16487(a,1,1)),rewrite([16487(2)]),flip(a)]. 26897 x / T(y * (y * (x / z)),z) = y \ (y \ z). [para(1925(a,1),21(a,1,2)),rewrite([3436(2),1607(8)]),flip(a)]. 26903 L(x,y,y \ z) = L(x,z,y). [para(1925(a,1),132(a,1,1,2)),rewrite([26897(6),7550(5),16(4),21(4),26897(6),2507(6),16465(4)]),flip(a)]. 26952 T(x,y) \ ((y \ x) * z) = L(y \ z,x,y). [back_rewrite(7981),rewrite([26903(3)]),flip(a)]. 26963 L(x \ y,x,x * z) = L(x \ y,z,x). [back_rewrite(24100),rewrite([26952(7)])]. 26968 a((x \ y) / z,x,L(x \ z,y,x)) = a(x \ y,x,L(x \ z,y,x)). [back_rewrite(11726),rewrite([26952(6),26952(10)])]. 26973 a((x * y) / z,x,L(x \ z,y,x)) = a(x,y * x,L(x \ z,y,x)). [back_rewrite(23662),rewrite([26963(5),26963(9)])]. 27047 x * ((x \ y) * T(z,x)) = (y / x) * (z * x). [para(165(a,1),10393(a,1,2,1,1)),rewrite([6564(3),3143(6),24002(4),6564(7),1014(7)])]. 27119 L(x,y * T(y,z),u * ((z \ y) * (z \ y))) = x. [back_rewrite(15120),rewrite([27047(4),3169(3),4505(2)])]. 27706 R(x,T(y,x) \ 1,z) = L(x,y \ x,z). [para(2711(a,1),5817(a,1,1,2,1,1)),rewrite([24229(7)]),flip(a)]. 28505 x / L(x,y,z) = L(x,y,z) \ x. [para(26839(a,1),7616(a,1,1))]. 28511 T(x,L(x,y,z) \ x) = x. [para(26839(a,1),7769(a,1,1))]. 28965 T(x,x / y) = T(x,y \ x). [para(19567(a,1),16716(a,1,2)),rewrite([26642(2)])]. 28991 K(x,y) * y = T(y,x \ y). [back_rewrite(26745),rewrite([28965(4)])]. 29339 T(x,y) / (y * x) = (y * x) \ x. [para(23443(a,1),7616(a,1,1))]. 30455 x \ (y * (x / z)) = T(y,x) / z. [para(6185(a,1),3683(a,1,2)),rewrite([1840(5),4505(2)]),flip(a)]. 30508 x * (T(y,x) / z) = y * (x / z). [para(6185(a,1),136(a,1,2,2)),rewrite([1840(5),4505(2),1014(6),90(7)])]. 30627 x * ((y * x) \ T(z,x / y)) = T(z,x) / y. [back_rewrite(7622),rewrite([30455(8)])]. 30654 L(x,T(y,z) / x,y \ z) = (y * (z / x)) \ (y * z). [back_rewrite(10748),rewrite([30508(7)])]. 30840 (T(K(x,y),z) * (z \ (K(y,x) * u))) \ T(w,u * z) = (u \ (u \ w)) * (u * z). [para(19486(a,1),6188(a,1,2,2,2)),rewrite([19486(18)])]. 32743 R(x * y,y * x,z) = x * y. [para(4209(a,1),493(a,1,1)),rewrite([4209(5)])]. 32749 (x * T(x,y)) * z = x * (T(x,y) * z). [para(493(a,1),84(a,1,1)),rewrite([21062(3),547(5)]),flip(a)]. 32816 R(x * y,K(y,x),z) = x * y. [back_rewrite(19707),rewrite([32743(7)]),flip(a)]. 33258 (x * y) \ ((y * x) * z) = K(y,x) * z. [para(63(a,1),166(a,1,2,1)),rewrite([32816(3)])]. 33300 R(x,K(x,y),z) \ (T(x,y) * z) = K(x,y) * z. [para(16716(a,1),166(a,1,2,1))]. 33324 T(x,y) \ (x * (T(x,y) * z)) = x * z. [para(493(a,1),166(a,1,1)),rewrite([547(3),32749(4)])]. 33334 L(x,K(y,z),z * y) = x. [back_rewrite(2857),rewrite([33258(6),8296(4)]),flip(a)]. 33346 (x * y) * (K(y,x) * z) = (y * x) * z. [back_rewrite(5116),rewrite([33334(4)]),flip(a)]. 33415 x * (y * (y * (x * T(z,y * x)))) = (x * y) * (z * (y * x)). [back_rewrite(20509),rewrite([33346(6)]),flip(a)]. 33450 (x \ (y / x)) * (x * z) = x \ (y * z). [para(18(a,1),168(a,1,2,1)),flip(a)]. 33472 (x \ (y \ 1)) * (x * z) = x \ ((y \ x) * z). [para(3143(a,1),168(a,1,2,1)),flip(a)]. 33476 (x \ (x \ y)) * (x * z) = x \ (T(y,x) * z). [para(4505(a,1),168(a,1,2,1)),flip(a)]. 33497 K(x,y) * (x * z) = T(x,y) * z. [para(16343(a,1),168(a,2,1)),rewrite([547(2),32749(3),15(4)]),flip(a)]. 33507 K(x,y) * (T(y,x) * z) = y * z. [para(16711(a,1),168(a,2,1)),rewrite([32749(4),33324(5)]),flip(a)]. 33545 R(x,x \ (y * z),u) = L(x,z \ (y \ 1),u). [back_rewrite(11625),rewrite([33450(4),33450(9),24638(9),4407(6)])]. 33575 R(x,x \ ((y \ x) * z),u) = L(x,z \ (x \ y),u). [back_rewrite(11645),rewrite([33472(8),24638(8),4407(4),4408(3),14(3),33472(8)]),flip(a)]. 33590 (T(K(x,y),z) * (z \ (K(y,x) * u))) \ T(w,u * z) = u \ (T(w,u) * z). [back_rewrite(30840),rewrite([33476(13)])]. 33664 L(x,y * (z * u),z) = L(x,z,T(y,z) * u). [back_rewrite(9195),rewrite([33476(6),16348(8)]),flip(a)]. 33734 L(x,y,K(y,z)) = x. [back_rewrite(23108),rewrite([33497(4),15(4)]),flip(a)]. 33796 L(x,T(y,z),K(z,y)) = x. [back_rewrite(23022),rewrite([33507(4),15(2)]),flip(a)]. 33957 x \ (y * (x * z)) = T(y,x) * z. [back_rewrite(24897),rewrite([33590(9),16(4)]),flip(a)]. 33981 L(a(x,y,z),y,T(x,y) * z) = a(y,x,y * z). [back_rewrite(2971),rewrite([33664(4)])]. 34091 x \ (K(y,x) * z) = T(x,y) \ z. [back_rewrite(23033),rewrite([33796(5)]),flip(a)]. 34275 L(T(x,y * z),y,z) = T(T(x,y),z). [back_rewrite(16484),rewrite([33957(3),23(3)]),flip(a)]. 34415 x / (K(y,z) * (T(y,z) \ x)) = y. [back_rewrite(24915),rewrite([34091(4)])]. 34554 R(x,K(x,y),T(x,y) \ z) = x. [back_rewrite(22947),rewrite([34415(9)])]. 34768 (x * y) \ T(z,y / x) = y \ (T(z,y) / x). [para(30627(a,1),15(a,1,2)),flip(a)]. 34823 (x * y) \ y = y \ (x \ y). [para(12386(a,1),30627(a,1,2,2)),rewrite([101(2),9050(4),29339(5)]),flip(a)]. 34860 R(x,y,y \ (T(z,y) / x)) = L(x,y / x,z). [back_rewrite(21510),rewrite([34768(4)])]. 35223 K(x,y) * (T(x,y) \ z) = x \ z. [para(16(a,1),33300(a,1,2)),rewrite([34554(4)]),flip(a)]. 35536 L(a(x,y,T(z,y)),x * (z * y),(x * y) * T(z,y)) = a(x,y,T(z,y)). [hyper(24,a,6438,a)]. 35645 (x \ (y \ 1)) * z = (y * x) \ z. [para(13(a,1),6953(a,1,1,2,1)),rewrite([46(3),45(8),45(7)])]. 35648 (x \ (y \ (z \ 1))) * u = ((z * y) * x) \ u. [para(16(a,1),6953(a,1,1,2,1)),rewrite([23717(10),16(9)])]. 35675 (x * ((y * z) \ (y \ 1))) * u = (x / z) * (y \ (y \ u)). [para(1014(a,1),6953(a,2,1)),rewrite([4408(7),45(2),10229(10)])]. 35683 x * (T(y,x) \ (x \ z)) = y \ z. [para(1091(a,1),6953(a,1,1)),rewrite([3143(3),35645(6),5162(4),16(5),4408(6),4408(3),169(6),6968(5)]),flip(a)]. 35698 (x \ ((y \ z) * z)) * u = (((y * x) \ z) * z) * u. [para(3143(a,1),6953(a,1,1,2,1)),rewrite([4408(5),45(3),14(3),4408(2),4408(10),45(9),4408(9),45(7),15452(8)])]. 35905 R(x,x \ (y \ 1),y * z) = z * ((y * z) \ (y * x)). [back_rewrite(11253),rewrite([35645(10),4155(9)])]. 35922 R(x,x \ (y \ 1),z) = L(x,y,z \ 1). [back_rewrite(3646),rewrite([35645(9),4155(8),6070(8)])]. 35944 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,y * (y * u),u \ x). [back_rewrite(24164),rewrite([35698(7)])]. 35945 (x * ((y * x) \ z)) / z = R(y \ 1,x,x \ z). [back_rewrite(21734),rewrite([35698(6),169(6),6968(5),35683(5)])]. 36021 x * ((y * x) \ (y * z)) = L(z,y,x \ (y \ 1)). [back_rewrite(35905),rewrite([35922(5),4407(3)]),flip(a)]. 36043 x / R(y,z,(y * z) \ u) = x * R(y \ 1,z,z \ u). [back_rewrite(12931),rewrite([35945(8)])]. 36066 R(x,y,(x * y) \ z) \ 1 = R(x \ 1,y,y \ z). [back_rewrite(10235),rewrite([35945(9)])]. 37107 L(x,K(y,z),y) = x. [para(33734(a,1),16487(a,1,1))]. 37216 L(x,K(y,z),z) = x. [para(17781(a,1),37107(a,1,2))]. 37224 T(x,y) * (x \ z) = K(x,y) * z. [back_rewrite(21504),rewrite([37216(4)]),flip(a)]. 38196 L(x,K(y,z),T(z,y)) = x. [para(17771(a,1),37216(a,1,2))]. 38207 T(x,y) * (K(y,x) * z) = x * z. [back_rewrite(21070),rewrite([38196(3)]),flip(a)]. 38314 x * (x * (y * ((y \ (x \ (x \ z))) * u))) = y * ((y \ z) * u). [para(37(a,1),169(a,2)),rewrite([5162(6),21713(7),5162(6)]),flip(a)]. 38342 (x \ y) * (y \ z) = y * ((x * y) \ z). [para(3143(a,1),169(a,1,1)),rewrite([35645(7)])]. 38356 T(x,y) * (y \ z) = y \ (x * z). [para(4505(a,1),169(a,1,1)),rewrite([7550(7)])]. 38365 (x * y) * T(y \ z,y) = (x / y) * (z * y). [para(7967(a,1),169(a,1,2)),rewrite([27047(8)])]. 38402 x * (y * (x * ((y * x) \ z))) = (y * x) * (T(y,x) \ z). [para(169(a,1),128(a,1)),rewrite([34823(3),6968(4)]),flip(a)]. 38445 (x * (y * (y * z))) * (z \ u) = z * ((z \ x) * (y * (y * u))). [back_rewrite(5200),rewrite([38314(9)]),flip(a)]. 38475 x * (y * ((x * y) \ z)) = L(z,y \ 1,x). [back_rewrite(24021),rewrite([38342(3)])]. 38485 R(x,x \ y,y \ z) = z / (y * ((x * y) \ z)). [back_rewrite(8328),rewrite([38342(6)])]. 38488 L(x,y,z \ (y \ 1)) = L(x,y,z \ 1). [back_rewrite(6070),rewrite([38342(4),36021(4)])]. 38503 L((x \ y) * z,y \ x,x) = x \ (y * z). [back_rewrite(21472),rewrite([38356(7)])]. 38534 R(x,y * (y * z),z \ u) = R(x,z,((z \ y) * y) * u). [back_rewrite(340),rewrite([38445(5),191(8),15452(3)]),flip(a)]. 38535 (x * y) * (T(x,y) \ z) = y * L(z,y \ 1,x). [back_rewrite(38402),rewrite([38475(4)]),flip(a)]. 38568 x * a(y,z,z \ (y \ x)) = L(x,y,z \ 1). [back_rewrite(9085),rewrite([38475(10),4407(7),16465(8)])]. 38590 x * ((y * x) \ (y * z)) = L(z,y,x \ 1). [back_rewrite(36021),rewrite([38488(8)])]. 38623 L(L(R(x,y,z),u,w),v5,x \ 1) = L(R(x,y,z),u,w). [back_rewrite(6793),rewrite([38488(6)])]. 38642 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(21715),rewrite([38534(9)]),flip(a)]. 38643 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,z,y)). [back_rewrite(21708),rewrite([38534(10)])]. 38644 R(x,y,((y \ z) * z) * ((z \ (z \ y)) * u)) = R(x,y,u). [back_rewrite(21704),rewrite([38534(7)])]. 39396 a(x / y,y * (y * z),u) = a(x * y,z,u). [para(33450(a,1),4636(a,1,1,2)),rewrite([23(2),90(2),16(5)]),flip(a)]. 39505 (x * y) \ (x \ 1) = y \ (x \ (x \ 1)). [para(1607(a,1),6591(a,1,1)),flip(a)]. 39506 (x * y) \ (y \ 1) = y \ (x \ (y \ 1)). [para(1667(a,1),6591(a,1,1)),flip(a)]. 39650 (x * (y \ (z \ (z \ 1)))) * u = (x / y) * (z \ (z \ u)). [back_rewrite(35675),rewrite([39505(4)])]. 39699 x / (y * (y * (z * x))) = z \ (y \ (y \ 1)). [back_rewrite(4420),rewrite([39505(8)])]. 39792 x / (y * (z * (y * x))) = y \ (z \ (y \ 1)). [back_rewrite(4421),rewrite([39506(8)])]. 41919 x \ ((y \ z) * z) = ((y * x) \ z) * z. [para(2748(a,1),6591(a,1,1)),rewrite([4408(5),4408(3),45(2),14(3),22398(2),4408(9),4408(7),45(6),14(7),22398(6)])]. 42198 a(x,x * y,(x * y) \ z) = a(x,y,y \ z). [para(1091(a,1),192(a,1,2,2,1)),rewrite([3143(5),169(4),192(5)]),flip(a)]. 42212 a(x,x * y,z) \ (y * z) = a(y,x,x \ z) * (y * z). [para(192(a,1),4505(a,1,1)),rewrite([24305(9)]),flip(a)]. 42295 T(x * ((x \ y) * z),a(x,x * y,z)) = a(y,x,x \ z) * (y * z). [back_rewrite(4031),rewrite([42212(10)])]. 42314 R(x * y,x,x \ T(z,y)) = (x * (z * y)) / T(z,y). [para(90(a,1),198(a,2,1,2))]. 42387 R(x * (y * z),x,x \ y) = (x * (y * (z * y))) / y. [para(101(a,1),198(a,2,1,2))]. 42429 T(x,R(y * z,y,y \ x)) = T(x,y * (z * x)). [para(198(a,2),26764(a,1,2))]. 42930 a(x \ (y / x),x,z) = a(x,y,z). [para(15(a,1),7682(a,1,2)),rewrite([1091(2),1091(4),1014(5),3143(4),1091(5),24189(6)])]. 42940 a(x * (y \ z),z \ y,u) = a(y \ z,(z \ y) * x,u). [para(4505(a,1),7682(a,1,1,2)),rewrite([90(4),4408(7)])]. 42971 a(x \ y,(y \ x) * z,T(y,x)) = ((z * (x \ y)) * x) \ (z * T(y,x)). [back_rewrite(4335),rewrite([42940(5)])]. 43418 ((x * (y \ z)) * y) * a(y \ z,(z \ y) * x,T(z,y)) = x * T(z,y). [para(7969(a,1),54(a,1,1)),rewrite([7715(13)])]. 44128 a(x,y,y \ z) \ 1 = a(y,y * x,z). [para(18(a,1),4007(a,1,1,2)),rewrite([92(4),169(4),18(7),42295(7),3691(6),18(7)])]. 44649 L(L(x,y / x,z),z * (y / x),z * y) = (z * (y / x)) \ (z * y). [para(76(a,2),6368(a,1,1))]. 44671 L(L(L(x,y,z),u,w),v5 \ 1,v5 \ x) = L(L(x,y,z),u,w). [para(6416(a,1),97(a,2,1,1))]. 44709 L(L(L(L(x,y,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(L(x,u,w),y,z),v5,v6). [para(6416(a,1),229(a,1,1,1)),flip(a)]. 45295 R(x,y,T(y \ z,y)) * T(z,y) = (x / y) * (z * y). [para(7967(a,1),200(a,1,1,3)),rewrite([27047(9)])]. 45676 (x * y) \ L(y \ z,y,x) = (y * (x * y)) \ z. [para(74(a,2),25093(a,2,2)),rewrite([25093(9),6073(5),1091(3),39506(4),35648(5),101(2)]),flip(a)]. 46495 (R(x / y,y,z) * (y * (z * y))) \ ((x * z) * y) = a(y * z,(y * z) * (x * z),y). [para(85(a,2),24428(a,1,1,1))]. 46497 (R(x \ 1,y,z) * (y * (z * y))) \ (((x \ y) * z) * y) = a(y * z,(y * z) * ((x \ y) * z),y). [para(6071(a,1),24428(a,1,1,1))]. 46815 a(x,y * (y * (x * (y * z))),u) = a(x,x * (y \ z),u). [para(37(a,1),4021(a,1,1)),rewrite([16103(4),16485(3),23718(9),1091(6),4407(6),23717(6),14(5),4498(7),101(7),128(8),2508(10)]),flip(a)]. 47034 L(L(L(R(x,y \ 1,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(R(x,y \ 1,z),v5,v6),u,w). [para(76(a,1),44709(a,1,1)),rewrite([24261(6),24016(16)])]. 47036 L(L(x,y,z),u \ 1,u \ L(x,w,v5)) = L(x,y,z). [para(16487(a,1),44709(a,1,1,1)),rewrite([16487(8)])]. 47734 L(x,y * z,y * (z * (y * y))) = x. [para(189(a,1),15035(a,1,3)),rewrite([4578(3)])]. 48405 T(x,y) \ (y \ z) = y \ (x \ z). [para(3143(a,1),38503(a,2,2)),rewrite([35645(4),4408(5),45(4),2975(4),5147(4)])]. 48721 L(x,y * K(z,u),K(u,z)) = L(x,K(z,u),K(u,z) * y). [para(18(a,1),8308(a,1,3,2)),rewrite([5005(6)]),flip(a)]. 48733 L(x,K(y,z),u * K(z,y)) = L(x,K(z,y),u). [para(4505(a,1),8308(a,1,3,2)),rewrite([90(5),6144(6),16229(8)])]. 48767 a(x * K(y,z),K(z,y),u) = a(K(y,z),K(z,y) * x,u). [para(4505(a,1),8311(a,1,1,2)),rewrite([90(4),6144(7)])]. 48772 a(K(x,y),K(y,x) * z,u) = a(K(x,y),K(x,y) * z,u). [para(101(a,1),8311(a,1,1,2)),rewrite([2508(8),48767(4)])]. 49860 L(x,T(y,z),y) = x. [para(18604(a,1),439(a,1,2,2,1)),rewrite([4247(3),23(2),4505(4),4505(6),480(8),4505(4),13(6),32749(5),21(6)])]. 50186 L(L(R(x,y \ 1,z),u,w),v5,v6) = L(L(L(x,y,z \ 1),u,w),v5,v6). [para(82(a,1),47034(a,2,1,1)),rewrite([1014(5),10229(4),10305(5),47034(10),1014(10),10229(9),3143(10),4155(9),10690(8),38590(9)])]. 50188 L(R(x,y \ 1,z),u \ 1,u \ L(x,w,v5)) = R(x,y \ 1,z). [para(16487(a,1),47034(a,1,1)),rewrite([16487(13)])]. 50190 L(R(x,y \ 1,z),u,w) = L(L(x,y,z \ 1),u,w). [para(18454(a,1),47034(a,1,3,2)),rewrite([18485(6),50186(8),44671(8),38623(11)]),flip(a)]. 50224 R(x,y \ 1,z) = L(x,y,z \ 1). [back_rewrite(50188),rewrite([50190(8),47036(8)]),flip(a)]. 50298 L(x,T(y,x),z \ 1) = L(x,y \ x,z). [back_rewrite(27706),rewrite([50224(4)])]. 50308 R(x,y,y \ z) = L(x,y,z \ 1). [back_rewrite(24043),rewrite([50224(4),4407(3),38488(4)]),flip(a)]. 50323 L(x,y / x,z \ 1) = L(x,y,z \ 1). [back_rewrite(10323),rewrite([50224(7)])]. 50345 ((x / y) * (z * y)) / T(z,y) = L(x,z \ 1,y). [back_rewrite(2802),rewrite([50224(9),4407(8),26903(9)])]. 50359 L(x,y * z,z * y) = x. [para(4209(a,1),49860(a,1,2))]. 50365 L(x,y,T(y,z)) = x. [para(7769(a,1),49860(a,1,2))]. 50404 K(x,y) * ((x * y) \ z) = (y * x) \ z. [back_rewrite(6238),rewrite([50359(5)]),flip(a)]. 50423 R(x,y * (z * (z * y)),(z * y) \ ((y * z) \ u)) = R(x,K(z,y),K(y,z) * u). [back_rewrite(21722),rewrite([50404(9)])]. 50785 L(L(x,y / x,z),z * y,z * (y / x)) = L(x,y / x,z). [para(6694(a,1),18608(a,1,2)),rewrite([72(11),18(8),4581(8)])]. 51470 R(x / (y * ((z * y) \ x)),z,u) = R(z,y,(z * y) \ x). [para(82(a,1),495(a,1,1))]. 52573 L(x,y \ 1,z) = L(x,y,z \ 1). [para(14(a,1),24267(a,1,1,2)),rewrite([38568(4),48(5)]),flip(a)]. 52576 x * (a(y,z,z \ (y \ x)) * u) = L(x,y,z \ 1) * u. [para(24267(a,1),18(a,1,1)),rewrite([52573(3)]),flip(a)]. 52596 L(x,y,z \ 1) = L(x,y,z). [para(7679(a,1),24267(a,2)),rewrite([45(2),45(2),45(4),45(4),42198(7),52576(7),4407(3),26903(4),52573(3),17(5),45(5)])]. 52653 ((x / y) * (z * y)) / T(z,y) = L(x,z,y). [back_rewrite(50345),rewrite([52573(8),52596(8)])]. 52760 (x * y) * (T(x,y) \ z) = y * L(z,y,x). [back_rewrite(38535),rewrite([52573(7),52596(7)])]. 52843 R(x,x \ y,z) = L(x,y,z). [back_rewrite(24264),rewrite([52573(5),52596(5)])]. 52858 L(x,y,z) = L(x,z,y). [back_rewrite(16398),rewrite([52573(4),4407(3),26903(4),52573(3),52596(3)])]. 52942 L(x,y,z / x) = L(x,z,y). [back_rewrite(50323),rewrite([52596(4),52858(2),52596(5)])]. 52953 R(x,y,y \ z) = L(x,y,z). [back_rewrite(50308),rewrite([52596(5)])]. 52963 L(x,y,z \ x) = L(x,y,T(z,x)). [back_rewrite(50298),rewrite([52596(4),52858(2),52858(4)]),flip(a)]. 53163 L(x,y,y * z) = L(x,y,z). [back_rewrite(16470),rewrite([52596(4),52858(2)])]. 53170 (x \ y) * L(z,x,y) = x \ (y * z). [back_rewrite(6145),rewrite([52596(4),52858(2)])]. 53473 x / (y * ((z * y) \ x)) = L(z,y,x). [back_rewrite(38485),rewrite([52843(3),26903(2),52858(1)]),flip(a)]. 53483 L(x,y,z \ (x \ u)) = L(x,y,(u \ x) * z). [back_rewrite(33575),rewrite([52843(4),52858(3),52858(6)]),flip(a)]. 53484 L(x,y,z \ (u \ 1)) = L(x,y,u * z). [back_rewrite(33545),rewrite([52843(3),52858(2),52858(6)]),flip(a)]. 53550 L(x,y,z) \ 1 = R(x \ 1,y,z). [back_rewrite(10233),rewrite([52843(2)])]. 53564 (x * y) \ L(z,x,y) = y \ (x \ z). [back_rewrite(8393),rewrite([52843(3)])]. 53600 (x * y) * (T(x,y) \ z) = y * L(z,x,y). [back_rewrite(52760),rewrite([52858(5)])]. 53634 ((x / y) * (z * y)) / T(z,y) = L(x,y,z). [back_rewrite(52653),rewrite([52858(6)])]. 53804 L(L(x,y,z),z * y,z * (y / x)) = L(x,y,z). [back_rewrite(50785),rewrite([52858(2),52942(2),52858(7),52942(7)])]. 53894 L(x,K(y,z),u * K(z,y)) = L(x,u,K(z,y)). [back_rewrite(48733),rewrite([52858(6)])]. 53895 L(x,K(y,z),K(z,y) * u) = L(x,u,K(y,z)). [back_rewrite(48721),rewrite([52858(4),53894(4)]),flip(a)]. 54309 (x * (y * x)) \ z = x \ (y \ (x \ z)). [back_rewrite(45676),rewrite([52858(3),53564(4)]),flip(a)]. 54371 (x * (y / z)) \ (x * y) = L(z,y,x). [back_rewrite(44649),rewrite([52858(2),52942(2),52858(5),53804(5)]),flip(a)]. 54757 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,y,z)). [back_rewrite(38643),rewrite([52858(12)])]. 54758 R(x,y * z,L(z \ u,y,z)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(38642),rewrite([52858(3)])]. 54855 L(x,y,T(z,y)) = L(x,y,z). [back_rewrite(34860),rewrite([52953(4),52942(3),52858(2),52858(4),52942(4)])]. 54918 L(x,y,T(z,y) * u) = L(x,y,z * (y * u)). [back_rewrite(33664),rewrite([52858(3)]),flip(a)]. 54976 L(x,T(y,z),y \ z) = L(x,y,z). [back_rewrite(30654),rewrite([52858(4),52942(4),54371(7),52858(4)])]. 55235 a((x * y) / z,x,L(x \ z,x,y)) = a(x,y * x,L(x \ z,x,y)). [back_rewrite(26973),rewrite([52858(4),52858(8)])]. 55237 a((x \ y) / z,x,L(x \ z,x,y)) = a(x \ y,x,L(x \ z,x,y)). [back_rewrite(26968),rewrite([52858(4),52858(8)])]. 55249 L(x,y,y \ z) = L(x,y,z). [back_rewrite(26903),rewrite([52858(3)])]. 55548 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y))))) = x * x. [back_rewrite(21507),rewrite([52858(6)])]. 55731 (x * (y \ z)) * T(y,z) = x * L(z,x,T(y,z)). [back_rewrite(16508),rewrite([52858(6),52963(6)])]. 55771 T(x,L(y * z,x,y)) = T(x,(x * y) * z). [back_rewrite(16362),rewrite([52858(2)])]. 55776 x \ (y * ((y \ x) * z)) = L(z,x,y). [back_rewrite(16348),rewrite([52858(5)])]. 55819 L(x,y,z * (u * u)) = L(x,y,z). [back_rewrite(14874),rewrite([52858(3),2507(3),52858(1)]),flip(a)]. 55915 L(K(x,y) * z,u,K(y,x)) = (u * K(y,x)) \ (u * z). [back_rewrite(11597),rewrite([52858(4)])]. 55954 L(T(x * y,x * z),u,L(y \ z,x,y)) = (u * L(y \ z,x,y)) \ (u * (x * z)). [back_rewrite(11076),rewrite([52858(5),52858(6),52858(8)])]. 56040 x * L(y,x,z) = L(x * y,x,z). [back_rewrite(8091),rewrite([54976(3),52858(1),52858(4)])]. 56084 L(x,y,x * z) = (y * (z \ (x \ 1))) \ (y / z). [back_rewrite(6676),rewrite([52858(4),53483(4),45(2)])]. 56136 (x * (y * (z * u))) \ (x * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),x,y * (z * u)). [back_rewrite(5337),rewrite([52858(13)])]. 56176 (x * (y * z)) \ (x * y) = R(z \ 1,x,y). [back_rewrite(4138),rewrite([52858(5),53550(7)])]. 56215 a(x,y,L(z,x,y)) = a(x,y,z) \ 1. [back_rewrite(1098),rewrite([52858(1),3204(3),2548(5),52858(4)]),flip(a)]. 56223 R(x,y * z,L(z \ u,y,z)) = L(x,y * z,y * u). [back_rewrite(648),rewrite([52858(3),52953(9)])]. 56231 (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),x,y * (z * u)). [back_rewrite(589),rewrite([52858(11)])]. 56576 T(x,(x * y) * z) = T(x,y * (z * x)). [back_rewrite(42429),rewrite([52953(3),52858(2),55771(3)])]. 56609 (x * (y * (z * y))) / y = (x * y) * z. [back_rewrite(42387),rewrite([52953(4),16364(3)]),flip(a)]. 56659 L(x * y,x,T(z,y)) = (x * (z * y)) / T(z,y). [back_rewrite(42314),rewrite([52953(4)])]. 56731 R(x,y,(x * y) \ z) \ 1 = L(x \ 1,y,z). [back_rewrite(36066),rewrite([52953(9)])]. 56746 x / R(y,z,(y * z) \ u) = x * L(y \ 1,z,u). [back_rewrite(36043),rewrite([52953(8)])]. 56903 R(x,y * z,z \ 1) = L(x,y,(u \ (u \ y)) * z). [back_rewrite(21721),rewrite([52953(8),52858(4)]),flip(a)]. 57033 L(x * y,y,z) = (x * (y * z)) / z. [back_rewrite(4583),rewrite([52953(3)])]. 57044 L(x,y,x * z) = L(x,z,y). [back_rewrite(3213),rewrite([52953(4),52858(2),52953(4)])]. 57097 (x * ((x \ y) * z)) / z = L(y,x,z). [back_rewrite(191),rewrite([52953(6)])]. 57210 R(x,y,(x * y) \ z) = L(x,z,y). [back_rewrite(51470),rewrite([53473(4),52858(1),33(2),480(1)]),flip(a)]. 57428 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = R(y \ (z \ (y \ x)),y * (z * y),u). [back_rewrite(8002),rewrite([54309(11)])]. 57506 L(a(x,y,z),y,x * (y * z)) = a(y,x,y * z). [back_rewrite(33981),rewrite([54918(4)])]. 57670 L(x,y,z * T(z,u)) = x. [back_rewrite(27119),rewrite([55819(7),52858(3)])]. 57837 L(x * y,x,T(z,y)) = (x * (z \ y)) * T(z,y). [back_rewrite(55731),rewrite([56040(7)]),flip(a)]. 57867 a(x,y * x,L(z,x,y)) = a(x,y,x * z). [back_rewrite(23643),rewrite([56040(5),3204(7),189(6),56231(7),57506(4)]),flip(a)]. 57908 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * w)) = L(x,y * z,y * w). [back_rewrite(54758),rewrite([56223(4)]),flip(a)]. 57975 T(x \ y,((y \ x) * z) * y) = T(x \ y,z * (y * (x \ y))). [back_rewrite(15924),rewrite([56576(10)])]. 57979 T(x \ y,(z * (x \ y)) * T(x,y)) = T(x \ y,z * (y * (x \ y))). [back_rewrite(15622),rewrite([56576(11)])]. 58091 (x * (y \ (z \ 1))) \ (x / y) = L(z,x,y). [back_rewrite(56084),rewrite([57044(2),52858(1)]),flip(a)]. 58133 x * L(y \ 1,z,u) = x / L(y,z,u). [back_rewrite(56746),rewrite([57210(3),52858(1)]),flip(a)]. 58139 R(x \ 1,y,z) = L(x \ 1,y,z). [back_rewrite(56731),rewrite([57210(3),52858(1),53550(3)])]. 58268 a((x * y) / z,x,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(55235),rewrite([57867(9),16(7)])]. 58275 L(x,y * z,y * (z * u)) = R(x,y * z,L(u,y,z)). [back_rewrite(54757),rewrite([57908(10)])]. 58306 ((x * (y \ z)) * T(y,z)) / T(y \ z,x * (z * (y \ z))) = ((z \ y) * x) * z. [back_rewrite(15940),rewrite([57975(9)])]. 58412 (x * (y * z)) \ (x * y) = L(z \ 1,x,y). [back_rewrite(56176),rewrite([58139(7)])]. 58458 (L(x \ 1,y,z) * (y * (z * y))) \ (((x \ y) * z) * y) = a(y * z,(y * z) * ((x \ y) * z),y). [back_rewrite(46497),rewrite([58139(3)])]. 58601 R(x,y * z,L(y * y,y,z)) = x. [back_rewrite(47734),rewrite([58275(5)])]. 62320 R(x,y,T(y \ z,y)) = L(x,y,z). [para(4505(a,1),516(a,1,2)),rewrite([38365(4),53634(5)]),flip(a)]. 62433 L(x,y,z) * T(z,y) = (x / y) * (z * y). [back_rewrite(45295),rewrite([62320(3)])]. 62444 (x * y) * T(T(z,u),y) = (x * y) * T(T(z,y),u). [para(517(a,1),104(a,1,2,2)),rewrite([522(5)])]. 64162 L(x * x,x,y) = x * x. [para(1077(a,1),55954(a,1,3)),rewrite([14(3),4209(2),52596(4),52858(2),1607(5),1014(5),14(5),10229(5),23697(5),6351(5)])]. 64186 R(x,y * z,y * y) = x. [back_rewrite(58601),rewrite([64162(3)])]. 64397 T(x,(T(T(T(T(T(y,z),x \ 1),u),w),v5) / x) / T(T(T(T(T(y,w),u),x \ 1),z),v5)) = x. [para(4097(a,2),14495(a,1,2,1))]. 65748 L(x \ 1,y,z) * x = L(x,y,z) \ x. [para(996(a,1),518(a,1,2,1)),rewrite([58133(4),28505(2)]),flip(a)]. 68754 x * ((y * x) \ (z * x)) = (y \ x) * T(z,x). [para(3143(a,1),522(a,2,1)),rewrite([35645(5)])]. 68796 x * (y * (x * T(z,y * x))) = x * L(z * (y * x),y,x). [para(128(a,1),522(a,2)),rewrite([34823(3),6968(6),53600(6)]),flip(a)]. 68958 (x * (y * (z * x))) \ L(x * (y * (z * x)),x,z) = a(x,z * x,T(y,z * x)). [back_rewrite(23655),rewrite([68796(8),52858(6),56040(7)])]. 70674 R(x / (y * T(y,z)),y * T(y,z),u) = (x * u) / (y * (T(y,z) * u)). [para(16623(a,1),342(a,1,1,2,2)),rewrite([547(2),16623(7),547(5),38207(12),21062(10)])]. 70983 (x * (y * (z * (y * x)))) \ (x * (y * (z * ((y * x) * (u * (x * y)))))) = x * (y * T(u,x * y)). [para(33415(a,1),2214(a,1,2,2,2,2))]. 72886 a(x,(x \ y) * z,u) = a(x,(x * y) * z,u). [para(16(a,1),13466(a,1,2,2)),rewrite([169(6),136(7)])]. 72954 x \ (y * (z * x)) = T(y,x) * T(z,x). [para(14(a,1),13641(a,1,2,2)),rewrite([4505(3),14(6)]),flip(a)]. 76377 T(x * (x * y),z \ 1) * (z / y) = z * (x * x). [para(10920(a,1),7616(a,1,1)),rewrite([10215(7),22250(11),10229(9),18(9)])]. 77469 ((x / y) * (z * u)) * a(y / x,z,u) = ((x / y) * z) * u. [para(15308(a,1),54(a,1,2)),rewrite([37(6),10287(7),10287(12)])]. 77479 a(x,x * (y \ (y \ (x \ z))),u) = a(x,y * (y * z),u). [para(3645(a,1),15308(a,1,2,1)),rewrite([10215(7),76377(7),3645(13),35648(11),4578(8),19474(9),35648(10),4578(4),19474(8),14882(9),16(7),16(6),3954(5),10215(12),76377(12),14882(8)])]. 79623 L(x,y,R(z \ (y \ 1),y,x)) = L(x,y,T(z,x)). [para(3143(a,1),10670(a,2,3)),rewrite([6120(3),52963(7)])]. 79632 L(x,y,z * x) = L(x,y,z). [para(101(a,1),10670(a,2,3)),rewrite([20016(3),57044(3),52858(2),3200(2),57044(4),52858(3)]),flip(a)]. 79704 L(x,y,R(z,y,x)) = L(x,y,z). [back_rewrite(8681),rewrite([79632(3),16256(2)]),flip(a)]. 79714 L(x,y,T(z,x)) = L(x,y,z). [back_rewrite(79623),rewrite([79704(5),53484(4),53163(2)]),flip(a)]. 79784 L(x,y,z \ x) = L(x,y,z). [back_rewrite(52963),rewrite([79714(4)])]. 79922 (x * (y * z)) / T(y,z) = L(x * z,z,y). [para(90(a,1),57033(a,2,1,2)),rewrite([54855(3)]),flip(a)]. 79974 R(x,y \ z,T(y,z)) = L(x,y,z). [para(4504(a,1),57033(a,2,1)),rewrite([7715(4),52858(3),79632(3),55249(2),52858(1),2708(6)]),flip(a)]. 79977 L(x * (y * z),y,z) = (x * y) * z. [para(101(a,1),57033(a,2,1,2)),rewrite([52858(4),53163(4),56609(7)])]. 80058 R(x,y \ z,y) = L(x,y,z). [para(7969(a,1),57033(a,2,1)),rewrite([7715(4),52858(4),79632(4),54976(3),52858(1),7966(6)]),flip(a)]. 80171 L(x * y,x,T(z,y)) = L(x * y,y,z). [back_rewrite(56659),rewrite([79922(7)])]. 80225 (x * (y \ z)) * T(y,z) = L(x,y,z) * z. [back_rewrite(10537),rewrite([79974(3)]),flip(a)]. 80273 x * (y * (x * T(z,y * x))) = L(x * (z * (y * x)),x,y). [back_rewrite(68796),rewrite([52858(8),56040(9)])]. 80501 (x * (y \ z)) * y = (x / y) * (z * y). [back_rewrite(10562),rewrite([80058(2),62433(3)]),flip(a)]. 80509 L(x,y,z) * y = L(x * y,y,z). [back_rewrite(57837),rewrite([80171(3),80225(6),52858(3)]),flip(a)]. 80615 (L(x,y,z) * z) / T(y \ z,x * (z * (y \ z))) = ((z \ y) * x) * z. [back_rewrite(58306),rewrite([80225(4)])]. 80627 T(x \ y,z * (y * (x \ y))) = T(x \ y,L(z,x,y) * y). [back_rewrite(57979),rewrite([80225(5)]),flip(a)]. 81010 ((x / y) * (z * y)) * a(y \ z,(z \ y) * x,T(z,y)) = x * T(z,y). [back_rewrite(43418),rewrite([80501(3)])]. 81016 a(x \ y,(y \ x) * z,T(y,x)) = a(x,x * z,T(y,x)). [back_rewrite(42971),rewrite([80501(8),24477(11)])]. 81224 (x \ y) * (L(z,y,x) * x) = ((x \ y) * z) * x. [back_rewrite(80615),rewrite([80627(7),2711(7),4408(4)])]. 81309 ((x / y) * (z * y)) * a(y,y * x,T(z,y)) = x * T(z,y). [back_rewrite(81010),rewrite([81016(8)])]. 82121 a(x,y / x,x * z) = a(x,y,z) \ 1. [para(1091(a,1),15593(a,1,1)),rewrite([1091(4),1014(5),4209(5),24189(5),1091(5),24189(6)])]. 82129 a(x,y,x \ z) \ 1 = a(x,y / x,z). [para(7769(a,1),15593(a,1,3)),rewrite([48405(3),46(1),48405(5),46(3),1014(5),24189(4),48405(5),46(3),24189(6)]),flip(a)]. 82774 x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y)))) = x. [para(55548(a,1),15(a,1,2)),rewrite([15(2)]),flip(a)]. 82800 R(x / y,y,x) = x / y. [para(55548(a,1),85(a,2,1)),rewrite([82774(11),82774(13),14868(5),3691(4),1014(5)])]. 82841 x * (y \ (z \ (z \ 1))) = x / (z * (z * y)). [para(55548(a,1),342(a,2,1)),rewrite([82774(15),82800(6),82774(14),14868(8),39699(7)]),flip(a)]. 82892 (x / (y * (y * z))) * u = (x / z) * (y \ (y \ u)). [back_rewrite(39650),rewrite([82841(5)])]. 82924 a(x,y * (y * (x * z)),u) = a(x,x * z,u). [back_rewrite(24479),rewrite([82892(7),15(5),15(4),23697(3),4032(5)]),flip(a)]. 82939 a(x,x * (y \ z),u) = a(x,x * (y * z),u). [back_rewrite(46815),rewrite([82924(5)]),flip(a)]. 82951 a(x,y * (y * z),u) = a(x,z,u). [back_rewrite(77479),rewrite([82939(5),16(3),16(2)]),flip(a)]. 83180 a(x / y,z,u) = a(x * y,z,u). [back_rewrite(39396),rewrite([82951(4)])]. 83185 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,u,u \ x). [back_rewrite(35944),rewrite([82951(13)])]. 83213 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,x / u,u). [back_rewrite(24163),rewrite([82951(13)])]. 83255 a(x \ (y / x),z,u) = a(y,z,u). [back_rewrite(19167),rewrite([82951(5)]),flip(a)]. 83266 a(x * (y * y),z,u) = a(x,z,u). [back_rewrite(14882),rewrite([82951(6)])]. 83285 a(x,y * (z * (z * y)),u) = 1. [back_rewrite(2486),rewrite([82951(6)])]. 83423 ((x / y) * (z * u)) * a(y * x,z,u) = ((x / y) * z) * u. [back_rewrite(77469),rewrite([83180(5)])]. 83804 a((x * y) * z,x,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(58268),rewrite([83180(5)])]. 83865 a((x \ y) * z,x,L(x \ z,x,y)) = a(x \ y,x,L(x \ z,x,y)). [back_rewrite(55237),rewrite([83180(5)])]. 84069 a(x,y,y \ z) = a(x,y,y * z). [back_rewrite(24279),rewrite([83180(4),83266(4)]),flip(a)]. 84171 a(x,y,z) = a(y,x,z). [back_rewrite(42930),rewrite([83255(3)])]. 84200 (x * (y * (z * (z * y)))) * u = x * (z * (y * (y * (z * u)))). [back_rewrite(20510),rewrite([83285(9),14(7)]),flip(a)]. 84365 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,u,u * x). [back_rewrite(83185),rewrite([84069(11)])]. 84641 a(x,y * x,z) = a(x,x * y,z). [back_rewrite(44128),rewrite([84069(2),7836(4),84171(2)])]. 84975 a(x,(x * y) * z,L(x \ z,x,y)) = a(x,x * y,L(x \ z,x,y)). [back_rewrite(83865),rewrite([84171(5),72886(5),84171(9),3954(9)])]. 85028 a(x,x * y,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(83804),rewrite([84171(5),84975(5)])]. 85167 ((x / y) * (z * u)) * a(z,y * x,u) = ((x / y) * z) * u. [back_rewrite(83423),rewrite([84171(5)])]. 85235 a(x,y \ (z / y),u) = a(z,x,u). [back_rewrite(83255),rewrite([84171(3)])]. 85263 a(x,y / z,u) = a(x,y * z,u). [back_rewrite(83180),rewrite([84171(2),84171(4)])]. 86984 ((x * y) \ z) * ((z \ x) * y) = a(x,z,y). [back_rewrite(24624),rewrite([84171(6)])]. 86989 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(y,z,T(x,y)). [back_rewrite(24566),rewrite([84171(8)])]. 86999 a(x,y \ 1,z) = a(y,x,z). [back_rewrite(24189),rewrite([84171(3)])]. 87019 a(x \ y,z * (x \ y),x) = a(z,x \ y,T(y,x)) \ 1. [back_rewrite(23629),rewrite([84171(7)])]. 87102 a(x \ y,z * (x \ y),T(x,y)) = a(z,x \ y,y) \ 1. [back_rewrite(15593),rewrite([84171(7)])]. 87206 R(x,y * (z * (z * y)),u) = x. [back_rewrite(20504),rewrite([84200(5),17(10)]),flip(a)]. 87367 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,x * u,u). [back_rewrite(83213),rewrite([85263(11)])]. 87375 a(x,y,x \ z) \ 1 = a(x,y * x,z). [back_rewrite(82129),rewrite([85263(6)])]. 87377 a(x,y * x,x * z) = a(x,y,z) \ 1. [back_rewrite(82121),rewrite([85263(3)])]. 88170 R(x,K(y,z),K(z,y) * u) = x. [back_rewrite(50423),rewrite([87206(8)]),flip(a)]. 88394 x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w)) = x \ w. [para(4714(a,1),15(a,1,2)),flip(a)]. 88400 R(x,y,((y \ z) * z) * u) = L(x,y,u). [para(4714(a,1),148(a,1,2,2,2)),rewrite([88394(16),38445(5),57097(8),2507(3),88394(16),38534(5)]),flip(a)]. 88449 L(x,y,(z \ (z \ y)) * u) = R(x,y,u). [back_rewrite(38644),rewrite([88400(7)])]. 88465 R(x,y * z,z \ 1) = R(x,y,z). [back_rewrite(56903),rewrite([88449(8)])]. 90470 (x * y) \ (x * z) = x \ ((x / y) * z). [para(15(a,1),15943(a,1,2,1,1)),rewrite([1091(2),3143(5),1091(5),4209(8),35645(8)]),flip(a)]. 90726 x * (y * T(z,x * y)) = (z * x) * y. [back_rewrite(70983),rewrite([90470(12),39792(4),35648(11),101(2),90470(9),3691(2),3143(8),15(6),24002(5),55776(6),79977(3)]),flip(a)]. 90841 x \ ((x / (y * z)) * y) = L(z \ 1,x,y). [back_rewrite(58412),rewrite([90470(4)])]. 90887 x \ ((x / (y * (z * u))) * ((y * z) * u)) = L(a(y,z,u),x,y * (z * u)). [back_rewrite(56231),rewrite([90470(7)])]. 90904 x \ ((x / (y * (z * u))) * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),x,y * (z * u)). [back_rewrite(56136),rewrite([90470(8)])]. 90948 L(K(x,y) * z,u,K(y,x)) = u * ((u \ K(x,y)) * z). [back_rewrite(55915),rewrite([90470(8),5005(6),24002(8)])]. 91332 L(x * (y * (z * x)),x,z) = x * ((y * z) * x). [back_rewrite(80273),rewrite([90726(4)]),flip(a)]. 91534 ((x * (y * z)) \ z) * T(x * y,z) = a(z,y * z,T(x,y * z)). [back_rewrite(68958),rewrite([91332(7),90470(7),72954(7),2643(4)])]. 93714 L(x,y * (z * u),(y * z) * u) = R(x,y * (z * u),a(y,z,u)). [para(597(a,1),57033(a,2,1)),rewrite([16(6),52858(6),79784(6),52858(5),592(13)])]. 98284 (x * (y * z)) * (a(x,y,z) * ((x * y) * z)) = (x * y) * (z * ((x * y) * z)). [para(601(a,1),209(a,1,2)),rewrite([84171(6),20692(6),45(9),54(13),189(12),101(11),84171(18),20692(18),88(14)])]. 98289 (x \ T(x \ 1,y * z)) * (((y * z) \ x) * (y * (z * x))) = a(y,z,x) \ 1. [para(601(a,1),1091(a,1,1)),rewrite([98284(7),23718(11),54309(5),6072(4,R)])]. 99656 ((x \ y) * z) * x = T(y,x) * T(z,x). [back_rewrite(81224),rewrite([52858(2),80509(3),53170(4),72954(3)]),flip(a)]. 103664 x * (y \ (z \ 1)) = x / (z * y). [para(64186(a,1),85(a,1)),rewrite([189(7),4578(6),4613(8),39792(6),16(7)]),flip(a)]. 103820 R(x,y,z \ 1) = L(x,z,y). [back_rewrite(58091),rewrite([103664(4),10229(4),10279(4)])]. 104117 R(x,y,z) = L(x,y,z). [back_rewrite(88465),rewrite([103820(4),16256(2),52858(1)]),flip(a)]. 105551 L(x,y * (z * u),(y * z) * u) = L(x,a(y,z,u),y * (z * u)). [back_rewrite(93714),rewrite([104117(9),52858(9)])]. 105864 L(x,y,K(z,u)) = x. [back_rewrite(88170),rewrite([104117(4),53895(4)])]. 106960 (x * y) / (z * (T(z,u) * y)) = x / (z * T(z,u)). [back_rewrite(70674),rewrite([104117(6),52858(6),57670(6)]),flip(a)]. 107917 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = L(y \ (z \ (y \ x)),u,y * (z * y)). [back_rewrite(57428),rewrite([104117(14),52858(14)])]. 108469 (L(x / y,y,z) * (y * (z * y))) \ ((x * z) * y) = a(y * z,(y * z) * (x * z),y). [back_rewrite(46495),rewrite([104117(2)])]. 109339 L(x,y,z) * (y * (z * y)) = (x * (y * z)) * y. [back_rewrite(18750),rewrite([104117(2),52858(2),53163(2)])]. 109537 (x * y) \ (z * y) = T(x \ z,y). [back_rewrite(10592),rewrite([104117(4),34275(4),92(2)]),flip(a)]. 110402 x * ((x \ K(y,z)) * u) = K(y,z) * u. [back_rewrite(90948),rewrite([105864(4)]),flip(a)]. 110793 a(x * y,(x * y) * (z * y),x) = a(z,y,x). [back_rewrite(108469),rewrite([109339(5),23697(3),101(4),99656(3),4525(4),90(2),23718(5),86984(5),84171(1)]),flip(a)]. 110800 T(a(x,y,z),y) = a(z,x \ y,y). [back_rewrite(58458),rewrite([109339(6),3143(4),109537(7),4408(5),86984(5),84171(1),110793(8),84171(4)])]. 110982 (x \ y) * T(z,y) = (x \ z) * y. [back_rewrite(68754),rewrite([109537(3),90(3)]),flip(a)]. 111960 a(x,x * K(y,z),K(z,y) * u) = 1. [back_rewrite(9444),rewrite([110402(6),8296(4),46(1)]),flip(a)]. 112152 a(x,y * x,T(z,y * x)) = L(x,z,y) \ x. [back_rewrite(91534),rewrite([110982(6),90470(4),90841(4),65748(4)]),flip(a)]. 112164 a(x,y,T(z,x)) = a(z,y,x). [back_rewrite(86989),rewrite([110982(5),86984(5)]),flip(a)]. 112420 ((x / y) * z) * y = x * T(z,y). [back_rewrite(81309),rewrite([112164(6),85167(6)])]. 112508 a(x,y,z * x) \ 1 = a(z,y * x,x). [back_rewrite(23663),rewrite([112164(3)]),flip(a)]. 112951 (x * (y / z)) * z = z * ((z \ x) * y). [back_rewrite(10393),rewrite([112420(4),23697(4),110982(3)]),flip(a)]. 113434 a(x,y * z,z) = a(x,z,z * y). [back_rewrite(87367),rewrite([112951(8),41919(6),84365(9)]),flip(a)]. 113707 a(x,y,z * x) \ 1 = a(x,z,x * y). [back_rewrite(112508),rewrite([113434(6),84171(6)])]. 114859 (x * y) * T(T(z,y),u) = (x * T(z,u)) * y. [para(62444(a,1),136(a,2)),rewrite([110982(4),136(5)]),flip(a)]. 114936 (x * y) * T(z,y) = (x * z) * y. [para(64397(a,1),62444(a,1,2,1)),rewrite([114859(23),64397(20)])]. 115350 L(a(x,y,T(z,y)),u,x * (z * y)) = L(a(x,z,y),u,x * (z * y)). [back_rewrite(90904),rewrite([114936(6),90887(7)]),flip(a)]. 115485 a(x,y,T(z,y)) = a(x,z,y). [back_rewrite(35536),rewrite([114936(7),105551(7),115350(6),6018(5)]),flip(a)]. 116274 L(x,y,z) \ x = a(x,z,y * x). [back_rewrite(112152),rewrite([115485(4),52858(3)]),flip(a)]. 116872 T(x,a(x,y,z * x)) = x. [back_rewrite(28511),rewrite([116274(2)])]. 118966 (x * T(x,y)) \ z = T(x,y) \ (x \ z). [para(16875(a,1),107917(a,1,1,1,2,2)),rewrite([547(2),33507(9),21062(7),106960(8),7616(6),6144(8),35223(8),16875(10),547(8),57670(9)])]. 118967 (x \ (x \ K(y,x))) * z = T(x,y) \ (x \ z). [para(16985(a,1),107917(a,1,1,1,2,2)),rewrite([33497(7),106960(8),7616(6),118966(3),6144(6),9490(7),12473(5),16985(9),57670(10)]),flip(a)]. 119011 (x \ T(x \ 1,y)) * z = T(x,y) \ (x \ z). [back_rewrite(17906),rewrite([118967(9)])]. 119022 T(x,y * z) \ (x \ (((y * z) \ x) * (y * (z * x)))) = a(y,z,x) \ 1. [back_rewrite(98289),rewrite([119011(11)])]. 123069 T(x,y) \ (x \ z) = x \ (T(x,y) \ z). [para(634(a,1),50365(a,1)),rewrite([547(2),118966(3)])]. 123146 a(x,y,z) \ 1 = z \ L(z,x,y). [back_rewrite(119022),rewrite([123069(9),26952(8),90470(4),23697(3),55776(4),6022(3)]),flip(a)]. 128856 x / (T(y,z) * ((y \ L(y,u,w)) * (T(y,z) \ x))) = a(y,w,u * y). [para(26839(a,1),19479(a,1,2,2,2,1,1)),rewrite([116274(10)])]. 129028 x / (T(y,z) * (a(y,u,w * y) * (T(y,z) \ x))) = y \ L(y,w,u). [para(26839(a,1),19536(a,1,2,1,1)),rewrite([116274(3)])]. 131120 T(x,a(x,y,z)) = x. [para(18(a,1),116872(a,1,2,3))]. 131212 T(a(x,y,z),x) = a(x,y,z). [hyper(26,a,131120,a)]. 131234 T(x,a(x,y,z) \ x) = x. [para(131120(a,1),7769(a,1,1))]. 131246 K(a(x,y,z),x) = 1. [para(131120(a,1),16687(a,1,2)),rewrite([47(1)]),flip(a)]. 133716 K(a(x,y,z),y) = 1. [para(84171(a,1),131246(a,1,1))]. 133728 a(x,y \ z,z) = a(y,z,x). [hyper(28,a,133716,a),rewrite([110800(2)])]. 133748 a(x \ y,z * (x \ y),T(x,y)) = a(x,y,z) \ 1. [back_rewrite(87102),rewrite([133728(7)])]. 136169 a(x,y,x * z) \ 1 = a(x,y * x,z). [para(15(a,1),87019(a,1,1)),rewrite([15(2),15(4),4209(4),84171(4)]),flip(a)]. 136177 a(x \ (y / x),z * (x \ (y / x)),x) = a(y,z,x \ y) \ 1. [para(92(a,1),87019(a,2,1,3)),rewrite([85235(10)])]. 136185 a(x \ 1,y * x,z * x) = a(y,z,x) \ 1. [para(1091(a,1),87019(a,1,1)),rewrite([1091(4),1014(5),85263(5),1091(7),1708(9),86999(9),112164(7),84171(6)])]. 136188 a(x \ 1,y * x,z) = a(x,y * x,z). [para(1829(a,1),87019(a,1,1)),rewrite([1829(4),1014(5),85263(4),1829(6),2643(8),86999(8),87375(8)])]. 136232 a(x,y,z * (x * x)) \ 1 = a(z,x,y) \ 1. [para(22354(a,1),87019(a,2,1,3)),rewrite([22283(6),15(3),15(2),89(1),22283(6),15(3),15(2),89(1),112164(4),113434(3),84171(3),87377(3),84171(1),22283(9),15(6),15(5),89(4),84171(6)]),flip(a)]. 136306 a(x,y * x,z * x) = a(y,z,x) \ 1. [back_rewrite(136185),rewrite([136188(5)])]. 151591 x \ (a(x,y,z) \ x) = a(x,y,z) \ 1. [para(131234(a,1),2711(a,1,2)),rewrite([3666(3)]),flip(a)]. 151649 x / (T(y,z) * (a(y,u,w) * (T(y,z) \ x))) = a(y,u,w) \ 1. [para(131234(a,1),19536(a,1,2,1,1)),rewrite([4408(4),4505(4),131212(3),151591(10)])]. 151677 x \ L(x,y,z) = a(x,z,x * y). [back_rewrite(129028),rewrite([151649(8),113707(4),52858(3)]),flip(a)]. 151698 a(x,y * x,z) = a(x,y,z * x). [back_rewrite(128856),rewrite([151677(3),151649(8),136169(4)])]. 151701 a(x,y,y * z) = a(z,x,y) \ 1. [back_rewrite(123146),rewrite([151677(5),84171(5)]),flip(a)]. 151954 a(x,y,z * (x * x)) = a(y,z,x) \ 1. [back_rewrite(136306),rewrite([151698(3),4578(2)])]. 152039 a(x,y,z * x) = a(y,z,x \ y) \ 1. [back_rewrite(136177),rewrite([151698(6),16(5),84171(4),133728(4),85263(2),151698(2)])]. 152050 a(x,y,z \ x) = a(z,x,y) \ 1. [back_rewrite(133748),rewrite([151698(5),37224(4),28991(3),84171(4),115485(4),84171(2)])]. 152337 a(x,x * y,z) = a(x,y,z * x). [back_rewrite(84641),rewrite([151698(2)]),flip(a)]. 152407 a(x,y,z) \ 1 = a(z,y,x). [back_rewrite(136232),rewrite([151954(3),4408(5),45(3),14(3),84171(2)]),flip(a)]. 153027 a(x,K(y,z),(K(z,y) * u) * x) = 1. [back_rewrite(111960),rewrite([152337(5)])]. 153242 a(x,y,z) = a(x,z,y). [back_rewrite(85028),rewrite([152337(4),80509(3),4505(2),56215(3),112164(2),84171(1),152407(3)])]. 153371 a(x,K(y,z),K(z,y) * u) = a(x,K(y,z),K(y,z) * u). [back_rewrite(48772),rewrite([153242(4),84171(4),153242(8),84171(8)])]. 153478 a(x,y,z \ x) = a(x,y,z). [back_rewrite(152050),rewrite([84171(3),153242(3),152407(5),84171(3),153242(3),84171(3)])]. 153484 a(x,y,z * x) = a(x,y,z). [back_rewrite(152039),rewrite([153478(4),153242(3),84171(3),152407(5),84171(3),153242(3),84171(3)])]. 153502 a(x,y,y * z) = a(x,y,z). [back_rewrite(151701),rewrite([84171(3),153242(3),152407(5),84171(3),153242(3),84171(3)])]. 158117 a(x,K(y,z),K(z,y) * u) = 1. [back_rewrite(153027),rewrite([153484(5)])]. 158590 a(x,y,K(z,u)) = 1. [back_rewrite(153371),rewrite([158117(4),153502(5),153242(3)]),flip(a)]. 158591 $F # answer("aK3"). [resolve(158590,a,40,a)]. ============================== end of proof ========================== % Redundant proof: 160385 $F # answer("aK3"). [back_rewrite(40),rewrite([158590(6)]),xx(a)]. % Disable descendants (x means already disabled): 40x 153x 56238 given #2055 (W0w,wt=8): 158590 a(x,y,K(z,u)) = 1. [back_rewrite(153371),rewrite([158117(4),153502(5),153242(3)]),flip(a)]. given #2056 (W0w,wt=8): 159811 a(x,1,y * z) = 1. [back_rewrite(155031),rewrite([155097(5),153242(3)])]. given #2057 (W0w,wt=8): 160286 T(x,a(y,z,x)) = x. [back_rewrite(53609),rewrite([158938(3),153734(3),153242(1),158832(3)])]. given #2058 (W0w,wt=9): 153242 a(x,y,z) = a(x,z,y). [back_rewrite(85028),rewrite([152337(4),80509(3),4505(2),56215(3),112164(2),84171(1),152407(3)])]. given #2059 (W0w,wt=9): 156787 a(c20,c21,a(c17,c18,c19)) != 1 # answer("aa1"). [back_rewrite(87200),rewrite([153242(7)])]. given #2060 (W0w,wt=9): 157238 L(x,y,a(y,z,u)) = x. [back_rewrite(84982),rewrite([153242(3),153874(3),84171(1)])]. given #2061 (W0w,wt=9): 157850 a(c22,c26,a(c23,c24,c25)) != 1 # answer("aa2"). [back_rewrite(43),rewrite([153242(7)])]. given #2062 (W0w,wt=9): 158212 a(x,1,a(y,z,u)) = 1. [back_rewrite(152711),rewrite([157752(7),153484(4)])]. given #2063 (W0w,wt=9): 161572 L(x,y,a(z,x,y)) = x. [back_rewrite(159201),rewrite([159328(5),29615(5)]),flip(a)]. given #2064 (W0w,wt=9): 164098 L(x,y,a(x,z,y)) = x. [para(161572(a,1),52858(a,1)),rewrite([84171(1),52858(2)]),flip(a)]. given #2065 (W0w,wt=9): 164099 L(x,y,a(x,y,z)) = x. [para(161572(a,1),55660(a,1,1)),rewrite([84171(1),153242(1)])]. given #2066 (W0w,wt=10): 133829 L(x,y * y,z * u) = x. [para(92(a,1),118611(a,1,3)),rewrite([105587(3)])]. given #2067 (W0w,wt=10): 133856 L(x,T(y,z),T(y,u)) = x. [para(7769(a,1),118619(a,1,3,1))]. given #2068 (W0w,wt=10): 133914 L(x,K(y,z),T(z,u)) = x. [para(17781(a,1),118644(a,1,2))]. given #2069 (W0w,wt=10): 139463 L(x * y,y,x) = x * y. [para(1607(a,1),105846(a,2)),rewrite([4505(2),90(2),52858(2)])]. given #2070 (W0a,wt=16): 1733 K(L(x \ y,x,z),(z * y) / (z * x)) = 1. [para(74(a,2),554(a,1,1))]. given #2071 (W0a,wt=15): 1839 (x * (x * y)) / z = x * (x * (y / z)). [para(1014(a,1),37(a,1)),rewrite([1014(6)])]. given #2072 (W0r,wt=15): 35978 T(x,y) / T(z,y) = y \ (x * (z \ y)). [back_rewrite(34798),rewrite([35829(5),7550(5)]),flip(a)]. given #2073 (W0r,wt=18): 142750 L(x * y,T(y \ 1,x \ 1),T(x,z)) = x * y. [para(27652(a,2),130479(a,1,2))]. given #2074 (W0r,wt=17): 97697 K(x * (x * x),x / y) = K(y,x * (x * x)). [para(10920(a,1),16830(a,1,2,2,2)),rewrite([23170(7),17781(5),15(5)]),flip(a)]. given #2075 (W0r,wt=15): 158546 a(x,y,z) * (L(x,y,z) * u) = x * u. [back_rewrite(116749),rewrite([153484(2),52858(2)])]. given #2076 (W0r,wt=19): 138516 (T(T(x,y),z) * u) \ T(T(x,y) * (z * u),z) = z. [back_rewrite(70992),rewrite([138261(7)])]. given #2077 (W1w,wt=21): 23201 (K(x,y) * (z * T(x,y))) / x = K(x,y) * (z * K(x,y)). [para(16985(a,1),106(a,1,1,2,2))]. given #2078 (W1w,wt=21): 23214 T(x * (K(x * y,z) * x),y) = y \ (x * T(x * y,z)). [para(16985(a,1),122(a,1,2,2)),flip(a)]. given #2079 (W1w,wt=21): 23362 K(T(T(x,y),z) * u,T(T(x,z),y)) = K(u,T(T(x,y),z)). [para(3398(a,1),17771(a,1,2)),rewrite([23356(7)]),flip(a)]. given #2080 (W1w,wt=21): 23367 K(x \ y,T(x * (z * z),y)) = K(x \ y,z * (z * x)). [para(10927(a,1),17771(a,1,2))]. given #2081 (W1w,wt=21): 23398 T(T(T(x,y),z),u) \ T(T(x,z),y) = K(u,T(T(x,y),z)). [back_rewrite(22836),rewrite([23362(12)])]. given #2082 (W1w,wt=21): 23435 T(T(T(x,y),z),u * T(T(x,z),y)) = T(T(T(x,z),y),u). [back_rewrite(8940),rewrite([23380(6)]),flip(a)]. given #2083 (W1w,wt=21): 23441 T(T(T(T(x,y),z),u),T(w,x)) = T(T(T(T(x,w),y),z),u). [back_rewrite(3839),rewrite([23380(2)]),flip(a)]. given #2084 (W1w,wt=21): 23536 T(x * (y * (x * z)),x * (y * x)) = z * (x * (y * x)). [para(128(a,1),4209(a,1,1))]. given #2085 (W1a,wt=29): 1919 x * (x * (((y * z) * u) / T(x * (x * (y * (z * u))),a(y,z,u)))) = a(y,z,u). [back_rewrite(1256),rewrite([1839(11)])]. given #2086 (W1a,wt=27): 2216 (x \ y) * (x * (z * (x * ((x \ y) * u)))) = ((x \ y) * (x * (z * y))) * u. [para(16(a,1),130(a,1,1,2,2,2)),flip(a)]. given #2087 (W1r,wt=27): 61052 T(T(T(T(T(x,y),z),u \ 1),w),v5) = T(T(T(T(T(x,w),v5),y),z),u \ 1). [para(4094(a,1),18(a,1,1)),rewrite([18(9)]),flip(a)]. given #2088 (W1r,wt=28): 110804 (x \ (((y * (x * z)) \ x) * ((z * x) * y))) * K(L(y,x,z),x * (z * x)) = 1. [back_rewrite(57173),rewrite([109339(4),35803(7)])]. given #2089 (W1r,wt=28): 147231 L(L(L(x,y,z),u,w),L(L(x,u,w),y,z) / v5,T(v5,v6)) = L(L(x,u,w),y,z). [para(130939(a,1),228(a,1)),flip(a)]. given #2090 (W1r,wt=22): 148319 L(x / y,y * K(z,x \ y),y * T(y \ x,z)) = x / y. [back_rewrite(114594),rewrite([147785(3)])]. given #2091 (W1r,wt=26): 132842 L(T(x,y * y),z * (y * (y * u)),T(z,y * y) * u) = T(x,y * y). [para(100(a,1),109881(a,1,2,2)),rewrite([3436(4),10809(7),4505(4),30703(4),2040(9),100(11),2507(12),108182(10)])]. given #2092 (W2w,wt=31): 9552 x * (x * (y * (z * (x * (x * (y * (((y * z) * (x * (x * y))) \ u))))))) = x * (x * u). [para(17(a,1),3947(a,1,2,2,2,2,2,2,2,1,2,2,2)),rewrite([169(9),4906(14)])]. given #2093 (W2w,wt=31): 9572 (x \ (x \ y)) * ((x \ (x \ y)) * (z \ ((y * (x \ (x \ (y / z)))) \ u))) = x \ (x \ u). [para(3947(a,1),3143(a,1)),rewrite([3143(5),3143(4),3143(14),3143(13),3143(16),3143(15),6073(13),3143(15),6073(14)]),flip(a)]. given #2094 (W2w,wt=31): 9578 x * (x * (y * (x * (x * (y * ((z * y) \ ((y * (x * (x / z))) \ u))))))) = x * (x * u). [para(3691(a,1),3947(a,1,2,2,2,2,2,2,2,1,2,2,2)),rewrite([1014(4)])]. given #2095 (W2w,wt=31): 10219 x / T(T(T(T(T(y,z),u),x \ 1),w),v5) = x / T(T(T(T(T(y,w),z),u),v5),x \ 1). [para(3794(a,1),6565(a,1,1)),rewrite([6565(10)]),flip(a)]. given #2096 (W2a,wt=33): 1560 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),y,z),v7,v8),u,w),v5,v6). [para(233(a,2),97(a,1))]. given #2097 (W2a,wt=33): 1576 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v7,v8),v5,v6),u,w),y,z),v9,v10). [para(34(a,1),1556(a,1,1,1,1))]. given #2098 (W2r,wt=32): 163220 a(x * (y * (x * (z * (x * (y * x))))),u * x,x * (y * (x * (z * (x * (y * u)))))) = 1. [back_rewrite(157817),rewrite([162398(14)])]. given #2099 (W2r,wt=34): 141221 a(x,y * (T(z * z,u) * ((z * u) * y)),y * (T(z * z,u) * ((z * u) * (y * (w * w))))) = 1. [para(15419(a,1),119425(a,1,2,2,2)),rewrite([68297(6),15419(14),68297(14)])]. given #2100 (W2r,wt=33): 117116 L(T(T(x \ 1,y),T((z * ((z \ u) * x)) / u,y) * w),u,z) = L(T(T(x \ 1,y),w),u,z). [back_rewrite(113571),rewrite([117093(9)])]. given #2101 (W2r,wt=32): 76014 L(x,K(y * T(z,u \ (u \ y)),y \ w),(y \ w) * (u * (u * (z * (u \ (u \ y)))))) = x. [para(33494(a,2),33334(a,1,3))]. given #2102 (W2r,wt=35): 142011 T(T((x * y) * T(z,K(y,x)),u),w * (T((x * y) * z,u) / w)) = T((x * y) * T(z,K(y,x)),u). [para(2918(a,1),80094(a,1,1,1,1)),rewrite([52858(10),105864(10),2918(14)])]. given #2103 (W0w,wt=9): 165728 K(K(x,y),K(z,x)) = 1. [para(23201(a,1),17814(a,1,2)),rewrite([145581(5),145608(3),126973(8),146031(4)])]. given #2104 (W0w,wt=9): 167969 K(K(x,y),K(y,z)) = 1. [para(165728(a,1),4993(a,1,1)),rewrite([13(5)])]. given #2105 (W0w,wt=9): 167972 K(K(x,y),K(z,y)) = 1. [para(165728(a,1),16710(a,2)),rewrite([6144(4),117616(5)])]. given #2106 (W0w,wt=9): 167975 K(K(x,y),K(x,z)) = 1. [para(165728(a,1),17822(a,2)),rewrite([5005(3),96031(5,R),17884(5)])]. given #2107 (W0w,wt=10): 139640 a(x,y,z * T(z,x)) = 1. [para(75898(a,1),133073(a,1,1)),rewrite([33957(4),547(3),13(5)])]. given #2108 (W0w,wt=10): 142785 L(x,y,T(x * y,z)) = x. [para(15(a,1),130507(a,1,2))]. given #2109 (W0w,wt=10): 147110 L(x,y,T(y / x,z)) = x. [para(18(a,1),130935(a,1,2))]. given #2110 (W0w,wt=10): 147135 L(x,y \ x,T(y,z)) = x. [para(3143(a,1),130935(a,1,2)),rewrite([106383(5)])]. given #2111 (W0w,wt=10): 152414 K(x \ y,a(y,x,z)) = 1. [back_rewrite(136294),rewrite([152020(5),147785(3,R)])]. given #2112 (W0w,wt=10): 156427 K(a(x,y,z),x * z) = 1. [back_rewrite(99742),rewrite([153242(3),153607(3),153242(1),84171(1)])]. given #2113 (W0w,wt=10): 157432 K(x * y,a(x,y,z)) = 1. [back_rewrite(80567),rewrite([153242(4),153607(4),84171(2),153242(2),84171(2)])]. given #2114 (W0w,wt=10): 158466 K(x * x,a(y,z,u)) = 1. [back_rewrite(151794),rewrite([153484(2),153528(4),84171(3),153242(3),124631(5)])]. given #2115 (W0w,wt=10): 158478 a(x,y,z * T(z,y)) = 1. [back_rewrite(149082),rewrite([153484(4),153242(3)])]. given #2116 (W0w,wt=10): 159176 K(x * y,a(z,x,y)) = 1. [back_rewrite(113610),rewrite([153528(7),84171(6),153242(6),158230(7),147785(6),10229(5),10215(4),30508(4),112951(4),158817(5),153528(4),84171(3),153242(3)]),flip(a)]. given #2117 (W0w,wt=10): 159183 K(a(x,y,z),y * z) = 1. [back_rewrite(105983),rewrite([153528(2),84171(1),153242(1)])]. given #2118 (W0w,wt=10): 159888 K(a(x,y,z),x * y) = 1. [back_rewrite(150613),rewrite([158938(4),14(3),153242(2),153815(2),153242(1)])]. given #2119 (W0a,wt=15): 1840 x * ((x \ y) * (x / z)) = (y * x) / z. [para(1014(a,1),104(a,1,2,2)),rewrite([1014(8)])]. given #2120 (W0a,wt=16): 1858 L(x \ (y \ 1),x,z) = (z * x) \ (z / y). [para(1014(a,1),74(a,2,2))]. given #2121 (W0r,wt=19): 97293 K(K(x,y * (x \ z)),(x * z) * T(y,x \ z)) = 1. [para(15(a,1),16576(a,1,1,2,2,2)),rewrite([15(6)])]. given #2122 (W0r,wt=16): 120029 L(x,T(y,z * z),T(z * (y * z),y)) = x. [back_rewrite(112120),rewrite([119977(6),110290(6),32749(5),7775(4),39006(5)])]. given #2123 (W0r,wt=13): 74393 K(K(x,K(y,z)),K(y,T(z,x))) = 1. [back_rewrite(42731),rewrite([74142(7),37429(4)])]. given #2124 (W0r,wt=14): 168561 K(x * (y * (x * y)),a(z,u,w)) = 1. [para(189(a,1),158466(a,1,1)),rewrite([101(2)])]. given #2125 (W0r,wt=18): 119622 a(x,y,(z * (u * y)) * (y * ((y \ z) * u))) = 1. [para(136(a,1),82987(a,1,3,2)),rewrite([100484(6)])]. given #2126 (W1w,wt=21): 23583 K(x * (y * x),x * (y * (x * z))) = K(x * (y * x),z). [para(128(a,1),16686(a,1,2))]. given #2127 (W1w,wt=21): 24062 x * (y * ((x \ z) * z)) = z * (z * T(y,(x \ z) * z)). [back_rewrite(1369),rewrite([23698(7)]),flip(a)]. given #2128 (W1w,wt=21): 24609 T(a(x,y,z),((x \ y) * z) * ((y * z) \ x)) = a(x,y,z). [back_rewrite(21693),rewrite([24189(3),24189(10)])]. given #2129 (W1w,wt=21): 24619 ((x \ y) * z) / T(x \ (y * z),a(x,y,z)) = a(x,y,z). [back_rewrite(6100),rewrite([24189(7),24189(10)])]. given #2130 (W1w,wt=21): 24764 x * (T(y / (y * x),K(x,y)) * (x * z)) = T(x,y) * z. [back_rewrite(17974),rewrite([24645(2)])]. given #2131 (W1w,wt=21): 24770 T(T(T(T(x,y),z),u),w / (w * x)) = T(T(T(x,y),z),u). [back_rewrite(13111),rewrite([24645(5)])]. given #2132 (W1w,wt=21): 24836 (x * (y * (z * (y \ z)))) / (x * (z * (y * (z / y)))) = 1. [para(20620(a,1),729(a,1,1,1,2)),rewrite([14(2),20620(15),51(13),88(10),20620(16),51(14)])]. given #2133 (W1w,wt=21): 24979 K(x * (x * (y * (z * y))),x * (y * (z * (y * x)))) = 1. [para(106(a,1),3951(a,1,1,2,2))]. given #2134 (W1a,wt=23): 2217 (x * (y * (z * (y * (x * u))))) / u = x * (y * (z * (y * x))). [para(130(a,1),17(a,1,1))]. given #2135 (W1a,wt=23): 2219 x * (y * ((z / (y * x)) * (y * (x * u)))) = (x * (y * z)) * u. [para(18(a,1),130(a,1,1,2,2)),flip(a)]. given #2136 (W1r,wt=26): 62914 L(x,y * (z \ (z \ T(x,u))),K(x,u) * T(y,z \ (z \ T(x,u)))) = x. [para(4404(a,1),38761(a,1,3)),rewrite([2507(13),52858(11)])]. given #2137 (W1r,wt=22): 167539 L(x \ y,x,z) \ (x \ (u * (u / z))) = y \ (u * (u / z)). [para(9572(a,1),6591(a,2,1)),rewrite([167479(9),52858(4),105587(4),16(3),52858(2),4408(7),4408(4),1014(7),39590(5),4408(11),4408(8),1014(11),39590(9)])]. given #2138 (W1r,wt=29): 125913 K(K(x,T(T(T(T(y,z),u),w),v5)),T(T(T(T(T(y,v5),w),z),u),x \ 1) / x) = 1. [para(5981(a,1),17814(a,1,2)),rewrite([45896(8)])]. given #2139 (W1r,wt=27): 144655 T(T(x \ y,z),u) * T(T(T(y \ x,z),w),u) = K(w,T(T(x \ y,z),u)). [para(537(a,1),22734(a,1,2,1,1)),rewrite([622(4),35978(8),70498(6),72954(8),622(12)])]. given #2140 (W1r,wt=25): 134741 K(x * T(T(T(T(y,z),u),w),v5),T(T(T(T(y,u),w),v5),z) * x) = 1. [para(20300(a,1),20911(a,1,1,1)),rewrite([13(7),20300(18),20300(19),14(12),13(11)])]. given #2141 (W2w,wt=31): 10228 x / T(T(T(T(T(y,z),u),w),x \ 1),v5) = x / T(T(T(T(T(y,v5),z),u),w),x \ 1). [para(4092(a,1),6565(a,1,1)),rewrite([6565(10)]),flip(a)]. given #2142 (W2w,wt=31): 10246 T(x,y \ 1) * (y \ ((z * (y / x)) * (x * (y \ u)))) = (T(x,y \ 1) * (y \ z)) * u. [back_rewrite(7417),rewrite([10215(5)])]. given #2143 (W2w,wt=31): 10338 ((x \ (y / z)) * z) \ ((((z / y) / x) * y) * (y / z)) = K(((z / y) / x) * y,y / z). [back_rewrite(6107),rewrite([10229(7),1014(7),10229(13),1014(13)])]. given #2144 (W2w,wt=31): 10339 (x / T(T(T(T(T(y,z),u),w),x \ 1),v5)) * T(T(T(T(T(y,v5),z),u),w),x \ 1) = x. [back_rewrite(5952),rewrite([10229(16)])]. given #2145 (W2a,wt=33): 1577 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),v7,v8),y,z),u,w),v5,v6). [para(1556(a,1),97(a,1)),flip(a)]. given #2146 (W2a,wt=33): 1578 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v5,v6),u,w),y,z),v7,v8),v9,v10). [para(97(a,2),1556(a,1,1))]. given #2147 (W2r,wt=35): 143144 K(L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10),L(L(L(L(L(x,v9,v10),v5,v6),v7,v8),y,z),u,w)) = 1. [para(938(a,2),1635(a,1,2))]. given #2148 (W2r,wt=34): 172549 T(x * ((L(y \ z,y,u) * x) \ (u * z)),w) = L(T(T(u * y,u * z),w),x,L(y \ z,y,u)). [back_rewrite(90814),rewrite([172060(6)])]. given #2149 (W2r,wt=32): 132815 L(T(x,y),((y \ z) * z) * ((u * y) * w),y * (x * (z * (z * ((u * y) * w))))) = T(x,y). [para(37(a,1),109881(a,1,3,2,2,1)),rewrite([15452(4),33451(6),37(10)])]. given #2150 (W2r,wt=33): 101402 (((x \ y) * (x * z)) * (x / u)) \ ((y * (x * (z * x))) / u) = T(x,(y * (x * (z * x))) / u). [back_rewrite(33524),rewrite([101264(8),101264(13)])]. given #2151 (W2r,wt=33): 149440 K(T(T(x,y),z) / u,T(T(w,v5),v6)) * T(T(T(w,v6),T(T(x,z),y) / u),v5) = T(T(w,v5),v6). [para(20921(a,1),23046(a,1,1))]. given #2152 (W0w,wt=10): 160317 a(x,K(x,y),z * u) = 1. [back_rewrite(157374),rewrite([158173(5)])]. given #2153 (W0w,wt=10): 162577 a(x,y * y,z * u) = 1. [back_rewrite(159386),rewrite([161865(6),160312(5)])]. given #2154 (W0w,wt=10): 162876 a(x,K(y,x),z * u) = 1. [back_rewrite(157375),rewrite([162028(6),84171(5),160335(5)])]. given #2155 (W0w,wt=10): 163184 a(x,x \ 1,y * z) = 1. [back_rewrite(162372),rewrite([162398(8),4505(6),162028(7),84171(6),153242(6),158171(6),84171(4)])]. given #2156 (W0w,wt=10): 168398 K(x \ 1,a(x,y,z)) = 1. [para(1091(a,1),152414(a,1,1)),rewrite([153242(4),153528(4)])]. given #2157 (W0w,wt=9): 173010 a(x,1,L(y,z,u)) = 1. [para(168398(a,1),89355(a,1,2)),rewrite([1014(5),131227(3),158938(4),157230(3)])]. given #2158 (W0w,wt=10): 168399 K(x \ y,a(x,y,z)) = 1. [para(152414(a,1),4993(a,1,1)),rewrite([147785(4,R),13(5)])]. given #2159 (W0w,wt=10): 168425 K(a(x,y,z),z * x) = 1. [para(90(a,1),156427(a,1,2)),rewrite([160751(2)])]. given #2160 (W0w,wt=10): 168426 K(a(x,y,z),x / z) = 1. [para(1014(a,1),156427(a,1,2)),rewrite([158938(3),14(2)])]. given #2161 (W0w,wt=8): 173047 K(x,a(y,z,x)) = 1. [para(3691(a,1),168426(a,1,2)),rewrite([153484(2),17781(4)])]. given #2162 (W0w,wt=10): 168429 K(x \ y,a(y,z,x)) = 1. [para(3143(a,1),156427(a,1,2)),rewrite([84171(3),153242(3),158938(3),14(2),153242(1),84171(1),147785(3,R)])]. given #2163 (W0w,wt=10): 168431 K(a(x,y,z),T(y,x)) = 1. [para(4505(a,1),156427(a,1,2)),rewrite([84171(2),153242(2),84171(2),158938(2),153528(2),84171(1)])]. given #2164 (W0w,wt=10): 168495 K(x / y,a(x,y,z)) = 1. [para(1014(a,1),157432(a,1,1)),rewrite([153242(4),158938(4),14(3),153242(2)])]. given #2165 (W0w,wt=10): 168563 K(a(x,y,z),u * u) = 1. [para(158466(a,1),4993(a,1,1)),rewrite([13(5)])]. given #2166 (W0w,wt=10): 168606 K(a(x,y,z),z * y) = 1. [para(90(a,1),159183(a,1,2)),rewrite([160751(2)])]. given #2167 (W0w,wt=10): 168607 K(a(x,y,z),y / z) = 1. [para(1014(a,1),159183(a,1,2)),rewrite([158938(3),14(2)])]. given #2168 (W0a,wt=13): 1874 (x / y) / T(x,y \ 1) = y \ 1. [para(1014(a,1),165(a,1,1))]. given #2169 (W0a,wt=15): 2040 (x * (y * y)) * z = x * (y * (y * z)). [back_rewrite(407),rewrite([2012(7)]),flip(a)]. given #2170 (W0r,wt=20): 163580 x * (y * (T(z,u) * K(u,L(z,x,y)))) = x * (y * z). [back_rewrite(110414),rewrite([163437(6),163437(5)])]. given #2171 (W0r,wt=14): 98160 L(x,y,z) * (y * ((x * y) \ z)) = z. [para(5660(a,1),84(a,2)),rewrite([98147(16),57210(3),52858(1),98147(17)])]. given #2172 (W0r,wt=16): 104501 K(L(x,y,z),((z * y) \ (z / x)) * y) = 1. [back_rewrite(103936),rewrite([104117(1)])]. given #2173 (W0r,wt=20): 53559 (x \ y) / ((z \ (x \ (x \ y))) * T(x,y)) = L(z,x,y). [back_rewrite(8400),rewrite([52843(5),52858(4),7554(4),52858(1)]),flip(a)]. given #2174 (W0r,wt=16): 56531 (x * ((x \ y) * z)) / L(T(y,z),x,z) = z. [back_rewrite(45267),rewrite([52953(6)])]. given #2175 (W1w,wt=21): 25040 T((x * y) * z,K((x \ y) * z,x * x)) = (x * y) * z. [para(136(a,1),5120(a,1,1)),rewrite([1607(5),136(11)])]. given #2176 (W1w,wt=21): 25071 (x * y) / T(z \ (z \ y),T(x,y)) = z * (z * T(x,y)). [para(3143(a,1),5364(a,1,2,1,2)),rewrite([3143(5),4408(12),45(10),4408(11),45(8)])]. given #2177 (W1w,wt=21): 25091 T(x,y) / T(z * (z * x),K(x,y)) = z \ (z \ K(x,y)). [para(12307(a,1),5364(a,1,2,2)),rewrite([16985(2),12307(8)])]. given #2178 (W1w,wt=21): 25094 K(x,y) / T(z * (z * (y / (y * x))),x) = z \ (z \ x). [para(12386(a,1),5364(a,1,2,2)),rewrite([23481(3),12386(10)])]. given #2179 (W1w,wt=21): 25096 K(x,y) / T(z * (z * (x \ (y \ x))),y) = z \ (z \ y). [para(14186(a,1),5364(a,1,2,2)),rewrite([16615(3),14186(10)])]. given #2180 (W1w,wt=21): 25211 x * (x * (y \ ((y / x) / T(z * z,x)))) = z \ (z \ x). [para(1014(a,1),5428(a,1,2,2,2,2)),rewrite([6120(7),4407(6),10229(6),1014(6)])]. given #2181 (W1w,wt=21): 25260 (x * (y * (z \ (z \ x)))) * T(z * z,x) = x * (y * x). [para(5428(a,1),106(a,1,1,2,2)),rewrite([25191(10),4155(8),4408(7),4408(6),15538(7)])]. given #2182 (W1w,wt=21): 25284 T(x * (y * x),x * (y * z)) = T(x * (y * x),x \ z). [para(16(a,1),5475(a,1,2,2,2))]. given #2183 (W1a,wt=25): 2225 x \ (y * (z * (u * (z * (y * x))))) = T(y * (z * (u * (z * y))),x). [para(130(a,1),23(a,1,2))]. given #2184 (W1a,wt=27): 2229 ((x \ y) * (x * (z * y))) * (x * u) = (x \ y) * (x * (z * ((y * x) * u))). [para(104(a,1),130(a,2,2,2,2)),rewrite([16(3)])]. given #2185 (W1r,wt=25): 169562 K(x,K(x * (y * (z \ (y / z))),T(z / y,y * (z \ (y / z))))) = 1. [para(5359(a,1),97293(a,1,2,1)),rewrite([10229(4),143411(4),10229(10),143411(10),13(12),96031(11),37242(11),37429(10)])]. given #2186 (W1r,wt=29): 134725 K(x * ((y \ x) * T(y \ x,z)),y * (x * ((y \ (x / y)) * T(x / y,z)))) = 1. [para(547(a,1),20911(a,1,2,2,2)),rewrite([62471(4),3169(5),115377(11)])]. given #2187 (W1r,wt=27): 102672 (x / y) * (z * (y * ((y \ x) * u))) = y * (((y \ x) * (y \ (z * x))) * u). [para(24045(a,1),15(a,1,2)),rewrite([24002(6),6135(4)]),flip(a)]. given #2188 (W1r,wt=21): 73654 x / (x * (y * (y * (z * x)))) = z \ (y \ (y \ (x \ 1))). [back_rewrite(66656),rewrite([73580(7)])]. given #2189 (W1r,wt=29): 172753 x * K(y * (z * (u * (u / y))),T(T(T(T(z * (u * u),w),v5),v6),x \ 1)) = x. [para(18932(a,1),10339(a,1,2,1,1,1,1)),rewrite([124421(23)])]. given #2190 (W2w,wt=31): 10340 (x / T(T(T(T(T(y,z),u),w),v5),x \ 1)) * T(T(T(T(T(y,u),w),v5),x \ 1),z) = x. [back_rewrite(5951),rewrite([10229(16)])]. given #2191 (W2w,wt=31): 10357 (x / T(T(T(T(T(y,z),u),x \ 1),w),v5)) * T(T(T(T(T(y,w),z),u),v5),x \ 1) = x. [back_rewrite(4068),rewrite([10229(16)])]. given #2192 (W2w,wt=31): 10358 (x / T(T(T(T(T(y,z),u),w),v5),x \ 1)) * T(T(T(T(T(y,u),w),x \ 1),z),v5) = x. [back_rewrite(4067),rewrite([10229(16)])]. given #2193 (W2w,wt=31): 10766 T(T(T(T(T(x,y),z),T(T(T(x,z),u),y) \ w),v5),u) = T(T(T(T(T(x,y),z),u),w),v5). [para(94(a,2),4213(a,1,1,1,2,1))]. given #2194 (W2a,wt=33): 1581 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),v7,v8),v5,v6),y,z),u,w). [para(1556(a,2),233(a,1))]. given #2195 (W2a,wt=35): 2221 (x * (y * (z * (y * (x * u))))) \ (u * (x * (y * (z * (y * x))))) = K(u,x * (y * (z * (y * x)))). [para(130(a,1),20(a,1,1))]. given #2196 (W2r,wt=31): 57609 x * (x * (y * (x * (x * (z \ (y * ((y * (x * (x * (z \ y)))) \ u))))))) = x * (x * u). [back_rewrite(9568),rewrite([55766(8)])]. given #2197 (W2r,wt=31): 43902 K(T(T(x * (y * y),z),u) / (y * x),(y * x) / T(T(y * (x * y),x \ z),u)) = 1. [para(10927(a,1),31324(a,1,1,1,1)),rewrite([101(9)])]. given #2198 (W2r,wt=33): 130087 T(T(T(T(x * y,z),u),w),T(T(T(y * x,w),z),v5)) / x = T(T(T(x * y,w),z),u) / x. [para(556(a,1),5988(a,1,1,1)),rewrite([3844(7),29(14)]),flip(a)]. given #2199 (W2r,wt=31): 40352 (x / T(y,z * z)) * (z * ((z / (z * x)) * (z \ y))) = K(z * (z / x),z \ (z \ y)). [back_rewrite(30689),rewrite([40152(4)])]. given #2200 (W2r,wt=33): 39779 (x * (y * (z * (y / u)))) \ (y \ (z \ (y \ 1))) = u / (y * (z * (y * (x * (y * (z * y)))))). [back_rewrite(11890),rewrite([39506(8)])]. given #2201 (W0w,wt=8): 173213 K(x,a(y,x,z)) = 1. [para(3666(a,1),168607(a,1,2)),rewrite([153242(2),158938(2),153815(2),153242(1),17781(4)])]. given #2202 (W0w,wt=10): 168608 K(x \ y,a(z,y,x)) = 1. [para(3143(a,1),159183(a,1,2)),rewrite([153242(3),158938(3),14(2),153242(1),147785(3,R)])]. given #2203 (W0w,wt=10): 168609 K(a(x,y,z),T(z,y)) = 1. [para(4505(a,1),159183(a,1,2)),rewrite([153242(2),158938(2),153502(2)])]. given #2204 (W0w,wt=10): 168635 K(a(x,y,z),y * x) = 1. [para(90(a,1),159888(a,1,2)),rewrite([153242(2),160751(2),153242(1)])]. given #2205 (W0w,wt=10): 168636 K(a(x,y,z),x / y) = 1. [para(1014(a,1),159888(a,1,2)),rewrite([153242(3),158938(3),14(2),153242(1)])]. given #2206 (W0w,wt=10): 172965 a(1,x \ y,z * u) = 1. [para(554(a,1),160317(a,1,2)),rewrite([84171(4)])]. given #2207 (W0w,wt=10): 172966 a(1,x * y,z * u) = 1. [para(2772(a,1),160317(a,1,2)),rewrite([84171(4)])]. given #2208 (W0w,wt=10): 172967 a(1,K(x,y),z * u) = 1. [para(3327(a,1),160317(a,1,2)),rewrite([84171(4)])]. given #2209 (W0w,wt=10): 172968 a(1,x / y,z * u) = 1. [para(9999(a,1),160317(a,1,2)),rewrite([84171(4)])]. given #2210 (W0w,wt=10): 173008 K(x \ 1,L(x,y,z)) = 1. [para(168398(a,1),16710(a,2)),rewrite([4408(6),45(4),157230(4)])]. given #2211 (W0w,wt=10): 173018 K(a(x,y,z),z / x) = 1. [para(1014(a,1),168425(a,1,2)),rewrite([84171(3),153242(3),158938(3),14(2),153242(1),84171(1)])]. given #2212 (W0w,wt=10): 173020 K(x \ y,a(x,z,y)) = 1. [para(3143(a,1),168425(a,1,2)),rewrite([158938(3),14(2),147785(3,R)])]. given #2213 (W0w,wt=10): 173052 K(x / y,a(y,z,x)) = 1. [para(168426(a,1),17822(a,2)),rewrite([10215(3),42703(5)])]. given #2214 (W0w,wt=10): 173097 K(a(x,y,z),T(x,y)) = 1. [para(1708(a,1),168431(a,1,2)),rewrite([84171(2),153242(2),153528(2),84171(1)])]. given #2215 (W0w,wt=10): 173117 K(a(x,y,z),T(y,u)) = 1. [para(13425(a,1),168431(a,1,2)),rewrite([153242(5),84171(5),160751(5),160751(4),153242(3),84171(3),158938(3),14(2),153242(1),84171(1)])]. given #2216 (W0w,wt=10): 173151 K(a(x,y,z),y / x) = 1. [para(168495(a,1),17781(a,2)),rewrite([10229(4),14(4)])]. given #2217 (W0a,wt=17): 2179 (T(x,y) / z) / T(T(x,z \ 1),y) = z \ 1. [para(997(a,1),1266(a,1,2,2)),rewrite([1014(4),1014(5),18(4),14(8)])]. given #2218 (W0a,wt=19): 2213 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(13(a,1),130(a,1,1,2,2)),rewrite([13(8)])]. given #2219 (W0r,wt=19): 103775 K(x,K(x / y,(y * ((z / y) * x)) / (y * z))) = 1. [back_rewrite(76892),rewrite([103664(8)])]. given #2220 (W0r,wt=19): 105128 L(x,(y \ z) * z,u * (z \ (z \ y))) = L(x,y,u). [back_rewrite(98205),rewrite([104117(6)])]. given #2221 (W0r,wt=17): 137283 a(x,L(y \ z,y,u),u * ((y * u) * z)) = 1. [para(2705(a,1),119457(a,1,3,2)),rewrite([90(7),189(5),84171(6)])]. given #2222 (W0r,wt=17): 148658 K(T(x \ y,z) * x,y * K(z,y \ x)) = 1. [back_rewrite(75581),rewrite([147785(5)])]. given #2223 (W0r,wt=15): 129788 K((x * y) / z,K(z,T(x * y,y))) = 1. [para(100398(a,1),71857(a,1,2))]. given #2224 (W1w,wt=21): 25342 T(x,y \ K(x * (x / y),z)) = T(x,T(x * (x / y),z)). [para(12307(a,1),5504(a,1,2,2)),rewrite([16985(11)])]. given #2225 (W1w,wt=21): 25524 (x * ((x * y) * z)) * ((x * (y * z)) \ T(y,x)) = y * x. [para(22239(a,1),17(a,1,1)),rewrite([4155(8)])]. given #2226 (W1w,wt=21): 25550 (x * ((x * y) * z)) \ (y * x) = (x * (y * z)) \ T(y,x). [para(22239(a,1),1091(a,1,1)),rewrite([4408(11),14(11)])]. given #2227 (W1w,wt=21): 26441 K((x \ y) * (x * z),(y * x) * z) = K((y * x) * z,x). [para(104(a,1),17884(a,1,2)),rewrite([23819(10),189(9),16568(10)])]. given #2228 (W1w,wt=21): 26556 K(K(x,T(T(y,z),u)),T(T(T(y,x \ 1),z),u) / x) = 1. [back_rewrite(26256),rewrite([26497(6)])]. given #2229 (W1w,wt=21): 26970 K(x * (x * y),y \ (x \ (x \ z))) = K(x * (x * y),z). [back_rewrite(15490),rewrite([26960(4)]),flip(a)]. given #2230 (W1w,wt=21): 27220 ((x \ y) * (x / z)) * T(x,(y * x) / z) = (y * x) / z. [para(1014(a,1),5543(a,1,1,2)),rewrite([1014(7),1014(11)])]. given #2231 (W1w,wt=21): 27274 K((x * y) * z,(y \ x) * (y * z)) = K(y,(x * y) * z). [para(5543(a,1),17884(a,1,2)),rewrite([17910(6),27257(10)]),flip(a)]. given #2232 (W1a,wt=25): 2241 (x * (y * (z * (y * (x * u))))) / T(x * (y * (z * (y * x))),u) = u. [para(130(a,1),165(a,1,1))]. given #2233 (W1a,wt=23): 2250 (x * (y * (z * (y * x)))) / u = x * (y * (z * (y * (x / u)))). [para(130(a,1),1014(a,1)),rewrite([1014(3)]),flip(a)]. given #2234 (W1r,wt=28): 63039 L(T(x \ (y \ (x \ z)),y * z),u,y * z) = T(x \ (y \ (x \ z)),y * z). [para(74(a,2),56854(a,1,1,1,2)),rewrite([52858(3),53564(4),52858(7),6073(12),1091(10),39506(11),35648(12),101(9),54309(10)])]. given #2235 (W1r,wt=29): 102151 T(((x / y) * z) * x,T(y \ (((z * (x / y)) \ y) / x),u)) = ((x / y) * z) * x. [para(10393(a,1),18271(a,1,1,2)),rewrite([2968(5),10229(10),10229(11),15452(12),35948(12),4505(10),10393(16),2968(15)])]. given #2236 (W1r,wt=23): 172005 (x * (y * ((x \ (z / y)) * y))) * u = (x * ((y / x) * z)) * u. [para(92(a,1),10246(a,1,1)),rewrite([4408(3),45(2),4155(4),45(3),3691(3),1014(4),4155(5),45(4),169(5),33957(7),113035(7),4155(9),45(8),2774(10),27608(9)])]. given #2237 (W1r,wt=29): 96845 K(x \ y,K(z,T(y / x,u * (u * (w * (w * (x * T(T(x \ y,u),z)))))))) = 1. [back_rewrite(50065),rewrite([96031(14),37242(13),37242(13),29(12),37242(13),37242(14),37429(13),30703(12),38975(12),37242(14),37429(13),29(12),17882(13),37242(13),37429(12),29(11),30703(4),26921(11)])]. given #2238 (W1r,wt=30): 150752 T(x * L(y / z,y,u),L(x * ((y * (z \ u)) / u),x,w)) = x * L(y / z,y,u). [para(56811(a,1),26839(a,1,2))]. given #2239 (W2w,wt=31): 10767 T(T(T(T(T(x,y),z),T(T(T(x,z),y),u) \ w),v5),u) = T(T(T(T(T(x,z),y),u),w),v5). [para(94(a,2),4213(a,1,1,1)),rewrite([29(7)])]. given #2240 (W2w,wt=31): 11038 T(T(T(T(T(x,y \ 1),z),u),w),y \ 1) / y = T(T(T(x,u),w),y \ (y \ z)) / y. [back_rewrite(6005),rewrite([10995(19),3143(17),3143(16)])]. given #2241 (W2w,wt=31): 11056 T(x,y * (y * y)) * T(z,T(x * (y * y),y)) = (y \ (y \ z)) * T(x * (y * y),y). [back_rewrite(6182),rewrite([11037(6),11037(13)])]. given #2242 (W2w,wt=31): 11170 x * (T(y * (x * (z \ x)),u) * (x \ (z / x))) = z * (x \ T(x * (z \ (x * y)),u)). [para(537(a,1),3575(a,1,2,2)),rewrite([4408(3),10229(2),4230(2),4247(3),4155(9),10229(8),4230(8)]),flip(a)]. given #2243 (W2a,wt=35): 2222 (x * (y * (z * (u * (z * y))))) \ (y * (z * (u * (z * (y * x))))) = K(y * (z * (u * (z * y))),x). [para(130(a,1),20(a,1,2))]. given #2244 (W2a,wt=35): 2267 L(x,y,z * (u * z)) \ (z * (u * (z * (y * x)))) = T(z * (u * (z * y)),L(x,y,z * (u * z))). [para(132(a,1),91(a,1,2)),rewrite([132(15)]),flip(a)]. given #2245 (W2r,wt=35): 125996 K(L(T(T(T(T(x,y),z),u),w) / v5,v6,v7),L(T(T(T(T(T(x,w),y),v5 \ 1),z),u) / v5,v6,v7)) = 1. [para(5982(a,2),79394(a,1,2,1)),rewrite([10404(8)])]. given #2246 (W2r,wt=33): 71137 x * (x * (x * ((y * (x * T(x,z))) * T(x,z \ x)))) = x * (x * (x * (y * (x * (x * x))))). [para(16716(a,1),4168(a,1,2,2,1,2,2,2)),rewrite([6144(6),28991(6),33065(7)])]. given #2247 (W2r,wt=33): 100577 (x * y) * (T(z * (z * (x * (y * x))),y) * u) = x * (z * (z * (x * (y * ((x * y) * u))))). [back_rewrite(51980),rewrite([100327(6),37(4),37(5),101(3)])]. given #2248 (W2r,wt=33): 107334 L(x,L(L(L(L(y,z,u),w,v5),v6,v7),v8,v9),L(L(L(L(L(y,v10,v11),v6,v7),w,v5),v8,v9),z,u)) = x. [back_rewrite(65049),rewrite([104117(10)])]. given #2249 (W2r,wt=31): 49619 T(T(T(T(T(x,y),z),u),w),v5 \ 1) / v5 = T(T(T(T(T(x,u),z),y),w),v5 \ 1) / v5. [para(94(a,2),4057(a,1,1))]. given #2250 (W0w,wt=10): 173197 K(x \ y,a(z,x,y)) = 1. [para(3143(a,1),168606(a,1,2)),rewrite([158938(3),14(2),147785(3,R)])]. given #2251 (W0w,wt=10): 173217 K(x / y,a(z,y,x)) = 1. [para(168607(a,1),17822(a,2)),rewrite([10215(3),42703(5)])]. given #2252 (W0w,wt=10): 176867 K(a(x,y,z),T(z,u)) = 1. [para(13425(a,1),168609(a,1,2)),rewrite([160751(5),160751(4),153242(3),158938(3),14(2),153242(1)])]. given #2253 (W0w,wt=10): 176901 K(x / y,a(y,x,z)) = 1. [para(168636(a,1),17822(a,2)),rewrite([10215(3),42703(5)])]. given #2254 (W0w,wt=10): 177046 K(x / y,a(x,z,y)) = 1. [para(173018(a,1),17822(a,2)),rewrite([10215(3),42703(5)])]. given #2255 (W0w,wt=10): 177079 K(a(x,y,z),T(x,u)) = 1. [para(13425(a,1),173097(a,1,2)),rewrite([84171(5),153242(5),84171(5),160751(5),160751(4),153242(3),84171(3),158938(3),14(2),153242(1)])]. given #2256 (W0w,wt=10): 177098 K(x,T(a(x,y,z),u)) = 1. [para(173117(a,1),4993(a,1,1)),rewrite([84171(3),37242(4),13(5)])]. given #2257 (W0w,wt=10): 177126 K(x,T(a(y,x,z),u)) = 1. [para(1018(a,1),173117(a,1,2)),rewrite([153242(4),160751(4),158938(3),14(2),153242(1),95403(5)])]. given #2258 (W0w,wt=10): 178756 K(x / y,a(z,x,y)) = 1. [back_rewrite(173196),rewrite([178629(3,R)])]. given #2259 (W0w,wt=10): 181291 K(x,T(a(y,z,x),u)) = 1. [para(1018(a,1),176867(a,1,2)),rewrite([160751(4),158938(3),14(2),95403(5)])]. given #2260 (W0w,wt=10): 181313 T(x,T(a(x,y,z),u)) = x. [hyper(28,a,177098,a)]. given #2261 (W0w,wt=11): 2759 T(x * y,y * x) = x * y. [back_rewrite(2560),rewrite([2755(4)])]. given #2262 (W0w,wt=11): 2771 T(x,y \ 1) = y * (x / y). [back_rewrite(1837),rewrite([2755(4)]),flip(a)]. given #2263 (W0w,wt=11): 2774 T(x * y,y \ 1) = y * x. [back_rewrite(1812),rewrite([2755(7)])]. given #2264 (W0w,wt=11): 2925 (x * y) / (y * x) = K(x,y). [back_rewrite(2887),rewrite([2918(4)])]. given #2265 (W0w,wt=11): 3436 (x * x) \ y = x \ (x \ y). [para(18(a,1),1324(a,1,2,2)),rewrite([92(8),1619(6)]),flip(a)]. given #2266 (W0a,wt=13): 2507 L(x,y,z * (z * u)) = L(x,y,u). [back_rewrite(144),rewrite([2495(8),21(4)]),flip(a)]. given #2267 (W0a,wt=13): 2644 T(T(x,y),x * z) = T(T(x,z),y). [para(1708(a,1),29(a,1,1)),flip(a)]. given #2268 (W0r,wt=16): 92425 K(x * ((x \ y) * z),K(y,L(z,x,y))) = 1. [para(16121(a,1),19567(a,1,2)),rewrite([16130(12)])]. given #2269 (W0r,wt=11): 18447 T(x \ 1,K(y,x)) = x \ 1. [back_rewrite(12517),rewrite([18412(4)])]. given #2270 (W0r,wt=17): 186277 L(x * y,z * x,L(z * y,x,y)) = x * y. [back_rewrite(107717),rewrite([184298(9),52858(5)])]. given #2271 (W0r,wt=18): 161256 a(x \ (y / x),K(x * z,u),x * (y * z)) = 1. [back_rewrite(130800),rewrite([158938(7)])]. given #2272 (W0r,wt=18): 162781 a(x,y * (y * z),K(y * (y * z),u) * z) = 1. [back_rewrite(160613),rewrite([162028(8)])]. given #2273 (W1w,wt=21): 27294 T(T(x,y),(x \ z) * (x / u)) = T(T(x,(z * x) / u),y). [para(1014(a,1),5557(a,1,2,2)),rewrite([1014(9)])]. given #2274 (W1w,wt=21): 27330 T(T(T(x,(y * x) * z),u),(x * z) \ (y \ x)) = T(x,u). [para(5557(a,1),12372(a,1,1)),rewrite([4407(9),4408(8),14(8)])]. given #2275 (W1w,wt=21): 27348 K((x \ y) * (x * z),T(x,u)) = K((y * x) * z,T(x,u)). [para(5557(a,1),16687(a,1,2)),rewrite([22726(6)]),flip(a)]. given #2276 (W1w,wt=21): 27388 ((x / y) * (z \ y)) * ((z * y) / x) = T(y,(z * y) / x). [para(5560(a,1),3143(a,2)),rewrite([4407(5),4408(4),14(4),10229(3)])]. given #2277 (W1w,wt=21): 27391 T(x,(y * x) / z) * (z / (y * x)) = (z / x) * (y \ x). [para(5560(a,1),3666(a,1,1)),rewrite([10215(6),4407(11),4408(10),14(10),10229(9)])]. given #2278 (W1w,wt=21): 27410 T(T((x * y) / z,y),(y \ x) * (y / z)) = (x * y) / z. [para(5560(a,1),7769(a,1,2)),rewrite([29(10),23380(6)])]. given #2279 (W1w,wt=21): 27468 (x \ (x \ (y \ (y \ K(y,x))))) * (y * (x * (y * x))) = 1. [para(90(a,1),5600(a,1,2,2,2)),rewrite([7775(4),4525(7),4525(5),90(3),4578(2),5162(6),16343(4),19474(5),21062(8),7775(7),26074(9)])]. given #2280 (W1w,wt=21): 27496 K(x * (y * (x * (y * z))),z * (x * (y * (x * y)))) = 1. [para(5600(a,1),2812(a,1,1,2)),rewrite([27454(5),4408(6),4408(5),4408(4),45(2),128(3),24558(4),14(6),27454(9),27465(14),27454(9),4155(10),4408(9),4408(8),45(6),128(7)])]. given #2281 (W1a,wt=23): 2307 x * (((y * z) * x) * (y * x)) = x * (y * ((z * x) * (y * x))). [para(16(a,1),422(a,1,2,1,1,2)),rewrite([104(10)])]. given #2282 (W1a,wt=24): 2498 L(x,y,z * (u * (w * (u * (z * (z * (u * (w * (u * z))))))))) = x. [para(130(a,1),2254(a,1,3))]. given #2283 (W1r,wt=25): 126293 K(x,T((T(x,y) \ T(T(T(x,y),z),u)) / T(T(T(x,y),u),z),y)) = 1. [para(2642(a,1),118849(a,1,2,2,1,1,1)),rewrite([2735(8),2642(5),28891(6),88(9),52619(12),53406(13),37242(11)])]. given #2284 (W1r,wt=24): 184581 K(L(x \ y,x,z),(u * (z * (u * y))) / (u * (z * (u * x)))) = 1. [back_rewrite(164383),rewrite([184265(4),184298(3)])]. given #2285 (W1r,wt=28): 186805 K(K(x \ y,x * (z * x)),L(T(y * (x * z),x) / (x * (z * y)),u,w)) = 1. [back_rewrite(138641),rewrite([185886(5)])]. given #2286 (W1r,wt=21): 174100 K(x,((T(x \ y,z) * y) \ (x \ T(y / x,z))) * y) = 1. [para(130919(a,1),104501(a,1,1)),rewrite([10401(6)])]. given #2287 (W1r,wt=30): 172093 K((x * ((y * x) \ (z \ K(u,w)))) * (w \ (w \ y)),L(w * (T(w,u) * z),x,y)) = 1. [back_rewrite(170806),rewrite([172060(5)])]. given #2288 (W2w,wt=31): 11189 T(x \ T(y,x \ (z / x)),(x * (y * (x \ (z / x)))) / z) = x \ T(y,x \ (z / x)). [para(3575(a,1),2810(a,1,2,1))]. given #2289 (W2w,wt=31): 11190 K((x \ y) * (z * (u * (z \ (x / z)))),((y * x) * (z \ T(u,z \ (x / z)))) / x) = 1. [para(3575(a,1),2812(a,1,1,2))]. given #2290 (W2w,wt=31): 11204 T(T(x * (y * (x \ (z / x))),z),x \ T(y,x \ (z / x))) = x * (y * (x \ (z / x))). [para(3575(a,1),4209(a,2)),rewrite([11203(5)])]. given #2291 (W2w,wt=31): 11211 (T(x,y \ (z / y)) \ y) * (y * (x * (y \ (z / y)))) = T(z,y * (x * (y \ (z / y)))). [back_rewrite(11160),rewrite([11175(14)])]. given #2292 (W2a,wt=33): 2388 K(x,(y * (z * (y * (u * (y * (z * (y * x))))))) / (y * (z * (y * (u * (y * (z * y))))))) = 1. [para(387(a,1),554(a,1,1))]. given #2293 (W2a,wt=33): 2390 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v5,v6),u,w),y,z),v9,v10),v7,v8). [para(97(a,1),235(a,2,1))]. given #2294 (W2r,wt=34): 107130 L(L((x \ y) * (z * z),x,u),x * u,T(y * (z * z),x) * u) = L((x \ y) * (z * z),x,u). [back_rewrite(67436),rewrite([104117(4),104117(14)])]. given #2295 (W2r,wt=31): 176823 x / (y * (K(z,y) * (u * T(y,z \ y)))) = (u * (y * (K(z,y) / x))) \ (y \ K(y,z)). [para(16623(a,1),39779(a,2,2,2,2,2,2,2)),rewrite([33507(6),6144(9),14(9),20951(8),6144(8),1014(8),12328(6),28991(12),38207(15),21063(13)]),flip(a)]. given #2296 (W2r,wt=35): 98155 x * (y * (z * (z * (y * ((u * y) * (x * ((x * (y * (z * (z * (y * ((u * y) * x)))))) \ w))))))) = w. [para(189(a,1),5660(a,1,2,2,2,2,2,2,2,1,2,2,2,2)),rewrite([189(12)])]. given #2297 (W2r,wt=33): 171447 x * (y * ((z / (y * x)) * (x \ T(x * (y * x),u)))) = x * (y * (z * K(x * (y * x),u))). [para(23142(a,1),2219(a,1,2,2,2)),rewrite([163437(15),163437(14)])]. given #2298 (W2r,wt=31): 144729 K(K(x,T(T(T(y,z),u),w)),T(T(T(y,T(x \ 1,u)),x * z),T(T(x,u),z) * w)) = 1. [back_rewrite(141363),rewrite([144670(6)])]. given #2299 (W0w,wt=9): 187475 K(x \ 1,K(y,x)) = 1. [hyper(27,a,18447,a)]. given #2300 (W0w,wt=9): 187493 K(x \ 1,K(x,y)) = 1. [para(18447(a,1),71857(a,1,2,2)),rewrite([17781(5)])]. given #2301 (W0w,wt=10): 185886 L(K(x,y),z,u) = K(x,y). [back_rewrite(150548),rewrite([184298(5),52858(4),2507(4),52858(2)])]. given #2302 (W0w,wt=10): 186142 L(x,K(y,z),u * y) = x. [back_rewrite(118664),rewrite([184298(3),52858(2),53163(2),184298(3),52858(2),55660(2)]),flip(a)]. given #2303 (W0w,wt=10): 186144 L(x,K(y,z),y * u) = x. [back_rewrite(118653),rewrite([184298(4),105587(3)])]. given #2304 (W0w,wt=9): 190227 K(x,K(y,K(x,z))) = 1. [back_rewrite(126995),rewrite([190186(5),96031(3),37242(4),37429(3),37429(2),89(1)])]. given #2305 (W0w,wt=9): 190254 T(x,K(y,K(x,z))) = x. [hyper(28,a,190227,a)]. given #2306 (W0w,wt=9): 190255 K(x,K(y,K(z,x))) = 1. [para(190227(a,1),4993(a,1,1)),rewrite([96031(4),96031(3),13(5)])]. given #2307 (W0w,wt=9): 190290 T(x,K(y,K(z,x))) = x. [para(190254(a,1),7769(a,1,1)),rewrite([6144(3),96031(2),190286(3),1708(4)])]. given #2308 (W0w,wt=10): 190047 L(x,K(y,z),z * u) = x. [para(1014(a,1),186142(a,1,3)),rewrite([147785(3),45(2),110290(3)])]. given #2309 (W0w,wt=10): 190055 L(x,K(y,z),u * z) = x. [para(17781(a,1),186142(a,1,2))]. given #2310 (W0w,wt=11): 4143 T(x \ y,y \ x) = x \ y. [para(2538(a,1),92(a,2)),rewrite([989(3),2538(3)])]. given #2311 (W0w,wt=11): 4155 x / (y \ z) = x * (z \ y). [para(2538(a,1),1013(a,1,2))]. given #2312 (W0w,wt=11): 4230 (x / y) * x = x * (y \ x). [para(2643(a,1),90(a,1,2)),flip(a)]. given #2313 (W0w,wt=11): 4231 T(x \ y,y) = T(x \ y,x). [para(2643(a,1),537(a,1,1)),flip(a)]. given #2314 (W0w,wt=11): 4278 T(x,y) \ y = T(x \ y,y). [para(2649(a,1),2642(a,1,2)),rewrite([2709(3)])]. given #2315 (W0a,wt=18): 2645 L(T(x,L(x,y,z) * u),y,z) = L(T(x,u),y,z). [para(1708(a,1),30(a,1)),rewrite([30(2)]),flip(a)]. given #2316 (W0a,wt=15): 2654 T(x \ y,(y / x) * z) = T(x \ y,z). [para(1708(a,1),537(a,1,1)),rewrite([537(3)]),flip(a)]. given #2317 (W0r,wt=18): 173500 L(x,y * (z * (z * (y * (z * z)))),u * w) = x. [para(2040(a,1),133829(a,1,2))]. given #2318 (W0r,wt=17): 100555 K(x * ((x \ y) * z),T(y,x) * T(z,x)) = 1. [back_rewrite(68250),rewrite([100327(9),100(5),169(8),1091(6),3143(7),169(6),4209(7),99656(6)])]. given #2319 (W0r,wt=17): 179935 T(T(x,y),y \ (y \ x)) \ T(x,y \ x) = 1. [back_rewrite(135430),rewrite([179923(3),29(5),1708(2)])]. given #2320 (W0r,wt=16): 134179 ((x \ y) * z) * L(z \ x,x,y) = T(y,x). [para(4505(a,1),1251(a,1,2,2)),rewrite([80501(4),81056(5),134004(9),2711(8),110366(6),4505(7)])]. given #2321 (W0r,wt=20): 177735 K(x * ((y * x) \ T(z,u)),L(T(z,u) \ y,x,z)) = 1. [back_rewrite(172444),rewrite([177639(9),52858(7)])]. given #2322 (W1w,wt=21): 27514 K(x * (y * (y * (y * x))),y * (x * (y * (x * y)))) = 1. [para(5600(a,1),8418(a,1,1,1)),rewrite([27454(10),27504(14),13(6)])]. given #2323 (W1w,wt=21): 27523 (T(x * (x * T(x,y)),K(x,y)) \ T(x,y)) * (x * x) = 1. [para(16623(a,1),5600(a,1,1,1,2,2,2)),rewrite([547(4),21062(5),21063(6),22987(6),547(2),16875(12),547(10),21063(11),16875(10)])]. given #2324 (W1w,wt=21): 27573 x * (y * (x * (z / (z * (x * (y * (x * z))))))) = z \ 1. [para(5674(a,1),15(a,1,2)),flip(a)]. given #2325 (W1w,wt=21): 27682 x * T(y \ z,y \ (y \ x)) = y * ((z / y) * (y \ x)). [back_rewrite(9019),rewrite([27608(9)])]. given #2326 (W1w,wt=21): 27800 x * ((T(y * x,x) * z) * ((x * z) \ (x \ (y \ 1)))) = 1. [para(189(a,1),5926(a,1,2,1)),rewrite([4209(7),4407(8),24002(11),168(4),10809(4)])]. given #2327 (W1w,wt=21): 27811 x * ((y * (x \ (x \ z))) * ((z \ x) / T(y,x \ 1))) = 1. [para(3143(a,1),5926(a,1,2,1,2,2)),rewrite([3143(6),3143(8),4408(12),1014(12),4408(12),45(2)])]. given #2328 (W1w,wt=21): 28103 K(x * (x * (y \ z)),K(x / y,y * ((x / y) * z))) = 1. [para(1022(a,1),17092(a,1,2,2,1)),rewrite([4505(3),87(2),13(2),1014(3),3228(3),1014(6),1014(7)])]. given #2329 (W1w,wt=21): 28149 a(L(x,y,z),z \ (y \ (y \ 1)),y * ((y * z) * x)) = 1. [para(46(a,1),16237(a,1,3,2,1,1)),rewrite([100(2),2507(3),13(8)])]. given #2330 (W1a,wt=25): 2824 K(x,(y * (z * (u * (z * (y * x))))) / (y * (z * (u * (z * y))))) = 1. [para(130(a,1),1723(a,1,2,1))]. given #2331 (W1a,wt=28): 2995 (x * (y * ((z * y) * u))) * a(x,y * z,y * u) = (x * (y * z)) * (y * u). [para(189(a,1),54(a,1,1,2))]. given #2332 (W1r,wt=27): 158596 (((x / y) * z) * (L(z \ y,x,z) * u)) \ (x * u) = a(x,u,(x / y) * z). [back_rewrite(153359),rewrite([153502(14),153242(11),84171(11)])]. given #2333 (W1r,wt=23): 25064 x \ (x \ T(T(T(y,z),u),w)) = x \ (x \ T(T(T(y,w),z),u)). [para(94(a,1),5364(a,2,2,2)),rewrite([5364(10)])]. given #2334 (W1r,wt=29): 170458 K(K(x * ((y \ (y \ z)) * (u * u)),y),z * (T(x,y \ (y \ z)) * (u * u))) = 1. [back_rewrite(120270),rewrite([170075(13)])]. given #2335 (W1r,wt=27): 194796 K(T(T(T(x \ y,y),z),u) * x,x \ T(T(y \ x,(x * y) * z),u)) = 1. [para(27573(a,1),43902(a,1,1,2)),rewrite([194557(7),115458(5),3143(3),4155(7),45(6),194557(12),16(9),194557(14),4505(11),90(11),3143(10),194557(15),4408(12),4408(11),45(10),6120(13),52619(12),52619(11),4408(8),14(8)])]. given #2336 (W1r,wt=29): 117654 K(x * T(y,z \ (z \ x)),z * (z * z)) = K(y * (z \ (z \ x)),z * (z * z)). [back_rewrite(117617),rewrite([117618(8)])]. given #2337 (W2w,wt=31): 11282 x * (x * ((y * z) / T(x * (x * (y * ((z * y) * u))),u \ (y \ 1)))) = u \ (y \ 1). [para(189(a,1),3641(a,1,2,2,2,1,2,2)),rewrite([4407(9),4407(16)])]. given #2338 (W2w,wt=31): 11450 x \ (x \ (T(T(T(y,z \ 1),u),w) / z)) = x \ (x \ (T(T(T(y,u),w),z \ 1) / z)). [para(3382(a,1),3710(a,2,2,2)),rewrite([3710(13)])]. given #2339 (W2w,wt=31): 12123 T(T(T(T(T(x,y),z),u),w),T(T(T(x,w),T(x,y) \ z),u)) = T(T(T(T(x,y),z),w),u). [para(29(a,1),10784(a,1,2,1))]. given #2340 (W2w,wt=31): 12146 T(T(T(T(T(x,y),z),u),w),T(T(T(x,u),T(x,y) \ z),w)) = T(T(T(T(x,y),z),w),u). [para(94(a,1),10784(a,1,2))]. given #2341 (W2a,wt=33): 2391 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),u,w),v7,v8),v5,v6),y,z). [para(235(a,1),231(a,1))]. given #2342 (W2a,wt=33): 2393 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),v5,v6),v7,v8),y,z),u,w). [para(235(a,1),235(a,2))]. given #2343 (W2r,wt=33): 121177 T(T(x * (y * (x * (z * z))),u),z * (z * (x * (y * x)))) = T(x * (y * (x * (z * z))),u). [para(128(a,1),18900(a,1,1,1)),rewrite([93680(14),93680(13)])]. given #2344 (W2r,wt=32): 172789 K(L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10),L(L(L(L(x,v5,v6),v7,v8),v9,v10),u,w)) = 1. [para(1577(a,1),28532(a,1,1))]. given #2345 (W2r,wt=35): 143093 K(L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10),L(L(L(L(L(x,v9,v10),y,z),v5,v6),v7,v8),u,w)) = 1. [para(450(a,1),1635(a,1,2))]. given #2346 (W2r,wt=31): 62557 K(T(T(x,y),z) * u,T(T(x,z) * y,y) / (T(T(x,y),z) * ((T(x,z) * y) * u))) = 1. [para(517(a,1),14557(a,1,2,2,2,1)),rewrite([22374(6)])]. given #2347 (W2r,wt=34): 115742 x * (x * (y * (L(z,x,y) * (x * (x * (y / u)))))) = x * (x * ((y * ((z * x) * (x * y))) / u)). [back_rewrite(40757),rewrite([115200(11),189(13),115200(12),1839(15)])]. given #2348 (W0w,wt=9): 194121 L(x,y,a(x,z,u)) = x. [para(181313(a,1),134179(a,2)),rewrite([52858(10),184298(10),157238(9),169(8),110241(8),181313(3),52858(3),184298(3)])]. given #2349 (W0w,wt=10): 196290 L(x,K(y,z),u * w) = x. [para(11282(a,1),186144(a,1,3)),rewrite([105587(5),1014(4),110290(3)])]. given #2350 (W0w,wt=10): 196936 T(x,L(y,x,z)) = T(x,y). [back_rewrite(56831),rewrite([196855(4),16(2)]),flip(a)]. given #2351 (W0w,wt=10): 197233 a(x,K(y,z),u * z) = 1. [back_rewrite(162630),rewrite([197202(5)]),flip(a)]. given #2352 (W0w,wt=10): 197287 K(x,L(y,x,z)) = K(x,y). [para(196936(a,1),16343(a,1,2)),rewrite([16343(2)]),flip(a)]. given #2353 (W0w,wt=10): 197293 K(L(x,y,z),y) = K(x,y). [para(196936(a,1),16687(a,1,2)),rewrite([16687(2)]),flip(a)]. given #2354 (W0w,wt=10): 197488 K(K(x,y),L(x,y,z)) = 1. [back_rewrite(80599),rewrite([197287(4),17884(3),96031(3,R)])]. given #2355 (W0w,wt=10): 197841 a(x,K(y,z),u * y) = 1. [para(1014(a,1),197233(a,1,3)),rewrite([17781(3),157156(3)])]. given #2356 (W0w,wt=10): 197977 K(K(x,y),L(y,x,z)) = 1. [para(197293(a,1),12309(a,1,2)),rewrite([96031(3,R)])]. given #2357 (W0w,wt=10): 198001 K(L(x,y,z),z) = K(x,z). [para(52858(a,1),197293(a,1,1))]. given #2358 (W0w,wt=10): 198621 K(K(x,y),L(y,z,x)) = 1. [para(198001(a,1),12309(a,1,2)),rewrite([96031(3,R)])]. given #2359 (W0w,wt=10): 198627 K(x,L(y,z,x)) = K(x,y). [para(17781(a,1),198001(a,2)),rewrite([105587(3),14(2),17781(4)])]. given #2360 (W0w,wt=10): 198749 K(K(x,y),L(x,z,y)) = 1. [para(198621(a,1),4993(a,1,1)),rewrite([96031(4,R),13(5)])]. given #2361 (W0w,wt=11): 4407 (x * y) \ 1 = y \ (x \ 1). [para(2755(a,1),2538(a,1,1))]. given #2362 (W0w,wt=11): 4408 (x \ y) \ z = (y \ x) * z. [para(2538(a,1),2755(a,1,1))]. given #2363 (W0w,wt=11): 4578 (x * y) * y = x * (y * y). [back_rewrite(669),rewrite([4525(3)]),flip(a)]. given #2364 (W0a,wt=19): 2655 T(T(x / y,z),y * T(y \ x,z)) = T(y \ x,z). [para(537(a,1),1708(a,2)),rewrite([625(5)])]. given #2365 (W0a,wt=18): 2734 L(T(x,L(x,y,z) \ u),y,z) = L(T(x,u),y,z). [back_rewrite(214),rewrite([2649(7),30(6)])]. given #2366 (W0r,wt=20): 179374 K(x * y,(x * (z * (x * y))) / L(x * z,x,y)) = 1. [back_rewrite(109190),rewrite([178629(8)])]. given #2367 (W0r,wt=17): 123864 K(K(x,y * z),K(z * y,T(x,K(y,z)))) = 1. [para(89(a,1),96688(a,1,1,2)),rewrite([112053(6)])]. given #2368 (W0r,wt=18): 168735 L(x,y * (K(x,z) / u),u * (y * K(x,z))) = x. [para(1840(a,1),38761(a,1,2)),rewrite([6144(6),163693(9),38207(10),57044(8),110290(7)])]. given #2369 (W0r,wt=19): 125276 T(x * (y * y),T(x,y) * z) = T(y * (y * x),z). [para(15(a,1),19060(a,1,1,2)),rewrite([4578(2),1708(4),15(7),51705(9)])]. given #2370 (W0r,wt=13): 163651 T(x * y,K(y,K(z,x))) = x * y. [back_rewrite(67555),rewrite([163437(5),68787(5),91404(5)])]. given #2371 (W1w,wt=21): 28528 T(T(x,y) \ L(x,z,u),T(x,y)) = T(x,y) \ L(x,z,u). [para(26839(a,1),5226(a,1,2,1)),rewrite([4505(7)])]. given #2372 (W1w,wt=21): 28774 K(((x / T(T(y,z),u)) / w) * (T(T(y,u),z) / x),w) = 1. [para(11449(a,1),18225(a,1,1,2)),rewrite([4408(10),10229(4),169(10),16568(11),23819(10),27608(9),16568(10)])]. given #2373 (W1w,wt=21): 28845 L(T(T(x,y),z),u,L(T(T(x,z),y),w,v5)) = T(T(x,z),y). [para(18461(a,1),95(a,1)),flip(a)]. given #2374 (W1w,wt=21): 28902 T(T(x \ y,z),T(T(T(y / x,z),u),w)) = T(x \ y,z). [para(19257(a,1),3835(a,1,2,1)),rewrite([28885(11),9209(6)]),flip(a)]. given #2375 (W1w,wt=21): 28918 T(x * (x * y),T(T(y * (x * x),z),u)) = x * (x * y). [para(10927(a,1),19257(a,1,2,1))]. given #2376 (W1w,wt=21): 28949 K((x / y) * (z * x),K((x / y) * (z * (x / y)),y)) = 1. [para(807(a,1),19567(a,1,2)),rewrite([20902(18)])]. given #2377 (W1w,wt=21): 29138 T(x * (y * y),T(y \ (y \ (x \ 1)),z)) = x * (y * y). [para(21133(a,1),10927(a,2)),rewrite([4407(6),3436(6),10927(9)])]. given #2378 (W1w,wt=21): 29173 K((x * y) / z,(y \ x) * (y / z)) = K(y,(x * y) / z). [para(5560(a,1),23360(a,1,1)),rewrite([17910(6)]),flip(a)]. given #2379 (W1a,wt=27): 3061 (x * ((y * x) * z)) * ((x * y) * u) = (x * y) * ((x * ((z * x) * y)) * u). [para(189(a,1),189(a,1,1)),rewrite([189(10)])]. given #2380 (W1a,wt=27): 3062 ((x * y) * z) * (x * ((y * x) * u)) = (x * y) * ((z * (x * y)) * (x * u)). [para(189(a,1),189(a,1,2))]. given #2381 (W1r,wt=25): 198353 T(x * x,L(y,z,u) * K(z,y)) = T(x * x,K(z,y) * L(y,z,u)). [para(197488(a,1),43648(a,1,1,1)),rewrite([13(3),5005(4),197488(8),14(7),6144(9)])]. given #2382 (W1r,wt=27): 158436 K(L(a(x,y,z),u,y * z),K(u * (x * ((x \ y) * z)),u * (y * z))) = 1. [back_rewrite(152067),rewrite([153484(2)])]. given #2383 (W1r,wt=27): 185126 L(x \ y,x,z * ((z * u) * y)) = (L(u,y,z) * x) \ (z * ((z \ u) * y)). [back_rewrite(56974),rewrite([184276(5)])]. given #2384 (W1r,wt=29): 79285 (x * (y \ z)) \ T((y \ z) * (x * K(z,y)),z / y) = K(z,T(y,x * (y \ z))). [para(37217(a,1),48016(a,1,1)),rewrite([17791(3),17791(5),37429(12),26764(11),17771(11),17791(13),37217(15),37429(13)])]. given #2385 (W1r,wt=29): 182650 K(x * T(T(T(T(y,z),u),w),v5 \ 1),T(v5 * (T(T(y,u),w) / v5),z) * x) = 1. [para(2771(a,1),134741(a,1,2,1,1))]. given #2386 (W2w,wt=31): 12176 T(T(T(T(T(x,y),z),u),w),T(T(T(T(T(x,z),y),v5),u),w)) = T(T(T(T(x,y),z),u),w). [hyper(26,a,8967,a)]. given #2387 (W2w,wt=31): 12187 T(T(T(T(T(x,y),z),u),w),T(T(T(x,z),y),w) * v5) = T(T(T(T(T(x,z),y),w),v5),u). [para(1708(a,1),8967(a,1,2)),rewrite([29(14),12184(9),2644(9)]),flip(a)]. given #2388 (W2w,wt=31): 12195 T(T(T(T(T(T(T(x,y),z),u),w),v5),v6),v7) = T(T(T(T(T(T(T(x,u),y),z),w),v5),v6),v7). [para(94(a,1),8967(a,2,1,1,1,1)),rewrite([8967(14)])]. given #2389 (W2w,wt=31): 12200 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,z),y),v5),u \ 1),w) / u. [para(8967(a,1),3794(a,1,1)),rewrite([29(22),8848(22)]),flip(a)]. given #2390 (W2a,wt=33): 2467 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,v9,v10),u,w),v5,v6),v7,v8),y,z). [para(97(a,2),454(a,1,1,1))]. given #2391 (W2a,wt=35): 3319 T(x * (y * (z * (y * (x * u)))),K(u,x * (y * (z * (y * x))))) = x * (y * (z * (y * (x * u)))). [para(130(a,1),2918(a,1,1)),rewrite([130(16)])]. given #2392 (W2r,wt=32): 179828 K(x,T(T(T(y,z),x),x \ (x \ u)) \ T(T(T(y,z),u),x \ (L(T(y,z),w,v5) / x))) = 1. [back_rewrite(126323),rewrite([178989(14),29(12),147585(13)])]. given #2393 (W2r,wt=33): 192981 K(x * (((y \ z) * z) * x),x * T(x,z \ (z \ y))) = K(z * ((y \ (y \ z)) * (z * z)),x). [back_rewrite(169996),rewrite([192977(14)])]. given #2394 (W2r,wt=35): 148944 T(T(T(T(T(T(x \ 1,y),z),u),w),v5),K(x,T(T(v6,z),u))) = T(T(T(T(T(x \ 1,y),z),u),w),v5). [para(13051(a,1),18092(a,1,1,1,1)),rewrite([70212(12),13051(17)])]. given #2395 (W2r,wt=35): 66199 T(T(T(T(x,y \ 1),z),u) / y,T(T(x,z),y \ (y \ u)) / y) = T(T(T(x,z),u),y \ 1) / y. [para(3382(a,1),8011(a,2)),rewrite([59158(15)])]. given #2396 (W2r,wt=31): 43731 T(T(K(x,y) * (z * z),x * y),z * (z * (x \ (y \ K(x,y))))) = z * (z * K(x,y)). [para(19765(a,2),29529(a,1,1)),rewrite([1839(10),39824(8)])]. given #2397 (W0w,wt=11): 5005 x / K(y,z) = x * K(z,y). [para(2917(a,1),1014(a,1,2)),flip(a)]. given #2398 (W0w,wt=11): 5208 (x * (y \ z)) * (z \ y) = x. [para(4151(a,1),209(a,1,1)),rewrite([45(6),4137(7),14(6),4151(7),88(6)])]. given #2399 (W0w,wt=11): 6072 T(x \ 1,y) = y \ (x \ y). [para(3143(a,1),23(a,1,2)),flip(a)]. given #2400 (W0w,wt=11): 6095 x \ T(y,x \ 1) = y / x. [para(3143(a,1),90(a,1)),rewrite([1014(7)])]. given #2401 (W0w,wt=11): 6120 (x \ 1) / y = x \ (y \ 1). [para(3143(a,1),1014(a,1)),flip(a)]. given #2402 (W0w,wt=11): 6144 K(x,y) \ z = K(y,x) * z. [para(2917(a,1),3143(a,1,1)),flip(a)]. given #2403 (W0w,wt=11): 6351 x * ((x \ y) * y) = y * y. [para(6258(a,1),435(a,2,1,2,1)),rewrite([16(2),16(5),16(6),3436(6),2044(7),16(5),13(6),100(5),1839(6),47(4),14(5)])]. given #2404 (W0w,wt=11): 7634 T(x * y,K(x,y)) = x * y. [hyper(28,a,4108,a)]. given #2405 (W0w,wt=11): 7715 (x \ y) * ((y \ x) * z) = z. [back_rewrite(6353),rewrite([7656(7)])]. given #2406 (W0w,wt=11): 7775 T(x,y) * y = T(x * y,y). [para(90(a,1),4209(a,1,1)),flip(a)]. given #2407 (W0w,wt=11): 7779 T(x \ y,x \ 1) = y / x. [para(1014(a,1),4209(a,2)),rewrite([3143(3)])]. given #2408 (W0w,wt=11): 8296 K(x,y) * (K(y,x) * z) = z. [para(4993(a,1),21(a,1,1)),rewrite([45(6),5011(7)])]. given #2409 (W0w,wt=11): 10006 T(x / y,y / x) = x / y. [para(5359(a,1),23(a,1,2)),rewrite([6565(3)]),flip(a)]. given #2410 (W0w,wt=11): 10099 (x * (y / z)) * (z / y) = x. [back_rewrite(10003),rewrite([10008(7)])]. given #2411 (W0w,wt=11): 10215 x / (y / z) = x * (z / y). [para(6565(a,1),1014(a,1,2)),flip(a)]. given #2412 (W0w,wt=8): 212483 T(x,a(y,x,z)) = x. [back_rewrite(157248),rewrite([211924(4),112951(5),98196(5),52858(5),30(6),29(5),12372(5),158520(3),84171(2),153242(2),157231(3),159030(3)])]. given #2413 (W0a,wt=13): 2735 T(T(x,y),x \ z) = T(T(x,z),y). [back_rewrite(213),rewrite([2649(5)])]. given #2414 (W0a,wt=15): 2773 T(T(x * y,z),y \ 1) = T(y * x,z). [back_rewrite(1813),rewrite([2755(8)])]. given #2415 (W0r,wt=13): 197493 K(K(x,y),z * ((z \ y) * x)) = 1. [back_rewrite(56987),rewrite([197287(2)])]. given #2416 (W0r,wt=19): 177562 K(x,K(x / y,(y * ((y \ z) * x)) / (z * y))) = 1. [para(90(a,1),103775(a,1,2,2,2)),rewrite([7616(3)])]. given #2417 (W0r,wt=20): 10731 L(x \ y,x,z) * ((z / y) * x) = T(z,(z / y) * x). [para(8701(a,2),4505(a,1,1))]. given #2418 (W0r,wt=20): 162175 a(x * y,z * (u * z),(u * (z / (x * y))) * z) = 1. [back_rewrite(154491),rewrite([160751(12),162028(10)])]. given #2419 (W0r,wt=17): 164659 ((x \ y) * z) * (x * ((y * (z * x)) \ x)) = 1. [back_rewrite(27645),rewrite([164484(13),103756(11),115200(5),29692(10),22398(7),1091(6),4407(6),35645(7)])]. given #2420 (W1w,wt=21): 29222 T(T(T(x,y),z) * u,T(T(x,z),y)) = u * T(T(x,y),z). [para(3398(a,1),23380(a,1,2)),rewrite([29200(7)]),flip(a)]. given #2421 (W1w,wt=21): 29225 T(T(x \ y,z),T(u,T(y / x,z))) = T(T(x \ y,z),u). [para(23380(a,1),3835(a,1,2,1)),rewrite([29206(11),3835(8)]),flip(a)]. given #2422 (W1w,wt=21): 29245 T(x \ y,T(x * (z * z),y)) = T(x \ y,z * (z * x)). [para(10927(a,1),23380(a,1,2))]. given #2423 (W1w,wt=21): 29255 T((x / y) * z,T(x \ y,z)) = T((x / y) * z,x \ y). [para(10379(a,1),23380(a,1,2))]. given #2424 (W1w,wt=21): 29335 T(T(x \ y,z),u * T(y / x,z)) = T(T(x \ y,z),u). [para(23443(a,1),3835(a,1,2,1)),rewrite([29318(11),3835(8)]),flip(a)]. given #2425 (W1w,wt=21): 29403 T(T(T(x,y),(z * x) * u),(x * u) \ (z \ x)) = T(x,y). [back_rewrite(27325),rewrite([29314(10),29(8)])]. given #2426 (W1w,wt=21): 29434 T(x,y * (y * (z * (x * (x * x))))) = T(x,y * (y * z)). [back_rewrite(25721),rewrite([29397(11)])]. given #2427 (W1w,wt=21): 29457 T(x * y,y) * (T(y,x) \ T(y / x,x * (y * y))) = y. [back_rewrite(22345),rewrite([29397(5)])]. given #2428 (W1a,wt=23): 3085 x * (y * (y * (z * (x * ((x * (y * (y * (z * x)))) \ u))))) = u. [para(37(a,1),103(a,1,2,2,2,1,2)),rewrite([37(9)])]. given #2429 (W1a,wt=23): 3148 (T(T(x,y),z) * (z * u)) \ w = (T(T(x,z),y) * (z * u)) \ w. [para(682(a,1),2495(a,1,1,2)),rewrite([3135(8),168(5),23(3)])]. given #2430 (W1r,wt=26): 200305 L(T(x \ (x \ y),T(x * x,y) * z),y,u) = T(x \ (x \ y),y * z). [para(56854(a,1),2734(a,1,1,2,1)),rewrite([60306(7),4408(5),175022(8),4525(7),44806(6),175022(11),175170(12)])]. given #2431 (W1r,wt=27): 144951 (T(T(T(x,y),z),u) * (z * w)) / T(T(T(T(x,z),y),z * w),u) = z * w. [para(1569(a,2),958(a,1,1))]. given #2432 (W1r,wt=29): 203947 (x / T(T(T(T(T(x,y),z),u),w),v5)) * (x \ T(T(T(T(T(x,y),w),z),u),v5)) = 1. [back_rewrite(49976),rewrite([203745(12)])]. given #2433 (W1r,wt=27): 174547 T(T(x,y) * z,K(((x \ y) * y) * z,(y \ x) * (y \ x))) = T(x,y) * z. [para(4505(a,1),25040(a,1,1,1)),rewrite([4408(4),4505(12)])]. given #2434 (W1r,wt=29): 62500 (x \ y) * T(T(T(T(T(x,y),z),u),w),v5) = T(T(T(T(x,z),u),w),v5) * (x \ y). [para(3825(a,1),517(a,1,2,1))]. given #2435 (W2w,wt=31): 12201 T(T(T(T(T(x,y),z),u),w),T(T(T(x,z),y),w) \ v5) = T(T(T(T(T(x,z),y),w),v5),u). [para(2642(a,1),8967(a,1,2)),rewrite([29(14),12184(9),2735(9)]),flip(a)]. given #2436 (W2w,wt=31): 12222 T(T(T(T(T(x,y),z),u),w),v5 * (T(T(T(x,z),y),w) / v5)) = T(T(T(T(x,z),y),w),u). [para(5067(a,1),8967(a,1,2)),rewrite([29(14),8800(8),9957(10)]),flip(a)]. given #2437 (W2w,wt=31): 12381 T(T(T(T(x \ y,z),u),w),x \ T(T(T(y / x,z),u),w)) = T(T(T(y / x,z),u),w). [para(3352(a,1),7769(a,1,1))]. given #2438 (W2w,wt=31): 12446 T(T(T(T(T(T(x,y),z),u),w),v5),T(T(T(x,z),v5),u)) = T(T(T(T(T(x,y),z),v5),u),w). [back_rewrite(12142),rewrite([12416(9)])]. given #2439 (W2a,wt=33): 3811 L(L(L(L(L(x,y,z),u,w),v5,v6),v7,v8),v9,v10) = L(L(L(L(L(x,u,w),y,z),v5,v6),v7,v8),v9,v10). [para(227(a,1),233(a,1))]. given #2440 (W2a,wt=33): 3897 (x * (y * (x * (z * (x * (y * (u * x))))))) / T(u,x) = x * (y * (x * (z * (x * (y * x))))). [para(90(a,1),389(a,1,1,2,2,2,2,2,2))]. given #2441 (W2r,wt=31): 209776 x * K(y * (T(z * z,u) * (T(z,u) / y)),T(z * (z * z),u * (w * (v5 / x)))) = x. [back_rewrite(176165),rewrite([208415(15),1014(13),208415(13),208415(13)])]. given #2442 (W2r,wt=35): 207357 T(T(T(T(T(T(x,y),z),u),w),v5) / v6,v6 \ 1) = T(T(T(T(T(T(x,w),y),u),z),v5) / v6,v6 \ 1). [back_rewrite(126017),rewrite([206077(9),205874(18)])]. given #2443 (W2r,wt=33): 41586 a(x,L(L(L(L(y,z,u),w,v5),v6,v7),v8,v9),L(L(L(L(L(y,v10,v11),v8,v9),w,v5),v6,v7),z,u)) = 1. [para(2466(a,1),32658(a,1,2))]. given #2444 (W2r,wt=35): 208106 T(T(T(T(T(x,y),z \ 1),u),w) / v5,v5 \ 1) = T(T(T(T(T(x,u),w),z \ 1),y) / v5,v5 \ 1). [back_rewrite(207177),rewrite([207751(10)]),flip(a)]. given #2445 (W2r,wt=33): 215410 T(x \ (x \ y),z * (z * T(u,(y \ z) * z))) = T(x \ (x \ y),y * (u * ((y \ z) * z))). [para(24062(a,1),200305(a,2,2)),rewrite([215365(9),215361(8)]),flip(a)]. given #2446 (W0w,wt=10): 213377 T(x,L(y,z,x)) = T(x,y). [para(1091(a,1),10731(a,1,1,1)),rewrite([52858(4),58413(4),52858(3),23697(6),113550(7),23697(5),197025(6)])]. given #2447 (W0w,wt=11): 10229 (x / y) \ z = (y / x) * z. [para(6565(a,1),3143(a,1,1)),flip(a)]. given #2448 (W0w,wt=11): 10287 (x / y) * ((y / x) * z) = z. [back_rewrite(10000),rewrite([10221(7)])]. given #2449 (W0w,wt=11): 10400 (x \ y) / x = x \ (y / x). [para(92(a,1),7616(a,1,1))]. given #2450 (W0w,wt=11): 12328 K(x,y) / x = x \ K(x,y). [para(12312(a,1),2711(a,1,2))]. given #2451 (W0w,wt=10): 218217 a(x,K(y,z),y * u) = 1. [para(12328(a,1),158596(a,1,1,1,1)),rewrite([124652(3),52858(6),105864(6),13639(6),186453(4),123095(8),113933(7),4408(6),186453(6),1091(6),4505(3),87(2),12328(4),124652(5),84171(6),153502(6),158938(4)]),flip(a)]. given #2452 (W0w,wt=10): 218233 a(x,K(y,z),z * u) = 1. [para(3143(a,1),218217(a,1,3)),rewrite([147785(3),45(2),158938(3)])]. given #2453 (W0w,wt=11): 12473 K(x,y) / y = y \ K(x,y). [para(12432(a,1),2711(a,1,2))]. given #2454 (W0w,wt=11): 12502 T(x \ y,K(y,x)) = x \ y. [para(16(a,1),7925(a,1,2,1))]. given #2455 (W0w,wt=11): 14109 T(x \ y,y \ 1) = y / x. [para(2643(a,1),12372(a,1,1))]. given #2456 (W0w,wt=11): 14156 T(x \ y,x / y) = x \ y. [para(16(a,1),12386(a,1,2,2))]. given #2457 (W0w,wt=11): 14349 T(x \ y,K(x,y)) = x \ y. [para(16(a,1),12563(a,1,2,2))]. given #2458 (W0w,wt=11): 14435 T(x / y,x \ y) = x / y. [para(92(a,1),14102(a,1,2,1)),rewrite([4408(4),14(4)])]. given #2459 (W0w,wt=11): 14868 (x * x) / y = x * (x / y). [para(100(a,1),1014(a,1)),rewrite([1014(3)]),flip(a)]. given #2460 (W0w,wt=11): 16256 L(x,y,z * y) = L(x,y,z). [back_rewrite(13884),rewrite([16103(3)])]. given #2461 (W0w,wt=11): 17793 T(x / y,K(x,y)) = x / y. [back_rewrite(15565),rewrite([17771(7),17730(4),17781(4)])]. given #2462 (W0a,wt=17): 2811 K(x,y * (y * ((z * x) / (y * (y * z))))) = 1. [para(37(a,1),1723(a,1,2,1)),rewrite([1839(6)])]. given #2463 (W0a,wt=17): 2832 K(x * (x * ((y * z) / (x * (x * y)))),z) = 1. [para(37(a,1),1780(a,1,1,1)),rewrite([1839(6)])]. given #2464 (W0r,wt=20): 182543 K(L((x / y) * z,y,x),(x * z) / T(y,x \ 1)) = 1. [para(2771(a,2),1733(a,1,2,2)),rewrite([10229(2),52858(4),110290(4),53163(4),52858(3)])]. given #2465 (W0r,wt=19): 147675 T(T(T(x,y \ x),z),u) * y = y * T(T(x,z),u). [para(29099(a,1),10402(a,1,1,1,1)),rewrite([4155(7),45(6),4408(10),45(7)])]. given #2466 (W0r,wt=18): 197749 K(K(x,y * z),L(x,y,z) / ((x * y) * z)) = 1. [back_rewrite(105280),rewrite([197638(3)])]. given #2467 (W0r,wt=16): 162318 a(x,y * z,z * ((y \ (z / y)) * x)) = 1. [back_rewrite(115812),rewrite([160751(7)])]. given #2468 (W0r,wt=13): 193790 K(x \ (y \ (y \ x)),T(y,z)) = 1. [para(19257(a,1),179935(a,1,1,1)),rewrite([140353(6),140353(4),23(5),23443(6),28907(9),16711(6),37242(5)])]. given #2469 (W1w,wt=21): 29479 T(T(T(x,y),z),u / T(T(x,z),y)) = T(T(T(x,z),y),u). [para(26764(a,1),94(a,2)),rewrite([29(6)])]. given #2470 (W1w,wt=21): 29507 T(T(x \ y,z),u / T(y / x,z)) = T(T(x \ y,z),u). [para(26764(a,1),3835(a,1,2,1)),rewrite([29481(11),3835(8)]),flip(a)]. given #2471 (W1w,wt=21): 29859 K(x * T(y,z * x),(x * z) / (x * (y * (z * x)))) = 1. [para(90(a,1),14557(a,1,2,2,2))]. given #2472 (W1w,wt=21): 29870 K(x * (y * z),(x * y) / (x * (y * ((x * y) * z)))) = 1. [para(189(a,1),14557(a,1,2,2,2))]. given #2473 (W1w,wt=21): 29873 K(T(x,y) * z,T(y,x \ y) / (T(x,y) * (y * z))) = 1. [para(2690(a,1),14557(a,1,2,2,2,1)),rewrite([7789(5)])]. given #2474 (W1w,wt=21): 29877 K(T(x,y) * z,(y / x) / (T(x,y) * ((x \ y) * z))) = 1. [para(4357(a,1),14557(a,1,2,2,2,1)),rewrite([21022(6)])]. given #2475 (W1w,wt=21): 29901 K(x * K(y * x,z),(x * y) / (x * T(y * x,z))) = 1. [para(16716(a,1),14557(a,1,2,2,2))]. given #2476 (W1w,wt=21): 30103 x \ (y * K(y * (x \ y),z)) = y \ T(y * (x \ y),z). [para(12307(a,1),6137(a,1,2,2)),rewrite([16985(11)])]. given #2477 (W1a,wt=23): 3149 x \ (T(T(y,z),u) * (u * w)) = x \ (T(T(y,u),z) * (u * w)). [para(682(a,1),2495(a,1,2,2)),rewrite([3136(8),168(5),23(3)])]. given #2478 (W1a,wt=23): 3306 T(x * (x * (y * z)),K(z,x * (x * y))) = x * (x * (y * z)). [para(37(a,1),2918(a,1,1)),rewrite([37(10)])]. given #2479 (W1r,wt=29): 40416 L(T(T(T(T(T(x,y),z),u),w),v5),v6,v7) = L(T(T(T(T(T(x,u),y),z),v5),w),v6,v7). [para(4214(a,1),7107(a,1,1,1,1)),rewrite([13081(14)]),flip(a)]. given #2480 (W1r,wt=26): 189202 K(L(x \ T(y,z),x,u),(z * (u * (y * z))) / (z * (u * (z * x)))) = 1. [para(90(a,1),184581(a,1,2,1,2,2))]. given #2481 (W1r,wt=24): 186361 ((T(T(x,y),z) * u) / w) * (w / T(T(T(x,z),u),y)) = L(u,x,w). [back_rewrite(104147),rewrite([184298(12),184298(11),52858(10)])]. given #2482 (W1r,wt=29): 120833 ((x \ y) * y) * (z * (T(z * (y * y),u) \ x)) = K(z \ u,T(y * (y * z),x)). [para(18894(a,1),16687(a,1,2)),rewrite([35978(8),37(7),15452(8)])]. given #2483 (W1r,wt=25): 115883 T(x * (y * (z \ (y / x))),y * (z \ y)) = x * (y * (z \ (y / x))). [back_rewrite(69984),rewrite([115377(5),39313(4),115377(12),39313(11)])]. given #2484 (W2w,wt=31): 12451 T(T(T(T(T(T(x,y),z),u),w),v5),T(T(T(x,z),w),u)) = T(T(T(T(T(x,y),z),w),u),v5). [back_rewrite(12119),rewrite([12416(9)])]. given #2485 (W2w,wt=31): 12954 (x * (y * (y * (z / x)))) * (y * (y * z)) = y * (y * (z * (x * (y * (y * (z / x)))))). [para(8260(a,1),63(a,1,2)),rewrite([14(9),37(14)])]. given #2486 (W2w,wt=31): 12965 K((x \ (x \ y)) * (x \ y),z * ((x \ (x \ y)) * ((x \ (x \ y)) * (T(x,y) / z)))) = 1. [para(4357(a,1),8260(a,1,1,2))]. given #2487 (W2w,wt=31): 13440 x * (x * ((x * (((x \ y) * (x * z)) * u)) * w)) = (x * ((x * ((y * x) * z)) * u)) * w. [para(187(a,1),37(a,1,1,2)),flip(a)]. given #2488 (W2a,wt=35): 3907 (x * (y * (x * z))) * (T(T(u,w),x) * (x * v5)) = (x * (y * (x * z))) * (T(T(u,x),w) * (x * v5)). [para(682(a,1),391(a,1,2,2,2,2,2,2)),rewrite([3904(13),168(8),23(6)])]. given #2489 (W2a,wt=35): 3920 x * (x * ((y * (x * (x * z))) * T(u,y \ z))) = x * (x * (y * (x * (x * (y * (u * (y \ z))))))). [para(90(a,1),397(a,1,2,2,2,2,2,2)),flip(a)]. given #2490 (W2r,wt=32): 124067 L((x * y) \ (z \ 1),u,L(y,x,z)) \ (u / (z * x)) = T(u * L(y,x,z),u / (z * x)). [para(59438(a,1),2705(a,1,1,1)),rewrite([52858(5),52858(6),103664(10),52858(10),103664(15)])]. given #2491 (W2r,wt=31): 209803 x * K(y * ((z * y) * (u * (u / (y * z)))),T(y * (u * u),w * (v5 * (v6 / x)))) = x. [back_rewrite(176129),rewrite([208415(15),1014(13),208415(13),208415(13)])]. given #2492 (W2r,wt=34): 142038 T(T(T(x * (x * y),z),u),w * (L(T(x * (x * y),u),z,y) / w)) = T(T(x * (x * y),z),u). [para(100(a,1),80094(a,1,2,2,1,1,1)),rewrite([68795(4),68795(15)])]. given #2493 (W2r,wt=31): 126394 K(x,y * (T(T(z,u),w) * ((v5 \ y) * y))) = K(x,y * (T(T(z,w),u) * ((v5 \ y) * y))). [back_rewrite(120503),rewrite([126345(5),126345(12)])]. given #2494 (W2r,wt=31): 128603 T(T(x,y) * (z * T(x,y)),y \ (x \ u)) = ((u \ x) * y) * (T(x,y) * (z * (y \ u))). [para(19355(a,1),122(a,1,2,2,2)),rewrite([128552(6),4408(7),4408(2),128552(17)]),flip(a)]. given #2495 (W0w,wt=11): 17816 T(x / y,K(y,x)) = x / y. [back_rewrite(15175),rewrite([17730(4),17781(4)])]. given #2496 (W0w,wt=11): 17843 (x / y) * (x \ y) = K(y,x). [back_rewrite(10366),rewrite([17730(6),17781(6)])]. given #2497 (W0w,wt=11): 17962 (x \ y) * (x / y) = K(y,x). [back_rewrite(4493),rewrite([17781(6)])]. given #2498 (W0w,wt=11): 17963 (x \ y) * K(x,y) = y / x. [back_rewrite(4113),rewrite([17781(4)])]. given #2499 (W0w,wt=11): 18071 T(x \ 1,K(x,y)) = x \ 1. [back_rewrite(14362),rewrite([17914(4)])]. given #2500 (W0w,wt=11): 18145 (x * (y / x)) / y = K(x,y). [back_rewrite(5069),rewrite([17924(5)])]. given #2501 (W0w,wt=10): 223990 K(x * y,a(z,y,x)) = 1. [para(168606(a,1),18145(a,2)),rewrite([153955(4),165503(5),16566(5)])]. given #2502 (W0w,wt=11): 18295 T(x \ 1,T(x,y)) = x \ 1. [para(3143(a,1),14577(a,1,2,1)),rewrite([4408(4),4505(4)])]. given #2503 (W0w,wt=11): 18389 K(x,y) * (x \ y) = y / x. [para(14802(a,1),63(a,1,2)),rewrite([14(5),17963(6)])]. given #2504 (W0w,wt=11): 19074 (x * y) / x = x * (y / x). [para(15056(a,1),72(a,1,2)),rewrite([1014(4),19065(8),1014(5)])]. given #2505 (W0w,wt=11): 20951 T(x,y) \ K(x,y) = x \ 1. [para(16566(a,1),1829(a,1,2))]. given #2506 (W0w,wt=11): 21513 K(x,y / (x * x)) = K(x,y). [back_rewrite(17902),rewrite([21468(4),46(2),1014(4),17962(3)]),flip(a)]. given #2507 (W0w,wt=11): 22398 x \ (y * y) = (x \ y) * y. [para(6257(a,1),6694(a,1,2)),rewrite([19771(3),18718(6),4230(4),4209(5)])]. given #2508 (W0w,wt=11): 22818 K(K(x,y),(y \ x) * x) = 1. [para(16710(a,1),14670(a,1,1)),rewrite([4408(3)])]. given #2509 (W0w,wt=11): 22940 T(x \ 1,y) = x \ K(y,x). [para(16716(a,1),3143(a,1)),rewrite([17913(6)])]. given #2510 (W0w,wt=11): 23481 x * (y / (y * x)) = K(x,y). [back_rewrite(17835),rewrite([23468(4)]),flip(a)]. given #2511 (W0a,wt=15): 2966 (x * ((y * x) * z)) / (x * z) = x * y. [para(189(a,1),17(a,1,1))]. given #2512 (W0a,wt=19): 2967 (x / y) * ((y * (x / y)) * z) = x * ((x / y) * z). [para(18(a,1),189(a,1,1)),flip(a)]. given #2513 (W0r,wt=19): 127685 (x \ y) * (x * ((z * x) \ y)) = ((x \ y) / z) * y. [para(1014(a,1),118038(a,2,1)),rewrite([35645(5)])]. given #2514 (W0r,wt=16): 121721 L((x * y) * z,x,y * z) = (x * y) * z. [back_rewrite(107889),rewrite([121655(5)]),flip(a)]. given #2515 (W0r,wt=14): 185544 L(x,y,z * (u * (T(u,w) / z))) = x. [back_rewrite(182165),rewrite([184298(6)])]. given #2516 (W0r,wt=17): 213863 K((x \ y) * z,T(z \ (y \ x),u * w)) = 1. [para(164659(a,1),128944(a,1,2,1,1,2)),rewrite([213752(4),213752(8),4408(7),4408(6),15(8),4408(3),4408(2),23(4),213752(7),14(7),37242(8),30(7),123034(7)])]. given #2517 (W0r,wt=14): 168613 K(a(x,y,z),u * (y * (u * z))) = 1. [para(128(a,1),159183(a,1,2)),rewrite([153242(3),161991(3),153242(1)])]. given #2518 (W1w,wt=21): 30213 T((x * y) * z,(y * z) \ (x \ y)) = T((x * y) * z,y). [para(6152(a,1),23443(a,1,2)),rewrite([23380(6)]),flip(a)]. given #2519 (W1w,wt=21): 30643 K(x * (y * (x * x)),z * (x * ((y * x) * (x / z)))) = 1. [back_rewrite(22346),rewrite([30508(7)])]. given #2520 (W1w,wt=21): 30677 x * ((y / x) * (z * (x / u))) = (x * y) * (T(z,x) / u). [back_rewrite(27678),rewrite([30621(8),136(6)]),flip(a)]. given #2521 (W1w,wt=21): 30881 ((T(x,y) * z) \ T(x,y * y)) * (x * z) = T(T(x,z),y). [back_rewrite(30202),rewrite([30703(4)])]. given #2522 (W1w,wt=21): 31025 (T(x \ y,z * z) * x) \ y = K(z * (z * x),x \ y). [back_rewrite(11029),rewrite([30703(3)])]. given #2523 (W1w,wt=21): 31054 x \ (T(y \ x,z * z) * y) = K(y \ x,z * (z * y)). [back_rewrite(10994),rewrite([30703(3)])]. given #2524 (W1w,wt=21): 31096 T(x \ y,x) * (x * (x * z)) = T(y * x,x * x) * z. [back_rewrite(10936),rewrite([30703(8)])]. given #2525 (W1w,wt=21): 31236 K(T(T(x,y),z) / u,u / T(T(T(x,z),u \ 1),y)) = 1. [para(6209(a,1),17781(a,2)),rewrite([10229(11),14(11)])]. given #2526 (W1a,wt=23): 3321 T(x * ((y * x) * z),K(x * z,x * y)) = x * ((y * x) * z). [para(189(a,1),2918(a,1,1)),rewrite([189(10)])]. given #2527 (W1a,wt=27): 3376 T(T(T(T(x,y),z),u),w) * (u * v5) = T(T(T(T(x,u),y),z),w) * (u * v5). [para(94(a,1),1295(a,2,1,1)),rewrite([1295(14)])]. given #2528 (W1r,wt=25): 218640 (x * (y / z)) / T(z / y,T(x,y / z)) = y * ((z \ x) * (y / z)). [back_rewrite(25085),rewrite([218361(11)])]. given #2529 (W1r,wt=25): 218926 T(x \ (x \ y),K(z,y) * (x * (x * (z / (z * y))))) = x \ (x \ y). [para(25094(a,1),14435(a,1,1)),rewrite([6144(9),89215(9),215431(10),25094(16)])]. given #2530 (W1r,wt=27): 131993 T(x \ (y \ (y \ 1)),x * (y * (y * (x \ z)))) = T(y \ (y \ (x \ 1)),z). [para(19846(a,1),10379(a,2)),rewrite([4155(8),4408(7),45(6),27608(8),14868(6),3228(7)])]. given #2531 (W1r,wt=22): 16813 L(L(T(x,K(L(x,y,z),u)),w,v5),y,z) = L(L(x,y,z),w,v5). [back_rewrite(12856),rewrite([16568(3)])]. given #2532 (W1r,wt=29): 215774 (x \ y) * T(T(T(T(T(x,z),y),u),w),v5) = T(T(T(T(x,z),u),w),v5) * (x \ y). [para(29(a,1),62500(a,1,2,1,1,1))]. given #2533 (W2w,wt=31): 13442 (x * y) * (y * (((y \ z) * (y * u)) * w)) = y * ((y \ x) * ((y * ((z * y) * u)) * w)). [para(187(a,1),104(a,1,2,2)),flip(a)]. given #2534 (W2w,wt=31): 13447 (x * ((y * x) * z)) * T(u,(x \ y) * (x * z)) = x * (x * (u * ((x \ y) * (x * z)))). [para(90(a,1),187(a,1,2,2)),flip(a)]. given #2535 (W2w,wt=31): 13490 (x \ y) * ((x \ y) * ((((y \ x) * z) * T(y,x)) * u)) = (((x \ y) * z) * T(y,x)) * u. [para(4505(a,1),187(a,1,2,2,1,2)),rewrite([4408(4),8020(14)])]. given #2536 (W2w,wt=31): 13495 ((x \ y) * (((y \ z) * (y * u)) * w)) * (y * x) = T((y * ((z * y) * u)) * w,y * x). [para(187(a,1),2705(a,2,1)),rewrite([3940(12),13450(6),4408(8),13451(6)])]. given #2537 (W2a,wt=33): 4619 x * (y * (x * (x * (y * (x * ((T(y,x) \ z) * u)))))) = (x * (y * (x * (x * (x * z))))) * u. [back_rewrite(4543),rewrite([4578(11),2040(13)])]. given #2538 (W2a,wt=35): 4635 T(T(T(T(x / y,z),u),w),v5) * (y * (y * v6)) = y * (T(T(T(T(y \ x,z),u),w),v5) * (y * v6)). [back_rewrite(3842),rewrite([4578(7),2040(8)])]. given #2539 (W2r,wt=32): 200427 K(x * y,(x * (z * (u * (u * (z * (x * y)))))) / L(x * (z * (u * (u * z))),x,y)) = 1. [para(2213(a,1),179374(a,1,2,1,2))]. given #2540 (W2r,wt=35): 195904 K(x \ (x \ T(T(T(y,z),u),w)),v5 * (v5 * x)) = K(x \ (x \ T(T(T(y,w),z),u)),v5 * (v5 * x)). [para(25064(a,1),23367(a,2,1)),rewrite([23367(13)])]. given #2541 (W2r,wt=35): 102173 T(x * (x * y),((y * z) \ (x \ (x \ z))) * ((y * z) \ (x \ (x \ z)))) * u = x * (x * (y * u)). [para(18271(a,1),33996(a,1,1)),rewrite([26790(9),13(4),37(3)]),flip(a)]. given #2542 (W2r,wt=31): 34800 K((x / T(y,z)) * ((y * (z / x)) * u),(T(y,z) / x) * ((u * (x / T(y,z))) * z)) = 1. [para(30627(a,1),2812(a,1,2,1,1)),rewrite([34768(4),4408(4),10229(3),4578(4),34768(8),2040(9),136(8),30508(5),34768(13),4155(13),10229(12),11604(13)])]. given #2543 (W2r,wt=31): 173994 T(x * (y * (z * (y * z))),K(y * (z * y),T(x * z,z))) = x * (y * (z * (y * z))). [back_rewrite(54746),rewrite([173978(8),37242(9)])]. given #2544 (W0w,wt=10): 230608 T(x,K(L(x,y,z),u)) = x. [para(16813(a,1),55660(a,1)),rewrite([55660(2)]),flip(a)]. given #2545 (W0w,wt=10): 231480 K(x,K(L(x,y,z),u)) = 1. [hyper(27,a,230608,a)]. given #2546 (W0w,wt=10): 231502 T(x,K(y,L(x,z,u))) = x. [para(230608(a,1),7769(a,1,1)),rewrite([6144(3),231501(3),1708(4)])]. given #2547 (W0w,wt=10): 232004 K(x,L(y,z,u)) = K(x,y). [para(231502(a,1),56531(a,1,2,1)),rewrite([110378(5),105864(6),19074(4),231954(3),231983(3),101793(4),16687(2)]),flip(a)]. -------- Proof 4 -------- "Ka". ============================== PROOF ================================= % Proof 4 at 133.72 (+ 0.54) seconds: "Ka". % Length of proof is 1980. % Level of proof is 75. % Maximum clause weight is 35. % Given clauses 2547. 1 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 2 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 3 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 4 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 5 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 9 K(a(x,y,z),u) = 1 # label("Ka") # label(non_clause) # label(goal). [goal]. 13 1 * x = x. [assumption]. 14 x * 1 = x. [assumption]. 15 x \ (x * y) = y. [assumption]. 16 x * (x \ y) = y. [assumption]. 17 (x * y) / y = x. [assumption]. 18 (x / y) * y = x. [assumption]. 19 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 20 (x * y) \ (y * x) = K(y,x). [assumption]. 21 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 22 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 23 x \ (y * x) = T(y,x). [assumption]. 24 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(1)]. 25 L(x,y,z) != x | a(z,y,x) = 1. [clausify(2)]. 26 T(x,y) != x | T(y,x) = y. [clausify(3)]. 27 T(x,y) != x | K(x,y) = 1. [clausify(4)]. 28 K(x,y) != 1 | T(x,y) = x. [clausify(5)]. 29 T(T(x,y),z) = T(T(x,z),y). [assumption]. 30 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 31 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 32 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 33 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(32),flip(a)]. 34 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 35 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 36 ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang (M1)"). [assumption]. 37 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 41 K(a(c13,c14,c15),c16) != 1 # label("Ka") # answer("Ka"). [deny(9)]. 45 1 \ x = x. [para(13(a,1),15(a,1,2))]. 46 x \ x = 1. [para(14(a,1),15(a,1,2))]. 47 x / x = 1. [para(13(a,1),17(a,1,1))]. 48 x / 1 = x. [para(14(a,1),17(a,1,1))]. 49 x / (y \ x) = y. [para(16(a,1),17(a,1,1))]. 50 (x / y) \ x = y. [para(18(a,1),15(a,1,2))]. 51 a(x,1,y) = 1. [para(13(a,1),19(a,1,1,2)),rewrite([14(3),46(3)]),flip(a)]. 52 a(1,x,y) = 1. [para(13(a,1),19(a,1,1)),rewrite([13(3),46(3)]),flip(a)]. 54 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(19(a,1),16(a,1,2))]. 55 (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y). [para(16(a,1),19(a,1,1,2))]. 56 (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z). [para(16(a,1),19(a,1,2,1))]. 57 (x * (y * ((x * y) \ z))) \ z = a(x,y,(x * y) \ z). [para(16(a,1),19(a,1,2))]. 58 (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z). [para(18(a,1),19(a,1,1,2))]. 59 x \ (((x / (y * z)) * y) * z) = a(x / (y * z),y,z). [para(18(a,1),19(a,1,1))]. 60 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(18(a,1),19(a,1,2,1))]. 63 (x * y) * K(y,x) = y * x. [para(20(a,1),16(a,1,2))]. 64 x \ ((y \ x) * y) = K(y \ x,y). [para(16(a,1),20(a,1,1))]. 65 ((x \ y) * x) \ y = K(x,x \ y). [para(16(a,1),20(a,1,2))]. 66 x \ (y * (x / y)) = K(y,x / y). [para(18(a,1),20(a,1,1))]. 67 (x * (y / x)) \ y = K(y / x,x). [para(18(a,1),20(a,1,2))]. 68 K(x * x,x) = a(x,x,x). [para(20(a,1),19(a,1))]. 70 L(x,1,y) = x. [para(13(a,1),21(a,1,2,2)),rewrite([14(2),15(2)]),flip(a)]. 72 (x * y) * L(z,y,x) = x * (y * z). [para(21(a,1),16(a,1,2))]. 73 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(16(a,1),21(a,1,1))]. 74 L(x \ y,x,z) = (z * x) \ (z * y). [para(16(a,1),21(a,1,2,2)),flip(a)]. 75 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(18(a,1),21(a,1,1))]. 76 L(x,y / x,z) = (z * (y / x)) \ (z * y). [para(18(a,1),21(a,1,2,2)),flip(a)]. 80 R(x,y,1) = x. [para(14(a,1),22(a,1,1)),rewrite([14(3),17(2)]),flip(a)]. 81 R(x,x \ y,z) = (y * z) / ((x \ y) * z). [para(16(a,1),22(a,1,1,1)),flip(a)]. 82 R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z)). [para(16(a,1),22(a,1,1)),flip(a)]. 83 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(16(a,1),22(a,1,2))]. 84 R(x,y,z) * (y * z) = (x * y) * z. [para(22(a,1),18(a,1,1))]. 85 R(x / y,y,z) = (x * z) / (y * z). [para(18(a,1),22(a,1,1,1)),flip(a)]. 86 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(18(a,1),22(a,1,2))]. 87 T(1,x) = 1. [para(13(a,1),23(a,1,2)),rewrite([46(1)]),flip(a)]. 88 T(x,1) = x. [para(14(a,1),23(a,1,2)),rewrite([45(2)]),flip(a)]. 89 T(x,x) = x. [para(23(a,1),15(a,1))]. 90 x * T(y,x) = y * x. [para(23(a,1),16(a,1,2))]. 91 T(x,x \ y) = (x \ y) \ y. [para(16(a,1),23(a,1,2)),flip(a)]. 92 T(x / y,y) = y \ x. [para(18(a,1),23(a,1,2)),flip(a)]. 94 T(T(T(x,y),z),u) = T(T(T(x,u),y),z). [para(29(a,1),29(a,1,1)),flip(a)]. 97 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,v5,v6),y,z),u,w). [para(34(a,1),34(a,1,1)),flip(a)]. 100 (x * x) * y = x * (x * y). [para(13(a,1),36(a,2,2)),rewrite([14(2)])]. 101 (x * y) * x = x * (y * x). [para(36(a,1),14(a,1)),rewrite([14(2)]),flip(a)]. 103 x * (y * (x * ((x * (y * x)) \ z))) = z. [para(36(a,1),16(a,1)),rewrite([101(2)])]. 104 x * ((x \ y) * (x * z)) = (y * x) * z. [para(16(a,1),36(a,1,1,1)),flip(a)]. 106 (x * (y * (x * z))) / z = x * (y * x). [para(36(a,1),17(a,1,1)),rewrite([101(6)])]. 107 (x / y) * (y * ((x / y) * z)) = (x * (x / y)) * z. [para(18(a,1),36(a,1,1,1)),flip(a)]. 110 (x * (y * (z * (y * u)))) \ ((x * (y * (z * y))) * u) = a(x,y * (z * y),u). [para(36(a,1),19(a,1,1,2)),rewrite([101(6),101(11)])]. 112 ((x * (y * x)) * (z * u)) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [para(36(a,1),19(a,1,2,1)),rewrite([101(2),101(11)])]. 113 ((x * y) * (x * z)) \ (x * (y * (x * z))) = a(x * y,x,z). [para(36(a,1),19(a,1,2))]. 114 (x * (y * (x * z))) \ (z * (x * (y * x))) = K(z,x * (y * x)). [para(36(a,1),20(a,1,1)),rewrite([101(5),101(9)])]. 117 (x * (y * (z * y))) \ (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(36(a,1),21(a,1,2,2)),rewrite([101(2),101(10)])]. 118 ((x * (y * x)) * z) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(36(a,1),21(a,1,2)),rewrite([101(2),101(10)])]. 121 ((x * (y * (z * y))) * u) / (y * (z * (y * u))) = R(x,y * (z * y),u). [para(36(a,1),22(a,1,2)),rewrite([101(2),101(10)])]. 122 x \ (y * (z * (y * x))) = T(y * (z * y),x). [para(36(a,1),23(a,1,2)),rewrite([101(6)])]. 125 ((x * (y * x)) * (z * (x * (y * x)))) * u = (x * (y * x)) * (z * (x * (y * (x * u)))). [para(36(a,1),36(a,2,2,2)),rewrite([101(2),101(5),101(6),101(9)])]. 126 (x * ((y * (z * y)) * x)) * u = x * (y * (z * (y * (x * u)))). [para(36(a,1),36(a,2,2)),rewrite([101(2),101(4)])]. 128 (x * (y * x)) * z = x * (y * (x * z)). [back_rewrite(36),rewrite([101(2)])]. 129 (x * (y * (x * (z * (x * (y * x)))))) * u = x * (y * (x * (z * (x * (y * (x * u)))))). [back_rewrite(125),rewrite([128(6),128(14)])]. 130 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [back_rewrite(126),rewrite([128(3)])]. 132 (x * (y * (x * z))) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [back_rewrite(118),rewrite([128(3)])]. 133 (x * (y * (x * (z * u)))) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [back_rewrite(112),rewrite([128(4)])]. 134 (x * (x * y)) \ (x * (x * (y * z))) = z. [para(37(a,1),15(a,1,2))]. 136 x * (x * ((x \ y) * z)) = (x * y) * z. [para(16(a,1),37(a,1,1,2)),flip(a)]. 139 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(37(a,1),19(a,1,1,2))]. 140 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(37(a,1),19(a,1,1)),rewrite([37(7),37(8)])]. 141 (x * ((x * y) * z)) \ (x * (x * (y * z))) = a(x,x * y,z). [para(37(a,1),19(a,1,2))]. 143 (x * (y * (y * z))) \ (y * (y * (z * x))) = K(y * (y * z),x). [para(37(a,1),20(a,1,2))]. 144 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(37(a,1),21(a,1,1)),rewrite([37(7)])]. 145 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(37(a,1),21(a,1,2,2))]. 146 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(37(a,1),22(a,1,1,1)),rewrite([37(4)])]. 148 ((x * (y * (y * z))) * u) / (y * (y * (z * u))) = R(x,y * (y * z),u). [para(37(a,1),22(a,1,2))]. 150 x * (x * ((y * (x * (x * (y * z)))) * u)) = x * (x * (y * (x * (x * (y * (z * u)))))). [para(37(a,1),37(a,1,1,2)),rewrite([37(6),37(7),37(13),37(14)])]. 159 T(T(x,y),x) = T(x,y). [para(89(a,1),29(a,1,1)),flip(a)]. 160 L(T(x,L(x,y,z)),y,z) = L(x,y,z). [para(89(a,1),30(a,1)),flip(a)]. 162 ((x * y) * z) / a(x,y,z) = x * (y * z). [para(19(a,1),49(a,1,2))]. 164 (x * (y * z)) / L(z,y,x) = x * y. [para(21(a,1),49(a,1,2))]. 165 (x * y) / T(x,y) = y. [para(23(a,1),49(a,1,2))]. 166 R(x,y,z) \ ((x * y) * z) = y * z. [para(22(a,1),50(a,1,1))]. 168 x \ ((y * x) * z) = (x \ y) * (x * z). [para(104(a,1),15(a,1,2))]. 169 (x * y) * (y \ z) = y * ((y \ x) * z). [para(16(a,1),104(a,1,2,2)),flip(a)]. 170 ((x * y) * z) / ((y \ x) * (y * z)) = y. [para(104(a,1),17(a,1,1))]. 171 (x / y) * (((x / y) \ z) * x) = (z * (x / y)) * y. [para(18(a,1),104(a,1,2,2))]. 173 a(x,x \ y,x * z) = ((y * x) * z) \ (y * (x * z)). [para(104(a,1),19(a,1,1)),rewrite([16(4)]),flip(a)]. 175 (x * (y * z)) * (a(x,y,z) * ((x * (y * z)) * u)) = (((x * y) * z) * (x * (y * z))) * u. [para(19(a,1),104(a,1,2,1))]. 176 ((x * y) * z) \ (((y \ x) * (y * z)) * y) = K((y \ x) * (y * z),y). [para(104(a,1),20(a,1,1))]. 177 (((x \ y) * (x * z)) * x) \ ((y * x) * z) = K(x,(x \ y) * (x * z)). [para(104(a,1),20(a,1,2))]. 178 (x * y) * (K(y,x) * ((x * y) * z)) = ((y * x) * (x * y)) * z. [para(20(a,1),104(a,1,2,1))]. 179 ((x * y) * z) \ (y * (((y \ x) * (y * z)) * u)) = L(u,(y \ x) * (y * z),y). [para(104(a,1),21(a,1,1))]. 180 L((x \ y) * (x * z),x,u) = (u * x) \ (u * ((y * x) * z)). [para(104(a,1),21(a,1,2,2)),flip(a)]. 181 L(x * y,x \ z,x) = z \ ((z * x) * y). [para(104(a,1),21(a,1,2)),rewrite([16(2)]),flip(a)]. 182 (x * y) * (L(z,y,x) * ((x * y) * u)) = ((x * (y * z)) * (x * y)) * u. [para(21(a,1),104(a,1,2,1))]. 183 (((x * y) * z) * u) / (((y \ x) * (y * z)) * u) = R(y,(y \ x) * (y * z),u). [para(104(a,1),22(a,1,1,1))]. 185 ((x \ y) * (x * z)) \ ((y * x) * z) = T(x,(x \ y) * (x * z)). [para(104(a,1),23(a,1,2))]. 186 x * (T(y,x) * (x * z)) = ((y * x) * x) * z. [para(23(a,1),104(a,1,2,1))]. 187 x * (x * (((x \ y) * (x * z)) * u)) = (x * ((y * x) * z)) * u. [para(104(a,1),37(a,1,1,2)),flip(a)]. 188 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * (y * u)))))) = (z * (x * (x * y))) * u. [para(104(a,1),37(a,1)),rewrite([37(10)]),flip(a)]. 189 (x * y) * (x * z) = x * ((y * x) * z). [para(104(a,1),37(a,2,2)),rewrite([16(2)])]. 190 (x * y) * ((y \ z) * (y * u)) = y * ((y \ x) * ((z * y) * u)). [para(104(a,1),104(a,1,2,2)),flip(a)]. 191 (x * ((x \ y) * z)) / z = R(y,x,x \ z). [back_rewrite(83),rewrite([169(3)])]. 192 (x * y) \ (z * ((z \ x) * y)) = a(x,z,z \ y). [back_rewrite(55),rewrite([169(4)])]. 193 (x * y) * (L(z,y,x) * ((x * y) * u)) = (x * (((y * z) * x) * y)) * u. [back_rewrite(182),rewrite([189(10)])]. 196 (x * ((y * x) * z)) \ (x * (y * (x * z))) = a(x * y,x,z). [back_rewrite(113),rewrite([189(3)])]. 197 R(x,y,y \ 1) = x. [para(14(a,1),191(a,1,1,2)),rewrite([16(2),48(2)]),flip(a)]. 198 R(x * y,x,x \ z) = (x * (y * z)) / z. [para(15(a,1),191(a,1,1,2,1)),flip(a)]. 199 R(x,y,y \ ((y \ x) \ z)) = (y * z) / ((y \ x) \ z). [para(16(a,1),191(a,1,1,2)),flip(a)]. 200 R(x,y,y \ z) * z = y * ((y \ x) * z). [para(191(a,1),18(a,1,1))]. 201 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) = ((x * (y * z)) * (a(x,y,z) * u)) / u. [para(19(a,1),191(a,1,1,2,1)),flip(a)]. 202 R(x * y,y * x,(y * x) \ z) = ((y * x) * (K(x,y) * z)) / z. [para(20(a,1),191(a,1,1,2,1)),flip(a)]. 203 R(x * (y * z),x * y,(x * y) \ u) = ((x * y) * (L(z,y,x) * u)) / u. [para(21(a,1),191(a,1,1,2,1)),flip(a)]. 204 R(x * y,y,y \ z) = (y * (T(x,y) * z)) / z. [para(23(a,1),191(a,1,1,2,1)),flip(a)]. 205 (x * (x * (y * (((x * (x * y)) \ z) * u)))) / u = R(z,x * (x * y),(x * (x * y)) \ u). [para(37(a,1),191(a,1,1))]. 206 R(x,x,x \ y) = x. [para(46(a,1),191(a,1,1,2,1)),rewrite([13(2),17(2)]),flip(a)]. 208 R(x,x / y,(x / y) \ z) = ((x / y) * (y * z)) / z. [para(50(a,1),191(a,1,1,2,1)),flip(a)]. 209 a(x,y,z) \ ((x * y) * z) = T(x * (y * z),a(x,y,z)). [para(19(a,1),91(a,1,2)),rewrite([19(9)]),flip(a)]. 218 x / T(y,y \ x) = y \ x. [para(91(a,2),49(a,1,2))]. 220 R(x,y \ z,T(y,y \ z)) = R(x,y \ z,(y \ z) \ z). [para(91(a,2),191(a,2,3)),rewrite([191(6)]),flip(a)]. 221 T(x \ y,T(x,x \ y)) = ((x \ y) \ y) \ y. [para(91(a,2),91(a,1,2))]. 228 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,u,w),y,z),v5,v6). [para(97(a,1),34(a,1))]. 229 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v5,v6),y,z),v7,v8),u,w). [para(97(a,2),34(a,1,1))]. 260 T(x * ((x \ y) * z),a(x,x \ y,z)) = a(x,x \ y,z) \ (y * z). [para(16(a,1),209(a,1,2,1)),flip(a)]. 262 a(x,y,y \ z) \ (y * ((y \ x) * z)) = T(x * z,a(x,y,y \ z)). [para(16(a,1),209(a,2,1,2)),rewrite([169(5)])]. 263 T((x / y) * (y * z),a(x / y,y,z)) = a(x / y,y,z) \ (x * z). [para(18(a,1),209(a,1,2,1)),flip(a)]. 265 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(209(a,1),49(a,1,2))]. 268 ((x * (y \ z)) * T(y,y \ z)) / z = R(x,y \ z,(y \ z) \ z). [para(220(a,1),22(a,2)),rewrite([90(9),16(7)])]. 311 (x * (y * (y * z))) \ ((x * (y * y)) * z) = a(x,y * y,z). [para(13(a,1),110(a,1,1,2,2)),rewrite([13(5),13(9)])]. 312 (x * (y * (z * (y * u)))) * a(x,y * (z * y),u) = (x * (y * (z * y))) * u. [para(110(a,1),16(a,1,2))]. 314 (x * ((y \ z) * (y * ((y \ z) * u)))) \ ((x * ((y \ z) * z)) * u) = a(x,(y \ z) * z,u). [para(16(a,1),110(a,1,2,1,2,2)),rewrite([16(14)])]. 326 ((x / y) * (z * x)) \ (y * ((x / y) * (z * (x / y)))) = K(y,(x / y) * (z * (x / y))). [para(18(a,1),114(a,1,1,2,2))]. 338 ((x * (y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(13(a,1),148(a,1,2,2,2)),rewrite([14(2),14(8)])]. 340 ((x * (y * (y * z))) * (z \ u)) / (y * (y * u)) = R(x,y * (y * z),z \ u). [para(16(a,1),148(a,1,2,2,2))]. 341 R(x,y * (y * z),u) * (y * (y * (z * u))) = (x * (y * (y * z))) * u. [para(148(a,1),18(a,1,1))]. 342 R(x / (y * (y * z)),y * (y * z),u) = (x * u) / (y * (y * (z * u))). [para(18(a,1),148(a,1,1,1)),flip(a)]. 345 (x * (x * ((x * y) * z))) / (x * (x * (y * z))) = R(x,x * (x * y),z). [para(37(a,1),148(a,1,1))]. 346 ((x * (y * z)) * (y * u)) / (y * ((z * y) * u)) = R(x,y * z,y * u). [para(104(a,1),148(a,1,2,2)),rewrite([16(2),16(10)])]. 350 ((x * y) * z) * K((y \ x) * (y * z),y) = ((y \ x) * (y * z)) * y. [para(176(a,1),16(a,1,2))]. 354 ((x * (y / z)) * z) \ ((((y / z) \ x) * y) * (y / z)) = K(((y / z) \ x) * y,y / z). [para(18(a,1),176(a,1,2,1,2)),rewrite([18(13)])]. 356 (x * (x * y)) \ (x * (y * x)) = K(x * y,x). [para(46(a,1),176(a,1,2,1,1)),rewrite([100(2),13(5),101(4),46(6),13(8)])]. 357 ((x * (x / y)) * z) \ ((y * ((x / y) * z)) * (x / y)) = K(y * ((x / y) * z),x / y). [para(50(a,1),176(a,1,2,1,1)),rewrite([50(11)])]. 393 x * (x * ((x * (y * (x * (x * x)))) * z)) = x * (x * (x * (y * (x * (x * (x * z)))))). [para(129(a,1),37(a,1)),flip(a)]. 398 x * (x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u))))))) = x * (x * u). [para(16(a,1),150(a,1,2,2)),flip(a)]. 405 x * ((y * x) * (x * ((x \ y) * (z * u)))) = x * (x * (((x \ y) * ((x * y) * z)) * u)). [para(104(a,1),150(a,2,2)),rewrite([136(5)]),flip(a)]. 407 x * (x * (((x * x) \ y) * (x * (x * z)))) = (y * (x * x)) * z. [para(13(a,1),188(a,1,2,2,2,2,2,2)),rewrite([14(3),13(7),14(9)])]. 411 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [para(16(a,1),188(a,1,2,2,2,2,2,2))]. 418 (x * y) * (((x * y) \ z) * (x * ((y * x) * u))) = (z * (x * y)) * (x * u). [para(104(a,1),188(a,1,2,2,2,2,2)),rewrite([16(3),136(10),16(10)])]. 426 (x * (y * (x * y))) * z = (x * y) * ((x * y) * z). [para(13(a,1),175(a,1,1,2)),rewrite([51(3),13(4),13(5),14(6),13(7),189(7),101(6)]),flip(a)]. 435 R(x * ((x \ y) * z),y * z,(y * z) \ u) = ((y * z) * (a(y,x,x \ z) * u)) / u. [para(16(a,1),201(a,1,2,2)),rewrite([169(3),16(6),16(9)])]. 437 R(((x / (y * z)) * y) * z,x,x \ u) = (x * (a(x / (y * z),y,z) * u)) / u. [para(18(a,1),201(a,1,2)),rewrite([18(8),18(10)])]. 439 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) \ ((x * (y * z)) * (a(x,y,z) * u)) = u. [para(201(a,2),50(a,1,1))]. 463 x * (x * (x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))))) = x * (x * z). [para(16(a,1),393(a,1,2,2)),flip(a)]. 478 R(x,1 / y,y) = x. [para(50(a,1),197(a,1,3))]. 480 R(x,x,y) = x. [para(15(a,1),206(a,1,3))]. 493 R(T(x,y),x,z) = T(x,y). [para(480(a,1),31(a,1,1)),flip(a)]. 495 R(R(x,y,z),x,u) = R(x,y,z). [para(480(a,1),35(a,1,1)),flip(a)]. 506 (x * (1 / y)) * y = x. [para(478(a,1),22(a,2)),rewrite([18(7),48(6)])]. 507 (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z)). [para(90(a,1),19(a,1,1,2))]. 508 (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z). [para(90(a,1),19(a,1,2,1))]. 510 (x * y) \ (T(x,y) * y) = K(T(x,y),y). [para(90(a,1),20(a,1,1))]. 511 (T(x,y) * y) \ (x * y) = K(y,T(x,y)). [para(90(a,1),20(a,1,2))]. 512 (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y). [para(90(a,1),21(a,1,1))]. 516 ((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,y)). [para(90(a,1),22(a,1,2))]. 517 x * T(T(y,x),z) = T(y,z) * x. [para(29(a,1),90(a,1,2))]. 518 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(30(a,1),90(a,1,2))]. 519 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(31(a,1),90(a,1,2))]. 520 x * (x * (T(y,x) * z)) = x * (y * (x * z)). [para(90(a,1),37(a,1,1,2)),rewrite([128(3)]),flip(a)]. 521 x * (x * (y * T(z,x * (x * y)))) = z * (x * (x * y)). [para(90(a,1),37(a,1)),flip(a)]. 522 x * ((x \ y) * (z * x)) = (y * x) * T(z,x). [para(90(a,1),104(a,1,2,2))]. 537 T(T(x / y,z),y) = T(y \ x,z). [para(92(a,1),29(a,1,1)),flip(a)]. 538 x \ (y * ((y \ z) * x)) = R(T(z,x),y,y \ x). [para(191(a,1),92(a,1,1)),rewrite([31(3)]),flip(a)]. 540 K(T(x,y),x) = 1. [hyper(27,a,159,a)]. 541 T(x,T(x,y)) = x. [hyper(26,a,159,a)]. 547 T(x,y) * x = x * T(x,y). [para(159(a,1),90(a,1,2)),flip(a)]. 554 K(x \ y,y / x) = 1. [para(92(a,1),540(a,1,1))]. 555 K(x,T(x,y)) = 1. [hyper(27,a,541,a)]. 560 T(x,(x \ y) \ y) = x. [para(91(a,1),541(a,1,2))]. 568 K(x / y,y \ x) = 1. [para(92(a,1),555(a,1,2))]. 582 x * a(x / (y * z),y,z) = ((x / (y * z)) * y) * z. [para(18(a,1),54(a,1,1))]. 588 ((x * y) * z) \ ((x * (y * z)) * (a(x,y,z) * u)) = L(u,a(x,y,z),x * (y * z)). [para(54(a,1),21(a,1,1))]. 589 (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),y * (z * u),x). [para(54(a,1),21(a,1,2,2))]. 592 ((x * (y * (z * u))) * a(y,z,u)) / ((y * z) * u) = R(x,y * (z * u),a(y,z,u)). [para(54(a,1),22(a,1,2))]. 597 (x * (y * z)) * (((x * (y * z)) \ u) * ((x * y) * z)) = (u * (x * (y * z))) * a(x,y,z). [para(54(a,1),104(a,1,2,2))]. 601 (((x * y) * z) * (x * (y * z))) * a(x,y,z) = (x * (y * z)) * (a(x,y,z) * ((x * y) * z)). [para(54(a,1),175(a,1,2,2)),flip(a)]. 602 (x * (y * z)) * a(x,z,T(y,z)) = (x * z) * T(y,z). [para(90(a,1),54(a,1,1,2))]. 614 (x * ((x \ y) * ((y \ z) * (y * u)))) \ ((z * y) * u) = a(x,x \ y,(y \ z) * (y * u)). [para(104(a,1),56(a,1,2))]. 625 T(x / y,z) * y = y * T(y \ x,z). [para(537(a,1),90(a,1,2)),flip(a)]. 632 L(x \ 1,x,y) = (y * x) \ y. [para(14(a,1),74(a,2,2))]. 634 L(x \ (y \ z),x,y) = (y * x) \ z. [para(16(a,1),74(a,2,2))]. 637 (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x). [para(20(a,1),74(a,1,1)),flip(a)]. 638 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(21(a,1),74(a,1,1)),flip(a)]. 639 L(T(x,y),y,x) = T(x,x * y). [para(74(a,2),23(a,1)),rewrite([23(2)])]. 648 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(y * z) \ (y * u)). [para(74(a,2),191(a,2,3)),rewrite([191(8)]),flip(a)]. 650 T(x * y,(x * y) \ (x * z)) = L(y \ z,y,x) \ (x * z). [para(74(a,2),91(a,2,1))]. 659 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(90(a,1),74(a,2,2))]. 662 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,(x * y) \ (x * z),u). [para(74(a,2),56(a,1,1,2,1))]. 666 L(K(x,y),y * x,y) = K(y * x,y). [back_rewrite(356),rewrite([637(5)])]. 667 L(L(x,y,z),z * y,z) = x. [back_rewrite(134),rewrite([638(6)])]. 669 x * (T(y,x) * x) = (y * x) * x. [para(14(a,1),186(a,1,2,2)),rewrite([14(7)])]. 673 (((x * y) * y) * z) \ ((x * y) * (y * z)) = a(y,T(x,y),y * z). [para(186(a,1),19(a,1,1)),rewrite([90(5)])]. 674 (x * ((T(y,x) * (x * z)) * u)) \ ((((y * x) * x) * z) * u) = a(x,T(y,x) * (x * z),u). [para(186(a,1),19(a,1,2,1))]. 675 ((T(x,y) * (y * z)) * y) \ (((x * y) * y) * z) = K(y,T(x,y) * (y * z)). [para(186(a,1),20(a,1,2))]. 682 x * (T(T(y,x),z) * (x * u)) = ((T(y,z) * x) * x) * u. [para(29(a,1),186(a,1,2,1))]. 684 x * (R(T(y,x),z,u) * (x * w)) = ((R(y,z,u) * x) * x) * w. [para(31(a,1),186(a,1,2,1))]. 690 a((x * y) * y,T(x,y),z) = a(y,T(x,y) * (x * y),z). [para(186(a,1),110(a,1,2,1)),rewrite([186(6),19(11),90(7)])]. 729 ((x * (y / z)) * z) / T(x * y,a(x,y / z,z)) = a(x,y / z,z). [para(18(a,1),265(a,1,2,1,2))]. 732 (x * (y * z)) / T((x * y) * z,a(y,y \ x,y * z)) = a(y,y \ x,y * z). [para(104(a,1),265(a,1,2,1)),rewrite([16(2)])]. 777 x * (x * T(y,x * x)) = y * (x * x). [para(13(a,1),521(a,1,2,2)),rewrite([14(2),14(6)])]. 778 x * (y * T(z,x * (x * y))) = x \ (z * (x * (x * y))). [para(521(a,1),15(a,1,2)),flip(a)]. 780 L(x * T(y,z * (z * x)),z,z) = (z * z) \ (y * (z * (z * x))). [para(521(a,1),21(a,1,2)),flip(a)]. 788 x * (y * (x * T(z,x * (y * x)))) = z * (x * (y * x)). [para(90(a,1),521(a,1,2,2,2,2,2)),rewrite([520(7),90(8)])]. 831 (x * ((x \ y) * y)) \ ((y * x) * ((x \ y) * z)) = L(z,(x \ y) * y,x). [para(104(a,1),117(a,1,1)),rewrite([169(3),104(9),16(11)])]. 843 (((x * y) * y) * z) / K(y,T(x,y) * (y * z)) = (T(x,y) * (y * z)) * y. [para(675(a,1),49(a,1,2))]. 863 (T(T(x,y),z) * (z * u)) * z = (T(T(x,z),y) * (z * u)) * z. [para(29(a,1),843(a,2,1,1)),rewrite([843(10)])]. 874 x * K((y \ z) * (y * ((z * y) \ x)),y) = ((y \ z) * (y * ((z * y) \ x))) * y. [para(16(a,1),350(a,1,1))]. 888 ((1 / x) * y) \ (x * ((1 / x) * (y * (1 / x)))) = K(x,(1 / x) * (y * (1 / x))). [para(14(a,1),326(a,1,1,2))]. 960 (R(x,y,z) * u) / R(T(x,u),y,z) = u. [para(31(a,1),165(a,1,2))]. 961 (x * (x * (y * z))) / T(x * (x * y),z) = z. [para(37(a,1),165(a,1,1))]. 965 (x * y) / T(y,T(x,y)) = T(x,y). [para(90(a,1),165(a,1,1))]. 969 (((x \ y) * (x * z)) * x) / T((y * x) * z,K((x \ y) * (x * z),x)) = K((x \ y) * (x * z),x). [para(350(a,1),165(a,1,1))]. 974 x * (1 / y) = x / y. [para(506(a,1),17(a,1,1)),flip(a)]. 975 x / (1 / y) = x * y. [para(18(a,1),506(a,1,1)),flip(a)]. 976 a(x,1 / y,y) = 1. [para(506(a,1),19(a,1,2)),rewrite([18(3),14(2),46(1)]),flip(a)]. 980 (x / y) / K(1 / y,T(x,1 / y)) = T(x,1 / y) / y. [para(506(a,1),843(a,1,1)),rewrite([974(3),18(9),14(8),18(14),14(13),974(14)])]. 982 K(x,1 / x) = 1. [para(506(a,1),357(a,1,1)),rewrite([18(4),14(3),974(4),47(2),46(3),18(4),14(3)]),flip(a)]. 985 ((1 / x) * y) \ (x * ((1 / x) * (y / x))) = K(x,(1 / x) * (y / x)). [back_rewrite(888),rewrite([974(8),974(14)])]. 986 T(x,1 / x) = x. [hyper(28,a,982,a)]. 989 1 / x = x \ 1. [hyper(26,a,986,a),rewrite([92(3)]),flip(a)]. 990 (x \ 1) \ 1 = x. [para(986(a,1),23(a,2)),rewrite([989(2),989(4),16(5)])]. 996 T(x \ 1,x) = x \ 1. [para(49(a,1),986(a,1,2))]. 997 (x \ 1) * x = 1. [para(986(a,1),90(a,1,2)),rewrite([989(2),989(5),16(6)])]. 1004 ((x \ 1) * y) \ (x * ((x \ 1) * (y / x))) = K(x,(x \ 1) * (y / x)). [back_rewrite(985),rewrite([989(2),989(5),989(11)])]. 1009 (x / y) / K(y \ 1,T(x,y \ 1)) = T(x,y \ 1) / y. [back_rewrite(980),rewrite([989(3),989(5),989(10)])]. 1012 a(x,y \ 1,y) = 1. [back_rewrite(976),rewrite([989(2)])]. 1013 x / (y \ 1) = x * y. [back_rewrite(975),rewrite([989(2)])]. 1014 x * (y \ 1) = x / y. [back_rewrite(974),rewrite([989(2)])]. 1022 L(x,x \ 1,y) = x. [para(990(a,1),74(a,1,1)),rewrite([1014(6),14(6),50(5)])]. 1025 (x \ 1) * (x * y) = L(y,x,x \ 1). [para(997(a,1),21(a,1,1)),rewrite([45(6)])]. 1026 L(x,y,(y * x) \ 1) = (((y * x) \ 1) * y) \ 1. [para(997(a,1),21(a,1,2)),flip(a)]. 1027 R(x \ 1,x,y) = y / (x * y). [para(997(a,1),22(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1039 R((x * (x * y)) \ 1,x * (x * y),z) = z / (x * (x * (y * z))). [para(997(a,1),148(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1051 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x \ (y \ 1),y). [para(997(a,1),56(a,1,2))]. 1072 a(x,y,y \ 1) = 1. [para(50(a,1),1012(a,1,2)),rewrite([989(2)])]. 1077 L(x \ 1,x,y) = x \ 1. [para(50(a,1),1022(a,1,2)),rewrite([989(2),989(5)])]. 1078 L(L(L(x,y,z),u,w),L(x,u,w) \ 1,v5) = L(L(x,u,w),y,z). [para(1022(a,1),97(a,1,1)),flip(a)]. 1080 L(L(L(x,y,z),u,w),x \ 1,v5) = L(L(x,y,z),u,w). [para(1022(a,1),97(a,2,1,1))]. 1091 (x * y) \ x = y \ 1. [back_rewrite(632),rewrite([1077(3)]),flip(a)]. 1097 (x * (y * K(y,x))) \ (y * x) = a(x,y,K(y,x)). [para(20(a,1),57(a,1,1,2,2)),rewrite([20(8)])]. 1098 (x * (y * L(z,y,x))) \ (x * (y * z)) = a(x,y,L(z,y,x)). [para(21(a,1),57(a,1,1,2,2)),rewrite([21(10)])]. 1105 (x * (y * L(y \ z,y,x))) \ (x * z) = a(x,y,(x * y) \ (x * z)). [para(74(a,2),57(a,1,1,2,2))]. 1141 L(x,y,(y * x) \ 1) \ 1 = ((y * x) \ 1) * y. [para(1026(a,2),49(a,1,2)),rewrite([989(6)])]. 1180 L(x,x \ y,x) = x. [para(14(a,1),181(a,1,1)),rewrite([14(5),15(4)])]. 1201 T(x,L(y * z,y \ x,y)) = T(x,x \ ((x * y) * z)). [para(181(a,2),91(a,1,2)),rewrite([91(10,R)])]. 1227 L(x * y,x \ (x \ 1),x) = (x \ 1) \ y. [para(997(a,1),181(a,2,2,1)),rewrite([13(9)])]. 1246 (x * (x * y)) / T(x * (x * (y / z)),z) = z. [para(18(a,1),961(a,1,1,2,2))]. 1251 (x * ((y * x) * z)) / T(x * y,x * z) = x * z. [para(104(a,1),961(a,1,1,2)),rewrite([16(5)])]. 1252 (x * (x * (y * z))) / T(x * (x * z),T(y,z)) = T(y,z). [para(90(a,1),961(a,1,1,2,2))]. 1266 (((T(x,y) * z) * z) * u) / (T(T(x,z),y) * (z * u)) = z. [para(682(a,1),17(a,1,1))]. 1300 a(x,x,y) = 1. [para(13(a,1),690(a,1,1,1)),rewrite([87(3),51(3),87(3),13(4),13(3)]),flip(a)]. 1301 a(x * (y \ x),T(y,y \ x),z) = a(y \ x,T(y,y \ x) * x,z). [para(16(a,1),690(a,1,1,1)),rewrite([16(10)])]. 1316 K(x * x,x) = 1. [back_rewrite(68),rewrite([1300(3)])]. 1323 x \ (y * (x * x)) = x * T(y,x * x). [para(13(a,1),778(a,1,2)),rewrite([14(2),14(5)]),flip(a)]. 1324 x \ (x \ (y * (x * (x * z)))) = z * T(y,x * (x * z)). [para(778(a,1),15(a,1,2))]. 1346 (x \ (y * (x * z))) \ (z * T(y,x * z)) = a(x,x \ z,T(y,x * z)). [para(778(a,1),56(a,1,1)),rewrite([16(2),16(5),16(10)])]. 1353 x * (y / (x * (x * y))) = x \ 1. [para(997(a,1),778(a,2,2)),rewrite([996(7),1014(5)])]. 1359 x * (y * T(z,y * (x * y))) = y \ (z * (y * (x * y))). [para(788(a,1),15(a,1,2)),flip(a)]. 1448 R((x * (y * x)) \ 1,x * (y * x),z) = z / (x * (y * (x * z))). [para(997(a,1),121(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1452 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,x \ y). [para(268(a,1),18(a,1,1)),rewrite([200(5)])]. 1457 R(x,y \ z,(y \ z) \ z) \ ((x * (y \ z)) * T(y,y \ z)) = z. [para(268(a,1),50(a,1,1))]. 1466 (T(T(x,y),z) * u) * z = (T(T(x,z),y) * u) * z. [para(16(a,1),863(a,1,1,2)),rewrite([16(8)])]. 1479 x * (x * ((T(T(y,z),u) * (u * w)) * u)) = x * (x * ((T(T(y,u),z) * (u * w)) * u)). [para(863(a,1),37(a,2,2,2)),rewrite([37(7)])]. 1517 (x * (y * z)) / T((x * z) * T(y,z),a(z,z \ x,y * z)) = a(z,z \ x,y * z). [para(90(a,1),732(a,1,1,2)),rewrite([90(8),90(13)])]. 1524 L(x * ((y * (y * x)) \ z),y,y) = (y * y) \ z. [para(18(a,1),780(a,2,2)),rewrite([92(6)])]. 1534 L(x / (y * (y * x)),y,y) = (y * y) \ 1. [para(997(a,1),780(a,2,2)),rewrite([996(7),1014(5)])]. 1603 (x * (x * ((T(T(y,z),u) * (u * w)) * u))) / (x * (x * ((T(T(y,u),z) * (u * w)) * u))) = 1. [para(1479(a,1),265(a,1,2,1)),rewrite([100(7),1300(20),88(16),1300(21)])]. 1607 L(x,y,y) = x. [hyper(24,a,1300,a)]. 1609 x / (y * (y * x)) = (y * y) \ 1. [back_rewrite(1534),rewrite([1607(4)])]. 1619 x * ((y * (y * x)) \ z) = (y * y) \ z. [back_rewrite(1524),rewrite([1607(5)])]. 1649 x / (x * x) = x \ 1. [back_rewrite(1353),rewrite([1609(3),1014(4)])]. 1659 T(x * x,x) = x * x. [hyper(28,a,1316,a)]. 1667 L(x,y,x) = x. [para(15(a,1),1180(a,1,2))]. 1684 a(x,y,x) = 1. [hyper(25,a,1667,a)]. 1685 L(T(x,y),z,x) = T(x,y). [para(1667(a,1),30(a,1,1)),flip(a)]. 1689 L(L(L(x,y,z),u,w),v5,L(x,u,w)) = L(L(x,u,w),y,z). [para(1667(a,1),97(a,1,1)),flip(a)]. 1699 ((x \ y) * x) \ ((x \ y) * y) = x \ y. [para(1667(a,1),74(a,1)),flip(a)]. 1702 a((x \ y) * x,x \ y,z) = a(x \ y,y,z). [para(1667(a,1),662(a,1,1,2,1)),rewrite([189(5),16(3),19(7),1699(9)]),flip(a)]. 1708 T(x,x * y) = T(x,y). [back_rewrite(639),rewrite([1685(2)]),flip(a)]. 1723 K(x,(y * x) / y) = 1. [para(15(a,1),554(a,1,1))]. 1812 T(x * y,y \ 1) = (y \ 1) \ x. [para(1013(a,1),92(a,1,1))]. 1826 K(x * y,(y \ 1) \ x) = 1. [para(1013(a,1),568(a,1,1))]. 1829 x \ (x / y) = y \ 1. [para(1014(a,1),15(a,1,2))]. 1832 (x / y) \ ((y \ 1) * x) = K(y \ 1,x). [para(1014(a,1),20(a,1,1))]. 1833 ((x \ 1) * y) \ (y / x) = K(y,x \ 1). [para(1014(a,1),20(a,1,2))]. 1834 (x / y) \ (x * ((y \ 1) * z)) = L(z,y \ 1,x). [para(1014(a,1),21(a,1,1))]. 1836 ((x * y) / z) / (y / z) = R(x,y,z \ 1). [para(1014(a,1),22(a,1,1)),rewrite([1014(5)])]. 1837 (x \ 1) \ (y / x) = T(y,x \ 1). [para(1014(a,1),23(a,1,2))]. 1838 x * (x * ((y \ 1) * z)) = (x * (x / y)) * z. [para(1014(a,1),37(a,1,1,2)),flip(a)]. 1839 (x * (x * y)) / z = x * (x * (y / z)). [para(1014(a,1),37(a,1)),rewrite([1014(6)])]. 1840 x * ((x \ y) * (x / z)) = (y * x) / z. [para(1014(a,1),104(a,1,2,2)),rewrite([1014(8)])]. 1851 (x * (y * (x * (z * (x * (y * x)))))) / u = x * (y * (x * (z * (x * (y * (x / u)))))). [para(1014(a,1),129(a,1)),rewrite([1014(10)])]. 1859 x * (T(y,x) * (x / z)) = ((y * x) * x) / z. [para(1014(a,1),186(a,1,2,2)),rewrite([1014(9)])]. 1864 ((T(x,y) * (y / z)) * y) \ (((x * y) * y) / z) = K(y,T(x,y) * (y / z)). [para(1014(a,1),675(a,1,1,1,2)),rewrite([1014(9),1014(12)])]. 1870 x * (x * ((y * (((x * (x * y)) \ z) * u)) / u)) = R(z,x * (x * y),(x * (x * y)) \ u). [para(205(a,1),1014(a,2)),rewrite([1014(10),1839(8)])]. 1884 x * (x * ((y / z) / T(x * (x * y),z \ 1))) = z \ 1. [para(1014(a,1),961(a,1,1,2,2)),rewrite([1839(9)])]. 1885 x * (x * ((y * z) / T(x * (x * y),z))) = z. [para(961(a,1),1014(a,2)),rewrite([1014(9),1839(7)])]. 1888 x * ((y \ 1) * T(z,x * (x / y))) = x \ (z * (x * (x / y))). [para(1014(a,1),778(a,1,2,2,2,2)),rewrite([1014(10)])]. 1907 x * (x * (((T(T(y,z),u) * (u * w)) * u) / (x * (x * ((T(T(y,u),z) * (u * w)) * u))))) = 1. [back_rewrite(1603),rewrite([1839(15)])]. 1921 x * (x * ((y * z) / T(x * (x * z),T(y,z)))) = T(y,z). [back_rewrite(1252),rewrite([1839(8)])]. 1925 x * (x * (y / T(x * (x * (y / z)),z))) = z. [back_rewrite(1246),rewrite([1839(7)])]. 1932 x * (x * (((x * y) * z) / (x * (x * (y * z))))) = R(x,x * (x * y),z). [back_rewrite(345),rewrite([1839(8)])]. 1935 x * (x * R(y,z,u)) = R(x * (x * y),z,u). [back_rewrite(146),rewrite([1839(6),22(4)])]. 1952 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(x / (y * (y * z)),y * (y * z),u). [para(37(a,1),60(a,1,1,2))]. 1958 ((x / y) * (z * y)) \ (x * T(z,y)) = a(x / y,y,T(z,y)). [para(90(a,1),60(a,1,1,2))]. 1961 L(a(x / y,y,z),(x / y) * (y * z),u) = (u * ((x / y) * (y * z))) \ (u * (x * z)). [para(60(a,1),74(a,1,1))]. 1972 R(x,x / y,(x / y) \ (y \ z)) = ((x / y) * z) / (y \ z). [para(16(a,1),208(a,2,1,2))]. 1990 R(x,x / y,(x / y) \ T(z,y)) = ((x / y) * (z * y)) / T(z,y). [para(90(a,1),208(a,2,1,2))]. 2004 R(x,x * y,(x * y) \ z) = ((x * y) * ((y \ 1) * z)) / z. [para(1013(a,1),208(a,1,2)),rewrite([1013(4),1013(7)])]. 2009 (x / y) * ((x / y) * ((y * z) / T((x / y) * x,z))) = z. [para(18(a,1),1885(a,1,2,2,2,1,2))]. 2010 (x * y) / T(z * (z * x),y) = (z * z) \ y. [para(1885(a,1),21(a,1,2)),rewrite([1607(8)]),flip(a)]. 2012 x * (x * (((x * x) \ y) * z)) = y * z. [para(1885(a,1),37(a,1,1)),rewrite([2010(6)]),flip(a)]. 2032 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (((T(y,z) * x) * x) * u),w))) = w. [para(682(a,1),1885(a,1,2,2,2,1,2))]. 2040 (x * (y * y)) * z = x * (y * (y * z)). [back_rewrite(407),rewrite([2012(7)]),flip(a)]. 2044 R(x,y * y,z) = x. [back_rewrite(338),rewrite([2040(3),17(6)]),flip(a)]. 2045 a(x,y * y,z) = 1. [back_rewrite(311),rewrite([2040(6),46(7)]),flip(a)]. 2166 x / (T(T(y,z),u) * (z * (((T(y,u) * z) * z) \ x))) = z. [para(16(a,1),1266(a,1,1))]. 2213 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(13(a,1),130(a,1,1,2,2)),rewrite([13(8)])]. 2214 (x * (y * (z * (y * x)))) \ (x * (y * (z * (y * (x * u))))) = u. [para(130(a,1),15(a,1,2))]. 2215 x * (y * (z * (y * (x * ((x * (y * (z * (y * x)))) \ u))))) = u. [para(130(a,1),16(a,1))]. 2234 T(x,y) * (y * (z * (y * (T(x,y) * u)))) = (T(x,y) * (y * (z * (x * y)))) * u. [para(90(a,1),130(a,1,1,2,2,2)),flip(a)]. 2243 x * (y * (((y * x) \ 1) * (y * (x * z)))) = (x * y) * z. [para(997(a,1),130(a,1,1,2,2)),rewrite([14(2)]),flip(a)]. 2254 L(x,y,z * z) = x. [para(13(a,1),132(a,1,1,2)),rewrite([13(6),638(6),667(3),13(2)]),flip(a)]. 2276 L(x,y,z * (((z * y) \ 1) * z)) = ((z * y) \ 1) * (z * (y * x)). [para(997(a,1),132(a,1,1,2)),rewrite([14(2),15(8)]),flip(a)]. 2278 L(x,y,z * (((z * (y * x)) \ 1) * z)) = (((z * (y * x)) \ 1) * (z * y)) \ 1. [para(997(a,1),132(a,1,2,2)),rewrite([14(9),1091(8)]),flip(a)]. 2356 L(L(L(x,y,z),u,(u * x) \ 1),((u * x) \ 1) * u,w) = L(L(x,u,(u * x) \ 1),y,z). [para(1026(a,1),1078(a,1,2,1)),rewrite([990(13)])]. 2357 L(L(x,y,(y * x) \ 1),z,u) = L((((y * x) \ 1) * y) \ 1,z,u). [para(1026(a,1),1078(a,2,1)),rewrite([1141(11),2356(10)])]. 2445 ((x \ y) * (x * ((x \ y) * z))) \ (((x \ y) * y) * z) = 1. [para(13(a,1),314(a,1,1)),rewrite([13(9),52(13)])]. 2485 L(x,y * y,z) = x. [hyper(24,a,2045,a)]. 2486 a(x,y * (y * (z * (y * (y * z)))),u) = 1. [para(37(a,1),2045(a,1,2))]. 2495 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(2254(a,1),74(a,1)),rewrite([100(3),100(5)]),flip(a)]. 2497 L(x,y,(z \ 1) / z) = x. [para(1014(a,1),2254(a,1,3))]. 2507 L(x,y,z * (z * u)) = L(x,y,u). [back_rewrite(144),rewrite([2495(8),21(4)]),flip(a)]. 2508 a(x * (x * y),z,u) = a(y,z,u). [back_rewrite(140),rewrite([2495(9),19(5)]),flip(a)]. 2522 L(x,y * (y * (z * (y * (y * z)))),u) = x. [para(37(a,1),2485(a,1,2))]. 2528 L(x,(y \ 1) / y,z) = x. [para(1014(a,1),2485(a,1,2))]. 2538 (x \ y) \ 1 = y \ x. [para(16(a,1),1091(a,1,1)),flip(a)]. 2540 ((x \ y) * (x * z)) \ 1 = ((y * x) * z) \ x. [para(104(a,1),1091(a,1,1)),flip(a)]. 2548 ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. [para(54(a,1),1091(a,1,1))]. 2551 x * (x * ((y * z) * K((y \ 1) * ((x * y) * z),x * y))) = ((y \ 1) * ((x * y) * z)) * (x * y). [para(1091(a,1),350(a,1,2,1,1)),rewrite([37(3),37(11),1091(13)])]. 2556 ((x / y) * ((y \ 1) \ z)) / z = R(x,y \ 1,(y \ 1) \ z). [para(1091(a,1),268(a,1,1,1,2)),rewrite([1014(3),1091(4),1812(5),1091(8),1091(10)])]. 2560 T(x * y,(y \ 1) \ x) = x * y. [para(1091(a,1),560(a,1,2,1))]. 2574 a(x,T(y,x),x * z) = a(y * x,x,z) \ 1. [back_rewrite(673),rewrite([2548(7)]),flip(a)]. 2575 a(x,x \ y,x * z) = a(y,x,z) \ 1. [back_rewrite(173),rewrite([2548(8)])]. 2599 ((x / y) * (y * y)) / T(x * y,a(x,y \ 1,y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),729(a,1,1,1,2)),rewrite([1014(3),1649(6),1649(12)])]. 2601 ((x / y) * (y * y)) \ ((y \ 1) \ x) = K(((y \ 1) \ x) * y,y \ 1). [para(1649(a,1),354(a,1,1,1,2)),rewrite([1014(3),1649(5),1649(9),1014(10),17(8),1649(9),1649(13)])]. 2604 (x * y) \ ((x / y) * (y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),58(a,1,2,1,2)),rewrite([1014(4),1649(7)])]. 2635 T(T(x * x,y),x) = T(x * x,y). [para(1659(a,1),29(a,1,1)),flip(a)]. 2639 T((x \ 1) / x,x \ 1) = (x \ 1) / x. [para(1014(a,1),1659(a,1,1)),rewrite([1014(11)])]. 2640 x * (x * (y * (y * (z / (T(x * x,y) * (y * z)))))) = y. [para(1659(a,1),1266(a,1,1,1,1,1)),rewrite([100(2),37(3),37(4),100(2),2635(7),1839(9),1839(7)])]. 2642 T(x,x \ y) = T(x,y). [para(16(a,1),1708(a,1,2)),flip(a)]. 2643 T(x / y,x) = y \ x. [para(18(a,1),1708(a,1,2)),rewrite([92(4)])]. 2644 T(T(x,y),x * z) = T(T(x,z),y). [para(1708(a,1),29(a,1,1)),flip(a)]. 2645 L(T(x,L(x,y,z) * u),y,z) = L(T(x,u),y,z). [para(1708(a,1),30(a,1)),rewrite([30(2)]),flip(a)]. 2647 T(x * (x * y),x * (x * (y * z))) = T(x * (x * y),z). [para(37(a,1),1708(a,1,2))]. 2648 T(x,(x \ y) * (x * z)) = T(x,(y * x) * z). [para(104(a,1),1708(a,1,2)),flip(a)]. 2649 (x \ y) \ y = T(x,y). [para(91(a,1),1708(a,2)),rewrite([16(2)]),flip(a)]. 2652 T(x,y * x) = T(x,T(y,x)). [para(90(a,1),1708(a,1,2))]. 2690 (x \ y) * T(x,y) = y. [back_rewrite(1457),rewrite([2649(3),2642(7),166(8)])]. 2692 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(1452),rewrite([2642(9)])]. 2697 a(x * (y \ x),T(y,x),z) = a(y \ x,T(y,x) * x,z). [back_rewrite(1301),rewrite([2642(4),2642(7)])]. 2700 T(x,L(y * z,y \ x,y)) = T(x,(x * y) * z). [back_rewrite(1201),rewrite([2642(8)])]. 2705 L(x \ y,x,z) \ (z * y) = T(z * x,z * y). [back_rewrite(650),rewrite([2642(5)]),flip(a)]. 2708 ((x * (y \ z)) * T(y,z)) / z = R(x,y \ z,T(y,z)). [back_rewrite(268),rewrite([2642(4),2649(8)])]. 2709 T(x \ y,T(x,y)) = T(x,y) \ y. [back_rewrite(221),rewrite([2642(3),2649(5)])]. 2711 x / T(y,x) = y \ x. [back_rewrite(218),rewrite([2642(2)])]. 2712 (x \ 1) / x = x \ (x \ 1). [back_rewrite(2639),rewrite([2643(6)]),flip(a)]. 2713 ((x \ y) * (x * z)) \ ((y * x) * z) = T(x,(y * x) * z). [back_rewrite(185),rewrite([2648(10)])]. 2747 L(x,y \ (y \ 1),z) = x. [back_rewrite(2528),rewrite([2712(3)])]. 2748 L(x,y,z \ (z \ 1)) = x. [back_rewrite(2497),rewrite([2712(3)])]. 2755 (x \ 1) \ y = x * y. [back_rewrite(1227),rewrite([2747(5)]),flip(a)]. 2757 ((x / y) * (y * y)) \ (y * x) = K(y * (x * y),y \ 1). [back_rewrite(2601),rewrite([2755(6),2755(8),101(7)])]. 2759 T(x * y,y * x) = x * y. [back_rewrite(2560),rewrite([2755(4)])]. 2760 ((x / y) * (y * z)) / z = R(x,y \ 1,y * z). [back_rewrite(2556),rewrite([2755(4),2755(9)])]. 2771 T(x,y \ 1) = y * (x / y). [back_rewrite(1837),rewrite([2755(4)]),flip(a)]. 2772 K(x * y,y * x) = 1. [back_rewrite(1826),rewrite([2755(4)])]. 2774 T(x * y,y \ 1) = y * x. [back_rewrite(1812),rewrite([2755(7)])]. 2796 R(x,x / y,(x / y) \ z) = R(x,y \ 1,y * z). [back_rewrite(208),rewrite([2760(8)])]. 2802 ((x / y) * (z * y)) / T(z,y) = R(x,y \ 1,z * y). [back_rewrite(1990),rewrite([2796(5),90(4)]),flip(a)]. 2806 ((x / y) * z) / (y \ z) = R(x,y \ 1,z). [back_rewrite(1972),rewrite([2796(5),16(4)]),flip(a)]. 2810 T(x,(y * x) / y) = x. [hyper(28,a,1723,a)]. 2852 x * K(y \ x,y) = (y \ x) * y. [para(16(a,1),63(a,1,1))]. 2853 x * K(y,x / y) = y * (x / y). [para(18(a,1),63(a,1,1))]. 2855 (x * y) \ (K(x,y) * (y * x)) = K(K(x,y),y * x). [para(63(a,1),20(a,1,1))]. 2857 (x * y) \ ((y * x) * (K(x,y) * z)) = L(z,K(x,y),y * x). [para(63(a,1),21(a,1,1))]. 2858 ((x * y) * z) / (K(x,y) * z) = R(y * x,K(x,y),z). [para(63(a,1),22(a,1,1,1))]. 2880 ((x * (y * z)) * K(z,y)) / T(x * (z * y),a(x,y * z,K(z,y))) = a(x,y * z,K(z,y)). [para(63(a,1),265(a,1,2,1,2))]. 2887 (x * y) / T(y * x,K(x,y)) = K(x,y). [para(63(a,1),165(a,1,1))]. 2903 (x / y) * (y \ x) = (y \ x) * (x / y). [para(554(a,1),63(a,1,2)),rewrite([14(5)])]. 2917 K(x,y) \ 1 = K(y,x). [para(63(a,1),1091(a,1,1)),rewrite([20(3)]),flip(a)]. 2918 T(x * y,K(y,x)) = x * y. [para(63(a,1),1708(a,1,2)),rewrite([2759(3)]),flip(a)]. 2925 (x * y) / (y * x) = K(x,y). [back_rewrite(2887),rewrite([2918(4)])]. 2934 (x * (y * z)) \ (L(z,y,x) * (x * y)) = K(L(z,y,x),x * y). [para(21(a,1),64(a,1,2,1)),rewrite([21(10)])]. 2935 x * (K(y \ x,y) * (x * z)) = (((y \ x) * y) * x) * z. [para(64(a,1),104(a,1,2,1))]. 2962 x \ ((y \ 1) * (x * y)) = K(y \ 1,x * y). [para(1091(a,1),64(a,1,2,1)),rewrite([1091(7)])]. 2965 x * (((x \ y) * x) * z) = y * (x * z). [para(16(a,1),189(a,1,1)),flip(a)]. 2971 L(a(x,y,z),x * (y * z),y) = a(y,x,y * z). [para(189(a,1),19(a,1,2)),rewrite([589(7)])]. 2975 L(x,y * z,z) = L(x,z,z * y). [para(189(a,1),21(a,1,2)),rewrite([101(2),21(6)])]. 2993 x * ((T(y,x) * x) * z) = (y * x) * (x * z). [para(90(a,1),189(a,1,1)),flip(a)]. 3018 L(x * (y * z),x \ y,x) = (x * y) * z. [para(189(a,1),181(a,2,2)),rewrite([15(8)])]. 3031 x * (((y \ 1) * x) * z) = (x / y) * (x * z). [para(1014(a,1),189(a,1,1)),flip(a)]. 3032 (x * y) * (x / z) = x * ((y * x) / z). [para(1014(a,1),189(a,1,2)),rewrite([1014(7)])]. 3050 L(x,y * (z * (y * z)),u) = x. [para(189(a,1),2485(a,1,2)),rewrite([101(2)])]. 3078 x * (y * ((y * (x * y)) \ z)) = y \ z. [para(103(a,1),15(a,1,2)),flip(a)]. 3093 x * a(y,z,y * ((y * (z * y)) \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [para(103(a,1),54(a,1,1)),rewrite([189(12)])]. 3097 (x \ y) * (T(x,y) * ((x \ y) * z)) = (y * (x \ y)) * z. [para(103(a,1),186(a,2,1,1)),rewrite([3078(5),3078(6),2642(3),3078(7),3078(11)])]. 3103 x * ((x \ 1) * y) = y. [para(997(a,1),103(a,1,2,2,2,1,2)),rewrite([14(4),16(4)])]. 3118 L((x * (y * x)) \ z,x,y * (x * y)) = (y * (x * (y * x))) \ (y * z). [para(103(a,1),132(a,1,2,2)),flip(a)]. 3130 K(x,(x \ 1) * (y / x)) = K(y,x \ 1). [back_rewrite(1004),rewrite([3103(8),1833(5)]),flip(a)]. 3135 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(16(a,1),2495(a,1,1,2))]. 3136 (x * (x * y)) \ (x * z) = y \ (x \ z). [para(16(a,1),2495(a,1,2,2))]. 3139 T(x * (x * (y / (x * (x * z)))),x * (x * z)) = z \ y. [para(2495(a,1),92(a,2)),rewrite([1839(5)])]. 3141 L(x \ y,z * (z * x),u) = (u * (z * (z * x))) \ (u * (z * (z * y))). [para(2495(a,1),74(a,1,1))]. 3143 (x \ 1) * y = x \ y. [para(997(a,1),2495(a,1,1,2)),rewrite([14(4),15(9)])]. 3162 (x \ ((x * y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(141),rewrite([3135(7)])]. 3163 K(x,x \ (y / x)) = K(y,x \ 1). [back_rewrite(3130),rewrite([3143(4)])]. 3169 (x / y) * (x * z) = x * ((y \ x) * z). [back_rewrite(3031),rewrite([3143(3)]),flip(a)]. 3171 K(x \ 1,y * x) = y \ T(y,x). [back_rewrite(2962),rewrite([3143(4),23(2)]),flip(a)]. 3184 x * (x * ((y * z) * K((y \ x) * (y * z),x * y))) = ((y \ x) * (y * z)) * (x * y). [back_rewrite(2551),rewrite([3143(6),168(4),3143(14),168(12)])]. 3191 L(L(x,y,(y * x) \ 1),z,u) = L(x,z,u). [back_rewrite(2357),rewrite([3143(9),1091(7),2649(9),88(7)])]. 3192 L(L(x,y,z),u,(u * x) \ 1) = L(x,y,z). [back_rewrite(2356),rewrite([3143(9),1091(7),1080(8),3191(10)])]. 3199 L(x,y,z / (y * x)) = L(x,y,z). [back_rewrite(2278),rewrite([3143(5),1091(3),1014(4),3143(9),2538(9),21(7)])]. 3200 L(x,y,z / y) = L(x,y,z). [back_rewrite(2276),rewrite([3143(4),1091(2),1014(3),3143(8),21(6)])]. 3204 x * (y * L(z,x,y)) = (x * y) * z. [back_rewrite(2243),rewrite([3143(6),21(4)])]. 3213 R(x,x * y,(x * y) \ z) = R(x,y,y \ z). [back_rewrite(2004),rewrite([3143(8),169(7),191(8)])]. 3218 x * (y \ T(z,x * (x / y))) = x \ (z * (x * (x / y))). [back_rewrite(1888),rewrite([3143(6)])]. 3228 (x * (x / y)) * z = x * (x * (y \ z)). [back_rewrite(1838),rewrite([3143(3)]),flip(a)]. 3229 (x / y) \ (x * (y \ z)) = L(z,y \ 1,x). [back_rewrite(1834),rewrite([3143(4)])]. 3230 (x \ y) \ (y / x) = K(y,x \ 1). [back_rewrite(1833),rewrite([3143(3)])]. 3231 (x / y) \ (y \ x) = K(y \ 1,x). [back_rewrite(1832),rewrite([3143(4)])]. 3266 L(x,y,y \ 1) = x. [back_rewrite(1025),rewrite([3143(4),15(2)]),flip(a)]. 3276 x \ ((x / y) * (y * z)) = L(z,y,x). [back_rewrite(75),rewrite([3200(6)])]. 3286 (x / y) * (y * ((x / y) * z)) = x * (x * (y \ z)). [back_rewrite(107),rewrite([3228(8)])]. 3302 K(x * y,K(y,x)) = 1. [hyper(27,a,2918,a)]. 3304 T(x,K(y \ x,y)) = x. [para(16(a,1),2918(a,1,1)),rewrite([16(5)])]. 3305 T(x,K(y,x / y)) = x. [para(18(a,1),2918(a,1,1)),rewrite([18(5)])]. 3307 T((x * y) * z,K((y \ x) * (y * z),y)) = (x * y) * z. [para(104(a,1),2918(a,1,1)),rewrite([104(11)])]. 3308 K(x,y) * (y * x) = x * y. [para(2918(a,1),90(a,1,2)),rewrite([63(6)])]. 3323 (((x \ y) * (x * z)) * x) / ((y * x) * z) = K((x \ y) * (x * z),x). [back_rewrite(969),rewrite([3307(11)])]. 3327 K(K(x,y),y * x) = 1. [back_rewrite(2855),rewrite([3308(4),46(3)]),flip(a)]. 3382 T(T(T(x,y \ 1),z),u) / y = T(T(T(x,z),u),y \ 1) / y. [para(94(a,1),1009(a,2,1)),rewrite([1009(12)]),flip(a)]. 3436 (x * x) \ y = x \ (x \ y). [para(18(a,1),1324(a,1,2,2)),rewrite([92(8),1619(6)]),flip(a)]. 3476 x * T(y * z,y * (y * x)) = (y \ z) * (y * (y * x)). [para(181(a,2),1324(a,1,2)),rewrite([3018(5),168(4)]),flip(a)]. 3482 x \ T(y,z * (z / x)) = z \ (z \ (y * (z * (z / x)))). [para(1014(a,1),1324(a,1,2,2,2,2)),rewrite([1014(10),3143(11)]),flip(a)]. 3541 x \ (y \ (z * (y * (x * y)))) = y * T(z,y * (x * y)). [para(1359(a,1),15(a,1,2))]. 3544 (x \ (y * (x * (z * x)))) / (x * T(y,x * (z * x))) = z. [para(1359(a,1),17(a,1,1))]. 3575 x * (y \ T(z,y \ (x / y))) = y * (z * (y \ (x / y))). [para(1014(a,1),1359(a,1,2,2,2,2)),rewrite([3143(6),3143(6),1014(12),3143(11),2755(11)])]. 3576 a(x / y,y,T(z,y * x)) = a(y,y \ x,T(z,y * x)). [para(1359(a,1),60(a,1,1)),rewrite([18(2),18(5),1346(7),18(7)]),flip(a)]. 3640 x * (x * (((x \ y) / z) / T(x * y,z \ 1))) = z \ 1. [para(16(a,1),1884(a,1,2,2,2,1,2))]. 3641 x * (x * (y / T(x * (x * (y * z)),z \ 1))) = z \ 1. [para(17(a,1),1884(a,1,2,2,1))]. 3645 (x / y) / T(z * (z * x),y \ 1) = z \ (z \ (y \ 1)). [para(1884(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 3646 R(x,x \ (y \ 1),z) = (y \ z) / ((x \ (y \ 1)) * z). [para(1884(a,1),22(a,1,1,1)),rewrite([3143(3),3645(8),16(6),3645(13),16(11)]),flip(a)]. 3666 (x \ y) / y = x \ 1. [para(1884(a,1),201(a,1,2)),rewrite([3645(8),100(6),16(5),16(4),3645(11),16(9),16(8),2755(7),480(6),3645(9),16(7),16(6),3645(11),1300(9),13(6),3143(5)]),flip(a)]. 3670 x * (x * (((T(y,x) * (x * z)) / u) / T(x * (((y * x) * x) * z),u \ 1))) = u \ 1. [para(186(a,1),1884(a,1,2,2,2,1,2))]. 3683 x * ((x \ (y \ 1)) * T(z,x / y)) = x \ (z * (x / y)). [para(1884(a,1),778(a,1,2,2,2,2)),rewrite([3645(7),16(5),1014(6),3645(14),16(12),16(11),1014(10)])]. 3691 x / (y * x) = y \ 1. [para(1884(a,1),1013(a,2)),rewrite([3645(7),16(5),2538(5),2755(3)])]. 3709 x \ (x \ (y * (x / z))) = (x \ (z \ 1)) * T(y,x / z). [para(1884(a,1),1324(a,1,2,2,2,2)),rewrite([1014(3),3645(11),16(9),3645(14),16(12),16(11),1014(10)])]. 3710 (x \ (x \ (y \ 1))) * T(z,y \ 1) = x \ (x \ (z / y)). [para(1884(a,1),1324(a,1,2,2,2)),rewrite([1014(3),3645(10),3645(14),16(12),16(11)]),flip(a)]. 3723 R(x \ 1,x,y) = x \ 1. [back_rewrite(1027),rewrite([3691(5)])]. 3724 x / (y * (z * (y * x))) = (y * (z * y)) \ 1. [back_rewrite(1448),rewrite([3723(7)]),flip(a)]. 3725 x / (y * (y * (z * x))) = (y * (y * z)) \ 1. [back_rewrite(1039),rewrite([3723(7)]),flip(a)]. 3735 a(x * (y * x),y,z) = a(x,y * (x * y),z). [para(133(a,1),110(a,1))]. 3752 (x * (y * (y * z))) \ ((x * (y * (y * u))) * (u \ z)) = a(x,y * (y * u),u \ z). [para(16(a,1),139(a,1,1,2,2,2))]. 3753 (x * (y * (y * z))) \ ((x * (y * (y * (z / u)))) * u) = a(x,y * (y * (z / u)),u). [para(18(a,1),139(a,1,1,2,2,2))]. 3762 a(x * ((y * x) * x),z,u) = a(x * y,x * (x * z),u). [para(189(a,1),139(a,1,1)),rewrite([189(9),133(11)])]. 3794 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,w),y),z),v5),u \ 1) / u. [para(94(a,1),3382(a,2,1,1,1))]. 3933 x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u)))))) = x * u. [para(398(a,1),15(a,1,2)),rewrite([15(3)]),flip(a)]. 3934 K(x * y,x) = y \ T(y,x). [para(398(a,1),20(a,1,1)),rewrite([3933(13),101(4),3136(5),23(2),3933(13)]),flip(a)]. 3935 K(x,x * y) = T(y,x) \ y. [para(398(a,1),20(a,1,2)),rewrite([3933(11),101(2),3135(5),23(2),3933(13)]),flip(a)]. 3936 x * (y * (y * (x * (z * ((x * (y * (y * (x * z)))) \ u))))) = u. [para(398(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 3940 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(398(a,1),74(a,2,1)),rewrite([3936(10),3936(12),3136(8)])]. 3941 L(x \ (y * z),x,y) = (y \ x) \ z. [para(398(a,1),74(a,2,2)),rewrite([3936(10),3135(7)])]. 3947 x * (x * (y * (x * (x * (y * (z \ ((y * (x * (x * (y / z)))) \ u))))))) = x * (x * u). [para(1014(a,1),398(a,1,2,2,2,2,2,2,2,1,2,2,2)),rewrite([3143(8)])]. 3949 x * (x * (y * ((x * (x * (x * (x * y)))) \ z))) = x \ (x \ z). [para(398(a,1),132(a,1,2)),rewrite([3135(6),15(3),3436(2),2507(13),1607(11)]),flip(a)]. 3954 a(x,x \ y,z) = a(x,x * y,z). [para(398(a,1),133(a,1,2,1)),rewrite([3949(8),16(3),136(4),37(6),3135(7),3162(5),3949(12),16(7),2508(6)]),flip(a)]. 3968 a(x / y,y,T(z,y * x)) = a(y,y * x,T(z,y * x)). [back_rewrite(3576),rewrite([3954(8)])]. 3982 a(x,x * y,x * z) = a(y,x,z) \ 1. [back_rewrite(2575),rewrite([3954(3)])]. 4007 (x * (y * z)) / T((x * z) * T(y,z),a(z,z * x,y * z)) = a(z,z * x,y * z). [back_rewrite(1517),rewrite([3954(8),3954(13)])]. 4013 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x / y,y). [back_rewrite(1051),rewrite([3954(11),1014(10)])]. 4021 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,x * ((y * x) * z),u). [back_rewrite(662),rewrite([3954(13),189(12)])]. 4025 (x * ((x \ y) * ((y \ z) * (y * u)))) \ ((z * y) * u) = a(x,x * y,(y \ z) * (y * u)). [back_rewrite(614),rewrite([3954(14)])]. 4031 T(x * ((x \ y) * z),a(x,x * y,z)) = a(x,x * y,z) \ (y * z). [back_rewrite(260),rewrite([3954(5),3954(8)])]. 4032 (x * ((x \ y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(56),rewrite([3954(7)])]. 4097 T(T(T(T(T(x,y),z \ 1),u),w),v5) / z = T(T(T(T(T(x,w),u),y),v5),z \ 1) / z. [para(94(a,2),3794(a,1,1,1,1))]. 4108 K(x * y,K(x,y)) = 1. [para(1684(a,1),2880(a,1,2,2)),rewrite([3308(3),88(8),2925(7),1684(7)])]. 4114 ((x * y) * z) \ R(x,y,z) = (y * z) \ 1. [para(22(a,1),1829(a,1,2))]. 4115 ((x / y) * x) * z = x * (y \ (x * z)). [para(1829(a,1),104(a,1,2,1)),rewrite([3143(4)]),flip(a)]. 4137 (x \ y) * (y \ x) = 1. [para(2538(a,1),16(a,1,2))]. 4138 (x * (y * z)) \ (x * y) = L(z,y,x) \ 1. [para(21(a,1),2538(a,1,1)),flip(a)]. 4145 L(x \ y,y \ x,z) = x \ y. [para(2538(a,1),74(a,1,1)),rewrite([14(7),1091(6),2538(6)])]. 4151 a(x,y \ z,z \ y) = 1. [para(2538(a,1),1012(a,1,2))]. 4155 x / (y \ z) = x * (z \ y). [para(2538(a,1),1013(a,1,2))]. 4157 (x * y) \ ((x / z) * (z * y)) = a(x / z,z,y) \ 1. [para(60(a,1),2538(a,1,1)),flip(a)]. 4165 L(x,y \ z,z \ y) = x. [para(2538(a,1),3266(a,1,3))]. 4180 x * ((x \ (y / z)) * z) = R(y,z \ 1,x). [back_rewrite(2806),rewrite([4155(4),169(4)])]. 4186 R(x,y,y \ ((y \ x) \ z)) = z * ((z \ y) * (y \ x)). [back_rewrite(199),rewrite([4155(8),169(8)])]. 4187 a(x / y,y,y) \ 1 = a(x,y \ 1,y * y). [back_rewrite(2604),rewrite([4157(5)])]. 4206 T((x / y) * (y * z),x * z) = a(x / y,y,z) \ (x * z). [para(60(a,1),2642(a,1,2)),rewrite([263(6)]),flip(a)]. 4209 T(x * y,x) = y * x. [para(1091(a,1),2642(a,1,2)),rewrite([2774(4)]),flip(a)]. 4210 T(x,(y \ x) * y) = x. [para(64(a,1),2642(a,1,2)),rewrite([3304(3)]),flip(a)]. 4214 T(T(T(x,y),z),T(T(x,z),y) \ u) = T(T(T(x,z),y),u). [para(2642(a,1),94(a,2)),rewrite([29(6)])]. 4230 (x / y) * x = x * (y \ x). [para(2643(a,1),90(a,1,2)),flip(a)]. 4231 T(x \ y,y) = T(x \ y,x). [para(2643(a,1),537(a,1,1)),flip(a)]. 4247 (x * (y \ x)) * z = x * (y \ (x * z)). [back_rewrite(4115),rewrite([4230(2)])]. 4254 (x / y) * ((x / y) * ((y * z) / T(x * (y \ x),z))) = z. [back_rewrite(2009),rewrite([4230(5)])]. 4261 (x \ y) * (T(x,y) * ((x \ y) * z)) = y * (x \ (y * z)). [back_rewrite(3097),rewrite([4247(9)])]. 4278 T(x,y) \ y = T(x \ y,y). [para(2649(a,1),2642(a,1,2)),rewrite([2709(3)])]. 4281 T(x \ y,T(x,y)) = T(x \ y,y). [back_rewrite(2709),rewrite([4278(5)])]. 4304 T(x,y) * T(x \ y,y) = y. [para(2690(a,1),90(a,2)),rewrite([4281(4)])]. 4308 (x * y) * a(x,z \ y,T(z,y)) = (x * (z \ y)) * T(z,y). [para(2690(a,1),54(a,1,1,2))]. 4314 T(x,y) * (T(x \ y,y) * (T(x,y) * z)) = (x * y) * z. [para(2690(a,1),186(a,2,1,1)),rewrite([4281(4),90(9)])]. 4315 ((x * (y \ z)) * T(y,z)) / T(x * z,a(x,y \ z,T(y,z))) = a(x,y \ z,T(y,z)). [para(2690(a,1),265(a,1,2,1,2))]. 4335 a(x * (y \ z),z \ y,T(z,y)) = ((x * (y \ z)) * y) \ (x * T(z,y)). [para(2690(a,1),60(a,1,1,2)),rewrite([4155(2),4155(8)]),flip(a)]. 4344 (x \ y) * ((z * (x \ y)) * T(x,y)) = ((x \ y) * z) * y. [para(2690(a,1),189(a,1,2)),flip(a)]. 4357 (x \ (x \ y)) * T(x,y) = x \ y. [para(2642(a,1),2690(a,1,2))]. 4365 x / T(x,y) = T(x,y) \ x. [para(159(a,1),2711(a,1,2))]. 4366 T(x,y) / x = x \ T(x,y). [para(541(a,1),2711(a,1,2))]. 4379 ((x \ y) * x) / y = K(x \ y,x). [para(64(a,1),2711(a,2)),rewrite([4210(5)])]. 4404 x * T(y,z \ (z \ x)) = z * (z * (y * (z \ (z \ x)))). [para(2755(a,1),1324(a,1,2)),rewrite([3143(7),3143(6),2755(7),3143(10),3143(9)]),flip(a)]. 4407 (x * y) \ 1 = y \ (x \ 1). [para(2755(a,1),2538(a,1,1))]. 4408 (x \ y) \ z = (y \ x) * z. [para(2538(a,1),2755(a,1,1))]. 4417 ((x * y) * z) \ R(x,y,z) = z \ (y \ 1). [back_rewrite(4114),rewrite([4407(7)])]. 4419 ((x \ (y \ 1)) * y) \ (x \ 1) = a(x,x / y,y). [back_rewrite(4013),rewrite([4407(7)])]. 4420 x / (y * (y * (z * x))) = (y * z) \ (y \ 1). [back_rewrite(3725),rewrite([4407(8)])]. 4421 x / (y * (z * (y * x))) = (z * y) \ (y \ 1). [back_rewrite(3724),rewrite([4407(8)])]. 4445 L(L(x,y,z),u,x \ (u \ 1)) = L(x,y,z). [back_rewrite(3192),rewrite([4407(4)])]. 4458 ((x * y) * z) \ y = (y * z) \ (x \ y). [back_rewrite(2540),rewrite([4407(5),4408(4),14(4)]),flip(a)]. 4470 R(x,y,y \ ((x \ y) * z)) = z * ((z \ y) * (y \ x)). [back_rewrite(4186),rewrite([4408(2)])]. 4480 L(x \ (y * z),x,y) = (x \ y) * z. [back_rewrite(3941),rewrite([4408(5)])]. 4493 (x \ y) * (x / y) = K(x,y \ 1). [back_rewrite(3230),rewrite([4408(3)])]. 4498 (((x * y) * z) \ x) * (y * z) = a(x,x * y,z). [back_rewrite(3162),rewrite([4408(5)])]. 4501 (x * y) \ (x * (x * z)) = (y \ x) * z. [back_rewrite(3135),rewrite([4408(6)])]. 4504 (x \ y) * (((y \ x) * z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(2692),rewrite([4408(3)])]. 4505 (x \ y) * x = T(y,x). [back_rewrite(2649),rewrite([4408(2)])]. 4516 K(x \ y,x) = y \ T(y,x). [back_rewrite(4379),rewrite([4505(2),4366(2)]),flip(a)]. 4525 x * (T(y,x) * z) = y * (x * z). [back_rewrite(2965),rewrite([4505(2)])]. 4534 x * (K(y \ x,y) * (x * z)) = (x * T(x,y)) * z. [back_rewrite(2935),rewrite([4505(7),547(7)])]. 4535 x * K(y \ x,y) = T(x,y). [back_rewrite(2852),rewrite([4505(5)])]. 4537 a(T(x,y),y \ x,z) = a(y \ x,x,z). [back_rewrite(1702),rewrite([4505(2)])]. 4539 K(x,x \ y) = T(y,x) \ y. [back_rewrite(65),rewrite([4505(2)]),flip(a)]. 4559 (T(x,y) * (y * (z * (x * y)))) * u = T(x,y) * (y * (z * (x * (y * u)))). [back_rewrite(2234),rewrite([4525(4)]),flip(a)]. 4562 ((x * y) * y) / z = x * (y * (y / z)). [back_rewrite(1859),rewrite([4525(4)]),flip(a)]. 4578 (x * y) * y = x * (y * y). [back_rewrite(669),rewrite([4525(3)]),flip(a)]. 4581 L(x,T(y,z),z) = L(x,z,y). [back_rewrite(512),rewrite([4525(4),21(4)]),flip(a)]. 4582 a(x,T(y,x),z) = a(y,x,z). [back_rewrite(508),rewrite([4525(3),19(5)]),flip(a)]. 4583 R(x * y,y,y \ z) = (x * (y * z)) / z. [back_rewrite(204),rewrite([4525(6)])]. 4596 ((T(x,y) * (y / z)) * y) \ ((x * (y * y)) / z) = K(y,T(x,y) * (y / z)). [back_rewrite(1864),rewrite([4578(6)])]. 4613 (x * (y * y)) / z = x * (y * (y / z)). [back_rewrite(4562),rewrite([4578(2)])]. 4636 a(x * (y * (x * x)),z,u) = a(x * y,x * (x * z),u). [back_rewrite(3762),rewrite([4578(2)])]. 4640 x * (x * (((T(y,x) * (x * z)) / u) / T(x * (y * (x * (x * z))),u \ 1))) = u \ 1. [back_rewrite(3670),rewrite([4578(6),2040(7)])]. 4713 x / (T(T(y,z),u) * (z * ((T(y,u) * (z * z)) \ x))) = z. [back_rewrite(2166),rewrite([4578(5)])]. 4714 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w))) = w. [back_rewrite(2032),rewrite([4578(8),2040(9)])]. 4770 x * (R(T(y,x),z,u) * (x * w)) = R(y,z,u) * (x * (x * w)). [back_rewrite(684),rewrite([4578(8),2040(9)])]. 4778 (x * ((T(y,x) * (x * z)) * u)) \ ((y * (x * (x * z))) * u) = a(x,T(y,x) * (x * z),u). [back_rewrite(674),rewrite([4578(7),2040(8)])]. 4795 a(x * y,y,z) \ 1 = a(x,y,y * z). [back_rewrite(2574),rewrite([4582(3)]),flip(a)]. 4809 ((T(x,y) * (y / z)) * y) \ (x * (y * (y / z))) = K(y,T(x,y) * (y / z)). [back_rewrite(4596),rewrite([4613(7)])]. 4813 (x / y) * (y * (y / T(x * y,a(x,y \ 1,y * y)))) = a(x,y \ 1,y * y). [back_rewrite(2599),rewrite([4613(10)])]. 4915 K(x,y * (x / y)) = 1. [para(18(a,1),2772(a,1,1))]. 4950 T(a(x,y,z),((x * y) * z) / (x * (y * z))) = a(x,y,z). [para(54(a,1),2810(a,1,2,1))]. 4993 K(x,y) * K(y,x) = 1. [para(2917(a,1),16(a,1,2))]. 4996 R(x,K(y,z),K(z,y)) = x. [para(2917(a,1),191(a,2,3)),rewrite([14(5),16(4),48(2)]),flip(a)]. 5005 x / K(y,z) = x * K(z,y). [para(2917(a,1),1014(a,1,2)),flip(a)]. 5011 L(x,K(y,z),K(z,y)) = x. [para(2917(a,1),3266(a,1,3))]. 5067 T(x,y * (x / y)) = x. [para(66(a,1),2642(a,1,2)),rewrite([3305(3)]),flip(a)]. 5068 K(x,y / x) * y = x * (y / x). [para(66(a,1),2690(a,1,1)),rewrite([5067(5)])]. 5070 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(16(a,1),72(a,1,1))]. 5116 (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). [para(63(a,1),72(a,1,1))]. 5129 x * L(y,T(z,x),z \ x) = (z \ x) * (T(z,x) * y). [para(2690(a,1),72(a,1,1))]. 5134 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(15(a,1),3940(a,1,1)),flip(a)]. 5138 L(T(x,y * z),y * z,y) = z \ (y \ (x * (y * z))). [para(23(a,1),3940(a,1,1))]. 5147 L((x * y) \ z,y,y * x) = T(x,y) \ (y \ z). [para(90(a,1),3940(a,1,1,1)),rewrite([90(4),2975(4)])]. 5152 K(x * (y / x),x) = K(x \ 1,y). [para(67(a,1),3940(a,1,1)),rewrite([666(5),3231(6)])]. 5155 L((x / y) \ z,x / y,x) = y * (x \ z). [para(1014(a,1),3940(a,1,1,1)),rewrite([1014(5),4408(8),45(6)])]. 5162 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(3940(a,1),2254(a,1)),rewrite([3436(2),100(5)]),flip(a)]. 5163 L((x * y) \ z,x * y,y * x) = K(x,y) \ ((y * x) \ z). [para(63(a,1),3940(a,1,1,1)),rewrite([63(5)])]. 5194 R(x,y * (y * z),z \ (y \ (y \ u))) = R(x,z,z \ u). [back_rewrite(1870),rewrite([5162(3),191(6),1935(6),16(3),16(2),5162(7)]),flip(a)]. 5200 x * (x * (y * ((y \ (x \ (x \ z))) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [back_rewrite(411),rewrite([5162(3)])]. 5208 (x * (y \ z)) * (z \ y) = x. [para(4151(a,1),209(a,1,1)),rewrite([45(6),4137(7),14(6),4151(7),88(6)])]. 5226 (T(x,y) \ (T(x,y) \ z)) * T(T(x,z),y) = T(x,y) \ z. [para(29(a,1),4357(a,1,2))]. 5332 a(x,y,y) = 1. [para(89(a,1),507(a,1,2,2)),rewrite([4578(4),46(5),89(2)]),flip(a)]. 5337 (x * (y * (z * u))) \ (x * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),y * (z * u),x). [para(507(a,1),74(a,1,1)),flip(a)]. 5358 a(x,y \ 1,y * y) = 1. [back_rewrite(4187),rewrite([5332(2),46(3)]),flip(a)]. 5359 (x / y) * (y / x) = 1. [back_rewrite(4813),rewrite([5358(6),88(4),3691(3),1014(4),5358(7)])]. 5364 (x * y) / T(z * (z * y),T(x,y)) = z \ (z \ T(x,y)). [para(1921(a,1),21(a,1,2)),rewrite([3436(3),1607(10)]),flip(a)]. 5392 (x \ y) * (x * ((x \ y) * z)) = ((x \ y) * y) * z. [para(2445(a,1),16(a,1,2)),rewrite([14(7)])]. 5410 (x \ (y \ (y \ z))) * (((z \ y) * y) * x) = 1. [para(2445(a,1),4357(a,1,1,2)),rewrite([5392(5),4407(5),4407(4),4408(3),14(3),5392(8),89(10),5392(12),46(14)])]. 5428 x * (x * (y / (T(z * z,x) * (x * y)))) = z \ (z \ x). [para(2640(a,1),21(a,1,2)),rewrite([3436(2),1607(10)]),flip(a)]. 5444 L(x,y \ (y \ z),y) = L(x,z,y). [para(2640(a,1),132(a,1,1,2)),rewrite([5428(8),136(6),16(3),21(4),5428(8),2507(6)]),flip(a)]. 5452 x * (x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u))))))) = y * z. [para(189(a,1),2640(a,1,2,2,2,2,2,2))]. 5468 T(x * (x * y),y \ z) = T(x * (x * y),x * (x * z)). [para(16(a,1),2647(a,1,2,2,2)),flip(a)]. 5480 T(x * (x * y),x * (x * (y / z))) = T(x * (x * y),z \ 1). [para(1014(a,1),2647(a,1,2,2,2))]. 5515 a(x \ y,T(x,y) * y,z) = 1. [para(2697(a,1),19(a,2)),rewrite([4247(5),4525(3),15(3),4247(6),90(4),15(4),100(4),46(5)]),flip(a)]. 5524 a((x * y) * L(z \ y,z,x),T(x * z,x * y),u) = 1. [para(74(a,2),2697(a,1,1,2)),rewrite([5515(17)])]. 5560 ((x \ y) * (x / z)) \ ((y * x) / z) = T(x,(y * x) / z). [para(1014(a,1),2713(a,1,1,2)),rewrite([1014(7),1014(10)])]. 5569 (((x \ y) * z) * x) \ ((z * (y \ x)) * T(y,x)) = T(y \ x,(z * (y \ x)) * T(y,x)). [para(2690(a,1),2713(a,1,1,2)),rewrite([4408(2)])]. 5600 ((x * (y * (y * (y * x)))) \ y) * (x * (y * (x * y))) = 1. [para(2772(a,1),143(a,2)),rewrite([101(2),189(5),4578(2),2040(4),101(7),4501(11)])]. 5610 (x \ (y \ (y \ (z \ 1)))) * (z * (y * (y * (x * u)))) = L(u,y * (y * x),z). [para(37(a,1),145(a,1,1)),rewrite([37(11),4501(12),1091(5),4407(5),5162(5),2507(15)])]. 5614 L(x,y * (y * z),z) = x. [para(1607(a,1),145(a,2)),rewrite([189(5),101(2),189(4),4578(2),101(3),100(2),189(11),101(7),189(10),4578(7),189(9),100(7),37(8),4501(12),1091(5),4407(5),5162(5),5610(10)])]. 5657 x * (y * (x * (z * ((z * (x * (y * (x * z)))) \ u)))) = z \ u. [para(2215(a,1),15(a,1,2)),flip(a)]. 5665 R(x,y,y \ ((x \ y) * z)) = (y * z) / ((x \ y) * z). [para(2215(a,1),191(a,1,1,2)),rewrite([5657(13),4408(3),5657(16),4408(6)]),flip(a)]. 5674 x * (y * (z * (y * (x / (x * (y * (z * (y * x)))))))) = 1. [para(1014(a,1),2215(a,1,2,2,2,2))]. 5742 K(L(x * y,x \ z,x),z) = K(z * ((z * x) * y),z). [para(181(a,1),2934(a,1,2,1)),rewrite([104(4),16(7),4505(6),3934(6,R),16(9)]),flip(a)]. 5752 (x * ((y * x) * z)) \ (L(z,x,x * y) * (x * (y * x))) = K(L(z,x,x * y),x * (y * x)). [para(189(a,1),2934(a,1,1)),rewrite([101(7),101(13)])]. 5783 x * ((y * x) * (x * ((x \ y) * z))) = (x * y) * ((x * y) * z). [para(13(a,1),405(a,1,2,2,2,2)),rewrite([14(10),187(12),101(8),426(10)])]. 5816 R(x * ((x \ y) * (y \ z)),z,z \ u) = (z * (a(y,x,x \ (y \ z)) * u)) / u. [para(16(a,1),435(a,1,2)),rewrite([16(6),16(8)])]. 5817 (x * (a(x / y,z,z \ y) * u)) / u = R(x,y \ 1,z). [para(18(a,1),435(a,1,2)),rewrite([4180(4),18(5),495(5),18(5)]),flip(a)]. 5841 R(x * ((x \ (y \ z)) * T(y,z)),z,z \ u) = (z * (a(y \ z,x,x \ T(y,z)) * u)) / u. [para(2690(a,1),435(a,1,2)),rewrite([2690(8),2690(10)])]. 5879 x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))) = z. [para(463(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 5885 (x \ (y \ 1)) * (y * (x * z)) = L(z,x,y). [para(463(a,1),132(a,1,1,2)),rewrite([5879(13),4501(8),1091(3),4407(3),5879(16),2507(9)])]. 5921 a(x,T(y,x) * x,z) = a(y,x,x * z) \ 1. [para(14(a,1),4778(a,1,1,2,1,2)),rewrite([2993(4),14(5),2040(6),2548(7),14(7)]),flip(a)]. 6018 L(x,x,y) = x. [hyper(24,a,5332,a)]. 6020 L(T(x,y),x,z) = T(x,y). [para(6018(a,1),30(a,1,1)),flip(a)]. 6022 L(L(x,y,z),x,u) = L(x,y,z). [para(6018(a,1),34(a,1,1)),flip(a)]. 6024 L(L(L(x,y,z),u,w),L(x,u,w),v5) = L(L(x,u,w),y,z). [para(6018(a,1),97(a,1,1)),flip(a)]. 6068 ((x * y) \ z) * ((z \ x) * y) = a(z \ 1,x,y). [para(3143(a,1),19(a,1,1)),rewrite([3143(5),4408(5)])]. 6069 (x \ (y \ 1)) * (x * y) = K(x,y). [para(20(a,1),3143(a,2)),rewrite([4407(3)])]. 6070 (x \ y) * (y \ (x * z)) = L(z,x,y \ 1). [para(3143(a,1),21(a,1,1)),rewrite([3143(5),4408(4)])]. 6071 ((x \ y) * z) / (y * z) = R(x \ 1,y,z). [para(3143(a,1),22(a,1,1,1))]. 6072 T(x \ 1,y) = y \ (x \ y). [para(3143(a,1),23(a,1,2)),flip(a)]. 6073 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [para(3143(a,1),37(a,1,1,2)),rewrite([3143(4),3143(9),3143(8)]),flip(a)]. 6095 x \ T(y,x \ 1) = y / x. [para(3143(a,1),90(a,1)),rewrite([1014(7)])]. 6120 (x \ 1) / y = x \ (y \ 1). [para(3143(a,1),1014(a,1)),flip(a)]. 6128 ((x * (y * z)) \ (y \ 1)) * (y * (x * (y * (z * u)))) = L(u,z,y * (x * y)). [para(132(a,1),3143(a,2)),rewrite([4407(5)])]. 6132 (x \ (y \ 1)) * y = x \ 1. [para(1091(a,1),3143(a,2)),rewrite([4407(3)])]. 6134 T(x \ 1,x \ y) = T(x \ 1,y). [para(3143(a,1),1708(a,1,2))]. 6135 x \ ((y / x) * z) = (x \ y) * (x \ z). [para(3143(a,1),189(a,1,1)),rewrite([3143(4),1014(8),3143(8)]),flip(a)]. 6141 ((x * y) \ (z \ (z \ (u \ 1)))) * ((u * (z * (z * x))) * y) = a(u,z * (z * x),y). [para(139(a,1),3143(a,2)),rewrite([4407(6),5162(6)])]. 6144 K(x,y) \ z = K(y,x) * z. [para(2917(a,1),3143(a,1,1)),flip(a)]. 6145 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(3143(a,1),72(a,1,1)),rewrite([3143(9)])]. 6149 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(z \ 1,y,T(x,y)). [para(3143(a,1),507(a,1,1)),rewrite([3143(5),4408(6)])]. 6151 ((x \ (y \ 1)) * (x * z)) \ ((y \ x) * z) = T(x,(y \ x) * z). [para(3143(a,1),2713(a,1,2,1)),rewrite([3143(11)])]. 6152 ((x * y) \ (z \ x)) * ((z * x) * y) = T(x,(z * x) * y). [para(2713(a,1),3143(a,2)),rewrite([4407(5),4408(4),14(4)])]. 6185 (x \ (y \ 1)) * T(z,x / y) = (x \ (x \ z)) * (x / y). [back_rewrite(3709),rewrite([6073(4)]),flip(a)]. 6188 x \ T(y,z * (z / x)) = (z \ (z \ y)) * (z * (z / x)). [back_rewrite(3482),rewrite([6073(9)])]. 6233 a(x,x / y,y) = 1. [back_rewrite(4419),rewrite([6132(4),46(5)]),flip(a)]. 6238 L((x * y) \ z,x * y,y * x) = K(y,x) * ((y * x) \ z). [back_rewrite(5163),rewrite([6144(9)])]. 6257 L(x,y / x,y) = x. [hyper(24,a,6233,a)]. 6258 a(x * y,x,y) = 1. [para(17(a,1),6233(a,1,2))]. 6279 L(x,y,y * x) = x. [para(17(a,1),6257(a,1,2))]. 6335 a(x,y,y \ x) = 1. [para(16(a,1),6258(a,1,1))]. 6351 x * ((x \ y) * y) = y * y. [para(6258(a,1),435(a,2,1,2,1)),rewrite([16(2),16(5),16(6),3436(6),2044(7),16(5),13(6),100(5),1839(6),47(4),14(5)])]. 6353 (x \ y) * ((y \ x) * z) = L(z,(y \ x) * x,y). [back_rewrite(831),rewrite([6351(3),3436(6),6073(6),15(2)])]. 6368 L(x \ y,x,y) = x \ y. [para(16(a,1),6279(a,1,3))]. 6416 L(x,y \ 1,y \ x) = x. [para(3143(a,1),6279(a,1,3))]. 6438 a((x * y) * T(z,y),x * (z * y),a(x,y,T(z,y))) = 1. [para(507(a,1),6335(a,1,3))]. 6446 K(x,K(y,x / y)) = 1. [para(18(a,1),3302(a,1,1))]. 6557 K(K(L(x,y,z),z * y),z * (y * x)) = 1. [para(72(a,1),3327(a,1,2))]. 6562 K(x,y) / (x * y) = x \ (y \ 1). [para(20(a,1),3666(a,1,1)),rewrite([4407(6)])]. 6564 T(x,y) / (x * y) = y \ 1. [para(23(a,1),3666(a,1,1))]. 6565 (x / y) \ 1 = y / x. [para(50(a,1),3666(a,1,1)),flip(a)]. 6567 (x * (y * z)) \ (y \ 1) = z \ ((x * y) \ (y \ 1)). [para(114(a,1),3666(a,1,1)),rewrite([6562(7),4407(4),4407(10)]),flip(a)]. 6575 (x / y) \ (y \ 1) = K(x / y,y) / x. [para(67(a,1),3666(a,1,1)),rewrite([4407(7)]),flip(a)]. 6591 L(x,y,z) \ (y \ (z \ 1)) = (y * x) \ (z \ 1). [para(2934(a,1),3666(a,1,1)),rewrite([6562(7),4407(4),4407(9)])]. 6600 (x \ ((y * z) \ (z \ 1))) * (z * (y * (z * (x * u)))) = L(u,x,z * (y * z)). [back_rewrite(6128),rewrite([6567(5)])]. 6606 x * (L(y,z \ x,z) * (x * u)) = ((z * ((z \ x) * y)) * x) * u. [para(73(a,1),104(a,1,2,1))]. 6618 L(x,y \ 1,z * y) = L(x,y \ z,y). [para(73(a,1),181(a,2)),rewrite([1091(2),3143(3),16(2),1091(4)]),flip(a)]. 6623 (((x / (y * z)) * y) * z) \ (x * (a(x / (y * z),y,z) * u)) = L(u,a(x / (y * z),y,z),x). [para(59(a,1),73(a,1,2,2,1)),rewrite([59(15)])]. 6634 L(x,y * z,y \ 1) = L(x,y * z,y). [para(3143(a,1),73(a,1,2)),rewrite([4408(3),45(2),5134(4),4408(5),45(4)]),flip(a)]. 6663 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,u,w),y,z))) \ (v6 * v5). [para(76(a,1),228(a,1)),flip(a)]. 6676 L(x,y \ (x \ 1),z) = (z * (y \ (x \ 1))) \ (z / y). [para(1014(a,1),76(a,2,2)),rewrite([6120(3),6120(7)])]. 6694 T(x * (y / z),L(z,y / z,x)) = T(x * (y / z),x * y). [para(76(a,2),2642(a,1,2))]. 6696 L(x,T(y,z) / x,y \ z) = ((y \ z) * (T(y,z) / x)) \ z. [para(2690(a,1),76(a,2,2))]. 6697 L(x,L(y,z,u) / x,u * z) = ((u * z) * (L(y,z,u) / x)) \ (u * (z * y)). [para(72(a,1),76(a,2,2))]. 6707 L(x,y / x,z \ 1) = ((y / x) \ z) * (z \ y). [para(3143(a,1),76(a,2,1)),rewrite([3143(9),4408(8)])]. 6793 L(L(R(x,y,z),u,w),v5,x \ (v5 \ 1)) = L(R(x,y,z),u,w). [para(4445(a,1),33(a,1,1)),rewrite([33(2),33(4)]),flip(a)]. 6878 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(y * (x \ y),y \ 1). [para(1014(a,1),2757(a,1,2)),rewrite([6120(3),3143(10)])]. 6887 L(K(x * (y * x),x \ 1),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [para(2757(a,1),3940(a,1,1)),rewrite([3436(15)])]. 6890 K(x * (y * x),x \ 1) = K(x,y). [para(2757(a,1),3143(a,2)),rewrite([4407(5),6565(4),3436(3),1829(2),6069(5)]),flip(a)]. 6897 L(K(x,y),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [back_rewrite(6887),rewrite([6890(5)])]. 6946 T(x * (x * (y / (x * z))),x * z) = (z \ x) * y. [para(16(a,1),3139(a,1,1,2,2,2,2)),rewrite([16(6),4408(8)])]. 6951 ((x \ y) * (x * z)) \ u = ((x * z) \ (y \ x)) * u. [para(104(a,1),3139(a,1,1,2,2,2,2)),rewrite([104(10),6946(10),4458(3)]),flip(a)]. 6953 (x \ ((y * z) \ (y \ 1))) * u = (z * x) \ (y \ (y \ u)). [para(341(a,1),3139(a,1,1,2,2,2,2)),rewrite([341(27),6946(26),4417(8),4407(4),5162(10)])]. 6955 ((x * y) \ y) * z = T(x,y) \ z. [para(90(a,1),3139(a,1,1,2,2,2,2)),rewrite([90(7),6946(8)])]. 6968 (x \ (y \ x)) * z = T(y,x) \ z. [para(2690(a,1),3139(a,1,1,2,2,2,2)),rewrite([2690(11),6946(10)])]. 6973 ((x * y) \ (z * x)) * ((z \ x) * y) = T(x,(z \ x) * y). [back_rewrite(6151),rewrite([6951(8),4408(4),45(3)])]. 7004 x * (y \ ((x * (x / y)) \ z)) = x \ z. [para(18(a,1),3218(a,2,2)),rewrite([92(6)])]. 7047 T(x,K((y \ z) * (y * ((z * y) \ x)),y)) = x. [para(16(a,1),3307(a,1,1)),rewrite([16(11)])]. 7257 (T(x,y) * (y * (x * y))) * z = T(x,y) * (y * (x * (y * z))). [para(13(a,1),4559(a,1,1,2,2)),rewrite([13(10)])]. 7262 T(x,y) * (y * ((z / (x * y)) * (x * (y * u)))) = (T(x,y) * (y * z)) * u. [para(18(a,1),4559(a,1,1,2,2)),flip(a)]. 7353 R(x,y,z) * (x * (x * u)) = x * (R(x,y,z) * (x * u)). [para(89(a,1),4770(a,1,2,1,1)),flip(a)]. 7412 a(x / (y * y),y,y * z) = (x * z) \ (y \ ((y * x) * z)). [para(7262(a,1),110(a,1,1)),rewrite([89(1),37(3),89(4),189(10),101(8),4578(7),18(7),5162(7),15(5),89(6),3982(11),4795(11)]),flip(a)]. 7416 x * (T(x,y) * ((z / (x * T(x,y))) * (x * (T(x,y) * u)))) = (x * (T(x,y) * z)) * u. [para(541(a,1),7262(a,1,1)),rewrite([541(12)])]. 7488 x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u)))))) = x \ (y * z). [para(5452(a,1),15(a,1,2)),flip(a)]. 7490 (x * y) * ((x * y) * ((x * z) / (T(u * u,x * y) * (x * ((y * x) * z))))) = (u \ (u \ x)) * y. [para(5452(a,1),21(a,1,2)),rewrite([3436(3),6073(3),1607(17)]),flip(a)]. 7495 x * (x * (((x \ (x \ y)) * z) * u)) = (y * z) * u. [para(5452(a,1),37(a,1,1)),rewrite([7490(15)]),flip(a)]. 7513 L(x,(y \ (y \ z)) * u,y) = L(x,z * u,y). [para(5452(a,1),132(a,1,1,2)),rewrite([7490(15),7495(8),21(6),7490(15),2507(8)]),flip(a)]. 7550 x * ((x \ (x \ y)) * z) = x \ (y * z). [back_rewrite(7488),rewrite([7490(13)])]. 7607 a(x / y,y,z) \ 1 = a(x,y \ 1,y * z). [para(3691(a,1),58(a,1,2,1,2)),rewrite([1014(4),4157(5),3691(6)])]. 7616 T(x,y) / y = y \ x. [para(2690(a,1),3691(a,1,2)),rewrite([4408(5),14(5)])]. 7617 T(x,y) * (y \ x) = (y \ x) * x. [para(4357(a,1),3691(a,1,2)),rewrite([4155(3),4408(7),4408(5),14(7)])]. 7622 x * ((y * x) \ T(z,x / y)) = x \ (z * (x / y)). [para(3691(a,1),3218(a,1,2,2,2,2)),rewrite([1014(4),3691(7),1014(8)])]. 7628 (x * y) \ ((x / z) * (z * y)) = a(x,z \ 1,z * y). [back_rewrite(4157),rewrite([7607(9)])]. 7636 K(x,K(x / y,y)) = 1. [para(18(a,1),4108(a,1,1))]. 7656 L(x,(y \ z) * z,y) = x. [para(4137(a,1),21(a,1,1)),rewrite([6353(5),45(5),4165(6)])]. 7662 K(x \ y,(y \ x) * (z * (y \ x))) = K(z,y \ x). [para(4137(a,1),114(a,1,1,2,2)),rewrite([14(3),6353(8),7656(7),20(5)]),flip(a)]. 7679 L(x,y \ z,(z \ y) * (u * (z \ y))) = L(x,u,z \ y). [para(4137(a,1),132(a,1,1,2,2)),rewrite([14(3),6353(7),7656(6),21(6)]),flip(a)]. 7681 (x \ y) * (z * (y \ x)) = T(z,y \ x). [para(4137(a,1),1359(a,1,2,2,2,2)),rewrite([14(5),90(5),4137(9),14(8),23(8)])]. 7682 a((x \ y) * (z * (x \ y)),y \ x,u) = a(x \ y,z,u). [para(4137(a,1),133(a,1,2,1,2,2)),rewrite([6353(5),7656(4),14(6),19(7)]),flip(a)]. 7701 ((L(x,y,y * z) * (y * (z * y))) \ (y * ((z * y) * x))) * K(L(x,y,y * z),y * (z * y)) = 1. [para(5752(a,1),4137(a,1,2))]. 7707 K(K(x \ y,z * (y \ x)),z) = 1. [para(4137(a,1),6557(a,1,2,2)),rewrite([4145(3),14(6)])]. 7713 K(x \ y,(y \ x) * z) = K(x \ y,z). [para(4137(a,1),177(a,1,1,1,2)),rewrite([4408(2),14(4),5208(8),4458(5),4408(4),20(5),4408(5),4137(8),14(7)]),flip(a)]. 7715 (x \ y) * ((y \ x) * z) = z. [back_rewrite(6353),rewrite([7656(7)])]. 7719 K(x \ y,z * (y \ x)) = K(z,y \ x). [back_rewrite(7662),rewrite([7713(6)])]. 7726 K(K(x,y \ z),x) = 1. [back_rewrite(7707),rewrite([7719(4)])]. 7769 T(T(x,y),y \ x) = x. [para(16(a,1),4209(a,2)),rewrite([4505(2)])]. 7772 ((x \ y) * (x * z)) * x = T((y * x) * z,x). [para(104(a,1),4209(a,1,1)),flip(a)]. 7775 T(x,y) * y = T(x * y,y). [para(90(a,1),4209(a,1,1)),flip(a)]. 7789 T(x,y) * (x \ y) = T(y,x \ y). [para(2690(a,1),4209(a,1,1)),flip(a)]. 7820 K((x \ y) * (x * z),x) = K(x * ((y * x) * z),x). [back_rewrite(3323),rewrite([7772(4),4366(6),3934(6,R)]),flip(a)]. 7826 x * K(y * x,y) = T(x,y). [back_rewrite(874),rewrite([7820(6),16(4),7772(9),16(7)])]. 7836 a(x,y,y * z) \ 1 = a(x * y,y,z). [back_rewrite(5921),rewrite([7775(2),4582(3)]),flip(a)]. 7875 K(x,x * (y * x)) = K(x,T(y,x)). [back_rewrite(511),rewrite([7775(2),3935(4,R)])]. 7876 K(x * (y * x),x) = K(T(y,x),x). [back_rewrite(510),rewrite([7775(3),3934(4,R)])]. 7925 T(x,K(y * x,y)) = x. [back_rewrite(7047),rewrite([7820(6),16(4)])]. 7966 ((x * (y \ z)) * y) / T(z,y) = R(x,y \ z,y). [para(4505(a,1),22(a,1,2))]. 7967 x \ T(y,x) = T(x \ y,x). [para(4505(a,1),23(a,1,2))]. 7969 (x \ y) * (((y \ x) * z) * T(y,x)) = (z * (x \ y)) * x. [para(4505(a,1),104(a,1,2,2)),rewrite([4408(3)])]. 7981 L(x \ y,x,x \ z) = T(z,x) \ ((x \ z) * y). [para(4505(a,1),74(a,2,1))]. 7982 L(x \ y,x,y \ z) = ((y \ z) * x) \ T(z,y). [para(4505(a,1),74(a,2,2))]. 7996 L(T(x,y),(x \ y) * z,y \ x) = z \ ((z * (y \ x)) * y). [para(4505(a,1),181(a,1,1)),rewrite([4408(3)])]. 7997 (x \ y) * (T(x,y) * z) = L(y * z,x,y). [para(4505(a,1),181(a,2,2,1)),rewrite([5444(4),4408(6)]),flip(a)]. 8002 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = R((y * (z * y)) \ x,y * (z * y),u). [para(4505(a,1),121(a,1,1,1))]. 8018 T(x,y) \ (y \ x) = y \ 1. [para(4505(a,1),1091(a,1,1))]. 8020 (x \ y) * ((z * (x \ y)) * x) = ((x \ y) * z) * T(y,x). [para(4505(a,1),189(a,1,2)),flip(a)]. 8036 T(x * (x * (y \ z)),x * (x * T(z,y))) = T(x * (x * (y \ z)),y). [para(4505(a,1),2647(a,1,2,2,2))]. 8054 a(x \ y,y,x) = 1. [para(4505(a,1),6258(a,1,1)),rewrite([4537(3)])]. 8061 T(x * ((x \ y) * z),y) = L(z,x \ y,x) * y. [para(73(a,1),4505(a,1,1)),flip(a)]. 8078 K(T(x,y),K(y \ x,y)) = 1. [para(4505(a,1),4108(a,1,1))]. 8091 x * L(y,T(z,x),z \ x) = L(x * y,z,x). [back_rewrite(5129),rewrite([7997(8)])]. 8098 L(x * ((y \ x) * z),y,x) = x * (y \ (x * z)). [back_rewrite(4261),rewrite([7997(6)])]. 8105 L(x,y,x \ y) = x. [hyper(24,a,8054,a)]. 8106 a(x,y * x,y) = 1. [para(15(a,1),8054(a,1,1))]. 8255 (x * (y / x)) * y = y * (x * (y / x)). [para(4915(a,1),63(a,1,2)),rewrite([14(5)])]. 8296 K(x,y) * (K(y,x) * z) = z. [para(4993(a,1),21(a,1,1)),rewrite([45(6),5011(7)])]. 8298 (x * K(y,z)) * K(z,y) = x. [para(4993(a,1),22(a,1,2)),rewrite([48(6),4996(7)])]. 8302 L(x \ K(y,z),x,K(z,y)) = x \ K(y,z). [para(4993(a,1),74(a,2,2)),rewrite([4407(8),6144(7),14(7)])]. 8308 L(x,K(y,z),K(z,y) * (u * K(z,y))) = L(x,u,K(z,y)). [para(4993(a,1),132(a,1,1,2,2)),rewrite([14(3),8296(7),21(6)]),flip(a)]. 8310 K(x,y) * (z * K(y,x)) = T(z,K(y,x)). [para(4993(a,1),1359(a,1,2,2,2,2)),rewrite([14(5),90(5),4993(9),14(8),23(8)])]. 8311 a(K(x,y) * (z * K(x,y)),K(y,x),u) = a(K(x,y),z,u). [para(4993(a,1),133(a,1,2,1,2,2)),rewrite([8296(5),14(6),19(7)]),flip(a)]. 8328 R(x,x \ y,y \ z) = z / ((x \ y) * (y \ z)). [para(16(a,1),81(a,2,1))]. 8379 R(x,x \ y,z) = z * ((z \ y) * (y \ x)). [para(81(a,2),1014(a,2)),rewrite([4407(5),4408(4),14(4),169(4)]),flip(a)]. 8393 (x * y) \ R(z,z \ x,y) = y \ (x \ z). [para(81(a,2),1829(a,1,2)),rewrite([4407(8),4408(7),14(7)])]. 8463 R(x,y \ 1,(x / y) \ z) = R(x,y \ 1,z). [para(1014(a,1),82(a,1,3,1)),rewrite([1014(10),3143(10),4155(9),4408(8),4180(9)])]. 8497 R(x,y,(x * y) \ T(z,y / x)) = T(z,y / x) * ((z * (y / x)) \ y). [para(3218(a,1),82(a,2,2)),rewrite([3691(3),1014(4),3691(7),1014(8),3691(9),1014(10),4155(11)])]. 8532 T(x,y) \ x = K(x \ y,x). [para(2642(a,1),4539(a,2,1)),rewrite([4408(3),7713(4)]),flip(a)]. 8534 K(x \ y,x) = K(y,y \ x). [para(4539(a,2),2711(a,2)),rewrite([159(2),4365(2),8532(2)])]. 8593 x / T(x,y) = K(x \ y,x). [back_rewrite(4365),rewrite([8532(4)])]. 8594 K(x \ y,x) = K(y,y * x). [back_rewrite(3935),rewrite([8532(4)]),flip(a)]. 8609 x * (L(y,z \ x,z) * x) = (z * ((z \ x) * y)) * x. [para(8061(a,1),90(a,1,2))]. 8679 L(x,y,z * (y * x)) = L(x,y,z). [para(17(a,1),3199(a,1,3)),flip(a)]. 8681 L(x,y,(z * y) * x) = L(x,y,R(z,y,x)). [para(22(a,1),3199(a,1,3)),flip(a)]. 8684 L(L(x,y,z),u,w / (u * x)) = L(L(x,u,w),y,z). [para(3199(a,1),34(a,1,1)),flip(a)]. 8701 L(x \ y,x,z) = ((z / y) * x) \ z. [para(3199(a,1),74(a,1)),rewrite([16(4),16(6),18(6)])]. 8972 (x \ y) * (x * x) = T(x * y,x * x). [para(3476(a,1),13(a,1)),rewrite([14(3),14(6)])]. 8992 ((x \ y) * (x * (x * z))) / T(z,T(x * y,x * (x * z))) = T(x * y,x * (x * z)). [para(3476(a,1),165(a,1,1))]. 9001 T(x,(y \ z) * (y * (y * x))) = T(x,T(y * z,y * (y * x))). [para(3476(a,1),1708(a,1,2))]. 9018 (x * y) * T(z * (z * x),y) = x * (z * (z * (x * y))). [para(2647(a,1),3476(a,1,2)),rewrite([15(7)])]. 9031 ((x \ y) * z) * (y \ x) = T(z,y \ x). [para(4137(a,1),3476(a,1,2,2,2)),rewrite([14(6),4209(5),7681(4),4408(4),4137(8),14(7)]),flip(a)]. 9037 (K(x,y) * z) * K(y,x) = T(z,K(y,x)). [para(4993(a,1),3476(a,1,2,2,2)),rewrite([14(6),4209(5),8310(4),6144(4),4993(8),14(7)]),flip(a)]. 9050 x * ((x * (y * x)) \ z) = y \ (x \ z). [para(18(a,1),3541(a,1,2,2)),rewrite([92(8)]),flip(a)]. 9085 x * a(y,z,z \ (y \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [back_rewrite(3093),rewrite([9050(4)])]. 9101 (x * (((y * z) * (z * y)) * u)) * a(x,(z * y) * (y * z),u) = (x * ((z * y) * (y * z))) * u. [para(178(a,1),312(a,1,1,2)),rewrite([3308(9),3308(14)])]. 9104 ((x * y) * (y * x)) * T(z,y * x) = (y * x) * (K(x,y) * (z * (y * x))). [para(90(a,1),178(a,1,2,2)),flip(a)]. 9114 ((x * ((y * z) * (z * y))) * u) / (((z * y) * (y * z)) * u) = R(x,(y * z) * (z * y),u). [para(178(a,1),121(a,1,2)),rewrite([3308(4),3308(14)])]. 9186 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,(y \ z) * (y * x),y). [para(179(a,1),3143(a,2)),rewrite([4407(4),4407(3)])]. 9191 x \ ((y \ z) * (((z \ y) * x) * u)) = L(u,(z \ y) * x,y \ z). [para(4137(a,1),179(a,1,1,1)),rewrite([13(2),4408(4),100(7),7715(6),4408(9),100(12),7715(11)])]. 9195 (T(x,y) * z) \ (y * (((y \ (y \ x)) * (y * z)) * u)) = L(u,x * (y * z),y). [para(4505(a,1),179(a,1,1,1)),rewrite([7513(14)])]. 9198 x \ (K(y,z) * ((K(z,y) * x) * u)) = L(u,K(z,y) * x,K(y,z)). [para(4993(a,1),179(a,1,1,1)),rewrite([13(2),6144(4),100(7),8296(6),6144(9),100(12),8296(11)])]. 9423 (x * ((x \ (y \ 1)) * ((y * z) * (y \ u)))) \ ((z / y) * u) = a(x,x / y,(y * z) * (y \ u)). [para(1014(a,1),4025(a,1,2,1)),rewrite([4408(6),45(5),3143(7),1014(14),4408(15),45(14),3143(16)])]. 9444 (x * ((x \ K(y,z)) * (K(z,y) * u))) \ u = a(x,x * K(y,z),K(z,y) * u). [para(4993(a,1),4025(a,1,1,2,2,2)),rewrite([6144(4),14(6),8298(10),6144(11),4993(14),14(13)])]. 9484 ((T(T(x,y),z) * (z * u)) * z) / (w * (w * ((T(T(x,z),y) * (z * u)) * z))) = w \ (w \ 1). [para(1907(a,1),21(a,1,2)),rewrite([3436(3),1607(17)]),flip(a)]. 9490 x \ (y * (x \ z)) = (x \ (y / x)) * z. [para(1907(a,1),129(a,1,1,2,2,2,2,2)),rewrite([9484(13),16(4),9484(15),16(6),9484(17),16(8),14(8),1014(7),3143(6),16(5),3143(4),9484(16),16(7),9484(18),16(9),9484(20),16(11),9484(22),16(13),3143(12),16(11),3143(10),3143(10),16(9),3143(8)]),flip(a)]. 9548 x * (x * (y * (x * (x * (y * (z \ ((y / z) \ (x \ (x \ (y \ 1)))))))))) = x * x. [para(14(a,1),3947(a,2,2)),rewrite([4407(6),5162(6)])]. 9553 x * (y * (y * (x * (z \ ((x * (y * (y * (x / z)))) \ u))))) = u. [para(3947(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 9559 L(x,y \ z,y) = L(x,y * z,y). [para(3947(a,1),132(a,1,1)),rewrite([5162(7),7004(9),16(6),16(5),136(6),21(6),5162(7),7004(9),16(6),16(5),2507(6)]),flip(a)]. 9575 L(x,(y * z) / x,y) = (((y * z) / x) \ y) * z. [para(3947(a,1),76(a,2,2)),rewrite([9553(10),9553(13),4501(9)])]. 9640 x * (L(y,z * x,z) * x) = (z * ((z \ x) * y)) * x. [back_rewrite(8609),rewrite([9559(2)])]. 9719 L(x,y \ 1,z * y) = L(x,y * z,y). [back_rewrite(6618),rewrite([9559(6)])]. 9729 x * (L(y,z * x,z) * (x * u)) = ((z * ((z \ x) * y)) * x) * u. [back_rewrite(6606),rewrite([9559(2)])]. 9737 K(L(x * y,x * z,x),z) = K(z * ((z * x) * y),z). [back_rewrite(5742),rewrite([9559(3)])]. 9755 x * L(y,z * x,z) = z * ((z \ x) * y). [back_rewrite(5070),rewrite([9559(2)])]. 9786 L(x * (y * z),x * y,x) = (x * y) * z. [back_rewrite(3018),rewrite([9559(4)])]. 9791 T(x,L(y * z,y * x,y)) = T(x,(x * y) * z). [back_rewrite(2700),rewrite([9559(3)])]. 9832 x \ (y * ((y \ x) * z)) = L(z,y * x,y). [back_rewrite(73),rewrite([9559(6)])]. 10000 (x / y) * ((y / x) * z) = L(z,y / x,x / y). [para(5359(a,1),21(a,1,1)),rewrite([45(6)])]. 10094 R(x,y,(x * y) \ z) * ((y * ((x * y) \ z)) / z) = 1. [para(82(a,2),5359(a,1,1))]. 10140 (x * (y / x)) * ((x * (y / x)) * z) = (x * (y * (y / x))) * z. [para(6446(a,1),178(a,1,2,1)),rewrite([5068(3),5068(6),13(7),2853(9),5068(11),189(11),18(8)])]. 10215 x / (y / z) = x * (z / y). [para(6565(a,1),1014(a,1,2)),flip(a)]. 10221 L(x,y / z,z / y) = x. [para(6565(a,1),3266(a,1,3))]. 10229 (x / y) \ z = (y / x) * z. [para(6565(a,1),3143(a,1,1)),flip(a)]. 10233 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(81(a,2),6565(a,1,1)),rewrite([6071(8)])]. 10235 R(x,y,(x * y) \ z) \ 1 = (y * ((x * y) \ z)) / z. [para(82(a,2),6565(a,1,1))]. 10279 ((x * y) / z) * (z / y) = R(x,y,z \ 1). [back_rewrite(1836),rewrite([10215(4)])]. 10287 (x / y) * ((y / x) * z) = z. [back_rewrite(10000),rewrite([10221(7)])]. 10295 L(x,(y * z) / x,y) = ((x / (y * z)) * y) * z. [back_rewrite(9575),rewrite([10229(6)])]. 10296 x * (x * (y * (x * (x * (y * (z \ ((z / y) * (x \ (x \ (y \ 1)))))))))) = x * x. [back_rewrite(9548),rewrite([10229(6)])]. 10305 R(x,y \ 1,(y / x) * z) = R(x,y \ 1,z). [back_rewrite(8463),rewrite([10229(4)])]. 10321 L(K(x,y),(y / x) * (x * x),y / x) = x \ T(x,y). [back_rewrite(6897),rewrite([10229(9),3169(9),4505(8),15(9)])]. 10323 L(x,y / x,z \ 1) = R(x,y \ 1,z). [back_rewrite(6707),rewrite([10229(6),169(8),4180(8)])]. 10326 K(x / y,y) / x = (y / x) / y. [back_rewrite(6575),rewrite([10229(4),1014(4)]),flip(a)]. 10347 L((x / y) * z,y / x,y) = x * (y \ z). [back_rewrite(5155),rewrite([10229(2)])]. 10366 (x / y) * (x \ y) = K(x \ 1,y). [back_rewrite(3231),rewrite([10229(3)])]. 10367 (x / y) * (y * (x \ z)) = L(z,x \ 1,y). [back_rewrite(3229),rewrite([10229(4)])]. 10393 (x / y) * (((y / x) * z) * x) = (z * (x / y)) * y. [back_rewrite(171),rewrite([10229(3)])]. 10400 (x \ y) / x = x \ (y / x). [para(92(a,1),7616(a,1,1))]. 10401 T(x \ y,z) / x = x \ T(y / x,z). [para(537(a,1),7616(a,1,1))]. 10408 (x / (x * y)) * y = y * (x / (x * y)). [para(2810(a,1),7616(a,1,1)),rewrite([10215(3),10229(6)]),flip(a)]. 10461 T(x,K(x / y,y)) = x. [hyper(28,a,7636,a)]. 10537 R(x,y \ z,T(y,z)) * z = (x * (y \ z)) * T(y,z). [para(2690(a,1),84(a,1,2))]. 10562 R(x,y \ z,y) * T(z,y) = (x * (y \ z)) * y. [para(4505(a,1),84(a,1,2))]. 10592 R(T(x / y,y * z),y,z) = (y * z) \ (x * z). [para(85(a,2),92(a,1,1)),rewrite([31(4)])]. 10670 L(x,y,R(z / y,y,x)) = L(x,y,z * x). [para(85(a,2),3199(a,1,3))]. 10690 ((x / y) * z) \ x = (x * z) \ (x * y). [para(8701(a,1),21(a,2)),rewrite([16(3)]),flip(a)]. 10700 a(x / y,z,(x * z) \ (x * y)) = a(x,z,(x * z) \ (x * y)). [para(8701(a,2),57(a,1,1,2,2)),rewrite([10690(6),1105(6),10690(8)]),flip(a)]. 10702 K(x * (y / x),x / y) = K(x \ 1,y). [para(8701(a,2),67(a,1)),rewrite([10215(2),67(3),10215(4),666(5),5152(3),10215(5)]),flip(a)]. 10707 ((x * (y / z)) * z) \ x = L(y \ 1,z,x). [para(1829(a,1),8701(a,1,1)),rewrite([10215(5)]),flip(a)]. 10710 ((x \ y) * z) \ y = (y * z) \ (x * y). [para(2711(a,1),8701(a,2,1,1)),rewrite([659(3)]),flip(a)]. 10725 L(x \ (y * z),x,z) = (x \ y) * z. [para(3691(a,1),8701(a,2,1,1)),rewrite([3143(6),4408(5)])]. 10748 L(x,T(y,z) / x,y \ z) = (z * (T(y,z) / x)) \ (y * z). [back_rewrite(6696),rewrite([10710(9)])]. 10809 (x \ y) * (x * (x * z)) = T(y * x,x) * z. [para(7967(a,1),104(a,1,2,1)),rewrite([4525(5),7775(6)])]. 10810 R(T(x,y),y,y \ z) = ((y \ x) * (y * z)) / z. [para(7967(a,1),191(a,1,1,2,1)),rewrite([4525(4)]),flip(a)]. 10885 T(x,T(y * z,y * (y * x))) = T(x,T(T(z * y,y),x)). [back_rewrite(9001),rewrite([10809(4),2652(4)]),flip(a)]. 10888 T(x * y,x * (x * z)) = T(T(y * x,x),z). [back_rewrite(8992),rewrite([10809(4),10885(8),965(8)]),flip(a)]. 10900 T((x \ y) * (z * z),T(y,x)) = T(z * (z * (x \ y)),x). [back_rewrite(8036),rewrite([10888(7),101(3),4209(4),4578(3)])]. 10920 T(x * (y * y),x / z) = T(y * (y * x),z \ 1). [back_rewrite(5480),rewrite([10888(6),101(2),4209(3),4578(2)])]. 10927 T(x * (x * y),y \ z) = T(y * (x * x),z). [back_rewrite(5468),rewrite([10888(9),101(6),4209(7),4578(6)])]. 11076 L(T(x * y,x * z),L(y \ z,y,x),u) = (u * L(y \ z,y,x)) \ (u * (x * z)). [para(2705(a,1),74(a,1,1))]. 11083 (x \ y) * (z * (z * x)) = T(y * (z * z),x). [para(2254(a,1),2705(a,1,1)),rewrite([100(3),4408(4),100(6),100(8),10888(9),101(6),4209(7),4578(6)])]. 11138 (x * (y * (x \ (z / x)))) * (T(y,x \ (z / x)) \ x) = z. [para(1014(a,1),3544(a,1,1,2,2,2)),rewrite([3143(6),4408(6),45(2),1014(11),3143(10),3143(10),4155(9)])]. 11215 x * (((x \ y) / z) / T(x * y,z \ 1)) = x \ (z \ 1). [para(3640(a,1),15(a,1,2)),flip(a)]. 11218 K(x * y,x \ 1) = K(y,y \ (x \ 1)). [para(3640(a,1),20(a,1,2)),rewrite([11215(8),4505(4),8532(6),4408(3),45(2),11215(12)])]. 11219 ((x \ y) / z) / T(x * y,z \ 1) = x \ (x \ (z \ 1)). [para(3640(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 11221 x * (x / T(x * y,y \ x)) = y \ x. [para(47(a,1),3640(a,1,2,2,1)),rewrite([4408(5),14(5),989(5),1014(6),4408(8),14(8)])]. 11253 R(x,x \ (y \ 1),y * z) = z / ((x \ (y \ 1)) * (y * z)). [para(3640(a,1),82(a,1,3,1)),rewrite([11219(7),16(5),4408(6),45(5),11219(12),16(10),11219(15),16(13),16(12),4408(11),45(10)])]. 11256 (x \ (K(y \ (x \ 1),y) / x)) * z = (x \ T(x \ 1,y)) * z. [para(3640(a,1),178(a,1,1)),rewrite([11219(9),16(7),11219(13),16(11),16(10),3143(9),3143(9),9490(7),11219(14),16(12),4505(11),11219(17),16(15),16(14),1014(13),10401(11),989(9)])]. 11276 x / T(y * (y * (x * z)),z \ 1) = y \ (y \ (z \ 1)). [para(3641(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 11282 x * (x * ((y * z) / T(x * (x * (y * ((z * y) * u))),u \ (y \ 1)))) = u \ (y \ 1). [para(189(a,1),3641(a,1,2,2,2,1,2,2)),rewrite([4407(9),4407(16)])]. 11295 x * (x * (x / T(x / y,y * (x * x)))) = y * (x * x). [para(3641(a,1),3641(a,1,2,2,2,1,2)),rewrite([1014(3),11276(8),4408(7),4408(5),4408(4),45(3),4578(3),14(5),11276(14),4408(13),4408(11),4408(10),45(9),4578(9),14(11)])]. 11597 L(K(x,y) * z,K(y,x),u) = (u * K(y,x)) \ (u * z). [para(4993(a,1),180(a,1,1,2)),rewrite([6144(2),14(4),8298(10)])]. 11625 R(x,(x \ (y / x)) * (x * z),u) = ((y * z) * u) / (((x \ (y / x)) * (x * z)) * u). [para(18(a,1),183(a,1,1,1,1)),flip(a)]. 11645 (((x \ y) * z) * u) / (((y \ (x \ 1)) * (y * z)) * u) = R(y,(y \ (x \ 1)) * (y * z),u). [para(3143(a,1),183(a,1,1,1,1))]. 11726 a((x \ y) / z,x,T(y,x) \ ((x \ y) * z)) = a(x \ y,x,T(y,x) \ ((x \ y) * z)). [para(4505(a,1),10700(a,1,3,1)),rewrite([4505(10)])]. 11803 (x * ((y \ z) * z)) \ (x * ((y \ z) * ((y \ z) * u))) = L(T(y,z) \ u,(y \ z) * z,x). [para(2690(a,1),3141(a,1,2,2)),rewrite([2690(9)]),flip(a)]. 11853 L(x,(y \ z) * u,z \ y) = L(x,y \ z,u * (z \ y)). [para(4505(a,1),7679(a,1,3,2)),rewrite([90(5),4408(6)]),flip(a)]. 11861 x \ ((y \ z) * (((z \ y) * x) * u)) = L(u,z \ y,x * (y \ z)). [back_rewrite(9191),rewrite([11853(10)])]. 11862 L(T(x,y),x \ y,z * (y \ x)) = z \ ((z * (y \ x)) * y). [back_rewrite(7996),rewrite([11853(5)])]. 12076 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,y,z),u,w))) \ (v6 * v5). [para(34(a,1),6663(a,2,1,2,2))]. 12077 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = ((L(L(x,u,w),y,z) / v5) / v6) * (v6 * v5). [para(37(a,1),6663(a,2,1)),rewrite([2507(8),37(15),4501(16),1091(12),4407(12),10229(12),1014(12)])]. 12303 K(K(x,y),x) = 1. [para(15(a,1),7726(a,1,1,2))]. 12307 T(K(x,y),x) = K(x,y). [hyper(28,a,12303,a)]. 12308 K(x,y) * x = x * K(x,y). [para(12303(a,1),63(a,1,2)),rewrite([14(4)]),flip(a)]. 12309 K(x,K(x,y)) = 1. [para(12303(a,1),4993(a,1,1)),rewrite([13(4)])]. 12310 (x * K(x,y)) * ((x * K(x,y)) * z) = x * (x * (K(x,y) * (K(x,y) * z))). [para(12303(a,1),178(a,1,2,1)),rewrite([13(7),12308(8),189(11),12308(8),4578(10),37(12),100(10)])]. 12312 T(x,K(x,y)) = x. [hyper(28,a,12309,a)]. 12328 K(x,y) / x = x \ K(x,y). [para(12312(a,1),2711(a,1,2))]. 12349 K(x,y) * y = y * K(x,y). [para(12312(a,1),7616(a,1,1)),rewrite([5005(2),6144(4)]),flip(a)]. 12372 T(T(x,y),y \ 1) = x. [para(1091(a,1),7769(a,1,2)),rewrite([1708(2)])]. 12386 T(x,y / (y * x)) = x. [para(2810(a,1),7769(a,1,1)),rewrite([10229(3),10408(3),1708(4)])]. 12432 T(x,K(y,x)) = x. [para(12312(a,1),7769(a,1,1)),rewrite([6144(2),12349(2),1708(3)])]. 12473 K(x,y) / y = y \ K(x,y). [para(12432(a,1),2711(a,1,2))]. 12504 K(x,x * y) * T(y,x) = y. [para(7925(a,1),23(a,2)),rewrite([7826(5),6144(4)])]. 12506 L(T(x,K(y * L(x,z,u),y)),z,u) = L(x,z,u). [para(7925(a,1),30(a,1)),flip(a)]. 12519 T(x * y,K(x * ((z * x) * y),x * z)) = x * y. [para(189(a,1),7925(a,1,2,1))]. 12671 x \ K(x / y,y) = (y / x) / y. [para(10461(a,1),2711(a,1,2)),rewrite([10326(3)]),flip(a)]. 12698 T(T(K(x,y),z),x) = T(K(x,y),z). [para(12307(a,1),29(a,1,1)),flip(a)]. 12705 x * ((x \ (y / x)) * K(x \ (y / x),z)) = y * (x \ K(x \ (y / x),z)). [para(12307(a,1),3575(a,1,2,2)),rewrite([12308(11)]),flip(a)]. 12830 (x \ K(y,z)) * K(z,y) = x \ 1. [para(4993(a,1),6071(a,1,2)),rewrite([48(6),4996(9)])]. 12856 L(L(T(x,K(y * L(x,z,u),y)),w,v5),z,u) = L(L(x,z,u),w,v5). [para(12506(a,1),34(a,1,1)),flip(a)]. 12884 (x * R(y,z,(y * z) \ u)) * ((z * ((y * z) \ u)) / u) = x. [para(10094(a,1),104(a,1,2,2)),rewrite([14(9),16(8)]),flip(a)]. 12928 R(x,R(y,z,(y * z) \ u),(z * ((y * z) \ u)) / u) = x. [para(10094(a,1),84(a,1,2)),rewrite([14(10),12884(17)])]. 12931 x / R(y,z,(y * z) \ u) = x * ((z * ((y * z) \ u)) / u). [para(10094(a,1),85(a,2,2)),rewrite([12928(12),48(11)])]. 13311 a(x \ y,x,T(z,y * x)) = a(x,y * x,T(z,y * x)). [para(90(a,1),3968(a,1,3,2)),rewrite([7616(2),90(6),90(7)])]. 13425 T(T(T(x,y),z),y \ 1) = T(x,z). [para(7769(a,1),4214(a,2)),rewrite([8018(7)])]. 13457 L(x,(y \ z) * (y * u),y) = L(x,y * ((z * y) * u),y). [para(187(a,1),132(a,1,2,2)),rewrite([104(4),21(10),2507(10)]),flip(a)]. 13466 a(x,(x \ y) * (x * z),u) = a(x,x * ((y * x) * z),u). [para(187(a,1),133(a,1,1,2)),rewrite([104(9),37(10),4501(11),4498(9),2508(10)]),flip(a)]. 13523 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,y * ((z * y) * x),y). [back_rewrite(9186),rewrite([13457(14)])]. 13639 (x * (y \ z)) * ((z \ y) * u) = (y \ z) * (((z \ y) * x) * u). [para(4137(a,1),190(a,1,2,2)),rewrite([4408(4),14(6),4408(8),5208(12)])]. 13641 T(x,y) * ((y \ z) * (y * u)) = y \ (x * ((z * y) * u)). [para(4505(a,1),190(a,1,1)),rewrite([7550(11)])]. 13663 x / T(x / y,y * (x * x)) = T(y,x * x). [para(11295(a,1),21(a,1,2)),rewrite([23(4),1607(8)]),flip(a)]. 13668 x * (x * (T(y,x * x) * z)) = y * (x * (x * z)). [para(11295(a,1),37(a,1,1)),rewrite([2040(3),13663(8)]),flip(a)]. 13687 ((x / y) * (z * (y * y))) \ (x * (y * T(z,y * y))) = a(x / y,y,y * T(z,y * y)). [para(11295(a,1),60(a,1,1,2)),rewrite([13663(9),13663(15)])]. 13702 (x * (y * (z * (z * u)))) \ ((x * (y * (z * z))) * u) = a(x,y * (z * z),u). [para(11295(a,1),139(a,1,2,1,2)),rewrite([13663(5),13668(5),13663(14),777(13)])]. 13709 L((x * (y * y)) \ z,x * (y * y),y) = (y * T(x,y * y)) \ (y \ z). [para(11295(a,1),3940(a,1,1,1)),rewrite([13663(8),777(7),13663(11)])]. 13734 x * (T(y,x * x) * x) = T(y * (x * x),x). [para(11295(a,1),4209(a,1,1)),rewrite([13663(8),101(7)]),flip(a)]. 13735 T(T(x * (y * y),y),y * T(x,y * y)) = x * (y * y). [para(11295(a,1),4209(a,2)),rewrite([13663(5),101(4),13734(4),13663(8)])]. 13845 L(x,(y * ((y \ z) * u)) * z,L(u,y * z,y)) = L(x,z,L(u,y * z,y) * (y * ((y \ z) * u))). [para(9729(a,1),132(a,1,2,2)),rewrite([9640(6),21(16),9755(12)])]. 13884 L(x,y * (z * y),y) = L(x,y,z). [para(14(a,1),13523(a,1,2,2,1,2)),rewrite([45(5),4505(5),4525(6),5885(6),14(4)]),flip(a)]. 13929 L(x,(y \ z) * u,y \ z) = L(x,z \ y,u * (y \ z)). [para(4137(a,1),13523(a,1,2,2,1,2)),rewrite([4408(5),1014(5),1829(4),4408(5),14(7),3143(8),11861(6),5208(9)]),flip(a)]. 13932 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y) * u,K(z,y)). [para(4993(a,1),13523(a,1,2,2,1,2)),rewrite([6144(5),1014(5),1829(4),6144(5),14(7),3143(8),9198(6),8298(9)])]. 14038 (x * ((x \ (y \ 1)) * ((y * z) * u))) \ ((z / y) * (y * u)) = a(x,x / y,(y * z) * u). [para(15(a,1),9423(a,1,1,2,2,2)),rewrite([15(15)])]. 14083 (x / y) * (y * (x * T(x \ (x \ 1),x * x))) = 1. [para(996(a,1),13687(a,2,3,2)),rewrite([3436(4),8972(6),16(4),87(4),14(3),3436(4),10229(9),3436(13),16(14),1072(13)])]. 14102 T(x,T(x,y) \ 1) = x. [para(541(a,1),12372(a,1,1))]. 14123 T(x,(y / x) / y) = x. [para(5067(a,1),12372(a,1,1)),rewrite([4407(4),10229(4),1014(4)])]. 14124 (x \ (x \ (y \ 1))) * z = x \ (x \ (y \ z)). [para(12372(a,1),3710(a,1,2)),rewrite([7616(7)])]. 14154 K(x,y / (y * x)) = 1. [hyper(27,a,12386,a)]. 14430 T(x,y) * K(x \ y,x) = x. [para(14102(a,1),23(a,2)),rewrite([1014(7),8593(5),4408(6),45(3)])]. 14495 T(x,(T(T(T(y,z),u),x \ 1) / x) / T(T(T(y,x \ 1),z),u)) = x. [para(3382(a,1),14123(a,1,2,1))]. 14546 K(x \ y,x / y) = 1. [para(16(a,1),14154(a,1,2,2))]. 14868 (x * x) / y = x * (x / y). [para(100(a,1),1014(a,1)),rewrite([1014(3)]),flip(a)]. 14874 L(x,y * (y * z),u) = L(x,z,u * (y * y)). [para(100(a,1),132(a,1,1,2,2)),rewrite([100(5),100(9),100(11),4501(12),1091(5),4407(5),5162(5),5610(10),100(7),2507(8)])]. 14882 a(x * (y * y),z,u) = a(x,y * (y * z),u). [para(100(a,1),133(a,1,1,2,2)),rewrite([100(6),100(9),100(11),37(12),4501(13),1091(6),4407(6),5162(6),6141(11),100(7),2508(8)]),flip(a)]. 15035 L(x,y,y * (z * z)) = x. [back_rewrite(5614),rewrite([14874(3)])]. 15045 L(x,y * (z * (z * y)),u * (z * z)) = x. [back_rewrite(2522),rewrite([14874(6)])]. 15052 x * (y * T(y \ (y \ 1),y * y)) = x / y. [para(14083(a,1),15(a,1,2)),rewrite([10229(3),14(3)]),flip(a)]. 15056 L(x * T(x \ (x \ 1),x * x),y,x) = x \ 1. [para(14083(a,1),21(a,1,2)),rewrite([18(2),3200(10)]),flip(a)]. 15079 a((x / y) * (z * (x / y)),y / x,u) = a(x / y,z,u). [para(14083(a,1),133(a,1,2,1,2,2)),rewrite([15052(9),10287(5),14(6),19(7),15052(13)]),flip(a)]. 15120 L(x,y * ((y \ z) * T(z,y)),u * ((y \ z) * (y \ z))) = x. [para(4505(a,1),15045(a,1,2,2,2))]. 15137 K(T(x * y,y),y \ 1) = K(T(x,y) \ 1,x * y). [para(165(a,1),10702(a,1,1,2)),rewrite([7775(2),6564(5)])]. 15143 K(x \ 1,T(y,x)) = K(y,y \ x). [para(2711(a,1),10702(a,1,2)),rewrite([7616(2),16(2)]),flip(a)]. 15144 K(T(x,y),y \ (x \ 1)) = K(y,x). [para(3143(a,1),10702(a,1,1)),rewrite([4155(3),45(2),23(2),6120(4),4408(9),45(7),14(7)])]. 15148 K(x \ 1,y \ x) = K(x / y,y). [para(3666(a,1),10702(a,1,1,2)),rewrite([1014(3),4155(3),16(3)]),flip(a)]. 15149 K(T(x,y),y \ 1) = K(x \ y,x). [para(3666(a,1),10702(a,1,2)),rewrite([4155(3),16(3),4505(2),4408(7),14(7)])]. 15266 (x / y) * ((y * z) / T(x * (y \ x),z)) = (y / x) * z. [para(4254(a,1),15(a,1,2)),rewrite([10229(2)]),flip(a)]. 15271 ((x / y) * (((y / x) * z) * u)) \ (z * u) = a(x / y,(y / x) * z,u). [para(4254(a,1),19(a,1,2,1)),rewrite([15266(8),15266(15)])]. 15276 (x * y) / T(z * (x \ z),y) = (x / z) * ((x / z) * y). [para(4254(a,1),21(a,1,2)),rewrite([3436(4),10229(3),10229(4),1607(12)]),flip(a)]. 15308 a(x / y,(y / x) * ((y / x) * z),u) = a(x / y,z,u). [para(4254(a,1),133(a,1,2,1,2)),rewrite([15276(8),37(8),10287(9),10287(6),19(7),15276(12),2508(12)]),flip(a)]. 15408 T(x \ y,y) * (T(x,y) * z) = T(x,y) \ ((x * y) * z). [para(4314(a,1),15(a,1,2)),flip(a)]. 15409 T(x,y) * (T(x \ y,y) * z) = (x * y) * (T(x,y) \ z). [para(16(a,1),4314(a,1,2,2))]. 15411 a(T(x,y),T(x \ y,y),T(x,y) * z) = a(x,y,z) \ 1. [para(4314(a,1),19(a,1,1)),rewrite([4304(6),4525(5),2548(5)]),flip(a)]. 15452 x \ (y * (y * z)) = ((x \ y) * y) * z. [para(7769(a,1),4314(a,1,1)),rewrite([8018(3),6134(4),7769(6),4525(6),3143(5),7617(6)])]. 15454 x * (T((y / x) / y,K(x / y,y)) * (x * z)) = (x * K(x / y,y)) * z. [para(10461(a,1),4314(a,1,1)),rewrite([12671(3),10461(8)])]. 15593 a(x \ y,z * (x \ y),T(x,y)) = a(x \ y,z,y) \ 1. [para(4344(a,1),19(a,1,1)),rewrite([128(9),2690(7),2548(7)]),flip(a)]. 15621 (((x \ y) * z) * y) \ (x \ y) = T(x,y) \ ((y \ x) / z). [para(4344(a,1),1091(a,1,1)),rewrite([4407(11),4407(10),4408(10),1014(10)])]. 15622 T(x \ y,(z * (x \ y)) * T(x,y)) = T(x \ y,((x \ y) * z) * y). [para(4344(a,1),1708(a,1,2)),flip(a)]. 15645 ((x * (y \ z)) * T(y,z)) * (y \ z) = T(((y \ z) * x) * z,y \ z). [para(4344(a,1),4209(a,1,1)),flip(a)]. 15646 T(T(((x \ y) * z) * y,x \ y),(z * (x \ y)) * T(x,y)) = ((x \ y) * z) * y. [para(4344(a,1),4209(a,2)),rewrite([15645(6)])]. 15674 (((x \ y) * z) * x) \ ((z * (y \ x)) * T(y,x)) = T(y \ x,((y \ x) * z) * x). [back_rewrite(5569),rewrite([15622(14)])]. 15862 x * ((x \ y) * (x \ y)) = y * (x \ y). [para(7769(a,1),4404(a,1,2)),rewrite([7617(7),6351(7)]),flip(a)]. 15916 x \ ((x * y) * z) = (y / x) * (x * z). [para(15(a,1),4504(a,1,2,1,1)),rewrite([1091(2),3143(5),1091(5),1014(6),4209(6)])]. 15922 L(x,x \ y,z * (y \ x)) = ((y \ x) / z) * (z * T(y,x)). [para(4504(a,1),21(a,1,2)),rewrite([7715(4),15916(5),11853(9)]),flip(a)]. 15924 T(x \ y,((y \ x) * z) * y) = T(x \ y,((x \ y) * z) * y). [para(4504(a,1),23(a,1,2)),rewrite([15674(8)]),flip(a)]. 15928 T(x,y \ z) * T(y,z) = (z \ y) * (x * z). [para(37(a,1),4504(a,1,2)),rewrite([7715(7),9031(7)]),flip(a)]. 15940 ((x * (y \ z)) * T(y,z)) / T(y \ z,((z \ y) * x) * z) = ((z \ y) * x) * z. [para(4504(a,1),165(a,1,1))]. 15943 (x \ y) * (((y \ x) / z) * y) = (z \ (x \ y)) * T(x,y). [para(1014(a,1),4504(a,1,2,1)),rewrite([3143(9)])]. 15957 x * L(y,y \ z,x * (z \ y)) = (x * (z \ y)) * T(z,y). [para(4504(a,1),72(a,2)),rewrite([7715(4),11853(4)])]. 16020 L(T(x,y),x \ y,z * (y \ x)) = ((y \ x) / z) * (z * y). [back_rewrite(11862),rewrite([15916(9)])]. 16096 a(x / (y * y),y,y * z) = a(x,y \ 1,y * z). [back_rewrite(7412),rewrite([15916(8),7628(9)])]. 16103 L(x,y * z,y) = L(x,y,z). [back_rewrite(5134),rewrite([15916(3),3276(4)]),flip(a)]. 16229 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y),u). [back_rewrite(13932),rewrite([16103(8)])]. 16231 L(x,y \ z,u * (z \ y)) = L(x,z \ y,u). [back_rewrite(13929),rewrite([16103(4)]),flip(a)]. 16256 L(x,y,z * y) = L(x,y,z). [back_rewrite(13884),rewrite([16103(3)])]. 16286 L(x,(y * ((y \ z) * u)) * z,L(u,y,z)) = L(x,z,L(u,y,z) * (y * ((y \ z) * u))). [back_rewrite(13845),rewrite([16103(6),16103(8)])]. 16343 x \ T(x,y) = K(x,y). [back_rewrite(10321),rewrite([16103(6),2254(4)]),flip(a)]. 16348 x \ (y * ((y \ x) * z)) = L(z,y,x). [back_rewrite(9832),rewrite([16103(6)])]. 16362 T(x,L(y * z,y,x)) = T(x,(x * y) * z). [back_rewrite(9791),rewrite([16103(3)])]. 16364 L(x * (y * z),x,y) = (x * y) * z. [back_rewrite(9786),rewrite([16103(4)])]. 16387 K(L(x * y,x,z),z) = K(z * ((z * x) * y),z). [back_rewrite(9737),rewrite([16103(3)])]. 16398 L(x,y \ 1,z * y) = L(x,y,z). [back_rewrite(9719),rewrite([16103(6)])]. 16465 L(x,y \ z,y) = L(x,y,z). [back_rewrite(9559),rewrite([16103(4)])]. 16470 L(x,y * z,y \ 1) = L(x,y,z). [back_rewrite(6634),rewrite([16103(6)])]. 16484 x \ (y \ (z * (y * x))) = L(T(z,y * x),y,x). [back_rewrite(5138),rewrite([16103(4)]),flip(a)]. 16485 L((x * y) \ z,x,y) = y \ (x \ z). [back_rewrite(3940),rewrite([16103(4)])]. 16487 L(L(x,y,z),z,y) = x. [back_rewrite(667),rewrite([16103(3)])]. 16505 L(T(x,y),y \ x,z) = ((y \ x) / z) * (z * y). [back_rewrite(16020),rewrite([16231(5)])]. 16508 (x * (y \ z)) * T(y,z) = x * L(z,y \ z,x). [back_rewrite(15957),rewrite([16231(4)]),flip(a)]. 16509 ((x \ y) / z) * (z * T(x,y)) = L(y,x \ y,z). [back_rewrite(15922),rewrite([16231(4)]),flip(a)]. 16517 L(x,(y \ z) * u,z \ y) = L(x,z \ y,u). [back_rewrite(11853),rewrite([16231(8)])]. 16564 K(x \ y,x) = K(y,x). [back_rewrite(4516),rewrite([16343(4)])]. 16566 T(x,y) / x = K(x,y). [back_rewrite(4366),rewrite([16343(4)])]. 16568 K(x * y,x) = K(y,x). [back_rewrite(3934),rewrite([16343(4)])]. 16569 K(x \ 1,y * x) = K(y,x). [back_rewrite(3171),rewrite([16343(6)])]. 16603 K(T(x,y),y \ 1) = K(y,x). [back_rewrite(15149),rewrite([16564(6)])]. 16623 T(x,y) * K(y,x) = x. [back_rewrite(14430),rewrite([16564(3)])]. 16660 (x \ (K(x \ 1,y) / x)) * z = (x \ T(x \ 1,y)) * z. [back_rewrite(11256),rewrite([16564(4)])]. 16686 K(x,x * y) = K(x,y). [back_rewrite(8594),rewrite([16564(2)]),flip(a)]. 16687 x / T(x,y) = K(y,x). [back_rewrite(8593),rewrite([16564(4)])]. 16710 K(x,x \ y) = K(x,y). [back_rewrite(8534),rewrite([16564(2)]),flip(a)]. 16711 T(x,y) \ x = K(y,x). [back_rewrite(8532),rewrite([16564(4)])]. 16712 K(T(x,y),K(x,y)) = 1. [back_rewrite(8078),rewrite([16564(3)])]. 16716 x * K(x,y) = T(x,y). [back_rewrite(4535),rewrite([16564(2)])]. 16717 x * (K(x,y) * (x * z)) = (x * T(x,y)) * z. [back_rewrite(4534),rewrite([16564(2)])]. 16735 K(L(x * y,x,z),z) = K((z * x) * y,z). [back_rewrite(16387),rewrite([16568(7)])]. 16813 L(L(T(x,K(L(x,y,z),u)),w,v5),y,z) = L(L(x,y,z),w,v5). [back_rewrite(12856),rewrite([16568(3)])]. 16827 K(x * y,y) = K(T(x,y),y). [back_rewrite(7876),rewrite([16568(3)])]. 16839 K(T(x,y) \ 1,x * y) = K(y,x * y). [back_rewrite(15137),rewrite([16603(5)]),flip(a)]. 16875 K(x,y) * T(y,x) = y. [back_rewrite(12504),rewrite([16686(2)])]. 16909 K(x,y * x) = K(x,T(y,x)). [back_rewrite(7875),rewrite([16686(3)])]. 16936 K(x \ 1,T(y,x)) = K(y,x). [back_rewrite(15143),rewrite([16710(6)])]. 16950 K(x * y,x \ 1) = K(y,x \ 1). [back_rewrite(11218),rewrite([16710(8)])]. 16967 K(x,y \ 1) = K(y,x / y). [back_rewrite(3163),rewrite([16710(3)]),flip(a)]. 16981 x * (y \ K(y \ (x / y),z)) = y * T(y \ (x / y),z). [back_rewrite(12705),rewrite([16716(6)]),flip(a)]. 16984 x * (x * (K(x,y) * (K(x,y) * z))) = T(x,y) * (T(x,y) * z). [back_rewrite(12310),rewrite([16716(2),16716(3)]),flip(a)]. 16985 K(x,y) * x = T(x,y). [back_rewrite(12308),rewrite([16716(4)])]. 16999 a(x,y,K(y,x)) = 1. [back_rewrite(1097),rewrite([16716(2),90(2),46(3)]),flip(a)]. 17019 K(T(x,y) \ 1,x * y) = K(y,T(x,y)). [back_rewrite(16839),rewrite([16909(7)])]. 17040 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(x \ y,y \ 1). [back_rewrite(6878),rewrite([16950(12)])]. 17093 (x \ y) * (((y \ x) * z) * ((z * (x \ y)) * u)) = z * (z * ((x \ y) * u)). [para(4137(a,1),193(a,2,1,2,1,1)),rewrite([4145(5),13639(8),13(10),37(12)])]. 17291 K(x,y \ 1) = K(x,x / y). [para(89(a,1),4809(a,1,1,1,1)),rewrite([101(3),4230(2),15452(7),1091(4),4407(4),4408(4),1014(4),10400(2),4505(3),92(2),4493(3),89(4),16686(6)])]. 17387 (x * T(y,x * x)) \ T(z,x) = ((y * (x * x)) \ z) * x. [para(23(a,1),13709(a,2,2)),rewrite([10725(7)]),flip(a)]. 17666 L(K(x,y),x,y) = K(x,y). [hyper(24,a,16999,a)]. 17730 K(x \ 1,y) = K(x,y \ 1). [para(14546(a,1),63(a,1,2)),rewrite([10366(3),14(5),4493(6)])]. 17771 K(x,T(y,x)) = K(x,y). [back_rewrite(17019),rewrite([17730(5),4407(4),15144(5)]),flip(a)]. 17772 K(x,T(y,x) \ 1) = K(y,x). [back_rewrite(16936),rewrite([17730(4)])]. 17778 (x \ (x \ K(x,y \ 1))) * z = (x \ T(x \ 1,y)) * z. [back_rewrite(16660),rewrite([17730(3),12328(4)])]. 17781 K(x,y \ 1) = K(y,x). [back_rewrite(16569),rewrite([17730(4),4407(3),16710(4)])]. 17822 K(x / y,y) = K(x,y). [back_rewrite(15148),rewrite([17730(4),4408(3),14(3),16710(2)]),flip(a)]. 17906 (x \ T(x \ 1,y)) * z = (x \ (x \ K(y,x))) * z. [back_rewrite(17778),rewrite([17781(3)]),flip(a)]. 17910 K(T(x,y),y) = K(x,y). [back_rewrite(17772),rewrite([17781(4)])]. 17913 K(x \ 1,y) = K(y,x). [back_rewrite(17730),rewrite([17781(6)])]. 17914 K(x,x / y) = K(y,x). [back_rewrite(17291),rewrite([17781(3)]),flip(a)]. 17919 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(y,x \ y). [back_rewrite(17040),rewrite([17781(11)])]. 17924 K(x,y / x) = K(x,y). [back_rewrite(16967),rewrite([17781(3)]),flip(a)]. 17974 x * (T((y / x) / y,K(x,y)) * (x * z)) = T(x,y) * z. [back_rewrite(15454),rewrite([17822(4),17822(9),16716(9)])]. 18023 (x * (y / x)) \ y = K(y,x). [back_rewrite(67),rewrite([17822(5)])]. 18043 K(x * y,y) = K(x,y). [back_rewrite(16827),rewrite([17910(4)])]. 18156 x \ (y * (x / y)) = K(y,x). [back_rewrite(66),rewrite([17924(5)])]. 18422 (T(x,y) * z) / (K(x,y) * z) = R(x,K(x,y),z). [para(16343(a,1),81(a,1,2)),rewrite([16343(6)]),flip(a)]. 18454 L(x,y,x \ 1) = x. [para(1022(a,1),16487(a,1,1))]. 18461 L(x,y,L(x,z,u)) = x. [para(16487(a,1),1689(a,1,1)),rewrite([16487(4)])]. 18472 L(x,x \ y,y) = x. [para(8105(a,1),16487(a,1,1))]. 18473 L(L(x,y,z),z / (y * x),y) = x. [para(3199(a,1),16487(a,1,1))]. 18485 L(R(x,y,z),u,x \ 1) = R(x,y,z). [para(18454(a,1),33(a,1,1)),flip(a)]. 18604 a(x,y \ x,y) = 1. [hyper(25,a,18472,a)]. 18608 L(x,T(y,x),y * x) = x. [para(23(a,1),18472(a,1,2))]. 18650 L(x,y \ 1,x / y) = x. [para(1829(a,1),18472(a,1,2))]. 18689 (x * (y * x)) \ ((x * y) * z) = L(x \ z,x,x * y). [para(101(a,1),74(a,2,1)),flip(a)]. 18690 L(x \ y,x,y * z) = ((y * z) * x) \ (y * (z * y)). [para(101(a,1),74(a,2,2))]. 18703 ((x / (y * z)) * (y * (z * y))) \ (x * y) = a(x / (y * z),y * z,y). [para(101(a,1),60(a,1,1,2))]. 18718 T(x * y,x * x) = T(y * x,x). [para(2690(a,1),101(a,2,2)),rewrite([7789(3),15928(4),8972(3),7775(5)])]. 18724 a(x * y,x,T(z,x)) = a(x,y,z * x) \ 1. [para(101(a,1),507(a,1,2,1)),rewrite([128(7),90(5),2548(7)]),flip(a)]. 18742 a(x,y,y * x) = 1. [para(101(a,1),8106(a,1,2)),rewrite([3982(4),4795(4)])]. 18750 R(x,y * z,y) * (y * (z * y)) = (x * (y * z)) * y. [para(101(a,1),84(a,1,2))]. 18752 R((x * y) / z,z,x) = (x * (y * x)) / (z * x). [para(101(a,1),85(a,2,1))]. 18763 a((x * y) / z,x,L(x \ z,x,x * y)) = a(x * y,x,L(x \ z,x,x * y)). [para(101(a,1),10700(a,1,3,1)),rewrite([18689(7),101(9),18689(12)])]. 18809 (x \ y) * (x * x) = T(y * x,x). [back_rewrite(8972),rewrite([18718(6)])]. 18848 L(x,y,z * (u * (z * (y * x)))) = L(x,y,z * (u * z)). [para(106(a,1),3199(a,1,3)),flip(a)]. 18870 (((x \ y) * z) * ((z * (y \ x)) * T(y,x))) / x = (x \ y) * (z * z). [para(4504(a,1),106(a,1,1,2)),rewrite([7715(14),4578(11)])]. 18962 x / T(x * y,y \ x) = x \ (y \ x). [para(11221(a,1),15(a,1,2)),flip(a)]. 19049 T(T(x,y) \ z,K(T(x,y) \ ((x \ y) * z),T(x \ y,y))) = T(x,y) \ z. [para(11221(a,1),12519(a,1,2,1,2,1)),rewrite([18962(4),6968(3),18962(6),6968(7),18962(10),4505(9),18962(14),6968(13)])]. 19065 x * T(x \ (x \ 1),x * x) = x \ 1. [para(15056(a,1),70(a,1)),flip(a)]. 19074 (x * y) / x = x * (y / x). [para(15056(a,1),72(a,1,2)),rewrite([1014(4),19065(8),1014(5)])]. 19167 a(x,(x / y) * ((x / y) * z),u) = a(y \ (x / y),z,u). [para(18(a,1),4636(a,2,1)),rewrite([3286(6),2508(5)]),flip(a)]. 19178 a(x * (y \ (x * x)),z,u) = a(x / y,x * (x * z),u). [para(1014(a,1),4636(a,2,1)),rewrite([3143(4)])]. 19195 a(T(x,y),(y \ x) * ((y \ x) * z),u) = a((y \ x) * (x * (y \ x)),z,u). [para(4505(a,1),4636(a,2,1)),rewrite([15862(5)]),flip(a)]. 19450 (x * ((T(y,z) * (x * x)) \ u)) \ (T(T(y,x),z) \ 1) = u \ x. [para(4713(a,1),1829(a,1,2)),rewrite([4407(11)]),flip(a)]. 19451 x / (T(T(y,z),u) * ((y \ z) * ((T(y,u) * ((y \ z) * (y \ z))) \ x))) = y \ z. [para(2642(a,1),4713(a,1,2,1,1))]. 19474 (x * (y * y)) \ z = y \ (y \ (x \ z)). [para(4713(a,1),3645(a,1,1)),rewrite([4407(12),19450(12),10927(4),2711(4),4407(13),19450(13)])]. 19479 x / (T(y,z) * ((y \ u) * (T(T(y,u),z) \ x))) = u \ y. [para(7769(a,1),4713(a,1,2,1,1)),rewrite([19474(9),4408(8),4408(9),7715(10)])]. 19486 x / (T(K(y,z),u) * (u \ (K(z,y) * x))) = u. [para(12307(a,1),4713(a,1,2,2,2,1,1)),rewrite([12698(3),19474(6),6144(4),6073(6),7550(7)])]. 19496 x / (T(y,z) * ((u / (u * y)) * ((u * (y * (y / u))) * (T(y,z) \ x)))) = u / (u * y). [para(12386(a,1),4713(a,1,2,1,1)),rewrite([19474(11),10229(10),19074(7),10229(11),19074(5),10140(11)])]. 19499 x / (T(y,z) * (T(y,u) \ ((T(y,z) * (T(y,u) \ (T(y,u) \ 1))) \ x))) = T(y,u) \ 1. [para(14102(a,1),4713(a,1,2,1,1)),rewrite([1014(12),10400(10),989(9),3143(13)])]. 19502 x / (T(y,z) * (((u / y) / u) * ((u * (y * (y / u))) * (T(y,z) \ x)))) = (u / y) / u. [para(14123(a,1),4713(a,1,2,1,1)),rewrite([19474(11),10229(10),10215(7),10229(11),10215(5),10140(11)])]. 19536 x / (T(T(y,z),u) * ((z \ y) * (T(y,u) \ x))) = y \ z. [back_rewrite(19451),rewrite([19474(9),4408(8),4408(9),7715(10)])]. 19567 K(x,y \ x) = K(y,x). [back_rewrite(17919),rewrite([19474(7),4408(5),4408(3),45(2),3032(3),19074(2),15(4),18156(3)]),flip(a)]. 19570 (x * T(y,x * x)) \ T(z,x) = T(x \ (y \ z),x). [back_rewrite(17387),rewrite([19474(8),4505(9)])]. 19639 (x * (y * (z * x))) \ (x * (z * (x * T(y,z * x)))) = a(x * z,x,T(y,z * x)). [para(90(a,1),196(a,1,1,2))]. 19647 (x * ((y \ x) * z)) \ (x * (y \ (x * z))) = a(x / y,x,z). [para(1014(a,1),196(a,2,1)),rewrite([3143(3),3143(7)])]. 19659 a(x / y,x,z) = a(x,y \ x,z). [para(2690(a,1),196(a,2,1)),rewrite([7789(4),4525(5),7997(9),8098(7),19647(7)])]. 19660 (x * (y * (x * z))) \ (x * (y * (x * L(z,x,y)))) = a(x * y,x,L(z,x,y)). [para(72(a,1),196(a,1,1,2))]. 19674 a((x \ y) * z,x \ y,x) = a(x \ y,z,T(y,x)) \ 1. [para(4505(a,1),196(a,1,2,2,2)),rewrite([8020(5),2548(9)]),flip(a)]. 19707 R(x * y,y * x,(y * x) \ (K(y,x) * z)) = R(x * y,K(y,x),z). [para(16(a,1),202(a,2,1,2)),rewrite([6144(5),6144(11),2858(12)])]. 19771 T(x * (x / y),y) = y \ (x * x). [para(87(a,1),10900(a,1,2)),rewrite([3143(4),88(4),1014(5)]),flip(a)]. 19991 (x * (y * x)) / z = x * (y * (x / z)). [para(13(a,1),1851(a,1,1,2,2,2,2)),rewrite([14(4),13(4),13(4),989(8),1014(9),13(8),13(8),13(8)])]. 20016 R((x * y) / z,z,x) = x * (y / z). [back_rewrite(18752),rewrite([19991(7),3691(5),1014(6)])]. 20095 L(a(x / y,y,z),(x / y) * (y * z),u) * ((u * (x * z)) \ (u * ((x / y) * (y * z)))) = 1. [para(1961(a,2),4137(a,1,1))]. 20341 a(x * y,y,x) = 1. [para(15(a,1),18604(a,1,2))]. 20387 a(x,y / x,y) = 1. [para(18(a,1),18742(a,1,3))]. 20390 (x * y) * (y * x) = x * (y * (y * x)). [para(18742(a,1),209(a,1,1)),rewrite([45(5),18742(8),88(8)])]. 20397 a(T(x,y),y,x * y) = 1. [para(90(a,1),18742(a,1,3))]. 20504 ((x * (y * (z * (z * y)))) * u) / (z * (y * (y * (z * u)))) = R(x,y * (z * (z * y)),u). [back_rewrite(9114),rewrite([20390(3),20390(8),2213(9),20390(13)])]. 20509 (x * y) * (K(y,x) * (z * (x * y))) = y * (x * (x * (y * T(z,x * y)))). [back_rewrite(9104),rewrite([20390(3),2213(6)]),flip(a)]. 20510 (x * (y * (z * (z * (y * u))))) * a(x,z * (y * (y * z)),u) = (x * (z * (y * (y * z)))) * u. [back_rewrite(9101),rewrite([20390(3),2213(4),20390(8),20390(13)])]. 20551 a(x,y,x \ y) = 1. [para(2690(a,1),20341(a,1,1)),rewrite([4582(3)])]. 20620 (x * (y * (x / y))) / (y * (x * (y \ x))) = 1. [para(20387(a,1),265(a,1,2,2)),rewrite([8255(3),4230(5),88(8),20387(9)])]. 20692 a(x * (y * z),(x * y) * z,a(x,y,z)) = 1. [para(19(a,1),20551(a,1,3))]. 20939 T(T(x,y),z) / T(x,z) = K(T(x,z),y). [para(29(a,1),16566(a,1,1))]. 20967 ((x * K(y,z)) * y) / T(y,z) = R(x,K(y,z),y). [para(16566(a,1),86(a,1,1,1,2)),rewrite([16566(7)])]. 21045 L(K(x,y) * z,K(y,x),T(x,y)) = x \ (T(x,y) * z). [para(16623(a,1),74(a,2,1)),rewrite([6144(2)])]. 21062 T(x,y) * (x * z) = x * (T(x,y) * z). [para(16623(a,1),189(a,1,1)),rewrite([16875(7)]),flip(a)]. 21063 K(x,y) * (y * z) = y * (K(x,y) * z). [para(16623(a,1),189(a,2,2,1)),rewrite([16875(3)]),flip(a)]. 21070 x * L(y,K(z,x),T(x,z)) = T(x,z) * (K(z,x) * y). [para(16623(a,1),72(a,1,1))]. 21095 R(x / T(y,z),T(y,z),K(z,y)) = (x * K(z,y)) / y. [para(16623(a,1),85(a,2,2))]. 21316 T((x / y) * (z * (x / y)),y) = (y \ x) * (y \ (z * x)). [para(18(a,1),122(a,1,2,2,2)),rewrite([6135(4)]),flip(a)]. 21447 x * (y \ ((y / x) * z)) = L(z,y / x,y). [para(16(a,1),10347(a,1,1)),rewrite([10229(4)]),flip(a)]. 21463 T(x,y) * ((x * y) \ z) = L(y \ z,y,x). [para(165(a,1),10347(a,1,2)),rewrite([6564(3),3143(3),16256(3)]),flip(a)]. 21472 L((x \ y) * z,y \ x,x) = T(y,x) * (x \ z). [para(2711(a,1),10347(a,1,2)),rewrite([7616(2)])]. 21500 L(x * (y \ z),y,y / x) = (x / y) * z. [para(10347(a,1),16487(a,1,1))]. 21504 L(K(x,y) * z,K(y,x),x) = T(x,y) * (x \ z). [para(16566(a,1),10347(a,1,1,1)),rewrite([16687(4)])]. 21505 L(K(x,y) * z,K(y,x),T(y,x)) = y * (T(y,x) \ z). [para(16566(a,1),10347(a,1,2)),rewrite([16687(2)])]. 21507 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z / y,z))))) = x * x. [back_rewrite(10296),rewrite([21447(8)])]. 21510 R(x,y,(x * y) \ T(z,y / x)) = L(x,y / x,z). [back_rewrite(8497),rewrite([21463(11),10229(7),18(7)])]. 21676 T(a(x,x * y,z),x * (x * ((y * z) / (x * ((x * y) * z))))) = a(x,x * y,z). [para(37(a,1),4950(a,1,2,1)),rewrite([1839(9)])]. 21704 R(x,y * (y * z),z \ ((y \ (y \ z)) * u)) = R(x,z,u). [para(15(a,1),5194(a,2,3)),rewrite([6073(5)])]. 21705 R(x,y * z,(z \ y) * (y \ (y \ u))) = R(x,y \ z,(z \ y) * u). [para(16(a,1),5194(a,1,2,2)),rewrite([4408(5),4408(9)])]. 21708 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * (u * w))) = R(x,z * u,L(w,u,z)). [para(21(a,1),5194(a,2,3)),rewrite([6073(8)])]. 21713 (x * (y * (y * z))) * (z \ (y \ (y \ u))) = z * ((z \ x) * u). [para(5194(a,1),341(a,1,1)),rewrite([16(6),16(5),16(4),200(3)]),flip(a)]. 21715 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * w)) = R(x,z * u,L(u \ w,u,z)). [para(74(a,2),5194(a,2,3)),rewrite([6073(7)])]. 21721 R(x,(y \ (y \ z)) * u,((y \ (y \ z)) * u) \ z) = R(x,z * u,u \ 1). [para(1091(a,1),5194(a,1,3)),rewrite([7550(4),16(3)]),flip(a)]. 21722 R(x,y * (z * (z * y)),K(y,z) * ((y * z) \ ((y * z) \ u))) = R(x,K(z,y),K(y,z) * u). [para(63(a,1),5194(a,1,2,2)),rewrite([20390(3),6144(9),6144(13)])]. 21734 (x * ((x \ ((y \ z) * z)) * (z \ (z \ u)))) / u = R(y \ 1,x,x \ u). [para(5194(a,1),6071(a,2)),rewrite([15452(3),169(7),37(13),16(11),16(10),16(9)])]. 22110 R(T(x,y),y \ x,(x \ y) * z) = ((y \ x) * (y * z)) / z. [para(18454(a,1),203(a,2,1,2,1)),rewrite([3143(4),23(2),3143(4),3143(5),4408(4),3143(8)])]. 22202 ((x \ y) * z) * ((z * (y \ x)) * u) = (x \ y) * (z * (z * ((y \ x) * u))). [para(17093(a,1),15(a,1,2)),rewrite([15452(6),4408(2),4578(3),2040(6)]),flip(a)]. 22239 (x * y) * (T(x,y) \ (y * (x * z))) = y * ((y * x) * z). [para(17093(a,1),190(a,2,2)),rewrite([16(5),6968(6),136(10)])]. 22250 x \ (y * (z * z)) = (x \ y) * (z * z). [back_rewrite(18870),rewrite([22202(7),2690(4),11083(4),7616(4)])]. 22270 x * T(y,x * x) = T(y * x,x). [back_rewrite(1323),rewrite([22250(3),18809(3)]),flip(a)]. 22283 T(x * y,y) \ T(z,y) = T(y \ (x \ z),y). [back_rewrite(19570),rewrite([22270(3)])]. 22354 T(T(x * (y * y),y),T(x * y,y)) = x * (y * y). [back_rewrite(13735),rewrite([22270(6)])]. 22386 L(x,y / x,z) \ (z * y) = T(z * (y / x),z * y). [para(6694(a,1),23(a,2)),rewrite([72(7),18(4)])]. 22398 x \ (y * y) = (x \ y) * y. [para(6257(a,1),6694(a,1,2)),rewrite([19771(3),18718(6),4230(4),4209(5)])]. 22429 a(x * ((y \ x) * x),z,u) = a(x / y,x * (x * z),u). [back_rewrite(19178),rewrite([22398(2)])]. 22608 L(x,y * (z * y),z) = L(x,y,z * (y * z)). [para(13(a,1),16286(a,1,2,1)),rewrite([45(2),101(2),70(4),70(5),45(6),13(6)])]. 22726 T(x,y) / T(T(x,z),y) = K(z,T(x,y)). [para(29(a,1),16687(a,1,2))]. 22862 T(x,y) * K(x,y) = K(x,y) * T(x,y). [para(16712(a,1),63(a,1,2)),rewrite([14(5)]),flip(a)]. 22892 ((x * y) * K(y,z)) / T(y,z) = R(x,y,K(y,z)). [para(16716(a,1),22(a,1,2))]. 22893 x * (x * (K(x,y) * z)) = (x * T(x,y)) * z. [para(16716(a,1),37(a,1,1,2)),flip(a)]. 22906 L(K(x,y) * z,K(y,x),y) = T(y,x) \ (y * z). [para(16716(a,1),74(a,2,1)),rewrite([6144(2)])]. 22923 (x * (y * T(x,z))) \ (x * (y * (x * (K(x,z) * u)))) = L(u,K(x,z),x * (y * x)). [para(16716(a,1),132(a,1,1,2,2))]. 22925 x * ((y * x) * K(x,z)) = (x * y) * T(x,z). [para(16716(a,1),189(a,1,2)),flip(a)]. 22926 T(x,y) * (K(x,y) * z) = K(x,y) * (T(x,y) * z). [para(16716(a,1),189(a,2,2,1)),rewrite([16985(2)])]. 22931 T(x,y) * L(z,K(x,y),x) = x * (K(x,y) * z). [para(16716(a,1),72(a,1,1))]. 22947 R(x,K(x,y),T(x,y) \ z) = z / (K(x,y) * (T(x,y) \ z)). [para(16716(a,1),82(a,1,3,1)),rewrite([16716(7)])]. 22976 a(T(x,y),x * (x * z),u) = a(T(x,y),z,u). [para(16716(a,1),4636(a,2,1)),rewrite([16717(4),101(3),547(2),2508(4)]),flip(a)]. 22979 a(x * y,x,K(x,z)) = a(x,y,T(x,z)) \ 1. [para(16716(a,1),196(a,1,2,2,2)),rewrite([22925(4),2548(7)]),flip(a)]. 23000 (x * T(x,y)) * (K(x,y) * z) = T(x,y) * (T(x,y) * z). [back_rewrite(16984),rewrite([22893(6)])]. 23022 x \ (K(y,x) * (T(x,y) * z)) = L(z,T(x,y),K(y,x)). [para(16875(a,1),21(a,1,1))]. 23033 L(T(x,y) \ z,T(x,y),K(y,x)) = x \ (K(y,x) * z). [para(16875(a,1),74(a,2,1))]. 23108 T(x,y) \ (K(x,y) * (x * z)) = L(z,x,K(x,y)). [para(16985(a,1),21(a,1,1))]. 23144 (x * (y * (y * T(z,u)))) \ ((x * (y * (y * K(z,u)))) * z) = a(x,y * (y * K(z,u)),z). [para(16985(a,1),139(a,1,1,2,2,2))]. 23173 R(x,K(y,z),y) * T(y,z) = (x * K(y,z)) * y. [para(16985(a,1),84(a,1,2))]. 23380 T(x,T(y,x)) = T(x,y). [para(17771(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 23443 T(x,y * x) = T(x,y). [back_rewrite(2652),rewrite([23380(4)])]. 23494 a(x * y,x,z) = a(x,y * x,z). [para(128(a,1),19(a,1,2)),rewrite([196(7)])]. 23575 K(x,y) * (T(y,x) * (K(x,y) * z)) = (y * K(x,y)) * z. [para(16623(a,1),128(a,1,1,2)),rewrite([12349(2)]),flip(a)]. 23584 K(x,y) * (x * (K(x,y) * z)) = (K(x,y) * T(x,y)) * z. [para(16716(a,1),128(a,1,1,2)),flip(a)]. 23589 a(x,y * x,K(x,z)) = a(x,y,T(x,z)) \ 1. [back_rewrite(22979),rewrite([23494(3)])]. 23629 a(x \ y,z * (x \ y),x) = a(x \ y,z,T(y,x)) \ 1. [back_rewrite(19674),rewrite([23494(4)])]. 23643 (x * (y * (x * z))) \ (x * (y * (x * L(z,x,y)))) = a(x,y * x,L(z,x,y)). [back_rewrite(19660),rewrite([23494(11)])]. 23655 (x * (y * (z * x))) \ (x * (z * (x * T(y,z * x)))) = a(x,z * x,T(y,z * x)). [back_rewrite(19639),rewrite([23494(13)])]. 23662 a((x * y) / z,x,L(x \ z,x,x * y)) = a(x,y * x,L(x \ z,x,x * y)). [back_rewrite(18763),rewrite([23494(11)])]. 23663 a(x,y * x,T(z,x)) = a(x,y,z * x) \ 1. [back_rewrite(18724),rewrite([23494(3)])]. 23697 (x / y) * (y * z) = y * ((y \ x) * z). [para(136(a,1),15(a,1,2)),rewrite([15916(3)])]. 23711 (x * y) * (y * ((y \ z) * u)) = y * ((y \ x) * ((y * z) * u)). [para(136(a,1),104(a,1,2,2)),flip(a)]. 23717 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(136(a,1),74(a,2,1)),rewrite([16103(8),16485(7)])]. 23718 (x * y) \ ((x * z) * u) = (y \ x) * ((x \ z) * u). [para(136(a,1),74(a,2,2)),rewrite([4480(5)]),flip(a)]. 23735 x * ((x \ y) * ((x * y) * z)) = y * (x * (y * z)). [para(1091(a,1),136(a,1,2,2,1)),rewrite([3143(5),169(4),23711(5),101(7),128(8)])]. 23736 T(x,(x \ y) * z) = T(x,(x * y) * z). [para(136(a,1),1708(a,1,2)),rewrite([1708(7)]),flip(a)]. 23766 x * (((x \ y) * z) * x) = T((x * y) * z,x). [para(136(a,1),4209(a,1,1)),rewrite([101(7)]),flip(a)]. 23819 K((x \ y) * z,x) = K((x * y) * z,x). [para(136(a,1),16568(a,1,1)),rewrite([16568(7)]),flip(a)]. 23885 L(a(x / y,y,z),y * ((y \ x) * z),u) * ((u * (x * z)) \ (u * (y * ((y \ x) * z)))) = 1. [back_rewrite(20095),rewrite([23697(5),23697(11)])]. 23926 x * ((x \ (y \ z)) * T(y,z)) = L(z,y \ z,x). [back_rewrite(16509),rewrite([23697(5)])]. 23927 L(T(x,y),y \ x,z) = z * ((z \ (y \ x)) * y). [back_rewrite(16505),rewrite([23697(7)])]. 24002 x \ ((x * y) * z) = x * ((x \ y) * z). [back_rewrite(15916),rewrite([23697(6)])]. 24009 (x * ((x \ (y \ 1)) * ((y * z) * u))) \ (y * ((y \ z) * u)) = a(x,x / y,(y * z) * u). [back_rewrite(14038),rewrite([23697(10)])]. 24016 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = L(L(R(x,v5 \ 1,v6),u,w),y,z). [back_rewrite(12077),rewrite([23697(12),4180(12),33(11),33(10)])]. 24021 x * ((x \ y) * (y \ z)) = L(z,y \ 1,x). [back_rewrite(10367),rewrite([23697(4)])]. 24030 a(x,y \ 1,y * z) = a(x,y,y \ z). [back_rewrite(7628),rewrite([23697(4),192(5)]),flip(a)]. 24034 T(x * ((x \ y) * z),y * z) = a(y / x,x,z) \ (y * z). [back_rewrite(4206),rewrite([23697(3)])]. 24035 x * ((x \ y) * ((y / x) * z)) = y * (y * (x \ z)). [back_rewrite(3286),rewrite([23697(5)])]. 24043 R(x,y \ 1,y * z) = R(x,y,y \ z). [back_rewrite(2760),rewrite([23697(3),191(4)]),flip(a)]. 24057 a(x / y,y,z) = a(y,y * x,z). [back_rewrite(60),rewrite([23697(3),4032(5)]),flip(a)]. 24066 (x * y) * ((x * y) * z) = x * (y * (x * (y * z))). [back_rewrite(5783),rewrite([23711(5),23735(5)]),flip(a)]. 24075 (T(x,y) \ (z \ (z \ u))) * ((((u \ z) * z) * K(x,y)) * x) = a(u,z * (z * K(x,y)),x). [back_rewrite(23144),rewrite([23718(10),5162(4),15452(8)])]. 24100 L(x \ y,x,x * z) = T(z,x) \ ((x \ z) * y). [back_rewrite(18689),rewrite([23718(5),6955(5)]),flip(a)]. 24114 a(x \ 1,y,z * (z * u)) = a(x,y * (z * z),u). [back_rewrite(13702),rewrite([23718(9),22250(7),2040(8),6068(9)])]. 24163 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,y * (y * (x / u)),u). [back_rewrite(3753),rewrite([23718(9),5162(3),15452(7)])]. 24164 (x \ (y \ (y \ z))) * (u * ((u \ ((z \ y) * y)) * x)) = a(z,y * (y * u),u \ x). [back_rewrite(3752),rewrite([23718(9),5162(3),15452(6),169(8)])]. 24189 a(x \ 1,y,z) = a(x,y,z). [back_rewrite(19),rewrite([23718(5),6068(5)])]. 24229 (x * (a(y \ x,z,z \ T(y,x)) * u)) / u = L(x,y \ x,z). [back_rewrite(5841),rewrite([23926(5),33(4),480(2)]),flip(a)]. 24261 (x * (y / L(L(z,u,w),v5,v6))) \ (x * y) = L(L(R(z,y \ 1,x),v5,v6),u,w). [back_rewrite(12076),rewrite([24016(6)]),flip(a)]. 24264 R(x,x \ y,z) = L(x,y \ 1,z). [back_rewrite(8379),rewrite([24021(6)])]. 24267 (x * (a(y,z,z \ (y \ x)) * u)) / u = L(x,y \ 1,z). [back_rewrite(5816),rewrite([24021(4),33(5),480(2)]),flip(a)]. 24268 R(x,y,y \ ((x \ y) * z)) = L(x,y \ 1,z). [back_rewrite(4470),rewrite([24021(8)])]. 24279 a(x / (y * y),y,y * z) = a(x,y,y \ z). [back_rewrite(16096),rewrite([24030(8)])]. 24285 a(x,x * y,z) \ 1 = a(y,x,x \ z). [back_rewrite(7607),rewrite([24057(2),24030(8)])]. 24305 T(x * ((x \ y) * z),y * z) = a(x,x * y,z) \ (y * z). [back_rewrite(24034),rewrite([24057(7)])]. 24350 L(a(x,x * y,z),x * ((x \ y) * z),u) * ((u * (y * z)) \ (u * (x * ((x \ y) * z)))) = 1. [back_rewrite(23885),rewrite([24057(2)])]. 24428 ((x / (y * z)) * (y * (z * y))) \ (x * y) = a(y * z,(y * z) * x,y). [back_rewrite(18703),rewrite([24057(11)])]. 24477 ((x / y) * (z * y)) \ (x * T(z,y)) = a(y,y * x,T(z,y)). [back_rewrite(1958),rewrite([24057(9)])]. 24479 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(z,y * (y * (z * x)),u). [back_rewrite(1952),rewrite([24057(15),37(14),2508(15)])]. 24531 (x * (y * (y / x))) * z = x * (y * (y * (x \ z))). [back_rewrite(10140),rewrite([24066(6),23697(5),24035(5)]),flip(a)]. 24558 (x * (y * (x * y))) * z = x * (y * (x * (y * z))). [back_rewrite(426),rewrite([24066(8)])]. 24566 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(z,y,T(x,y)). [back_rewrite(6149),rewrite([24189(10)])]. 24596 a(x,y * (z * z),u) = a(x,y,z * (z * u)). [back_rewrite(24114),rewrite([24189(5)]),flip(a)]. 24624 ((x * y) \ z) * ((z \ x) * y) = a(z,x,y). [back_rewrite(6068),rewrite([24189(8)])]. 24638 (x * y) / ((z \ x) * y) = L(z,x \ 1,y). [back_rewrite(5665),rewrite([24268(4)]),flip(a)]. 24644 x / (T(y,z) * (u * (y * (u \ (T(y,z) \ x))))) = (u / y) / u. [back_rewrite(19502),rewrite([24531(9),23697(10),1829(3),10809(9),13(3),89(2)])]. 24645 (x / y) / x = x / (x * y). [back_rewrite(19496),rewrite([24531(9),3169(10),1091(3),10809(9),13(3),89(2),24644(8)])]. 24764 x * (T(y / (y * x),K(x,y)) * (x * z)) = T(x,y) * z. [back_rewrite(17974),rewrite([24645(2)])]. 24890 ((K(x,y) * z) \ u) / T(K(y,x),u) = z \ u. [para(19486(a,1),1829(a,1,2)),rewrite([4407(9),4408(9),1014(9)]),flip(a)]. 24897 x * ((T(K(y,z),u) * (u \ (K(z,y) * x))) \ T(w,x * u)) = x \ (w * (x * u)). [para(19486(a,1),3218(a,1,2,2,2,2)),rewrite([19486(17)])]. 24915 x / (K(y,z) * (y \ (K(z,y) * x))) = y. [para(12307(a,1),19486(a,1,2,1))]. 25093 (x \ y) / T(z * (z / x),y) = z \ (z \ y). [para(12372(a,1),5364(a,1,2,2)),rewrite([1014(4),7616(2),1014(4),12372(9)])]. 25357 a(x,y * (x * y),z) = 1. [para(14(a,1),5524(a,1,2,1)),rewrite([45(3),70(3),4578(2),1708(4),14882(4),90(2)])]. 25410 a(x * (y * x),y,z) = 1. [back_rewrite(3735),rewrite([25357(6)])]. 25524 (x * ((x * y) * z)) * ((x * (y * z)) \ T(y,x)) = y * x. [para(22239(a,1),17(a,1,1)),rewrite([4155(8)])]. 26340 (x * (y / x)) * K(y,x) = y. [para(17822(a,1),63(a,1,2)),rewrite([18(6)])]. 26495 K(x,y) * T(x,y) = T(T(x,y),y). [para(17910(a,1),16716(a,1,2)),rewrite([22862(3)])]. 26526 K(x,y) * (x * (K(x,y) * z)) = T(T(x,y),y) * z. [back_rewrite(23584),rewrite([26495(8)])]. 26642 x * K(y,x) = T(x,x / y). [para(17914(a,1),16716(a,1,2))]. 26699 K(x,y) * (T(y,x) * (K(x,y) * z)) = T(y,y / x) * z. [back_rewrite(23575),rewrite([26642(8)])]. 26745 K(x,y) * y = T(y,y / x). [back_rewrite(12349),rewrite([26642(4)])]. 26764 T(x,y / x) = T(x,y). [para(17924(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 26839 T(x,L(x,y,z)) = x. [para(160(a,1),16487(a,1,1)),rewrite([16487(2)]),flip(a)]. 26897 x / T(y * (y * (x / z)),z) = y \ (y \ z). [para(1925(a,1),21(a,1,2)),rewrite([3436(2),1607(8)]),flip(a)]. 26903 L(x,y,y \ z) = L(x,z,y). [para(1925(a,1),132(a,1,1,2)),rewrite([26897(6),7550(5),16(4),21(4),26897(6),2507(6),16465(4)]),flip(a)]. 26952 T(x,y) \ ((y \ x) * z) = L(y \ z,x,y). [back_rewrite(7981),rewrite([26903(3)]),flip(a)]. 26963 L(x \ y,x,x * z) = L(x \ y,z,x). [back_rewrite(24100),rewrite([26952(7)])]. 26968 a((x \ y) / z,x,L(x \ z,y,x)) = a(x \ y,x,L(x \ z,y,x)). [back_rewrite(11726),rewrite([26952(6),26952(10)])]. 26973 a((x * y) / z,x,L(x \ z,y,x)) = a(x,y * x,L(x \ z,y,x)). [back_rewrite(23662),rewrite([26963(5),26963(9)])]. 27047 x * ((x \ y) * T(z,x)) = (y / x) * (z * x). [para(165(a,1),10393(a,1,2,1,1)),rewrite([6564(3),3143(6),24002(4),6564(7),1014(7)])]. 27119 L(x,y * T(y,z),u * ((z \ y) * (z \ y))) = x. [back_rewrite(15120),rewrite([27047(4),3169(3),4505(2)])]. 27447 ((x * (y * (x \ y))) / (x * (y / x))) * K(x,y) = x * (y / x). [para(20620(a,1),5560(a,1,2)),rewrite([18023(3),4407(10),6144(9),14(9),10229(8),20620(17),88(12)])]. 27454 (x * (y * (y * (y * x)))) \ y = y \ ((y * x) \ (x \ 1)). [para(5600(a,1),17(a,1,1)),rewrite([989(5),4407(5),6567(5)]),flip(a)]. 27459 L(x,y,z * (y * z)) = x. [para(5600(a,1),21(a,1,1)),rewrite([27454(6),24558(10),6600(11),45(5),27454(11),3050(12)])]. 27549 L(x,y * (z * y),z) = x. [back_rewrite(22608),rewrite([27459(6)])]. 27556 (x * (y * (x * y))) \ (x * z) = (y * (x * y)) \ z. [back_rewrite(3118),rewrite([27459(6)]),flip(a)]. 27573 x * (y * (x * (z / (z * (x * (y * (x * z))))))) = z \ 1. [para(5674(a,1),15(a,1,2)),flip(a)]. 27619 (((x * y) * z) * x) * (((z * x) \ ((x * y) \ z)) / z) = 1. [para(5674(a,1),193(a,2)),rewrite([27573(23),4407(9),193(12),169(11),4458(7),1014(10)])]. 27689 (x * (a(x / (y * z),y,z) * u)) / u = R(x,z \ (y \ 1),y). [para(15(a,1),5817(a,1,1,2,1,3)),rewrite([4407(9)])]. 27706 R(x,T(y,x) \ 1,z) = L(x,y \ x,z). [para(2711(a,1),5817(a,1,1,2,1,1)),rewrite([24229(7)]),flip(a)]. 27732 R(((x / (y * z)) * y) * z,x,x \ u) = R(x,z \ (y \ 1),y). [back_rewrite(437),rewrite([27689(12)])]. 27871 L(x,L(x,y,z),u) = x. [para(16487(a,1),6024(a,1,1)),rewrite([16487(4)])]. 28029 L(x,((y * z) \ (y * u)) / x,y * z) = ((y * z) * (L(z \ u,z,y) / x)) \ (y * u). [para(74(a,1),6697(a,1,2,1)),rewrite([16(13)])]. 28379 L(x,(y \ K(z,u)) / x,K(u,z) * y) = (x * (K(u,z) * y)) * (y \ K(z,u)). [para(4993(a,1),28029(a,1,2,1,2)),rewrite([4407(4),6144(3),14(3),8302(12),4993(15),4407(14),4407(13),6144(12),14(12),10229(12),4155(9),6144(8)])]. 28464 T(T(x,y),L(x,z,u)) = T(x,y). [para(26839(a,1),29(a,1,1)),flip(a)]. 28473 L(x,y,z) * x = x * L(x,y,z). [para(26839(a,1),90(a,1,2))]. 28505 x / L(x,y,z) = L(x,y,z) \ x. [para(26839(a,1),7616(a,1,1))]. 28511 T(x,L(x,y,z) \ x) = x. [para(26839(a,1),7769(a,1,1))]. 28851 T(L(x,y,z) * (u / x),L(x,y,z) * u) = T(L(x,y,z) * (u / x),x). [para(18461(a,1),6694(a,1,2)),flip(a)]. 28965 T(x,x / y) = T(x,y \ x). [para(19567(a,1),16716(a,1,2)),rewrite([26642(2)])]. 28991 K(x,y) * y = T(y,x \ y). [back_rewrite(26745),rewrite([28965(4)])]. 29035 K(x,y) * (T(y,x) * (K(x,y) * z)) = T(y,x \ y) * z. [back_rewrite(26699),rewrite([28965(8)])]. 29216 T(x \ y,y) * T(x,y) = T(y,x). [para(23380(a,1),4505(a,2)),rewrite([4278(2)])]. 29325 (x \ y) * (y / x) = y * (x \ (x \ y)). [para(23443(a,1),3218(a,1,2,2)),rewrite([2643(2),3169(7),15(8)]),flip(a)]. 29339 T(x,y) / (y * x) = (y * x) \ x. [para(23443(a,1),7616(a,1,1))]. 29418 (x / y) * (y \ x) = x * (y \ (y \ x)). [back_rewrite(2903),rewrite([29325(6)])]. 29584 (T(x,y) * z) / a(y \ x,y,z) = (y \ x) * (y * z). [para(4505(a,1),162(a,1,1,1))]. 30202 ((T(x,y) * z) \ T(T(x,y),y)) * (x * z) = T(T(x,z),y). [para(16875(a,1),6152(a,1,2,1)),rewrite([6144(5),26495(5),16875(11),2644(10)])]. 30410 (x \ (T(y,x) \ 1)) * T(z,y \ x) = (x \ (x \ z)) * (y \ x). [para(2711(a,1),6185(a,1,2,2)),rewrite([2711(11)])]. 30432 (x \ (x \ y)) / z = x \ (x \ (y / z)). [para(3691(a,1),6185(a,1,2,2)),rewrite([4407(3),14124(8),6095(4),3691(7),1014(8)]),flip(a)]. 30455 x \ (y * (x / z)) = T(y,x) / z. [para(6185(a,1),3683(a,1,2)),rewrite([1840(5),4505(2)]),flip(a)]. 30508 x * (T(y,x) / z) = y * (x / z). [para(6185(a,1),136(a,1,2,2)),rewrite([1840(5),4505(2),1014(6),90(7)])]. 30512 (x \ (x \ y)) * T(z,y) = (x \ (x \ z)) * y. [para(19486(a,1),6185(a,1,2,2)),rewrite([4407(8),4408(8),1014(8),24890(6),19486(13)])]. 30627 x * ((y * x) \ T(z,x / y)) = T(z,x) / y. [back_rewrite(7622),rewrite([30455(8)])]. 30654 L(x,T(y,z) / x,y \ z) = (y * (z / x)) \ (y * z). [back_rewrite(10748),rewrite([30508(7)])]. 30703 T(T(x,y),y) = T(x,y * y). [para(6188(a,1),45(a,1)),rewrite([48(4),18809(4),4505(2),48(4)])]. 30840 (T(K(x,y),z) * (z \ (K(y,x) * u))) \ T(w,u * z) = (u \ (u \ w)) * (u * z). [para(19486(a,1),6188(a,1,2,2,2)),rewrite([19486(18)])]. 30881 ((T(x,y) * z) \ T(x,y * y)) * (x * z) = T(T(x,z),y). [back_rewrite(30202),rewrite([30703(4)])]. 30944 K(x,y) * (x * (K(x,y) * z)) = T(x,y * y) * z. [back_rewrite(26526),rewrite([30703(7)])]. 30953 K(x,y) * T(x,y) = T(x,y * y). [back_rewrite(26495),rewrite([30703(5)])]. 32180 (x * L(y,z,u)) * y = x * (y * L(y,z,u)). [para(27871(a,1),72(a,1,2)),rewrite([28473(5)])]. 32743 R(x * y,y * x,z) = x * y. [para(4209(a,1),493(a,1,1)),rewrite([4209(5)])]. 32749 (x * T(x,y)) * z = x * (T(x,y) * z). [para(493(a,1),84(a,1,1)),rewrite([21062(3),547(5)]),flip(a)]. 32816 R(x * y,K(y,x),z) = x * y. [back_rewrite(19707),rewrite([32743(7)]),flip(a)]. 32894 x * (K(x,y) * (T(x,y) * z)) = T(x,y) * (T(x,y) * z). [back_rewrite(23000),rewrite([32749(5),22926(4)])]. 33039 L(T(x \ 1,y),x,z) = T(x \ 1,y). [para(1077(a,1),30(a,1,1)),flip(a)]. 33049 a(x,y,T(x,z)) = 1. [hyper(25,a,1685,a)]. 33075 L(x,y,T(x,z)) = x. [para(7769(a,1),1685(a,1,1)),rewrite([7769(5)])]. 33091 a(x,y * x,K(x,z)) = 1. [back_rewrite(23589),rewrite([33049(5),46(6)])]. 33119 a(x / y,z,y \ x) = 1. [para(92(a,1),33049(a,1,3))]. 33180 (T(x,y) * z) * x = T(x,y) * (z * x). [para(33075(a,1),72(a,1,2))]. 33181 (T(x,y) * (z * x)) \ (x * (T(x,y) * z)) = K(x,T(x,y) * z). [para(33075(a,1),2934(a,1,2,1)),rewrite([33075(9)])]. 33249 R(x,y * z,a(x,y,z)) \ ((x * y) * z) = (y * z) * a(x,y,z). [para(54(a,1),166(a,1,2))]. 33258 (x * y) \ ((y * x) * z) = K(y,x) * z. [para(63(a,1),166(a,1,2,1)),rewrite([32816(3)])]. 33300 R(x,K(x,y),z) \ (T(x,y) * z) = K(x,y) * z. [para(16716(a,1),166(a,1,2,1))]. 33324 T(x,y) \ (x * (T(x,y) * z)) = x * z. [para(493(a,1),166(a,1,1)),rewrite([547(3),32749(4)])]. 33334 L(x,K(y,z),z * y) = x. [back_rewrite(2857),rewrite([33258(6),8296(4)]),flip(a)]. 33346 (x * y) * (K(y,x) * z) = (y * x) * z. [back_rewrite(5116),rewrite([33334(4)]),flip(a)]. 33415 x * (y * (y * (x * T(z,y * x)))) = (x * y) * (z * (y * x)). [back_rewrite(20509),rewrite([33346(6)]),flip(a)]. 33450 (x \ (y / x)) * (x * z) = x \ (y * z). [para(18(a,1),168(a,1,2,1)),flip(a)]. 33472 (x \ (y \ 1)) * (x * z) = x \ ((y \ x) * z). [para(3143(a,1),168(a,1,2,1)),flip(a)]. 33476 (x \ (x \ y)) * (x * z) = x \ (T(y,x) * z). [para(4505(a,1),168(a,1,2,1)),flip(a)]. 33497 K(x,y) * (x * z) = T(x,y) * z. [para(16343(a,1),168(a,2,1)),rewrite([547(2),32749(3),15(4)]),flip(a)]. 33507 K(x,y) * (T(y,x) * z) = y * z. [para(16711(a,1),168(a,2,1)),rewrite([32749(4),33324(5)]),flip(a)]. 33511 (x \ K(x,y)) * (x * z) = x \ (T(x,y) * z). [para(16985(a,1),168(a,1,2,1)),flip(a)]. 33545 R(x,x \ (y * z),u) = L(x,z \ (y \ 1),u). [back_rewrite(11625),rewrite([33450(4),33450(9),24638(9),4407(6)])]. 33575 R(x,x \ ((y \ x) * z),u) = L(x,z \ (x \ y),u). [back_rewrite(11645),rewrite([33472(8),24638(8),4407(4),4408(3),14(3),33472(8)]),flip(a)]. 33590 (T(K(x,y),z) * (z \ (K(y,x) * u))) \ T(w,u * z) = u \ (T(w,u) * z). [back_rewrite(30840),rewrite([33476(13)])]. 33664 L(x,y * (z * u),z) = L(x,z,T(y,z) * u). [back_rewrite(9195),rewrite([33476(6),16348(8)]),flip(a)]. 33705 K(x,y) * (T(x,y) * z) = T(x,y * y) * z. [back_rewrite(30944),rewrite([33497(5),22926(4)])]. 33734 L(x,y,K(y,z)) = x. [back_rewrite(23108),rewrite([33497(4),15(4)]),flip(a)]. 33781 T(x,y \ x) * z = x * (K(y,x) * z). [back_rewrite(29035),rewrite([33507(6)]),flip(a)]. 33796 L(x,T(y,z),K(z,y)) = x. [back_rewrite(23022),rewrite([33507(4),15(2)]),flip(a)]. 33957 x \ (y * (x * z)) = T(y,x) * z. [back_rewrite(24897),rewrite([33590(9),16(4)]),flip(a)]. 33969 L(x,y,z * T(z,y)) = x. [back_rewrite(27549),rewrite([33664(3),547(2)])]. 33981 L(a(x,y,z),y,T(x,y) * z) = a(y,x,y * z). [back_rewrite(2971),rewrite([33664(4)])]. 33992 T(x,y) * (T(x,y) * z) = x * (T(x,y * y) * z). [back_rewrite(32894),rewrite([33705(4)]),flip(a)]. 34091 x \ (K(y,x) * z) = T(x,y) \ z. [back_rewrite(23033),rewrite([33796(5)]),flip(a)]. 34275 L(T(x,y * z),y,z) = T(T(x,y),z). [back_rewrite(16484),rewrite([33957(3),23(3)]),flip(a)]. 34415 x / (K(y,z) * (T(y,z) \ x)) = y. [back_rewrite(24915),rewrite([34091(4)])]. 34554 R(x,K(x,y),T(x,y) \ z) = x. [back_rewrite(22947),rewrite([34415(9)])]. 34768 (x * y) \ T(z,y / x) = y \ (T(z,y) / x). [para(30627(a,1),15(a,1,2)),flip(a)]. 34798 x * (T(y * x,x) \ T(z,y \ x)) = T(z,x) / T(y,x). [para(2711(a,1),30627(a,1,2,2,2)),rewrite([7775(2)])]. 34823 (x * y) \ y = y \ (x \ y). [para(12386(a,1),30627(a,1,2,2)),rewrite([101(2),9050(4),29339(5)]),flip(a)]. 34860 R(x,y,y \ (T(z,y) / x)) = L(x,y / x,z). [back_rewrite(21510),rewrite([34768(4)])]. 35223 K(x,y) * (T(x,y) \ z) = x \ z. [para(16(a,1),33300(a,1,2)),rewrite([34554(4)]),flip(a)]. 35247 (K(x,y) * z) * R(x,K(x,y),z) = T(T(x,y) * z,R(x,K(x,y),z)). [para(33300(a,1),4505(a,1,1))]. 35274 K(R(x,K(x,y),z),T(x,y) * z) = K(R(x,K(x,y),z),K(x,y) * z). [para(33300(a,1),16710(a,1,2)),flip(a)]. 35287 K(R(x,K(x,y),z),K(x,y) * z) = K(T(x,y) * z,K(x,y) * z). [para(33300(a,1),19567(a,1,2)),rewrite([35274(10)]),flip(a)]. 35301 K(R(x,K(x,y),z),T(x,y) * z) = K(T(x,y) * z,K(x,y) * z). [back_rewrite(35274),rewrite([35287(10)])]. 35536 L(a(x,y,T(z,y)),x * (z * y),(x * y) * T(z,y)) = a(x,y,T(z,y)). [hyper(24,a,6438,a)]. 35645 (x \ (y \ 1)) * z = (y * x) \ z. [para(13(a,1),6953(a,1,1,2,1)),rewrite([46(3),45(8),45(7)])]. 35648 (x \ (y \ (z \ 1))) * u = ((z * y) * x) \ u. [para(16(a,1),6953(a,1,1,2,1)),rewrite([23717(10),16(9)])]. 35675 (x * ((y * z) \ (y \ 1))) * u = (x / z) * (y \ (y \ u)). [para(1014(a,1),6953(a,2,1)),rewrite([4408(7),45(2),10229(10)])]. 35683 x * (T(y,x) \ (x \ z)) = y \ z. [para(1091(a,1),6953(a,1,1)),rewrite([3143(3),35645(6),5162(4),16(5),4408(6),4408(3),169(6),6968(5)]),flip(a)]. 35698 (x \ ((y \ z) * z)) * u = (((y * x) \ z) * z) * u. [para(3143(a,1),6953(a,1,1,2,1)),rewrite([4408(5),45(3),14(3),4408(2),4408(10),45(9),4408(9),45(7),15452(8)])]. 35803 (x * y) \ (y * z) = y \ ((x \ y) * z). [back_rewrite(33472),rewrite([35645(5)])]. 35829 T(x * y,y) \ T(z,x \ y) = (y \ (y \ z)) * (x \ y). [back_rewrite(30410),rewrite([35645(7),7775(2)])]. 35865 a(x,x / y,(y * z) * u) = a(x,x * y,(y \ z) * u). [back_rewrite(24009),rewrite([35645(6),23718(4),4032(9)]),flip(a)]. 35905 R(x,x \ (y \ 1),y * z) = z * ((y * z) \ (y * x)). [back_rewrite(11253),rewrite([35645(10),4155(9)])]. 35922 R(x,x \ (y \ 1),z) = L(x,y,z \ 1). [back_rewrite(3646),rewrite([35645(9),4155(8),6070(8)])]. 35944 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,y * (y * u),u \ x). [back_rewrite(24164),rewrite([35698(7)])]. 35945 (x * ((y * x) \ z)) / z = R(y \ 1,x,x \ z). [back_rewrite(21734),rewrite([35698(6),169(6),6968(5),35683(5)])]. 35978 T(x,y) / T(z,y) = y \ (x * (z \ y)). [back_rewrite(34798),rewrite([35829(5),7550(5)]),flip(a)]. 36021 x * ((y * x) \ (y * z)) = L(z,y,x \ (y \ 1)). [back_rewrite(35905),rewrite([35922(5),4407(3)]),flip(a)]. 36043 x / R(y,z,(y * z) \ u) = x * R(y \ 1,z,z \ u). [back_rewrite(12931),rewrite([35945(8)])]. 36066 R(x,y,(x * y) \ z) \ 1 = R(x \ 1,y,y \ z). [back_rewrite(10235),rewrite([35945(9)])]. 36081 x \ (y * (T(y,z) \ x)) = K(z,T(y,x)). [back_rewrite(22726),rewrite([35978(4)])]. 36084 x \ (T(y,z) * (y \ x)) = K(T(y,x),z). [back_rewrite(20939),rewrite([35978(4)])]. 36652 (x * y) * T(x * y,y) = x * (x * (y * y)). [para(100(a,1),3184(a,1,2,2)),rewrite([18809(3),540(4),14(2),18809(6),547(7)]),flip(a)]. 37107 L(x,K(y,z),y) = x. [para(33734(a,1),16487(a,1,1))]. 37125 x * (K(x,y) * z) = T(x,y) * z. [back_rewrite(22931),rewrite([37107(3)]),flip(a)]. 37126 T(x,y) \ (x * z) = K(y,x) * z. [back_rewrite(22906),rewrite([37107(4)]),flip(a)]. 37146 L(L(x,T(y,z),u),u * T(y,z),y) = L(x,K(y,z),y * (u * y)). [back_rewrite(22923),rewrite([37125(6),638(8)])]. 37216 L(x,K(y,z),z) = x. [para(17781(a,1),37107(a,1,2))]. 37218 L(x,K(y,z),T(y,z)) = x. [para(17910(a,1),37107(a,1,2))]. 37224 T(x,y) * (x \ z) = K(x,y) * z. [back_rewrite(21504),rewrite([37216(4)]),flip(a)]. 37229 x * (T(x,y) \ z) = K(y,x) * z. [back_rewrite(21505),rewrite([37218(5)]),flip(a)]. 37231 T(K(x,y),z) = K(T(x,z),y). [back_rewrite(36084),rewrite([37224(3),23(3)])]. 37242 K(T(x,y),z) = K(x,T(z,y)). [back_rewrite(36081),rewrite([37229(3),23(3),37231(2)])]. 37402 ((K(x,y) * z) \ u) * K(x,T(y,u)) = z \ u. [back_rewrite(24890),rewrite([37231(5),37242(5),5005(6),37242(5)])]. 37429 T(K(x,y),z) = K(x,T(y,z)). [back_rewrite(37231),rewrite([37242(4)])]. 38196 L(x,K(y,z),T(z,y)) = x. [para(17771(a,1),37216(a,1,2))]. 38207 T(x,y) * (K(y,x) * z) = x * z. [back_rewrite(21070),rewrite([38196(3)]),flip(a)]. 38208 x \ (T(x,y) * z) = K(x,y) * z. [back_rewrite(21045),rewrite([38196(5)]),flip(a)]. 38223 (x \ K(x,y)) * (x * z) = K(x,y) * z. [back_rewrite(33511),rewrite([38208(7)])]. 38305 x * ((x \ (y / x)) * z) = y * (x \ z). [para(18(a,1),169(a,1,1)),flip(a)]. 38314 x * (x * (y * ((y \ (x \ (x \ z))) * u))) = y * ((y \ z) * u). [para(37(a,1),169(a,2)),rewrite([5162(6),21713(7),5162(6)]),flip(a)]. 38342 (x \ y) * (y \ z) = y * ((x * y) \ z). [para(3143(a,1),169(a,1,1)),rewrite([35645(7)])]. 38356 T(x,y) * (y \ z) = y \ (x * z). [para(4505(a,1),169(a,1,1)),rewrite([7550(7)])]. 38365 (x * y) * T(y \ z,y) = (x / y) * (z * y). [para(7967(a,1),169(a,1,2)),rewrite([27047(8)])]. 38393 K(x,y) * (T(y,x * x) * z) = T(y,x) * z. [para(16623(a,1),169(a,1,1)),rewrite([6144(2),37125(3),6144(6),30953(6)]),flip(a)]. 38402 x * (y * (x * ((y * x) \ z))) = (y * x) * (T(y,x) \ z). [para(169(a,1),128(a,1)),rewrite([34823(3),6968(4)]),flip(a)]. 38445 (x * (y * (y * z))) * (z \ u) = z * ((z \ x) * (y * (y * u))). [back_rewrite(5200),rewrite([38314(9)]),flip(a)]. 38475 x * (y * ((x * y) \ z)) = L(z,y \ 1,x). [back_rewrite(24021),rewrite([38342(3)])]. 38476 R(x,y * z,y * ((z * y) \ (y \ u))) = R(x,y \ z,(z \ y) * u). [back_rewrite(21705),rewrite([38342(5)])]. 38485 R(x,x \ y,y \ z) = z / (y * ((x * y) \ z)). [back_rewrite(8328),rewrite([38342(6)])]. 38488 L(x,y,z \ (y \ 1)) = L(x,y,z \ 1). [back_rewrite(6070),rewrite([38342(4),36021(4)])]. 38503 L((x \ y) * z,y \ x,x) = x \ (y * z). [back_rewrite(21472),rewrite([38356(7)])]. 38534 R(x,y * (y * z),z \ u) = R(x,z,((z \ y) * y) * u). [back_rewrite(340),rewrite([38445(5),191(8),15452(3)]),flip(a)]. 38535 (x * y) * (T(x,y) \ z) = y * L(z,y \ 1,x). [back_rewrite(38402),rewrite([38475(4)]),flip(a)]. 38568 x * a(y,z,z \ (y \ x)) = L(x,y,z \ 1). [back_rewrite(9085),rewrite([38475(10),4407(7),16465(8)])]. 38590 x * ((y * x) \ (y * z)) = L(z,y,x \ 1). [back_rewrite(36021),rewrite([38488(8)])]. 38623 L(L(R(x,y,z),u,w),v5,x \ 1) = L(R(x,y,z),u,w). [back_rewrite(6793),rewrite([38488(6)])]. 38642 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(21715),rewrite([38534(9)]),flip(a)]. 38643 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,z,y)). [back_rewrite(21708),rewrite([38534(10)])]. 38644 R(x,y,((y \ z) * z) * ((z \ (z \ y)) * u)) = R(x,y,u). [back_rewrite(21704),rewrite([38534(7)])]. 38658 T(x,y) * (T(x \ y,y) * z) = y * L(z,y \ 1,x). [back_rewrite(15409),rewrite([38535(9)])]. 38713 R(x,K(x,y),z) = x. [para(16985(a,1),170(a,1,1,1)),rewrite([38223(6),18422(5)])]. 38747 K(T(x,y) * z,K(x,y) * z) = K(x,T(x,y) * z). [back_rewrite(35301),rewrite([38713(2)]),flip(a)]. 38752 K(x,T(x,y) * z) = K(x,K(x,y) * z). [back_rewrite(35287),rewrite([38713(2),38747(8)]),flip(a)]. 38770 (K(x,y) * z) * x = T(T(x,y) * z,x). [back_rewrite(35247),rewrite([38713(4),38713(7)])]. 38815 (T(x,y) * (z * x)) \ (x * (T(x,y) * z)) = K(x,K(x,y) * z). [back_rewrite(33181),rewrite([38752(10)])]. 39396 a(x / y,y * (y * z),u) = a(x * y,z,u). [para(33450(a,1),4636(a,1,1,2)),rewrite([23(2),90(2),16(5)]),flip(a)]. 39505 (x * y) \ (x \ 1) = y \ (x \ (x \ 1)). [para(1607(a,1),6591(a,1,1)),flip(a)]. 39506 (x * y) \ (y \ 1) = y \ (x \ (y \ 1)). [para(1667(a,1),6591(a,1,1)),flip(a)]. 39650 (x * (y \ (z \ (z \ 1)))) * u = (x / y) * (z \ (z \ u)). [back_rewrite(35675),rewrite([39505(4)])]. 39699 x / (y * (y * (z * x))) = z \ (y \ (y \ 1)). [back_rewrite(4420),rewrite([39505(8)])]. 39792 x / (y * (z * (y * x))) = y \ (z \ (y \ 1)). [back_rewrite(4421),rewrite([39506(8)])]. 41620 T(x \ 1,y) * z = T(x,y) \ z. [para(104(a,1),11803(a,1,1)),rewrite([101(2),128(3),15(5),15(5),27556(7),15452(5),1091(3),4407(3),4505(4),1708(6),15(8),33664(9),547(8),33969(9)])]. 41919 x \ ((y \ z) * z) = ((y * x) \ z) * z. [para(2748(a,1),6591(a,1,1)),rewrite([4408(5),4408(3),45(2),14(3),22398(2),4408(9),4408(7),45(6),14(7),22398(6)])]. 42192 (x * (y * z)) \ (x * (u * ((u \ y) * z))) = L(a(y,u,u \ z),y * z,x). [para(192(a,1),74(a,1,1)),flip(a)]. 42198 a(x,x * y,(x * y) \ z) = a(x,y,y \ z). [para(1091(a,1),192(a,1,2,2,1)),rewrite([3143(5),169(4),192(5)]),flip(a)]. 42212 a(x,x * y,z) \ (y * z) = a(y,x,x \ z) * (y * z). [para(192(a,1),4505(a,1,1)),rewrite([24305(9)]),flip(a)]. 42284 L(a(x,x * y,z),x * ((x \ y) * z),u) * L(a(y,x,x \ z),y * z,u) = 1. [back_rewrite(24350),rewrite([42192(13)])]. 42295 T(x * ((x \ y) * z),a(x,x * y,z)) = a(y,x,x \ z) * (y * z). [back_rewrite(4031),rewrite([42212(10)])]. 42314 R(x * y,x,x \ T(z,y)) = (x * (z * y)) / T(z,y). [para(90(a,1),198(a,2,1,2))]. 42356 R(x * (y \ z),x,x \ y) = (x * T(z,y)) / y. [para(4505(a,1),198(a,2,1,2))]. 42387 R(x * (y * z),x,x \ y) = (x * (y * (z * y))) / y. [para(101(a,1),198(a,2,1,2))]. 42416 K(R(x * y,x,x \ z),z) = K(x * (y * z),z). [para(198(a,2),17822(a,1,1))]. 42429 T(x,R(y * z,y,y \ x)) = T(x,y * (z * x)). [para(198(a,2),26764(a,1,2))]. 42829 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(16(a,1),7353(a,1,2,2)),rewrite([16(6)])]. 42834 T(R(x,y,z) \ x,x) * (R(x,y,z) * u) = L(x * u,x,R(x,y,z)). [para(7353(a,1),21(a,1,2)),rewrite([42829(5),15452(7),34823(3),4505(4)])]. 42930 a(x \ (y / x),x,z) = a(x,y,z). [para(15(a,1),7682(a,1,2)),rewrite([1091(2),1091(4),1014(5),3143(4),1091(5),24189(6)])]. 42940 a(x * (y \ z),z \ y,u) = a(y \ z,(z \ y) * x,u). [para(4505(a,1),7682(a,1,1,2)),rewrite([90(4),4408(7)])]. 42971 a(x \ y,(y \ x) * z,T(y,x)) = ((z * (x \ y)) * x) \ (z * T(y,x)). [back_rewrite(4335),rewrite([42940(5)])]. 43418 ((x * (y \ z)) * y) * a(y \ z,(z \ y) * x,T(z,y)) = x * T(z,y). [para(7969(a,1),54(a,1,1)),rewrite([7715(13)])]. 44128 a(x,y,y \ z) \ 1 = a(y,y * x,z). [para(18(a,1),4007(a,1,1,2)),rewrite([92(4),169(4),18(7),42295(7),3691(6),18(7)])]. 44649 L(L(x,y / x,z),z * (y / x),z * y) = (z * (y / x)) \ (z * y). [para(76(a,2),6368(a,1,1))]. 44671 L(L(L(x,y,z),u,w),v5 \ 1,v5 \ x) = L(L(x,y,z),u,w). [para(6416(a,1),97(a,2,1,1))]. 44709 L(L(L(L(x,y,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(L(x,u,w),y,z),v5,v6). [para(6416(a,1),229(a,1,1,1)),flip(a)]. 45267 (x * ((x \ y) * z)) / R(T(y,z),x,x \ z) = z. [para(200(a,1),165(a,1,1)),rewrite([31(6)])]. 45271 x * (a(x / (y * z),y,z) * u) = R(x,z \ (y \ 1),y) * u. [para(59(a,1),200(a,2,2,1)),rewrite([27732(6)]),flip(a)]. 45295 R(x,y,T(y \ z,y)) * T(z,y) = (x / y) * (z * y). [para(7967(a,1),200(a,1,1,3)),rewrite([27047(9)])]. 45359 (((x / (y * z)) * y) * z) \ (R(x,z \ (y \ 1),y) * u) = L(u,a(x / (y * z),y,z),x). [back_rewrite(6623),rewrite([45271(9)])]. 45676 (x * y) \ L(y \ z,y,x) = (y * (x * y)) \ z. [para(74(a,2),25093(a,2,2)),rewrite([25093(9),6073(5),1091(3),39506(4),35648(5),101(2)]),flip(a)]. 46495 (R(x / y,y,z) * (y * (z * y))) \ ((x * z) * y) = a(y * z,(y * z) * (x * z),y). [para(85(a,2),24428(a,1,1,1))]. 46497 (R(x \ 1,y,z) * (y * (z * y))) \ (((x \ y) * z) * y) = a(y * z,(y * z) * ((x \ y) * z),y). [para(6071(a,1),24428(a,1,1,1))]. 46810 a(x * y,x * (y * x),z) = a(y,y * x,z). [para(14(a,1),4021(a,1,2,1)),rewrite([1077(4),3143(4),169(3),4032(5),14(6)]),flip(a)]. 46815 a(x,y * (y * (x * (y * z))),u) = a(x,x * (y \ z),u). [para(37(a,1),4021(a,1,1)),rewrite([16103(4),16485(3),23718(9),1091(6),4407(6),23717(6),14(5),4498(7),101(7),128(8),2508(10)]),flip(a)]. 47034 L(L(L(R(x,y \ 1,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(R(x,y \ 1,z),v5,v6),u,w). [para(76(a,1),44709(a,1,1)),rewrite([24261(6),24016(16)])]. 47036 L(L(x,y,z),u \ 1,u \ L(x,w,v5)) = L(x,y,z). [para(16487(a,1),44709(a,1,1,1)),rewrite([16487(8)])]. 47734 L(x,y * z,y * (z * (y * y))) = x. [para(189(a,1),15035(a,1,3)),rewrite([4578(3)])]. 47883 L(K(x,T(y,z)),x,y) = K(x,T(y,z)). [para(17666(a,1),30(a,1,1)),rewrite([37429(2),37429(4)]),flip(a)]. 48247 T(x,R(x,y,z) \ 1) = x. [para(89(a,1),960(a,1,2,1)),rewrite([19074(4),2771(4,R)])]. 48405 T(x,y) \ (y \ z) = y \ (x \ z). [para(3143(a,1),38503(a,2,2)),rewrite([35645(4),4408(5),45(4),2975(4),5147(4)])]. 48721 L(x,y * K(z,u),K(u,z)) = L(x,K(z,u),K(u,z) * y). [para(18(a,1),8308(a,1,3,2)),rewrite([5005(6)]),flip(a)]. 48733 L(x,K(y,z),u * K(z,y)) = L(x,K(z,y),u). [para(4505(a,1),8308(a,1,3,2)),rewrite([90(5),6144(6),16229(8)])]. 48767 a(x * K(y,z),K(z,y),u) = a(K(y,z),K(z,y) * x,u). [para(4505(a,1),8311(a,1,1,2)),rewrite([90(4),6144(7)])]. 48772 a(K(x,y),K(y,x) * z,u) = a(K(x,y),K(x,y) * z,u). [para(101(a,1),8311(a,1,1,2)),rewrite([2508(8),48767(4)])]. 49860 L(x,T(y,z),y) = x. [para(18604(a,1),439(a,1,2,2,1)),rewrite([4247(3),23(2),4505(4),4505(6),480(8),4505(4),13(6),32749(5),21(6)])]. 50186 L(L(R(x,y \ 1,z),u,w),v5,v6) = L(L(L(x,y,z \ 1),u,w),v5,v6). [para(82(a,1),47034(a,2,1,1)),rewrite([1014(5),10229(4),10305(5),47034(10),1014(10),10229(9),3143(10),4155(9),10690(8),38590(9)])]. 50188 L(R(x,y \ 1,z),u \ 1,u \ L(x,w,v5)) = R(x,y \ 1,z). [para(16487(a,1),47034(a,1,1)),rewrite([16487(13)])]. 50190 L(R(x,y \ 1,z),u,w) = L(L(x,y,z \ 1),u,w). [para(18454(a,1),47034(a,1,3,2)),rewrite([18485(6),50186(8),44671(8),38623(11)]),flip(a)]. 50224 R(x,y \ 1,z) = L(x,y,z \ 1). [back_rewrite(50188),rewrite([50190(8),47036(8)]),flip(a)]. 50298 L(x,T(y,x),z \ 1) = L(x,y \ x,z). [back_rewrite(27706),rewrite([50224(4)])]. 50308 R(x,y,y \ z) = L(x,y,z \ 1). [back_rewrite(24043),rewrite([50224(4),4407(3),38488(4)]),flip(a)]. 50323 L(x,y / x,z \ 1) = L(x,y,z \ 1). [back_rewrite(10323),rewrite([50224(7)])]. 50345 ((x / y) * (z * y)) / T(z,y) = L(x,z \ 1,y). [back_rewrite(2802),rewrite([50224(9),4407(8),26903(9)])]. 50347 a(x,T(x,y),z) = 1. [hyper(25,a,49860,a)]. 50359 L(x,y * z,z * y) = x. [para(4209(a,1),49860(a,1,2))]. 50365 L(x,y,T(y,z)) = x. [para(7769(a,1),49860(a,1,2))]. 50404 K(x,y) * ((x * y) \ z) = (y * x) \ z. [back_rewrite(6238),rewrite([50359(5)]),flip(a)]. 50423 R(x,y * (z * (z * y)),(z * y) \ ((y * z) \ u)) = R(x,K(z,y),K(y,z) * u). [back_rewrite(21722),rewrite([50404(9)])]. 50785 L(L(x,y / x,z),z * y,z * (y / x)) = L(x,y / x,z). [para(6694(a,1),18608(a,1,2)),rewrite([72(11),18(8),4581(8)])]. 50886 x * (y \ (y \ 1)) = (x / y) / y. [para(18650(a,1),164(a,1,2)),rewrite([3143(4),29418(3),19074(4),30432(3),47(1),1014(8)])]. 51015 x / (T(y,z) * (T(y,u) * (T(y,z) \ x))) = T(y,u) \ 1. [back_rewrite(19499),rewrite([50886(9),10229(8),10215(7),3228(8),33992(8),37126(9),38393(8)])]. 51318 T(x,y) * (y * (x * y)) = x * (x * (y * y)). [para(20397(a,1),209(a,1,1)),rewrite([7775(3),547(5),36652(5),15452(5),45(2),100(3),20397(10),88(9)]),flip(a)]. 51385 T(x,y) * (y * (x * (y * z))) = x * (x * (y * (y * z))). [back_rewrite(7257),rewrite([51318(4),37(4),100(2)]),flip(a)]. 51470 R(x / (y * ((z * y) \ x)),z,u) = R(z,y,(z * y) \ x). [para(82(a,1),495(a,1,1))]. 51780 (x / (y * (z * x))) * y = L(z \ 1,x \ 1,y). [para(1014(a,1),10707(a,1,1)),rewrite([4155(3),45(2),10229(4)])]. 52573 L(x,y \ 1,z) = L(x,y,z \ 1). [para(14(a,1),24267(a,1,1,2)),rewrite([38568(4),48(5)]),flip(a)]. 52576 x * (a(y,z,z \ (y \ x)) * u) = L(x,y,z \ 1) * u. [para(24267(a,1),18(a,1,1)),rewrite([52573(3)]),flip(a)]. 52596 L(x,y,z \ 1) = L(x,y,z). [para(7679(a,1),24267(a,2)),rewrite([45(2),45(2),45(4),45(4),42198(7),52576(7),4407(3),26903(4),52573(3),17(5),45(5)])]. 52619 T(x,y) \ 1 = T(x \ 1,y). [para(6020(a,1),24267(a,2)),rewrite([52576(11),52596(6),33039(4),41620(4),3666(3)])]. 52627 L(x,y,T(y \ 1,z)) = x. [para(50347(a,1),24267(a,1,1,2,1)),rewrite([13(2),17(2),52573(4),52619(3)]),flip(a)]. 52635 (x / (y * (z * x))) * y = L(z \ 1,x,y). [back_rewrite(51780),rewrite([52573(9),52596(9)])]. 52653 ((x / y) * (z * y)) / T(z,y) = L(x,z,y). [back_rewrite(50345),rewrite([52573(8),52596(8)])]. 52724 T(x,y) * (T(x \ y,y) * z) = y * L(z,y,x). [back_rewrite(38658),rewrite([52573(8),52596(8)])]. 52760 (x * y) * (T(x,y) \ z) = y * L(z,y,x). [back_rewrite(38535),rewrite([52573(7),52596(7)])]. 52764 x * (y * ((x * y) \ z)) = L(z,y,x). [back_rewrite(38475),rewrite([52573(7),52596(7)])]. 52843 R(x,x \ y,z) = L(x,y,z). [back_rewrite(24264),rewrite([52573(5),52596(5)])]. 52858 L(x,y,z) = L(x,z,y). [back_rewrite(16398),rewrite([52573(4),4407(3),26903(4),52573(3),52596(3)])]. 52942 L(x,y,z / x) = L(x,z,y). [back_rewrite(50323),rewrite([52596(4),52858(2),52596(5)])]. 52953 R(x,y,y \ z) = L(x,y,z). [back_rewrite(50308),rewrite([52596(5)])]. 52963 L(x,y,z \ x) = L(x,y,T(z,x)). [back_rewrite(50298),rewrite([52596(4),52858(2),52858(4)]),flip(a)]. 53065 x * ((y * x) \ (y * z)) = L(z,x,y). [back_rewrite(38590),rewrite([52596(7),52858(5)])]. 53163 L(x,y,y * z) = L(x,y,z). [back_rewrite(16470),rewrite([52596(4),52858(2)])]. 53170 (x \ y) * L(z,x,y) = x \ (y * z). [back_rewrite(6145),rewrite([52596(4),52858(2)])]. 53195 x / (T(y,z) * (T(y,u) * (T(y,z) \ x))) = T(y \ 1,u). [back_rewrite(51015),rewrite([52619(10)])]. 53473 x / (y * ((z * y) \ x)) = L(z,y,x). [back_rewrite(38485),rewrite([52843(3),26903(2),52858(1)]),flip(a)]. 53483 L(x,y,z \ (x \ u)) = L(x,y,(u \ x) * z). [back_rewrite(33575),rewrite([52843(4),52858(3),52858(6)]),flip(a)]. 53484 L(x,y,z \ (u \ 1)) = L(x,y,u * z). [back_rewrite(33545),rewrite([52843(3),52858(2),52858(6)]),flip(a)]. 53550 L(x,y,z) \ 1 = R(x \ 1,y,z). [back_rewrite(10233),rewrite([52843(2)])]. 53564 (x * y) \ L(z,x,y) = y \ (x \ z). [back_rewrite(8393),rewrite([52843(3)])]. 53598 x * (y * ((x * y) \ z)) = L(z,x,y). [back_rewrite(52764),rewrite([52858(5)])]. 53600 (x * y) * (T(x,y) \ z) = y * L(z,x,y). [back_rewrite(52760),rewrite([52858(5)])]. 53617 T(x,y) * (T(x \ y,y) * z) = y * L(z,x,y). [back_rewrite(52724),rewrite([52858(6)])]. 53634 ((x / y) * (z * y)) / T(z,y) = L(x,y,z). [back_rewrite(52653),rewrite([52858(6)])]. 53804 L(L(x,y,z),z * y,z * (y / x)) = L(x,y,z). [back_rewrite(50785),rewrite([52858(2),52942(2),52858(7),52942(7)])]. 53894 L(x,K(y,z),u * K(z,y)) = L(x,u,K(z,y)). [back_rewrite(48733),rewrite([52858(6)])]. 53895 L(x,K(y,z),K(z,y) * u) = L(x,u,K(y,z)). [back_rewrite(48721),rewrite([52858(4),53894(4)]),flip(a)]. 54309 (x * (y * x)) \ z = x \ (y \ (x \ z)). [back_rewrite(45676),rewrite([52858(3),53564(4)]),flip(a)]. 54321 (((x / (y * z)) * y) * z) \ (R(x,z \ (y \ 1),y) * u) = L(u,x,a(x / (y * z),y,z)). [back_rewrite(45359),rewrite([52858(14)])]. 54371 (x * (y / z)) \ (x * y) = L(z,y,x). [back_rewrite(44649),rewrite([52858(2),52942(2),52858(5),53804(5)]),flip(a)]. 54493 L(a(x,x * y,z),u,x * ((x \ y) * z)) * L(a(y,x,x \ z),u,y * z) = 1. [back_rewrite(42284),rewrite([52858(6),52858(10)])]. 54757 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,y,z)). [back_rewrite(38643),rewrite([52858(12)])]. 54758 R(x,y * z,L(z \ u,y,z)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(38642),rewrite([52858(3)])]. 54785 L(L(x,y,T(z,u)),z,y * T(z,u)) = L(x,K(z,u),z * (y * z)). [back_rewrite(37146),rewrite([52858(2),52858(5)])]. 54855 L(x,y,T(z,y)) = L(x,y,z). [back_rewrite(34860),rewrite([52953(4),52942(3),52858(2),52858(4),52942(4)])]. 54918 L(x,y,T(z,y) * u) = L(x,y,z * (y * u)). [back_rewrite(33664),rewrite([52858(3)]),flip(a)]. 54976 L(x,T(y,z),y \ z) = L(x,y,z). [back_rewrite(30654),rewrite([52858(4),52942(4),54371(7),52858(4)])]. 55103 (x * (K(y,z) * u)) * (u \ K(z,y)) = L(x,K(y,z) * u,u \ K(z,y)). [back_rewrite(28379),rewrite([52858(6),52942(6),52858(5)]),flip(a)]. 55235 a((x * y) / z,x,L(x \ z,x,y)) = a(x,y * x,L(x \ z,x,y)). [back_rewrite(26973),rewrite([52858(4),52858(8)])]. 55237 a((x \ y) / z,x,L(x \ z,x,y)) = a(x \ y,x,L(x \ z,x,y)). [back_rewrite(26968),rewrite([52858(4),52858(8)])]. 55249 L(x,y,y \ z) = L(x,y,z). [back_rewrite(26903),rewrite([52858(3)])]. 55404 L(T(x,y),z,y \ x) = z * ((z \ (y \ x)) * y). [back_rewrite(23927),rewrite([52858(3)])]. 55494 T(x * (y / z),x * y) = L(z,y,x) \ (x * y). [back_rewrite(22386),rewrite([52858(2),52942(2)]),flip(a)]. 55548 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y))))) = x * x. [back_rewrite(21507),rewrite([52858(6)])]. 55568 x * (y \ ((y / x) * z)) = L(z,y,y / x). [back_rewrite(21447),rewrite([52858(6)])]. 55660 L(L(x,y,z),y,z) = x. [back_rewrite(18473),rewrite([52858(4),8684(4)])]. 55725 L(x,y \ z,(z \ y) * u) = L(x,u,y \ z). [back_rewrite(16517),rewrite([52858(4),52858(6)])]. 55731 (x * (y \ z)) * T(y,z) = x * L(z,x,T(y,z)). [back_rewrite(16508),rewrite([52858(6),52963(6)])]. 55771 T(x,L(y * z,x,y)) = T(x,(x * y) * z). [back_rewrite(16362),rewrite([52858(2)])]. 55776 x \ (y * ((y \ x) * z)) = L(z,x,y). [back_rewrite(16348),rewrite([52858(5)])]. 55819 L(x,y,z * (u * u)) = L(x,y,z). [back_rewrite(14874),rewrite([52858(3),2507(3),52858(1)]),flip(a)]. 55915 L(K(x,y) * z,u,K(y,x)) = (u * K(y,x)) \ (u * z). [back_rewrite(11597),rewrite([52858(4)])]. 55954 L(T(x * y,x * z),u,L(y \ z,x,y)) = (u * L(y \ z,x,y)) \ (u * (x * z)). [back_rewrite(11076),rewrite([52858(5),52858(6),52858(8)])]. 56000 ((x / (y * z)) * y) * z = L(x,y,z). [back_rewrite(10295),rewrite([52858(3),52942(3),52858(2),53163(2)]),flip(a)]. 56040 x * L(y,x,z) = L(x * y,x,z). [back_rewrite(8091),rewrite([54976(3),52858(1),52858(4)])]. 56084 L(x,y,x * z) = (y * (z \ (x \ 1))) \ (y / z). [back_rewrite(6676),rewrite([52858(4),53483(4),45(2)])]. 56136 (x * (y * (z * u))) \ (x * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),x,y * (z * u)). [back_rewrite(5337),rewrite([52858(13)])]. 56176 (x * (y * z)) \ (x * y) = R(z \ 1,x,y). [back_rewrite(4138),rewrite([52858(5),53550(7)])]. 56215 a(x,y,L(z,x,y)) = a(x,y,z) \ 1. [back_rewrite(1098),rewrite([52858(1),3204(3),2548(5),52858(4)]),flip(a)]. 56223 R(x,y * z,L(z \ u,y,z)) = L(x,y * z,y * u). [back_rewrite(648),rewrite([52858(3),52953(9)])]. 56231 (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),x,y * (z * u)). [back_rewrite(589),rewrite([52858(11)])]. 56531 (x * ((x \ y) * z)) / L(T(y,z),x,z) = z. [back_rewrite(45267),rewrite([52953(6)])]. 56576 T(x,(x * y) * z) = T(x,y * (z * x)). [back_rewrite(42429),rewrite([52953(3),52858(2),55771(3)])]. 56588 K((x * y) * z,x) = K(y * (z * x),x). [back_rewrite(42416),rewrite([52953(3),16735(3)])]. 56609 (x * (y * (z * y))) / y = (x * y) * z. [back_rewrite(42387),rewrite([52953(4),16364(3)]),flip(a)]. 56632 L(x * (y \ z),x,y) = (x * T(z,y)) / y. [back_rewrite(42356),rewrite([52953(4)])]. 56659 L(x * y,x,T(z,y)) = (x * (z * y)) / T(z,y). [back_rewrite(42314),rewrite([52953(4)])]. 56731 R(x,y,(x * y) \ z) \ 1 = L(x \ 1,y,z). [back_rewrite(36066),rewrite([52953(9)])]. 56746 x / R(y,z,(y * z) \ u) = x * L(y \ 1,z,u). [back_rewrite(36043),rewrite([52953(8)])]. 56835 R(x,y \ (z \ 1),z) = L(x,z,y). [back_rewrite(27732),rewrite([56000(4),52953(3),6022(2)]),flip(a)]. 56903 R(x,y * z,z \ 1) = L(x,y,(u \ (u \ y)) * z). [back_rewrite(21721),rewrite([52953(8),52858(4)]),flip(a)]. 56973 ((x \ y) * (x * z)) / z = L(T(y,x),x,z). [back_rewrite(10810),rewrite([52953(3)]),flip(a)]. 57033 L(x * y,y,z) = (x * (y * z)) / z. [back_rewrite(4583),rewrite([52953(3)])]. 57044 L(x,y,x * z) = L(x,z,y). [back_rewrite(3213),rewrite([52953(4),52858(2),52953(4)])]. 57089 x \ (y * ((y \ z) * x)) = L(T(z,x),x,y). [back_rewrite(538),rewrite([52953(7),52858(6)])]. 57097 (x * ((x \ y) * z)) / z = L(y,x,z). [back_rewrite(191),rewrite([52953(6)])]. 57173 ((L(x,y,z) * (y * (z * y))) \ (y * ((z * y) * x))) * K(L(x,y,z),y * (z * y)) = 1. [back_rewrite(7701),rewrite([53163(2),53163(10)])]. 57210 R(x,y,(x * y) \ z) = L(x,z,y). [back_rewrite(51470),rewrite([53473(4),52858(1),33(2),480(1)]),flip(a)]. 57428 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = R(y \ (z \ (y \ x)),y * (z * y),u). [back_rewrite(8002),rewrite([54309(11)])]. 57506 L(a(x,y,z),y,x * (y * z)) = a(y,x,y * z). [back_rewrite(33981),rewrite([54918(4)])]. 57568 T(L(x,y,z) * (u / x),x) = x \ (L(x,y,z) * u). [back_rewrite(28851),rewrite([55494(6),18461(2)]),flip(a)]. 57670 L(x,y,z * T(z,u)) = x. [back_rewrite(27119),rewrite([55819(7),52858(3)])]. 57764 L(x,y,a(y / (z * u),z,u)) = x. [back_rewrite(54321),rewrite([56000(4),56835(5),15(4)]),flip(a)]. 57831 x * a(x / (y * z),y,z) = L(x,y,z). [back_rewrite(582),rewrite([56000(8)])]. 57837 L(x * y,x,T(z,y)) = (x * (z \ y)) * T(z,y). [back_rewrite(55731),rewrite([56040(7)]),flip(a)]. 57867 a(x,y * x,L(z,x,y)) = a(x,y,x * z). [back_rewrite(23643),rewrite([56040(5),3204(7),189(6),56231(7),57506(4)]),flip(a)]. 57908 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * w)) = L(x,y * z,y * w). [back_rewrite(54758),rewrite([56223(4)]),flip(a)]. 57969 T(x,(x \ y) * z) = T(x,y * (z * x)). [back_rewrite(23736),rewrite([56576(6)])]. 57975 T(x \ y,((y \ x) * z) * y) = T(x \ y,z * (y * (x \ y))). [back_rewrite(15924),rewrite([56576(10)])]. 57979 T(x \ y,(z * (x \ y)) * T(x,y)) = T(x \ y,z * (y * (x \ y))). [back_rewrite(15622),rewrite([56576(11)])]. 58035 K((x \ y) * z,x) = K(y * (z * x),x). [back_rewrite(23819),rewrite([56588(6)])]. 58065 R(T(x,y),y \ x,(x \ y) * z) = L(T(x,y),y,z). [back_rewrite(22110),rewrite([56973(9)])]. 58091 (x * (y \ (z \ 1))) \ (x / y) = L(z,x,y). [back_rewrite(56084),rewrite([57044(2),52858(1)]),flip(a)]. 58133 x * L(y \ 1,z,u) = x / L(y,z,u). [back_rewrite(56746),rewrite([57210(3),52858(1)]),flip(a)]. 58139 R(x \ 1,y,z) = L(x \ 1,y,z). [back_rewrite(56731),rewrite([57210(3),52858(1),53550(3)])]. 58268 a((x * y) / z,x,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(55235),rewrite([57867(9),16(7)])]. 58275 L(x,y * z,y * (z * u)) = R(x,y * z,L(u,y,z)). [back_rewrite(54757),rewrite([57908(10)])]. 58306 ((x * (y \ z)) * T(y,z)) / T(y \ z,x * (z * (y \ z))) = ((z \ y) * x) * z. [back_rewrite(15940),rewrite([57975(9)])]. 58412 (x * (y * z)) \ (x * y) = L(z \ 1,x,y). [back_rewrite(56176),rewrite([58139(7)])]. 58434 L(x,y,z) \ 1 = L(x \ 1,y,z). [back_rewrite(53550),rewrite([58139(6)])]. 58458 (L(x \ 1,y,z) * (y * (z * y))) \ (((x \ y) * z) * y) = a(y * z,(y * z) * ((x \ y) * z),y). [back_rewrite(46497),rewrite([58139(3)])]. 58601 R(x,y * z,L(y * y,y,z)) = x. [back_rewrite(47734),rewrite([58275(5)])]. 62320 R(x,y,T(y \ z,y)) = L(x,y,z). [para(4505(a,1),516(a,1,2)),rewrite([38365(4),53634(5)]),flip(a)]. 62433 L(x,y,z) * T(z,y) = (x / y) * (z * y). [back_rewrite(45295),rewrite([62320(3)])]. 62444 (x * y) * T(T(z,u),y) = (x * y) * T(T(z,y),u). [para(517(a,1),104(a,1,2,2)),rewrite([522(5)])]. 63757 (x * (y \ L(y,z,y \ (x / y)))) * a(y,z * (y \ (x / y)),T(z,y \ (x / y)) \ y) = x. [para(11138(a,1),54(a,2)),rewrite([53600(8),38305(7)])]. 64162 L(x * x,x,y) = x * x. [para(1077(a,1),55954(a,1,3)),rewrite([14(3),4209(2),52596(4),52858(2),1607(5),1014(5),14(5),10229(5),23697(5),6351(5)])]. 64186 R(x,y * z,y * y) = x. [back_rewrite(58601),rewrite([64162(3)])]. 64241 K(T(x,y) \ z,K(T(x,y) \ ((x \ y) * z),T(x \ y,y))) = 1. [hyper(27,a,19049,a)]. 64397 T(x,(T(T(T(T(T(y,z),x \ 1),u),w),v5) / x) / T(T(T(T(T(y,w),u),x \ 1),z),v5)) = x. [para(4097(a,2),14495(a,1,2,1))]. 65408 x * (y * (T(y,x) * z)) = y * (x * (y * z)). [para(25410(a,1),262(a,1,1)),rewrite([33957(4),547(3),32749(4),45(6),128(7),25410(11),88(9)])]. 65748 L(x \ 1,y,z) * x = L(x,y,z) \ x. [para(996(a,1),518(a,1,2,1)),rewrite([58133(4),28505(2)]),flip(a)]. 65880 x * K(y,T(z,x)) = K(y,z) * x. [para(17666(a,1),518(a,2,1)),rewrite([37429(2),47883(3)])]. 65951 R(x,y,z) * x = x * R(x,y,z). [para(89(a,1),519(a,1,2,1)),flip(a)]. 67485 a(x \ (y \ (x \ 1)),x * (y * (x * z)),u) = a(T(y,x),T(y,x) * z,u). [para(106(a,1),15271(a,1,1,2,1,1)),rewrite([39792(4),128(7),35648(9),101(2),23718(7),34823(2),33957(5),6968(6),24002(5),4032(7),39792(8),106(12),128(11)]),flip(a)]. 68727 ((x * y) * T(z,y)) / T(y,x * (z * (y * y))) = (y \ x) * (z * y). [para(522(a,1),165(a,1,1)),rewrite([57969(7),4578(5)])]. 68754 x * ((y * x) \ (z * x)) = (y \ x) * T(z,x). [para(3143(a,1),522(a,2,1)),rewrite([35645(5)])]. 68763 ((x \ y) * (z * x)) * x = T((y * x) * T(z,x),x). [para(522(a,1),4209(a,1,1)),flip(a)]. 68786 K((x * y) * T(z,y),y) = K(x * (z * (y * y)),y). [para(522(a,1),16568(a,1,1)),rewrite([58035(8),4578(6)])]. 68796 x * (y * (x * T(z,y * x))) = x * L(z * (y * x),y,x). [para(128(a,1),522(a,2)),rewrite([34823(3),6968(6),53600(6)]),flip(a)]. 68958 (x * (y * (z * x))) \ L(x * (y * (z * x)),x,z) = a(x,z * x,T(y,z * x)). [back_rewrite(23655),rewrite([68796(8),52858(6),56040(7)])]. 70643 ((x * y) * z) / (x * (x * (y * z))) = L(x \ 1,y,z). [para(3691(a,1),342(a,1,1)),rewrite([58139(5),52858(5),2507(5),52858(3)]),flip(a)]. 70649 R(x * K(y,z),K(z,y),u) = (x * u) / (K(z,y) * u). [para(4993(a,1),342(a,1,1,2,2)),rewrite([14(3),5005(2),4993(6),14(5),8296(10)])]. 70674 R(x / (y * T(y,z)),y * T(y,z),u) = (x * u) / (y * (T(y,z) * u)). [para(16623(a,1),342(a,1,1,2,2)),rewrite([547(2),16623(7),547(5),38207(12),21062(10)])]. 70731 x * (L(x,y,z) \ x) = R(x,x * (x * y),z). [back_rewrite(1932),rewrite([70643(6),58133(4),28505(2)])]. 70983 (x * (y * (z * (y * x)))) \ (x * (y * (z * ((y * x) * (u * (x * y)))))) = x * (y * T(u,x * y)). [para(33415(a,1),2214(a,1,2,2,2,2))]. 72562 K(L(x,y,z),T(x,u)) = 1. [para(28464(a,1),16687(a,1,2)),rewrite([47(3)]),flip(a)]. 72844 a(T(x \ y,y),T(x,y),T(z,x * y)) = a(T(x,y),x * y,T(z,x * y)). [para(90(a,1),13311(a,1,3,2)),rewrite([4278(2),90(9),90(10)])]. 72886 a(x,(x \ y) * z,u) = a(x,(x * y) * z,u). [para(16(a,1),13466(a,1,2,2)),rewrite([169(6),136(7)])]. 72954 x \ (y * (z * x)) = T(y,x) * T(z,x). [para(14(a,1),13641(a,1,2,2)),rewrite([4505(3),14(6)]),flip(a)]. 73156 T(x,y) * T(x \ z,y) = L(T(z,y),y,x). [back_rewrite(57089),rewrite([72954(4)])]. 73876 ((x * (y * z)) * (y * ((z * y) \ u))) / (y * u) = R(x,y * z,y * ((z * y) \ u)). [para(16(a,1),346(a,1,2,2))]. 74086 (x * (y * (x \ y))) / (x * (y / x)) = y. [para(27447(a,1),17(a,1,1)),rewrite([5005(4),26340(4)]),flip(a)]. 74176 a(x * (y / x),y * (y * z),u) = a(T(y,x \ y),z,u). [para(27447(a,1),4636(a,2,1)),rewrite([74086(6),74086(7),74086(7),21063(3),28991(2),2508(5),74086(11),74086(11)]),flip(a)]. 74728 K((x * (y \ z)) * T(y,z),T(x * z,a(x,y \ z,T(y,z)))) = K(a(x,y \ z,T(y,z)),x * z). [para(4315(a,1),17822(a,1,1)),rewrite([17771(9)]),flip(a)]. 75476 a(x,y,K(x,z)) = 1. [para(18(a,1),33091(a,1,2))]. 75493 (x * y) * K(y,z) = x * T(y,z). [para(33091(a,1),33249(a,1,1,3)),rewrite([80(5),128(4),16716(2),15(4),75476(8),14(7)]),flip(a)]. 75570 R(x,y,K(y,z)) = x. [back_rewrite(22892),rewrite([75493(3),17(4)]),flip(a)]. 75628 R(x,y,K(z,y)) = x. [para(17781(a,1),75570(a,1,3))]. 75689 R(x,T(y,z),K(z,y)) = x. [para(17771(a,1),75628(a,1,3))]. 75750 (x * K(y,z)) / z = x / T(z,y). [back_rewrite(21095),rewrite([75689(5)]),flip(a)]. 75804 a(x,y,z \ (x \ z)) = 1. [para(3666(a,1),33119(a,1,1)),rewrite([24189(5)])]. 76377 T(x * (x * y),z \ 1) * (z / y) = z * (x * x). [para(10920(a,1),7616(a,1,1)),rewrite([10215(7),22250(11),10229(9),18(9)])]. 77305 a(x \ ((y \ ((x \ (z / x)) / y)) / x),x * (y * x),u) = a(x \ (y \ (x \ 1)),z,u). [para(106(a,1),15079(a,1,2)),rewrite([39792(4),39792(8),35648(10),101(2),54309(8),9490(6),9490(7),1014(7),39792(13)])]. 77469 ((x / y) * (z * u)) * a(y / x,z,u) = ((x / y) * z) * u. [para(15308(a,1),54(a,1,2)),rewrite([37(6),10287(7),10287(12)])]. 77479 a(x,x * (y \ (y \ (x \ z))),u) = a(x,y * (y * z),u). [para(3645(a,1),15308(a,1,2,1)),rewrite([10215(7),76377(7),3645(13),35648(11),4578(8),19474(9),35648(10),4578(4),19474(8),14882(9),16(7),16(6),3954(5),10215(12),76377(12),14882(8)])]. 77481 a(T(x,y),y * (y * z),u) = a(y \ (x \ (y \ 1)),z,u). [para(106(a,1),15308(a,1,2,1)),rewrite([39792(4),106(10),128(9),189(10),4578(6),189(9),100(6),189(8),101(6),128(7),67485(11),51385(6),22976(6),39792(8)])]. 78102 x * (((T(y,x) * (x * z)) / u) / T(x * (y * (x * (x * z))),u \ 1)) = x \ (u \ 1). [para(4640(a,1),15(a,1,2)),flip(a)]. 78147 a((x \ y) * y,z,u) = a(x,y * (y * z),u). [para(4640(a,1),4636(a,2,1)),rewrite([78102(13),18809(5),3143(3),90(3),24189(8)])]. 79623 L(x,y,R(z \ (y \ 1),y,x)) = L(x,y,T(z,x)). [para(3143(a,1),10670(a,2,3)),rewrite([6120(3),52963(7)])]. 79632 L(x,y,z * x) = L(x,y,z). [para(101(a,1),10670(a,2,3)),rewrite([20016(3),57044(3),52858(2),3200(2),57044(4),52858(3)]),flip(a)]. 79704 L(x,y,R(z,y,x)) = L(x,y,z). [back_rewrite(8681),rewrite([79632(3),16256(2)]),flip(a)]. 79714 L(x,y,T(z,x)) = L(x,y,z). [back_rewrite(79623),rewrite([79704(5),53484(4),53163(2)]),flip(a)]. 79784 L(x,y,z \ x) = L(x,y,z). [back_rewrite(52963),rewrite([79714(4)])]. 79922 (x * (y * z)) / T(y,z) = L(x * z,z,y). [para(90(a,1),57033(a,2,1,2)),rewrite([54855(3)]),flip(a)]. 79940 L(x * (y \ z),y,z) = (x * z) / T(y,z). [para(2690(a,1),57033(a,2,1,2)),rewrite([52858(5),54976(5)])]. 79946 (x * T(y,z)) / z = (x * y) / T(z,y). [para(4505(a,1),57033(a,2,1,2)),rewrite([52858(4),55249(4),79940(3)]),flip(a)]. 79974 R(x,y \ z,T(y,z)) = L(x,y,z). [para(4504(a,1),57033(a,2,1)),rewrite([7715(4),52858(3),79632(3),55249(2),52858(1),2708(6)]),flip(a)]. 79977 L(x * (y * z),y,z) = (x * y) * z. [para(101(a,1),57033(a,2,1,2)),rewrite([52858(4),53163(4),56609(7)])]. 79991 (x * y) / T(y,z) = x * K(z,y). [para(16875(a,1),57033(a,2,1,2)),rewrite([38196(5)]),flip(a)]. 80058 R(x,y \ z,y) = L(x,y,z). [para(7969(a,1),57033(a,2,1)),rewrite([7715(4),52858(4),79632(4),54976(3),52858(1),7966(6)]),flip(a)]. 80171 L(x * y,x,T(z,y)) = L(x * y,y,z). [back_rewrite(56659),rewrite([79922(7)])]. 80225 (x * (y \ z)) * T(y,z) = L(x,y,z) * z. [back_rewrite(10537),rewrite([79974(3)]),flip(a)]. 80273 x * (y * (x * T(z,y * x))) = L(x * (z * (y * x)),x,y). [back_rewrite(68796),rewrite([52858(8),56040(9)])]. 80289 R(x,K(y,z),y) = x. [back_rewrite(20967),rewrite([79991(5),8298(4)]),flip(a)]. 80501 (x * (y \ z)) * y = (x / y) * (z * y). [back_rewrite(10562),rewrite([80058(2),62433(3)]),flip(a)]. 80509 L(x,y,z) * y = L(x * y,y,z). [back_rewrite(57837),rewrite([80171(3),80225(6),52858(3)]),flip(a)]. 80568 K(L(x,y,z) * z,T(x * z,a(x,y \ z,T(y,z)))) = K(a(x,y \ z,T(y,z)),x * z). [back_rewrite(74728),rewrite([80225(4)])]. 80615 (L(x,y,z) * z) / T(y \ z,x * (z * (y \ z))) = ((z \ y) * x) * z. [back_rewrite(58306),rewrite([80225(4)])]. 80627 T(x \ y,z * (y * (x \ y))) = T(x \ y,L(z,x,y) * y). [back_rewrite(57979),rewrite([80225(5)]),flip(a)]. 80744 T(T(((x \ y) * z) * y,x \ y),L(z,x,y) * y) = ((x \ y) * z) * y. [back_rewrite(15646),rewrite([80225(9)])]. 80745 T(((x \ y) * z) * y,x \ y) = (L(z,x,y) * y) * (x \ y). [back_rewrite(15645),rewrite([80225(4)]),flip(a)]. 80766 (x * y) * a(x,z \ y,T(z,y)) = L(x * y,y,z). [back_rewrite(4308),rewrite([80225(9),52858(6),80509(7)])]. 80776 (x * K(y,z)) * y = x * T(y,z). [back_rewrite(23173),rewrite([80289(2)]),flip(a)]. 81010 ((x / y) * (z * y)) * a(y \ z,(z \ y) * x,T(z,y)) = x * T(z,y). [back_rewrite(43418),rewrite([80501(3)])]. 81016 a(x \ y,(y \ x) * z,T(y,x)) = a(x,x * z,T(y,x)). [back_rewrite(42971),rewrite([80501(8),24477(11)])]. 81056 (x \ y) * ((z / x) * (y * x)) = ((x \ y) * z) * T(y,x). [back_rewrite(8020),rewrite([80501(4)])]. 81224 (x \ y) * (L(z,y,x) * x) = ((x \ y) * z) * x. [back_rewrite(80615),rewrite([80627(7),2711(7),4408(4)])]. 81235 (x \ y) * (L(z,x,y) * y) = ((x \ y) * z) * y. [back_rewrite(80744),rewrite([80745(5),4209(7)])]. 81262 a(x,y * (y * K(z,u)),z) = 1. [back_rewrite(24075),rewrite([80776(9),5410(9)]),flip(a)]. 81309 ((x / y) * (z * y)) * a(y,y * x,T(z,y)) = x * T(z,y). [back_rewrite(81010),rewrite([81016(8)])]. 81564 (T(x,y) * z) / a(T(y \ x,x),T(y,x),z) = T(y,x) \ ((y * x) * z). [para(15408(a,1),162(a,2)),rewrite([29216(4)])]. 81596 T(x,y) \ ((x * y) * (y * L(z,x,y))) = (T(x \ y,y) * z) * T(T(x * y,y),z). [para(15408(a,1),9018(a,2)),rewrite([73156(8),89(5),6018(5),7775(5),53617(14)]),flip(a)]. 81698 a(x \ y,(y \ x) * x,(x \ y) * z) = a(y,x,x \ z). [para(92(a,1),15411(a,1,1)),rewrite([10229(3),4230(3),4209(4),92(5),24057(8),24285(10)])]. 82112 a(x \ y,z * (y \ x),y) \ 1 = a(x \ y,z,T(x,y)). [para(18(a,1),15593(a,1,2)),rewrite([4155(6)]),flip(a)]. 82121 a(x,y / x,x * z) = a(x,y,z) \ 1. [para(1091(a,1),15593(a,1,1)),rewrite([1091(4),1014(5),4209(5),24189(5),1091(5),24189(6)])]. 82123 a(x,y / x,T(z,x \ z)) = a(x,y,z / x) \ 1. [para(1829(a,1),15593(a,1,1)),rewrite([1829(4),1014(5),28965(5),24189(6),1829(6),24189(8)])]. 82129 a(x,y,x \ z) \ 1 = a(x,y / x,z). [para(7769(a,1),15593(a,1,3)),rewrite([48405(3),46(1),48405(5),46(3),1014(5),24189(4),48405(5),46(3),24189(6)]),flip(a)]. 82165 ((x * y) * z) \ x = (x * z) \ (x / y). [para(15(a,1),15621(a,2,2,1)),rewrite([1091(2),3143(3),1091(4),23717(5),14(4),4209(5)])]. 82190 x * ((y * x) \ (z \ 1)) = (x * y) \ (x / z). [para(1829(a,1),15621(a,2,2,1)),rewrite([10229(2),18(2),10229(4),18(4),82165(3),2643(5),6120(7),4408(8),38342(8)]),flip(a)]. 82774 x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y)))) = x. [para(55548(a,1),15(a,1,2)),rewrite([15(2)]),flip(a)]. 82800 R(x / y,y,x) = x / y. [para(55548(a,1),85(a,2,1)),rewrite([82774(11),82774(13),14868(5),3691(4),1014(5)])]. 82841 x * (y \ (z \ (z \ 1))) = x / (z * (z * y)). [para(55548(a,1),342(a,2,1)),rewrite([82774(15),82800(6),82774(14),14868(8),39699(7)]),flip(a)]. 82892 (x / (y * (y * z))) * u = (x / z) * (y \ (y \ u)). [back_rewrite(39650),rewrite([82841(5)])]. 82924 a(x,y * (y * (x * z)),u) = a(x,x * z,u). [back_rewrite(24479),rewrite([82892(7),15(5),15(4),23697(3),4032(5)]),flip(a)]. 82939 a(x,x * (y \ z),u) = a(x,x * (y * z),u). [back_rewrite(46815),rewrite([82924(5)]),flip(a)]. 82951 a(x,y * (y * z),u) = a(x,z,u). [back_rewrite(77479),rewrite([82939(5),16(3),16(2)]),flip(a)]. 82978 a(x,K(y,z),y) = 1. [back_rewrite(81262),rewrite([82951(4)])]. 83003 a((x \ y) * y,z,u) = a(x,z,u). [back_rewrite(78147),rewrite([82951(6)])]. 83005 a(x \ (y \ (x \ 1)),z,u) = a(T(y,x),z,u). [back_rewrite(77481),rewrite([82951(4)]),flip(a)]. 83038 a(T(x,y \ x),z,u) = a(y * (x / y),z,u). [back_rewrite(74176),rewrite([82951(5)]),flip(a)]. 83180 a(x / y,z,u) = a(x * y,z,u). [back_rewrite(39396),rewrite([82951(4)])]. 83185 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,u,u \ x). [back_rewrite(35944),rewrite([82951(13)])]. 83213 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,x / u,u). [back_rewrite(24163),rewrite([82951(13)])]. 83221 a(x * ((y \ x) * x),z,u) = a(x * y,z,u). [back_rewrite(22429),rewrite([82951(8),83180(6)])]. 83245 a((x \ y) * (y * (x \ y)),z,u) = a(T(y,x),z,u). [back_rewrite(19195),rewrite([82951(6)]),flip(a)]. 83255 a(x \ (y / x),z,u) = a(y,z,u). [back_rewrite(19167),rewrite([82951(5)]),flip(a)]. 83266 a(x * (y * y),z,u) = a(x,z,u). [back_rewrite(14882),rewrite([82951(6)])]. 83285 a(x,y * (z * (z * y)),u) = 1. [back_rewrite(2486),rewrite([82951(6)])]. 83292 a(x,y * (z * y),u) = a(T(z,y),x,u). [back_rewrite(77305),rewrite([83255(9),83255(7),83255(5),83005(8)])]. 83423 ((x / y) * (z * u)) * a(y * x,z,u) = ((x / y) * z) * u. [back_rewrite(77469),rewrite([83180(5)])]. 83804 a((x * y) * z,x,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(58268),rewrite([83180(5)])]. 83819 x * a(x * (y * z),y,z) = L(x,y,z). [back_rewrite(57831),rewrite([83180(3)])]. 83854 L(x,y,a(y * (z * u),z,u)) = x. [back_rewrite(57764),rewrite([83180(3)])]. 83865 a((x \ y) * z,x,L(x \ z,x,y)) = a(x \ y,x,L(x \ z,x,y)). [back_rewrite(55237),rewrite([83180(5)])]. 84069 a(x,y,y \ z) = a(x,y,y * z). [back_rewrite(24279),rewrite([83180(4),83266(4)]),flip(a)]. 84082 a(x,y \ x,z) = a(x,y * x,z). [back_rewrite(19659),rewrite([83180(2),23494(2)]),flip(a)]. 84171 a(x,y,z) = a(y,x,z). [back_rewrite(42930),rewrite([83255(3)])]. 84200 (x * (y * (z * (z * y)))) * u = x * (z * (y * (y * (z * u)))). [back_rewrite(20510),rewrite([83285(9),14(7)]),flip(a)]. 84267 a(T(x,y),y * x,z) = a(x,x * y,z). [back_rewrite(46810),rewrite([83292(4)])]. 84365 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,u,u * x). [back_rewrite(83185),rewrite([84069(11)])]. 84378 a(x \ y,(y \ x) * x,(x \ y) * z) = a(x,y,x \ z). [back_rewrite(81698),rewrite([84171(8)])]. 84525 L(a(x,x * y,z),u,x * ((x \ y) * z)) * L(a(x,y,x \ z),u,y * z) = 1. [back_rewrite(54493),rewrite([84171(8)])]. 84641 a(x,y * x,z) = a(x,x * y,z). [back_rewrite(44128),rewrite([84069(2),7836(4),84171(2)])]. 84738 a(x,x * y,z) \ 1 = a(x,y,x \ z). [back_rewrite(24285),rewrite([84171(6)])]. 84799 a(x,y * x,z) \ 1 = a(y,x,x * z). [back_rewrite(4795),rewrite([84171(2)])]. 84975 a(x,(x * y) * z,L(x \ z,x,y)) = a(x,x * y,L(x \ z,x,y)). [back_rewrite(83865),rewrite([84171(5),72886(5),84171(9),3954(9)])]. 84982 L(x,y,a(z,y * (z * u),u)) = x. [back_rewrite(83854),rewrite([84171(3)])]. 85014 x * a(y,x * (y * z),z) = L(x,y,z). [back_rewrite(83819),rewrite([84171(3)])]. 85028 a(x,x * y,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(83804),rewrite([84171(5),84975(5)])]. 85167 ((x / y) * (z * u)) * a(z,y * x,u) = ((x / y) * z) * u. [back_rewrite(83423),rewrite([84171(5)])]. 85230 a(x,y * (z * y),u) = a(x,T(z,y),u). [back_rewrite(83292),rewrite([84171(5)])]. 85233 a(x,y,z * (z * u)) = a(x,y,u). [back_rewrite(83266),rewrite([84171(3),24596(3),84171(3)])]. 85235 a(x,y \ (z / y),u) = a(z,x,u). [back_rewrite(83255),rewrite([84171(3)])]. 85241 a(x,T(y,z \ y),u) = a(x,T(y,z),u). [back_rewrite(83245),rewrite([84171(5),85230(5),84171(5)])]. 85251 a(x,T(y \ z,z),u) = a(x,z * y,u). [back_rewrite(83221),rewrite([84171(4),85230(4),84171(5)])]. 85263 a(x,y / z,u) = a(x,y * z,u). [back_rewrite(83180),rewrite([84171(2),84171(4)])]. 85290 a(x,y * (z / y),u) = a(x,T(z,y),u). [back_rewrite(83038),rewrite([84171(3),85241(3),84171(5)]),flip(a)]. 85298 a(x,(y \ z) * z,u) = a(y,x,u). [back_rewrite(83003),rewrite([84171(3)])]. 85357 a(x \ y,z * (y \ x),y) \ 1 = a(z,x \ y,T(x,y)). [back_rewrite(82112),rewrite([84171(9)])]. 85392 (T(x,y) * z) / a(y,y * x,z) = T(y,x) \ ((y * x) * z). [back_rewrite(81564),rewrite([84171(6),85251(6),84267(5)])]. 85865 a(T(x,y),x * y,T(z,x * y)) = a(x,x * y,T(z,x * y)). [back_rewrite(72844),rewrite([84171(6),85251(6),84267(5)]),flip(a)]. 86937 T(x,y) \ ((x * y) * z) = (x \ y) * (x * z). [back_rewrite(29584),rewrite([84171(4),3954(4),85392(5)])]. 86984 ((x * y) \ z) * ((z \ x) * y) = a(x,z,y). [back_rewrite(24624),rewrite([84171(6)])]. 86989 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(y,z,T(x,y)). [back_rewrite(24566),rewrite([84171(8)])]. 86999 a(x,y \ 1,z) = a(y,x,z). [back_rewrite(24189),rewrite([84171(3)])]. 87019 a(x \ y,z * (x \ y),x) = a(z,x \ y,T(y,x)) \ 1. [back_rewrite(23629),rewrite([84171(7)])]. 87102 a(x \ y,z * (x \ y),T(x,y)) = a(z,x \ y,y) \ 1. [back_rewrite(15593),rewrite([84171(7)])]. 87185 a(x,T(y,x),z) = a(x,y,z). [back_rewrite(4582),rewrite([84171(3)])]. 87186 a(T(x,y),y \ x,z) = a(x,y * x,z). [back_rewrite(4537),rewrite([84171(5),84082(5)])]. 87206 R(x,y * (z * (z * y)),u) = x. [back_rewrite(20504),rewrite([84200(5),17(10)]),flip(a)]. 87367 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,x * u,u). [back_rewrite(83213),rewrite([85263(11)])]. 87375 a(x,y,x \ z) \ 1 = a(x,y * x,z). [back_rewrite(82129),rewrite([85263(6)])]. 87376 a(x,y * x,T(z,x \ z)) = a(x,y,z / x) \ 1. [back_rewrite(82123),rewrite([85263(4)])]. 87377 a(x,y * x,x * z) = a(x,y,z) \ 1. [back_rewrite(82121),rewrite([85263(3)])]. 87830 a(x,x * y,(y \ z) * u) = a(x,x * y,(y * z) * u). [back_rewrite(35865),rewrite([85263(4)]),flip(a)]. 87988 a(x,y * x,(y \ x) * z) = a(y,x,y \ z). [back_rewrite(84378),rewrite([85298(6),84082(4)])]. 88057 (T(x \ y,y) * z) * T(T(x * y,y),z) = (x \ y) * ((x * y) * z). [back_rewrite(81596),rewrite([86937(6),3204(4)]),flip(a)]. 88170 R(x,K(y,z),K(z,y) * u) = x. [back_rewrite(50423),rewrite([87206(8)]),flip(a)]. 88394 x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w)) = x \ w. [para(4714(a,1),15(a,1,2)),flip(a)]. 88400 R(x,y,((y \ z) * z) * u) = L(x,y,u). [para(4714(a,1),148(a,1,2,2,2)),rewrite([88394(16),38445(5),57097(8),2507(3),88394(16),38534(5)]),flip(a)]. 88449 L(x,y,(z \ (z \ y)) * u) = R(x,y,u). [back_rewrite(38644),rewrite([88400(7)])]. 88465 R(x,y * z,z \ 1) = R(x,y,z). [back_rewrite(56903),rewrite([88449(8)])]. 89358 a(x,K(y,z),z \ 1) = 1. [para(17913(a,1),82978(a,1,2))]. 90470 (x * y) \ (x * z) = x \ ((x / y) * z). [para(15(a,1),15943(a,1,2,1,1)),rewrite([1091(2),3143(5),1091(5),4209(8),35645(8)]),flip(a)]. 90726 x * (y * T(z,x * y)) = (z * x) * y. [back_rewrite(70983),rewrite([90470(12),39792(4),35648(11),101(2),90470(9),3691(2),3143(8),15(6),24002(5),55776(6),79977(3)]),flip(a)]. 90841 x \ ((x / (y * z)) * y) = L(z \ 1,x,y). [back_rewrite(58412),rewrite([90470(4)])]. 90887 x \ ((x / (y * (z * u))) * ((y * z) * u)) = L(a(y,z,u),x,y * (z * u)). [back_rewrite(56231),rewrite([90470(7)])]. 90904 x \ ((x / (y * (z * u))) * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),x,y * (z * u)). [back_rewrite(56136),rewrite([90470(8)])]. 90948 L(K(x,y) * z,u,K(y,x)) = u * ((u \ K(x,y)) * z). [back_rewrite(55915),rewrite([90470(8),5005(6),24002(8)])]. 91095 L(x,y,y / z) = L(x,z,y). [back_rewrite(53065),rewrite([90470(3),55568(4)])]. 91332 L(x * (y * (z * x)),x,z) = x * ((y * z) * x). [back_rewrite(80273),rewrite([90726(4)]),flip(a)]. 91469 (x * T(y,z)) / z = (x / z) * y. [back_rewrite(21500),rewrite([91095(4),56632(3)])]. 91534 ((x * (y * z)) \ z) * T(x * y,z) = a(z,y * z,T(x,y * z)). [back_rewrite(68958),rewrite([91332(7),90470(7),72954(7),2643(4)])]. 91628 (x * y) / T(z,y) = (x / z) * y. [back_rewrite(79946),rewrite([91469(3)]),flip(a)]. 92765 (x * (y * z)) * (y * ((z * y) \ u)) = (y * z) * (((y * z) \ x) * (y * u)). [para(16(a,1),418(a,1,2,2,2)),flip(a)]. 92871 R(x,y * z,y * ((z * y) \ u)) = L(x,y * z,y * u). [back_rewrite(73876),rewrite([92765(6),57097(8)]),flip(a)]. 92882 R(x,y \ z,(z \ y) * u) = L(x,u,y * z). [back_rewrite(38476),rewrite([92871(6),16(3),52858(2)]),flip(a)]. 92926 L(T(x,y),z,y * x) = L(T(x,y),y,z). [back_rewrite(58065),rewrite([92882(5)])]. 92946 K(a(x,x * y,z),x * (x * ((y * z) / (x * ((x * y) * z))))) = 1. [hyper(27,a,21676,a)]. 92952 T(T(a(x,x * y,z),u),x * (x * ((y * z) / (x * ((x * y) * z))))) = T(a(x,x * y,z),u). [para(21676(a,1),29(a,1,1)),flip(a)]. 92963 a(x,x * y,z) \ u = a(x,y,x \ z) * u. [para(21676(a,1),5226(a,1,1,1)),rewrite([21676(12),92952(17),30512(10),46(7),84738(4),21676(13)]),flip(a)]. 92967 ((a(x,y,x \ z) / u) * a(x,x * y,z)) * u = K(a(x,x * y,z),u). [para(21676(a,1),38815(a,1,1,1)),rewrite([21676(18),15452(13),1091(9),4407(5),92963(5),1014(5),92946(19),13(11)])]. 93030 (T(x,K(y,z)) * K(z,y)) * (x \ K(y,z)) = 1. [para(4993(a,1),27619(a,1,2,1,1)),rewrite([9037(4),45(10),5005(10),12830(10),4407(8),6144(7),14(7)])]. 93714 L(x,y * (z * u),(y * z) * u) = R(x,y * (z * u),a(y,z,u)). [para(597(a,1),57033(a,2,1)),rewrite([16(6),52858(6),79784(6),52858(5),592(13)])]. 94677 T(x,R(x,y,z)) = x. [para(48247(a,1),7769(a,1,1)),rewrite([4408(4),45(3),65951(2),1708(3)])]. 94843 T(R(x,y,z) \ x,x) = R(x,y,z) \ x. [para(94677(a,1),7967(a,1,2)),rewrite([4231(6,R)]),flip(a)]. 94910 ((x * R(y,z,u)) * y) / (y * R(y,z,u)) = R(x,R(y,z,u),y). [para(94677(a,1),516(a,1,1,2)),rewrite([94677(9)])]. 94948 (R(x,y,z) \ x) * (R(x,y,z) * u) = L(x * u,x,R(x,y,z)). [back_rewrite(42834),rewrite([94843(3)])]. 95623 T(x,K(y,z)) * K(z,y) = K(z,y) * x. [para(93030(a,1),17(a,1,1)),rewrite([4155(4),6144(3),13(4)]),flip(a)]. 95624 R(K(x,y) * z,z \ K(y,x),u) = K(x,y) * z. [para(93030(a,1),22(a,1,1,1)),rewrite([13(2),3691(4),4408(4),6144(2),14(4),95623(6)]),flip(a)]. 95626 R(x,K(y,z) * u,u \ K(z,y)) = L(x,K(y,z) * u,u \ K(z,y)). [para(93030(a,1),22(a,1,2)),rewrite([95623(4),55103(6),48(7),95623(9)]),flip(a)]. 95631 L(x,K(y,z) * u,u \ K(z,y)) = x. [para(93030(a,1),104(a,1,2,2)),rewrite([95623(4),95623(6),14(7),16(6),95623(4),55103(6)]),flip(a)]. 95652 x / (K(y,z) * u) = x * (u \ K(z,y)). [para(93030(a,1),85(a,2,2)),rewrite([95623(4),95623(7),95626(8),95631(8),48(8)])]. 95681 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(93030(a,1),166(a,1,2,1)),rewrite([95623(4),95624(5),13(4)])]. 95687 (x \ K(y,z)) * (K(z,y) * (x * (K(z,y) * (x * u)))) = (K(z,y) * x) * u. [para(93030(a,1),169(a,1,1)),rewrite([4408(4),6144(3),13(5),95623(11),4408(10),6144(7),189(10),101(9),24558(11)]),flip(a)]. 95798 R(x * K(y,z),K(z,y),u) = u * ((u \ x) * K(y,z)). [back_rewrite(70649),rewrite([95652(8),169(8)])]. 95979 ((x \ K(y,z)) * u) * K(z,T(y,u)) = x \ u. [back_rewrite(37402),rewrite([95681(3)])]. 98284 (x * (y * z)) * (a(x,y,z) * ((x * y) * z)) = (x * y) * (z * ((x * y) * z)). [para(601(a,1),209(a,1,2)),rewrite([84171(6),20692(6),45(9),54(13),189(12),101(11),84171(18),20692(18),88(14)])]. 98289 (x \ T(x \ 1,y * z)) * (((y * z) \ x) * (y * (z * x))) = a(y,z,x) \ 1. [para(601(a,1),1091(a,1,1)),rewrite([98284(7),23718(11),54309(5),6072(4,R)])]. 98840 (x * y) \ T(x,z) = y \ K(x,z). [para(52627(a,1),6591(a,1,1)),rewrite([52619(5),4408(4),45(2),14(2),16343(2),52619(8),4408(7),45(5),14(5)]),flip(a)]. 99352 L(x,y,z) * z = L(x * z,y,z). [para(2642(a,1),602(a,1,2,3)),rewrite([16(2),80766(5),52858(2),2642(6),80225(6)]),flip(a)]. 99651 x \ (y * (z * y)) = ((x \ y) * z) * y. [back_rewrite(81235),rewrite([99352(3),53170(4)])]. 99656 ((x \ y) * z) * x = T(y,x) * T(z,x). [back_rewrite(81224),rewrite([52858(2),80509(3),53170(4),72954(3)]),flip(a)]. 99742 K(a(x,y \ z,T(y,z)),x * z) = 1. [back_rewrite(80568),rewrite([99352(2),72562(8)]),flip(a)]. 100197 L(x \ y,x,y * z) = (((y * x) \ (y / z)) * z) * y. [back_rewrite(18690),rewrite([99651(8),82165(6)])]. 100284 T(x,y) * T(z * y,y) = T((x * y) * T(z,y),y). [back_rewrite(68763),rewrite([99656(4)])]. 100316 T((x * y) * z,x) = y * (z * x). [back_rewrite(23766),rewrite([99656(3),4525(4),90(2)]),flip(a)]. 101793 x * T(y \ 1,z) = x / T(y,z). [para(19049(a,1),16981(a,2,2)),rewrite([64241(15),52619(3),16(10)])]. 103664 x * (y \ (z \ 1)) = x / (z * y). [para(64186(a,1),85(a,1)),rewrite([189(7),4578(6),4613(8),39792(6),16(7)]),flip(a)]. 103756 x / (y * (z * x)) = (x * z) \ (x / y). [back_rewrite(82190),rewrite([103664(5)])]. 103820 R(x,y,z \ 1) = L(x,z,y). [back_rewrite(58091),rewrite([103664(4),10229(4),10279(4)])]. 103993 ((x * y) \ (x / z)) * z = L(y \ 1,x,z). [back_rewrite(52635),rewrite([103756(3)])]. 104117 R(x,y,z) = L(x,y,z). [back_rewrite(88465),rewrite([103820(4),16256(2),52858(1)]),flip(a)]. 104458 L(x \ y,x,y * z) = L(x \ y,y,z). [back_rewrite(100197),rewrite([103993(7),80509(7),3143(6)])]. 105327 L(x * K(y,z),u,K(z,y)) = u * ((u \ x) * K(y,z)). [back_rewrite(95798),rewrite([104117(4),52858(4)])]. 105371 (L(x,y,z) \ x) * (L(x,y,z) * u) = L(x * u,x,L(x,y,z)). [back_rewrite(94948),rewrite([104117(1),104117(3),104117(7)])]. 105379 L(x,y,L(y,z,u)) = x. [back_rewrite(94910),rewrite([104117(1),32180(3),104117(4),17(6),104117(1),104117(2),52858(2)]),flip(a)]. 105551 L(x,y * (z * u),(y * z) * u) = L(x,a(y,z,u),y * (z * u)). [back_rewrite(93714),rewrite([104117(9),52858(9)])]. 105587 L(x,y,z \ u) = L(x,y,z * u). [back_rewrite(92882),rewrite([104117(4),55725(4)])]. 105864 L(x,y,K(z,u)) = x. [back_rewrite(88170),rewrite([104117(4),53895(4)])]. 106927 x * (L(x,y,z) \ x) = L(x,y,z). [back_rewrite(70731),rewrite([104117(6),52858(6),57044(6),52858(5),57044(5)])]. 106960 (x * y) / (z * (T(z,u) * y)) = x / (z * T(z,u)). [back_rewrite(70674),rewrite([104117(6),52858(6),57670(6)]),flip(a)]. 107917 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = L(y \ (z \ (y \ x)),u,y * (z * y)). [back_rewrite(57428),rewrite([104117(14),52858(14)])]. 108469 (L(x / y,y,z) * (y * (z * y))) \ ((x * z) * y) = a(y * z,(y * z) * (x * z),y). [back_rewrite(46495),rewrite([104117(2)])]. 109339 L(x,y,z) * (y * (z * y)) = (x * (y * z)) * y. [back_rewrite(18750),rewrite([104117(2),52858(2),53163(2)])]. 109537 (x * y) \ (z * y) = T(x \ z,y). [back_rewrite(10592),rewrite([104117(4),34275(4),92(2)]),flip(a)]. 109828 (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. [back_rewrite(105371),rewrite([105379(8)])]. 110184 (x * (y \ L(y,x,z))) * a(y,z * (y \ (x / y)),T(z,y \ (x / y)) \ y) = x. [back_rewrite(63757),rewrite([105587(3),57044(3),52858(2),52942(2)])]. 110241 x * ((x \ (y \ z)) * y) = L(T(z,y),y,x). [back_rewrite(55404),rewrite([105587(3),92926(3)]),flip(a)]. 110290 L(x,y,z / u) = L(x,y,u * z). [back_rewrite(53484),rewrite([105587(4),1014(3)])]. 110366 ((x \ y) * z) \ T(y,x) = L(z \ x,x,y). [back_rewrite(7982),rewrite([105587(3),104458(3)]),flip(a)]. 110378 x * ((x \ y) * K(z,u)) = y * K(z,u). [back_rewrite(105327),rewrite([105864(4)]),flip(a)]. 110402 x * ((x \ K(y,z)) * u) = K(y,z) * u. [back_rewrite(90948),rewrite([105864(4)]),flip(a)]. 110793 a(x * y,(x * y) * (z * y),x) = a(z,y,x). [back_rewrite(108469),rewrite([109339(5),23697(3),101(4),99656(3),4525(4),90(2),23718(5),86984(5),84171(1)]),flip(a)]. 110800 T(a(x,y,z),y) = a(z,x \ y,y). [back_rewrite(58458),rewrite([109339(6),3143(4),109537(7),4408(5),86984(5),84171(1),110793(8),84171(4)])]. 110804 (x \ (((y * (x * z)) \ x) * ((z * x) * y))) * K(L(y,x,z),x * (z * x)) = 1. [back_rewrite(57173),rewrite([109339(4),35803(7)])]. 110982 (x \ y) * T(z,y) = (x \ z) * y. [back_rewrite(68754),rewrite([109537(3),90(3)]),flip(a)]. 111960 a(x,x * K(y,z),K(z,y) * u) = 1. [back_rewrite(9444),rewrite([110402(6),8296(4),46(1)]),flip(a)]. 112152 a(x,y * x,T(z,y * x)) = L(x,z,y) \ x. [back_rewrite(91534),rewrite([110982(6),90470(4),90841(4),65748(4)]),flip(a)]. 112164 a(x,y,T(z,x)) = a(z,y,x). [back_rewrite(86989),rewrite([110982(5),86984(5)]),flip(a)]. 112420 ((x / y) * z) * y = x * T(z,y). [back_rewrite(81309),rewrite([112164(6),85167(6)])]. 112421 a(x \ y,(y \ x) * z,T(y,x)) = a(y,x * z,x). [back_rewrite(81016),rewrite([112164(8)])]. 112508 a(x,y,z * x) \ 1 = a(z,y * x,x). [back_rewrite(23663),rewrite([112164(3)]),flip(a)]. 112766 a(x,y,x \ z) * T(a(x,x * y,z),u) = K(a(x,x * y,z),u). [back_rewrite(92967),rewrite([112420(7)])]. 112951 (x * (y / z)) * z = z * ((z \ x) * y). [back_rewrite(10393),rewrite([112420(4),23697(4),110982(3)]),flip(a)]. 113434 a(x,y * z,z) = a(x,z,z * y). [back_rewrite(87367),rewrite([112951(8),41919(6),84365(9)]),flip(a)]. 113707 a(x,y,z * x) \ 1 = a(x,z,x * y). [back_rewrite(112508),rewrite([113434(6),84171(6)])]. 113933 (x * y) \ K(z,u) = y \ (x \ K(z,u)). [para(105864(a,1),6591(a,1,1)),rewrite([6144(3),14(3),6144(7),14(7)]),flip(a)]. 114859 (x * y) * T(T(z,y),u) = (x * T(z,u)) * y. [para(62444(a,1),136(a,2)),rewrite([110982(4),136(5)]),flip(a)]. 114936 (x * y) * T(z,y) = (x * z) * y. [para(64397(a,1),62444(a,1,2,1)),rewrite([114859(23),64397(20)])]. 115135 (x \ y) * ((x * y) * z) = y * (T(y,x) * z). [back_rewrite(88057),rewrite([114936(7),100284(5),114936(4),4505(2),547(2),4209(3),547(2),32749(3)]),flip(a)]. 115350 L(a(x,y,T(z,y)),u,x * (z * y)) = L(a(x,z,y),u,x * (z * y)). [back_rewrite(90904),rewrite([114936(6),90887(7)]),flip(a)]. 115440 K(x * (y * (z * z)),z) = K(x * y,z). [back_rewrite(68786),rewrite([114936(3),18043(3)]),flip(a)]. 115458 (x \ y) * (z * x) = T(y * z,x). [back_rewrite(68727),rewrite([114936(3),79991(7),115440(5),16716(4)]),flip(a)]. 115485 a(x,y,T(z,y)) = a(x,z,y). [back_rewrite(35536),rewrite([114936(7),105551(7),115350(6),6018(5)]),flip(a)]. 116274 L(x,y,z) \ x = a(x,z,y * x). [back_rewrite(112152),rewrite([115485(4),52858(3)]),flip(a)]. 116288 a(x,T(y,z),y * z) = a(y,x,y * z). [back_rewrite(85865),rewrite([115485(5),84171(3),115485(7)])]. 116749 a(x,y,z * x) * (L(x,z,y) * u) = x * u. [back_rewrite(109828),rewrite([116274(2)])]. 116751 x * a(x,y,z * x) = L(x,z,y). [back_rewrite(106927),rewrite([116274(2)])]. 116872 T(x,a(x,y,z * x)) = x. [back_rewrite(28511),rewrite([116274(2)])]. 118635 L(x,K(y,z),y * (u * y)) = x. [para(52858(a,1),54785(a,2)),rewrite([54785(5),105864(8)])]. 118636 L(x,y,z * T(y,u)) = L(x,z,T(y,u)). [para(54785(a,1),55660(a,1,1)),rewrite([118635(4)])]. 118653 L(x,K(y,z),T(y \ u,w)) = x. [para(625(a,1),54785(a,2,3,2)),rewrite([118636(9),55660(8),2507(6)]),flip(a)]. 118966 (x * T(x,y)) \ z = T(x,y) \ (x \ z). [para(16875(a,1),107917(a,1,1,1,2,2)),rewrite([547(2),33507(9),21062(7),106960(8),7616(6),6144(8),35223(8),16875(10),547(8),57670(9)])]. 118967 (x \ (x \ K(y,x))) * z = T(x,y) \ (x \ z). [para(16985(a,1),107917(a,1,1,1,2,2)),rewrite([33497(7),106960(8),7616(6),118966(3),6144(6),9490(7),12473(5),16985(9),57670(10)]),flip(a)]. 119011 (x \ T(x \ 1,y)) * z = T(x,y) \ (x \ z). [back_rewrite(17906),rewrite([118967(9)])]. 119022 T(x,y * z) \ (x \ (((y * z) \ x) * (y * (z * x)))) = a(y,z,x) \ 1. [back_rewrite(98289),rewrite([119011(11)])]. 119325 a(x,y,x \ K(z,x)) = 1. [para(23(a,1),75804(a,1,3,2)),rewrite([98840(3)])]. 121557 x \ (L(x,y,z) * (a(y,z,(y * z) \ x) * u)) = L(u,L(x,y,z),a(y,z,(y * z) \ x)). [para(16(a,1),588(a,1,1)),rewrite([53598(4),53598(14),52858(12)])]. 122955 x * (y \ K(z,y)) = x / T(y,z). [para(89358(a,1),209(a,1,1)),rewrite([1014(6),75750(4),45(4),1014(6),12473(4),89358(9),88(7)]),flip(a)]. 123069 T(x,y) \ (x \ z) = x \ (T(x,y) \ z). [para(634(a,1),50365(a,1)),rewrite([547(2),118966(3)])]. 123095 x \ (K(y,z) * u) = (x \ K(y,z)) * u. [para(634(a,1),105864(a,1)),rewrite([95681(3),6144(5)]),flip(a)]. 123146 a(x,y,z) \ 1 = z \ L(z,x,y). [back_rewrite(119022),rewrite([123069(9),26952(8),90470(4),23697(3),55776(4),6022(3)]),flip(a)]. 128856 x / (T(y,z) * ((y \ L(y,u,w)) * (T(y,z) \ x))) = a(y,w,u * y). [para(26839(a,1),19479(a,1,2,2,2,1,1)),rewrite([116274(10)])]. 129028 x / (T(y,z) * (a(y,u,w * y) * (T(y,z) \ x))) = y \ L(y,w,u). [para(26839(a,1),19536(a,1,2,1,1)),rewrite([116274(3)])]. 131120 T(x,a(x,y,z)) = x. [para(18(a,1),116872(a,1,2,3))]. 131121 a(x,y,z * x) \ L(x,y,z) = x. [para(116872(a,1),23(a,2)),rewrite([116751(5),52858(3)])]. 131133 T(x,a(y,z,x)) = x. [para(4505(a,1),116872(a,1,2,3)),rewrite([112164(2),84171(1)])]. 131212 T(a(x,y,z),x) = a(x,y,z). [hyper(26,a,131120,a)]. 131234 T(x,a(x,y,z) \ x) = x. [para(131120(a,1),7769(a,1,1))]. 131246 K(a(x,y,z),x) = 1. [para(131120(a,1),16687(a,1,2)),rewrite([47(1)]),flip(a)]. 133057 L(a(x,x * y,z),u,x * ((x \ y) * z)) = L(a(x,y * x,z),u,y * z). [para(84525(a,1),17(a,1,1)),rewrite([989(6),58434(6),87375(4)]),flip(a)]. 133073 a(x,y * x,z) * a(x,y,x \ z) = 1. [para(1607(a,1),84525(a,1,2)),rewrite([133057(7),1607(5)])]. 133580 x / a(y,z,x) = a(y,z,x) \ x. [para(131133(a,1),7616(a,1,1))]. 133716 K(a(x,y,z),y) = 1. [para(84171(a,1),131246(a,1,1))]. 133728 a(x,y \ z,z) = a(y,z,x). [hyper(28,a,133716,a),rewrite([110800(2)])]. 133748 a(x \ y,z * (x \ y),T(x,y)) = a(x,y,z) \ 1. [back_rewrite(87102),rewrite([133728(7)])]. 134004 (x * y) / T(x,z) = x * (y / T(x,z)). [para(119325(a,1),209(a,1,1)),rewrite([122955(5),45(5),122955(6),119325(9),88(8)])]. 134179 ((x \ y) * z) * L(z \ x,x,y) = T(y,x). [para(4505(a,1),1251(a,1,2,2)),rewrite([80501(4),81056(5),134004(9),2711(8),110366(6),4505(7)])]. 135160 T(x * (y / z),z) = (z \ x) * y. [para(4505(a,1),21316(a,1,1,2)),rewrite([90(4),10229(6),112420(7),15(7),110982(6)])]. 135282 x \ (L(x,y,z) * u) = (x \ L(x,y,z)) * u. [back_rewrite(57568),rewrite([135160(4)]),flip(a)]. 135292 (x \ L(x,y,z)) * (a(y,z,(y * z) \ x) * u) = L(u,L(x,y,z),a(y,z,(y * z) \ x)). [back_rewrite(121557),rewrite([135282(7)])]. 136169 a(x,y,x * z) \ 1 = a(x,y * x,z). [para(15(a,1),87019(a,1,1)),rewrite([15(2),15(4),4209(4),84171(4)]),flip(a)]. 136171 a(x \ y,z * (y \ x),T(y,x)) \ 1 = a(z,x \ y,x). [para(18(a,1),87019(a,1,2)),rewrite([84171(2),4155(4),84171(7)]),flip(a)]. 136177 a(x \ (y / x),z * (x \ (y / x)),x) = a(y,z,x \ y) \ 1. [para(92(a,1),87019(a,2,1,3)),rewrite([85235(10)])]. 136185 a(x \ 1,y * x,z * x) = a(y,z,x) \ 1. [para(1091(a,1),87019(a,1,1)),rewrite([1091(4),1014(5),85263(5),1091(7),1708(9),86999(9),112164(7),84171(6)])]. 136188 a(x \ 1,y * x,z) = a(x,y * x,z). [para(1829(a,1),87019(a,1,1)),rewrite([1829(4),1014(5),85263(4),1829(6),2643(8),86999(8),87375(8)])]. 136196 a(x,y * z,y) \ 1 = a(z,y \ x,y). [para(4505(a,1),87019(a,1,2)),rewrite([87185(4),84171(2),4408(4),84171(7),112421(7)]),flip(a)]. 136206 a(x * y,z * (x * y),y \ 1) = a(y,x \ z,x). [para(12372(a,1),87019(a,2,1,3)),rewrite([4408(4),45(2),90(2),4408(5),45(3),90(3),4408(10),45(8),90(8),136196(10)])]. 136217 a(T(x \ y,y),z * T(x \ y,y),T(x,y)) = a(z,y * x,T(y,x)) \ 1. [para(23380(a,1),87019(a,2,1,3)),rewrite([4278(2),4278(4),4278(9),85251(11)])]. 136223 a(x \ y,x * ((x \ z) * y),x) = a(z * x,x \ y,T(y,x)) \ 1. [para(169(a,1),87019(a,1,2))]. 136232 a(x,y,z * (x * x)) \ 1 = a(z,x,y) \ 1. [para(22354(a,1),87019(a,2,1,3)),rewrite([22283(6),15(3),15(2),89(1),22283(6),15(3),15(2),89(1),112164(4),113434(3),84171(3),87377(3),84171(1),22283(9),15(6),15(5),89(4),84171(6)]),flip(a)]. 136306 a(x,y * x,z * x) = a(y,z,x) \ 1. [back_rewrite(136185),rewrite([136188(5)])]. 138261 (T(T(x,y),z) * u) * y = T(T(x,z) * (y * u),y). [para(1466(a,1),4209(a,2)),rewrite([4525(4)]),flip(a)]. 138368 (T(x,y) * z) * y = T(x * (y * z),y). [para(64397(a,1),1466(a,1,1,1,1)),rewrite([138261(23),64397(20)])]. 139543 a(x,y,x \ z) = a(x,y,x * z). [para(133073(a,1),15(a,1,2)),rewrite([84799(4),84171(2)]),flip(a)]. 139565 T(a(x,y,x * z),a(x,y * x,z)) = a(x,y,x * z). [para(133073(a,1),12386(a,1,2,2)),rewrite([139543(2),48(6),139543(7)])]. 139577 a(a(x,y,x * z),a(x,y * x,z),u) \ u = a(x,y * x,z) * (a(x,y,x * z) * u). [para(133073(a,1),162(a,1,1,1)),rewrite([13(2),139543(4),84171(5),133580(6),139543(10)])]. 139595 T(a(x,y,x * z),(a(x,y * x,z) \ a(x,y,x * z)) * u) = T(a(x,y,x * z),u). [para(133073(a,1),6973(a,1,1,2)),rewrite([139543(2),4407(5),136169(4),139543(7),115458(10),16(8),139543(5),139543(9)]),flip(a)]. 139610 L(x,a(y,z,y * u),a(y,z * y,u)) = x. [para(133073(a,1),27459(a,1,3,2)),rewrite([139543(4),14(6),52858(5)])]. 139615 x / a(y,z,y * u) = x * a(y,z * y,u). [para(133073(a,1),57033(a,2,1,2)),rewrite([139543(7),52858(8),139610(8),14(5),139543(5)]),flip(a)]. 139762 a(x,y,x * z) * T(a(x,x * y,z),u) = K(a(x,x * y,z),u). [back_rewrite(112766),rewrite([139543(2)])]. 139811 a(x,y * x,(y \ x) * z) = a(x,y,y * z). [back_rewrite(87988),rewrite([84171(6),84069(6)])]. 141555 T(x,y) * ((z / (x * T(x,y))) * (x * (T(x,y) * u))) = x * ((K(x,y) * z) * u). [para(7416(a,1),15(a,1,2)),rewrite([24002(5),38208(3)]),flip(a)]. 141573 x * (((K(x,y) * z) * u) * x) = (T(x,y) * z) * (u * x). [para(7416(a,1),4209(a,1,1)),rewrite([100316(5),141555(13),101(9)]),flip(a)]. 146366 a(x,y,x * z) \ ((a(x,y * x,z) \ a(x,y,x * z)) * u) = a(x,y,x * z) * u. [para(139595(a,1),2711(a,1,2)),rewrite([91628(10),139615(8),4505(8),139565(5)]),flip(a)]. 151591 x \ (a(x,y,z) \ x) = a(x,y,z) \ 1. [para(131234(a,1),2711(a,1,2)),rewrite([3666(3)]),flip(a)]. 151649 x / (T(y,z) * (a(y,u,w) * (T(y,z) \ x))) = a(y,u,w) \ 1. [para(131234(a,1),19536(a,1,2,1,1)),rewrite([4408(4),4505(4),131212(3),151591(10)])]. 151677 x \ L(x,y,z) = a(x,z,x * y). [back_rewrite(129028),rewrite([151649(8),113707(4),52858(3)]),flip(a)]. 151689 a(x,y,x * z) * (a(z,y,(z * y) \ x) * u) = L(u,L(x,z,y),a(z,y,(z * y) \ x)). [back_rewrite(135292),rewrite([151677(2)])]. 151698 a(x,y * x,z) = a(x,y,z * x). [back_rewrite(128856),rewrite([151677(3),151649(8),136169(4)])]. 151701 a(x,y,y * z) = a(z,x,y) \ 1. [back_rewrite(123146),rewrite([151677(5),84171(5)]),flip(a)]. 151723 (x * a(y,z,y * x)) * a(y,z * (y \ (x / y)),T(z,y \ (x / y)) \ y) = x. [back_rewrite(110184),rewrite([151677(2)])]. 151813 a(x,y,x * z) \ ((a(x,y,z * x) \ a(x,y,x * z)) * u) = a(x,y,x * z) * u. [back_rewrite(146366),rewrite([151698(4)])]. 151860 a(x,y,((y \ x) * z) * x) = a(x,y,y * z). [back_rewrite(139811),rewrite([151698(4)])]. 151925 a(a(x,y,x * z),a(x,y,z * x),u) \ u = a(x,y,z * x) * (a(x,y,x * z) * u). [back_rewrite(139577),rewrite([151698(4),151698(8)])]. 151954 a(x,y,z * (x * x)) = a(y,z,x) \ 1. [back_rewrite(136306),rewrite([151698(3),4578(2)])]. 152016 a(x,y * z,T(y,z)) \ 1 = a(x,y * z,y). [back_rewrite(136217),rewrite([151698(7),73156(6),89(3),6018(3),84171(3),85251(3)]),flip(a)]. 152025 a(x,y * z,T(y,z)) = a(z,y \ x,y). [back_rewrite(136206),rewrite([151698(6),115458(5),13(3),84171(3)])]. 152039 a(x,y,z * x) = a(y,z,x \ y) \ 1. [back_rewrite(136177),rewrite([151698(6),16(5),84171(4),133728(4),85263(2),151698(2)])]. 152050 a(x,y,z \ x) = a(z,x,y) \ 1. [back_rewrite(133748),rewrite([151698(5),37224(4),28991(3),84171(4),115485(4),84171(2)])]. 152277 a(x,y,z / x) \ 1 = a(x,y,x * z). [back_rewrite(87376),rewrite([151698(4),33781(3),16985(2),90(2)]),flip(a)]. 152280 a(T(x,y),y \ x,z) = a(x,y,z * x). [back_rewrite(87186),rewrite([151698(5)])]. 152337 a(x,x * y,z) = a(x,y,z * x). [back_rewrite(84641),rewrite([151698(2)]),flip(a)]. 152342 a(x,y \ x,z) = a(x,y,z * x). [back_rewrite(84082),rewrite([151698(4)])]. 152407 a(x,y,z) \ 1 = a(z,y,x). [back_rewrite(136232),rewrite([151954(3),4408(5),45(3),14(3),84171(2)]),flip(a)]. 152415 a(x,y * z,y) = a(x,y,z * y). [back_rewrite(152016),rewrite([152025(3),152407(4),3954(2),152337(2),84171(2)]),flip(a)]. 152485 a(x,y * (x * z),z) = a(z,x,(y * z) * x). [back_rewrite(136223),rewrite([152415(5),99656(4),84171(5),3954(5),152337(5),138368(4),90(2),112164(4),84171(3),152407(9),152280(7),84171(6)])]. 152683 a(x,y,x * z) * T(a(x,y,z * x),u) = K(a(x,y,z * x),u). [back_rewrite(139762),rewrite([152337(4),152337(8)])]. 153027 a(x,K(y,z),(K(z,y) * u) * x) = 1. [back_rewrite(111960),rewrite([152337(5)])]. 153030 a(x,y,y * (z * y)) = a(y,z,x). [back_rewrite(110793),rewrite([152337(5),85233(5),113434(3),84171(3),151698(3),101(2),84171(3),84171(4)])]. 153147 a(x,y,((y \ z) * u) * x) = a(x,y,((y * z) * u) * x). [back_rewrite(87830),rewrite([152337(4),152337(8)])]. 153242 a(x,y,z) = a(x,z,y). [back_rewrite(85028),rewrite([152337(4),80509(3),4505(2),56215(3),112164(2),84171(1),152407(3)])]. 153314 a(x,y,x * (z \ u)) = a(x,y,x * (z * u)). [back_rewrite(82939),rewrite([153242(3),153242(6)])]. 153371 a(x,K(y,z),K(z,y) * u) = a(x,K(y,z),K(y,z) * u). [back_rewrite(48772),rewrite([153242(4),84171(4),153242(8),84171(8)])]. 153473 a(x,y,z / x) = a(x,y,x * z). [back_rewrite(152277),rewrite([152407(4),84171(2),153242(2),84171(2)])]. 153478 a(x,y,z \ x) = a(x,y,z). [back_rewrite(152050),rewrite([84171(3),153242(3),152407(5),84171(3),153242(3),84171(3)])]. 153484 a(x,y,z * x) = a(x,y,z). [back_rewrite(152039),rewrite([153478(4),153242(3),84171(3),152407(5),84171(3),153242(3),84171(3)])]. 153502 a(x,y,y * z) = a(x,y,z). [back_rewrite(151701),rewrite([84171(3),153242(3),152407(5),84171(3),153242(3),84171(3)])]. 153528 a(x,y,x * z) = a(z,x,y). [back_rewrite(136196),rewrite([153242(2),153502(2),152407(3),84171(1),153242(1),84171(1),153242(3),84171(3),139543(3)]),flip(a)]. 153530 a(x,y,(z / y) * (x * y)) = a(x,y,z). [back_rewrite(136171),rewrite([153242(5),84171(5),152280(5),80501(3),84171(4),152407(6),84171(4),153242(4),84171(4),153242(6),84171(6),139543(6),153528(6),84171(5)])]. 153607 a(x,T(y,z),y \ z) = a(y,z,x). [back_rewrite(85357),rewrite([153242(4),84171(4),152342(4),80501(3),84171(4),153530(4),152407(3),84171(1),153242(1),84171(1),153242(4)]),flip(a)]. 153757 a(x,y,z) * (a(x,y,z) * u) = u. [back_rewrite(151925),rewrite([153528(2),84171(1),153242(1),153484(3),1300(3),45(2),153484(2),153528(3),84171(2),153242(2)]),flip(a)]. 153764 a(x,y,z) \ u = a(x,y,z) * u. [back_rewrite(151813),rewrite([153528(2),84171(1),153242(1),153484(3),153528(4),84171(3),153242(3),46(4),13(3),153528(4),84171(3),153242(3)])]. 153769 a(x,y,z) * L(x,y,z) = x. [back_rewrite(131121),rewrite([153484(2),153764(3)])]. 153777 a(x,y,(y \ x) * z) = a(x,y,z). [back_rewrite(151860),rewrite([153484(4),153502(5)])]. 153815 a(x,y,z * y) = a(x,y,z). [back_rewrite(153030),rewrite([153502(3),153242(3),84171(3)])]. 153874 a(x,y,z * (x * y)) = a(x,z,y). [back_rewrite(152485),rewrite([153242(3),84171(6),153484(6),153815(5),153242(4)])]. 156427 K(a(x,y,z),x * z) = 1. [back_rewrite(99742),rewrite([153242(3),153607(3),153242(1),84171(1)])]. 157152 a(x,y,z * (u / z)) = a(x,y,T(u,z)). [back_rewrite(85290),rewrite([153242(3),153242(5)])]. 157169 a(x,y,z \ (u / z)) = a(x,u,y). [back_rewrite(85235),rewrite([153242(3),84171(4)])]. 157230 x * a(x,y,z) = L(x,y,z). [back_rewrite(85014),rewrite([153242(3),153874(3),84171(1)])]. 157238 L(x,y,a(y,z,u)) = x. [back_rewrite(84982),rewrite([153242(3),153874(3),84171(1)])]. 157958 L(x,y,z) * a(x,y,z) = x. [back_rewrite(151723),rewrite([153528(2),157230(2),153478(9),153242(8),116288(8),84171(5),153502(5),139543(4),153528(4),84171(3),153242(3),153473(3),153528(3)])]. 158059 a(x,y,(y \ z) * u) = a(x,y,(y * z) * u). [back_rewrite(153147),rewrite([153484(4),153484(7)])]. 158117 a(x,K(y,z),K(z,y) * u) = 1. [back_rewrite(153027),rewrite([153484(5)])]. 158223 a(x,y,z) * T(a(x,y,z),u) = K(a(x,y,z),u). [back_rewrite(152683),rewrite([153528(2),84171(1),153242(1),153484(3),153484(6)])]. 158546 a(x,y,z) * (L(x,y,z) * u) = x * u. [back_rewrite(116749),rewrite([153484(2),52858(2)])]. 158590 a(x,y,K(z,u)) = 1. [back_rewrite(153371),rewrite([158117(4),153502(5),153242(3)]),flip(a)]. 158938 a(x,y,z \ u) = a(x,y,z * u). [back_rewrite(153314),rewrite([153528(3),84171(2),153242(2),153528(5),84171(4),153242(4)])]. 158992 a(x,y,z) * (a(y,z,(z * y) * x) * u) = L(u,L(x,y,z),a(y,z,(z * y) * x)). [back_rewrite(151689),rewrite([153528(2),84171(1),153242(1),84171(4),158938(4),52858(7),84171(10),158938(10)])]. 160232 a(x,y,(y * x) * z) = a(x,y,z). [back_rewrite(153777),rewrite([158059(3)])]. 160751 a(x,y,T(z,u)) = a(x,y,z). [back_rewrite(157169),rewrite([158938(3),157152(3),153242(3)])]. 161700 L(x,a(y,z,u),L(y,z,u)) = x. [back_rewrite(158992),rewrite([160232(4),153242(2),84171(2),153757(4),160232(4),153242(2),84171(2),52858(3)]),flip(a)]. 163437 (x * y) * K(z,u) = x * (y * K(z,u)). [para(158590(a,1),54(a,1,2)),rewrite([14(5)]),flip(a)]. 163614 (x \ K(y,z)) * (K(z,y) * u) = x \ u. [back_rewrite(95979),rewrite([163437(6),65880(5)])]. 163693 (K(x,y) * z) * u = K(x,y) * (z * u). [back_rewrite(95687),rewrite([163614(9),15(5)]),flip(a)]. 163798 (T(x,y) * z) * (u * x) = T(x,y) * ((z * u) * x). [back_rewrite(141573),rewrite([163693(3),38770(4),90(5),33180(4)]),flip(a)]. 165291 a(x,y,z) * (u * L(x,y,z)) = x * T(u,L(x,y,z)). [para(90(a,1),158546(a,1,2))]. 167247 a(x,y,z) * (((u * x) \ a(x,y,z)) * (x * T(u,L(x,y,z)))) = 1. [para(158546(a,1),110804(a,1,2,2)),rewrite([153769(4),157958(7),153764(7),161700(10),157230(9),163437(10),163437(9),163437(8),16716(7)])]. 168431 K(a(x,y,z),T(y,x)) = 1. [para(4505(a,1),156427(a,1,2)),rewrite([84171(2),153242(2),84171(2),158938(2),153528(2),84171(1)])]. 170607 T(x / (x * y),K(y,x)) * (y * z) = K(y,x) * z. [para(24764(a,1),15(a,1,2)),rewrite([38208(3)]),flip(a)]. 170861 a(x,y,z) * (L(T(x,u),y,z) * w) = x * (K(L(x,y,z),u) * w). [para(24764(a,1),158546(a,1,2)),rewrite([30(3),170607(14)])]. 173117 K(a(x,y,z),T(y,u)) = 1. [para(13425(a,1),168431(a,1,2)),rewrite([153242(5),84171(5),160751(5),160751(4),153242(3),84171(3),158938(3),14(2),153242(1),84171(1)])]. 177098 K(x,T(a(x,y,z),u)) = 1. [para(173117(a,1),4993(a,1,1)),rewrite([84171(3),37242(4),13(5)])]. 181313 T(x,T(a(x,y,z),u)) = x. [hyper(28,a,177098,a)]. 181315 T(T(a(x,y,z),u),x) = T(a(x,y,z),u). [para(177098(a,1),16623(a,1,2)),rewrite([14(5)])]. 184265 L(x,y,z * (u * z)) = L(x,y,T(u,z)). [para(90(a,1),2507(a,1,3,2))]. 184282 L(x,y,z * (u * (z * w))) = L(x,y,u * w). [para(169(a,1),2507(a,1,3,2)),rewrite([23711(5),115135(4),65408(4),105587(6)])]. 184298 L(x,y,T(z,u)) = L(x,y,z). [para(18848(a,1),2507(a,2)),rewrite([2507(7),184282(5),8679(3),184265(4)]),flip(a)]. 186144 L(x,K(y,z),y * u) = x. [back_rewrite(118653),rewrite([184298(4),105587(3)])]. 187171 T(T(x,y),z) / (x * y) = y \ K(x,z). [para(2644(a,1),7616(a,1,1)),rewrite([98840(7)])]. 193371 T(x,L(x,y,z) * u) = T(x,u). [para(2645(a,1),55660(a,1,1)),rewrite([55660(3)]),flip(a)]. 193392 x * (K(L(x,y,z),u) * w) = T(x,u) * w. [para(2645(a,1),158546(a,1,2,1)),rewrite([193371(3),84171(2),153242(2),160751(2),153242(1),84171(1),170861(5),193371(7)])]. 194121 L(x,y,a(x,z,u)) = x. [para(181313(a,1),134179(a,2)),rewrite([52858(10),184298(10),157238(9),169(8),110241(8),181313(3),52858(3),184298(3)])]. 196290 L(x,K(y,z),u * w) = x. [para(11282(a,1),186144(a,1,3)),rewrite([105587(5),1014(4),110290(3)])]. 196821 (x * y) \ a(y,z,u) = y \ (x \ a(y,z,u)). [para(194121(a,1),6591(a,1,1)),rewrite([153764(3),14(3),153764(7),14(7)]),flip(a)]. 196856 a(x,y,z) * ((x \ (u \ a(x,y,z))) * (x * T(u,L(x,y,z)))) = 1. [back_rewrite(167247),rewrite([196821(4)])]. 204095 (x * K(y,z)) * u = x * (K(y,z) * u). [para(6144(a,1),104(a,1,2,1)),rewrite([163693(6),8296(7)]),flip(a)]. 208399 T(T(x,K(y,z)),u) = T(x,K(y,z) * u). [para(8296(a,1),2705(a,2,1)),rewrite([95681(3),52858(7),196290(7),123095(6),113933(5),4408(4),6144(2),163437(4),8310(4),4505(4)])]. 208429 T(T(x,y),K(z,u)) = T(x,K(z,u) * y). [para(517(a,1),8296(a,1,2)),rewrite([8310(5),208399(6)])]. 228215 (T(x,y) * z) \ T(x,y * y) = z \ K(x,y). [para(30881(a,1),17(a,1,1)),rewrite([187171(4)]),flip(a)]. 228407 T(x,T(y,L(x,z,u))) = T(x,y). [para(131120(a,1),30881(a,2,1)),rewrite([228215(6),153764(3),157230(5),204095(5),165291(5),37429(3),16716(4)])]. 230608 T(x,K(L(x,y,z),u)) = x. [para(16813(a,1),55660(a,1)),rewrite([55660(2)]),flip(a)]. 231489 K(L(x,y,z),u) * x = x * K(L(x,y,z),u). [para(230608(a,1),90(a,1,2))]. 231501 K(x,L(y,z,u)) * y = y * K(x,L(y,z,u)). [para(230608(a,1),7616(a,1,1)),rewrite([5005(3),6144(6)]),flip(a)]. 231502 T(x,K(y,L(x,z,u))) = x. [para(230608(a,1),7769(a,1,1)),rewrite([6144(3),231501(3),1708(4)])]. 231568 x * K(L(x,y,z),u) = T(x,u). [para(230608(a,1),25524(a,1,2,2)),rewrite([231489(5),204095(6),193392(6),95681(10),113933(9),163693(11),163798(10),16(8),4505(7),37429(6),30(5),89(4),8310(7),208429(4),16985(3),228407(3)]),flip(a)]. 231594 K(L(x,y,z),u) * x = T(x,u). [back_rewrite(231489),rewrite([231568(6)])]. 231954 K(x,L(y,z,u)) / y = y \ K(x,L(y,z,u)). [para(231502(a,1),2711(a,1,2))]. 231983 x \ K(y,L(x,z,u)) = T(x \ 1,y). [para(231502(a,1),19536(a,1,2,1,1)),rewrite([6144(4),231594(4),53195(7)]),flip(a)]. 232004 K(x,L(y,z,u)) = K(x,y). [para(231502(a,1),56531(a,1,2,1)),rewrite([110378(5),105864(6),19074(4),231954(3),231983(3),101793(4),16687(2)]),flip(a)]. 235046 T(x,L(y,z,u)) = T(x,y). [para(232004(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 235228 K(a(x,y,z),u) = 1. [back_rewrite(196856),rewrite([235046(6),90(6),115458(6),4505(4),181315(4),158223(4)])]. 235229 $F # answer("Ka"). [resolve(235228,a,41,a)]. ============================== end of proof ========================== % Redundant proof: 236092 $F # answer("Ka"). [resolve(236091,a,505,a)]. % Redundant proof: 236094 $F # answer("Ka"). [back_rewrite(41),rewrite([235228(6)]),xx(a)]. % Redundant proof: 236264 $F # answer("Ka"). [back_rewrite(505),rewrite([236091(6)]),xx(a)]. % Redundant proof: 236762 $F # answer("Ka"). [resolve(236761,a,477,a)]. % Redundant proof: 243817 $F # answer("Ka"). [back_rewrite(477),rewrite([236761(6)]),xx(a)]. % Disable descendants (x means already disabled): 41x 154 477x 505x given #2548 (W0w,wt=7): 236155 K(x,K(y,z)) = 1. [back_rewrite(212064),rewrite([235697(8),15(3),37125(4),125439(5),166656(5),16985(4),79992(5),96103(4)])]. given #2549 (W0w,wt=7): 236404 K(K(x,y),z) = 1. [back_rewrite(96031),rewrite([236155(4)])]. given #2550 (W0w,wt=7): 237155 T(x,K(y,z)) = x. [back_rewrite(225563),rewrite([236297(5),12372(4)]),flip(a)]. given #2551 (W0w,wt=8): 235228 K(a(x,y,z),u) = 1. [back_rewrite(196856),rewrite([235046(6),90(6),115458(6),4505(4),181315(4),158223(4)])]. given #2552 (W0w,wt=8): 236091 K(x,a(y,z,u)) = 1. [back_rewrite(153957),rewrite([235228(2)]),flip(a)]. given #2553 (W0w,wt=8): 236761 T(x,a(y,z,u)) = x. [back_rewrite(236078),rewrite([236297(3)])]. given #2554 (W0w,wt=9): 236297 T(x,T(y,z)) = T(x,y). [back_rewrite(225441),rewrite([236155(2),13(4),16716(3)])]. given #2555 (W0w,wt=9): 236300 K(x,T(y,z)) = K(x,y). [back_rewrite(224989),rewrite([236155(4),14(4)])]. given #2556 (W0w,wt=9): 242398 T(K(x,y),z) = K(x,y). [back_rewrite(37429),rewrite([236300(4)])]. given #2557 (W0w,wt=9): 242400 K(T(x,y),z) = K(x,z). [back_rewrite(37242),rewrite([236300(4)])]. given #2558 (W0w,wt=9): 254998 K(x,y * x) = K(x,y). [back_rewrite(239908),rewrite([246014(4)])]. given #2559 (W0w,wt=9): 255569 a(x,y,a(z,u,y)) = 1. [back_rewrite(160267),rewrite([251809(4),162028(7),162028(6),161913(5)])]. given #2560 (W0a,wt=15): 3032 (x * y) * (x / z) = x * ((y * x) / z). [para(1014(a,1),189(a,1,2)),rewrite([1014(7)])]. given #2561 (W0a,wt=19): 3055 T(x * y,x * ((y * x) * z)) = T(x * y,x * z). [para(189(a,1),1708(a,1,2))]. given #2562 (W0r,wt=15): 239016 (x * T(y,z)) / T(T(y,x),z) = T(x,y). [back_rewrite(127259),rewrite([236297(7)])]. given #2563 (W0r,wt=17): 97636 K(x * (x * y),z \ (y \ (x \ (x \ z)))) = 1. [para(14186(a,1),16830(a,1,2,2,2)),rewrite([15(3),15(2),46(1),5162(6)]),flip(a)]. given #2564 (W0r,wt=19): 238433 (x * y) \ (z / T(y,x)) = T(y \ ((z / y) / x),x). [back_rewrite(176086),rewrite([236297(5)]),flip(a)]. given #2565 (W0r,wt=16): 161521 a(x * y,y * z,L(z,x,y)) = a(x,y,z). [back_rewrite(87342),rewrite([159209(7)])]. given #2566 (W0r,wt=19): 120211 K(x * x,y) * (x * (x * z)) = T(x * x,y) * z. [para(69551(a,1),116727(a,1,1,2,2)),rewrite([37429(3),71567(3),16985(4)]),flip(a)]. given #2567 (W1w,wt=21): 32641 a(x,L(L(y,z,u),w,v5),L(L(L(y,v6,v7),z,u),w,v5)) = 1. [para(97(a,1),32506(a,1,3))]. given #2568 (W1w,wt=21): 32642 a(x,L(L(y,z,u),w,v5),L(L(L(y,w,v5),v6,v7),z,u)) = 1. [para(97(a,2),32506(a,1,3))]. given #2569 (W1w,wt=21): 32645 a(x,L(L(y,z,u),w,v5),L(L(L(y,w,v5),z,u),v6,v7)) = 1. [para(228(a,1),32506(a,1,3))]. given #2570 (W1w,wt=21): 32646 a(x,L(L(y,z,u),w,v5),L(L(L(y,v6,v7),w,v5),z,u)) = 1. [para(230(a,1),32506(a,1,3))]. given #2571 (W1w,wt=21): 32676 a(x,T(T(T(y,z),u),w),L(T(T(T(y,w),z),u),v5,v6)) = 1. [para(3337(a,1),32506(a,1,3))]. given #2572 (W1w,wt=21): 32677 a(x,T(T(T(y,z),u),w),L(T(T(T(y,u),w),z),v5,v6)) = 1. [para(3337(a,2),32506(a,1,3))]. given #2573 (W1w,wt=21): 33639 (T(x,y * (y / z)) * z) * u = (z * T(x,y * y)) * u. [back_rewrite(30704),rewrite([33476(5),30455(4),30703(2),23697(5),136(6)]),flip(a)]. given #2574 (W1w,wt=21): 33704 T(x,y) * ((x \ y) * (y * y)) = y * (y * T(y,x \ y)). [back_rewrite(31518),rewrite([33497(6)])]. given #2575 (W1a,wt=23): 3377 T(T(T(x,y),z),u) * (u * w) = T(T(T(x,z),u),y) * (u * w). [para(94(a,1),1295(a,2,1)),rewrite([1295(12)]),flip(a)]. given #2576 (W1a,wt=27): 3378 T(T(T(T(x,y),z),u),w) * (u * v5) = T(T(T(T(x,z),u),y),w) * (u * v5). [para(94(a,2),1295(a,2,1,1)),rewrite([1295(14)])]. given #2577 (W1r,wt=26): 193096 L(x,y,z) \ T(z \ (y \ 1),y \ 1) = (T(z,y \ 1) * x) \ (y \ 1). [para(4278(a,1),59438(a,1,2)),rewrite([184298(4)])]. given #2578 (W1r,wt=30): 254512 L(T(x * (x * T(x,y)),z * (T(x,y) * u)),u,z) = T(T(x * (x * T(x,y)),u),z). [back_rewrite(106567),rewrite([244185(7)])]. given #2579 (W1r,wt=24): 155575 a(x,(y \ z) * (y * u),(z * y) * (u * T((z * y) * u,y))) = 1. [back_rewrite(119227),rewrite([153242(10),84171(10)])]. given #2580 (W1r,wt=27): 183206 T(x / T(T(T(y,z),u),w),x \ 1) = T(x / T(T(T(y,z),w),u),x \ 1). [back_rewrite(171968),rewrite([183038(10),69624(4),182294(14)])]. given #2581 (W1r,wt=27): 249582 K(x * (y * z),x * ((T((y * z) * (x * T(y,z)),z) * x) \ T(y,z))) = 1. [back_rewrite(220757),rewrite([241515(13),172619(12),244180(13),239812(12)])]. given #2582 (W2w,wt=31): 13576 x * (x * (y * (((x * y) \ z) * ((x * y) * u)))) = y * ((y \ x) * ((z * (x * y)) * u)). [para(190(a,1),37(a,1)),rewrite([1091(3),3143(7),169(6)]),flip(a)]. given #2583 (W2w,wt=31): 13579 (x * y) * (((x * y) \ z) * (x * (x * (y * u)))) = (z * (x * y)) * ((y \ x) * (y * u)). [para(37(a,1),190(a,2,2,2)),rewrite([1091(4),3143(7),168(5)]),flip(a)]. given #2584 (W2w,wt=31): 13596 (x * ((x \ y) * ((z * x) * u))) / T(y * x,(x \ z) * (x * u)) = (x \ z) * (x * u). [para(190(a,1),165(a,1,1))]. given #2585 (W2w,wt=31): 13879 ((x * ((x \ y) * T(T(z,u),w))) * y) * v5 = ((x * ((x \ y) * T(T(z,w),u))) * y) * v5. [para(95(a,1),9729(a,1,2,1)),rewrite([9729(7)])]. given #2586 (W2a,wt=35): 4639 x * (x * (((T(T(y,x),z) * (x * u)) / w) / T(x * (T(y,z) * (x * (x * u))),w \ 1))) = w \ 1. [back_rewrite(3681),rewrite([4578(8),2040(9)])]. given #2587 (W2a,wt=35): 4800 (T(x,y) * (z * (u * (z * (u * (z * w)))))) / (T(T(x,z * u),y) * (z * ((u * z) * w))) = z * u. [back_rewrite(4585),rewrite([4617(7)])]. given #2588 (W2r,wt=35): 208102 T(T(T(T(T(x,y \ 1),z),u),w) / v5,v5 \ 1) = T(T(T(T(T(x,w),z),y \ x),u) / v5,v5 \ 1). [back_rewrite(207194),rewrite([207751(19)]),flip(a)]. given #2589 (W2r,wt=33): 172432 L((x * ((y * x) \ z)) * u,(x * z) * u,L(x * y,u,x * z)) = (x * ((y * x) \ z)) * u. [back_rewrite(91080),rewrite([172060(3),172060(13)])]. given #2590 (W2r,wt=31): 70435 T(T(T(T(T(T(T(x,y),z),u),w),v5),v6),v7) = T(T(T(T(T(T(T(x,v7),y),z),u),w),v5),v6). [para(13104(a,1),13104(a,1,1,1,1,1)),rewrite([4408(10),45(8),14(8)])]. given #2591 (W2r,wt=31): 256525 (((x \ (y / z)) * (y / z)) * (((z / y) * x) / u)) * T((z / y) * x,u \ x) = x / u. [back_rewrite(217994),rewrite([253123(12)])]. given #2592 (W2r,wt=32): 138407 L(x \ ((T(T(y,z),x) * u) \ w),x,T(y,z) * (x * u)) = T(T(y,z) * (x * u),x) \ w. [para(1466(a,1),634(a,2,1)),rewrite([54918(9),138261(13)])]. given #2593 (W0w,wt=9): 258575 T(x,y * x) = T(x,y). [back_rewrite(237471),rewrite([258381(6),186139(4),186905(4),38975(4),16(2)])]. given #2594 (W0w,wt=9): 259053 a(x,y,a(x,z,u)) = 1. [para(255569(a,1),84171(a,1)),rewrite([153242(2),84171(2)]),flip(a)]. given #2595 (W0w,wt=9): 259054 a(x,y,a(y,z,u)) = 1. [para(84171(a,1),255569(a,1,3)),rewrite([153242(1),84171(1)])]. given #2596 (W0w,wt=10): 233675 K(L(x,y,z),u) = K(x,u). [back_rewrite(232452),rewrite([233597(4)])]. given #2597 (W0w,wt=10): 235046 T(x,L(y,z,u)) = T(x,y). [para(232004(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. given #2598 (W0w,wt=10): 252012 a(x,y,z * T(z,u)) = 1. [back_rewrite(191370),rewrite([244128(4),160751(4)])]. given #2599 (W0w,wt=10): 260056 a(x,K(y,z),u * w) = 1. [para(196290(a,1),161521(a,1,3)),rewrite([153242(6),84171(6),153484(6),153242(5),153815(5),158590(3),153242(4),84171(4)]),flip(a)]. given #2600 (W0w,wt=11): 24645 (x / y) / x = x / (x * y). [back_rewrite(19496),rewrite([24531(9),3169(10),1091(3),10809(9),13(3),89(2),24644(8)])]. given #2601 (W0w,wt=11): 24762 x \ K(x,y) = y / (y * x). [back_rewrite(17981),rewrite([24645(4)])]. given #2602 (W0w,wt=11): 29084 x * K(y,x) = T(x,y \ x). [back_rewrite(26642),rewrite([28965(4)])]. given #2603 (W0w,wt=11): 29097 x \ T(y,x \ y) = y / x. [back_rewrite(4356),rewrite([28965(2)])]. given #2604 (W0w,wt=11): 29098 T(x,y \ x) = y * (x / y). [back_rewrite(4276),rewrite([28965(2)])]. given #2605 (W0w,wt=11): 30703 T(T(x,y),y) = T(x,y * y). [para(6188(a,1),45(a,1)),rewrite([48(4),18809(4),4505(2),48(4)])]. given #2606 (W0w,wt=11): 34823 (x * y) \ y = y \ (x \ y). [para(12386(a,1),30627(a,1,2,2)),rewrite([101(2),9050(4),29339(5)]),flip(a)]. given #2607 (W0w,wt=11): 34903 x \ K(y,x) = y \ (x \ y). [back_rewrite(18276),rewrite([34823(2)]),flip(a)]. given #2608 (W0w,wt=11): 40091 T(x,y \ 1) \ y = y / x. [para(13(a,1),7021(a,1,1,2)),rewrite([989(2),989(7),1014(8),989(6),1014(7),10229(7),14(7),14(7)])]. given #2609 (W0a,wt=17): 3154 K(x \ y,z * (z * (y / (z * (z * x))))) = 1. [para(2495(a,1),554(a,1,1)),rewrite([1839(6)])]. given #2610 (W0a,wt=15): 3169 (x / y) * (x * z) = x * ((y \ x) * z). [back_rewrite(3031),rewrite([3143(3)]),flip(a)]. given #2611 (W0r,wt=18): 110254 L(L(x \ y,z,u),w,y * x) = L(x \ y,z,u). [back_rewrite(54832),rewrite([105587(4)])]. given #2612 (W0r,wt=19): 80132 L((x * (y * z)) / z,u,x * y) = L(x * y,y,z). [para(57033(a,1),6022(a,1,1)),rewrite([52858(5)])]. given #2613 (W0r,wt=19): 35156 x \ (T(y * x,x) / z) = T(x \ y,x) * (x / z). [back_rewrite(30369),rewrite([35052(7)])]. given #2614 (W0r,wt=16): 216804 (x * (y \ z)) * (z \ (y / x)) = a(x,y,z). [back_rewrite(161619),rewrite([216707(5)])]. given #2615 (W0r,wt=20): 238101 a(x,y,L(T(z,y),u,w) * (T(y,v5) * L(z,u,w))) = 1. [back_rewrite(193402),rewrite([236297(2)])]. given #2616 (W1w,wt=21): 33876 T(x \ (x \ y),x) * (x / z) = x \ (T(y,x * x) / z). [back_rewrite(30758),rewrite([33538(4)]),flip(a)]. given #2617 (W1w,wt=21): 33888 K(T(x,y * y) / z,y * ((y / (y * z)) * (y \ x))) = 1. [back_rewrite(30738),rewrite([33538(4)])]. given #2618 (W1w,wt=21): 33899 T(x \ y,x) * (x * (x / z)) = T(y * x,x * x) / z. [back_rewrite(30697),rewrite([33538(5)]),flip(a)]. given #2619 (W1w,wt=21): 33942 K(T(x,y * y) / z,y * ((x * (y * (y / z))) \ y)) = 1. [back_rewrite(14561),rewrite([33538(4)])]. given #2620 (W1w,wt=21): 33952 (T(x,y * y) / z) * ((x * (y * (y / z))) \ y) = y \ 1. [back_rewrite(7623),rewrite([33538(4)])]. given #2621 (W1w,wt=21): 34283 x * T(y,x * (z * (z * x))) = T(T(y,z * z) * x,x). [back_rewrite(14905),rewrite([33957(5),33957(5),33957(5),30703(3),22374(4)]),flip(a)]. given #2622 (W1w,wt=21): 34531 T(T(x,y) * z,z) * (((x * (z * (y * z))) \ z) * y) = 1. [back_rewrite(9074),rewrite([34336(4)])]. given #2623 (W1w,wt=21): 34537 x * T(T(y,x * (z * x)),u) = T(T(T(y,u),z) * x,x). [back_rewrite(9051),rewrite([34336(10)])]. given #2624 (W1a,wt=23): 3379 T(T(T(x,y),z),u) * (z * w) = T(T(T(x,z),u),y) * (z * w). [para(94(a,2),1295(a,2,1)),rewrite([1295(12)])]. given #2625 (W1a,wt=23): 3403 T(T(T(T(T(x,y),z),u),w),v5) = T(T(T(T(T(x,w),y),z),v5),u). [para(94(a,1),94(a,1,1,1)),flip(a)]. given #2626 (W1r,wt=27): 261387 K(x \ (y * z),x * ((T((y * z) * (x \ T(y,z)),z) * x) \ T(y,z))) = 1. [para(1014(a,1),249582(a,1,2,2,1)),rewrite([3143(4),3143(9),10229(12),3143(13),172060(11)])]. given #2627 (W1r,wt=26): 251341 x * ((K(y,z) * (x \ (y \ K(z,y * y)))) * u) = L(T(y,z) \ u,x,y). [back_rewrite(185012),rewrite([243049(6)])]. given #2628 (W1r,wt=22): 235890 K(x * ((y * x) * z),z \ (x \ L(y \ (x \ 1),y,z))) = 1. [back_rewrite(152390),rewrite([235054(10),186245(8),235054(10)])]. given #2629 (W1r,wt=25): 214421 T(T(x \ y,z),u * T(y * (x \ (x \ y)),z)) = T(T(x \ y,z),u). [para(23380(a,1),29335(a,2)),rewrite([33956(9),95058(7)])]. given #2630 (W1r,wt=25): 38738 (T(x * (y * x),z) * u) / (x * (y * (x * u))) = K(x * (y * x),z). [back_rewrite(23130),rewrite([38710(14)])]. given #2631 (W2w,wt=31): 14894 K(x * (y * (y * (z * (z * (x * (y * (y * (z * z)))))))),x * (y * (y * (z * z)))) = 1. [para(100(a,1),2051(a,1,1,2,2,2,1)),rewrite([37(6)])]. given #2632 (W2w,wt=31): 14901 (T(x,y) * (y * (z * (z * (x * y))))) * u = T(x,y) * (y * (z * (z * (x * (y * u))))). [para(100(a,1),4559(a,1,1,2,2)),rewrite([100(12)])]. given #2633 (W2w,wt=31): 15114 (x * (y * (y * (z * (y * (y * z)))))) * u = x * (y * (y * (z * (y * (y * (z * u)))))). [para(15045(a,1),72(a,1,2)),rewrite([2040(6),2213(13),2040(14)])]. given #2634 (W2w,wt=31): 15469 x * ((((x \ y) * y) * z) * ((u * x) * w)) = y * (y * (x * ((x \ z) * ((u * x) * w)))). [back_rewrite(13578),rewrite([15452(3)])]. given #2635 (W2a,wt=35): 4906 x * (x * ((y * z) * (x * (x * (z * ((z \ y) * u)))))) = x * (x * (y * (z * (x * (x * (y * u)))))). [back_rewrite(3927),rewrite([4782(16)])]. given #2636 (W2a,wt=33): 4926 K(x * (y * (x * (z * (x * (y * (x * u)))))),u * (x * (y * (x * (z * (x * (y * x))))))) = 1. [para(129(a,1),2772(a,1,1))]. given #2637 (W2r,wt=31): 39735 T(T(x \ (y \ (x \ (y \ 1))),z),y * (x * (y * x))) = T(x \ (y \ (x \ (y \ 1))),z). [back_rewrite(27528),rewrite([39506(4),39506(14)])]. given #2638 (W2r,wt=31): 254628 T(T(T(T(T(x \ 1,y),z),u),w),v5 * T(x,z)) = T(T(T(T(T(x \ 1,y),z),v5),u),w). [back_rewrite(70189),rewrite([244185(9)])]. given #2639 (W2r,wt=35): 247571 x \ (y * (K(x * y,z) * (y * ((u * x) * w)))) = (x \ (y * T(y * x,z))) * ((x \ u) * (x * w)). [back_rewrite(165835),rewrite([239812(2)])]. given #2640 (W2r,wt=35): 175945 T(x \ (y \ (x \ (z \ (u \ (u \ 1))))),x \ (y \ (x \ 1))) = z \ (u \ (u \ (x \ (y \ (x \ 1))))). [para(128(a,1),73654(a,1,2)),rewrite([19991(11),128043(11),4407(7),39505(7),39662(7),54309(7),4407(16),124674(16),4407(15)])]. given #2641 (W2r,wt=31): 215892 T(T(T(T(T(x / y,z),u),w),v5),v6) * y = y * T(T(T(T(T(y \ x,z),u),w),v5),v6). [para(2655(a,1),62500(a,1,2,1,1,1,1)),rewrite([117093(6),117112(6),117093(19),117112(19)]),flip(a)]. given #2642 (W0w,wt=11): 52619 T(x,y) \ 1 = T(x \ 1,y). [para(6020(a,1),24267(a,2)),rewrite([52576(11),52596(6),33039(4),41620(4),3666(3)])]. given #2643 (W0w,wt=11): 53163 L(x,y,y * z) = L(x,y,z). [back_rewrite(16470),rewrite([52596(4),52858(2)])]. given #2644 (W0w,wt=11): 54615 L(x,y,L(T(x,z),u,w)) = x. [back_rewrite(40927),rewrite([52858(3)])]. given #2645 (W0w,wt=11): 57044 L(x,y,x * z) = L(x,z,y). [back_rewrite(3213),rewrite([52953(4),52858(2),52953(4)])]. given #2646 (W0w,wt=11): 62506 T(x,y \ 1) * y = y * x. [para(12372(a,1),517(a,1,2)),flip(a)]. given #2647 (W0w,wt=11): 68205 x * T(x \ y,y) = T(y,x). [para(27009(a,1),209(a,1,1)),rewrite([16615(4),16985(3),45(3),4505(4),27009(7),88(6)]),flip(a)]. given #2648 (W0w,wt=11): 69578 T(x,T(x,y) \ z) = T(x,z). [para(2642(a,1),13425(a,1,1)),rewrite([13425(5)]),flip(a)]. given #2649 (W0w,wt=11): 69613 T(x,y * T(x,z)) = T(x,y). [para(23443(a,1),13425(a,1,1)),rewrite([13425(5)]),flip(a)]. given #2650 (W0w,wt=11): 79632 L(x,y,z * x) = L(x,y,z). [para(101(a,1),10670(a,2,3)),rewrite([20016(3),57044(3),52858(2),3200(2),57044(4),52858(3)]),flip(a)]. given #2651 (W0w,wt=11): 89254 T(x \ K(x,y),y) = x \ 1. [back_rewrite(23478),rewrite([89215(5),1014(4),12328(2)])]. given #2652 (W0w,wt=11): 103837 (x / y) / y = x / (y * y). [back_rewrite(50886),rewrite([103664(4)]),flip(a)]. given #2653 (W0w,wt=11): 104957 L(x,y,L(T(y,z),u,w)) = x. [back_rewrite(100033),rewrite([104117(3),52858(3)])]. given #2654 (W0w,wt=11): 117243 K(x * x,y) = K(x,y * y). [para(112983(a,1),3691(a,1,2)),rewrite([5005(3),78027(3),117216(5),6144(6),14(6)]),flip(a)]. given #2655 (W0w,wt=11): 118999 T(x,y) \ T(x * y,y) = y. [back_rewrite(39112),rewrite([118966(6),34517(5)])]. given #2656 (W0w,wt=11): 133834 L(x,y * y,a(z,u,w)) = x. [para(4950(a,1),118611(a,1,3))]. given #2657 (W0w,wt=11): 139367 K(x,T(x,y) \ z) = K(x,z). [back_rewrite(123143),rewrite([138934(6)])]. given #2658 (W0a,wt=15): 3228 (x * (x / y)) * z = x * (x * (y \ z)). [back_rewrite(1838),rewrite([3143(3)]),flip(a)]. given #2659 (W0a,wt=19): 3295 L(L(x,y,z),u,w) * v5 = L(L(x,u,w),y,z) * v5. [back_rewrite(2139),rewrite([3266(3),3266(8)])]. given #2660 (W0r,wt=19): 247141 K(x * (y * z),T(y * z,z) \ (x \ K(y,z))) = 1. [back_rewrite(220945),rewrite([239812(8)])]. given #2661 (W0r,wt=13): 172174 K(x \ y,z * ((y * z) \ x)) = 1. [back_rewrite(148591),rewrite([172060(4)])]. given #2662 (W0r,wt=19): 224494 T(x,y \ (z \ (z \ 1))) = T(x,y \ (z \ (z \ x))). [back_rewrite(223609),rewrite([224409(10)]),flip(a)]. given #2663 (W0r,wt=17): 270391 x * T(y * z,y \ 1) = x * T(y * z,z). [back_rewrite(254780),rewrite([270283(4),244462(7)])]. given #2664 (W0r,wt=17): 105737 a(x,y * (z * (u * y)),L(z / u,y,u)) = 1. [back_rewrite(90018),rewrite([104117(6),53163(6),52858(5)])]. given #2665 (W1w,wt=21): 34861 (x \ y) * (T(z,y \ x) / y) = x \ T(z,y \ (x / y)). [back_rewrite(30397),rewrite([34769(6)])]. given #2666 (W1w,wt=21): 34862 (T(x,y \ z) / y) * (T(x,y \ (z / y)) \ z) = y \ z. [back_rewrite(11498),rewrite([34769(5)])]. given #2667 (W1w,wt=21): 34868 (x / y) * T(z,x \ (y \ 1)) = x * (T(z,x \ 1) / y). [back_rewrite(15808),rewrite([34791(11)])]. given #2668 (W1w,wt=21): 35117 T(x / y,x \ (T(z,x) / y)) = T(x / y,x \ (x \ z)). [back_rewrite(30526),rewrite([35052(7)])]. given #2669 (W1w,wt=21): 35667 (T(x,y) * z) \ (y \ (y \ u)) = (y * (x * (y * z))) \ u. [para(90(a,1),6953(a,1,1,2,1)),rewrite([35648(6),128(3)]),flip(a)]. given #2670 (W1w,wt=21): 36367 x * (T(T(T(y,x),z),u) * w) = T(T(y,z),u) * (x * w). [para(16(a,1),4747(a,1,2,2)),rewrite([16(9)])]. given #2671 (W1w,wt=21): 38377 x * T(y * z,z \ (z \ x)) = z * (z * ((y / z) * x)). [para(169(a,1),4404(a,2,2,2)),rewrite([136(10),27608(8)])]. given #2672 (W1w,wt=21): 38455 x * ((y * x) \ T(z,y \ (x / y))) = T(z,y \ x) / y. [back_rewrite(34863),rewrite([38342(6)])]. given #2673 (W1a,wt=23): 3405 T(T(T(T(T(x,y),z),u),w),v5) = T(T(T(T(T(x,v5),y),z),u),w). [para(94(a,1),94(a,2,1,1))]. given #2674 (W1a,wt=23): 3407 T(T(T(T(T(x,y),z),u),w),v5) = T(T(T(T(T(x,u),y),v5),z),w). [para(94(a,2),94(a,1,1,1))]. given #2675 (W1r,wt=21): 205364 T(x * x,(y * z) * T(x,y * y)) = T(x * x,y * z). [back_rewrite(90106),rewrite([204570(3),204570(6),204570(9)])]. given #2676 (W1r,wt=26): 266418 (T(x * (y * x),z) * ((x * (y * (x * z))) \ u)) * (u \ z) = a(y,z,u). [para(1253(a,1),216804(a,1,2,2)),rewrite([153242(17),84171(17),162028(17),158736(15),163200(16),4578(12),84171(13),156781(13),84171(11)])]. given #2677 (W1r,wt=29): 164772 K(x * (x * (y / z)),T(u * (u * y),z \ 1) * (x * (x / (z * (u * u))))) = 1. [back_rewrite(12982),rewrite([164676(13)])]. given #2678 (W1r,wt=25): 270721 T(T(T(x \ 1,y),z * T(T(x,y),u)),w) = T(T(T(x \ 1,y),z),w). [para(69578(a,1),3840(a,1,1,1)),rewrite([3840(6),70498(13),45(10),244185(12)]),flip(a)]. given #2679 (W1r,wt=24): 221816 ((x \ T(T(y,z),u)) / w) * (w / T(T(y,u),z)) = L(x \ 1,y,w). [para(13425(a,1),186361(a,1,2,2,1)),rewrite([1014(6),10402(4),52858(12),184298(12),52858(11)])]. given #2680 (W2w,wt=31): 15691 x * (T(y * ((z \ x) * x),u) * (x \ (x \ z))) = x \ (z * T(((z \ x) * x) * y,u)). [para(537(a,1),4397(a,1,2,2)),rewrite([4408(3),4408(2),4155(9),4408(8)]),flip(a)]. given #2681 (W2w,wt=31): 15859 ((x * (y \ (y \ z))) / u) / T(z * T(x,y \ (y \ z)),u \ 1) = y \ (y \ (u \ 1)). [para(4404(a,2),3645(a,1,2,1))]. given #2682 (W2w,wt=31): 15865 K(x * (y * (y * (z * (y \ (y \ x))))),u * (x * (x * (T(z,y \ (y \ x)) / u)))) = 1. [para(4404(a,1),8260(a,1,1,2))]. given #2683 (W2w,wt=31): 17207 x * (y * (z * (y * (y * (z * (x * ((x * (y * (z * (y * (y * (z * x)))))) \ u))))))) = u. [back_rewrite(5682),rewrite([17151(7),17151(13)])]. given #2684 (W2a,wt=33): 4927 K(x * (y * (z * (y * (u * (y * (z * y)))))),y * (z * (y * (u * (y * (z * (y * x))))))) = 1. [para(129(a,1),2772(a,1,2))]. given #2685 (W2a,wt=35): 5089 x * (y * L(L(L(L(z,u,w),v5,v6),v7,v8),v9,v10)) = x * (y * L(L(L(L(z,v7,v8),u,w),v9,v10),v5,v6)). [para(295(a,1),72(a,1,2)),rewrite([5084(7)]),flip(a)]. given #2686 (W2r,wt=33): 196806 L(L(L(T(T(T(x,y),z),u),w,v5),v6,v7),v8,a(x,v9,v10)) = L(L(T(T(T(x,z),u),y),w,v5),v6,v7). [para(194121(a,1),7114(a,1,1,1)),rewrite([84171(14),153242(14),160751(14),160751(13),160751(12),153242(11),84171(11)]),flip(a)]. given #2687 (W2r,wt=31): 254374 T(T(T(T(x,y),z),u \ 1),w * T(T(T(x,u),y),z)) = T(T(T(T(x,y),z),u \ 1),w). [back_rewrite(125379),rewrite([244185(10)])]. given #2688 (W2r,wt=31): 206795 T(T(T(T(T(x,y),z),u),w) / v5,v5 \ 1) = T(T(T(T(v5 * (x / v5),y),z),u),w) / v5. [back_rewrite(181749),rewrite([205874(8)])]. given #2689 (W2r,wt=31): 228190 T(x * (x * (y * ((z / y) / x))),(y \ x) * (y * z)) = x * (x * (y * ((z / y) / x))). [back_rewrite(21870),rewrite([227859(3),227859(12)])]. given #2690 (W2r,wt=33): 227936 (x \ y) * (x * (T(T(T(T(z,x),u),w),v5) / (v6 * x))) = (x \ y) * (T(T(T(z,u),w),v5) / v6). [para(13104(a,1),30677(a,2,2,1)),rewrite([4155(5),45(4),6120(10),103664(11),3143(11),168(9),3143(12)])]. given #2691 (W0w,wt=11): 147785 K(x \ y,z) = K(z,y \ x). [back_rewrite(97516),rewrite([147745(8),21662(4),147745(8)])]. given #2692 (W0w,wt=11): 153484 a(x,y,z * x) = a(x,y,z). [back_rewrite(152039),rewrite([153478(4),153242(3),84171(3),152407(5),84171(3),153242(3),84171(3)])]. given #2693 (W0w,wt=11): 153502 a(x,y,y * z) = a(x,y,z). [back_rewrite(151701),rewrite([84171(3),153242(3),152407(5),84171(3),153242(3),84171(3)])]. given #2694 (W0w,wt=11): 153528 a(x,y,x * z) = a(z,x,y). [back_rewrite(136196),rewrite([153242(2),153502(2),152407(3),84171(1),153242(1),84171(1),153242(3),84171(3),139543(3)]),flip(a)]. given #2695 (W0w,wt=11): 153769 a(x,y,z) * L(x,y,z) = x. [back_rewrite(131121),rewrite([153484(2),153764(3)])]. given #2696 (W0w,wt=10): 278304 L(x,x \ 1,y * z) = x. [para(163184(a,1),153769(a,1,1)),rewrite([13(6)])]. given #2697 (W0w,wt=11): 153815 a(x,y,z * y) = a(x,y,z). [back_rewrite(153030),rewrite([153502(3),153242(3),84171(3)])]. given #2698 (W0w,wt=11): 153968 a(x,y,L(x \ y,z,u)) = 1. [back_rewrite(151920),rewrite([153242(4),151698(4),153484(4)])]. given #2699 (W0w,wt=11): 154773 a(x,y,z) * a(x,y,z) = 1. [back_rewrite(139562),rewrite([153528(2),84171(1),153242(1),153242(3),84171(3),139543(3),153528(3),84171(2)])]. given #2700 (W0w,wt=11): 157230 x * a(x,y,z) = L(x,y,z). [back_rewrite(85014),rewrite([153242(3),153874(3),84171(1)])]. given #2701 (W0w,wt=11): 157231 a(x,y,z) * y = L(y,x,z). [back_rewrite(85008),rewrite([153242(3),153874(3)])]. given #2702 (W0w,wt=11): 157630 a(x,y,L(T(y,z),u,w)) = 1. [back_rewrite(57575),rewrite([153242(3)])]. given #2703 (W0w,wt=11): 157958 L(x,y,z) * a(x,y,z) = x. [back_rewrite(151723),rewrite([153528(2),157230(2),153478(9),153242(8),116288(8),84171(5),153502(5),139543(4),153528(4),84171(3),153242(3),153473(3),153528(3)])]. given #2704 (W0w,wt=11): 158520 x / L(x,y,z) = a(x,y,z). [back_rewrite(116874),rewrite([153484(4),153242(3)])]. given #2705 (W0w,wt=11): 158552 L(x,y,z) \ x = a(x,y,z). [back_rewrite(116274),rewrite([153484(4),153242(3)])]. given #2706 (W0w,wt=11): 158961 L(x,y,z) / x = a(x,y,z). [back_rewrite(151779),rewrite([153528(4),84171(3)])]. given #2707 (W0a,wt=19): 3333 T(T(T(T(x,y),z),u),w) = T(T(T(T(x,w),y),z),u). [para(94(a,1),29(a,1,1)),flip(a)]. given #2708 (W0a,wt=15): 3334 T(T(T(x,y),z),u) = T(T(T(x,z),y),u). [para(94(a,1),29(a,1))]. given #2709 (W0r,wt=15): 244176 T(x,y) \ (z / x) = x \ (z / T(x,y)). [back_rewrite(125144),rewrite([237155(4)]),flip(a)]. given #2710 (W0r,wt=15): 80160 (x * (y \ z)) * (y / z) = x * K(z,y). [para(57033(a,1),37217(a,1)),rewrite([17791(3),10215(4)])]. given #2711 (W0r,wt=20): 251606 a(x,y \ z,z * (u * (T(z * z,y) * (y * u)))) = 1. [back_rewrite(119499),rewrite([243307(8),68297(6)])]. given #2712 (W0r,wt=17): 235697 T(T(x * (y / z),u),z) = T((z \ x) * y,u). [back_rewrite(57547),rewrite([235046(5)])]. given #2713 (W0r,wt=14): 161304 a(x,y * (z \ u),(z * y) * u) = 1. [back_rewrite(123060),rewrite([158938(5),153242(5),158938(5),153242(5)])]. given #2714 (W1w,wt=21): 39054 x \ T(T(y,z * (z / x)),u) = T(y,z * (z * u)) / x. [back_rewrite(33655),rewrite([38975(8)])]. given #2715 (W1w,wt=21): 39318 T(x \ (y / x),x \ (y * z)) = T(x \ (y / x),x * z). [para(33450(a,1),1708(a,1,2))]. given #2716 (W1w,wt=21): 39352 T(x \ (y * z),x \ (y / x)) = x * ((z / x) * (y / x)). [para(33450(a,1),4209(a,1,1)),rewrite([27608(9)])]. given #2717 (W1w,wt=21): 39402 K(x \ (y * z),x \ (y / x)) = K(x * z,x \ (y / x)). [para(33450(a,1),16568(a,1,1))]. given #2718 (W1w,wt=21): 39422 (x \ (y / x)) * ((x * z) * u) = T(y,x) * ((x \ z) * u). [para(136(a,1),33450(a,1,2)),rewrite([33957(10)])]. given #2719 (W1w,wt=21): 39755 x / (y * (z * (y * (z * x)))) = z \ (y \ (z \ (y \ 1))). [back_rewrite(27462),rewrite([39506(9)])]. given #2720 (W1w,wt=21): 39759 (x * (y * (y * (y * x)))) \ y = y \ (x \ (y \ (x \ 1))). [back_rewrite(27454),rewrite([39506(9)])]. given #2721 (W1w,wt=21): 40308 K(x * (x / y),(x \ (x \ z)) * (y / T(z,x * x))) = 1. [back_rewrite(30796),rewrite([40152(8)])]. given #2722 (W1a,wt=23): 3409 T(T(T(T(T(x,y),z),u),w),v5) = T(T(T(T(T(x,u),y),w),v5),z). [para(94(a,2),94(a,2,1,1)),flip(a)]. given #2723 (W1a,wt=25): 3630 L(L(L(T(x,y),z,u),w,L(x,v5,v6)),v5,v6) = L(L(T(x,y),v5,v6),z,u). [para(1696(a,1),30(a,1,1)),rewrite([30(3),30(2),30(7),30(5)]),flip(a)]. given #2724 (W1r,wt=22): 238271 x * ((x \ T(y,z \ 1)) * T(z,u)) = L(T(z,u) * y,x,z). [back_rewrite(186074),rewrite([236297(4)])]. given #2725 (W1r,wt=23): 244166 T(x * ((y / x) * z),(x \ z) * (x * y)) = x * ((y / x) * z). [back_rewrite(129477),rewrite([237155(14)])]. given #2726 (W1r,wt=25): 238898 T(x,y) * (T(T(y,x),z) \ (u * (T(y,z) * x))) = T(x * (u * x),y). [back_rewrite(135252),rewrite([236297(2),236297(13),236297(12)])]. given #2727 (W1r,wt=21): 63804 ((x * y) * (z / x)) * (T(y * x,x \ (z / x)) \ x) = z. [para(169(a,1),11138(a,1,1,2)),rewrite([136(5)])]. given #2728 (W1r,wt=22): 184362 L(x * (y * (x \ (y / x))),x,z) = T(y * (x \ y),x \ 1). [back_rewrite(143548),rewrite([184262(7),52858(5)])]. given #2729 (W2w,wt=31): 17208 (x * (y * (z * (y * (y * (z * x)))))) * u = x * (y * (z * (y * (y * (z * (x * u)))))). [back_rewrite(3042),rewrite([17151(5),17151(13)])]. given #2730 (W2w,wt=31): 17223 x \ (x \ (T(T(T(T(y,z),u),w),v5) / v6)) = x \ (x \ (T(T(T(T(y,v5),z),u),w) / v6)). [para(94(a,1),11449(a,1,2,2,1,1)),flip(a)]. given #2731 (W2w,wt=31): 17225 x \ (x \ (T(T(T(T(y,z),u),w),v5) / v6)) = x \ (x \ (T(T(T(T(y,w),z),v5),u) / v6)). [para(94(a,2),11449(a,1,2,2,1,1))]. given #2732 (W2w,wt=31): 17252 x \ ((T(T(y,z),u) / w) * ((v5 * x) * v6)) = x \ ((T(T(y,u),z) / w) * ((v5 * x) * v6)). [para(11449(a,1),190(a,2,2,1)),rewrite([4505(5),13641(8),7550(16)])]. given #2733 (W2a,wt=35): 5096 x * (y * L(L(L(L(z,u,w),v5,v6),v7,v8),v9,v10)) = x * (y * L(L(L(L(z,v9,v10),u,w),v7,v8),v5,v6)). [para(448(a,1),72(a,1,2)),rewrite([5084(7)]),flip(a)]. given #2734 (W2a,wt=35): 5104 x * (y * L(L(L(L(z,u,w),v5,v6),v7,v8),v9,v10)) = x * (y * L(L(L(L(z,v9,v10),u,w),v5,v6),v7,v8)). [para(231(a,1),72(a,1,2)),rewrite([5079(7)]),flip(a)]. given #2735 (W2r,wt=35): 284418 K(x * (x / y),T((x \ z) * (u * (u * z)),x) * (y / T(z * (u * (u * (z * x))),x * x))) = 1. [para(21377(a,1),40308(a,1,2,1,2)),rewrite([7967(7),38510(6)])]. given #2736 (W2r,wt=35): 250079 K(x,T(T(T(T(T(y * z,u),w),v5),v6),v7) \ y) = K(x,T(T(T(T(T(y * z,v6),w),v5),u),v7) \ y). [back_rewrite(178926),rewrite([241515(8),241515(16)])]. given #2737 (W2r,wt=31): 93234 (x \ y) * (((z * x) * (y \ x)) * (z * (x * y))) = (z * x) * (T(z * x,y \ x) * y). [para(57033(a,1),80698(a,1,2,2,1)),rewrite([18(8)])]. given #2738 (W2r,wt=32): 279559 T(T(x * (x * T(x,y)),z),u) \ T(x * (x * T(x,y)),u * (T(x,y) * z)) = a(x,z,u). [para(254512(a,1),158552(a,1,1)),rewrite([84171(21),153242(21),160751(21),85233(17),160751(15),153242(14),84171(14)])]. given #2739 (W2r,wt=33): 221313 T(T(T(x,y),z) * (y * u),w) \ (T(T(x,z),y) * (y * u)) = K(w,T(T(x,y),z) * (y * u)). [para(3149(a,2),16711(a,1))]. given #2740 (W0w,wt=11): 158997 x \ L(x,y,z) = a(x,y,z). [back_rewrite(151677),rewrite([153528(4),84171(3)])]. given #2741 (W0w,wt=11): 159074 a(x,y,L(y * x,z,u)) = 1. [back_rewrite(139585),rewrite([153528(4),84171(3),153242(3)])]. given #2742 (W0w,wt=11): 159328 x * a(y,z,x) = L(x,y,z). [back_rewrite(53610),rewrite([158938(3),153734(3),153242(1),153764(2),133565(2)])]. given #2743 (W0w,wt=11): 160147 a(x,y,z) * x = L(x,y,z). [back_rewrite(131216),rewrite([157230(4)])]. given #2744 (W0w,wt=11): 160298 a(x,x \ 1,L(y,z,u)) = 1. [back_rewrite(157540),rewrite([158136(7),84171(5),156248(5)])]. given #2745 (W0w,wt=11): 160751 a(x,y,T(z,u)) = a(x,y,z). [back_rewrite(157169),rewrite([158938(3),157152(3),153242(3)])]. given #2746 (W0w,wt=11): 161590 a(x,y,z) * z = L(z,x,y). [back_rewrite(133565),rewrite([159328(4)])]. given #2747 (W0w,wt=11): 164014 L(x,y,z) * a(y,z,x) = x. [para(160286(a,1),4505(a,2)),rewrite([153764(2),161590(2)])]. given #2748 (W0w,wt=11): 164117 x * a(y,x,z) = L(x,y,z). [back_rewrite(158770),rewrite([164099(2),55776(4)]),flip(a)]. given #2749 (W0w,wt=11): 172977 a(1,a(x,y,z),u * w) = 1. [para(131246(a,1),160317(a,1,2)),rewrite([84171(4)])]. given #2750 (W0w,wt=11): 184298 L(x,y,T(z,u)) = L(x,y,z). [para(18848(a,1),2507(a,2)),rewrite([2507(7),184282(5),8679(3),184265(4)]),flip(a)]. given #2751 (W0w,wt=11): 191858 T(T(x,y \ z),z \ y) = x. [para(4155(a,1),29529(a,1,2)),rewrite([2644(5),29(4)])]. given #2752 (W0w,wt=11): 202082 a(x,y * z,a(y,z,u)) = 1. [back_rewrite(155871),rewrite([201946(6),87(2)]),flip(a)]. given #2753 (W0w,wt=11): 212713 L(x,y,z) * a(y,x,z) = x. [para(212483(a,1),4505(a,2)),rewrite([153764(2),157231(2)])]. given #2754 (W0w,wt=11): 213089 K(x,y \ T(x,z)) = K(y,x). [back_rewrite(147839),rewrite([212905(7),541(2)]),flip(a)]. given #2755 (W0w,wt=11): 217900 L(x,y * z,a(u,y,z)) = x. [para(57033(a,2),10287(a,1,2,1)),rewrite([103756(3),52858(5),159120(7),153242(2)])]. given #2756 (W0a,wt=19): 3335 T(T(T(T(x,y),z),u),w) = T(T(T(T(x,u),y),w),z). [para(94(a,2),29(a,1,1))]. given #2757 (W0a,wt=15): 3336 T(T(T(x,y),z),u) = T(T(T(x,u),z),y). [para(94(a,2),29(a,1))]. given #2758 (W0r,wt=14): 277790 a(x,y,z * (u * (u * (y / z)))) = 1. [para(12954(a,1),153502(a,1,3)),rewrite([85233(12),153815(10),153242(5),153242(12),260074(12)])]. given #2759 (W0r,wt=13): 244466 T(x,y * T(x * x,z)) = T(x,y). [back_rewrite(69693),rewrite([243355(4),4209(5),37045(4),45965(3),243307(8),46094(6),23(8)])]. given #2760 (W0r,wt=18): 109798 L(x \ (y / (z * z)),y,x) = x \ (y / (z * z)). [back_rewrite(74394),rewrite([104439(9),34874(7),63087(7),26952(6)])]. given #2761 (W0r,wt=18): 289927 a(x,y * T(z,u * u),u * ((y / u) * z)) = 1. [back_rewrite(260039),rewrite([289361(9),27608(6),153242(7),157156(7),153242(7)])]. given #2762 (W0r,wt=19): 73707 T(T(T(x,y \ 1),z),u) = T(T(T(x,z),u),y \ x). [para(12372(a,1),14132(a,1,1,1,1)),flip(a)]. given #2763 (W1w,wt=21): 40388 (T(T(x,y),z) * (z / u)) * (u / T(x,z * (z * y))) = z. [back_rewrite(31141),rewrite([40301(9)])]. given #2764 (W1w,wt=21): 41603 L(L(x,y,L(L(L(x,z,u),w,v5),v6,v7)),z,u) = L(x,z,u). [para(28849(a,1),16487(a,1)),rewrite([16487(3)]),flip(a)]. given #2765 (W1w,wt=21): 43036 (x \ y) * (x * (y * ((y \ z) * x))) = T((y * x) * z,x). [para(18(a,1),7822(a,2,1,2)),rewrite([23697(4)])]. given #2766 (W1w,wt=21): 43165 (x \ y) * (x * (y \ (z * x))) = T(y * ((x / y) * z),x). [para(33450(a,1),7822(a,1,2,2)),rewrite([4505(9),92(8),27608(8)])]. given #2767 (W1w,wt=21): 43282 (x * y) * (T(x * y,y) * z) = x * (x * (y * (y * z))). [para(2918(a,1),7968(a,2,1,2)),rewrite([6144(3),33497(3),7775(2),6144(5),33497(5),7775(4),33462(7),21062(5),6144(8),33497(8),7775(7),547(9),36652(9),37(9),100(7)])]. given #2768 (W1w,wt=21): 43404 (x * (T(x * y,y) * z)) / (T(x,y * y) * z) = x * y. [back_rewrite(31061),rewrite([43394(6),37126(5),33403(4)])]. given #2769 (W1w,wt=21): 43425 (x \ y) * (((y \ x) / z) * T(y,x)) = (z \ (x \ y)) * x. [para(1014(a,1),7969(a,1,2,1)),rewrite([3143(10)])]. given #2770 (W1w,wt=21): 44099 x * (x * ((T(y,x) * z) / u)) = (x * (y * (x * z))) / u. [para(33450(a,1),3925(a,1,2,2)),rewrite([4408(5),10229(4),4230(4),4247(5),38305(8),44096(5),15452(8),23499(8),2738(9),44071(8),16(3),10809(9),18(6)]),flip(a)]. given #2771 (W1a,wt=29): 3770 L(T(T(T(x,y \ 1),z),u),w,v5) / y = L(T(T(T(x,z),u),y \ 1),w,v5) / y. [para(30(a,1),3382(a,1,1,1,1)),rewrite([30(5),30(6),30(9),30(10),30(13)])]. given #2772 (W1a,wt=27): 3801 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v7,v8),v5,v6),u,w),y,z). [para(227(a,2),230(a,1))]. given #2773 (W1r,wt=28): 190776 T(x * ((x \ (y \ z)) * L(y,z,u)),w) = L(L(T(T(z,y),w),y,u),x,z * y). [back_rewrite(172869),rewrite([190692(4)])]. given #2774 (W1r,wt=29): 216279 (x / T(T(T(T(T(y,z),u),w),v5),v6)) * (T(T(T(T(T(y,v5),z),u),w),v6) / x) = 1. [para(12446(a,1),20322(a,1,2,1)),rewrite([8846(8)])]. given #2775 (W1r,wt=21): 258997 T(x * x,y * (z * (y \ K(x * x,z)))) = T(x * x,z). [back_rewrite(244015),rewrite([258949(5)])]. given #2776 (W1r,wt=25): 261132 (x \ y) * T(x / (y * y),y \ (y \ 1)) = y \ K(y * (y * y),x). [para(19307(a,1),193096(a,2,1)),rewrite([3143(3),6072(9,R),7967(9),4408(6),45(3),1014(4),184298(6),110290(3),16256(3),6368(2),6072(9,R),7967(9),4408(6),45(3),1014(4),4278(8),10229(5),1014(5),103837(3),30703(9),1014(8),10400(6),989(5),4408(8),1014(15),10400(13),989(12),103664(14),259065(12),989(10),10400(11),989(10),147785(13),4408(12),4408(11),45(10),100(10),246329(14),3143(14)])]. given #2777 (W1r,wt=26): 243020 ((x / y) / z) * (y \ K(x,y * (z * y))) = L(y \ (z \ (y \ x)),x,z). [back_rewrite(184792),rewrite([236333(7),113933(7),216726(7),52858(11)])]. given #2778 (W2w,wt=31): 17256 x * (y * (x \ (x \ (T(T(z,u),w) / v5)))) = x * (y * (x \ (x \ (T(T(z,w),u) / v5)))). [para(11449(a,1),4397(a,2,2,2)),rewrite([4397(11)])]. given #2779 (W2w,wt=31): 17966 L(L(x \ K(y,z),u,L(((z * (y / z)) * x) \ y,w,v5)),w,v5) = L(x \ K(y,z),w,v5). [back_rewrite(17354),rewrite([17822(2),17822(11)])]. given #2780 (W2w,wt=31): 18825 (x * (y * (z * (u * (z * (y * (x * w))))))) / w = x * (y * (z * (u * (z * (y * x))))). [para(130(a,1),106(a,1,1,2)),rewrite([130(13)])]. given #2781 (W2w,wt=31): 18950 T(x * (y * y),z * T(u,x \ (x \ z))) = T(y * (y * x),x * (u * (x \ (x \ z)))). [para(4397(a,1),10927(a,1,2)),flip(a)]. given #2782 (W2a,wt=35): 5105 x * (y * L(L(L(L(z,u,w),v5,v6),v7,v8),v9,v10)) = x * (y * L(L(L(L(z,v7,v8),u,w),v5,v6),v9,v10)). [para(231(a,2),72(a,1,2)),rewrite([5084(7)])]. given #2783 (W2a,wt=35): 5106 x * (y * L(L(L(L(z,u,w),v5,v6),v7,v8),v9,v10)) = x * (y * L(L(L(L(z,v9,v10),v7,v8),u,w),v5,v6)). [para(1556(a,1),72(a,1,2)),rewrite([72(7)]),flip(a)]. given #2784 (W2r,wt=35): 282856 T(K(x,y) * ((z * u) * w),(u \ (z \ K(y,x * x))) * (w \ K(x,y))) = K(x,y) * ((z * u) * w). [back_rewrite(255744),rewrite([282552(12)])]. given #2785 (W2r,wt=31): 236891 T(x * (y \ K(y,x)),y * (y * (x \ (x \ K(x,y))))) * z = K(y,x) * ((x / y) * z). [back_rewrite(231314),rewrite([236297(10)])]. given #2786 (W2r,wt=31): 264554 (x * ((y * x) * z)) * T(u,y \ (x \ 1)) = (x * ((y * x) * z)) * T(u,y \ (x \ u)). [para(29098(a,2),3061(a,1,2)),rewrite([263021(6),201747(15)]),flip(a)]. given #2787 (W2r,wt=31): 277339 T(T(T(x,y \ (z \ 1)),u),w) / (z * y) = T(T(T(x,u),w) / (z * y),y \ (z \ 1)). [para(7773(a,1),206795(a,2,1,1,1)),rewrite([181715(6),256908(7),29(3),7769(3),4407(7),2771(12,R),4407(11)]),flip(a)]. given #2788 (W2r,wt=34): 222274 a(x,(y * (z * (z * (u / y)))) \ w,u * (z * (z * ((u * (y * (z * (z * (u / y))))) * w)))) = 1. [para(12954(a,1),137283(a,1,3,2,1)),rewrite([52858(12),184292(12),185460(11),37(15),189(16),101(7),189(15),4578(7),2040(14),85233(17)])]. given #2789 (W0w,wt=11): 221863 L(x,y * y,L(z,u,w)) = x. [para(186361(a,1),133829(a,1,3))]. given #2790 (W0w,wt=11): 221904 L(x,K(y,z),L(u,w,v5)) = x. [para(186361(a,1),196290(a,1,3))]. given #2791 (W0w,wt=11): 236333 K(x,y) / z = z \ K(x,y). [back_rewrite(208990),rewrite([236300(3),236155(3),1014(4)])]. given #2792 (W0w,wt=11): 238644 K(x,y) * z = z * K(x,y). [back_rewrite(163577),rewrite([236300(2),236297(4),236300(5),194209(6),237155(5),123132(4),37126(3),236300(4)])]. given #2793 (W0w,wt=11): 239344 T(x,y * (z / y)) = T(x,z). [back_rewrite(75703),rewrite([236297(3)]),flip(a)]. given #2794 (W0w,wt=11): 239812 K(x * y,z) = K(y * x,z). [back_rewrite(230135),rewrite([236300(6),236300(7)])]. given #2795 (W0w,wt=11): 240593 K(x,y * z) = K(x,z * y). [back_rewrite(211493),rewrite([236300(6)])]. given #2796 (W0w,wt=11): 241014 K(x,y * (z / y)) = K(x,z). [back_rewrite(209625),rewrite([236300(4),236300(6)])]. given #2797 (W0w,wt=11): 241213 K(x,y * K(z,u)) = K(x,y). [back_rewrite(208409),rewrite([237155(2),238644(2),16343(4),237155(5)])]. given #2798 (W0w,wt=11): 241432 K(x,y \ (z \ y)) = K(z,x). [back_rewrite(203425),rewrite([236300(5)])]. given #2799 (W0w,wt=11): 241515 K(x,y / z) = K(x,z \ y). [back_rewrite(198107),rewrite([236300(5),147785(2),236300(6),178629(4)]),flip(a)]. given #2800 (W0w,wt=11): 241930 K(x * K(y,z),u) = K(x,u). [back_rewrite(163857),rewrite([236300(2),208476(7),238644(2)])]. given #2801 (W0w,wt=11): 242147 T(T(x,y),y \ K(z,u)) = x. [back_rewrite(123301),rewrite([236300(3),237483(7),29303(5),29(4)])]. given #2802 (W0w,wt=11): 242307 K(x * (y / x),z) = K(y,z). [back_rewrite(75644),rewrite([236300(6)])]. given #2803 (W0w,wt=11): 244006 T(x,y * K(z,u)) = T(x,y). [back_rewrite(208429),rewrite([237155(3),238644(3)]),flip(a)]. given #2804 (W0w,wt=11): 244185 T(x,y * z) = T(x,z * y). [back_rewrite(112076),rewrite([237155(5),23(4)])]. given #2805 (W0a,wt=17): 3339 x * T(T(T(y,x),z),u) = T(T(y,z),u) * x. [para(94(a,1),90(a,1,2))]. given #2806 (W0a,wt=15): 3340 T(T(x,y),z) * u = T(T(x,z),y) * u. [para(94(a,2),90(a,1,2)),rewrite([517(4)])]. given #2807 (W0r,wt=19): 181562 (x / y) * (T(x,y \ 1) * z) = x * ((x / y) * z). [para(2771(a,2),189(a,2,2,1)),rewrite([18(2)]),flip(a)]. given #2808 (W0r,wt=17): 57526 T((x \ y) * z,y * (z / x)) = (x \ y) * z. [back_rewrite(53562),rewrite([55053(5)])]. given #2809 (W0r,wt=16): 198284 L(x,y,z) \ T(T(x,y),z) = K(x,y * z). [back_rewrite(147739),rewrite([198251(8)])]. -------- Proof 5 -------- "aa2". ============================== PROOF ================================= % Proof 5 at 186.32 (+ 0.64) seconds: "aa2". % Length of proof is 2025. % Level of proof is 80. % Maximum clause weight is 35. % Given clauses 2809. 1 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 2 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 3 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 4 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 5 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 11 a(x,a(y,z,u),w) = 1 # label("aa2") # label(non_clause) # label(goal). [goal]. 13 1 * x = x. [assumption]. 14 x * 1 = x. [assumption]. 15 x \ (x * y) = y. [assumption]. 16 x * (x \ y) = y. [assumption]. 17 (x * y) / y = x. [assumption]. 18 (x / y) * y = x. [assumption]. 19 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 20 (x * y) \ (y * x) = K(y,x). [assumption]. 21 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 22 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 23 x \ (y * x) = T(y,x). [assumption]. 24 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(1)]. 25 L(x,y,z) != x | a(z,y,x) = 1. [clausify(2)]. 26 T(x,y) != x | T(y,x) = y. [clausify(3)]. 27 T(x,y) != x | K(x,y) = 1. [clausify(4)]. 28 K(x,y) != 1 | T(x,y) = x. [clausify(5)]. 29 T(T(x,y),z) = T(T(x,z),y). [assumption]. 30 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 31 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 32 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 33 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(32),flip(a)]. 34 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 35 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 36 ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang (M1)"). [assumption]. 37 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 43 a(c22,a(c23,c24,c25),c26) != 1 # label("aa2") # answer("aa2"). [deny(11)]. 45 1 \ x = x. [para(13(a,1),15(a,1,2))]. 46 x \ x = 1. [para(14(a,1),15(a,1,2))]. 47 x / x = 1. [para(13(a,1),17(a,1,1))]. 48 x / 1 = x. [para(14(a,1),17(a,1,1))]. 49 x / (y \ x) = y. [para(16(a,1),17(a,1,1))]. 50 (x / y) \ x = y. [para(18(a,1),15(a,1,2))]. 51 a(x,1,y) = 1. [para(13(a,1),19(a,1,1,2)),rewrite([14(3),46(3)]),flip(a)]. 52 a(1,x,y) = 1. [para(13(a,1),19(a,1,1)),rewrite([13(3),46(3)]),flip(a)]. 54 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(19(a,1),16(a,1,2))]. 55 (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y). [para(16(a,1),19(a,1,1,2))]. 56 (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z). [para(16(a,1),19(a,1,2,1))]. 57 (x * (y * ((x * y) \ z))) \ z = a(x,y,(x * y) \ z). [para(16(a,1),19(a,1,2))]. 58 (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z). [para(18(a,1),19(a,1,1,2))]. 59 x \ (((x / (y * z)) * y) * z) = a(x / (y * z),y,z). [para(18(a,1),19(a,1,1))]. 60 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(18(a,1),19(a,1,2,1))]. 63 (x * y) * K(y,x) = y * x. [para(20(a,1),16(a,1,2))]. 64 x \ ((y \ x) * y) = K(y \ x,y). [para(16(a,1),20(a,1,1))]. 65 ((x \ y) * x) \ y = K(x,x \ y). [para(16(a,1),20(a,1,2))]. 66 x \ (y * (x / y)) = K(y,x / y). [para(18(a,1),20(a,1,1))]. 67 (x * (y / x)) \ y = K(y / x,x). [para(18(a,1),20(a,1,2))]. 68 K(x * x,x) = a(x,x,x). [para(20(a,1),19(a,1))]. 70 L(x,1,y) = x. [para(13(a,1),21(a,1,2,2)),rewrite([14(2),15(2)]),flip(a)]. 72 (x * y) * L(z,y,x) = x * (y * z). [para(21(a,1),16(a,1,2))]. 73 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(16(a,1),21(a,1,1))]. 74 L(x \ y,x,z) = (z * x) \ (z * y). [para(16(a,1),21(a,1,2,2)),flip(a)]. 75 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(18(a,1),21(a,1,1))]. 76 L(x,y / x,z) = (z * (y / x)) \ (z * y). [para(18(a,1),21(a,1,2,2)),flip(a)]. 80 R(x,y,1) = x. [para(14(a,1),22(a,1,1)),rewrite([14(3),17(2)]),flip(a)]. 81 R(x,x \ y,z) = (y * z) / ((x \ y) * z). [para(16(a,1),22(a,1,1,1)),flip(a)]. 82 R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z)). [para(16(a,1),22(a,1,1)),flip(a)]. 83 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(16(a,1),22(a,1,2))]. 84 R(x,y,z) * (y * z) = (x * y) * z. [para(22(a,1),18(a,1,1))]. 85 R(x / y,y,z) = (x * z) / (y * z). [para(18(a,1),22(a,1,1,1)),flip(a)]. 86 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(18(a,1),22(a,1,2))]. 87 T(1,x) = 1. [para(13(a,1),23(a,1,2)),rewrite([46(1)]),flip(a)]. 88 T(x,1) = x. [para(14(a,1),23(a,1,2)),rewrite([45(2)]),flip(a)]. 89 T(x,x) = x. [para(23(a,1),15(a,1))]. 90 x * T(y,x) = y * x. [para(23(a,1),16(a,1,2))]. 91 T(x,x \ y) = (x \ y) \ y. [para(16(a,1),23(a,1,2)),flip(a)]. 92 T(x / y,y) = y \ x. [para(18(a,1),23(a,1,2)),flip(a)]. 94 T(T(T(x,y),z),u) = T(T(T(x,u),y),z). [para(29(a,1),29(a,1,1)),flip(a)]. 97 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,v5,v6),y,z),u,w). [para(34(a,1),34(a,1,1)),flip(a)]. 100 (x * x) * y = x * (x * y). [para(13(a,1),36(a,2,2)),rewrite([14(2)])]. 101 (x * y) * x = x * (y * x). [para(36(a,1),14(a,1)),rewrite([14(2)]),flip(a)]. 103 x * (y * (x * ((x * (y * x)) \ z))) = z. [para(36(a,1),16(a,1)),rewrite([101(2)])]. 104 x * ((x \ y) * (x * z)) = (y * x) * z. [para(16(a,1),36(a,1,1,1)),flip(a)]. 106 (x * (y * (x * z))) / z = x * (y * x). [para(36(a,1),17(a,1,1)),rewrite([101(6)])]. 107 (x / y) * (y * ((x / y) * z)) = (x * (x / y)) * z. [para(18(a,1),36(a,1,1,1)),flip(a)]. 110 (x * (y * (z * (y * u)))) \ ((x * (y * (z * y))) * u) = a(x,y * (z * y),u). [para(36(a,1),19(a,1,1,2)),rewrite([101(6),101(11)])]. 112 ((x * (y * x)) * (z * u)) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [para(36(a,1),19(a,1,2,1)),rewrite([101(2),101(11)])]. 113 ((x * y) * (x * z)) \ (x * (y * (x * z))) = a(x * y,x,z). [para(36(a,1),19(a,1,2))]. 114 (x * (y * (x * z))) \ (z * (x * (y * x))) = K(z,x * (y * x)). [para(36(a,1),20(a,1,1)),rewrite([101(5),101(9)])]. 117 (x * (y * (z * y))) \ (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(36(a,1),21(a,1,2,2)),rewrite([101(2),101(10)])]. 118 ((x * (y * x)) * z) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(36(a,1),21(a,1,2)),rewrite([101(2),101(10)])]. 121 ((x * (y * (z * y))) * u) / (y * (z * (y * u))) = R(x,y * (z * y),u). [para(36(a,1),22(a,1,2)),rewrite([101(2),101(10)])]. 122 x \ (y * (z * (y * x))) = T(y * (z * y),x). [para(36(a,1),23(a,1,2)),rewrite([101(6)])]. 125 ((x * (y * x)) * (z * (x * (y * x)))) * u = (x * (y * x)) * (z * (x * (y * (x * u)))). [para(36(a,1),36(a,2,2,2)),rewrite([101(2),101(5),101(6),101(9)])]. 126 (x * ((y * (z * y)) * x)) * u = x * (y * (z * (y * (x * u)))). [para(36(a,1),36(a,2,2)),rewrite([101(2),101(4)])]. 128 (x * (y * x)) * z = x * (y * (x * z)). [back_rewrite(36),rewrite([101(2)])]. 129 (x * (y * (x * (z * (x * (y * x)))))) * u = x * (y * (x * (z * (x * (y * (x * u)))))). [back_rewrite(125),rewrite([128(6),128(14)])]. 130 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [back_rewrite(126),rewrite([128(3)])]. 132 (x * (y * (x * z))) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [back_rewrite(118),rewrite([128(3)])]. 133 (x * (y * (x * (z * u)))) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [back_rewrite(112),rewrite([128(4)])]. 134 (x * (x * y)) \ (x * (x * (y * z))) = z. [para(37(a,1),15(a,1,2))]. 136 x * (x * ((x \ y) * z)) = (x * y) * z. [para(16(a,1),37(a,1,1,2)),flip(a)]. 139 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(37(a,1),19(a,1,1,2))]. 140 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(37(a,1),19(a,1,1)),rewrite([37(7),37(8)])]. 141 (x * ((x * y) * z)) \ (x * (x * (y * z))) = a(x,x * y,z). [para(37(a,1),19(a,1,2))]. 143 (x * (y * (y * z))) \ (y * (y * (z * x))) = K(y * (y * z),x). [para(37(a,1),20(a,1,2))]. 144 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(37(a,1),21(a,1,1)),rewrite([37(7)])]. 145 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(37(a,1),21(a,1,2,2))]. 146 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(37(a,1),22(a,1,1,1)),rewrite([37(4)])]. 148 ((x * (y * (y * z))) * u) / (y * (y * (z * u))) = R(x,y * (y * z),u). [para(37(a,1),22(a,1,2))]. 150 x * (x * ((y * (x * (x * (y * z)))) * u)) = x * (x * (y * (x * (x * (y * (z * u)))))). [para(37(a,1),37(a,1,1,2)),rewrite([37(6),37(7),37(13),37(14)])]. 159 T(T(x,y),x) = T(x,y). [para(89(a,1),29(a,1,1)),flip(a)]. 160 L(T(x,L(x,y,z)),y,z) = L(x,y,z). [para(89(a,1),30(a,1)),flip(a)]. 162 ((x * y) * z) / a(x,y,z) = x * (y * z). [para(19(a,1),49(a,1,2))]. 164 (x * (y * z)) / L(z,y,x) = x * y. [para(21(a,1),49(a,1,2))]. 165 (x * y) / T(x,y) = y. [para(23(a,1),49(a,1,2))]. 166 R(x,y,z) \ ((x * y) * z) = y * z. [para(22(a,1),50(a,1,1))]. 168 x \ ((y * x) * z) = (x \ y) * (x * z). [para(104(a,1),15(a,1,2))]. 169 (x * y) * (y \ z) = y * ((y \ x) * z). [para(16(a,1),104(a,1,2,2)),flip(a)]. 170 ((x * y) * z) / ((y \ x) * (y * z)) = y. [para(104(a,1),17(a,1,1))]. 171 (x / y) * (((x / y) \ z) * x) = (z * (x / y)) * y. [para(18(a,1),104(a,1,2,2))]. 173 a(x,x \ y,x * z) = ((y * x) * z) \ (y * (x * z)). [para(104(a,1),19(a,1,1)),rewrite([16(4)]),flip(a)]. 175 (x * (y * z)) * (a(x,y,z) * ((x * (y * z)) * u)) = (((x * y) * z) * (x * (y * z))) * u. [para(19(a,1),104(a,1,2,1))]. 176 ((x * y) * z) \ (((y \ x) * (y * z)) * y) = K((y \ x) * (y * z),y). [para(104(a,1),20(a,1,1))]. 177 (((x \ y) * (x * z)) * x) \ ((y * x) * z) = K(x,(x \ y) * (x * z)). [para(104(a,1),20(a,1,2))]. 178 (x * y) * (K(y,x) * ((x * y) * z)) = ((y * x) * (x * y)) * z. [para(20(a,1),104(a,1,2,1))]. 179 ((x * y) * z) \ (y * (((y \ x) * (y * z)) * u)) = L(u,(y \ x) * (y * z),y). [para(104(a,1),21(a,1,1))]. 180 L((x \ y) * (x * z),x,u) = (u * x) \ (u * ((y * x) * z)). [para(104(a,1),21(a,1,2,2)),flip(a)]. 181 L(x * y,x \ z,x) = z \ ((z * x) * y). [para(104(a,1),21(a,1,2)),rewrite([16(2)]),flip(a)]. 182 (x * y) * (L(z,y,x) * ((x * y) * u)) = ((x * (y * z)) * (x * y)) * u. [para(21(a,1),104(a,1,2,1))]. 183 (((x * y) * z) * u) / (((y \ x) * (y * z)) * u) = R(y,(y \ x) * (y * z),u). [para(104(a,1),22(a,1,1,1))]. 185 ((x \ y) * (x * z)) \ ((y * x) * z) = T(x,(x \ y) * (x * z)). [para(104(a,1),23(a,1,2))]. 186 x * (T(y,x) * (x * z)) = ((y * x) * x) * z. [para(23(a,1),104(a,1,2,1))]. 187 x * (x * (((x \ y) * (x * z)) * u)) = (x * ((y * x) * z)) * u. [para(104(a,1),37(a,1,1,2)),flip(a)]. 188 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * (y * u)))))) = (z * (x * (x * y))) * u. [para(104(a,1),37(a,1)),rewrite([37(10)]),flip(a)]. 189 (x * y) * (x * z) = x * ((y * x) * z). [para(104(a,1),37(a,2,2)),rewrite([16(2)])]. 190 (x * y) * ((y \ z) * (y * u)) = y * ((y \ x) * ((z * y) * u)). [para(104(a,1),104(a,1,2,2)),flip(a)]. 191 (x * ((x \ y) * z)) / z = R(y,x,x \ z). [back_rewrite(83),rewrite([169(3)])]. 192 (x * y) \ (z * ((z \ x) * y)) = a(x,z,z \ y). [back_rewrite(55),rewrite([169(4)])]. 193 (x * y) * (L(z,y,x) * ((x * y) * u)) = (x * (((y * z) * x) * y)) * u. [back_rewrite(182),rewrite([189(10)])]. 196 (x * ((y * x) * z)) \ (x * (y * (x * z))) = a(x * y,x,z). [back_rewrite(113),rewrite([189(3)])]. 197 R(x,y,y \ 1) = x. [para(14(a,1),191(a,1,1,2)),rewrite([16(2),48(2)]),flip(a)]. 198 R(x * y,x,x \ z) = (x * (y * z)) / z. [para(15(a,1),191(a,1,1,2,1)),flip(a)]. 199 R(x,y,y \ ((y \ x) \ z)) = (y * z) / ((y \ x) \ z). [para(16(a,1),191(a,1,1,2)),flip(a)]. 200 R(x,y,y \ z) * z = y * ((y \ x) * z). [para(191(a,1),18(a,1,1))]. 201 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) = ((x * (y * z)) * (a(x,y,z) * u)) / u. [para(19(a,1),191(a,1,1,2,1)),flip(a)]. 202 R(x * y,y * x,(y * x) \ z) = ((y * x) * (K(x,y) * z)) / z. [para(20(a,1),191(a,1,1,2,1)),flip(a)]. 203 R(x * (y * z),x * y,(x * y) \ u) = ((x * y) * (L(z,y,x) * u)) / u. [para(21(a,1),191(a,1,1,2,1)),flip(a)]. 204 R(x * y,y,y \ z) = (y * (T(x,y) * z)) / z. [para(23(a,1),191(a,1,1,2,1)),flip(a)]. 205 (x * (x * (y * (((x * (x * y)) \ z) * u)))) / u = R(z,x * (x * y),(x * (x * y)) \ u). [para(37(a,1),191(a,1,1))]. 206 R(x,x,x \ y) = x. [para(46(a,1),191(a,1,1,2,1)),rewrite([13(2),17(2)]),flip(a)]. 208 R(x,x / y,(x / y) \ z) = ((x / y) * (y * z)) / z. [para(50(a,1),191(a,1,1,2,1)),flip(a)]. 209 a(x,y,z) \ ((x * y) * z) = T(x * (y * z),a(x,y,z)). [para(19(a,1),91(a,1,2)),rewrite([19(9)]),flip(a)]. 218 x / T(y,y \ x) = y \ x. [para(91(a,2),49(a,1,2))]. 220 R(x,y \ z,T(y,y \ z)) = R(x,y \ z,(y \ z) \ z). [para(91(a,2),191(a,2,3)),rewrite([191(6)]),flip(a)]. 221 T(x \ y,T(x,x \ y)) = ((x \ y) \ y) \ y. [para(91(a,2),91(a,1,2))]. 228 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,u,w),y,z),v5,v6). [para(97(a,1),34(a,1))]. 229 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v5,v6),y,z),v7,v8),u,w). [para(97(a,2),34(a,1,1))]. 260 T(x * ((x \ y) * z),a(x,x \ y,z)) = a(x,x \ y,z) \ (y * z). [para(16(a,1),209(a,1,2,1)),flip(a)]. 262 a(x,y,y \ z) \ (y * ((y \ x) * z)) = T(x * z,a(x,y,y \ z)). [para(16(a,1),209(a,2,1,2)),rewrite([169(5)])]. 263 T((x / y) * (y * z),a(x / y,y,z)) = a(x / y,y,z) \ (x * z). [para(18(a,1),209(a,1,2,1)),flip(a)]. 265 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(209(a,1),49(a,1,2))]. 268 ((x * (y \ z)) * T(y,y \ z)) / z = R(x,y \ z,(y \ z) \ z). [para(220(a,1),22(a,2)),rewrite([90(9),16(7)])]. 311 (x * (y * (y * z))) \ ((x * (y * y)) * z) = a(x,y * y,z). [para(13(a,1),110(a,1,1,2,2)),rewrite([13(5),13(9)])]. 312 (x * (y * (z * (y * u)))) * a(x,y * (z * y),u) = (x * (y * (z * y))) * u. [para(110(a,1),16(a,1,2))]. 314 (x * ((y \ z) * (y * ((y \ z) * u)))) \ ((x * ((y \ z) * z)) * u) = a(x,(y \ z) * z,u). [para(16(a,1),110(a,1,2,1,2,2)),rewrite([16(14)])]. 326 ((x / y) * (z * x)) \ (y * ((x / y) * (z * (x / y)))) = K(y,(x / y) * (z * (x / y))). [para(18(a,1),114(a,1,1,2,2))]. 338 ((x * (y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(13(a,1),148(a,1,2,2,2)),rewrite([14(2),14(8)])]. 340 ((x * (y * (y * z))) * (z \ u)) / (y * (y * u)) = R(x,y * (y * z),z \ u). [para(16(a,1),148(a,1,2,2,2))]. 341 R(x,y * (y * z),u) * (y * (y * (z * u))) = (x * (y * (y * z))) * u. [para(148(a,1),18(a,1,1))]. 342 R(x / (y * (y * z)),y * (y * z),u) = (x * u) / (y * (y * (z * u))). [para(18(a,1),148(a,1,1,1)),flip(a)]. 345 (x * (x * ((x * y) * z))) / (x * (x * (y * z))) = R(x,x * (x * y),z). [para(37(a,1),148(a,1,1))]. 346 ((x * (y * z)) * (y * u)) / (y * ((z * y) * u)) = R(x,y * z,y * u). [para(104(a,1),148(a,1,2,2)),rewrite([16(2),16(10)])]. 350 ((x * y) * z) * K((y \ x) * (y * z),y) = ((y \ x) * (y * z)) * y. [para(176(a,1),16(a,1,2))]. 354 ((x * (y / z)) * z) \ ((((y / z) \ x) * y) * (y / z)) = K(((y / z) \ x) * y,y / z). [para(18(a,1),176(a,1,2,1,2)),rewrite([18(13)])]. 356 (x * (x * y)) \ (x * (y * x)) = K(x * y,x). [para(46(a,1),176(a,1,2,1,1)),rewrite([100(2),13(5),101(4),46(6),13(8)])]. 357 ((x * (x / y)) * z) \ ((y * ((x / y) * z)) * (x / y)) = K(y * ((x / y) * z),x / y). [para(50(a,1),176(a,1,2,1,1)),rewrite([50(11)])]. 393 x * (x * ((x * (y * (x * (x * x)))) * z)) = x * (x * (x * (y * (x * (x * (x * z)))))). [para(129(a,1),37(a,1)),flip(a)]. 398 x * (x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u))))))) = x * (x * u). [para(16(a,1),150(a,1,2,2)),flip(a)]. 405 x * ((y * x) * (x * ((x \ y) * (z * u)))) = x * (x * (((x \ y) * ((x * y) * z)) * u)). [para(104(a,1),150(a,2,2)),rewrite([136(5)]),flip(a)]. 407 x * (x * (((x * x) \ y) * (x * (x * z)))) = (y * (x * x)) * z. [para(13(a,1),188(a,1,2,2,2,2,2,2)),rewrite([14(3),13(7),14(9)])]. 411 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [para(16(a,1),188(a,1,2,2,2,2,2,2))]. 418 (x * y) * (((x * y) \ z) * (x * ((y * x) * u))) = (z * (x * y)) * (x * u). [para(104(a,1),188(a,1,2,2,2,2,2)),rewrite([16(3),136(10),16(10)])]. 426 (x * (y * (x * y))) * z = (x * y) * ((x * y) * z). [para(13(a,1),175(a,1,1,2)),rewrite([51(3),13(4),13(5),14(6),13(7),189(7),101(6)]),flip(a)]. 435 R(x * ((x \ y) * z),y * z,(y * z) \ u) = ((y * z) * (a(y,x,x \ z) * u)) / u. [para(16(a,1),201(a,1,2,2)),rewrite([169(3),16(6),16(9)])]. 437 R(((x / (y * z)) * y) * z,x,x \ u) = (x * (a(x / (y * z),y,z) * u)) / u. [para(18(a,1),201(a,1,2)),rewrite([18(8),18(10)])]. 439 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) \ ((x * (y * z)) * (a(x,y,z) * u)) = u. [para(201(a,2),50(a,1,1))]. 463 x * (x * (x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))))) = x * (x * z). [para(16(a,1),393(a,1,2,2)),flip(a)]. 478 R(x,1 / y,y) = x. [para(50(a,1),197(a,1,3))]. 480 R(x,x,y) = x. [para(15(a,1),206(a,1,3))]. 493 R(T(x,y),x,z) = T(x,y). [para(480(a,1),31(a,1,1)),flip(a)]. 495 R(R(x,y,z),x,u) = R(x,y,z). [para(480(a,1),35(a,1,1)),flip(a)]. 506 (x * (1 / y)) * y = x. [para(478(a,1),22(a,2)),rewrite([18(7),48(6)])]. 507 (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z)). [para(90(a,1),19(a,1,1,2))]. 508 (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z). [para(90(a,1),19(a,1,2,1))]. 510 (x * y) \ (T(x,y) * y) = K(T(x,y),y). [para(90(a,1),20(a,1,1))]. 511 (T(x,y) * y) \ (x * y) = K(y,T(x,y)). [para(90(a,1),20(a,1,2))]. 512 (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y). [para(90(a,1),21(a,1,1))]. 516 ((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,y)). [para(90(a,1),22(a,1,2))]. 517 x * T(T(y,x),z) = T(y,z) * x. [para(29(a,1),90(a,1,2))]. 518 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(30(a,1),90(a,1,2))]. 519 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(31(a,1),90(a,1,2))]. 520 x * (x * (T(y,x) * z)) = x * (y * (x * z)). [para(90(a,1),37(a,1,1,2)),rewrite([128(3)]),flip(a)]. 521 x * (x * (y * T(z,x * (x * y)))) = z * (x * (x * y)). [para(90(a,1),37(a,1)),flip(a)]. 522 x * ((x \ y) * (z * x)) = (y * x) * T(z,x). [para(90(a,1),104(a,1,2,2))]. 536 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(22(a,1),92(a,1,1)),rewrite([31(3)]),flip(a)]. 537 T(T(x / y,z),y) = T(y \ x,z). [para(92(a,1),29(a,1,1)),flip(a)]. 538 x \ (y * ((y \ z) * x)) = R(T(z,x),y,y \ x). [para(191(a,1),92(a,1,1)),rewrite([31(3)]),flip(a)]. 540 K(T(x,y),x) = 1. [hyper(27,a,159,a)]. 541 T(x,T(x,y)) = x. [hyper(26,a,159,a)]. 547 T(x,y) * x = x * T(x,y). [para(159(a,1),90(a,1,2)),flip(a)]. 554 K(x \ y,y / x) = 1. [para(92(a,1),540(a,1,1))]. 555 K(x,T(x,y)) = 1. [hyper(27,a,541,a)]. 560 T(x,(x \ y) \ y) = x. [para(91(a,1),541(a,1,2))]. 568 K(x / y,y \ x) = 1. [para(92(a,1),555(a,1,2))]. 582 x * a(x / (y * z),y,z) = ((x / (y * z)) * y) * z. [para(18(a,1),54(a,1,1))]. 588 ((x * y) * z) \ ((x * (y * z)) * (a(x,y,z) * u)) = L(u,a(x,y,z),x * (y * z)). [para(54(a,1),21(a,1,1))]. 589 (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),y * (z * u),x). [para(54(a,1),21(a,1,2,2))]. 592 ((x * (y * (z * u))) * a(y,z,u)) / ((y * z) * u) = R(x,y * (z * u),a(y,z,u)). [para(54(a,1),22(a,1,2))]. 597 (x * (y * z)) * (((x * (y * z)) \ u) * ((x * y) * z)) = (u * (x * (y * z))) * a(x,y,z). [para(54(a,1),104(a,1,2,2))]. 601 (((x * y) * z) * (x * (y * z))) * a(x,y,z) = (x * (y * z)) * (a(x,y,z) * ((x * y) * z)). [para(54(a,1),175(a,1,2,2)),flip(a)]. 602 (x * (y * z)) * a(x,z,T(y,z)) = (x * z) * T(y,z). [para(90(a,1),54(a,1,1,2))]. 614 (x * ((x \ y) * ((y \ z) * (y * u)))) \ ((z * y) * u) = a(x,x \ y,(y \ z) * (y * u)). [para(104(a,1),56(a,1,2))]. 625 T(x / y,z) * y = y * T(y \ x,z). [para(537(a,1),90(a,1,2)),flip(a)]. 632 L(x \ 1,x,y) = (y * x) \ y. [para(14(a,1),74(a,2,2))]. 634 L(x \ (y \ z),x,y) = (y * x) \ z. [para(16(a,1),74(a,2,2))]. 637 (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x). [para(20(a,1),74(a,1,1)),flip(a)]. 638 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(21(a,1),74(a,1,1)),flip(a)]. 639 L(T(x,y),y,x) = T(x,x * y). [para(74(a,2),23(a,1)),rewrite([23(2)])]. 648 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(y * z) \ (y * u)). [para(74(a,2),191(a,2,3)),rewrite([191(8)]),flip(a)]. 650 T(x * y,(x * y) \ (x * z)) = L(y \ z,y,x) \ (x * z). [para(74(a,2),91(a,2,1))]. 659 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(90(a,1),74(a,2,2))]. 662 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,(x * y) \ (x * z),u). [para(74(a,2),56(a,1,1,2,1))]. 666 L(K(x,y),y * x,y) = K(y * x,y). [back_rewrite(356),rewrite([637(5)])]. 667 L(L(x,y,z),z * y,z) = x. [back_rewrite(134),rewrite([638(6)])]. 669 x * (T(y,x) * x) = (y * x) * x. [para(14(a,1),186(a,1,2,2)),rewrite([14(7)])]. 673 (((x * y) * y) * z) \ ((x * y) * (y * z)) = a(y,T(x,y),y * z). [para(186(a,1),19(a,1,1)),rewrite([90(5)])]. 674 (x * ((T(y,x) * (x * z)) * u)) \ ((((y * x) * x) * z) * u) = a(x,T(y,x) * (x * z),u). [para(186(a,1),19(a,1,2,1))]. 675 ((T(x,y) * (y * z)) * y) \ (((x * y) * y) * z) = K(y,T(x,y) * (y * z)). [para(186(a,1),20(a,1,2))]. 682 x * (T(T(y,x),z) * (x * u)) = ((T(y,z) * x) * x) * u. [para(29(a,1),186(a,1,2,1))]. 684 x * (R(T(y,x),z,u) * (x * w)) = ((R(y,z,u) * x) * x) * w. [para(31(a,1),186(a,1,2,1))]. 690 a((x * y) * y,T(x,y),z) = a(y,T(x,y) * (x * y),z). [para(186(a,1),110(a,1,2,1)),rewrite([186(6),19(11),90(7)])]. 729 ((x * (y / z)) * z) / T(x * y,a(x,y / z,z)) = a(x,y / z,z). [para(18(a,1),265(a,1,2,1,2))]. 732 (x * (y * z)) / T((x * y) * z,a(y,y \ x,y * z)) = a(y,y \ x,y * z). [para(104(a,1),265(a,1,2,1)),rewrite([16(2)])]. 777 x * (x * T(y,x * x)) = y * (x * x). [para(13(a,1),521(a,1,2,2)),rewrite([14(2),14(6)])]. 778 x * (y * T(z,x * (x * y))) = x \ (z * (x * (x * y))). [para(521(a,1),15(a,1,2)),flip(a)]. 780 L(x * T(y,z * (z * x)),z,z) = (z * z) \ (y * (z * (z * x))). [para(521(a,1),21(a,1,2)),flip(a)]. 788 x * (y * (x * T(z,x * (y * x)))) = z * (x * (y * x)). [para(90(a,1),521(a,1,2,2,2,2,2)),rewrite([520(7),90(8)])]. 831 (x * ((x \ y) * y)) \ ((y * x) * ((x \ y) * z)) = L(z,(x \ y) * y,x). [para(104(a,1),117(a,1,1)),rewrite([169(3),104(9),16(11)])]. 843 (((x * y) * y) * z) / K(y,T(x,y) * (y * z)) = (T(x,y) * (y * z)) * y. [para(675(a,1),49(a,1,2))]. 863 (T(T(x,y),z) * (z * u)) * z = (T(T(x,z),y) * (z * u)) * z. [para(29(a,1),843(a,2,1,1)),rewrite([843(10)])]. 874 x * K((y \ z) * (y * ((z * y) \ x)),y) = ((y \ z) * (y * ((z * y) \ x))) * y. [para(16(a,1),350(a,1,1))]. 888 ((1 / x) * y) \ (x * ((1 / x) * (y * (1 / x)))) = K(x,(1 / x) * (y * (1 / x))). [para(14(a,1),326(a,1,1,2))]. 960 (R(x,y,z) * u) / R(T(x,u),y,z) = u. [para(31(a,1),165(a,1,2))]. 961 (x * (x * (y * z))) / T(x * (x * y),z) = z. [para(37(a,1),165(a,1,1))]. 965 (x * y) / T(y,T(x,y)) = T(x,y). [para(90(a,1),165(a,1,1))]. 969 (((x \ y) * (x * z)) * x) / T((y * x) * z,K((x \ y) * (x * z),x)) = K((x \ y) * (x * z),x). [para(350(a,1),165(a,1,1))]. 974 x * (1 / y) = x / y. [para(506(a,1),17(a,1,1)),flip(a)]. 975 x / (1 / y) = x * y. [para(18(a,1),506(a,1,1)),flip(a)]. 976 a(x,1 / y,y) = 1. [para(506(a,1),19(a,1,2)),rewrite([18(3),14(2),46(1)]),flip(a)]. 980 (x / y) / K(1 / y,T(x,1 / y)) = T(x,1 / y) / y. [para(506(a,1),843(a,1,1)),rewrite([974(3),18(9),14(8),18(14),14(13),974(14)])]. 982 K(x,1 / x) = 1. [para(506(a,1),357(a,1,1)),rewrite([18(4),14(3),974(4),47(2),46(3),18(4),14(3)]),flip(a)]. 985 ((1 / x) * y) \ (x * ((1 / x) * (y / x))) = K(x,(1 / x) * (y / x)). [back_rewrite(888),rewrite([974(8),974(14)])]. 986 T(x,1 / x) = x. [hyper(28,a,982,a)]. 989 1 / x = x \ 1. [hyper(26,a,986,a),rewrite([92(3)]),flip(a)]. 990 (x \ 1) \ 1 = x. [para(986(a,1),23(a,2)),rewrite([989(2),989(4),16(5)])]. 996 T(x \ 1,x) = x \ 1. [para(49(a,1),986(a,1,2))]. 997 (x \ 1) * x = 1. [para(986(a,1),90(a,1,2)),rewrite([989(2),989(5),16(6)])]. 1004 ((x \ 1) * y) \ (x * ((x \ 1) * (y / x))) = K(x,(x \ 1) * (y / x)). [back_rewrite(985),rewrite([989(2),989(5),989(11)])]. 1009 (x / y) / K(y \ 1,T(x,y \ 1)) = T(x,y \ 1) / y. [back_rewrite(980),rewrite([989(3),989(5),989(10)])]. 1012 a(x,y \ 1,y) = 1. [back_rewrite(976),rewrite([989(2)])]. 1013 x / (y \ 1) = x * y. [back_rewrite(975),rewrite([989(2)])]. 1014 x * (y \ 1) = x / y. [back_rewrite(974),rewrite([989(2)])]. 1022 L(x,x \ 1,y) = x. [para(990(a,1),74(a,1,1)),rewrite([1014(6),14(6),50(5)])]. 1025 (x \ 1) * (x * y) = L(y,x,x \ 1). [para(997(a,1),21(a,1,1)),rewrite([45(6)])]. 1026 L(x,y,(y * x) \ 1) = (((y * x) \ 1) * y) \ 1. [para(997(a,1),21(a,1,2)),flip(a)]. 1027 R(x \ 1,x,y) = y / (x * y). [para(997(a,1),22(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1039 R((x * (x * y)) \ 1,x * (x * y),z) = z / (x * (x * (y * z))). [para(997(a,1),148(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1051 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x \ (y \ 1),y). [para(997(a,1),56(a,1,2))]. 1072 a(x,y,y \ 1) = 1. [para(50(a,1),1012(a,1,2)),rewrite([989(2)])]. 1077 L(x \ 1,x,y) = x \ 1. [para(50(a,1),1022(a,1,2)),rewrite([989(2),989(5)])]. 1078 L(L(L(x,y,z),u,w),L(x,u,w) \ 1,v5) = L(L(x,u,w),y,z). [para(1022(a,1),97(a,1,1)),flip(a)]. 1080 L(L(L(x,y,z),u,w),x \ 1,v5) = L(L(x,y,z),u,w). [para(1022(a,1),97(a,2,1,1))]. 1091 (x * y) \ x = y \ 1. [back_rewrite(632),rewrite([1077(3)]),flip(a)]. 1097 (x * (y * K(y,x))) \ (y * x) = a(x,y,K(y,x)). [para(20(a,1),57(a,1,1,2,2)),rewrite([20(8)])]. 1098 (x * (y * L(z,y,x))) \ (x * (y * z)) = a(x,y,L(z,y,x)). [para(21(a,1),57(a,1,1,2,2)),rewrite([21(10)])]. 1105 (x * (y * L(y \ z,y,x))) \ (x * z) = a(x,y,(x * y) \ (x * z)). [para(74(a,2),57(a,1,1,2,2))]. 1141 L(x,y,(y * x) \ 1) \ 1 = ((y * x) \ 1) * y. [para(1026(a,2),49(a,1,2)),rewrite([989(6)])]. 1180 L(x,x \ y,x) = x. [para(14(a,1),181(a,1,1)),rewrite([14(5),15(4)])]. 1201 T(x,L(y * z,y \ x,y)) = T(x,x \ ((x * y) * z)). [para(181(a,2),91(a,1,2)),rewrite([91(10,R)])]. 1227 L(x * y,x \ (x \ 1),x) = (x \ 1) \ y. [para(997(a,1),181(a,2,2,1)),rewrite([13(9)])]. 1246 (x * (x * y)) / T(x * (x * (y / z)),z) = z. [para(18(a,1),961(a,1,1,2,2))]. 1251 (x * ((y * x) * z)) / T(x * y,x * z) = x * z. [para(104(a,1),961(a,1,1,2)),rewrite([16(5)])]. 1252 (x * (x * (y * z))) / T(x * (x * z),T(y,z)) = T(y,z). [para(90(a,1),961(a,1,1,2,2))]. 1266 (((T(x,y) * z) * z) * u) / (T(T(x,z),y) * (z * u)) = z. [para(682(a,1),17(a,1,1))]. 1300 a(x,x,y) = 1. [para(13(a,1),690(a,1,1,1)),rewrite([87(3),51(3),87(3),13(4),13(3)]),flip(a)]. 1301 a(x * (y \ x),T(y,y \ x),z) = a(y \ x,T(y,y \ x) * x,z). [para(16(a,1),690(a,1,1,1)),rewrite([16(10)])]. 1316 K(x * x,x) = 1. [back_rewrite(68),rewrite([1300(3)])]. 1323 x \ (y * (x * x)) = x * T(y,x * x). [para(13(a,1),778(a,1,2)),rewrite([14(2),14(5)]),flip(a)]. 1324 x \ (x \ (y * (x * (x * z)))) = z * T(y,x * (x * z)). [para(778(a,1),15(a,1,2))]. 1346 (x \ (y * (x * z))) \ (z * T(y,x * z)) = a(x,x \ z,T(y,x * z)). [para(778(a,1),56(a,1,1)),rewrite([16(2),16(5),16(10)])]. 1353 x * (y / (x * (x * y))) = x \ 1. [para(997(a,1),778(a,2,2)),rewrite([996(7),1014(5)])]. 1359 x * (y * T(z,y * (x * y))) = y \ (z * (y * (x * y))). [para(788(a,1),15(a,1,2)),flip(a)]. 1448 R((x * (y * x)) \ 1,x * (y * x),z) = z / (x * (y * (x * z))). [para(997(a,1),121(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1452 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,x \ y). [para(268(a,1),18(a,1,1)),rewrite([200(5)])]. 1457 R(x,y \ z,(y \ z) \ z) \ ((x * (y \ z)) * T(y,y \ z)) = z. [para(268(a,1),50(a,1,1))]. 1466 (T(T(x,y),z) * u) * z = (T(T(x,z),y) * u) * z. [para(16(a,1),863(a,1,1,2)),rewrite([16(8)])]. 1479 x * (x * ((T(T(y,z),u) * (u * w)) * u)) = x * (x * ((T(T(y,u),z) * (u * w)) * u)). [para(863(a,1),37(a,2,2,2)),rewrite([37(7)])]. 1517 (x * (y * z)) / T((x * z) * T(y,z),a(z,z \ x,y * z)) = a(z,z \ x,y * z). [para(90(a,1),732(a,1,1,2)),rewrite([90(8),90(13)])]. 1524 L(x * ((y * (y * x)) \ z),y,y) = (y * y) \ z. [para(18(a,1),780(a,2,2)),rewrite([92(6)])]. 1534 L(x / (y * (y * x)),y,y) = (y * y) \ 1. [para(997(a,1),780(a,2,2)),rewrite([996(7),1014(5)])]. 1603 (x * (x * ((T(T(y,z),u) * (u * w)) * u))) / (x * (x * ((T(T(y,u),z) * (u * w)) * u))) = 1. [para(1479(a,1),265(a,1,2,1)),rewrite([100(7),1300(20),88(16),1300(21)])]. 1607 L(x,y,y) = x. [hyper(24,a,1300,a)]. 1609 x / (y * (y * x)) = (y * y) \ 1. [back_rewrite(1534),rewrite([1607(4)])]. 1619 x * ((y * (y * x)) \ z) = (y * y) \ z. [back_rewrite(1524),rewrite([1607(5)])]. 1649 x / (x * x) = x \ 1. [back_rewrite(1353),rewrite([1609(3),1014(4)])]. 1659 T(x * x,x) = x * x. [hyper(28,a,1316,a)]. 1667 L(x,y,x) = x. [para(15(a,1),1180(a,1,2))]. 1684 a(x,y,x) = 1. [hyper(25,a,1667,a)]. 1685 L(T(x,y),z,x) = T(x,y). [para(1667(a,1),30(a,1,1)),flip(a)]. 1689 L(L(L(x,y,z),u,w),v5,L(x,u,w)) = L(L(x,u,w),y,z). [para(1667(a,1),97(a,1,1)),flip(a)]. 1699 ((x \ y) * x) \ ((x \ y) * y) = x \ y. [para(1667(a,1),74(a,1)),flip(a)]. 1702 a((x \ y) * x,x \ y,z) = a(x \ y,y,z). [para(1667(a,1),662(a,1,1,2,1)),rewrite([189(5),16(3),19(7),1699(9)]),flip(a)]. 1708 T(x,x * y) = T(x,y). [back_rewrite(639),rewrite([1685(2)]),flip(a)]. 1723 K(x,(y * x) / y) = 1. [para(15(a,1),554(a,1,1))]. 1812 T(x * y,y \ 1) = (y \ 1) \ x. [para(1013(a,1),92(a,1,1))]. 1826 K(x * y,(y \ 1) \ x) = 1. [para(1013(a,1),568(a,1,1))]. 1829 x \ (x / y) = y \ 1. [para(1014(a,1),15(a,1,2))]. 1832 (x / y) \ ((y \ 1) * x) = K(y \ 1,x). [para(1014(a,1),20(a,1,1))]. 1833 ((x \ 1) * y) \ (y / x) = K(y,x \ 1). [para(1014(a,1),20(a,1,2))]. 1834 (x / y) \ (x * ((y \ 1) * z)) = L(z,y \ 1,x). [para(1014(a,1),21(a,1,1))]. 1836 ((x * y) / z) / (y / z) = R(x,y,z \ 1). [para(1014(a,1),22(a,1,1)),rewrite([1014(5)])]. 1837 (x \ 1) \ (y / x) = T(y,x \ 1). [para(1014(a,1),23(a,1,2))]. 1838 x * (x * ((y \ 1) * z)) = (x * (x / y)) * z. [para(1014(a,1),37(a,1,1,2)),flip(a)]. 1839 (x * (x * y)) / z = x * (x * (y / z)). [para(1014(a,1),37(a,1)),rewrite([1014(6)])]. 1840 x * ((x \ y) * (x / z)) = (y * x) / z. [para(1014(a,1),104(a,1,2,2)),rewrite([1014(8)])]. 1851 (x * (y * (x * (z * (x * (y * x)))))) / u = x * (y * (x * (z * (x * (y * (x / u)))))). [para(1014(a,1),129(a,1)),rewrite([1014(10)])]. 1859 x * (T(y,x) * (x / z)) = ((y * x) * x) / z. [para(1014(a,1),186(a,1,2,2)),rewrite([1014(9)])]. 1864 ((T(x,y) * (y / z)) * y) \ (((x * y) * y) / z) = K(y,T(x,y) * (y / z)). [para(1014(a,1),675(a,1,1,1,2)),rewrite([1014(9),1014(12)])]. 1870 x * (x * ((y * (((x * (x * y)) \ z) * u)) / u)) = R(z,x * (x * y),(x * (x * y)) \ u). [para(205(a,1),1014(a,2)),rewrite([1014(10),1839(8)])]. 1884 x * (x * ((y / z) / T(x * (x * y),z \ 1))) = z \ 1. [para(1014(a,1),961(a,1,1,2,2)),rewrite([1839(9)])]. 1885 x * (x * ((y * z) / T(x * (x * y),z))) = z. [para(961(a,1),1014(a,2)),rewrite([1014(9),1839(7)])]. 1888 x * ((y \ 1) * T(z,x * (x / y))) = x \ (z * (x * (x / y))). [para(1014(a,1),778(a,1,2,2,2,2)),rewrite([1014(10)])]. 1907 x * (x * (((T(T(y,z),u) * (u * w)) * u) / (x * (x * ((T(T(y,u),z) * (u * w)) * u))))) = 1. [back_rewrite(1603),rewrite([1839(15)])]. 1921 x * (x * ((y * z) / T(x * (x * z),T(y,z)))) = T(y,z). [back_rewrite(1252),rewrite([1839(8)])]. 1925 x * (x * (y / T(x * (x * (y / z)),z))) = z. [back_rewrite(1246),rewrite([1839(7)])]. 1932 x * (x * (((x * y) * z) / (x * (x * (y * z))))) = R(x,x * (x * y),z). [back_rewrite(345),rewrite([1839(8)])]. 1935 x * (x * R(y,z,u)) = R(x * (x * y),z,u). [back_rewrite(146),rewrite([1839(6),22(4)])]. 1952 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(x / (y * (y * z)),y * (y * z),u). [para(37(a,1),60(a,1,1,2))]. 1958 ((x / y) * (z * y)) \ (x * T(z,y)) = a(x / y,y,T(z,y)). [para(90(a,1),60(a,1,1,2))]. 1961 L(a(x / y,y,z),(x / y) * (y * z),u) = (u * ((x / y) * (y * z))) \ (u * (x * z)). [para(60(a,1),74(a,1,1))]. 1972 R(x,x / y,(x / y) \ (y \ z)) = ((x / y) * z) / (y \ z). [para(16(a,1),208(a,2,1,2))]. 1990 R(x,x / y,(x / y) \ T(z,y)) = ((x / y) * (z * y)) / T(z,y). [para(90(a,1),208(a,2,1,2))]. 2004 R(x,x * y,(x * y) \ z) = ((x * y) * ((y \ 1) * z)) / z. [para(1013(a,1),208(a,1,2)),rewrite([1013(4),1013(7)])]. 2009 (x / y) * ((x / y) * ((y * z) / T((x / y) * x,z))) = z. [para(18(a,1),1885(a,1,2,2,2,1,2))]. 2010 (x * y) / T(z * (z * x),y) = (z * z) \ y. [para(1885(a,1),21(a,1,2)),rewrite([1607(8)]),flip(a)]. 2012 x * (x * (((x * x) \ y) * z)) = y * z. [para(1885(a,1),37(a,1,1)),rewrite([2010(6)]),flip(a)]. 2032 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (((T(y,z) * x) * x) * u),w))) = w. [para(682(a,1),1885(a,1,2,2,2,1,2))]. 2040 (x * (y * y)) * z = x * (y * (y * z)). [back_rewrite(407),rewrite([2012(7)]),flip(a)]. 2044 R(x,y * y,z) = x. [back_rewrite(338),rewrite([2040(3),17(6)]),flip(a)]. 2045 a(x,y * y,z) = 1. [back_rewrite(311),rewrite([2040(6),46(7)]),flip(a)]. 2166 x / (T(T(y,z),u) * (z * (((T(y,u) * z) * z) \ x))) = z. [para(16(a,1),1266(a,1,1))]. 2213 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(13(a,1),130(a,1,1,2,2)),rewrite([13(8)])]. 2214 (x * (y * (z * (y * x)))) \ (x * (y * (z * (y * (x * u))))) = u. [para(130(a,1),15(a,1,2))]. 2215 x * (y * (z * (y * (x * ((x * (y * (z * (y * x)))) \ u))))) = u. [para(130(a,1),16(a,1))]. 2234 T(x,y) * (y * (z * (y * (T(x,y) * u)))) = (T(x,y) * (y * (z * (x * y)))) * u. [para(90(a,1),130(a,1,1,2,2,2)),flip(a)]. 2243 x * (y * (((y * x) \ 1) * (y * (x * z)))) = (x * y) * z. [para(997(a,1),130(a,1,1,2,2)),rewrite([14(2)]),flip(a)]. 2254 L(x,y,z * z) = x. [para(13(a,1),132(a,1,1,2)),rewrite([13(6),638(6),667(3),13(2)]),flip(a)]. 2276 L(x,y,z * (((z * y) \ 1) * z)) = ((z * y) \ 1) * (z * (y * x)). [para(997(a,1),132(a,1,1,2)),rewrite([14(2),15(8)]),flip(a)]. 2278 L(x,y,z * (((z * (y * x)) \ 1) * z)) = (((z * (y * x)) \ 1) * (z * y)) \ 1. [para(997(a,1),132(a,1,2,2)),rewrite([14(9),1091(8)]),flip(a)]. 2356 L(L(L(x,y,z),u,(u * x) \ 1),((u * x) \ 1) * u,w) = L(L(x,u,(u * x) \ 1),y,z). [para(1026(a,1),1078(a,1,2,1)),rewrite([990(13)])]. 2357 L(L(x,y,(y * x) \ 1),z,u) = L((((y * x) \ 1) * y) \ 1,z,u). [para(1026(a,1),1078(a,2,1)),rewrite([1141(11),2356(10)])]. 2445 ((x \ y) * (x * ((x \ y) * z))) \ (((x \ y) * y) * z) = 1. [para(13(a,1),314(a,1,1)),rewrite([13(9),52(13)])]. 2485 L(x,y * y,z) = x. [hyper(24,a,2045,a)]. 2486 a(x,y * (y * (z * (y * (y * z)))),u) = 1. [para(37(a,1),2045(a,1,2))]. 2495 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(2254(a,1),74(a,1)),rewrite([100(3),100(5)]),flip(a)]. 2497 L(x,y,(z \ 1) / z) = x. [para(1014(a,1),2254(a,1,3))]. 2507 L(x,y,z * (z * u)) = L(x,y,u). [back_rewrite(144),rewrite([2495(8),21(4)]),flip(a)]. 2508 a(x * (x * y),z,u) = a(y,z,u). [back_rewrite(140),rewrite([2495(9),19(5)]),flip(a)]. 2522 L(x,y * (y * (z * (y * (y * z)))),u) = x. [para(37(a,1),2485(a,1,2))]. 2528 L(x,(y \ 1) / y,z) = x. [para(1014(a,1),2485(a,1,2))]. 2538 (x \ y) \ 1 = y \ x. [para(16(a,1),1091(a,1,1)),flip(a)]. 2540 ((x \ y) * (x * z)) \ 1 = ((y * x) * z) \ x. [para(104(a,1),1091(a,1,1)),flip(a)]. 2548 ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. [para(54(a,1),1091(a,1,1))]. 2551 x * (x * ((y * z) * K((y \ 1) * ((x * y) * z),x * y))) = ((y \ 1) * ((x * y) * z)) * (x * y). [para(1091(a,1),350(a,1,2,1,1)),rewrite([37(3),37(11),1091(13)])]. 2556 ((x / y) * ((y \ 1) \ z)) / z = R(x,y \ 1,(y \ 1) \ z). [para(1091(a,1),268(a,1,1,1,2)),rewrite([1014(3),1091(4),1812(5),1091(8),1091(10)])]. 2560 T(x * y,(y \ 1) \ x) = x * y. [para(1091(a,1),560(a,1,2,1))]. 2574 a(x,T(y,x),x * z) = a(y * x,x,z) \ 1. [back_rewrite(673),rewrite([2548(7)]),flip(a)]. 2575 a(x,x \ y,x * z) = a(y,x,z) \ 1. [back_rewrite(173),rewrite([2548(8)])]. 2599 ((x / y) * (y * y)) / T(x * y,a(x,y \ 1,y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),729(a,1,1,1,2)),rewrite([1014(3),1649(6),1649(12)])]. 2601 ((x / y) * (y * y)) \ ((y \ 1) \ x) = K(((y \ 1) \ x) * y,y \ 1). [para(1649(a,1),354(a,1,1,1,2)),rewrite([1014(3),1649(5),1649(9),1014(10),17(8),1649(9),1649(13)])]. 2604 (x * y) \ ((x / y) * (y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),58(a,1,2,1,2)),rewrite([1014(4),1649(7)])]. 2635 T(T(x * x,y),x) = T(x * x,y). [para(1659(a,1),29(a,1,1)),flip(a)]. 2639 T((x \ 1) / x,x \ 1) = (x \ 1) / x. [para(1014(a,1),1659(a,1,1)),rewrite([1014(11)])]. 2640 x * (x * (y * (y * (z / (T(x * x,y) * (y * z)))))) = y. [para(1659(a,1),1266(a,1,1,1,1,1)),rewrite([100(2),37(3),37(4),100(2),2635(7),1839(9),1839(7)])]. 2642 T(x,x \ y) = T(x,y). [para(16(a,1),1708(a,1,2)),flip(a)]. 2643 T(x / y,x) = y \ x. [para(18(a,1),1708(a,1,2)),rewrite([92(4)])]. 2644 T(T(x,y),x * z) = T(T(x,z),y). [para(1708(a,1),29(a,1,1)),flip(a)]. 2645 L(T(x,L(x,y,z) * u),y,z) = L(T(x,u),y,z). [para(1708(a,1),30(a,1)),rewrite([30(2)]),flip(a)]. 2647 T(x * (x * y),x * (x * (y * z))) = T(x * (x * y),z). [para(37(a,1),1708(a,1,2))]. 2648 T(x,(x \ y) * (x * z)) = T(x,(y * x) * z). [para(104(a,1),1708(a,1,2)),flip(a)]. 2649 (x \ y) \ y = T(x,y). [para(91(a,1),1708(a,2)),rewrite([16(2)]),flip(a)]. 2652 T(x,y * x) = T(x,T(y,x)). [para(90(a,1),1708(a,1,2))]. 2690 (x \ y) * T(x,y) = y. [back_rewrite(1457),rewrite([2649(3),2642(7),166(8)])]. 2692 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(1452),rewrite([2642(9)])]. 2697 a(x * (y \ x),T(y,x),z) = a(y \ x,T(y,x) * x,z). [back_rewrite(1301),rewrite([2642(4),2642(7)])]. 2700 T(x,L(y * z,y \ x,y)) = T(x,(x * y) * z). [back_rewrite(1201),rewrite([2642(8)])]. 2705 L(x \ y,x,z) \ (z * y) = T(z * x,z * y). [back_rewrite(650),rewrite([2642(5)]),flip(a)]. 2708 ((x * (y \ z)) * T(y,z)) / z = R(x,y \ z,T(y,z)). [back_rewrite(268),rewrite([2642(4),2649(8)])]. 2709 T(x \ y,T(x,y)) = T(x,y) \ y. [back_rewrite(221),rewrite([2642(3),2649(5)])]. 2711 x / T(y,x) = y \ x. [back_rewrite(218),rewrite([2642(2)])]. 2712 (x \ 1) / x = x \ (x \ 1). [back_rewrite(2639),rewrite([2643(6)]),flip(a)]. 2713 ((x \ y) * (x * z)) \ ((y * x) * z) = T(x,(y * x) * z). [back_rewrite(185),rewrite([2648(10)])]. 2747 L(x,y \ (y \ 1),z) = x. [back_rewrite(2528),rewrite([2712(3)])]. 2748 L(x,y,z \ (z \ 1)) = x. [back_rewrite(2497),rewrite([2712(3)])]. 2755 (x \ 1) \ y = x * y. [back_rewrite(1227),rewrite([2747(5)]),flip(a)]. 2757 ((x / y) * (y * y)) \ (y * x) = K(y * (x * y),y \ 1). [back_rewrite(2601),rewrite([2755(6),2755(8),101(7)])]. 2759 T(x * y,y * x) = x * y. [back_rewrite(2560),rewrite([2755(4)])]. 2760 ((x / y) * (y * z)) / z = R(x,y \ 1,y * z). [back_rewrite(2556),rewrite([2755(4),2755(9)])]. 2771 T(x,y \ 1) = y * (x / y). [back_rewrite(1837),rewrite([2755(4)]),flip(a)]. 2772 K(x * y,y * x) = 1. [back_rewrite(1826),rewrite([2755(4)])]. 2774 T(x * y,y \ 1) = y * x. [back_rewrite(1812),rewrite([2755(7)])]. 2796 R(x,x / y,(x / y) \ z) = R(x,y \ 1,y * z). [back_rewrite(208),rewrite([2760(8)])]. 2802 ((x / y) * (z * y)) / T(z,y) = R(x,y \ 1,z * y). [back_rewrite(1990),rewrite([2796(5),90(4)]),flip(a)]. 2806 ((x / y) * z) / (y \ z) = R(x,y \ 1,z). [back_rewrite(1972),rewrite([2796(5),16(4)]),flip(a)]. 2810 T(x,(y * x) / y) = x. [hyper(28,a,1723,a)]. 2852 x * K(y \ x,y) = (y \ x) * y. [para(16(a,1),63(a,1,1))]. 2853 x * K(y,x / y) = y * (x / y). [para(18(a,1),63(a,1,1))]. 2855 (x * y) \ (K(x,y) * (y * x)) = K(K(x,y),y * x). [para(63(a,1),20(a,1,1))]. 2857 (x * y) \ ((y * x) * (K(x,y) * z)) = L(z,K(x,y),y * x). [para(63(a,1),21(a,1,1))]. 2858 ((x * y) * z) / (K(x,y) * z) = R(y * x,K(x,y),z). [para(63(a,1),22(a,1,1,1))]. 2880 ((x * (y * z)) * K(z,y)) / T(x * (z * y),a(x,y * z,K(z,y))) = a(x,y * z,K(z,y)). [para(63(a,1),265(a,1,2,1,2))]. 2887 (x * y) / T(y * x,K(x,y)) = K(x,y). [para(63(a,1),165(a,1,1))]. 2903 (x / y) * (y \ x) = (y \ x) * (x / y). [para(554(a,1),63(a,1,2)),rewrite([14(5)])]. 2917 K(x,y) \ 1 = K(y,x). [para(63(a,1),1091(a,1,1)),rewrite([20(3)]),flip(a)]. 2918 T(x * y,K(y,x)) = x * y. [para(63(a,1),1708(a,1,2)),rewrite([2759(3)]),flip(a)]. 2925 (x * y) / (y * x) = K(x,y). [back_rewrite(2887),rewrite([2918(4)])]. 2934 (x * (y * z)) \ (L(z,y,x) * (x * y)) = K(L(z,y,x),x * y). [para(21(a,1),64(a,1,2,1)),rewrite([21(10)])]. 2935 x * (K(y \ x,y) * (x * z)) = (((y \ x) * y) * x) * z. [para(64(a,1),104(a,1,2,1))]. 2962 x \ ((y \ 1) * (x * y)) = K(y \ 1,x * y). [para(1091(a,1),64(a,1,2,1)),rewrite([1091(7)])]. 2965 x * (((x \ y) * x) * z) = y * (x * z). [para(16(a,1),189(a,1,1)),flip(a)]. 2971 L(a(x,y,z),x * (y * z),y) = a(y,x,y * z). [para(189(a,1),19(a,1,2)),rewrite([589(7)])]. 2975 L(x,y * z,z) = L(x,z,z * y). [para(189(a,1),21(a,1,2)),rewrite([101(2),21(6)])]. 2993 x * ((T(y,x) * x) * z) = (y * x) * (x * z). [para(90(a,1),189(a,1,1)),flip(a)]. 3018 L(x * (y * z),x \ y,x) = (x * y) * z. [para(189(a,1),181(a,2,2)),rewrite([15(8)])]. 3031 x * (((y \ 1) * x) * z) = (x / y) * (x * z). [para(1014(a,1),189(a,1,1)),flip(a)]. 3032 (x * y) * (x / z) = x * ((y * x) / z). [para(1014(a,1),189(a,1,2)),rewrite([1014(7)])]. 3050 L(x,y * (z * (y * z)),u) = x. [para(189(a,1),2485(a,1,2)),rewrite([101(2)])]. 3078 x * (y * ((y * (x * y)) \ z)) = y \ z. [para(103(a,1),15(a,1,2)),flip(a)]. 3093 x * a(y,z,y * ((y * (z * y)) \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [para(103(a,1),54(a,1,1)),rewrite([189(12)])]. 3097 (x \ y) * (T(x,y) * ((x \ y) * z)) = (y * (x \ y)) * z. [para(103(a,1),186(a,2,1,1)),rewrite([3078(5),3078(6),2642(3),3078(7),3078(11)])]. 3103 x * ((x \ 1) * y) = y. [para(997(a,1),103(a,1,2,2,2,1,2)),rewrite([14(4),16(4)])]. 3118 L((x * (y * x)) \ z,x,y * (x * y)) = (y * (x * (y * x))) \ (y * z). [para(103(a,1),132(a,1,2,2)),flip(a)]. 3130 K(x,(x \ 1) * (y / x)) = K(y,x \ 1). [back_rewrite(1004),rewrite([3103(8),1833(5)]),flip(a)]. 3135 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(16(a,1),2495(a,1,1,2))]. 3136 (x * (x * y)) \ (x * z) = y \ (x \ z). [para(16(a,1),2495(a,1,2,2))]. 3139 T(x * (x * (y / (x * (x * z)))),x * (x * z)) = z \ y. [para(2495(a,1),92(a,2)),rewrite([1839(5)])]. 3141 L(x \ y,z * (z * x),u) = (u * (z * (z * x))) \ (u * (z * (z * y))). [para(2495(a,1),74(a,1,1))]. 3143 (x \ 1) * y = x \ y. [para(997(a,1),2495(a,1,1,2)),rewrite([14(4),15(9)])]. 3162 (x \ ((x * y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(141),rewrite([3135(7)])]. 3163 K(x,x \ (y / x)) = K(y,x \ 1). [back_rewrite(3130),rewrite([3143(4)])]. 3169 (x / y) * (x * z) = x * ((y \ x) * z). [back_rewrite(3031),rewrite([3143(3)]),flip(a)]. 3171 K(x \ 1,y * x) = y \ T(y,x). [back_rewrite(2962),rewrite([3143(4),23(2)]),flip(a)]. 3184 x * (x * ((y * z) * K((y \ x) * (y * z),x * y))) = ((y \ x) * (y * z)) * (x * y). [back_rewrite(2551),rewrite([3143(6),168(4),3143(14),168(12)])]. 3191 L(L(x,y,(y * x) \ 1),z,u) = L(x,z,u). [back_rewrite(2357),rewrite([3143(9),1091(7),2649(9),88(7)])]. 3192 L(L(x,y,z),u,(u * x) \ 1) = L(x,y,z). [back_rewrite(2356),rewrite([3143(9),1091(7),1080(8),3191(10)])]. 3199 L(x,y,z / (y * x)) = L(x,y,z). [back_rewrite(2278),rewrite([3143(5),1091(3),1014(4),3143(9),2538(9),21(7)])]. 3200 L(x,y,z / y) = L(x,y,z). [back_rewrite(2276),rewrite([3143(4),1091(2),1014(3),3143(8),21(6)])]. 3204 x * (y * L(z,x,y)) = (x * y) * z. [back_rewrite(2243),rewrite([3143(6),21(4)])]. 3213 R(x,x * y,(x * y) \ z) = R(x,y,y \ z). [back_rewrite(2004),rewrite([3143(8),169(7),191(8)])]. 3218 x * (y \ T(z,x * (x / y))) = x \ (z * (x * (x / y))). [back_rewrite(1888),rewrite([3143(6)])]. 3228 (x * (x / y)) * z = x * (x * (y \ z)). [back_rewrite(1838),rewrite([3143(3)]),flip(a)]. 3229 (x / y) \ (x * (y \ z)) = L(z,y \ 1,x). [back_rewrite(1834),rewrite([3143(4)])]. 3230 (x \ y) \ (y / x) = K(y,x \ 1). [back_rewrite(1833),rewrite([3143(3)])]. 3231 (x / y) \ (y \ x) = K(y \ 1,x). [back_rewrite(1832),rewrite([3143(4)])]. 3266 L(x,y,y \ 1) = x. [back_rewrite(1025),rewrite([3143(4),15(2)]),flip(a)]. 3276 x \ ((x / y) * (y * z)) = L(z,y,x). [back_rewrite(75),rewrite([3200(6)])]. 3286 (x / y) * (y * ((x / y) * z)) = x * (x * (y \ z)). [back_rewrite(107),rewrite([3228(8)])]. 3302 K(x * y,K(y,x)) = 1. [hyper(27,a,2918,a)]. 3304 T(x,K(y \ x,y)) = x. [para(16(a,1),2918(a,1,1)),rewrite([16(5)])]. 3305 T(x,K(y,x / y)) = x. [para(18(a,1),2918(a,1,1)),rewrite([18(5)])]. 3307 T((x * y) * z,K((y \ x) * (y * z),y)) = (x * y) * z. [para(104(a,1),2918(a,1,1)),rewrite([104(11)])]. 3308 K(x,y) * (y * x) = x * y. [para(2918(a,1),90(a,1,2)),rewrite([63(6)])]. 3323 (((x \ y) * (x * z)) * x) / ((y * x) * z) = K((x \ y) * (x * z),x). [back_rewrite(969),rewrite([3307(11)])]. 3327 K(K(x,y),y * x) = 1. [back_rewrite(2855),rewrite([3308(4),46(3)]),flip(a)]. 3382 T(T(T(x,y \ 1),z),u) / y = T(T(T(x,z),u),y \ 1) / y. [para(94(a,1),1009(a,2,1)),rewrite([1009(12)]),flip(a)]. 3436 (x * x) \ y = x \ (x \ y). [para(18(a,1),1324(a,1,2,2)),rewrite([92(8),1619(6)]),flip(a)]. 3476 x * T(y * z,y * (y * x)) = (y \ z) * (y * (y * x)). [para(181(a,2),1324(a,1,2)),rewrite([3018(5),168(4)]),flip(a)]. 3482 x \ T(y,z * (z / x)) = z \ (z \ (y * (z * (z / x)))). [para(1014(a,1),1324(a,1,2,2,2,2)),rewrite([1014(10),3143(11)]),flip(a)]. 3541 x \ (y \ (z * (y * (x * y)))) = y * T(z,y * (x * y)). [para(1359(a,1),15(a,1,2))]. 3544 (x \ (y * (x * (z * x)))) / (x * T(y,x * (z * x))) = z. [para(1359(a,1),17(a,1,1))]. 3575 x * (y \ T(z,y \ (x / y))) = y * (z * (y \ (x / y))). [para(1014(a,1),1359(a,1,2,2,2,2)),rewrite([3143(6),3143(6),1014(12),3143(11),2755(11)])]. 3576 a(x / y,y,T(z,y * x)) = a(y,y \ x,T(z,y * x)). [para(1359(a,1),60(a,1,1)),rewrite([18(2),18(5),1346(7),18(7)]),flip(a)]. 3640 x * (x * (((x \ y) / z) / T(x * y,z \ 1))) = z \ 1. [para(16(a,1),1884(a,1,2,2,2,1,2))]. 3641 x * (x * (y / T(x * (x * (y * z)),z \ 1))) = z \ 1. [para(17(a,1),1884(a,1,2,2,1))]. 3645 (x / y) / T(z * (z * x),y \ 1) = z \ (z \ (y \ 1)). [para(1884(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 3646 R(x,x \ (y \ 1),z) = (y \ z) / ((x \ (y \ 1)) * z). [para(1884(a,1),22(a,1,1,1)),rewrite([3143(3),3645(8),16(6),3645(13),16(11)]),flip(a)]. 3666 (x \ y) / y = x \ 1. [para(1884(a,1),201(a,1,2)),rewrite([3645(8),100(6),16(5),16(4),3645(11),16(9),16(8),2755(7),480(6),3645(9),16(7),16(6),3645(11),1300(9),13(6),3143(5)]),flip(a)]. 3670 x * (x * (((T(y,x) * (x * z)) / u) / T(x * (((y * x) * x) * z),u \ 1))) = u \ 1. [para(186(a,1),1884(a,1,2,2,2,1,2))]. 3683 x * ((x \ (y \ 1)) * T(z,x / y)) = x \ (z * (x / y)). [para(1884(a,1),778(a,1,2,2,2,2)),rewrite([3645(7),16(5),1014(6),3645(14),16(12),16(11),1014(10)])]. 3691 x / (y * x) = y \ 1. [para(1884(a,1),1013(a,2)),rewrite([3645(7),16(5),2538(5),2755(3)])]. 3709 x \ (x \ (y * (x / z))) = (x \ (z \ 1)) * T(y,x / z). [para(1884(a,1),1324(a,1,2,2,2,2)),rewrite([1014(3),3645(11),16(9),3645(14),16(12),16(11),1014(10)])]. 3710 (x \ (x \ (y \ 1))) * T(z,y \ 1) = x \ (x \ (z / y)). [para(1884(a,1),1324(a,1,2,2,2)),rewrite([1014(3),3645(10),3645(14),16(12),16(11)]),flip(a)]. 3723 R(x \ 1,x,y) = x \ 1. [back_rewrite(1027),rewrite([3691(5)])]. 3724 x / (y * (z * (y * x))) = (y * (z * y)) \ 1. [back_rewrite(1448),rewrite([3723(7)]),flip(a)]. 3725 x / (y * (y * (z * x))) = (y * (y * z)) \ 1. [back_rewrite(1039),rewrite([3723(7)]),flip(a)]. 3735 a(x * (y * x),y,z) = a(x,y * (x * y),z). [para(133(a,1),110(a,1))]. 3752 (x * (y * (y * z))) \ ((x * (y * (y * u))) * (u \ z)) = a(x,y * (y * u),u \ z). [para(16(a,1),139(a,1,1,2,2,2))]. 3753 (x * (y * (y * z))) \ ((x * (y * (y * (z / u)))) * u) = a(x,y * (y * (z / u)),u). [para(18(a,1),139(a,1,1,2,2,2))]. 3762 a(x * ((y * x) * x),z,u) = a(x * y,x * (x * z),u). [para(189(a,1),139(a,1,1)),rewrite([189(9),133(11)])]. 3794 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,w),y),z),v5),u \ 1) / u. [para(94(a,1),3382(a,2,1,1,1))]. 3933 x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u)))))) = x * u. [para(398(a,1),15(a,1,2)),rewrite([15(3)]),flip(a)]. 3934 K(x * y,x) = y \ T(y,x). [para(398(a,1),20(a,1,1)),rewrite([3933(13),101(4),3136(5),23(2),3933(13)]),flip(a)]. 3935 K(x,x * y) = T(y,x) \ y. [para(398(a,1),20(a,1,2)),rewrite([3933(11),101(2),3135(5),23(2),3933(13)]),flip(a)]. 3936 x * (y * (y * (x * (z * ((x * (y * (y * (x * z)))) \ u))))) = u. [para(398(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 3940 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(398(a,1),74(a,2,1)),rewrite([3936(10),3936(12),3136(8)])]. 3941 L(x \ (y * z),x,y) = (y \ x) \ z. [para(398(a,1),74(a,2,2)),rewrite([3936(10),3135(7)])]. 3947 x * (x * (y * (x * (x * (y * (z \ ((y * (x * (x * (y / z)))) \ u))))))) = x * (x * u). [para(1014(a,1),398(a,1,2,2,2,2,2,2,2,1,2,2,2)),rewrite([3143(8)])]. 3949 x * (x * (y * ((x * (x * (x * (x * y)))) \ z))) = x \ (x \ z). [para(398(a,1),132(a,1,2)),rewrite([3135(6),15(3),3436(2),2507(13),1607(11)]),flip(a)]. 3954 a(x,x \ y,z) = a(x,x * y,z). [para(398(a,1),133(a,1,2,1)),rewrite([3949(8),16(3),136(4),37(6),3135(7),3162(5),3949(12),16(7),2508(6)]),flip(a)]. 3968 a(x / y,y,T(z,y * x)) = a(y,y * x,T(z,y * x)). [back_rewrite(3576),rewrite([3954(8)])]. 3982 a(x,x * y,x * z) = a(y,x,z) \ 1. [back_rewrite(2575),rewrite([3954(3)])]. 4007 (x * (y * z)) / T((x * z) * T(y,z),a(z,z * x,y * z)) = a(z,z * x,y * z). [back_rewrite(1517),rewrite([3954(8),3954(13)])]. 4013 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x / y,y). [back_rewrite(1051),rewrite([3954(11),1014(10)])]. 4021 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,x * ((y * x) * z),u). [back_rewrite(662),rewrite([3954(13),189(12)])]. 4025 (x * ((x \ y) * ((y \ z) * (y * u)))) \ ((z * y) * u) = a(x,x * y,(y \ z) * (y * u)). [back_rewrite(614),rewrite([3954(14)])]. 4031 T(x * ((x \ y) * z),a(x,x * y,z)) = a(x,x * y,z) \ (y * z). [back_rewrite(260),rewrite([3954(5),3954(8)])]. 4032 (x * ((x \ y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(56),rewrite([3954(7)])]. 4097 T(T(T(T(T(x,y),z \ 1),u),w),v5) / z = T(T(T(T(T(x,w),u),y),v5),z \ 1) / z. [para(94(a,2),3794(a,1,1,1,1))]. 4108 K(x * y,K(x,y)) = 1. [para(1684(a,1),2880(a,1,2,2)),rewrite([3308(3),88(8),2925(7),1684(7)])]. 4114 ((x * y) * z) \ R(x,y,z) = (y * z) \ 1. [para(22(a,1),1829(a,1,2))]. 4115 ((x / y) * x) * z = x * (y \ (x * z)). [para(1829(a,1),104(a,1,2,1)),rewrite([3143(4)]),flip(a)]. 4137 (x \ y) * (y \ x) = 1. [para(2538(a,1),16(a,1,2))]. 4138 (x * (y * z)) \ (x * y) = L(z,y,x) \ 1. [para(21(a,1),2538(a,1,1)),flip(a)]. 4145 L(x \ y,y \ x,z) = x \ y. [para(2538(a,1),74(a,1,1)),rewrite([14(7),1091(6),2538(6)])]. 4151 a(x,y \ z,z \ y) = 1. [para(2538(a,1),1012(a,1,2))]. 4155 x / (y \ z) = x * (z \ y). [para(2538(a,1),1013(a,1,2))]. 4157 (x * y) \ ((x / z) * (z * y)) = a(x / z,z,y) \ 1. [para(60(a,1),2538(a,1,1)),flip(a)]. 4165 L(x,y \ z,z \ y) = x. [para(2538(a,1),3266(a,1,3))]. 4180 x * ((x \ (y / z)) * z) = R(y,z \ 1,x). [back_rewrite(2806),rewrite([4155(4),169(4)])]. 4186 R(x,y,y \ ((y \ x) \ z)) = z * ((z \ y) * (y \ x)). [back_rewrite(199),rewrite([4155(8),169(8)])]. 4187 a(x / y,y,y) \ 1 = a(x,y \ 1,y * y). [back_rewrite(2604),rewrite([4157(5)])]. 4206 T((x / y) * (y * z),x * z) = a(x / y,y,z) \ (x * z). [para(60(a,1),2642(a,1,2)),rewrite([263(6)]),flip(a)]. 4209 T(x * y,x) = y * x. [para(1091(a,1),2642(a,1,2)),rewrite([2774(4)]),flip(a)]. 4210 T(x,(y \ x) * y) = x. [para(64(a,1),2642(a,1,2)),rewrite([3304(3)]),flip(a)]. 4214 T(T(T(x,y),z),T(T(x,z),y) \ u) = T(T(T(x,z),y),u). [para(2642(a,1),94(a,2)),rewrite([29(6)])]. 4230 (x / y) * x = x * (y \ x). [para(2643(a,1),90(a,1,2)),flip(a)]. 4231 T(x \ y,y) = T(x \ y,x). [para(2643(a,1),537(a,1,1)),flip(a)]. 4247 (x * (y \ x)) * z = x * (y \ (x * z)). [back_rewrite(4115),rewrite([4230(2)])]. 4254 (x / y) * ((x / y) * ((y * z) / T(x * (y \ x),z))) = z. [back_rewrite(2009),rewrite([4230(5)])]. 4261 (x \ y) * (T(x,y) * ((x \ y) * z)) = y * (x \ (y * z)). [back_rewrite(3097),rewrite([4247(9)])]. 4278 T(x,y) \ y = T(x \ y,y). [para(2649(a,1),2642(a,1,2)),rewrite([2709(3)])]. 4281 T(x \ y,T(x,y)) = T(x \ y,y). [back_rewrite(2709),rewrite([4278(5)])]. 4304 T(x,y) * T(x \ y,y) = y. [para(2690(a,1),90(a,2)),rewrite([4281(4)])]. 4308 (x * y) * a(x,z \ y,T(z,y)) = (x * (z \ y)) * T(z,y). [para(2690(a,1),54(a,1,1,2))]. 4314 T(x,y) * (T(x \ y,y) * (T(x,y) * z)) = (x * y) * z. [para(2690(a,1),186(a,2,1,1)),rewrite([4281(4),90(9)])]. 4315 ((x * (y \ z)) * T(y,z)) / T(x * z,a(x,y \ z,T(y,z))) = a(x,y \ z,T(y,z)). [para(2690(a,1),265(a,1,2,1,2))]. 4335 a(x * (y \ z),z \ y,T(z,y)) = ((x * (y \ z)) * y) \ (x * T(z,y)). [para(2690(a,1),60(a,1,1,2)),rewrite([4155(2),4155(8)]),flip(a)]. 4344 (x \ y) * ((z * (x \ y)) * T(x,y)) = ((x \ y) * z) * y. [para(2690(a,1),189(a,1,2)),flip(a)]. 4357 (x \ (x \ y)) * T(x,y) = x \ y. [para(2642(a,1),2690(a,1,2))]. 4365 x / T(x,y) = T(x,y) \ x. [para(159(a,1),2711(a,1,2))]. 4366 T(x,y) / x = x \ T(x,y). [para(541(a,1),2711(a,1,2))]. 4379 ((x \ y) * x) / y = K(x \ y,x). [para(64(a,1),2711(a,2)),rewrite([4210(5)])]. 4404 x * T(y,z \ (z \ x)) = z * (z * (y * (z \ (z \ x)))). [para(2755(a,1),1324(a,1,2)),rewrite([3143(7),3143(6),2755(7),3143(10),3143(9)]),flip(a)]. 4407 (x * y) \ 1 = y \ (x \ 1). [para(2755(a,1),2538(a,1,1))]. 4408 (x \ y) \ z = (y \ x) * z. [para(2538(a,1),2755(a,1,1))]. 4417 ((x * y) * z) \ R(x,y,z) = z \ (y \ 1). [back_rewrite(4114),rewrite([4407(7)])]. 4419 ((x \ (y \ 1)) * y) \ (x \ 1) = a(x,x / y,y). [back_rewrite(4013),rewrite([4407(7)])]. 4420 x / (y * (y * (z * x))) = (y * z) \ (y \ 1). [back_rewrite(3725),rewrite([4407(8)])]. 4421 x / (y * (z * (y * x))) = (z * y) \ (y \ 1). [back_rewrite(3724),rewrite([4407(8)])]. 4445 L(L(x,y,z),u,x \ (u \ 1)) = L(x,y,z). [back_rewrite(3192),rewrite([4407(4)])]. 4458 ((x * y) * z) \ y = (y * z) \ (x \ y). [back_rewrite(2540),rewrite([4407(5),4408(4),14(4)]),flip(a)]. 4470 R(x,y,y \ ((x \ y) * z)) = z * ((z \ y) * (y \ x)). [back_rewrite(4186),rewrite([4408(2)])]. 4480 L(x \ (y * z),x,y) = (x \ y) * z. [back_rewrite(3941),rewrite([4408(5)])]. 4493 (x \ y) * (x / y) = K(x,y \ 1). [back_rewrite(3230),rewrite([4408(3)])]. 4498 (((x * y) * z) \ x) * (y * z) = a(x,x * y,z). [back_rewrite(3162),rewrite([4408(5)])]. 4501 (x * y) \ (x * (x * z)) = (y \ x) * z. [back_rewrite(3135),rewrite([4408(6)])]. 4504 (x \ y) * (((y \ x) * z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(2692),rewrite([4408(3)])]. 4505 (x \ y) * x = T(y,x). [back_rewrite(2649),rewrite([4408(2)])]. 4516 K(x \ y,x) = y \ T(y,x). [back_rewrite(4379),rewrite([4505(2),4366(2)]),flip(a)]. 4525 x * (T(y,x) * z) = y * (x * z). [back_rewrite(2965),rewrite([4505(2)])]. 4534 x * (K(y \ x,y) * (x * z)) = (x * T(x,y)) * z. [back_rewrite(2935),rewrite([4505(7),547(7)])]. 4535 x * K(y \ x,y) = T(x,y). [back_rewrite(2852),rewrite([4505(5)])]. 4537 a(T(x,y),y \ x,z) = a(y \ x,x,z). [back_rewrite(1702),rewrite([4505(2)])]. 4539 K(x,x \ y) = T(y,x) \ y. [back_rewrite(65),rewrite([4505(2)]),flip(a)]. 4559 (T(x,y) * (y * (z * (x * y)))) * u = T(x,y) * (y * (z * (x * (y * u)))). [back_rewrite(2234),rewrite([4525(4)]),flip(a)]. 4562 ((x * y) * y) / z = x * (y * (y / z)). [back_rewrite(1859),rewrite([4525(4)]),flip(a)]. 4578 (x * y) * y = x * (y * y). [back_rewrite(669),rewrite([4525(3)]),flip(a)]. 4581 L(x,T(y,z),z) = L(x,z,y). [back_rewrite(512),rewrite([4525(4),21(4)]),flip(a)]. 4582 a(x,T(y,x),z) = a(y,x,z). [back_rewrite(508),rewrite([4525(3),19(5)]),flip(a)]. 4583 R(x * y,y,y \ z) = (x * (y * z)) / z. [back_rewrite(204),rewrite([4525(6)])]. 4596 ((T(x,y) * (y / z)) * y) \ ((x * (y * y)) / z) = K(y,T(x,y) * (y / z)). [back_rewrite(1864),rewrite([4578(6)])]. 4613 (x * (y * y)) / z = x * (y * (y / z)). [back_rewrite(4562),rewrite([4578(2)])]. 4636 a(x * (y * (x * x)),z,u) = a(x * y,x * (x * z),u). [back_rewrite(3762),rewrite([4578(2)])]. 4640 x * (x * (((T(y,x) * (x * z)) / u) / T(x * (y * (x * (x * z))),u \ 1))) = u \ 1. [back_rewrite(3670),rewrite([4578(6),2040(7)])]. 4713 x / (T(T(y,z),u) * (z * ((T(y,u) * (z * z)) \ x))) = z. [back_rewrite(2166),rewrite([4578(5)])]. 4714 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w))) = w. [back_rewrite(2032),rewrite([4578(8),2040(9)])]. 4770 x * (R(T(y,x),z,u) * (x * w)) = R(y,z,u) * (x * (x * w)). [back_rewrite(684),rewrite([4578(8),2040(9)])]. 4778 (x * ((T(y,x) * (x * z)) * u)) \ ((y * (x * (x * z))) * u) = a(x,T(y,x) * (x * z),u). [back_rewrite(674),rewrite([4578(7),2040(8)])]. 4795 a(x * y,y,z) \ 1 = a(x,y,y * z). [back_rewrite(2574),rewrite([4582(3)]),flip(a)]. 4809 ((T(x,y) * (y / z)) * y) \ (x * (y * (y / z))) = K(y,T(x,y) * (y / z)). [back_rewrite(4596),rewrite([4613(7)])]. 4813 (x / y) * (y * (y / T(x * y,a(x,y \ 1,y * y)))) = a(x,y \ 1,y * y). [back_rewrite(2599),rewrite([4613(10)])]. 4915 K(x,y * (x / y)) = 1. [para(18(a,1),2772(a,1,1))]. 4950 T(a(x,y,z),((x * y) * z) / (x * (y * z))) = a(x,y,z). [para(54(a,1),2810(a,1,2,1))]. 4993 K(x,y) * K(y,x) = 1. [para(2917(a,1),16(a,1,2))]. 4996 R(x,K(y,z),K(z,y)) = x. [para(2917(a,1),191(a,2,3)),rewrite([14(5),16(4),48(2)]),flip(a)]. 5005 x / K(y,z) = x * K(z,y). [para(2917(a,1),1014(a,1,2)),flip(a)]. 5011 L(x,K(y,z),K(z,y)) = x. [para(2917(a,1),3266(a,1,3))]. 5067 T(x,y * (x / y)) = x. [para(66(a,1),2642(a,1,2)),rewrite([3305(3)]),flip(a)]. 5068 K(x,y / x) * y = x * (y / x). [para(66(a,1),2690(a,1,1)),rewrite([5067(5)])]. 5070 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(16(a,1),72(a,1,1))]. 5116 (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). [para(63(a,1),72(a,1,1))]. 5129 x * L(y,T(z,x),z \ x) = (z \ x) * (T(z,x) * y). [para(2690(a,1),72(a,1,1))]. 5134 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(15(a,1),3940(a,1,1)),flip(a)]. 5138 L(T(x,y * z),y * z,y) = z \ (y \ (x * (y * z))). [para(23(a,1),3940(a,1,1))]. 5147 L((x * y) \ z,y,y * x) = T(x,y) \ (y \ z). [para(90(a,1),3940(a,1,1,1)),rewrite([90(4),2975(4)])]. 5152 K(x * (y / x),x) = K(x \ 1,y). [para(67(a,1),3940(a,1,1)),rewrite([666(5),3231(6)])]. 5155 L((x / y) \ z,x / y,x) = y * (x \ z). [para(1014(a,1),3940(a,1,1,1)),rewrite([1014(5),4408(8),45(6)])]. 5162 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(3940(a,1),2254(a,1)),rewrite([3436(2),100(5)]),flip(a)]. 5163 L((x * y) \ z,x * y,y * x) = K(x,y) \ ((y * x) \ z). [para(63(a,1),3940(a,1,1,1)),rewrite([63(5)])]. 5194 R(x,y * (y * z),z \ (y \ (y \ u))) = R(x,z,z \ u). [back_rewrite(1870),rewrite([5162(3),191(6),1935(6),16(3),16(2),5162(7)]),flip(a)]. 5200 x * (x * (y * ((y \ (x \ (x \ z))) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [back_rewrite(411),rewrite([5162(3)])]. 5208 (x * (y \ z)) * (z \ y) = x. [para(4151(a,1),209(a,1,1)),rewrite([45(6),4137(7),14(6),4151(7),88(6)])]. 5226 (T(x,y) \ (T(x,y) \ z)) * T(T(x,z),y) = T(x,y) \ z. [para(29(a,1),4357(a,1,2))]. 5332 a(x,y,y) = 1. [para(89(a,1),507(a,1,2,2)),rewrite([4578(4),46(5),89(2)]),flip(a)]. 5337 (x * (y * (z * u))) \ (x * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),y * (z * u),x). [para(507(a,1),74(a,1,1)),flip(a)]. 5358 a(x,y \ 1,y * y) = 1. [back_rewrite(4187),rewrite([5332(2),46(3)]),flip(a)]. 5359 (x / y) * (y / x) = 1. [back_rewrite(4813),rewrite([5358(6),88(4),3691(3),1014(4),5358(7)])]. 5364 (x * y) / T(z * (z * y),T(x,y)) = z \ (z \ T(x,y)). [para(1921(a,1),21(a,1,2)),rewrite([3436(3),1607(10)]),flip(a)]. 5392 (x \ y) * (x * ((x \ y) * z)) = ((x \ y) * y) * z. [para(2445(a,1),16(a,1,2)),rewrite([14(7)])]. 5410 (x \ (y \ (y \ z))) * (((z \ y) * y) * x) = 1. [para(2445(a,1),4357(a,1,1,2)),rewrite([5392(5),4407(5),4407(4),4408(3),14(3),5392(8),89(10),5392(12),46(14)])]. 5428 x * (x * (y / (T(z * z,x) * (x * y)))) = z \ (z \ x). [para(2640(a,1),21(a,1,2)),rewrite([3436(2),1607(10)]),flip(a)]. 5444 L(x,y \ (y \ z),y) = L(x,z,y). [para(2640(a,1),132(a,1,1,2)),rewrite([5428(8),136(6),16(3),21(4),5428(8),2507(6)]),flip(a)]. 5452 x * (x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u))))))) = y * z. [para(189(a,1),2640(a,1,2,2,2,2,2,2))]. 5468 T(x * (x * y),y \ z) = T(x * (x * y),x * (x * z)). [para(16(a,1),2647(a,1,2,2,2)),flip(a)]. 5480 T(x * (x * y),x * (x * (y / z))) = T(x * (x * y),z \ 1). [para(1014(a,1),2647(a,1,2,2,2))]. 5515 a(x \ y,T(x,y) * y,z) = 1. [para(2697(a,1),19(a,2)),rewrite([4247(5),4525(3),15(3),4247(6),90(4),15(4),100(4),46(5)]),flip(a)]. 5524 a((x * y) * L(z \ y,z,x),T(x * z,x * y),u) = 1. [para(74(a,2),2697(a,1,1,2)),rewrite([5515(17)])]. 5560 ((x \ y) * (x / z)) \ ((y * x) / z) = T(x,(y * x) / z). [para(1014(a,1),2713(a,1,1,2)),rewrite([1014(7),1014(10)])]. 5569 (((x \ y) * z) * x) \ ((z * (y \ x)) * T(y,x)) = T(y \ x,(z * (y \ x)) * T(y,x)). [para(2690(a,1),2713(a,1,1,2)),rewrite([4408(2)])]. 5600 ((x * (y * (y * (y * x)))) \ y) * (x * (y * (x * y))) = 1. [para(2772(a,1),143(a,2)),rewrite([101(2),189(5),4578(2),2040(4),101(7),4501(11)])]. 5610 (x \ (y \ (y \ (z \ 1)))) * (z * (y * (y * (x * u)))) = L(u,y * (y * x),z). [para(37(a,1),145(a,1,1)),rewrite([37(11),4501(12),1091(5),4407(5),5162(5),2507(15)])]. 5614 L(x,y * (y * z),z) = x. [para(1607(a,1),145(a,2)),rewrite([189(5),101(2),189(4),4578(2),101(3),100(2),189(11),101(7),189(10),4578(7),189(9),100(7),37(8),4501(12),1091(5),4407(5),5162(5),5610(10)])]. 5657 x * (y * (x * (z * ((z * (x * (y * (x * z)))) \ u)))) = z \ u. [para(2215(a,1),15(a,1,2)),flip(a)]. 5665 R(x,y,y \ ((x \ y) * z)) = (y * z) / ((x \ y) * z). [para(2215(a,1),191(a,1,1,2)),rewrite([5657(13),4408(3),5657(16),4408(6)]),flip(a)]. 5674 x * (y * (z * (y * (x / (x * (y * (z * (y * x)))))))) = 1. [para(1014(a,1),2215(a,1,2,2,2,2))]. 5742 K(L(x * y,x \ z,x),z) = K(z * ((z * x) * y),z). [para(181(a,1),2934(a,1,2,1)),rewrite([104(4),16(7),4505(6),3934(6,R),16(9)]),flip(a)]. 5752 (x * ((y * x) * z)) \ (L(z,x,x * y) * (x * (y * x))) = K(L(z,x,x * y),x * (y * x)). [para(189(a,1),2934(a,1,1)),rewrite([101(7),101(13)])]. 5783 x * ((y * x) * (x * ((x \ y) * z))) = (x * y) * ((x * y) * z). [para(13(a,1),405(a,1,2,2,2,2)),rewrite([14(10),187(12),101(8),426(10)])]. 5816 R(x * ((x \ y) * (y \ z)),z,z \ u) = (z * (a(y,x,x \ (y \ z)) * u)) / u. [para(16(a,1),435(a,1,2)),rewrite([16(6),16(8)])]. 5817 (x * (a(x / y,z,z \ y) * u)) / u = R(x,y \ 1,z). [para(18(a,1),435(a,1,2)),rewrite([4180(4),18(5),495(5),18(5)]),flip(a)]. 5841 R(x * ((x \ (y \ z)) * T(y,z)),z,z \ u) = (z * (a(y \ z,x,x \ T(y,z)) * u)) / u. [para(2690(a,1),435(a,1,2)),rewrite([2690(8),2690(10)])]. 5879 x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))) = z. [para(463(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 5885 (x \ (y \ 1)) * (y * (x * z)) = L(z,x,y). [para(463(a,1),132(a,1,1,2)),rewrite([5879(13),4501(8),1091(3),4407(3),5879(16),2507(9)])]. 5921 a(x,T(y,x) * x,z) = a(y,x,x * z) \ 1. [para(14(a,1),4778(a,1,1,2,1,2)),rewrite([2993(4),14(5),2040(6),2548(7),14(7)]),flip(a)]. 6018 L(x,x,y) = x. [hyper(24,a,5332,a)]. 6020 L(T(x,y),x,z) = T(x,y). [para(6018(a,1),30(a,1,1)),flip(a)]. 6022 L(L(x,y,z),x,u) = L(x,y,z). [para(6018(a,1),34(a,1,1)),flip(a)]. 6024 L(L(L(x,y,z),u,w),L(x,u,w),v5) = L(L(x,u,w),y,z). [para(6018(a,1),97(a,1,1)),flip(a)]. 6068 ((x * y) \ z) * ((z \ x) * y) = a(z \ 1,x,y). [para(3143(a,1),19(a,1,1)),rewrite([3143(5),4408(5)])]. 6069 (x \ (y \ 1)) * (x * y) = K(x,y). [para(20(a,1),3143(a,2)),rewrite([4407(3)])]. 6070 (x \ y) * (y \ (x * z)) = L(z,x,y \ 1). [para(3143(a,1),21(a,1,1)),rewrite([3143(5),4408(4)])]. 6071 ((x \ y) * z) / (y * z) = R(x \ 1,y,z). [para(3143(a,1),22(a,1,1,1))]. 6072 T(x \ 1,y) = y \ (x \ y). [para(3143(a,1),23(a,1,2)),flip(a)]. 6073 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [para(3143(a,1),37(a,1,1,2)),rewrite([3143(4),3143(9),3143(8)]),flip(a)]. 6095 x \ T(y,x \ 1) = y / x. [para(3143(a,1),90(a,1)),rewrite([1014(7)])]. 6120 (x \ 1) / y = x \ (y \ 1). [para(3143(a,1),1014(a,1)),flip(a)]. 6128 ((x * (y * z)) \ (y \ 1)) * (y * (x * (y * (z * u)))) = L(u,z,y * (x * y)). [para(132(a,1),3143(a,2)),rewrite([4407(5)])]. 6132 (x \ (y \ 1)) * y = x \ 1. [para(1091(a,1),3143(a,2)),rewrite([4407(3)])]. 6134 T(x \ 1,x \ y) = T(x \ 1,y). [para(3143(a,1),1708(a,1,2))]. 6135 x \ ((y / x) * z) = (x \ y) * (x \ z). [para(3143(a,1),189(a,1,1)),rewrite([3143(4),1014(8),3143(8)]),flip(a)]. 6141 ((x * y) \ (z \ (z \ (u \ 1)))) * ((u * (z * (z * x))) * y) = a(u,z * (z * x),y). [para(139(a,1),3143(a,2)),rewrite([4407(6),5162(6)])]. 6144 K(x,y) \ z = K(y,x) * z. [para(2917(a,1),3143(a,1,1)),flip(a)]. 6145 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(3143(a,1),72(a,1,1)),rewrite([3143(9)])]. 6149 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(z \ 1,y,T(x,y)). [para(3143(a,1),507(a,1,1)),rewrite([3143(5),4408(6)])]. 6151 ((x \ (y \ 1)) * (x * z)) \ ((y \ x) * z) = T(x,(y \ x) * z). [para(3143(a,1),2713(a,1,2,1)),rewrite([3143(11)])]. 6152 ((x * y) \ (z \ x)) * ((z * x) * y) = T(x,(z * x) * y). [para(2713(a,1),3143(a,2)),rewrite([4407(5),4408(4),14(4)])]. 6185 (x \ (y \ 1)) * T(z,x / y) = (x \ (x \ z)) * (x / y). [back_rewrite(3709),rewrite([6073(4)]),flip(a)]. 6188 x \ T(y,z * (z / x)) = (z \ (z \ y)) * (z * (z / x)). [back_rewrite(3482),rewrite([6073(9)])]. 6233 a(x,x / y,y) = 1. [back_rewrite(4419),rewrite([6132(4),46(5)]),flip(a)]. 6238 L((x * y) \ z,x * y,y * x) = K(y,x) * ((y * x) \ z). [back_rewrite(5163),rewrite([6144(9)])]. 6257 L(x,y / x,y) = x. [hyper(24,a,6233,a)]. 6258 a(x * y,x,y) = 1. [para(17(a,1),6233(a,1,2))]. 6279 L(x,y,y * x) = x. [para(17(a,1),6257(a,1,2))]. 6335 a(x,y,y \ x) = 1. [para(16(a,1),6258(a,1,1))]. 6351 x * ((x \ y) * y) = y * y. [para(6258(a,1),435(a,2,1,2,1)),rewrite([16(2),16(5),16(6),3436(6),2044(7),16(5),13(6),100(5),1839(6),47(4),14(5)])]. 6353 (x \ y) * ((y \ x) * z) = L(z,(y \ x) * x,y). [back_rewrite(831),rewrite([6351(3),3436(6),6073(6),15(2)])]. 6368 L(x \ y,x,y) = x \ y. [para(16(a,1),6279(a,1,3))]. 6416 L(x,y \ 1,y \ x) = x. [para(3143(a,1),6279(a,1,3))]. 6438 a((x * y) * T(z,y),x * (z * y),a(x,y,T(z,y))) = 1. [para(507(a,1),6335(a,1,3))]. 6446 K(x,K(y,x / y)) = 1. [para(18(a,1),3302(a,1,1))]. 6557 K(K(L(x,y,z),z * y),z * (y * x)) = 1. [para(72(a,1),3327(a,1,2))]. 6562 K(x,y) / (x * y) = x \ (y \ 1). [para(20(a,1),3666(a,1,1)),rewrite([4407(6)])]. 6564 T(x,y) / (x * y) = y \ 1. [para(23(a,1),3666(a,1,1))]. 6565 (x / y) \ 1 = y / x. [para(50(a,1),3666(a,1,1)),flip(a)]. 6567 (x * (y * z)) \ (y \ 1) = z \ ((x * y) \ (y \ 1)). [para(114(a,1),3666(a,1,1)),rewrite([6562(7),4407(4),4407(10)]),flip(a)]. 6575 (x / y) \ (y \ 1) = K(x / y,y) / x. [para(67(a,1),3666(a,1,1)),rewrite([4407(7)]),flip(a)]. 6591 L(x,y,z) \ (y \ (z \ 1)) = (y * x) \ (z \ 1). [para(2934(a,1),3666(a,1,1)),rewrite([6562(7),4407(4),4407(9)])]. 6600 (x \ ((y * z) \ (z \ 1))) * (z * (y * (z * (x * u)))) = L(u,x,z * (y * z)). [back_rewrite(6128),rewrite([6567(5)])]. 6606 x * (L(y,z \ x,z) * (x * u)) = ((z * ((z \ x) * y)) * x) * u. [para(73(a,1),104(a,1,2,1))]. 6618 L(x,y \ 1,z * y) = L(x,y \ z,y). [para(73(a,1),181(a,2)),rewrite([1091(2),3143(3),16(2),1091(4)]),flip(a)]. 6623 (((x / (y * z)) * y) * z) \ (x * (a(x / (y * z),y,z) * u)) = L(u,a(x / (y * z),y,z),x). [para(59(a,1),73(a,1,2,2,1)),rewrite([59(15)])]. 6634 L(x,y * z,y \ 1) = L(x,y * z,y). [para(3143(a,1),73(a,1,2)),rewrite([4408(3),45(2),5134(4),4408(5),45(4)]),flip(a)]. 6663 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,u,w),y,z))) \ (v6 * v5). [para(76(a,1),228(a,1)),flip(a)]. 6676 L(x,y \ (x \ 1),z) = (z * (y \ (x \ 1))) \ (z / y). [para(1014(a,1),76(a,2,2)),rewrite([6120(3),6120(7)])]. 6694 T(x * (y / z),L(z,y / z,x)) = T(x * (y / z),x * y). [para(76(a,2),2642(a,1,2))]. 6696 L(x,T(y,z) / x,y \ z) = ((y \ z) * (T(y,z) / x)) \ z. [para(2690(a,1),76(a,2,2))]. 6697 L(x,L(y,z,u) / x,u * z) = ((u * z) * (L(y,z,u) / x)) \ (u * (z * y)). [para(72(a,1),76(a,2,2))]. 6707 L(x,y / x,z \ 1) = ((y / x) \ z) * (z \ y). [para(3143(a,1),76(a,2,1)),rewrite([3143(9),4408(8)])]. 6793 L(L(R(x,y,z),u,w),v5,x \ (v5 \ 1)) = L(R(x,y,z),u,w). [para(4445(a,1),33(a,1,1)),rewrite([33(2),33(4)]),flip(a)]. 6878 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(y * (x \ y),y \ 1). [para(1014(a,1),2757(a,1,2)),rewrite([6120(3),3143(10)])]. 6887 L(K(x * (y * x),x \ 1),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [para(2757(a,1),3940(a,1,1)),rewrite([3436(15)])]. 6890 K(x * (y * x),x \ 1) = K(x,y). [para(2757(a,1),3143(a,2)),rewrite([4407(5),6565(4),3436(3),1829(2),6069(5)]),flip(a)]. 6897 L(K(x,y),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [back_rewrite(6887),rewrite([6890(5)])]. 6946 T(x * (x * (y / (x * z))),x * z) = (z \ x) * y. [para(16(a,1),3139(a,1,1,2,2,2,2)),rewrite([16(6),4408(8)])]. 6951 ((x \ y) * (x * z)) \ u = ((x * z) \ (y \ x)) * u. [para(104(a,1),3139(a,1,1,2,2,2,2)),rewrite([104(10),6946(10),4458(3)]),flip(a)]. 6953 (x \ ((y * z) \ (y \ 1))) * u = (z * x) \ (y \ (y \ u)). [para(341(a,1),3139(a,1,1,2,2,2,2)),rewrite([341(27),6946(26),4417(8),4407(4),5162(10)])]. 6955 ((x * y) \ y) * z = T(x,y) \ z. [para(90(a,1),3139(a,1,1,2,2,2,2)),rewrite([90(7),6946(8)])]. 6968 (x \ (y \ x)) * z = T(y,x) \ z. [para(2690(a,1),3139(a,1,1,2,2,2,2)),rewrite([2690(11),6946(10)])]. 6973 ((x * y) \ (z * x)) * ((z \ x) * y) = T(x,(z \ x) * y). [back_rewrite(6151),rewrite([6951(8),4408(4),45(3)])]. 7004 x * (y \ ((x * (x / y)) \ z)) = x \ z. [para(18(a,1),3218(a,2,2)),rewrite([92(6)])]. 7047 T(x,K((y \ z) * (y * ((z * y) \ x)),y)) = x. [para(16(a,1),3307(a,1,1)),rewrite([16(11)])]. 7257 (T(x,y) * (y * (x * y))) * z = T(x,y) * (y * (x * (y * z))). [para(13(a,1),4559(a,1,1,2,2)),rewrite([13(10)])]. 7262 T(x,y) * (y * ((z / (x * y)) * (x * (y * u)))) = (T(x,y) * (y * z)) * u. [para(18(a,1),4559(a,1,1,2,2)),flip(a)]. 7353 R(x,y,z) * (x * (x * u)) = x * (R(x,y,z) * (x * u)). [para(89(a,1),4770(a,1,2,1,1)),flip(a)]. 7412 a(x / (y * y),y,y * z) = (x * z) \ (y \ ((y * x) * z)). [para(7262(a,1),110(a,1,1)),rewrite([89(1),37(3),89(4),189(10),101(8),4578(7),18(7),5162(7),15(5),89(6),3982(11),4795(11)]),flip(a)]. 7416 x * (T(x,y) * ((z / (x * T(x,y))) * (x * (T(x,y) * u)))) = (x * (T(x,y) * z)) * u. [para(541(a,1),7262(a,1,1)),rewrite([541(12)])]. 7488 x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u)))))) = x \ (y * z). [para(5452(a,1),15(a,1,2)),flip(a)]. 7490 (x * y) * ((x * y) * ((x * z) / (T(u * u,x * y) * (x * ((y * x) * z))))) = (u \ (u \ x)) * y. [para(5452(a,1),21(a,1,2)),rewrite([3436(3),6073(3),1607(17)]),flip(a)]. 7495 x * (x * (((x \ (x \ y)) * z) * u)) = (y * z) * u. [para(5452(a,1),37(a,1,1)),rewrite([7490(15)]),flip(a)]. 7513 L(x,(y \ (y \ z)) * u,y) = L(x,z * u,y). [para(5452(a,1),132(a,1,1,2)),rewrite([7490(15),7495(8),21(6),7490(15),2507(8)]),flip(a)]. 7550 x * ((x \ (x \ y)) * z) = x \ (y * z). [back_rewrite(7488),rewrite([7490(13)])]. 7607 a(x / y,y,z) \ 1 = a(x,y \ 1,y * z). [para(3691(a,1),58(a,1,2,1,2)),rewrite([1014(4),4157(5),3691(6)])]. 7616 T(x,y) / y = y \ x. [para(2690(a,1),3691(a,1,2)),rewrite([4408(5),14(5)])]. 7617 T(x,y) * (y \ x) = (y \ x) * x. [para(4357(a,1),3691(a,1,2)),rewrite([4155(3),4408(7),4408(5),14(7)])]. 7622 x * ((y * x) \ T(z,x / y)) = x \ (z * (x / y)). [para(3691(a,1),3218(a,1,2,2,2,2)),rewrite([1014(4),3691(7),1014(8)])]. 7628 (x * y) \ ((x / z) * (z * y)) = a(x,z \ 1,z * y). [back_rewrite(4157),rewrite([7607(9)])]. 7636 K(x,K(x / y,y)) = 1. [para(18(a,1),4108(a,1,1))]. 7656 L(x,(y \ z) * z,y) = x. [para(4137(a,1),21(a,1,1)),rewrite([6353(5),45(5),4165(6)])]. 7662 K(x \ y,(y \ x) * (z * (y \ x))) = K(z,y \ x). [para(4137(a,1),114(a,1,1,2,2)),rewrite([14(3),6353(8),7656(7),20(5)]),flip(a)]. 7679 L(x,y \ z,(z \ y) * (u * (z \ y))) = L(x,u,z \ y). [para(4137(a,1),132(a,1,1,2,2)),rewrite([14(3),6353(7),7656(6),21(6)]),flip(a)]. 7681 (x \ y) * (z * (y \ x)) = T(z,y \ x). [para(4137(a,1),1359(a,1,2,2,2,2)),rewrite([14(5),90(5),4137(9),14(8),23(8)])]. 7682 a((x \ y) * (z * (x \ y)),y \ x,u) = a(x \ y,z,u). [para(4137(a,1),133(a,1,2,1,2,2)),rewrite([6353(5),7656(4),14(6),19(7)]),flip(a)]. 7701 ((L(x,y,y * z) * (y * (z * y))) \ (y * ((z * y) * x))) * K(L(x,y,y * z),y * (z * y)) = 1. [para(5752(a,1),4137(a,1,2))]. 7707 K(K(x \ y,z * (y \ x)),z) = 1. [para(4137(a,1),6557(a,1,2,2)),rewrite([4145(3),14(6)])]. 7713 K(x \ y,(y \ x) * z) = K(x \ y,z). [para(4137(a,1),177(a,1,1,1,2)),rewrite([4408(2),14(4),5208(8),4458(5),4408(4),20(5),4408(5),4137(8),14(7)]),flip(a)]. 7715 (x \ y) * ((y \ x) * z) = z. [back_rewrite(6353),rewrite([7656(7)])]. 7719 K(x \ y,z * (y \ x)) = K(z,y \ x). [back_rewrite(7662),rewrite([7713(6)])]. 7726 K(K(x,y \ z),x) = 1. [back_rewrite(7707),rewrite([7719(4)])]. 7769 T(T(x,y),y \ x) = x. [para(16(a,1),4209(a,2)),rewrite([4505(2)])]. 7772 ((x \ y) * (x * z)) * x = T((y * x) * z,x). [para(104(a,1),4209(a,1,1)),flip(a)]. 7775 T(x,y) * y = T(x * y,y). [para(90(a,1),4209(a,1,1)),flip(a)]. 7789 T(x,y) * (x \ y) = T(y,x \ y). [para(2690(a,1),4209(a,1,1)),flip(a)]. 7820 K((x \ y) * (x * z),x) = K(x * ((y * x) * z),x). [back_rewrite(3323),rewrite([7772(4),4366(6),3934(6,R)]),flip(a)]. 7826 x * K(y * x,y) = T(x,y). [back_rewrite(874),rewrite([7820(6),16(4),7772(9),16(7)])]. 7836 a(x,y,y * z) \ 1 = a(x * y,y,z). [back_rewrite(5921),rewrite([7775(2),4582(3)]),flip(a)]. 7875 K(x,x * (y * x)) = K(x,T(y,x)). [back_rewrite(511),rewrite([7775(2),3935(4,R)])]. 7876 K(x * (y * x),x) = K(T(y,x),x). [back_rewrite(510),rewrite([7775(3),3934(4,R)])]. 7925 T(x,K(y * x,y)) = x. [back_rewrite(7047),rewrite([7820(6),16(4)])]. 7966 ((x * (y \ z)) * y) / T(z,y) = R(x,y \ z,y). [para(4505(a,1),22(a,1,2))]. 7967 x \ T(y,x) = T(x \ y,x). [para(4505(a,1),23(a,1,2))]. 7969 (x \ y) * (((y \ x) * z) * T(y,x)) = (z * (x \ y)) * x. [para(4505(a,1),104(a,1,2,2)),rewrite([4408(3)])]. 7981 L(x \ y,x,x \ z) = T(z,x) \ ((x \ z) * y). [para(4505(a,1),74(a,2,1))]. 7982 L(x \ y,x,y \ z) = ((y \ z) * x) \ T(z,y). [para(4505(a,1),74(a,2,2))]. 7996 L(T(x,y),(x \ y) * z,y \ x) = z \ ((z * (y \ x)) * y). [para(4505(a,1),181(a,1,1)),rewrite([4408(3)])]. 7997 (x \ y) * (T(x,y) * z) = L(y * z,x,y). [para(4505(a,1),181(a,2,2,1)),rewrite([5444(4),4408(6)]),flip(a)]. 8002 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = R((y * (z * y)) \ x,y * (z * y),u). [para(4505(a,1),121(a,1,1,1))]. 8018 T(x,y) \ (y \ x) = y \ 1. [para(4505(a,1),1091(a,1,1))]. 8020 (x \ y) * ((z * (x \ y)) * x) = ((x \ y) * z) * T(y,x). [para(4505(a,1),189(a,1,2)),flip(a)]. 8036 T(x * (x * (y \ z)),x * (x * T(z,y))) = T(x * (x * (y \ z)),y). [para(4505(a,1),2647(a,1,2,2,2))]. 8054 a(x \ y,y,x) = 1. [para(4505(a,1),6258(a,1,1)),rewrite([4537(3)])]. 8061 T(x * ((x \ y) * z),y) = L(z,x \ y,x) * y. [para(73(a,1),4505(a,1,1)),flip(a)]. 8078 K(T(x,y),K(y \ x,y)) = 1. [para(4505(a,1),4108(a,1,1))]. 8091 x * L(y,T(z,x),z \ x) = L(x * y,z,x). [back_rewrite(5129),rewrite([7997(8)])]. 8098 L(x * ((y \ x) * z),y,x) = x * (y \ (x * z)). [back_rewrite(4261),rewrite([7997(6)])]. 8105 L(x,y,x \ y) = x. [hyper(24,a,8054,a)]. 8106 a(x,y * x,y) = 1. [para(15(a,1),8054(a,1,1))]. 8255 (x * (y / x)) * y = y * (x * (y / x)). [para(4915(a,1),63(a,1,2)),rewrite([14(5)])]. 8296 K(x,y) * (K(y,x) * z) = z. [para(4993(a,1),21(a,1,1)),rewrite([45(6),5011(7)])]. 8298 (x * K(y,z)) * K(z,y) = x. [para(4993(a,1),22(a,1,2)),rewrite([48(6),4996(7)])]. 8302 L(x \ K(y,z),x,K(z,y)) = x \ K(y,z). [para(4993(a,1),74(a,2,2)),rewrite([4407(8),6144(7),14(7)])]. 8308 L(x,K(y,z),K(z,y) * (u * K(z,y))) = L(x,u,K(z,y)). [para(4993(a,1),132(a,1,1,2,2)),rewrite([14(3),8296(7),21(6)]),flip(a)]. 8310 K(x,y) * (z * K(y,x)) = T(z,K(y,x)). [para(4993(a,1),1359(a,1,2,2,2,2)),rewrite([14(5),90(5),4993(9),14(8),23(8)])]. 8311 a(K(x,y) * (z * K(x,y)),K(y,x),u) = a(K(x,y),z,u). [para(4993(a,1),133(a,1,2,1,2,2)),rewrite([8296(5),14(6),19(7)]),flip(a)]. 8328 R(x,x \ y,y \ z) = z / ((x \ y) * (y \ z)). [para(16(a,1),81(a,2,1))]. 8331 T((x * y) / ((z \ x) * y),u) = R(T(z,u),z \ x,y). [para(81(a,1),31(a,1,1))]. 8379 R(x,x \ y,z) = z * ((z \ y) * (y \ x)). [para(81(a,2),1014(a,2)),rewrite([4407(5),4408(4),14(4),169(4)]),flip(a)]. 8393 (x * y) \ R(z,z \ x,y) = y \ (x \ z). [para(81(a,2),1829(a,1,2)),rewrite([4407(8),4408(7),14(7)])]. 8394 R(T(x,y * z),x \ y,z) = ((x \ y) * z) \ (y * z). [para(81(a,2),2643(a,1,1)),rewrite([31(4)])]. 8463 R(x,y \ 1,(x / y) \ z) = R(x,y \ 1,z). [para(1014(a,1),82(a,1,3,1)),rewrite([1014(10),3143(10),4155(9),4408(8),4180(9)])]. 8497 R(x,y,(x * y) \ T(z,y / x)) = T(z,y / x) * ((z * (y / x)) \ y). [para(3218(a,1),82(a,2,2)),rewrite([3691(3),1014(4),3691(7),1014(8),3691(9),1014(10),4155(11)])]. 8532 T(x,y) \ x = K(x \ y,x). [para(2642(a,1),4539(a,2,1)),rewrite([4408(3),7713(4)]),flip(a)]. 8534 K(x \ y,x) = K(y,y \ x). [para(4539(a,2),2711(a,2)),rewrite([159(2),4365(2),8532(2)])]. 8593 x / T(x,y) = K(x \ y,x). [back_rewrite(4365),rewrite([8532(4)])]. 8594 K(x \ y,x) = K(y,y * x). [back_rewrite(3935),rewrite([8532(4)]),flip(a)]. 8609 x * (L(y,z \ x,z) * x) = (z * ((z \ x) * y)) * x. [para(8061(a,1),90(a,1,2))]. 8679 L(x,y,z * (y * x)) = L(x,y,z). [para(17(a,1),3199(a,1,3)),flip(a)]. 8681 L(x,y,(z * y) * x) = L(x,y,R(z,y,x)). [para(22(a,1),3199(a,1,3)),flip(a)]. 8684 L(L(x,y,z),u,w / (u * x)) = L(L(x,u,w),y,z). [para(3199(a,1),34(a,1,1)),flip(a)]. 8701 L(x \ y,x,z) = ((z / y) * x) \ z. [para(3199(a,1),74(a,1)),rewrite([16(4),16(6),18(6)])]. 8972 (x \ y) * (x * x) = T(x * y,x * x). [para(3476(a,1),13(a,1)),rewrite([14(3),14(6)])]. 8992 ((x \ y) * (x * (x * z))) / T(z,T(x * y,x * (x * z))) = T(x * y,x * (x * z)). [para(3476(a,1),165(a,1,1))]. 9001 T(x,(y \ z) * (y * (y * x))) = T(x,T(y * z,y * (y * x))). [para(3476(a,1),1708(a,1,2))]. 9018 (x * y) * T(z * (z * x),y) = x * (z * (z * (x * y))). [para(2647(a,1),3476(a,1,2)),rewrite([15(7)])]. 9031 ((x \ y) * z) * (y \ x) = T(z,y \ x). [para(4137(a,1),3476(a,1,2,2,2)),rewrite([14(6),4209(5),7681(4),4408(4),4137(8),14(7)]),flip(a)]. 9037 (K(x,y) * z) * K(y,x) = T(z,K(y,x)). [para(4993(a,1),3476(a,1,2,2,2)),rewrite([14(6),4209(5),8310(4),6144(4),4993(8),14(7)]),flip(a)]. 9050 x * ((x * (y * x)) \ z) = y \ (x \ z). [para(18(a,1),3541(a,1,2,2)),rewrite([92(8)]),flip(a)]. 9085 x * a(y,z,z \ (y \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [back_rewrite(3093),rewrite([9050(4)])]. 9101 (x * (((y * z) * (z * y)) * u)) * a(x,(z * y) * (y * z),u) = (x * ((z * y) * (y * z))) * u. [para(178(a,1),312(a,1,1,2)),rewrite([3308(9),3308(14)])]. 9104 ((x * y) * (y * x)) * T(z,y * x) = (y * x) * (K(x,y) * (z * (y * x))). [para(90(a,1),178(a,1,2,2)),flip(a)]. 9114 ((x * ((y * z) * (z * y))) * u) / (((z * y) * (y * z)) * u) = R(x,(y * z) * (z * y),u). [para(178(a,1),121(a,1,2)),rewrite([3308(4),3308(14)])]. 9186 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,(y \ z) * (y * x),y). [para(179(a,1),3143(a,2)),rewrite([4407(4),4407(3)])]. 9191 x \ ((y \ z) * (((z \ y) * x) * u)) = L(u,(z \ y) * x,y \ z). [para(4137(a,1),179(a,1,1,1)),rewrite([13(2),4408(4),100(7),7715(6),4408(9),100(12),7715(11)])]. 9195 (T(x,y) * z) \ (y * (((y \ (y \ x)) * (y * z)) * u)) = L(u,x * (y * z),y). [para(4505(a,1),179(a,1,1,1)),rewrite([7513(14)])]. 9198 x \ (K(y,z) * ((K(z,y) * x) * u)) = L(u,K(z,y) * x,K(y,z)). [para(4993(a,1),179(a,1,1,1)),rewrite([13(2),6144(4),100(7),8296(6),6144(9),100(12),8296(11)])]. 9423 (x * ((x \ (y \ 1)) * ((y * z) * (y \ u)))) \ ((z / y) * u) = a(x,x / y,(y * z) * (y \ u)). [para(1014(a,1),4025(a,1,2,1)),rewrite([4408(6),45(5),3143(7),1014(14),4408(15),45(14),3143(16)])]. 9444 (x * ((x \ K(y,z)) * (K(z,y) * u))) \ u = a(x,x * K(y,z),K(z,y) * u). [para(4993(a,1),4025(a,1,1,2,2,2)),rewrite([6144(4),14(6),8298(10),6144(11),4993(14),14(13)])]. 9484 ((T(T(x,y),z) * (z * u)) * z) / (w * (w * ((T(T(x,z),y) * (z * u)) * z))) = w \ (w \ 1). [para(1907(a,1),21(a,1,2)),rewrite([3436(3),1607(17)]),flip(a)]. 9490 x \ (y * (x \ z)) = (x \ (y / x)) * z. [para(1907(a,1),129(a,1,1,2,2,2,2,2)),rewrite([9484(13),16(4),9484(15),16(6),9484(17),16(8),14(8),1014(7),3143(6),16(5),3143(4),9484(16),16(7),9484(18),16(9),9484(20),16(11),9484(22),16(13),3143(12),16(11),3143(10),3143(10),16(9),3143(8)]),flip(a)]. 9548 x * (x * (y * (x * (x * (y * (z \ ((y / z) \ (x \ (x \ (y \ 1)))))))))) = x * x. [para(14(a,1),3947(a,2,2)),rewrite([4407(6),5162(6)])]. 9553 x * (y * (y * (x * (z \ ((x * (y * (y * (x / z)))) \ u))))) = u. [para(3947(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 9559 L(x,y \ z,y) = L(x,y * z,y). [para(3947(a,1),132(a,1,1)),rewrite([5162(7),7004(9),16(6),16(5),136(6),21(6),5162(7),7004(9),16(6),16(5),2507(6)]),flip(a)]. 9575 L(x,(y * z) / x,y) = (((y * z) / x) \ y) * z. [para(3947(a,1),76(a,2,2)),rewrite([9553(10),9553(13),4501(9)])]. 9640 x * (L(y,z * x,z) * x) = (z * ((z \ x) * y)) * x. [back_rewrite(8609),rewrite([9559(2)])]. 9719 L(x,y \ 1,z * y) = L(x,y * z,y). [back_rewrite(6618),rewrite([9559(6)])]. 9729 x * (L(y,z * x,z) * (x * u)) = ((z * ((z \ x) * y)) * x) * u. [back_rewrite(6606),rewrite([9559(2)])]. 9737 K(L(x * y,x * z,x),z) = K(z * ((z * x) * y),z). [back_rewrite(5742),rewrite([9559(3)])]. 9755 x * L(y,z * x,z) = z * ((z \ x) * y). [back_rewrite(5070),rewrite([9559(2)])]. 9786 L(x * (y * z),x * y,x) = (x * y) * z. [back_rewrite(3018),rewrite([9559(4)])]. 9791 T(x,L(y * z,y * x,y)) = T(x,(x * y) * z). [back_rewrite(2700),rewrite([9559(3)])]. 9832 x \ (y * ((y \ x) * z)) = L(z,y * x,y). [back_rewrite(73),rewrite([9559(6)])]. 10000 (x / y) * ((y / x) * z) = L(z,y / x,x / y). [para(5359(a,1),21(a,1,1)),rewrite([45(6)])]. 10094 R(x,y,(x * y) \ z) * ((y * ((x * y) \ z)) / z) = 1. [para(82(a,2),5359(a,1,1))]. 10140 (x * (y / x)) * ((x * (y / x)) * z) = (x * (y * (y / x))) * z. [para(6446(a,1),178(a,1,2,1)),rewrite([5068(3),5068(6),13(7),2853(9),5068(11),189(11),18(8)])]. 10215 x / (y / z) = x * (z / y). [para(6565(a,1),1014(a,1,2)),flip(a)]. 10221 L(x,y / z,z / y) = x. [para(6565(a,1),3266(a,1,3))]. 10229 (x / y) \ z = (y / x) * z. [para(6565(a,1),3143(a,1,1)),flip(a)]. 10233 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(81(a,2),6565(a,1,1)),rewrite([6071(8)])]. 10235 R(x,y,(x * y) \ z) \ 1 = (y * ((x * y) \ z)) / z. [para(82(a,2),6565(a,1,1))]. 10279 ((x * y) / z) * (z / y) = R(x,y,z \ 1). [back_rewrite(1836),rewrite([10215(4)])]. 10287 (x / y) * ((y / x) * z) = z. [back_rewrite(10000),rewrite([10221(7)])]. 10295 L(x,(y * z) / x,y) = ((x / (y * z)) * y) * z. [back_rewrite(9575),rewrite([10229(6)])]. 10296 x * (x * (y * (x * (x * (y * (z \ ((z / y) * (x \ (x \ (y \ 1)))))))))) = x * x. [back_rewrite(9548),rewrite([10229(6)])]. 10305 R(x,y \ 1,(y / x) * z) = R(x,y \ 1,z). [back_rewrite(8463),rewrite([10229(4)])]. 10321 L(K(x,y),(y / x) * (x * x),y / x) = x \ T(x,y). [back_rewrite(6897),rewrite([10229(9),3169(9),4505(8),15(9)])]. 10323 L(x,y / x,z \ 1) = R(x,y \ 1,z). [back_rewrite(6707),rewrite([10229(6),169(8),4180(8)])]. 10326 K(x / y,y) / x = (y / x) / y. [back_rewrite(6575),rewrite([10229(4),1014(4)]),flip(a)]. 10347 L((x / y) * z,y / x,y) = x * (y \ z). [back_rewrite(5155),rewrite([10229(2)])]. 10366 (x / y) * (x \ y) = K(x \ 1,y). [back_rewrite(3231),rewrite([10229(3)])]. 10367 (x / y) * (y * (x \ z)) = L(z,x \ 1,y). [back_rewrite(3229),rewrite([10229(4)])]. 10393 (x / y) * (((y / x) * z) * x) = (z * (x / y)) * y. [back_rewrite(171),rewrite([10229(3)])]. 10400 (x \ y) / x = x \ (y / x). [para(92(a,1),7616(a,1,1))]. 10401 T(x \ y,z) / x = x \ T(y / x,z). [para(537(a,1),7616(a,1,1))]. 10402 T(T(T(x,y),z),u) / y = y \ T(T(x,z),u). [para(94(a,1),7616(a,1,1))]. 10408 (x / (x * y)) * y = y * (x / (x * y)). [para(2810(a,1),7616(a,1,1)),rewrite([10215(3),10229(6)]),flip(a)]. 10461 T(x,K(x / y,y)) = x. [hyper(28,a,7636,a)]. 10537 R(x,y \ z,T(y,z)) * z = (x * (y \ z)) * T(y,z). [para(2690(a,1),84(a,1,2))]. 10561 T((x * y) * z,R(x,y,z)) = (y * z) * R(x,y,z). [para(84(a,1),4209(a,1,1))]. 10562 R(x,y \ z,y) * T(z,y) = (x * (y \ z)) * y. [para(4505(a,1),84(a,1,2))]. 10592 R(T(x / y,y * z),y,z) = (y * z) \ (x * z). [para(85(a,2),92(a,1,1)),rewrite([31(4)])]. 10670 L(x,y,R(z / y,y,x)) = L(x,y,z * x). [para(85(a,2),3199(a,1,3))]. 10690 ((x / y) * z) \ x = (x * z) \ (x * y). [para(8701(a,1),21(a,2)),rewrite([16(3)]),flip(a)]. 10700 a(x / y,z,(x * z) \ (x * y)) = a(x,z,(x * z) \ (x * y)). [para(8701(a,2),57(a,1,1,2,2)),rewrite([10690(6),1105(6),10690(8)]),flip(a)]. 10702 K(x * (y / x),x / y) = K(x \ 1,y). [para(8701(a,2),67(a,1)),rewrite([10215(2),67(3),10215(4),666(5),5152(3),10215(5)]),flip(a)]. 10707 ((x * (y / z)) * z) \ x = L(y \ 1,z,x). [para(1829(a,1),8701(a,1,1)),rewrite([10215(5)]),flip(a)]. 10710 ((x \ y) * z) \ y = (y * z) \ (x * y). [para(2711(a,1),8701(a,2,1,1)),rewrite([659(3)]),flip(a)]. 10725 L(x \ (y * z),x,z) = (x \ y) * z. [para(3691(a,1),8701(a,2,1,1)),rewrite([3143(6),4408(5)])]. 10748 L(x,T(y,z) / x,y \ z) = (z * (T(y,z) / x)) \ (y * z). [back_rewrite(6696),rewrite([10710(9)])]. 10809 (x \ y) * (x * (x * z)) = T(y * x,x) * z. [para(7967(a,1),104(a,1,2,1)),rewrite([4525(5),7775(6)])]. 10810 R(T(x,y),y,y \ z) = ((y \ x) * (y * z)) / z. [para(7967(a,1),191(a,1,1,2,1)),rewrite([4525(4)]),flip(a)]. 10885 T(x,T(y * z,y * (y * x))) = T(x,T(T(z * y,y),x)). [back_rewrite(9001),rewrite([10809(4),2652(4)]),flip(a)]. 10888 T(x * y,x * (x * z)) = T(T(y * x,x),z). [back_rewrite(8992),rewrite([10809(4),10885(8),965(8)]),flip(a)]. 10900 T((x \ y) * (z * z),T(y,x)) = T(z * (z * (x \ y)),x). [back_rewrite(8036),rewrite([10888(7),101(3),4209(4),4578(3)])]. 10920 T(x * (y * y),x / z) = T(y * (y * x),z \ 1). [back_rewrite(5480),rewrite([10888(6),101(2),4209(3),4578(2)])]. 10927 T(x * (x * y),y \ z) = T(y * (x * x),z). [back_rewrite(5468),rewrite([10888(9),101(6),4209(7),4578(6)])]. 11076 L(T(x * y,x * z),L(y \ z,y,x),u) = (u * L(y \ z,y,x)) \ (u * (x * z)). [para(2705(a,1),74(a,1,1))]. 11083 (x \ y) * (z * (z * x)) = T(y * (z * z),x). [para(2254(a,1),2705(a,1,1)),rewrite([100(3),4408(4),100(6),100(8),10888(9),101(6),4209(7),4578(6)])]. 11138 (x * (y * (x \ (z / x)))) * (T(y,x \ (z / x)) \ x) = z. [para(1014(a,1),3544(a,1,1,2,2,2)),rewrite([3143(6),4408(6),45(2),1014(11),3143(10),3143(10),4155(9)])]. 11215 x * (((x \ y) / z) / T(x * y,z \ 1)) = x \ (z \ 1). [para(3640(a,1),15(a,1,2)),flip(a)]. 11218 K(x * y,x \ 1) = K(y,y \ (x \ 1)). [para(3640(a,1),20(a,1,2)),rewrite([11215(8),4505(4),8532(6),4408(3),45(2),11215(12)])]. 11219 ((x \ y) / z) / T(x * y,z \ 1) = x \ (x \ (z \ 1)). [para(3640(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 11221 x * (x / T(x * y,y \ x)) = y \ x. [para(47(a,1),3640(a,1,2,2,1)),rewrite([4408(5),14(5),989(5),1014(6),4408(8),14(8)])]. 11253 R(x,x \ (y \ 1),y * z) = z / ((x \ (y \ 1)) * (y * z)). [para(3640(a,1),82(a,1,3,1)),rewrite([11219(7),16(5),4408(6),45(5),11219(12),16(10),11219(15),16(13),16(12),4408(11),45(10)])]. 11256 (x \ (K(y \ (x \ 1),y) / x)) * z = (x \ T(x \ 1,y)) * z. [para(3640(a,1),178(a,1,1)),rewrite([11219(9),16(7),11219(13),16(11),16(10),3143(9),3143(9),9490(7),11219(14),16(12),4505(11),11219(17),16(15),16(14),1014(13),10401(11),989(9)])]. 11276 x / T(y * (y * (x * z)),z \ 1) = y \ (y \ (z \ 1)). [para(3641(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 11282 x * (x * ((y * z) / T(x * (x * (y * ((z * y) * u))),u \ (y \ 1)))) = u \ (y \ 1). [para(189(a,1),3641(a,1,2,2,2,1,2,2)),rewrite([4407(9),4407(16)])]. 11295 x * (x * (x / T(x / y,y * (x * x)))) = y * (x * x). [para(3641(a,1),3641(a,1,2,2,2,1,2)),rewrite([1014(3),11276(8),4408(7),4408(5),4408(4),45(3),4578(3),14(5),11276(14),4408(13),4408(11),4408(10),45(9),4578(9),14(11)])]. 11597 L(K(x,y) * z,K(y,x),u) = (u * K(y,x)) \ (u * z). [para(4993(a,1),180(a,1,1,2)),rewrite([6144(2),14(4),8298(10)])]. 11625 R(x,(x \ (y / x)) * (x * z),u) = ((y * z) * u) / (((x \ (y / x)) * (x * z)) * u). [para(18(a,1),183(a,1,1,1,1)),flip(a)]. 11645 (((x \ y) * z) * u) / (((y \ (x \ 1)) * (y * z)) * u) = R(y,(y \ (x \ 1)) * (y * z),u). [para(3143(a,1),183(a,1,1,1,1))]. 11726 a((x \ y) / z,x,T(y,x) \ ((x \ y) * z)) = a(x \ y,x,T(y,x) \ ((x \ y) * z)). [para(4505(a,1),10700(a,1,3,1)),rewrite([4505(10)])]. 11803 (x * ((y \ z) * z)) \ (x * ((y \ z) * ((y \ z) * u))) = L(T(y,z) \ u,(y \ z) * z,x). [para(2690(a,1),3141(a,1,2,2)),rewrite([2690(9)]),flip(a)]. 11853 L(x,(y \ z) * u,z \ y) = L(x,y \ z,u * (z \ y)). [para(4505(a,1),7679(a,1,3,2)),rewrite([90(5),4408(6)]),flip(a)]. 11861 x \ ((y \ z) * (((z \ y) * x) * u)) = L(u,z \ y,x * (y \ z)). [back_rewrite(9191),rewrite([11853(10)])]. 11862 L(T(x,y),x \ y,z * (y \ x)) = z \ ((z * (y \ x)) * y). [back_rewrite(7996),rewrite([11853(5)])]. 12076 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,y,z),u,w))) \ (v6 * v5). [para(34(a,1),6663(a,2,1,2,2))]. 12077 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = ((L(L(x,u,w),y,z) / v5) / v6) * (v6 * v5). [para(37(a,1),6663(a,2,1)),rewrite([2507(8),37(15),4501(16),1091(12),4407(12),10229(12),1014(12)])]. 12303 K(K(x,y),x) = 1. [para(15(a,1),7726(a,1,1,2))]. 12307 T(K(x,y),x) = K(x,y). [hyper(28,a,12303,a)]. 12308 K(x,y) * x = x * K(x,y). [para(12303(a,1),63(a,1,2)),rewrite([14(4)]),flip(a)]. 12309 K(x,K(x,y)) = 1. [para(12303(a,1),4993(a,1,1)),rewrite([13(4)])]. 12310 (x * K(x,y)) * ((x * K(x,y)) * z) = x * (x * (K(x,y) * (K(x,y) * z))). [para(12303(a,1),178(a,1,2,1)),rewrite([13(7),12308(8),189(11),12308(8),4578(10),37(12),100(10)])]. 12312 T(x,K(x,y)) = x. [hyper(28,a,12309,a)]. 12328 K(x,y) / x = x \ K(x,y). [para(12312(a,1),2711(a,1,2))]. 12349 K(x,y) * y = y * K(x,y). [para(12312(a,1),7616(a,1,1)),rewrite([5005(2),6144(4)]),flip(a)]. 12372 T(T(x,y),y \ 1) = x. [para(1091(a,1),7769(a,1,2)),rewrite([1708(2)])]. 12386 T(x,y / (y * x)) = x. [para(2810(a,1),7769(a,1,1)),rewrite([10229(3),10408(3),1708(4)])]. 12432 T(x,K(y,x)) = x. [para(12312(a,1),7769(a,1,1)),rewrite([6144(2),12349(2),1708(3)])]. 12473 K(x,y) / y = y \ K(x,y). [para(12432(a,1),2711(a,1,2))]. 12504 K(x,x * y) * T(y,x) = y. [para(7925(a,1),23(a,2)),rewrite([7826(5),6144(4)])]. 12506 L(T(x,K(y * L(x,z,u),y)),z,u) = L(x,z,u). [para(7925(a,1),30(a,1)),flip(a)]. 12519 T(x * y,K(x * ((z * x) * y),x * z)) = x * y. [para(189(a,1),7925(a,1,2,1))]. 12671 x \ K(x / y,y) = (y / x) / y. [para(10461(a,1),2711(a,1,2)),rewrite([10326(3)]),flip(a)]. 12698 T(T(K(x,y),z),x) = T(K(x,y),z). [para(12307(a,1),29(a,1,1)),flip(a)]. 12705 x * ((x \ (y / x)) * K(x \ (y / x),z)) = y * (x \ K(x \ (y / x),z)). [para(12307(a,1),3575(a,1,2,2)),rewrite([12308(11)]),flip(a)]. 12809 R(T(x \ 1,(x \ y) * z),y,z) = (y * z) \ ((x \ y) * z). [para(6071(a,1),2643(a,1,1)),rewrite([31(6)])]. 12830 (x \ K(y,z)) * K(z,y) = x \ 1. [para(4993(a,1),6071(a,1,2)),rewrite([48(6),4996(9)])]. 12856 L(L(T(x,K(y * L(x,z,u),y)),w,v5),z,u) = L(L(x,z,u),w,v5). [para(12506(a,1),34(a,1,1)),flip(a)]. 12884 (x * R(y,z,(y * z) \ u)) * ((z * ((y * z) \ u)) / u) = x. [para(10094(a,1),104(a,1,2,2)),rewrite([14(9),16(8)]),flip(a)]. 12928 R(x,R(y,z,(y * z) \ u),(z * ((y * z) \ u)) / u) = x. [para(10094(a,1),84(a,1,2)),rewrite([14(10),12884(17)])]. 12931 x / R(y,z,(y * z) \ u) = x * ((z * ((y * z) \ u)) / u). [para(10094(a,1),85(a,2,2)),rewrite([12928(12),48(11)])]. 13311 a(x \ y,x,T(z,y * x)) = a(x,y * x,T(z,y * x)). [para(90(a,1),3968(a,1,3,2)),rewrite([7616(2),90(6),90(7)])]. 13425 T(T(T(x,y),z),y \ 1) = T(x,z). [para(7769(a,1),4214(a,2)),rewrite([8018(7)])]. 13457 L(x,(y \ z) * (y * u),y) = L(x,y * ((z * y) * u),y). [para(187(a,1),132(a,1,2,2)),rewrite([104(4),21(10),2507(10)]),flip(a)]. 13466 a(x,(x \ y) * (x * z),u) = a(x,x * ((y * x) * z),u). [para(187(a,1),133(a,1,1,2)),rewrite([104(9),37(10),4501(11),4498(9),2508(10)]),flip(a)]. 13523 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,y * ((z * y) * x),y). [back_rewrite(9186),rewrite([13457(14)])]. 13639 (x * (y \ z)) * ((z \ y) * u) = (y \ z) * (((z \ y) * x) * u). [para(4137(a,1),190(a,1,2,2)),rewrite([4408(4),14(6),4408(8),5208(12)])]. 13641 T(x,y) * ((y \ z) * (y * u)) = y \ (x * ((z * y) * u)). [para(4505(a,1),190(a,1,1)),rewrite([7550(11)])]. 13663 x / T(x / y,y * (x * x)) = T(y,x * x). [para(11295(a,1),21(a,1,2)),rewrite([23(4),1607(8)]),flip(a)]. 13668 x * (x * (T(y,x * x) * z)) = y * (x * (x * z)). [para(11295(a,1),37(a,1,1)),rewrite([2040(3),13663(8)]),flip(a)]. 13687 ((x / y) * (z * (y * y))) \ (x * (y * T(z,y * y))) = a(x / y,y,y * T(z,y * y)). [para(11295(a,1),60(a,1,1,2)),rewrite([13663(9),13663(15)])]. 13702 (x * (y * (z * (z * u)))) \ ((x * (y * (z * z))) * u) = a(x,y * (z * z),u). [para(11295(a,1),139(a,1,2,1,2)),rewrite([13663(5),13668(5),13663(14),777(13)])]. 13709 L((x * (y * y)) \ z,x * (y * y),y) = (y * T(x,y * y)) \ (y \ z). [para(11295(a,1),3940(a,1,1,1)),rewrite([13663(8),777(7),13663(11)])]. 13734 x * (T(y,x * x) * x) = T(y * (x * x),x). [para(11295(a,1),4209(a,1,1)),rewrite([13663(8),101(7)]),flip(a)]. 13735 T(T(x * (y * y),y),y * T(x,y * y)) = x * (y * y). [para(11295(a,1),4209(a,2)),rewrite([13663(5),101(4),13734(4),13663(8)])]. 13845 L(x,(y * ((y \ z) * u)) * z,L(u,y * z,y)) = L(x,z,L(u,y * z,y) * (y * ((y \ z) * u))). [para(9729(a,1),132(a,1,2,2)),rewrite([9640(6),21(16),9755(12)])]. 13884 L(x,y * (z * y),y) = L(x,y,z). [para(14(a,1),13523(a,1,2,2,1,2)),rewrite([45(5),4505(5),4525(6),5885(6),14(4)]),flip(a)]. 13929 L(x,(y \ z) * u,y \ z) = L(x,z \ y,u * (y \ z)). [para(4137(a,1),13523(a,1,2,2,1,2)),rewrite([4408(5),1014(5),1829(4),4408(5),14(7),3143(8),11861(6),5208(9)]),flip(a)]. 13932 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y) * u,K(z,y)). [para(4993(a,1),13523(a,1,2,2,1,2)),rewrite([6144(5),1014(5),1829(4),6144(5),14(7),3143(8),9198(6),8298(9)])]. 14038 (x * ((x \ (y \ 1)) * ((y * z) * u))) \ ((z / y) * (y * u)) = a(x,x / y,(y * z) * u). [para(15(a,1),9423(a,1,1,2,2,2)),rewrite([15(15)])]. 14083 (x / y) * (y * (x * T(x \ (x \ 1),x * x))) = 1. [para(996(a,1),13687(a,2,3,2)),rewrite([3436(4),8972(6),16(4),87(4),14(3),3436(4),10229(9),3436(13),16(14),1072(13)])]. 14102 T(x,T(x,y) \ 1) = x. [para(541(a,1),12372(a,1,1))]. 14123 T(x,(y / x) / y) = x. [para(5067(a,1),12372(a,1,1)),rewrite([4407(4),10229(4),1014(4)])]. 14124 (x \ (x \ (y \ 1))) * z = x \ (x \ (y \ z)). [para(12372(a,1),3710(a,1,2)),rewrite([7616(7)])]. 14154 K(x,y / (y * x)) = 1. [hyper(27,a,12386,a)]. 14430 T(x,y) * K(x \ y,x) = x. [para(14102(a,1),23(a,2)),rewrite([1014(7),8593(5),4408(6),45(3)])]. 14495 T(x,(T(T(T(y,z),u),x \ 1) / x) / T(T(T(y,x \ 1),z),u)) = x. [para(3382(a,1),14123(a,1,2,1))]. 14546 K(x \ y,x / y) = 1. [para(16(a,1),14154(a,1,2,2))]. 14868 (x * x) / y = x * (x / y). [para(100(a,1),1014(a,1)),rewrite([1014(3)]),flip(a)]. 14874 L(x,y * (y * z),u) = L(x,z,u * (y * y)). [para(100(a,1),132(a,1,1,2,2)),rewrite([100(5),100(9),100(11),4501(12),1091(5),4407(5),5162(5),5610(10),100(7),2507(8)])]. 14882 a(x * (y * y),z,u) = a(x,y * (y * z),u). [para(100(a,1),133(a,1,1,2,2)),rewrite([100(6),100(9),100(11),37(12),4501(13),1091(6),4407(6),5162(6),6141(11),100(7),2508(8)]),flip(a)]. 15035 L(x,y,y * (z * z)) = x. [back_rewrite(5614),rewrite([14874(3)])]. 15045 L(x,y * (z * (z * y)),u * (z * z)) = x. [back_rewrite(2522),rewrite([14874(6)])]. 15052 x * (y * T(y \ (y \ 1),y * y)) = x / y. [para(14083(a,1),15(a,1,2)),rewrite([10229(3),14(3)]),flip(a)]. 15056 L(x * T(x \ (x \ 1),x * x),y,x) = x \ 1. [para(14083(a,1),21(a,1,2)),rewrite([18(2),3200(10)]),flip(a)]. 15079 a((x / y) * (z * (x / y)),y / x,u) = a(x / y,z,u). [para(14083(a,1),133(a,1,2,1,2,2)),rewrite([15052(9),10287(5),14(6),19(7),15052(13)]),flip(a)]. 15120 L(x,y * ((y \ z) * T(z,y)),u * ((y \ z) * (y \ z))) = x. [para(4505(a,1),15045(a,1,2,2,2))]. 15137 K(T(x * y,y),y \ 1) = K(T(x,y) \ 1,x * y). [para(165(a,1),10702(a,1,1,2)),rewrite([7775(2),6564(5)])]. 15143 K(x \ 1,T(y,x)) = K(y,y \ x). [para(2711(a,1),10702(a,1,2)),rewrite([7616(2),16(2)]),flip(a)]. 15144 K(T(x,y),y \ (x \ 1)) = K(y,x). [para(3143(a,1),10702(a,1,1)),rewrite([4155(3),45(2),23(2),6120(4),4408(9),45(7),14(7)])]. 15148 K(x \ 1,y \ x) = K(x / y,y). [para(3666(a,1),10702(a,1,1,2)),rewrite([1014(3),4155(3),16(3)]),flip(a)]. 15149 K(T(x,y),y \ 1) = K(x \ y,x). [para(3666(a,1),10702(a,1,2)),rewrite([4155(3),16(3),4505(2),4408(7),14(7)])]. 15266 (x / y) * ((y * z) / T(x * (y \ x),z)) = (y / x) * z. [para(4254(a,1),15(a,1,2)),rewrite([10229(2)]),flip(a)]. 15271 ((x / y) * (((y / x) * z) * u)) \ (z * u) = a(x / y,(y / x) * z,u). [para(4254(a,1),19(a,1,2,1)),rewrite([15266(8),15266(15)])]. 15276 (x * y) / T(z * (x \ z),y) = (x / z) * ((x / z) * y). [para(4254(a,1),21(a,1,2)),rewrite([3436(4),10229(3),10229(4),1607(12)]),flip(a)]. 15308 a(x / y,(y / x) * ((y / x) * z),u) = a(x / y,z,u). [para(4254(a,1),133(a,1,2,1,2)),rewrite([15276(8),37(8),10287(9),10287(6),19(7),15276(12),2508(12)]),flip(a)]. 15408 T(x \ y,y) * (T(x,y) * z) = T(x,y) \ ((x * y) * z). [para(4314(a,1),15(a,1,2)),flip(a)]. 15409 T(x,y) * (T(x \ y,y) * z) = (x * y) * (T(x,y) \ z). [para(16(a,1),4314(a,1,2,2))]. 15411 a(T(x,y),T(x \ y,y),T(x,y) * z) = a(x,y,z) \ 1. [para(4314(a,1),19(a,1,1)),rewrite([4304(6),4525(5),2548(5)]),flip(a)]. 15452 x \ (y * (y * z)) = ((x \ y) * y) * z. [para(7769(a,1),4314(a,1,1)),rewrite([8018(3),6134(4),7769(6),4525(6),3143(5),7617(6)])]. 15454 x * (T((y / x) / y,K(x / y,y)) * (x * z)) = (x * K(x / y,y)) * z. [para(10461(a,1),4314(a,1,1)),rewrite([12671(3),10461(8)])]. 15593 a(x \ y,z * (x \ y),T(x,y)) = a(x \ y,z,y) \ 1. [para(4344(a,1),19(a,1,1)),rewrite([128(9),2690(7),2548(7)]),flip(a)]. 15621 (((x \ y) * z) * y) \ (x \ y) = T(x,y) \ ((y \ x) / z). [para(4344(a,1),1091(a,1,1)),rewrite([4407(11),4407(10),4408(10),1014(10)])]. 15622 T(x \ y,(z * (x \ y)) * T(x,y)) = T(x \ y,((x \ y) * z) * y). [para(4344(a,1),1708(a,1,2)),flip(a)]. 15645 ((x * (y \ z)) * T(y,z)) * (y \ z) = T(((y \ z) * x) * z,y \ z). [para(4344(a,1),4209(a,1,1)),flip(a)]. 15646 T(T(((x \ y) * z) * y,x \ y),(z * (x \ y)) * T(x,y)) = ((x \ y) * z) * y. [para(4344(a,1),4209(a,2)),rewrite([15645(6)])]. 15674 (((x \ y) * z) * x) \ ((z * (y \ x)) * T(y,x)) = T(y \ x,((y \ x) * z) * x). [back_rewrite(5569),rewrite([15622(14)])]. 15862 x * ((x \ y) * (x \ y)) = y * (x \ y). [para(7769(a,1),4404(a,1,2)),rewrite([7617(7),6351(7)]),flip(a)]. 15916 x \ ((x * y) * z) = (y / x) * (x * z). [para(15(a,1),4504(a,1,2,1,1)),rewrite([1091(2),3143(5),1091(5),1014(6),4209(6)])]. 15922 L(x,x \ y,z * (y \ x)) = ((y \ x) / z) * (z * T(y,x)). [para(4504(a,1),21(a,1,2)),rewrite([7715(4),15916(5),11853(9)]),flip(a)]. 15924 T(x \ y,((y \ x) * z) * y) = T(x \ y,((x \ y) * z) * y). [para(4504(a,1),23(a,1,2)),rewrite([15674(8)]),flip(a)]. 15928 T(x,y \ z) * T(y,z) = (z \ y) * (x * z). [para(37(a,1),4504(a,1,2)),rewrite([7715(7),9031(7)]),flip(a)]. 15940 ((x * (y \ z)) * T(y,z)) / T(y \ z,((z \ y) * x) * z) = ((z \ y) * x) * z. [para(4504(a,1),165(a,1,1))]. 15943 (x \ y) * (((y \ x) / z) * y) = (z \ (x \ y)) * T(x,y). [para(1014(a,1),4504(a,1,2,1)),rewrite([3143(9)])]. 15957 x * L(y,y \ z,x * (z \ y)) = (x * (z \ y)) * T(z,y). [para(4504(a,1),72(a,2)),rewrite([7715(4),11853(4)])]. 16020 L(T(x,y),x \ y,z * (y \ x)) = ((y \ x) / z) * (z * y). [back_rewrite(11862),rewrite([15916(9)])]. 16096 a(x / (y * y),y,y * z) = a(x,y \ 1,y * z). [back_rewrite(7412),rewrite([15916(8),7628(9)])]. 16103 L(x,y * z,y) = L(x,y,z). [back_rewrite(5134),rewrite([15916(3),3276(4)]),flip(a)]. 16229 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y),u). [back_rewrite(13932),rewrite([16103(8)])]. 16231 L(x,y \ z,u * (z \ y)) = L(x,z \ y,u). [back_rewrite(13929),rewrite([16103(4)]),flip(a)]. 16256 L(x,y,z * y) = L(x,y,z). [back_rewrite(13884),rewrite([16103(3)])]. 16286 L(x,(y * ((y \ z) * u)) * z,L(u,y,z)) = L(x,z,L(u,y,z) * (y * ((y \ z) * u))). [back_rewrite(13845),rewrite([16103(6),16103(8)])]. 16343 x \ T(x,y) = K(x,y). [back_rewrite(10321),rewrite([16103(6),2254(4)]),flip(a)]. 16348 x \ (y * ((y \ x) * z)) = L(z,y,x). [back_rewrite(9832),rewrite([16103(6)])]. 16362 T(x,L(y * z,y,x)) = T(x,(x * y) * z). [back_rewrite(9791),rewrite([16103(3)])]. 16364 L(x * (y * z),x,y) = (x * y) * z. [back_rewrite(9786),rewrite([16103(4)])]. 16387 K(L(x * y,x,z),z) = K(z * ((z * x) * y),z). [back_rewrite(9737),rewrite([16103(3)])]. 16398 L(x,y \ 1,z * y) = L(x,y,z). [back_rewrite(9719),rewrite([16103(6)])]. 16465 L(x,y \ z,y) = L(x,y,z). [back_rewrite(9559),rewrite([16103(4)])]. 16470 L(x,y * z,y \ 1) = L(x,y,z). [back_rewrite(6634),rewrite([16103(6)])]. 16484 x \ (y \ (z * (y * x))) = L(T(z,y * x),y,x). [back_rewrite(5138),rewrite([16103(4)]),flip(a)]. 16485 L((x * y) \ z,x,y) = y \ (x \ z). [back_rewrite(3940),rewrite([16103(4)])]. 16487 L(L(x,y,z),z,y) = x. [back_rewrite(667),rewrite([16103(3)])]. 16505 L(T(x,y),y \ x,z) = ((y \ x) / z) * (z * y). [back_rewrite(16020),rewrite([16231(5)])]. 16508 (x * (y \ z)) * T(y,z) = x * L(z,y \ z,x). [back_rewrite(15957),rewrite([16231(4)]),flip(a)]. 16509 ((x \ y) / z) * (z * T(x,y)) = L(y,x \ y,z). [back_rewrite(15922),rewrite([16231(4)]),flip(a)]. 16517 L(x,(y \ z) * u,z \ y) = L(x,z \ y,u). [back_rewrite(11853),rewrite([16231(8)])]. 16564 K(x \ y,x) = K(y,x). [back_rewrite(4516),rewrite([16343(4)])]. 16566 T(x,y) / x = K(x,y). [back_rewrite(4366),rewrite([16343(4)])]. 16568 K(x * y,x) = K(y,x). [back_rewrite(3934),rewrite([16343(4)])]. 16569 K(x \ 1,y * x) = K(y,x). [back_rewrite(3171),rewrite([16343(6)])]. 16603 K(T(x,y),y \ 1) = K(y,x). [back_rewrite(15149),rewrite([16564(6)])]. 16623 T(x,y) * K(y,x) = x. [back_rewrite(14430),rewrite([16564(3)])]. 16660 (x \ (K(x \ 1,y) / x)) * z = (x \ T(x \ 1,y)) * z. [back_rewrite(11256),rewrite([16564(4)])]. 16686 K(x,x * y) = K(x,y). [back_rewrite(8594),rewrite([16564(2)]),flip(a)]. 16687 x / T(x,y) = K(y,x). [back_rewrite(8593),rewrite([16564(4)])]. 16710 K(x,x \ y) = K(x,y). [back_rewrite(8534),rewrite([16564(2)]),flip(a)]. 16711 T(x,y) \ x = K(y,x). [back_rewrite(8532),rewrite([16564(4)])]. 16712 K(T(x,y),K(x,y)) = 1. [back_rewrite(8078),rewrite([16564(3)])]. 16716 x * K(x,y) = T(x,y). [back_rewrite(4535),rewrite([16564(2)])]. 16717 x * (K(x,y) * (x * z)) = (x * T(x,y)) * z. [back_rewrite(4534),rewrite([16564(2)])]. 16735 K(L(x * y,x,z),z) = K((z * x) * y,z). [back_rewrite(16387),rewrite([16568(7)])]. 16813 L(L(T(x,K(L(x,y,z),u)),w,v5),y,z) = L(L(x,y,z),w,v5). [back_rewrite(12856),rewrite([16568(3)])]. 16827 K(x * y,y) = K(T(x,y),y). [back_rewrite(7876),rewrite([16568(3)])]. 16839 K(T(x,y) \ 1,x * y) = K(y,x * y). [back_rewrite(15137),rewrite([16603(5)]),flip(a)]. 16875 K(x,y) * T(y,x) = y. [back_rewrite(12504),rewrite([16686(2)])]. 16909 K(x,y * x) = K(x,T(y,x)). [back_rewrite(7875),rewrite([16686(3)])]. 16936 K(x \ 1,T(y,x)) = K(y,x). [back_rewrite(15143),rewrite([16710(6)])]. 16950 K(x * y,x \ 1) = K(y,x \ 1). [back_rewrite(11218),rewrite([16710(8)])]. 16967 K(x,y \ 1) = K(y,x / y). [back_rewrite(3163),rewrite([16710(3)]),flip(a)]. 16981 x * (y \ K(y \ (x / y),z)) = y * T(y \ (x / y),z). [back_rewrite(12705),rewrite([16716(6)]),flip(a)]. 16984 x * (x * (K(x,y) * (K(x,y) * z))) = T(x,y) * (T(x,y) * z). [back_rewrite(12310),rewrite([16716(2),16716(3)]),flip(a)]. 16985 K(x,y) * x = T(x,y). [back_rewrite(12308),rewrite([16716(4)])]. 16999 a(x,y,K(y,x)) = 1. [back_rewrite(1097),rewrite([16716(2),90(2),46(3)]),flip(a)]. 17019 K(T(x,y) \ 1,x * y) = K(y,T(x,y)). [back_rewrite(16839),rewrite([16909(7)])]. 17040 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(x \ y,y \ 1). [back_rewrite(6878),rewrite([16950(12)])]. 17093 (x \ y) * (((y \ x) * z) * ((z * (x \ y)) * u)) = z * (z * ((x \ y) * u)). [para(4137(a,1),193(a,2,1,2,1,1)),rewrite([4145(5),13639(8),13(10),37(12)])]. 17291 K(x,y \ 1) = K(x,x / y). [para(89(a,1),4809(a,1,1,1,1)),rewrite([101(3),4230(2),15452(7),1091(4),4407(4),4408(4),1014(4),10400(2),4505(3),92(2),4493(3),89(4),16686(6)])]. 17387 (x * T(y,x * x)) \ T(z,x) = ((y * (x * x)) \ z) * x. [para(23(a,1),13709(a,2,2)),rewrite([10725(7)]),flip(a)]. 17666 L(K(x,y),x,y) = K(x,y). [hyper(24,a,16999,a)]. 17730 K(x \ 1,y) = K(x,y \ 1). [para(14546(a,1),63(a,1,2)),rewrite([10366(3),14(5),4493(6)])]. 17771 K(x,T(y,x)) = K(x,y). [back_rewrite(17019),rewrite([17730(5),4407(4),15144(5)]),flip(a)]. 17772 K(x,T(y,x) \ 1) = K(y,x). [back_rewrite(16936),rewrite([17730(4)])]. 17778 (x \ (x \ K(x,y \ 1))) * z = (x \ T(x \ 1,y)) * z. [back_rewrite(16660),rewrite([17730(3),12328(4)])]. 17781 K(x,y \ 1) = K(y,x). [back_rewrite(16569),rewrite([17730(4),4407(3),16710(4)])]. 17822 K(x / y,y) = K(x,y). [back_rewrite(15148),rewrite([17730(4),4408(3),14(3),16710(2)]),flip(a)]. 17906 (x \ T(x \ 1,y)) * z = (x \ (x \ K(y,x))) * z. [back_rewrite(17778),rewrite([17781(3)]),flip(a)]. 17910 K(T(x,y),y) = K(x,y). [back_rewrite(17772),rewrite([17781(4)])]. 17913 K(x \ 1,y) = K(y,x). [back_rewrite(17730),rewrite([17781(6)])]. 17914 K(x,x / y) = K(y,x). [back_rewrite(17291),rewrite([17781(3)]),flip(a)]. 17919 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(y,x \ y). [back_rewrite(17040),rewrite([17781(11)])]. 17924 K(x,y / x) = K(x,y). [back_rewrite(16967),rewrite([17781(3)]),flip(a)]. 17974 x * (T((y / x) / y,K(x,y)) * (x * z)) = T(x,y) * z. [back_rewrite(15454),rewrite([17822(4),17822(9),16716(9)])]. 18023 (x * (y / x)) \ y = K(y,x). [back_rewrite(67),rewrite([17822(5)])]. 18043 K(x * y,y) = K(x,y). [back_rewrite(16827),rewrite([17910(4)])]. 18156 x \ (y * (x / y)) = K(y,x). [back_rewrite(66),rewrite([17924(5)])]. 18422 (T(x,y) * z) / (K(x,y) * z) = R(x,K(x,y),z). [para(16343(a,1),81(a,1,2)),rewrite([16343(6)]),flip(a)]. 18454 L(x,y,x \ 1) = x. [para(1022(a,1),16487(a,1,1))]. 18461 L(x,y,L(x,z,u)) = x. [para(16487(a,1),1689(a,1,1)),rewrite([16487(4)])]. 18472 L(x,x \ y,y) = x. [para(8105(a,1),16487(a,1,1))]. 18473 L(L(x,y,z),z / (y * x),y) = x. [para(3199(a,1),16487(a,1,1))]. 18485 L(R(x,y,z),u,x \ 1) = R(x,y,z). [para(18454(a,1),33(a,1,1)),flip(a)]. 18604 a(x,y \ x,y) = 1. [hyper(25,a,18472,a)]. 18608 L(x,T(y,x),y * x) = x. [para(23(a,1),18472(a,1,2))]. 18650 L(x,y \ 1,x / y) = x. [para(1829(a,1),18472(a,1,2))]. 18689 (x * (y * x)) \ ((x * y) * z) = L(x \ z,x,x * y). [para(101(a,1),74(a,2,1)),flip(a)]. 18690 L(x \ y,x,y * z) = ((y * z) * x) \ (y * (z * y)). [para(101(a,1),74(a,2,2))]. 18703 ((x / (y * z)) * (y * (z * y))) \ (x * y) = a(x / (y * z),y * z,y). [para(101(a,1),60(a,1,1,2))]. 18718 T(x * y,x * x) = T(y * x,x). [para(2690(a,1),101(a,2,2)),rewrite([7789(3),15928(4),8972(3),7775(5)])]. 18724 a(x * y,x,T(z,x)) = a(x,y,z * x) \ 1. [para(101(a,1),507(a,1,2,1)),rewrite([128(7),90(5),2548(7)]),flip(a)]. 18742 a(x,y,y * x) = 1. [para(101(a,1),8106(a,1,2)),rewrite([3982(4),4795(4)])]. 18750 R(x,y * z,y) * (y * (z * y)) = (x * (y * z)) * y. [para(101(a,1),84(a,1,2))]. 18752 R((x * y) / z,z,x) = (x * (y * x)) / (z * x). [para(101(a,1),85(a,2,1))]. 18763 a((x * y) / z,x,L(x \ z,x,x * y)) = a(x * y,x,L(x \ z,x,x * y)). [para(101(a,1),10700(a,1,3,1)),rewrite([18689(7),101(9),18689(12)])]. 18809 (x \ y) * (x * x) = T(y * x,x). [back_rewrite(8972),rewrite([18718(6)])]. 18848 L(x,y,z * (u * (z * (y * x)))) = L(x,y,z * (u * z)). [para(106(a,1),3199(a,1,3)),flip(a)]. 18870 (((x \ y) * z) * ((z * (y \ x)) * T(y,x))) / x = (x \ y) * (z * z). [para(4504(a,1),106(a,1,1,2)),rewrite([7715(14),4578(11)])]. 18962 x / T(x * y,y \ x) = x \ (y \ x). [para(11221(a,1),15(a,1,2)),flip(a)]. 19049 T(T(x,y) \ z,K(T(x,y) \ ((x \ y) * z),T(x \ y,y))) = T(x,y) \ z. [para(11221(a,1),12519(a,1,2,1,2,1)),rewrite([18962(4),6968(3),18962(6),6968(7),18962(10),4505(9),18962(14),6968(13)])]. 19065 x * T(x \ (x \ 1),x * x) = x \ 1. [para(15056(a,1),70(a,1)),flip(a)]. 19074 (x * y) / x = x * (y / x). [para(15056(a,1),72(a,1,2)),rewrite([1014(4),19065(8),1014(5)])]. 19167 a(x,(x / y) * ((x / y) * z),u) = a(y \ (x / y),z,u). [para(18(a,1),4636(a,2,1)),rewrite([3286(6),2508(5)]),flip(a)]. 19178 a(x * (y \ (x * x)),z,u) = a(x / y,x * (x * z),u). [para(1014(a,1),4636(a,2,1)),rewrite([3143(4)])]. 19195 a(T(x,y),(y \ x) * ((y \ x) * z),u) = a((y \ x) * (x * (y \ x)),z,u). [para(4505(a,1),4636(a,2,1)),rewrite([15862(5)]),flip(a)]. 19450 (x * ((T(y,z) * (x * x)) \ u)) \ (T(T(y,x),z) \ 1) = u \ x. [para(4713(a,1),1829(a,1,2)),rewrite([4407(11)]),flip(a)]. 19451 x / (T(T(y,z),u) * ((y \ z) * ((T(y,u) * ((y \ z) * (y \ z))) \ x))) = y \ z. [para(2642(a,1),4713(a,1,2,1,1))]. 19474 (x * (y * y)) \ z = y \ (y \ (x \ z)). [para(4713(a,1),3645(a,1,1)),rewrite([4407(12),19450(12),10927(4),2711(4),4407(13),19450(13)])]. 19479 x / (T(y,z) * ((y \ u) * (T(T(y,u),z) \ x))) = u \ y. [para(7769(a,1),4713(a,1,2,1,1)),rewrite([19474(9),4408(8),4408(9),7715(10)])]. 19486 x / (T(K(y,z),u) * (u \ (K(z,y) * x))) = u. [para(12307(a,1),4713(a,1,2,2,2,1,1)),rewrite([12698(3),19474(6),6144(4),6073(6),7550(7)])]. 19496 x / (T(y,z) * ((u / (u * y)) * ((u * (y * (y / u))) * (T(y,z) \ x)))) = u / (u * y). [para(12386(a,1),4713(a,1,2,1,1)),rewrite([19474(11),10229(10),19074(7),10229(11),19074(5),10140(11)])]. 19499 x / (T(y,z) * (T(y,u) \ ((T(y,z) * (T(y,u) \ (T(y,u) \ 1))) \ x))) = T(y,u) \ 1. [para(14102(a,1),4713(a,1,2,1,1)),rewrite([1014(12),10400(10),989(9),3143(13)])]. 19502 x / (T(y,z) * (((u / y) / u) * ((u * (y * (y / u))) * (T(y,z) \ x)))) = (u / y) / u. [para(14123(a,1),4713(a,1,2,1,1)),rewrite([19474(11),10229(10),10215(7),10229(11),10215(5),10140(11)])]. 19536 x / (T(T(y,z),u) * ((z \ y) * (T(y,u) \ x))) = y \ z. [back_rewrite(19451),rewrite([19474(9),4408(8),4408(9),7715(10)])]. 19567 K(x,y \ x) = K(y,x). [back_rewrite(17919),rewrite([19474(7),4408(5),4408(3),45(2),3032(3),19074(2),15(4),18156(3)]),flip(a)]. 19570 (x * T(y,x * x)) \ T(z,x) = T(x \ (y \ z),x). [back_rewrite(17387),rewrite([19474(8),4505(9)])]. 19639 (x * (y * (z * x))) \ (x * (z * (x * T(y,z * x)))) = a(x * z,x,T(y,z * x)). [para(90(a,1),196(a,1,1,2))]. 19647 (x * ((y \ x) * z)) \ (x * (y \ (x * z))) = a(x / y,x,z). [para(1014(a,1),196(a,2,1)),rewrite([3143(3),3143(7)])]. 19659 a(x / y,x,z) = a(x,y \ x,z). [para(2690(a,1),196(a,2,1)),rewrite([7789(4),4525(5),7997(9),8098(7),19647(7)])]. 19660 (x * (y * (x * z))) \ (x * (y * (x * L(z,x,y)))) = a(x * y,x,L(z,x,y)). [para(72(a,1),196(a,1,1,2))]. 19674 a((x \ y) * z,x \ y,x) = a(x \ y,z,T(y,x)) \ 1. [para(4505(a,1),196(a,1,2,2,2)),rewrite([8020(5),2548(9)]),flip(a)]. 19707 R(x * y,y * x,(y * x) \ (K(y,x) * z)) = R(x * y,K(y,x),z). [para(16(a,1),202(a,2,1,2)),rewrite([6144(5),6144(11),2858(12)])]. 19771 T(x * (x / y),y) = y \ (x * x). [para(87(a,1),10900(a,1,2)),rewrite([3143(4),88(4),1014(5)]),flip(a)]. 19991 (x * (y * x)) / z = x * (y * (x / z)). [para(13(a,1),1851(a,1,1,2,2,2,2)),rewrite([14(4),13(4),13(4),989(8),1014(9),13(8),13(8),13(8)])]. 20016 R((x * y) / z,z,x) = x * (y / z). [back_rewrite(18752),rewrite([19991(7),3691(5),1014(6)])]. 20095 L(a(x / y,y,z),(x / y) * (y * z),u) * ((u * (x * z)) \ (u * ((x / y) * (y * z)))) = 1. [para(1961(a,2),4137(a,1,1))]. 20341 a(x * y,y,x) = 1. [para(15(a,1),18604(a,1,2))]. 20387 a(x,y / x,y) = 1. [para(18(a,1),18742(a,1,3))]. 20390 (x * y) * (y * x) = x * (y * (y * x)). [para(18742(a,1),209(a,1,1)),rewrite([45(5),18742(8),88(8)])]. 20397 a(T(x,y),y,x * y) = 1. [para(90(a,1),18742(a,1,3))]. 20504 ((x * (y * (z * (z * y)))) * u) / (z * (y * (y * (z * u)))) = R(x,y * (z * (z * y)),u). [back_rewrite(9114),rewrite([20390(3),20390(8),2213(9),20390(13)])]. 20509 (x * y) * (K(y,x) * (z * (x * y))) = y * (x * (x * (y * T(z,x * y)))). [back_rewrite(9104),rewrite([20390(3),2213(6)]),flip(a)]. 20510 (x * (y * (z * (z * (y * u))))) * a(x,z * (y * (y * z)),u) = (x * (z * (y * (y * z)))) * u. [back_rewrite(9101),rewrite([20390(3),2213(4),20390(8),20390(13)])]. 20551 a(x,y,x \ y) = 1. [para(2690(a,1),20341(a,1,1)),rewrite([4582(3)])]. 20620 (x * (y * (x / y))) / (y * (x * (y \ x))) = 1. [para(20387(a,1),265(a,1,2,2)),rewrite([8255(3),4230(5),88(8),20387(9)])]. 20692 a(x * (y * z),(x * y) * z,a(x,y,z)) = 1. [para(19(a,1),20551(a,1,3))]. 20939 T(T(x,y),z) / T(x,z) = K(T(x,z),y). [para(29(a,1),16566(a,1,1))]. 20967 ((x * K(y,z)) * y) / T(y,z) = R(x,K(y,z),y). [para(16566(a,1),86(a,1,1,1,2)),rewrite([16566(7)])]. 20994 K((x * y) * z,R(x,y,z)) = K(y * z,R(x,y,z)). [para(84(a,1),16568(a,1,1))]. 21045 L(K(x,y) * z,K(y,x),T(x,y)) = x \ (T(x,y) * z). [para(16623(a,1),74(a,2,1)),rewrite([6144(2)])]. 21062 T(x,y) * (x * z) = x * (T(x,y) * z). [para(16623(a,1),189(a,1,1)),rewrite([16875(7)]),flip(a)]. 21063 K(x,y) * (y * z) = y * (K(x,y) * z). [para(16623(a,1),189(a,2,2,1)),rewrite([16875(3)]),flip(a)]. 21070 x * L(y,K(z,x),T(x,z)) = T(x,z) * (K(z,x) * y). [para(16623(a,1),72(a,1,1))]. 21095 R(x / T(y,z),T(y,z),K(z,y)) = (x * K(z,y)) / y. [para(16623(a,1),85(a,2,2))]. 21316 T((x / y) * (z * (x / y)),y) = (y \ x) * (y \ (z * x)). [para(18(a,1),122(a,1,2,2,2)),rewrite([6135(4)]),flip(a)]. 21447 x * (y \ ((y / x) * z)) = L(z,y / x,y). [para(16(a,1),10347(a,1,1)),rewrite([10229(4)]),flip(a)]. 21463 T(x,y) * ((x * y) \ z) = L(y \ z,y,x). [para(165(a,1),10347(a,1,2)),rewrite([6564(3),3143(3),16256(3)]),flip(a)]. 21472 L((x \ y) * z,y \ x,x) = T(y,x) * (x \ z). [para(2711(a,1),10347(a,1,2)),rewrite([7616(2)])]. 21500 L(x * (y \ z),y,y / x) = (x / y) * z. [para(10347(a,1),16487(a,1,1))]. 21504 L(K(x,y) * z,K(y,x),x) = T(x,y) * (x \ z). [para(16566(a,1),10347(a,1,1,1)),rewrite([16687(4)])]. 21505 L(K(x,y) * z,K(y,x),T(y,x)) = y * (T(y,x) \ z). [para(16566(a,1),10347(a,1,2)),rewrite([16687(2)])]. 21507 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z / y,z))))) = x * x. [back_rewrite(10296),rewrite([21447(8)])]. 21510 R(x,y,(x * y) \ T(z,y / x)) = L(x,y / x,z). [back_rewrite(8497),rewrite([21463(11),10229(7),18(7)])]. 21676 T(a(x,x * y,z),x * (x * ((y * z) / (x * ((x * y) * z))))) = a(x,x * y,z). [para(37(a,1),4950(a,1,2,1)),rewrite([1839(9)])]. 21704 R(x,y * (y * z),z \ ((y \ (y \ z)) * u)) = R(x,z,u). [para(15(a,1),5194(a,2,3)),rewrite([6073(5)])]. 21705 R(x,y * z,(z \ y) * (y \ (y \ u))) = R(x,y \ z,(z \ y) * u). [para(16(a,1),5194(a,1,2,2)),rewrite([4408(5),4408(9)])]. 21708 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * (u * w))) = R(x,z * u,L(w,u,z)). [para(21(a,1),5194(a,2,3)),rewrite([6073(8)])]. 21713 (x * (y * (y * z))) * (z \ (y \ (y \ u))) = z * ((z \ x) * u). [para(5194(a,1),341(a,1,1)),rewrite([16(6),16(5),16(4),200(3)]),flip(a)]. 21715 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * w)) = R(x,z * u,L(u \ w,u,z)). [para(74(a,2),5194(a,2,3)),rewrite([6073(7)])]. 21721 R(x,(y \ (y \ z)) * u,((y \ (y \ z)) * u) \ z) = R(x,z * u,u \ 1). [para(1091(a,1),5194(a,1,3)),rewrite([7550(4),16(3)]),flip(a)]. 21722 R(x,y * (z * (z * y)),K(y,z) * ((y * z) \ ((y * z) \ u))) = R(x,K(z,y),K(y,z) * u). [para(63(a,1),5194(a,1,2,2)),rewrite([20390(3),6144(9),6144(13)])]. 21734 (x * ((x \ ((y \ z) * z)) * (z \ (z \ u)))) / u = R(y \ 1,x,x \ u). [para(5194(a,1),6071(a,2)),rewrite([15452(3),169(7),37(13),16(11),16(10),16(9)])]. 22110 R(T(x,y),y \ x,(x \ y) * z) = ((y \ x) * (y * z)) / z. [para(18454(a,1),203(a,2,1,2,1)),rewrite([3143(4),23(2),3143(4),3143(5),4408(4),3143(8)])]. 22202 ((x \ y) * z) * ((z * (y \ x)) * u) = (x \ y) * (z * (z * ((y \ x) * u))). [para(17093(a,1),15(a,1,2)),rewrite([15452(6),4408(2),4578(3),2040(6)]),flip(a)]. 22239 (x * y) * (T(x,y) \ (y * (x * z))) = y * ((y * x) * z). [para(17093(a,1),190(a,2,2)),rewrite([16(5),6968(6),136(10)])]. 22250 x \ (y * (z * z)) = (x \ y) * (z * z). [back_rewrite(18870),rewrite([22202(7),2690(4),11083(4),7616(4)])]. 22270 x * T(y,x * x) = T(y * x,x). [back_rewrite(1323),rewrite([22250(3),18809(3)]),flip(a)]. 22283 T(x * y,y) \ T(z,y) = T(y \ (x \ z),y). [back_rewrite(19570),rewrite([22270(3)])]. 22354 T(T(x * (y * y),y),T(x * y,y)) = x * (y * y). [back_rewrite(13735),rewrite([22270(6)])]. 22386 L(x,y / x,z) \ (z * y) = T(z * (y / x),z * y). [para(6694(a,1),23(a,2)),rewrite([72(7),18(4)])]. 22398 x \ (y * y) = (x \ y) * y. [para(6257(a,1),6694(a,1,2)),rewrite([19771(3),18718(6),4230(4),4209(5)])]. 22429 a(x * ((y \ x) * x),z,u) = a(x / y,x * (x * z),u). [back_rewrite(19178),rewrite([22398(2)])]. 22608 L(x,y * (z * y),z) = L(x,y,z * (y * z)). [para(13(a,1),16286(a,1,2,1)),rewrite([45(2),101(2),70(4),70(5),45(6),13(6)])]. 22726 T(x,y) / T(T(x,z),y) = K(z,T(x,y)). [para(29(a,1),16687(a,1,2))]. 22862 T(x,y) * K(x,y) = K(x,y) * T(x,y). [para(16712(a,1),63(a,1,2)),rewrite([14(5)]),flip(a)]. 22892 ((x * y) * K(y,z)) / T(y,z) = R(x,y,K(y,z)). [para(16716(a,1),22(a,1,2))]. 22893 x * (x * (K(x,y) * z)) = (x * T(x,y)) * z. [para(16716(a,1),37(a,1,1,2)),flip(a)]. 22906 L(K(x,y) * z,K(y,x),y) = T(y,x) \ (y * z). [para(16716(a,1),74(a,2,1)),rewrite([6144(2)])]. 22923 (x * (y * T(x,z))) \ (x * (y * (x * (K(x,z) * u)))) = L(u,K(x,z),x * (y * x)). [para(16716(a,1),132(a,1,1,2,2))]. 22925 x * ((y * x) * K(x,z)) = (x * y) * T(x,z). [para(16716(a,1),189(a,1,2)),flip(a)]. 22926 T(x,y) * (K(x,y) * z) = K(x,y) * (T(x,y) * z). [para(16716(a,1),189(a,2,2,1)),rewrite([16985(2)])]. 22931 T(x,y) * L(z,K(x,y),x) = x * (K(x,y) * z). [para(16716(a,1),72(a,1,1))]. 22947 R(x,K(x,y),T(x,y) \ z) = z / (K(x,y) * (T(x,y) \ z)). [para(16716(a,1),82(a,1,3,1)),rewrite([16716(7)])]. 22976 a(T(x,y),x * (x * z),u) = a(T(x,y),z,u). [para(16716(a,1),4636(a,2,1)),rewrite([16717(4),101(3),547(2),2508(4)]),flip(a)]. 22979 a(x * y,x,K(x,z)) = a(x,y,T(x,z)) \ 1. [para(16716(a,1),196(a,1,2,2,2)),rewrite([22925(4),2548(7)]),flip(a)]. 23000 (x * T(x,y)) * (K(x,y) * z) = T(x,y) * (T(x,y) * z). [back_rewrite(16984),rewrite([22893(6)])]. 23022 x \ (K(y,x) * (T(x,y) * z)) = L(z,T(x,y),K(y,x)). [para(16875(a,1),21(a,1,1))]. 23033 L(T(x,y) \ z,T(x,y),K(y,x)) = x \ (K(y,x) * z). [para(16875(a,1),74(a,2,1))]. 23108 T(x,y) \ (K(x,y) * (x * z)) = L(z,x,K(x,y)). [para(16985(a,1),21(a,1,1))]. 23144 (x * (y * (y * T(z,u)))) \ ((x * (y * (y * K(z,u)))) * z) = a(x,y * (y * K(z,u)),z). [para(16985(a,1),139(a,1,1,2,2,2))]. 23173 R(x,K(y,z),y) * T(y,z) = (x * K(y,z)) * y. [para(16985(a,1),84(a,1,2))]. 23380 T(x,T(y,x)) = T(x,y). [para(17771(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 23443 T(x,y * x) = T(x,y). [back_rewrite(2652),rewrite([23380(4)])]. 23494 a(x * y,x,z) = a(x,y * x,z). [para(128(a,1),19(a,1,2)),rewrite([196(7)])]. 23575 K(x,y) * (T(y,x) * (K(x,y) * z)) = (y * K(x,y)) * z. [para(16623(a,1),128(a,1,1,2)),rewrite([12349(2)]),flip(a)]. 23584 K(x,y) * (x * (K(x,y) * z)) = (K(x,y) * T(x,y)) * z. [para(16716(a,1),128(a,1,1,2)),flip(a)]. 23589 a(x,y * x,K(x,z)) = a(x,y,T(x,z)) \ 1. [back_rewrite(22979),rewrite([23494(3)])]. 23629 a(x \ y,z * (x \ y),x) = a(x \ y,z,T(y,x)) \ 1. [back_rewrite(19674),rewrite([23494(4)])]. 23643 (x * (y * (x * z))) \ (x * (y * (x * L(z,x,y)))) = a(x,y * x,L(z,x,y)). [back_rewrite(19660),rewrite([23494(11)])]. 23655 (x * (y * (z * x))) \ (x * (z * (x * T(y,z * x)))) = a(x,z * x,T(y,z * x)). [back_rewrite(19639),rewrite([23494(13)])]. 23662 a((x * y) / z,x,L(x \ z,x,x * y)) = a(x,y * x,L(x \ z,x,x * y)). [back_rewrite(18763),rewrite([23494(11)])]. 23663 a(x,y * x,T(z,x)) = a(x,y,z * x) \ 1. [back_rewrite(18724),rewrite([23494(3)])]. 23697 (x / y) * (y * z) = y * ((y \ x) * z). [para(136(a,1),15(a,1,2)),rewrite([15916(3)])]. 23711 (x * y) * (y * ((y \ z) * u)) = y * ((y \ x) * ((y * z) * u)). [para(136(a,1),104(a,1,2,2)),flip(a)]. 23717 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(136(a,1),74(a,2,1)),rewrite([16103(8),16485(7)])]. 23718 (x * y) \ ((x * z) * u) = (y \ x) * ((x \ z) * u). [para(136(a,1),74(a,2,2)),rewrite([4480(5)]),flip(a)]. 23735 x * ((x \ y) * ((x * y) * z)) = y * (x * (y * z)). [para(1091(a,1),136(a,1,2,2,1)),rewrite([3143(5),169(4),23711(5),101(7),128(8)])]. 23736 T(x,(x \ y) * z) = T(x,(x * y) * z). [para(136(a,1),1708(a,1,2)),rewrite([1708(7)]),flip(a)]. 23766 x * (((x \ y) * z) * x) = T((x * y) * z,x). [para(136(a,1),4209(a,1,1)),rewrite([101(7)]),flip(a)]. 23819 K((x \ y) * z,x) = K((x * y) * z,x). [para(136(a,1),16568(a,1,1)),rewrite([16568(7)]),flip(a)]. 23885 L(a(x / y,y,z),y * ((y \ x) * z),u) * ((u * (x * z)) \ (u * (y * ((y \ x) * z)))) = 1. [back_rewrite(20095),rewrite([23697(5),23697(11)])]. 23926 x * ((x \ (y \ z)) * T(y,z)) = L(z,y \ z,x). [back_rewrite(16509),rewrite([23697(5)])]. 23927 L(T(x,y),y \ x,z) = z * ((z \ (y \ x)) * y). [back_rewrite(16505),rewrite([23697(7)])]. 24002 x \ ((x * y) * z) = x * ((x \ y) * z). [back_rewrite(15916),rewrite([23697(6)])]. 24009 (x * ((x \ (y \ 1)) * ((y * z) * u))) \ (y * ((y \ z) * u)) = a(x,x / y,(y * z) * u). [back_rewrite(14038),rewrite([23697(10)])]. 24016 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = L(L(R(x,v5 \ 1,v6),u,w),y,z). [back_rewrite(12077),rewrite([23697(12),4180(12),33(11),33(10)])]. 24021 x * ((x \ y) * (y \ z)) = L(z,y \ 1,x). [back_rewrite(10367),rewrite([23697(4)])]. 24030 a(x,y \ 1,y * z) = a(x,y,y \ z). [back_rewrite(7628),rewrite([23697(4),192(5)]),flip(a)]. 24034 T(x * ((x \ y) * z),y * z) = a(y / x,x,z) \ (y * z). [back_rewrite(4206),rewrite([23697(3)])]. 24035 x * ((x \ y) * ((y / x) * z)) = y * (y * (x \ z)). [back_rewrite(3286),rewrite([23697(5)])]. 24043 R(x,y \ 1,y * z) = R(x,y,y \ z). [back_rewrite(2760),rewrite([23697(3),191(4)]),flip(a)]. 24057 a(x / y,y,z) = a(y,y * x,z). [back_rewrite(60),rewrite([23697(3),4032(5)]),flip(a)]. 24066 (x * y) * ((x * y) * z) = x * (y * (x * (y * z))). [back_rewrite(5783),rewrite([23711(5),23735(5)]),flip(a)]. 24075 (T(x,y) \ (z \ (z \ u))) * ((((u \ z) * z) * K(x,y)) * x) = a(u,z * (z * K(x,y)),x). [back_rewrite(23144),rewrite([23718(10),5162(4),15452(8)])]. 24100 L(x \ y,x,x * z) = T(z,x) \ ((x \ z) * y). [back_rewrite(18689),rewrite([23718(5),6955(5)]),flip(a)]. 24114 a(x \ 1,y,z * (z * u)) = a(x,y * (z * z),u). [back_rewrite(13702),rewrite([23718(9),22250(7),2040(8),6068(9)])]. 24163 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,y * (y * (x / u)),u). [back_rewrite(3753),rewrite([23718(9),5162(3),15452(7)])]. 24164 (x \ (y \ (y \ z))) * (u * ((u \ ((z \ y) * y)) * x)) = a(z,y * (y * u),u \ x). [back_rewrite(3752),rewrite([23718(9),5162(3),15452(6),169(8)])]. 24189 a(x \ 1,y,z) = a(x,y,z). [back_rewrite(19),rewrite([23718(5),6068(5)])]. 24229 (x * (a(y \ x,z,z \ T(y,x)) * u)) / u = L(x,y \ x,z). [back_rewrite(5841),rewrite([23926(5),33(4),480(2)]),flip(a)]. 24261 (x * (y / L(L(z,u,w),v5,v6))) \ (x * y) = L(L(R(z,y \ 1,x),v5,v6),u,w). [back_rewrite(12076),rewrite([24016(6)]),flip(a)]. 24264 R(x,x \ y,z) = L(x,y \ 1,z). [back_rewrite(8379),rewrite([24021(6)])]. 24267 (x * (a(y,z,z \ (y \ x)) * u)) / u = L(x,y \ 1,z). [back_rewrite(5816),rewrite([24021(4),33(5),480(2)]),flip(a)]. 24268 R(x,y,y \ ((x \ y) * z)) = L(x,y \ 1,z). [back_rewrite(4470),rewrite([24021(8)])]. 24279 a(x / (y * y),y,y * z) = a(x,y,y \ z). [back_rewrite(16096),rewrite([24030(8)])]. 24285 a(x,x * y,z) \ 1 = a(y,x,x \ z). [back_rewrite(7607),rewrite([24057(2),24030(8)])]. 24305 T(x * ((x \ y) * z),y * z) = a(x,x * y,z) \ (y * z). [back_rewrite(24034),rewrite([24057(7)])]. 24350 L(a(x,x * y,z),x * ((x \ y) * z),u) * ((u * (y * z)) \ (u * (x * ((x \ y) * z)))) = 1. [back_rewrite(23885),rewrite([24057(2)])]. 24428 ((x / (y * z)) * (y * (z * y))) \ (x * y) = a(y * z,(y * z) * x,y). [back_rewrite(18703),rewrite([24057(11)])]. 24477 ((x / y) * (z * y)) \ (x * T(z,y)) = a(y,y * x,T(z,y)). [back_rewrite(1958),rewrite([24057(9)])]. 24479 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(z,y * (y * (z * x)),u). [back_rewrite(1952),rewrite([24057(15),37(14),2508(15)])]. 24531 (x * (y * (y / x))) * z = x * (y * (y * (x \ z))). [back_rewrite(10140),rewrite([24066(6),23697(5),24035(5)]),flip(a)]. 24558 (x * (y * (x * y))) * z = x * (y * (x * (y * z))). [back_rewrite(426),rewrite([24066(8)])]. 24566 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(z,y,T(x,y)). [back_rewrite(6149),rewrite([24189(10)])]. 24596 a(x,y * (z * z),u) = a(x,y,z * (z * u)). [back_rewrite(24114),rewrite([24189(5)]),flip(a)]. 24624 ((x * y) \ z) * ((z \ x) * y) = a(z,x,y). [back_rewrite(6068),rewrite([24189(8)])]. 24638 (x * y) / ((z \ x) * y) = L(z,x \ 1,y). [back_rewrite(5665),rewrite([24268(4)]),flip(a)]. 24644 x / (T(y,z) * (u * (y * (u \ (T(y,z) \ x))))) = (u / y) / u. [back_rewrite(19502),rewrite([24531(9),23697(10),1829(3),10809(9),13(3),89(2)])]. 24645 (x / y) / x = x / (x * y). [back_rewrite(19496),rewrite([24531(9),3169(10),1091(3),10809(9),13(3),89(2),24644(8)])]. 24749 R(T(x,y),x \ z,u) = L(T(x,y),z \ 1,u). [back_rewrite(8331),rewrite([24638(4),30(4)]),flip(a)]. 24764 x * (T(y / (y * x),K(x,y)) * (x * z)) = T(x,y) * z. [back_rewrite(17974),rewrite([24645(2)])]. 24890 ((K(x,y) * z) \ u) / T(K(y,x),u) = z \ u. [para(19486(a,1),1829(a,1,2)),rewrite([4407(9),4408(9),1014(9)]),flip(a)]. 24897 x * ((T(K(y,z),u) * (u \ (K(z,y) * x))) \ T(w,x * u)) = x \ (w * (x * u)). [para(19486(a,1),3218(a,1,2,2,2,2)),rewrite([19486(17)])]. 24915 x / (K(y,z) * (y \ (K(z,y) * x))) = y. [para(12307(a,1),19486(a,1,2,1))]. 25093 (x \ y) / T(z * (z / x),y) = z \ (z \ y). [para(12372(a,1),5364(a,1,2,2)),rewrite([1014(4),7616(2),1014(4),12372(9)])]. 25357 a(x,y * (x * y),z) = 1. [para(14(a,1),5524(a,1,2,1)),rewrite([45(3),70(3),4578(2),1708(4),14882(4),90(2)])]. 25410 a(x * (y * x),y,z) = 1. [back_rewrite(3735),rewrite([25357(6)])]. 25524 (x * ((x * y) * z)) * ((x * (y * z)) \ T(y,x)) = y * x. [para(22239(a,1),17(a,1,1)),rewrite([4155(8)])]. 26340 (x * (y / x)) * K(y,x) = y. [para(17822(a,1),63(a,1,2)),rewrite([18(6)])]. 26495 K(x,y) * T(x,y) = T(T(x,y),y). [para(17910(a,1),16716(a,1,2)),rewrite([22862(3)])]. 26526 K(x,y) * (x * (K(x,y) * z)) = T(T(x,y),y) * z. [back_rewrite(23584),rewrite([26495(8)])]. 26628 K((x \ y) * z,R(x \ 1,y,z)) = K(y * z,(x \ y) * z). [para(6071(a,1),17914(a,1,2))]. 26642 x * K(y,x) = T(x,x / y). [para(17914(a,1),16716(a,1,2))]. 26699 K(x,y) * (T(y,x) * (K(x,y) * z)) = T(y,y / x) * z. [back_rewrite(23575),rewrite([26642(8)])]. 26745 K(x,y) * y = T(y,y / x). [back_rewrite(12349),rewrite([26642(4)])]. 26753 K(x * y,R(z \ 1,x,y)) = K(x * y,(z \ x) * y). [para(6071(a,1),17924(a,1,2))]. 26764 T(x,y / x) = T(x,y). [para(17924(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 26839 T(x,L(x,y,z)) = x. [para(160(a,1),16487(a,1,1)),rewrite([16487(2)]),flip(a)]. 26897 x / T(y * (y * (x / z)),z) = y \ (y \ z). [para(1925(a,1),21(a,1,2)),rewrite([3436(2),1607(8)]),flip(a)]. 26903 L(x,y,y \ z) = L(x,z,y). [para(1925(a,1),132(a,1,1,2)),rewrite([26897(6),7550(5),16(4),21(4),26897(6),2507(6),16465(4)]),flip(a)]. 26952 T(x,y) \ ((y \ x) * z) = L(y \ z,x,y). [back_rewrite(7981),rewrite([26903(3)]),flip(a)]. 26963 L(x \ y,x,x * z) = L(x \ y,z,x). [back_rewrite(24100),rewrite([26952(7)])]. 26968 a((x \ y) / z,x,L(x \ z,y,x)) = a(x \ y,x,L(x \ z,y,x)). [back_rewrite(11726),rewrite([26952(6),26952(10)])]. 26973 a((x * y) / z,x,L(x \ z,y,x)) = a(x,y * x,L(x \ z,y,x)). [back_rewrite(23662),rewrite([26963(5),26963(9)])]. 27047 x * ((x \ y) * T(z,x)) = (y / x) * (z * x). [para(165(a,1),10393(a,1,2,1,1)),rewrite([6564(3),3143(6),24002(4),6564(7),1014(7)])]. 27119 L(x,y * T(y,z),u * ((z \ y) * (z \ y))) = x. [back_rewrite(15120),rewrite([27047(4),3169(3),4505(2)])]. 27447 ((x * (y * (x \ y))) / (x * (y / x))) * K(x,y) = x * (y / x). [para(20620(a,1),5560(a,1,2)),rewrite([18023(3),4407(10),6144(9),14(9),10229(8),20620(17),88(12)])]. 27454 (x * (y * (y * (y * x)))) \ y = y \ ((y * x) \ (x \ 1)). [para(5600(a,1),17(a,1,1)),rewrite([989(5),4407(5),6567(5)]),flip(a)]. 27459 L(x,y,z * (y * z)) = x. [para(5600(a,1),21(a,1,1)),rewrite([27454(6),24558(10),6600(11),45(5),27454(11),3050(12)])]. 27549 L(x,y * (z * y),z) = x. [back_rewrite(22608),rewrite([27459(6)])]. 27556 (x * (y * (x * y))) \ (x * z) = (y * (x * y)) \ z. [back_rewrite(3118),rewrite([27459(6)]),flip(a)]. 27573 x * (y * (x * (z / (z * (x * (y * (x * z))))))) = z \ 1. [para(5674(a,1),15(a,1,2)),flip(a)]. 27619 (((x * y) * z) * x) * (((z * x) \ ((x * y) \ z)) / z) = 1. [para(5674(a,1),193(a,2)),rewrite([27573(23),4407(9),193(12),169(11),4458(7),1014(10)])]. 27689 (x * (a(x / (y * z),y,z) * u)) / u = R(x,z \ (y \ 1),y). [para(15(a,1),5817(a,1,1,2,1,3)),rewrite([4407(9)])]. 27706 R(x,T(y,x) \ 1,z) = L(x,y \ x,z). [para(2711(a,1),5817(a,1,1,2,1,1)),rewrite([24229(7)]),flip(a)]. 27732 R(((x / (y * z)) * y) * z,x,x \ u) = R(x,z \ (y \ 1),y). [back_rewrite(437),rewrite([27689(12)])]. 27871 L(x,L(x,y,z),u) = x. [para(16487(a,1),6024(a,1,1)),rewrite([16487(4)])]. 28029 L(x,((y * z) \ (y * u)) / x,y * z) = ((y * z) * (L(z \ u,z,y) / x)) \ (y * u). [para(74(a,1),6697(a,1,2,1)),rewrite([16(13)])]. 28379 L(x,(y \ K(z,u)) / x,K(u,z) * y) = (x * (K(u,z) * y)) * (y \ K(z,u)). [para(4993(a,1),28029(a,1,2,1,2)),rewrite([4407(4),6144(3),14(3),8302(12),4993(15),4407(14),4407(13),6144(12),14(12),10229(12),4155(9),6144(8)])]. 28464 T(T(x,y),L(x,z,u)) = T(x,y). [para(26839(a,1),29(a,1,1)),flip(a)]. 28473 L(x,y,z) * x = x * L(x,y,z). [para(26839(a,1),90(a,1,2))]. 28505 x / L(x,y,z) = L(x,y,z) \ x. [para(26839(a,1),7616(a,1,1))]. 28511 T(x,L(x,y,z) \ x) = x. [para(26839(a,1),7769(a,1,1))]. 28851 T(L(x,y,z) * (u / x),L(x,y,z) * u) = T(L(x,y,z) * (u / x),x). [para(18461(a,1),6694(a,1,2)),flip(a)]. 28965 T(x,x / y) = T(x,y \ x). [para(19567(a,1),16716(a,1,2)),rewrite([26642(2)])]. 28991 K(x,y) * y = T(y,x \ y). [back_rewrite(26745),rewrite([28965(4)])]. 29035 K(x,y) * (T(y,x) * (K(x,y) * z)) = T(y,x \ y) * z. [back_rewrite(26699),rewrite([28965(8)])]. 29216 T(x \ y,y) * T(x,y) = T(y,x). [para(23380(a,1),4505(a,2)),rewrite([4278(2)])]. 29325 (x \ y) * (y / x) = y * (x \ (x \ y)). [para(23443(a,1),3218(a,1,2,2)),rewrite([2643(2),3169(7),15(8)]),flip(a)]. 29339 T(x,y) / (y * x) = (y * x) \ x. [para(23443(a,1),7616(a,1,1))]. 29418 (x / y) * (y \ x) = x * (y \ (y \ x)). [back_rewrite(2903),rewrite([29325(6)])]. 29466 T(x,y * ((y \ z) * x)) = T(x,R(z,y,y \ x)). [para(191(a,1),26764(a,1,2)),flip(a)]. 29584 (T(x,y) * z) / a(y \ x,y,z) = (y \ x) * (y * z). [para(4505(a,1),162(a,1,1,1))]. 30202 ((T(x,y) * z) \ T(T(x,y),y)) * (x * z) = T(T(x,z),y). [para(16875(a,1),6152(a,1,2,1)),rewrite([6144(5),26495(5),16875(11),2644(10)])]. 30410 (x \ (T(y,x) \ 1)) * T(z,y \ x) = (x \ (x \ z)) * (y \ x). [para(2711(a,1),6185(a,1,2,2)),rewrite([2711(11)])]. 30432 (x \ (x \ y)) / z = x \ (x \ (y / z)). [para(3691(a,1),6185(a,1,2,2)),rewrite([4407(3),14124(8),6095(4),3691(7),1014(8)]),flip(a)]. 30455 x \ (y * (x / z)) = T(y,x) / z. [para(6185(a,1),3683(a,1,2)),rewrite([1840(5),4505(2)]),flip(a)]. 30508 x * (T(y,x) / z) = y * (x / z). [para(6185(a,1),136(a,1,2,2)),rewrite([1840(5),4505(2),1014(6),90(7)])]. 30512 (x \ (x \ y)) * T(z,y) = (x \ (x \ z)) * y. [para(19486(a,1),6185(a,1,2,2)),rewrite([4407(8),4408(8),1014(8),24890(6),19486(13)])]. 30627 x * ((y * x) \ T(z,x / y)) = T(z,x) / y. [back_rewrite(7622),rewrite([30455(8)])]. 30654 L(x,T(y,z) / x,y \ z) = (y * (z / x)) \ (y * z). [back_rewrite(10748),rewrite([30508(7)])]. 30703 T(T(x,y),y) = T(x,y * y). [para(6188(a,1),45(a,1)),rewrite([48(4),18809(4),4505(2),48(4)])]. 30840 (T(K(x,y),z) * (z \ (K(y,x) * u))) \ T(w,u * z) = (u \ (u \ w)) * (u * z). [para(19486(a,1),6188(a,1,2,2,2)),rewrite([19486(18)])]. 30881 ((T(x,y) * z) \ T(x,y * y)) * (x * z) = T(T(x,z),y). [back_rewrite(30202),rewrite([30703(4)])]. 30944 K(x,y) * (x * (K(x,y) * z)) = T(x,y * y) * z. [back_rewrite(26526),rewrite([30703(7)])]. 30953 K(x,y) * T(x,y) = T(x,y * y). [back_rewrite(26495),rewrite([30703(5)])]. 32180 (x * L(y,z,u)) * y = x * (y * L(y,z,u)). [para(27871(a,1),72(a,1,2)),rewrite([28473(5)])]. 32743 R(x * y,y * x,z) = x * y. [para(4209(a,1),493(a,1,1)),rewrite([4209(5)])]. 32749 (x * T(x,y)) * z = x * (T(x,y) * z). [para(493(a,1),84(a,1,1)),rewrite([21062(3),547(5)]),flip(a)]. 32816 R(x * y,K(y,x),z) = x * y. [back_rewrite(19707),rewrite([32743(7)]),flip(a)]. 32894 x * (K(x,y) * (T(x,y) * z)) = T(x,y) * (T(x,y) * z). [back_rewrite(23000),rewrite([32749(5),22926(4)])]. 33039 L(T(x \ 1,y),x,z) = T(x \ 1,y). [para(1077(a,1),30(a,1,1)),flip(a)]. 33049 a(x,y,T(x,z)) = 1. [hyper(25,a,1685,a)]. 33075 L(x,y,T(x,z)) = x. [para(7769(a,1),1685(a,1,1)),rewrite([7769(5)])]. 33091 a(x,y * x,K(x,z)) = 1. [back_rewrite(23589),rewrite([33049(5),46(6)])]. 33119 a(x / y,z,y \ x) = 1. [para(92(a,1),33049(a,1,3))]. 33180 (T(x,y) * z) * x = T(x,y) * (z * x). [para(33075(a,1),72(a,1,2))]. 33181 (T(x,y) * (z * x)) \ (x * (T(x,y) * z)) = K(x,T(x,y) * z). [para(33075(a,1),2934(a,1,2,1)),rewrite([33075(9)])]. 33249 R(x,y * z,a(x,y,z)) \ ((x * y) * z) = (y * z) * a(x,y,z). [para(54(a,1),166(a,1,2))]. 33258 (x * y) \ ((y * x) * z) = K(y,x) * z. [para(63(a,1),166(a,1,2,1)),rewrite([32816(3)])]. 33300 R(x,K(x,y),z) \ (T(x,y) * z) = K(x,y) * z. [para(16716(a,1),166(a,1,2,1))]. 33324 T(x,y) \ (x * (T(x,y) * z)) = x * z. [para(493(a,1),166(a,1,1)),rewrite([547(3),32749(4)])]. 33334 L(x,K(y,z),z * y) = x. [back_rewrite(2857),rewrite([33258(6),8296(4)]),flip(a)]. 33346 (x * y) * (K(y,x) * z) = (y * x) * z. [back_rewrite(5116),rewrite([33334(4)]),flip(a)]. 33415 x * (y * (y * (x * T(z,y * x)))) = (x * y) * (z * (y * x)). [back_rewrite(20509),rewrite([33346(6)]),flip(a)]. 33450 (x \ (y / x)) * (x * z) = x \ (y * z). [para(18(a,1),168(a,1,2,1)),flip(a)]. 33472 (x \ (y \ 1)) * (x * z) = x \ ((y \ x) * z). [para(3143(a,1),168(a,1,2,1)),flip(a)]. 33476 (x \ (x \ y)) * (x * z) = x \ (T(y,x) * z). [para(4505(a,1),168(a,1,2,1)),flip(a)]. 33497 K(x,y) * (x * z) = T(x,y) * z. [para(16343(a,1),168(a,2,1)),rewrite([547(2),32749(3),15(4)]),flip(a)]. 33507 K(x,y) * (T(y,x) * z) = y * z. [para(16711(a,1),168(a,2,1)),rewrite([32749(4),33324(5)]),flip(a)]. 33511 (x \ K(x,y)) * (x * z) = x \ (T(x,y) * z). [para(16985(a,1),168(a,1,2,1)),flip(a)]. 33545 R(x,x \ (y * z),u) = L(x,z \ (y \ 1),u). [back_rewrite(11625),rewrite([33450(4),33450(9),24638(9),4407(6)])]. 33575 R(x,x \ ((y \ x) * z),u) = L(x,z \ (x \ y),u). [back_rewrite(11645),rewrite([33472(8),24638(8),4407(4),4408(3),14(3),33472(8)]),flip(a)]. 33590 (T(K(x,y),z) * (z \ (K(y,x) * u))) \ T(w,u * z) = u \ (T(w,u) * z). [back_rewrite(30840),rewrite([33476(13)])]. 33664 L(x,y * (z * u),z) = L(x,z,T(y,z) * u). [back_rewrite(9195),rewrite([33476(6),16348(8)]),flip(a)]. 33705 K(x,y) * (T(x,y) * z) = T(x,y * y) * z. [back_rewrite(30944),rewrite([33497(5),22926(4)])]. 33734 L(x,y,K(y,z)) = x. [back_rewrite(23108),rewrite([33497(4),15(4)]),flip(a)]. 33781 T(x,y \ x) * z = x * (K(y,x) * z). [back_rewrite(29035),rewrite([33507(6)]),flip(a)]. 33796 L(x,T(y,z),K(z,y)) = x. [back_rewrite(23022),rewrite([33507(4),15(2)]),flip(a)]. 33957 x \ (y * (x * z)) = T(y,x) * z. [back_rewrite(24897),rewrite([33590(9),16(4)]),flip(a)]. 33969 L(x,y,z * T(z,y)) = x. [back_rewrite(27549),rewrite([33664(3),547(2)])]. 33981 L(a(x,y,z),y,T(x,y) * z) = a(y,x,y * z). [back_rewrite(2971),rewrite([33664(4)])]. 33992 T(x,y) * (T(x,y) * z) = x * (T(x,y * y) * z). [back_rewrite(32894),rewrite([33705(4)]),flip(a)]. 34091 x \ (K(y,x) * z) = T(x,y) \ z. [back_rewrite(23033),rewrite([33796(5)]),flip(a)]. 34275 L(T(x,y * z),y,z) = T(T(x,y),z). [back_rewrite(16484),rewrite([33957(3),23(3)]),flip(a)]. 34415 x / (K(y,z) * (T(y,z) \ x)) = y. [back_rewrite(24915),rewrite([34091(4)])]. 34554 R(x,K(x,y),T(x,y) \ z) = x. [back_rewrite(22947),rewrite([34415(9)])]. 34768 (x * y) \ T(z,y / x) = y \ (T(z,y) / x). [para(30627(a,1),15(a,1,2)),flip(a)]. 34798 x * (T(y * x,x) \ T(z,y \ x)) = T(z,x) / T(y,x). [para(2711(a,1),30627(a,1,2,2,2)),rewrite([7775(2)])]. 34823 (x * y) \ y = y \ (x \ y). [para(12386(a,1),30627(a,1,2,2)),rewrite([101(2),9050(4),29339(5)]),flip(a)]. 34860 R(x,y,y \ (T(z,y) / x)) = L(x,y / x,z). [back_rewrite(21510),rewrite([34768(4)])]. 35223 K(x,y) * (T(x,y) \ z) = x \ z. [para(16(a,1),33300(a,1,2)),rewrite([34554(4)]),flip(a)]. 35247 (K(x,y) * z) * R(x,K(x,y),z) = T(T(x,y) * z,R(x,K(x,y),z)). [para(33300(a,1),4505(a,1,1))]. 35274 K(R(x,K(x,y),z),T(x,y) * z) = K(R(x,K(x,y),z),K(x,y) * z). [para(33300(a,1),16710(a,1,2)),flip(a)]. 35287 K(R(x,K(x,y),z),K(x,y) * z) = K(T(x,y) * z,K(x,y) * z). [para(33300(a,1),19567(a,1,2)),rewrite([35274(10)]),flip(a)]. 35301 K(R(x,K(x,y),z),T(x,y) * z) = K(T(x,y) * z,K(x,y) * z). [back_rewrite(35274),rewrite([35287(10)])]. 35536 L(a(x,y,T(z,y)),x * (z * y),(x * y) * T(z,y)) = a(x,y,T(z,y)). [hyper(24,a,6438,a)]. 35645 (x \ (y \ 1)) * z = (y * x) \ z. [para(13(a,1),6953(a,1,1,2,1)),rewrite([46(3),45(8),45(7)])]. 35648 (x \ (y \ (z \ 1))) * u = ((z * y) * x) \ u. [para(16(a,1),6953(a,1,1,2,1)),rewrite([23717(10),16(9)])]. 35675 (x * ((y * z) \ (y \ 1))) * u = (x / z) * (y \ (y \ u)). [para(1014(a,1),6953(a,2,1)),rewrite([4408(7),45(2),10229(10)])]. 35683 x * (T(y,x) \ (x \ z)) = y \ z. [para(1091(a,1),6953(a,1,1)),rewrite([3143(3),35645(6),5162(4),16(5),4408(6),4408(3),169(6),6968(5)]),flip(a)]. 35698 (x \ ((y \ z) * z)) * u = (((y * x) \ z) * z) * u. [para(3143(a,1),6953(a,1,1,2,1)),rewrite([4408(5),45(3),14(3),4408(2),4408(10),45(9),4408(9),45(7),15452(8)])]. 35803 (x * y) \ (y * z) = y \ ((x \ y) * z). [back_rewrite(33472),rewrite([35645(5)])]. 35829 T(x * y,y) \ T(z,x \ y) = (y \ (y \ z)) * (x \ y). [back_rewrite(30410),rewrite([35645(7),7775(2)])]. 35865 a(x,x / y,(y * z) * u) = a(x,x * y,(y \ z) * u). [back_rewrite(24009),rewrite([35645(6),23718(4),4032(9)]),flip(a)]. 35905 R(x,x \ (y \ 1),y * z) = z * ((y * z) \ (y * x)). [back_rewrite(11253),rewrite([35645(10),4155(9)])]. 35922 R(x,x \ (y \ 1),z) = L(x,y,z \ 1). [back_rewrite(3646),rewrite([35645(9),4155(8),6070(8)])]. 35944 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,y * (y * u),u \ x). [back_rewrite(24164),rewrite([35698(7)])]. 35945 (x * ((y * x) \ z)) / z = R(y \ 1,x,x \ z). [back_rewrite(21734),rewrite([35698(6),169(6),6968(5),35683(5)])]. 35978 T(x,y) / T(z,y) = y \ (x * (z \ y)). [back_rewrite(34798),rewrite([35829(5),7550(5)]),flip(a)]. 36021 x * ((y * x) \ (y * z)) = L(z,y,x \ (y \ 1)). [back_rewrite(35905),rewrite([35922(5),4407(3)]),flip(a)]. 36043 x / R(y,z,(y * z) \ u) = x * R(y \ 1,z,z \ u). [back_rewrite(12931),rewrite([35945(8)])]. 36066 R(x,y,(x * y) \ z) \ 1 = R(x \ 1,y,y \ z). [back_rewrite(10235),rewrite([35945(9)])]. 36081 x \ (y * (T(y,z) \ x)) = K(z,T(y,x)). [back_rewrite(22726),rewrite([35978(4)])]. 36084 x \ (T(y,z) * (y \ x)) = K(T(y,x),z). [back_rewrite(20939),rewrite([35978(4)])]. 36652 (x * y) * T(x * y,y) = x * (x * (y * y)). [para(100(a,1),3184(a,1,2,2)),rewrite([18809(3),540(4),14(2),18809(6),547(7)]),flip(a)]. 37107 L(x,K(y,z),y) = x. [para(33734(a,1),16487(a,1,1))]. 37125 x * (K(x,y) * z) = T(x,y) * z. [back_rewrite(22931),rewrite([37107(3)]),flip(a)]. 37126 T(x,y) \ (x * z) = K(y,x) * z. [back_rewrite(22906),rewrite([37107(4)]),flip(a)]. 37146 L(L(x,T(y,z),u),u * T(y,z),y) = L(x,K(y,z),y * (u * y)). [back_rewrite(22923),rewrite([37125(6),638(8)])]. 37216 L(x,K(y,z),z) = x. [para(17781(a,1),37107(a,1,2))]. 37218 L(x,K(y,z),T(y,z)) = x. [para(17910(a,1),37107(a,1,2))]. 37224 T(x,y) * (x \ z) = K(x,y) * z. [back_rewrite(21504),rewrite([37216(4)]),flip(a)]. 37229 x * (T(x,y) \ z) = K(y,x) * z. [back_rewrite(21505),rewrite([37218(5)]),flip(a)]. 37231 T(K(x,y),z) = K(T(x,z),y). [back_rewrite(36084),rewrite([37224(3),23(3)])]. 37242 K(T(x,y),z) = K(x,T(z,y)). [back_rewrite(36081),rewrite([37229(3),23(3),37231(2)])]. 37402 ((K(x,y) * z) \ u) * K(x,T(y,u)) = z \ u. [back_rewrite(24890),rewrite([37231(5),37242(5),5005(6),37242(5)])]. 37429 T(K(x,y),z) = K(x,T(y,z)). [back_rewrite(37231),rewrite([37242(4)])]. 38196 L(x,K(y,z),T(z,y)) = x. [para(17771(a,1),37216(a,1,2))]. 38207 T(x,y) * (K(y,x) * z) = x * z. [back_rewrite(21070),rewrite([38196(3)]),flip(a)]. 38208 x \ (T(x,y) * z) = K(x,y) * z. [back_rewrite(21045),rewrite([38196(5)]),flip(a)]. 38223 (x \ K(x,y)) * (x * z) = K(x,y) * z. [back_rewrite(33511),rewrite([38208(7)])]. 38305 x * ((x \ (y / x)) * z) = y * (x \ z). [para(18(a,1),169(a,1,1)),flip(a)]. 38314 x * (x * (y * ((y \ (x \ (x \ z))) * u))) = y * ((y \ z) * u). [para(37(a,1),169(a,2)),rewrite([5162(6),21713(7),5162(6)]),flip(a)]. 38342 (x \ y) * (y \ z) = y * ((x * y) \ z). [para(3143(a,1),169(a,1,1)),rewrite([35645(7)])]. 38356 T(x,y) * (y \ z) = y \ (x * z). [para(4505(a,1),169(a,1,1)),rewrite([7550(7)])]. 38365 (x * y) * T(y \ z,y) = (x / y) * (z * y). [para(7967(a,1),169(a,1,2)),rewrite([27047(8)])]. 38393 K(x,y) * (T(y,x * x) * z) = T(y,x) * z. [para(16623(a,1),169(a,1,1)),rewrite([6144(2),37125(3),6144(6),30953(6)]),flip(a)]. 38402 x * (y * (x * ((y * x) \ z))) = (y * x) * (T(y,x) \ z). [para(169(a,1),128(a,1)),rewrite([34823(3),6968(4)]),flip(a)]. 38445 (x * (y * (y * z))) * (z \ u) = z * ((z \ x) * (y * (y * u))). [back_rewrite(5200),rewrite([38314(9)]),flip(a)]. 38475 x * (y * ((x * y) \ z)) = L(z,y \ 1,x). [back_rewrite(24021),rewrite([38342(3)])]. 38476 R(x,y * z,y * ((z * y) \ (y \ u))) = R(x,y \ z,(z \ y) * u). [back_rewrite(21705),rewrite([38342(5)])]. 38485 R(x,x \ y,y \ z) = z / (y * ((x * y) \ z)). [back_rewrite(8328),rewrite([38342(6)])]. 38488 L(x,y,z \ (y \ 1)) = L(x,y,z \ 1). [back_rewrite(6070),rewrite([38342(4),36021(4)])]. 38503 L((x \ y) * z,y \ x,x) = x \ (y * z). [back_rewrite(21472),rewrite([38356(7)])]. 38534 R(x,y * (y * z),z \ u) = R(x,z,((z \ y) * y) * u). [back_rewrite(340),rewrite([38445(5),191(8),15452(3)]),flip(a)]. 38535 (x * y) * (T(x,y) \ z) = y * L(z,y \ 1,x). [back_rewrite(38402),rewrite([38475(4)]),flip(a)]. 38568 x * a(y,z,z \ (y \ x)) = L(x,y,z \ 1). [back_rewrite(9085),rewrite([38475(10),4407(7),16465(8)])]. 38590 x * ((y * x) \ (y * z)) = L(z,y,x \ 1). [back_rewrite(36021),rewrite([38488(8)])]. 38623 L(L(R(x,y,z),u,w),v5,x \ 1) = L(R(x,y,z),u,w). [back_rewrite(6793),rewrite([38488(6)])]. 38642 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(21715),rewrite([38534(9)]),flip(a)]. 38643 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,z,y)). [back_rewrite(21708),rewrite([38534(10)])]. 38644 R(x,y,((y \ z) * z) * ((z \ (z \ y)) * u)) = R(x,y,u). [back_rewrite(21704),rewrite([38534(7)])]. 38658 T(x,y) * (T(x \ y,y) * z) = y * L(z,y \ 1,x). [back_rewrite(15409),rewrite([38535(9)])]. 38713 R(x,K(x,y),z) = x. [para(16985(a,1),170(a,1,1,1)),rewrite([38223(6),18422(5)])]. 38747 K(T(x,y) * z,K(x,y) * z) = K(x,T(x,y) * z). [back_rewrite(35301),rewrite([38713(2)]),flip(a)]. 38752 K(x,T(x,y) * z) = K(x,K(x,y) * z). [back_rewrite(35287),rewrite([38713(2),38747(8)]),flip(a)]. 38770 (K(x,y) * z) * x = T(T(x,y) * z,x). [back_rewrite(35247),rewrite([38713(4),38713(7)])]. 38815 (T(x,y) * (z * x)) \ (x * (T(x,y) * z)) = K(x,K(x,y) * z). [back_rewrite(33181),rewrite([38752(10)])]. 39396 a(x / y,y * (y * z),u) = a(x * y,z,u). [para(33450(a,1),4636(a,1,1,2)),rewrite([23(2),90(2),16(5)]),flip(a)]. 39505 (x * y) \ (x \ 1) = y \ (x \ (x \ 1)). [para(1607(a,1),6591(a,1,1)),flip(a)]. 39506 (x * y) \ (y \ 1) = y \ (x \ (y \ 1)). [para(1667(a,1),6591(a,1,1)),flip(a)]. 39650 (x * (y \ (z \ (z \ 1)))) * u = (x / y) * (z \ (z \ u)). [back_rewrite(35675),rewrite([39505(4)])]. 39699 x / (y * (y * (z * x))) = z \ (y \ (y \ 1)). [back_rewrite(4420),rewrite([39505(8)])]. 39792 x / (y * (z * (y * x))) = y \ (z \ (y \ 1)). [back_rewrite(4421),rewrite([39506(8)])]. 40866 (((x \ y) * z) \ (y * z)) * R(x \ 1,y,z) = K(y * z,(x \ y) * z). [para(26628(a,1),16711(a,2)),rewrite([31(6),12809(6),4408(8)])]. 41620 T(x \ 1,y) * z = T(x,y) \ z. [para(104(a,1),11803(a,1,1)),rewrite([101(2),128(3),15(5),15(5),27556(7),15452(5),1091(3),4407(3),4505(4),1708(6),15(8),33664(9),547(8),33969(9)])]. 41919 x \ ((y \ z) * z) = ((y * x) \ z) * z. [para(2748(a,1),6591(a,1,1)),rewrite([4408(5),4408(3),45(2),14(3),22398(2),4408(9),4408(7),45(6),14(7),22398(6)])]. 42192 (x * (y * z)) \ (x * (u * ((u \ y) * z))) = L(a(y,u,u \ z),y * z,x). [para(192(a,1),74(a,1,1)),flip(a)]. 42198 a(x,x * y,(x * y) \ z) = a(x,y,y \ z). [para(1091(a,1),192(a,1,2,2,1)),rewrite([3143(5),169(4),192(5)]),flip(a)]. 42212 a(x,x * y,z) \ (y * z) = a(y,x,x \ z) * (y * z). [para(192(a,1),4505(a,1,1)),rewrite([24305(9)]),flip(a)]. 42284 L(a(x,x * y,z),x * ((x \ y) * z),u) * L(a(y,x,x \ z),y * z,u) = 1. [back_rewrite(24350),rewrite([42192(13)])]. 42295 T(x * ((x \ y) * z),a(x,x * y,z)) = a(y,x,x \ z) * (y * z). [back_rewrite(4031),rewrite([42212(10)])]. 42314 R(x * y,x,x \ T(z,y)) = (x * (z * y)) / T(z,y). [para(90(a,1),198(a,2,1,2))]. 42356 R(x * (y \ z),x,x \ y) = (x * T(z,y)) / y. [para(4505(a,1),198(a,2,1,2))]. 42387 R(x * (y * z),x,x \ y) = (x * (y * (z * y))) / y. [para(101(a,1),198(a,2,1,2))]. 42416 K(R(x * y,x,x \ z),z) = K(x * (y * z),z). [para(198(a,2),17822(a,1,1))]. 42429 T(x,R(y * z,y,y \ x)) = T(x,y * (z * x)). [para(198(a,2),26764(a,1,2))]. 42662 ((x * y) * R(z,x,y)) / ((z * x) * y) = K(x * y,R(z,x,y)). [para(20994(a,1),16566(a,2)),rewrite([10561(4)])]. 42829 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(16(a,1),7353(a,1,2,2)),rewrite([16(6)])]. 42834 T(R(x,y,z) \ x,x) * (R(x,y,z) * u) = L(x * u,x,R(x,y,z)). [para(7353(a,1),21(a,1,2)),rewrite([42829(5),15452(7),34823(3),4505(4)])]. 42930 a(x \ (y / x),x,z) = a(x,y,z). [para(15(a,1),7682(a,1,2)),rewrite([1091(2),1091(4),1014(5),3143(4),1091(5),24189(6)])]. 42940 a(x * (y \ z),z \ y,u) = a(y \ z,(z \ y) * x,u). [para(4505(a,1),7682(a,1,1,2)),rewrite([90(4),4408(7)])]. 42971 a(x \ y,(y \ x) * z,T(y,x)) = ((z * (x \ y)) * x) \ (z * T(y,x)). [back_rewrite(4335),rewrite([42940(5)])]. 43418 ((x * (y \ z)) * y) * a(y \ z,(z \ y) * x,T(z,y)) = x * T(z,y). [para(7969(a,1),54(a,1,1)),rewrite([7715(13)])]. 44128 a(x,y,y \ z) \ 1 = a(y,y * x,z). [para(18(a,1),4007(a,1,1,2)),rewrite([92(4),169(4),18(7),42295(7),3691(6),18(7)])]. 44649 L(L(x,y / x,z),z * (y / x),z * y) = (z * (y / x)) \ (z * y). [para(76(a,2),6368(a,1,1))]. 44671 L(L(L(x,y,z),u,w),v5 \ 1,v5 \ x) = L(L(x,y,z),u,w). [para(6416(a,1),97(a,2,1,1))]. 44709 L(L(L(L(x,y,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(L(x,u,w),y,z),v5,v6). [para(6416(a,1),229(a,1,1,1)),flip(a)]. 45267 (x * ((x \ y) * z)) / R(T(y,z),x,x \ z) = z. [para(200(a,1),165(a,1,1)),rewrite([31(6)])]. 45271 x * (a(x / (y * z),y,z) * u) = R(x,z \ (y \ 1),y) * u. [para(59(a,1),200(a,2,2,1)),rewrite([27732(6)]),flip(a)]. 45295 R(x,y,T(y \ z,y)) * T(z,y) = (x / y) * (z * y). [para(7967(a,1),200(a,1,1,3)),rewrite([27047(9)])]. 45359 (((x / (y * z)) * y) * z) \ (R(x,z \ (y \ 1),y) * u) = L(u,a(x / (y * z),y,z),x). [back_rewrite(6623),rewrite([45271(9)])]. 45676 (x * y) \ L(y \ z,y,x) = (y * (x * y)) \ z. [para(74(a,2),25093(a,2,2)),rewrite([25093(9),6073(5),1091(3),39506(4),35648(5),101(2)]),flip(a)]. 46495 (R(x / y,y,z) * (y * (z * y))) \ ((x * z) * y) = a(y * z,(y * z) * (x * z),y). [para(85(a,2),24428(a,1,1,1))]. 46497 (R(x \ 1,y,z) * (y * (z * y))) \ (((x \ y) * z) * y) = a(y * z,(y * z) * ((x \ y) * z),y). [para(6071(a,1),24428(a,1,1,1))]. 46810 a(x * y,x * (y * x),z) = a(y,y * x,z). [para(14(a,1),4021(a,1,2,1)),rewrite([1077(4),3143(4),169(3),4032(5),14(6)]),flip(a)]. 46815 a(x,y * (y * (x * (y * z))),u) = a(x,x * (y \ z),u). [para(37(a,1),4021(a,1,1)),rewrite([16103(4),16485(3),23718(9),1091(6),4407(6),23717(6),14(5),4498(7),101(7),128(8),2508(10)]),flip(a)]. 47034 L(L(L(R(x,y \ 1,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(R(x,y \ 1,z),v5,v6),u,w). [para(76(a,1),44709(a,1,1)),rewrite([24261(6),24016(16)])]. 47036 L(L(x,y,z),u \ 1,u \ L(x,w,v5)) = L(x,y,z). [para(16487(a,1),44709(a,1,1,1)),rewrite([16487(8)])]. 47734 L(x,y * z,y * (z * (y * y))) = x. [para(189(a,1),15035(a,1,3)),rewrite([4578(3)])]. 47883 L(K(x,T(y,z)),x,y) = K(x,T(y,z)). [para(17666(a,1),30(a,1,1)),rewrite([37429(2),37429(4)]),flip(a)]. 48247 T(x,R(x,y,z) \ 1) = x. [para(89(a,1),960(a,1,2,1)),rewrite([19074(4),2771(4,R)])]. 48405 T(x,y) \ (y \ z) = y \ (x \ z). [para(3143(a,1),38503(a,2,2)),rewrite([35645(4),4408(5),45(4),2975(4),5147(4)])]. 48721 L(x,y * K(z,u),K(u,z)) = L(x,K(z,u),K(u,z) * y). [para(18(a,1),8308(a,1,3,2)),rewrite([5005(6)]),flip(a)]. 48733 L(x,K(y,z),u * K(z,y)) = L(x,K(z,y),u). [para(4505(a,1),8308(a,1,3,2)),rewrite([90(5),6144(6),16229(8)])]. 48767 a(x * K(y,z),K(z,y),u) = a(K(y,z),K(z,y) * x,u). [para(4505(a,1),8311(a,1,1,2)),rewrite([90(4),6144(7)])]. 48772 a(K(x,y),K(y,x) * z,u) = a(K(x,y),K(x,y) * z,u). [para(101(a,1),8311(a,1,1,2)),rewrite([2508(8),48767(4)])]. 49860 L(x,T(y,z),y) = x. [para(18604(a,1),439(a,1,2,2,1)),rewrite([4247(3),23(2),4505(4),4505(6),480(8),4505(4),13(6),32749(5),21(6)])]. 50186 L(L(R(x,y \ 1,z),u,w),v5,v6) = L(L(L(x,y,z \ 1),u,w),v5,v6). [para(82(a,1),47034(a,2,1,1)),rewrite([1014(5),10229(4),10305(5),47034(10),1014(10),10229(9),3143(10),4155(9),10690(8),38590(9)])]. 50188 L(R(x,y \ 1,z),u \ 1,u \ L(x,w,v5)) = R(x,y \ 1,z). [para(16487(a,1),47034(a,1,1)),rewrite([16487(13)])]. 50190 L(R(x,y \ 1,z),u,w) = L(L(x,y,z \ 1),u,w). [para(18454(a,1),47034(a,1,3,2)),rewrite([18485(6),50186(8),44671(8),38623(11)]),flip(a)]. 50224 R(x,y \ 1,z) = L(x,y,z \ 1). [back_rewrite(50188),rewrite([50190(8),47036(8)]),flip(a)]. 50298 L(x,T(y,x),z \ 1) = L(x,y \ x,z). [back_rewrite(27706),rewrite([50224(4)])]. 50308 R(x,y,y \ z) = L(x,y,z \ 1). [back_rewrite(24043),rewrite([50224(4),4407(3),38488(4)]),flip(a)]. 50323 L(x,y / x,z \ 1) = L(x,y,z \ 1). [back_rewrite(10323),rewrite([50224(7)])]. 50345 ((x / y) * (z * y)) / T(z,y) = L(x,z \ 1,y). [back_rewrite(2802),rewrite([50224(9),4407(8),26903(9)])]. 50347 a(x,T(x,y),z) = 1. [hyper(25,a,49860,a)]. 50359 L(x,y * z,z * y) = x. [para(4209(a,1),49860(a,1,2))]. 50365 L(x,y,T(y,z)) = x. [para(7769(a,1),49860(a,1,2))]. 50404 K(x,y) * ((x * y) \ z) = (y * x) \ z. [back_rewrite(6238),rewrite([50359(5)]),flip(a)]. 50423 R(x,y * (z * (z * y)),(z * y) \ ((y * z) \ u)) = R(x,K(z,y),K(y,z) * u). [back_rewrite(21722),rewrite([50404(9)])]. 50785 L(L(x,y / x,z),z * y,z * (y / x)) = L(x,y / x,z). [para(6694(a,1),18608(a,1,2)),rewrite([72(11),18(8),4581(8)])]. 50886 x * (y \ (y \ 1)) = (x / y) / y. [para(18650(a,1),164(a,1,2)),rewrite([3143(4),29418(3),19074(4),30432(3),47(1),1014(8)])]. 51015 x / (T(y,z) * (T(y,u) * (T(y,z) \ x))) = T(y,u) \ 1. [back_rewrite(19499),rewrite([50886(9),10229(8),10215(7),3228(8),33992(8),37126(9),38393(8)])]. 51318 T(x,y) * (y * (x * y)) = x * (x * (y * y)). [para(20397(a,1),209(a,1,1)),rewrite([7775(3),547(5),36652(5),15452(5),45(2),100(3),20397(10),88(9)]),flip(a)]. 51385 T(x,y) * (y * (x * (y * z))) = x * (x * (y * (y * z))). [back_rewrite(7257),rewrite([51318(4),37(4),100(2)]),flip(a)]. 51470 R(x / (y * ((z * y) \ x)),z,u) = R(z,y,(z * y) \ x). [para(82(a,1),495(a,1,1))]. 51780 (x / (y * (z * x))) * y = L(z \ 1,x \ 1,y). [para(1014(a,1),10707(a,1,1)),rewrite([4155(3),45(2),10229(4)])]. 52573 L(x,y \ 1,z) = L(x,y,z \ 1). [para(14(a,1),24267(a,1,1,2)),rewrite([38568(4),48(5)]),flip(a)]. 52576 x * (a(y,z,z \ (y \ x)) * u) = L(x,y,z \ 1) * u. [para(24267(a,1),18(a,1,1)),rewrite([52573(3)]),flip(a)]. 52596 L(x,y,z \ 1) = L(x,y,z). [para(7679(a,1),24267(a,2)),rewrite([45(2),45(2),45(4),45(4),42198(7),52576(7),4407(3),26903(4),52573(3),17(5),45(5)])]. 52619 T(x,y) \ 1 = T(x \ 1,y). [para(6020(a,1),24267(a,2)),rewrite([52576(11),52596(6),33039(4),41620(4),3666(3)])]. 52627 L(x,y,T(y \ 1,z)) = x. [para(50347(a,1),24267(a,1,1,2,1)),rewrite([13(2),17(2),52573(4),52619(3)]),flip(a)]. 52635 (x / (y * (z * x))) * y = L(z \ 1,x,y). [back_rewrite(51780),rewrite([52573(9),52596(9)])]. 52653 ((x / y) * (z * y)) / T(z,y) = L(x,z,y). [back_rewrite(50345),rewrite([52573(8),52596(8)])]. 52724 T(x,y) * (T(x \ y,y) * z) = y * L(z,y,x). [back_rewrite(38658),rewrite([52573(8),52596(8)])]. 52760 (x * y) * (T(x,y) \ z) = y * L(z,y,x). [back_rewrite(38535),rewrite([52573(7),52596(7)])]. 52764 x * (y * ((x * y) \ z)) = L(z,y,x). [back_rewrite(38475),rewrite([52573(7),52596(7)])]. 52794 R(T(x,y),x \ z,u) = L(T(x,y),z,u). [back_rewrite(24749),rewrite([52573(7),52596(7)])]. 52843 R(x,x \ y,z) = L(x,y,z). [back_rewrite(24264),rewrite([52573(5),52596(5)])]. 52858 L(x,y,z) = L(x,z,y). [back_rewrite(16398),rewrite([52573(4),4407(3),26903(4),52573(3),52596(3)])]. 52942 L(x,y,z / x) = L(x,z,y). [back_rewrite(50323),rewrite([52596(4),52858(2),52596(5)])]. 52953 R(x,y,y \ z) = L(x,y,z). [back_rewrite(50308),rewrite([52596(5)])]. 52963 L(x,y,z \ x) = L(x,y,T(z,x)). [back_rewrite(50298),rewrite([52596(4),52858(2),52858(4)]),flip(a)]. 53065 x * ((y * x) \ (y * z)) = L(z,x,y). [back_rewrite(38590),rewrite([52596(7),52858(5)])]. 53163 L(x,y,y * z) = L(x,y,z). [back_rewrite(16470),rewrite([52596(4),52858(2)])]. 53170 (x \ y) * L(z,x,y) = x \ (y * z). [back_rewrite(6145),rewrite([52596(4),52858(2)])]. 53195 x / (T(y,z) * (T(y,u) * (T(y,z) \ x))) = T(y \ 1,u). [back_rewrite(51015),rewrite([52619(10)])]. 53431 ((x \ y) * z) \ (y * z) = T(T(x,y),z). [back_rewrite(8394),rewrite([52794(4),34275(3)]),flip(a)]. 53473 x / (y * ((z * y) \ x)) = L(z,y,x). [back_rewrite(38485),rewrite([52843(3),26903(2),52858(1)]),flip(a)]. 53483 L(x,y,z \ (x \ u)) = L(x,y,(u \ x) * z). [back_rewrite(33575),rewrite([52843(4),52858(3),52858(6)]),flip(a)]. 53484 L(x,y,z \ (u \ 1)) = L(x,y,u * z). [back_rewrite(33545),rewrite([52843(3),52858(2),52858(6)]),flip(a)]. 53550 L(x,y,z) \ 1 = R(x \ 1,y,z). [back_rewrite(10233),rewrite([52843(2)])]. 53564 (x * y) \ L(z,x,y) = y \ (x \ z). [back_rewrite(8393),rewrite([52843(3)])]. 53598 x * (y * ((x * y) \ z)) = L(z,x,y). [back_rewrite(52764),rewrite([52858(5)])]. 53600 (x * y) * (T(x,y) \ z) = y * L(z,x,y). [back_rewrite(52760),rewrite([52858(5)])]. 53617 T(x,y) * (T(x \ y,y) * z) = y * L(z,x,y). [back_rewrite(52724),rewrite([52858(6)])]. 53634 ((x / y) * (z * y)) / T(z,y) = L(x,y,z). [back_rewrite(52653),rewrite([52858(6)])]. 53804 L(L(x,y,z),z * y,z * (y / x)) = L(x,y,z). [back_rewrite(50785),rewrite([52858(2),52942(2),52858(7),52942(7)])]. 53894 L(x,K(y,z),u * K(z,y)) = L(x,u,K(z,y)). [back_rewrite(48733),rewrite([52858(6)])]. 53895 L(x,K(y,z),K(z,y) * u) = L(x,u,K(y,z)). [back_rewrite(48721),rewrite([52858(4),53894(4)]),flip(a)]. 54309 (x * (y * x)) \ z = x \ (y \ (x \ z)). [back_rewrite(45676),rewrite([52858(3),53564(4)]),flip(a)]. 54321 (((x / (y * z)) * y) * z) \ (R(x,z \ (y \ 1),y) * u) = L(u,x,a(x / (y * z),y,z)). [back_rewrite(45359),rewrite([52858(14)])]. 54371 (x * (y / z)) \ (x * y) = L(z,y,x). [back_rewrite(44649),rewrite([52858(2),52942(2),52858(5),53804(5)]),flip(a)]. 54493 L(a(x,x * y,z),u,x * ((x \ y) * z)) * L(a(y,x,x \ z),u,y * z) = 1. [back_rewrite(42284),rewrite([52858(6),52858(10)])]. 54757 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,y,z)). [back_rewrite(38643),rewrite([52858(12)])]. 54758 R(x,y * z,L(z \ u,y,z)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(38642),rewrite([52858(3)])]. 54785 L(L(x,y,T(z,u)),z,y * T(z,u)) = L(x,K(z,u),z * (y * z)). [back_rewrite(37146),rewrite([52858(2),52858(5)])]. 54855 L(x,y,T(z,y)) = L(x,y,z). [back_rewrite(34860),rewrite([52953(4),52942(3),52858(2),52858(4),52942(4)])]. 54918 L(x,y,T(z,y) * u) = L(x,y,z * (y * u)). [back_rewrite(33664),rewrite([52858(3)]),flip(a)]. 54976 L(x,T(y,z),y \ z) = L(x,y,z). [back_rewrite(30654),rewrite([52858(4),52942(4),54371(7),52858(4)])]. 55103 (x * (K(y,z) * u)) * (u \ K(z,y)) = L(x,K(y,z) * u,u \ K(z,y)). [back_rewrite(28379),rewrite([52858(6),52942(6),52858(5)]),flip(a)]. 55235 a((x * y) / z,x,L(x \ z,x,y)) = a(x,y * x,L(x \ z,x,y)). [back_rewrite(26973),rewrite([52858(4),52858(8)])]. 55237 a((x \ y) / z,x,L(x \ z,x,y)) = a(x \ y,x,L(x \ z,x,y)). [back_rewrite(26968),rewrite([52858(4),52858(8)])]. 55249 L(x,y,y \ z) = L(x,y,z). [back_rewrite(26903),rewrite([52858(3)])]. 55404 L(T(x,y),z,y \ x) = z * ((z \ (y \ x)) * y). [back_rewrite(23927),rewrite([52858(3)])]. 55494 T(x * (y / z),x * y) = L(z,y,x) \ (x * y). [back_rewrite(22386),rewrite([52858(2),52942(2)]),flip(a)]. 55548 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y))))) = x * x. [back_rewrite(21507),rewrite([52858(6)])]. 55568 x * (y \ ((y / x) * z)) = L(z,y,y / x). [back_rewrite(21447),rewrite([52858(6)])]. 55660 L(L(x,y,z),y,z) = x. [back_rewrite(18473),rewrite([52858(4),8684(4)])]. 55725 L(x,y \ z,(z \ y) * u) = L(x,u,y \ z). [back_rewrite(16517),rewrite([52858(4),52858(6)])]. 55731 (x * (y \ z)) * T(y,z) = x * L(z,x,T(y,z)). [back_rewrite(16508),rewrite([52858(6),52963(6)])]. 55771 T(x,L(y * z,x,y)) = T(x,(x * y) * z). [back_rewrite(16362),rewrite([52858(2)])]. 55776 x \ (y * ((y \ x) * z)) = L(z,x,y). [back_rewrite(16348),rewrite([52858(5)])]. 55819 L(x,y,z * (u * u)) = L(x,y,z). [back_rewrite(14874),rewrite([52858(3),2507(3),52858(1)]),flip(a)]. 55915 L(K(x,y) * z,u,K(y,x)) = (u * K(y,x)) \ (u * z). [back_rewrite(11597),rewrite([52858(4)])]. 55954 L(T(x * y,x * z),u,L(y \ z,x,y)) = (u * L(y \ z,x,y)) \ (u * (x * z)). [back_rewrite(11076),rewrite([52858(5),52858(6),52858(8)])]. 56000 ((x / (y * z)) * y) * z = L(x,y,z). [back_rewrite(10295),rewrite([52858(3),52942(3),52858(2),53163(2)]),flip(a)]. 56040 x * L(y,x,z) = L(x * y,x,z). [back_rewrite(8091),rewrite([54976(3),52858(1),52858(4)])]. 56084 L(x,y,x * z) = (y * (z \ (x \ 1))) \ (y / z). [back_rewrite(6676),rewrite([52858(4),53483(4),45(2)])]. 56136 (x * (y * (z * u))) \ (x * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),x,y * (z * u)). [back_rewrite(5337),rewrite([52858(13)])]. 56176 (x * (y * z)) \ (x * y) = R(z \ 1,x,y). [back_rewrite(4138),rewrite([52858(5),53550(7)])]. 56215 a(x,y,L(z,x,y)) = a(x,y,z) \ 1. [back_rewrite(1098),rewrite([52858(1),3204(3),2548(5),52858(4)]),flip(a)]. 56223 R(x,y * z,L(z \ u,y,z)) = L(x,y * z,y * u). [back_rewrite(648),rewrite([52858(3),52953(9)])]. 56231 (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),x,y * (z * u)). [back_rewrite(589),rewrite([52858(11)])]. 56240 (x * y) * L(z,x,y) = x * (y * z). [back_rewrite(72),rewrite([52858(2)])]. 56531 (x * ((x \ y) * z)) / L(T(y,z),x,z) = z. [back_rewrite(45267),rewrite([52953(6)])]. 56576 T(x,(x * y) * z) = T(x,y * (z * x)). [back_rewrite(42429),rewrite([52953(3),52858(2),55771(3)])]. 56588 K((x * y) * z,x) = K(y * (z * x),x). [back_rewrite(42416),rewrite([52953(3),16735(3)])]. 56609 (x * (y * (z * y))) / y = (x * y) * z. [back_rewrite(42387),rewrite([52953(4),16364(3)]),flip(a)]. 56632 L(x * (y \ z),x,y) = (x * T(z,y)) / y. [back_rewrite(42356),rewrite([52953(4)])]. 56659 L(x * y,x,T(z,y)) = (x * (z * y)) / T(z,y). [back_rewrite(42314),rewrite([52953(4)])]. 56731 R(x,y,(x * y) \ z) \ 1 = L(x \ 1,y,z). [back_rewrite(36066),rewrite([52953(9)])]. 56746 x / R(y,z,(y * z) \ u) = x * L(y \ 1,z,u). [back_rewrite(36043),rewrite([52953(8)])]. 56831 T(x,y * ((y \ z) * x)) = T(x,L(z,x,y)). [back_rewrite(29466),rewrite([52953(6),52858(5)])]. 56835 R(x,y \ (z \ 1),z) = L(x,z,y). [back_rewrite(27732),rewrite([56000(4),52953(3),6022(2)]),flip(a)]. 56903 R(x,y * z,z \ 1) = L(x,y,(u \ (u \ y)) * z). [back_rewrite(21721),rewrite([52953(8),52858(4)]),flip(a)]. 56973 ((x \ y) * (x * z)) / z = L(T(y,x),x,z). [back_rewrite(10810),rewrite([52953(3)]),flip(a)]. 57033 L(x * y,y,z) = (x * (y * z)) / z. [back_rewrite(4583),rewrite([52953(3)])]. 57044 L(x,y,x * z) = L(x,z,y). [back_rewrite(3213),rewrite([52953(4),52858(2),52953(4)])]. 57089 x \ (y * ((y \ z) * x)) = L(T(z,x),x,y). [back_rewrite(538),rewrite([52953(7),52858(6)])]. 57097 (x * ((x \ y) * z)) / z = L(y,x,z). [back_rewrite(191),rewrite([52953(6)])]. 57173 ((L(x,y,z) * (y * (z * y))) \ (y * ((z * y) * x))) * K(L(x,y,z),y * (z * y)) = 1. [back_rewrite(7701),rewrite([53163(2),53163(10)])]. 57197 T(T(x,y),z) * R(x \ 1,y,z) = K(y * z,(x \ y) * z). [back_rewrite(40866),rewrite([53431(4)])]. 57210 R(x,y,(x * y) \ z) = L(x,z,y). [back_rewrite(51470),rewrite([53473(4),52858(1),33(2),480(1)]),flip(a)]. 57428 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = R(y \ (z \ (y \ x)),y * (z * y),u). [back_rewrite(8002),rewrite([54309(11)])]. 57506 L(a(x,y,z),y,x * (y * z)) = a(y,x,y * z). [back_rewrite(33981),rewrite([54918(4)])]. 57568 T(L(x,y,z) * (u / x),x) = x \ (L(x,y,z) * u). [back_rewrite(28851),rewrite([55494(6),18461(2)]),flip(a)]. 57670 L(x,y,z * T(z,u)) = x. [back_rewrite(27119),rewrite([55819(7),52858(3)])]. 57764 L(x,y,a(y / (z * u),z,u)) = x. [back_rewrite(54321),rewrite([56000(4),56835(5),15(4)]),flip(a)]. 57831 x * a(x / (y * z),y,z) = L(x,y,z). [back_rewrite(582),rewrite([56000(8)])]. 57837 L(x * y,x,T(z,y)) = (x * (z \ y)) * T(z,y). [back_rewrite(55731),rewrite([56040(7)]),flip(a)]. 57867 a(x,y * x,L(z,x,y)) = a(x,y,x * z). [back_rewrite(23643),rewrite([56040(5),3204(7),189(6),56231(7),57506(4)]),flip(a)]. 57908 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * w)) = L(x,y * z,y * w). [back_rewrite(54758),rewrite([56223(4)]),flip(a)]. 57969 T(x,(x \ y) * z) = T(x,y * (z * x)). [back_rewrite(23736),rewrite([56576(6)])]. 57975 T(x \ y,((y \ x) * z) * y) = T(x \ y,z * (y * (x \ y))). [back_rewrite(15924),rewrite([56576(10)])]. 57979 T(x \ y,(z * (x \ y)) * T(x,y)) = T(x \ y,z * (y * (x \ y))). [back_rewrite(15622),rewrite([56576(11)])]. 58035 K((x \ y) * z,x) = K(y * (z * x),x). [back_rewrite(23819),rewrite([56588(6)])]. 58065 R(T(x,y),y \ x,(x \ y) * z) = L(T(x,y),y,z). [back_rewrite(22110),rewrite([56973(9)])]. 58091 (x * (y \ (z \ 1))) \ (x / y) = L(z,x,y). [back_rewrite(56084),rewrite([57044(2),52858(1)]),flip(a)]. 58133 x * L(y \ 1,z,u) = x / L(y,z,u). [back_rewrite(56746),rewrite([57210(3),52858(1)]),flip(a)]. 58139 R(x \ 1,y,z) = L(x \ 1,y,z). [back_rewrite(56731),rewrite([57210(3),52858(1),53550(3)])]. 58268 a((x * y) / z,x,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(55235),rewrite([57867(9),16(7)])]. 58275 L(x,y * z,y * (z * u)) = R(x,y * z,L(u,y,z)). [back_rewrite(54757),rewrite([57908(10)])]. 58306 ((x * (y \ z)) * T(y,z)) / T(y \ z,x * (z * (y \ z))) = ((z \ y) * x) * z. [back_rewrite(15940),rewrite([57975(9)])]. 58399 T(T(x,y),z) / L(x,y,z) = K(y * z,(x \ y) * z). [back_rewrite(57197),rewrite([58139(5),58133(6)])]. 58412 (x * (y * z)) \ (x * y) = L(z \ 1,x,y). [back_rewrite(56176),rewrite([58139(7)])]. 58434 L(x,y,z) \ 1 = L(x \ 1,y,z). [back_rewrite(53550),rewrite([58139(6)])]. 58458 (L(x \ 1,y,z) * (y * (z * y))) \ (((x \ y) * z) * y) = a(y * z,(y * z) * ((x \ y) * z),y). [back_rewrite(46497),rewrite([58139(3)])]. 58518 K(x * y,L(z \ 1,x,y)) = K(x * y,(z \ x) * y). [back_rewrite(26753),rewrite([58139(4)])]. 58601 R(x,y * z,L(y * y,y,z)) = x. [back_rewrite(47734),rewrite([58275(5)])]. 58647 R(T(x,(y * z) * a(x,y,z)),y * z,a(x,y,z)) = R(T(x,y * (z * x)),y * z,a(x,y,z)). [para(33249(a,1),2642(a,1,2)),rewrite([31(7),31(13),56576(10)])]. 62320 R(x,y,T(y \ z,y)) = L(x,y,z). [para(4505(a,1),516(a,1,2)),rewrite([38365(4),53634(5)]),flip(a)]. 62433 L(x,y,z) * T(z,y) = (x / y) * (z * y). [back_rewrite(45295),rewrite([62320(3)])]. 62444 (x * y) * T(T(z,u),y) = (x * y) * T(T(z,y),u). [para(517(a,1),104(a,1,2,2)),rewrite([522(5)])]. 63757 (x * (y \ L(y,z,y \ (x / y)))) * a(y,z * (y \ (x / y)),T(z,y \ (x / y)) \ y) = x. [para(11138(a,1),54(a,2)),rewrite([53600(8),38305(7)])]. 64162 L(x * x,x,y) = x * x. [para(1077(a,1),55954(a,1,3)),rewrite([14(3),4209(2),52596(4),52858(2),1607(5),1014(5),14(5),10229(5),23697(5),6351(5)])]. 64186 R(x,y * z,y * y) = x. [back_rewrite(58601),rewrite([64162(3)])]. 64241 K(T(x,y) \ z,K(T(x,y) \ ((x \ y) * z),T(x \ y,y))) = 1. [hyper(27,a,19049,a)]. 64397 T(x,(T(T(T(T(T(y,z),x \ 1),u),w),v5) / x) / T(T(T(T(T(y,w),u),x \ 1),z),v5)) = x. [para(4097(a,2),14495(a,1,2,1))]. 65408 x * (y * (T(y,x) * z)) = y * (x * (y * z)). [para(25410(a,1),262(a,1,1)),rewrite([33957(4),547(3),32749(4),45(6),128(7),25410(11),88(9)])]. 65748 L(x \ 1,y,z) * x = L(x,y,z) \ x. [para(996(a,1),518(a,1,2,1)),rewrite([58133(4),28505(2)]),flip(a)]. 65880 x * K(y,T(z,x)) = K(y,z) * x. [para(17666(a,1),518(a,2,1)),rewrite([37429(2),47883(3)])]. 65951 R(x,y,z) * x = x * R(x,y,z). [para(89(a,1),519(a,1,2,1)),flip(a)]. 67485 a(x \ (y \ (x \ 1)),x * (y * (x * z)),u) = a(T(y,x),T(y,x) * z,u). [para(106(a,1),15271(a,1,1,2,1,1)),rewrite([39792(4),128(7),35648(9),101(2),23718(7),34823(2),33957(5),6968(6),24002(5),4032(7),39792(8),106(12),128(11)]),flip(a)]. 68727 ((x * y) * T(z,y)) / T(y,x * (z * (y * y))) = (y \ x) * (z * y). [para(522(a,1),165(a,1,1)),rewrite([57969(7),4578(5)])]. 68754 x * ((y * x) \ (z * x)) = (y \ x) * T(z,x). [para(3143(a,1),522(a,2,1)),rewrite([35645(5)])]. 68763 ((x \ y) * (z * x)) * x = T((y * x) * T(z,x),x). [para(522(a,1),4209(a,1,1)),flip(a)]. 68786 K((x * y) * T(z,y),y) = K(x * (z * (y * y)),y). [para(522(a,1),16568(a,1,1)),rewrite([58035(8),4578(6)])]. 68796 x * (y * (x * T(z,y * x))) = x * L(z * (y * x),y,x). [para(128(a,1),522(a,2)),rewrite([34823(3),6968(6),53600(6)]),flip(a)]. 68958 (x * (y * (z * x))) \ L(x * (y * (z * x)),x,z) = a(x,z * x,T(y,z * x)). [back_rewrite(23655),rewrite([68796(8),52858(6),56040(7)])]. 68979 R(T(x,y * (z * x)),y * z,a(x,y,z)) = ((y * z) * a(x,y,z)) \ ((x * y) * z). [para(54(a,1),536(a,1,2)),rewrite([58647(13)]),flip(a)]. 69080 R(T(x,(y * z) * a(x,y,z)),y * z,a(x,y,z)) = ((y * z) * a(x,y,z)) \ ((x * y) * z). [back_rewrite(58647),rewrite([68979(13)])]. 70643 ((x * y) * z) / (x * (x * (y * z))) = L(x \ 1,y,z). [para(3691(a,1),342(a,1,1)),rewrite([58139(5),52858(5),2507(5),52858(3)]),flip(a)]. 70649 R(x * K(y,z),K(z,y),u) = (x * u) / (K(z,y) * u). [para(4993(a,1),342(a,1,1,2,2)),rewrite([14(3),5005(2),4993(6),14(5),8296(10)])]. 70674 R(x / (y * T(y,z)),y * T(y,z),u) = (x * u) / (y * (T(y,z) * u)). [para(16623(a,1),342(a,1,1,2,2)),rewrite([547(2),16623(7),547(5),38207(12),21062(10)])]. 70731 x * (L(x,y,z) \ x) = R(x,x * (x * y),z). [back_rewrite(1932),rewrite([70643(6),58133(4),28505(2)])]. 70983 (x * (y * (z * (y * x)))) \ (x * (y * (z * ((y * x) * (u * (x * y)))))) = x * (y * T(u,x * y)). [para(33415(a,1),2214(a,1,2,2,2,2))]. 72562 K(L(x,y,z),T(x,u)) = 1. [para(28464(a,1),16687(a,1,2)),rewrite([47(3)]),flip(a)]. 72844 a(T(x \ y,y),T(x,y),T(z,x * y)) = a(T(x,y),x * y,T(z,x * y)). [para(90(a,1),13311(a,1,3,2)),rewrite([4278(2),90(9),90(10)])]. 72886 a(x,(x \ y) * z,u) = a(x,(x * y) * z,u). [para(16(a,1),13466(a,1,2,2)),rewrite([169(6),136(7)])]. 72954 x \ (y * (z * x)) = T(y,x) * T(z,x). [para(14(a,1),13641(a,1,2,2)),rewrite([4505(3),14(6)]),flip(a)]. 73156 T(x,y) * T(x \ z,y) = L(T(z,y),y,x). [back_rewrite(57089),rewrite([72954(4)])]. 73876 ((x * (y * z)) * (y * ((z * y) \ u))) / (y * u) = R(x,y * z,y * ((z * y) \ u)). [para(16(a,1),346(a,1,2,2))]. 74086 (x * (y * (x \ y))) / (x * (y / x)) = y. [para(27447(a,1),17(a,1,1)),rewrite([5005(4),26340(4)]),flip(a)]. 74176 a(x * (y / x),y * (y * z),u) = a(T(y,x \ y),z,u). [para(27447(a,1),4636(a,2,1)),rewrite([74086(6),74086(7),74086(7),21063(3),28991(2),2508(5),74086(11),74086(11)]),flip(a)]. 74728 K((x * (y \ z)) * T(y,z),T(x * z,a(x,y \ z,T(y,z)))) = K(a(x,y \ z,T(y,z)),x * z). [para(4315(a,1),17822(a,1,1)),rewrite([17771(9)]),flip(a)]. 75476 a(x,y,K(x,z)) = 1. [para(18(a,1),33091(a,1,2))]. 75493 (x * y) * K(y,z) = x * T(y,z). [para(33091(a,1),33249(a,1,1,3)),rewrite([80(5),128(4),16716(2),15(4),75476(8),14(7)]),flip(a)]. 75570 R(x,y,K(y,z)) = x. [back_rewrite(22892),rewrite([75493(3),17(4)]),flip(a)]. 75628 R(x,y,K(z,y)) = x. [para(17781(a,1),75570(a,1,3))]. 75689 R(x,T(y,z),K(z,y)) = x. [para(17771(a,1),75628(a,1,3))]. 75750 (x * K(y,z)) / z = x / T(z,y). [back_rewrite(21095),rewrite([75689(5)]),flip(a)]. 75804 a(x,y,z \ (x \ z)) = 1. [para(3666(a,1),33119(a,1,1)),rewrite([24189(5)])]. 76377 T(x * (x * y),z \ 1) * (z / y) = z * (x * x). [para(10920(a,1),7616(a,1,1)),rewrite([10215(7),22250(11),10229(9),18(9)])]. 77305 a(x \ ((y \ ((x \ (z / x)) / y)) / x),x * (y * x),u) = a(x \ (y \ (x \ 1)),z,u). [para(106(a,1),15079(a,1,2)),rewrite([39792(4),39792(8),35648(10),101(2),54309(8),9490(6),9490(7),1014(7),39792(13)])]. 77469 ((x / y) * (z * u)) * a(y / x,z,u) = ((x / y) * z) * u. [para(15308(a,1),54(a,1,2)),rewrite([37(6),10287(7),10287(12)])]. 77479 a(x,x * (y \ (y \ (x \ z))),u) = a(x,y * (y * z),u). [para(3645(a,1),15308(a,1,2,1)),rewrite([10215(7),76377(7),3645(13),35648(11),4578(8),19474(9),35648(10),4578(4),19474(8),14882(9),16(7),16(6),3954(5),10215(12),76377(12),14882(8)])]. 77481 a(T(x,y),y * (y * z),u) = a(y \ (x \ (y \ 1)),z,u). [para(106(a,1),15308(a,1,2,1)),rewrite([39792(4),106(10),128(9),189(10),4578(6),189(9),100(6),189(8),101(6),128(7),67485(11),51385(6),22976(6),39792(8)])]. 78102 x * (((T(y,x) * (x * z)) / u) / T(x * (y * (x * (x * z))),u \ 1)) = x \ (u \ 1). [para(4640(a,1),15(a,1,2)),flip(a)]. 78147 a((x \ y) * y,z,u) = a(x,y * (y * z),u). [para(4640(a,1),4636(a,2,1)),rewrite([78102(13),18809(5),3143(3),90(3),24189(8)])]. 79623 L(x,y,R(z \ (y \ 1),y,x)) = L(x,y,T(z,x)). [para(3143(a,1),10670(a,2,3)),rewrite([6120(3),52963(7)])]. 79632 L(x,y,z * x) = L(x,y,z). [para(101(a,1),10670(a,2,3)),rewrite([20016(3),57044(3),52858(2),3200(2),57044(4),52858(3)]),flip(a)]. 79704 L(x,y,R(z,y,x)) = L(x,y,z). [back_rewrite(8681),rewrite([79632(3),16256(2)]),flip(a)]. 79714 L(x,y,T(z,x)) = L(x,y,z). [back_rewrite(79623),rewrite([79704(5),53484(4),53163(2)]),flip(a)]. 79784 L(x,y,z \ x) = L(x,y,z). [back_rewrite(52963),rewrite([79714(4)])]. 79922 (x * (y * z)) / T(y,z) = L(x * z,z,y). [para(90(a,1),57033(a,2,1,2)),rewrite([54855(3)]),flip(a)]. 79940 L(x * (y \ z),y,z) = (x * z) / T(y,z). [para(2690(a,1),57033(a,2,1,2)),rewrite([52858(5),54976(5)])]. 79946 (x * T(y,z)) / z = (x * y) / T(z,y). [para(4505(a,1),57033(a,2,1,2)),rewrite([52858(4),55249(4),79940(3)]),flip(a)]. 79974 R(x,y \ z,T(y,z)) = L(x,y,z). [para(4504(a,1),57033(a,2,1)),rewrite([7715(4),52858(3),79632(3),55249(2),52858(1),2708(6)]),flip(a)]. 79977 L(x * (y * z),y,z) = (x * y) * z. [para(101(a,1),57033(a,2,1,2)),rewrite([52858(4),53163(4),56609(7)])]. 79991 (x * y) / T(y,z) = x * K(z,y). [para(16875(a,1),57033(a,2,1,2)),rewrite([38196(5)]),flip(a)]. 80004 K(L(x * y,y,z),z) = K(x * (y * z),z). [para(57033(a,2),17822(a,1,1))]. 80058 R(x,y \ z,y) = L(x,y,z). [para(7969(a,1),57033(a,2,1)),rewrite([7715(4),52858(4),79632(4),54976(3),52858(1),7966(6)]),flip(a)]. 80171 L(x * y,x,T(z,y)) = L(x * y,y,z). [back_rewrite(56659),rewrite([79922(7)])]. 80225 (x * (y \ z)) * T(y,z) = L(x,y,z) * z. [back_rewrite(10537),rewrite([79974(3)]),flip(a)]. 80273 x * (y * (x * T(z,y * x))) = L(x * (z * (y * x)),x,y). [back_rewrite(68796),rewrite([52858(8),56040(9)])]. 80289 R(x,K(y,z),y) = x. [back_rewrite(20967),rewrite([79991(5),8298(4)]),flip(a)]. 80501 (x * (y \ z)) * y = (x / y) * (z * y). [back_rewrite(10562),rewrite([80058(2),62433(3)]),flip(a)]. 80509 L(x,y,z) * y = L(x * y,y,z). [back_rewrite(57837),rewrite([80171(3),80225(6),52858(3)]),flip(a)]. 80568 K(L(x,y,z) * z,T(x * z,a(x,y \ z,T(y,z)))) = K(a(x,y \ z,T(y,z)),x * z). [back_rewrite(74728),rewrite([80225(4)])]. 80615 (L(x,y,z) * z) / T(y \ z,x * (z * (y \ z))) = ((z \ y) * x) * z. [back_rewrite(58306),rewrite([80225(4)])]. 80627 T(x \ y,z * (y * (x \ y))) = T(x \ y,L(z,x,y) * y). [back_rewrite(57979),rewrite([80225(5)]),flip(a)]. 80744 T(T(((x \ y) * z) * y,x \ y),L(z,x,y) * y) = ((x \ y) * z) * y. [back_rewrite(15646),rewrite([80225(9)])]. 80745 T(((x \ y) * z) * y,x \ y) = (L(z,x,y) * y) * (x \ y). [back_rewrite(15645),rewrite([80225(4)]),flip(a)]. 80766 (x * y) * a(x,z \ y,T(z,y)) = L(x * y,y,z). [back_rewrite(4308),rewrite([80225(9),52858(6),80509(7)])]. 80776 (x * K(y,z)) * y = x * T(y,z). [back_rewrite(23173),rewrite([80289(2)]),flip(a)]. 81010 ((x / y) * (z * y)) * a(y \ z,(z \ y) * x,T(z,y)) = x * T(z,y). [back_rewrite(43418),rewrite([80501(3)])]. 81016 a(x \ y,(y \ x) * z,T(y,x)) = a(x,x * z,T(y,x)). [back_rewrite(42971),rewrite([80501(8),24477(11)])]. 81056 (x \ y) * ((z / x) * (y * x)) = ((x \ y) * z) * T(y,x). [back_rewrite(8020),rewrite([80501(4)])]. 81224 (x \ y) * (L(z,y,x) * x) = ((x \ y) * z) * x. [back_rewrite(80615),rewrite([80627(7),2711(7),4408(4)])]. 81235 (x \ y) * (L(z,x,y) * y) = ((x \ y) * z) * y. [back_rewrite(80744),rewrite([80745(5),4209(7)])]. 81262 a(x,y * (y * K(z,u)),z) = 1. [back_rewrite(24075),rewrite([80776(9),5410(9)]),flip(a)]. 81309 ((x / y) * (z * y)) * a(y,y * x,T(z,y)) = x * T(z,y). [back_rewrite(81010),rewrite([81016(8)])]. 81564 (T(x,y) * z) / a(T(y \ x,x),T(y,x),z) = T(y,x) \ ((y * x) * z). [para(15408(a,1),162(a,2)),rewrite([29216(4)])]. 81596 T(x,y) \ ((x * y) * (y * L(z,x,y))) = (T(x \ y,y) * z) * T(T(x * y,y),z). [para(15408(a,1),9018(a,2)),rewrite([73156(8),89(5),6018(5),7775(5),53617(14)]),flip(a)]. 81698 a(x \ y,(y \ x) * x,(x \ y) * z) = a(y,x,x \ z). [para(92(a,1),15411(a,1,1)),rewrite([10229(3),4230(3),4209(4),92(5),24057(8),24285(10)])]. 82112 a(x \ y,z * (y \ x),y) \ 1 = a(x \ y,z,T(x,y)). [para(18(a,1),15593(a,1,2)),rewrite([4155(6)]),flip(a)]. 82121 a(x,y / x,x * z) = a(x,y,z) \ 1. [para(1091(a,1),15593(a,1,1)),rewrite([1091(4),1014(5),4209(5),24189(5),1091(5),24189(6)])]. 82123 a(x,y / x,T(z,x \ z)) = a(x,y,z / x) \ 1. [para(1829(a,1),15593(a,1,1)),rewrite([1829(4),1014(5),28965(5),24189(6),1829(6),24189(8)])]. 82129 a(x,y,x \ z) \ 1 = a(x,y / x,z). [para(7769(a,1),15593(a,1,3)),rewrite([48405(3),46(1),48405(5),46(3),1014(5),24189(4),48405(5),46(3),24189(6)]),flip(a)]. 82165 ((x * y) * z) \ x = (x * z) \ (x / y). [para(15(a,1),15621(a,2,2,1)),rewrite([1091(2),3143(3),1091(4),23717(5),14(4),4209(5)])]. 82190 x * ((y * x) \ (z \ 1)) = (x * y) \ (x / z). [para(1829(a,1),15621(a,2,2,1)),rewrite([10229(2),18(2),10229(4),18(4),82165(3),2643(5),6120(7),4408(8),38342(8)]),flip(a)]. 82774 x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y)))) = x. [para(55548(a,1),15(a,1,2)),rewrite([15(2)]),flip(a)]. 82800 R(x / y,y,x) = x / y. [para(55548(a,1),85(a,2,1)),rewrite([82774(11),82774(13),14868(5),3691(4),1014(5)])]. 82841 x * (y \ (z \ (z \ 1))) = x / (z * (z * y)). [para(55548(a,1),342(a,2,1)),rewrite([82774(15),82800(6),82774(14),14868(8),39699(7)]),flip(a)]. 82892 (x / (y * (y * z))) * u = (x / z) * (y \ (y \ u)). [back_rewrite(39650),rewrite([82841(5)])]. 82924 a(x,y * (y * (x * z)),u) = a(x,x * z,u). [back_rewrite(24479),rewrite([82892(7),15(5),15(4),23697(3),4032(5)]),flip(a)]. 82939 a(x,x * (y \ z),u) = a(x,x * (y * z),u). [back_rewrite(46815),rewrite([82924(5)]),flip(a)]. 82951 a(x,y * (y * z),u) = a(x,z,u). [back_rewrite(77479),rewrite([82939(5),16(3),16(2)]),flip(a)]. 82978 a(x,K(y,z),y) = 1. [back_rewrite(81262),rewrite([82951(4)])]. 83003 a((x \ y) * y,z,u) = a(x,z,u). [back_rewrite(78147),rewrite([82951(6)])]. 83005 a(x \ (y \ (x \ 1)),z,u) = a(T(y,x),z,u). [back_rewrite(77481),rewrite([82951(4)]),flip(a)]. 83038 a(T(x,y \ x),z,u) = a(y * (x / y),z,u). [back_rewrite(74176),rewrite([82951(5)]),flip(a)]. 83180 a(x / y,z,u) = a(x * y,z,u). [back_rewrite(39396),rewrite([82951(4)])]. 83185 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,u,u \ x). [back_rewrite(35944),rewrite([82951(13)])]. 83213 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,x / u,u). [back_rewrite(24163),rewrite([82951(13)])]. 83221 a(x * ((y \ x) * x),z,u) = a(x * y,z,u). [back_rewrite(22429),rewrite([82951(8),83180(6)])]. 83245 a((x \ y) * (y * (x \ y)),z,u) = a(T(y,x),z,u). [back_rewrite(19195),rewrite([82951(6)]),flip(a)]. 83255 a(x \ (y / x),z,u) = a(y,z,u). [back_rewrite(19167),rewrite([82951(5)]),flip(a)]. 83266 a(x * (y * y),z,u) = a(x,z,u). [back_rewrite(14882),rewrite([82951(6)])]. 83285 a(x,y * (z * (z * y)),u) = 1. [back_rewrite(2486),rewrite([82951(6)])]. 83292 a(x,y * (z * y),u) = a(T(z,y),x,u). [back_rewrite(77305),rewrite([83255(9),83255(7),83255(5),83005(8)])]. 83423 ((x / y) * (z * u)) * a(y * x,z,u) = ((x / y) * z) * u. [back_rewrite(77469),rewrite([83180(5)])]. 83804 a((x * y) * z,x,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(58268),rewrite([83180(5)])]. 83819 x * a(x * (y * z),y,z) = L(x,y,z). [back_rewrite(57831),rewrite([83180(3)])]. 83854 L(x,y,a(y * (z * u),z,u)) = x. [back_rewrite(57764),rewrite([83180(3)])]. 83865 a((x \ y) * z,x,L(x \ z,x,y)) = a(x \ y,x,L(x \ z,x,y)). [back_rewrite(55237),rewrite([83180(5)])]. 84069 a(x,y,y \ z) = a(x,y,y * z). [back_rewrite(24279),rewrite([83180(4),83266(4)]),flip(a)]. 84082 a(x,y \ x,z) = a(x,y * x,z). [back_rewrite(19659),rewrite([83180(2),23494(2)]),flip(a)]. 84171 a(x,y,z) = a(y,x,z). [back_rewrite(42930),rewrite([83255(3)])]. 84200 (x * (y * (z * (z * y)))) * u = x * (z * (y * (y * (z * u)))). [back_rewrite(20510),rewrite([83285(9),14(7)]),flip(a)]. 84267 a(T(x,y),y * x,z) = a(x,x * y,z). [back_rewrite(46810),rewrite([83292(4)])]. 84365 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,u,u * x). [back_rewrite(83185),rewrite([84069(11)])]. 84378 a(x \ y,(y \ x) * x,(x \ y) * z) = a(x,y,x \ z). [back_rewrite(81698),rewrite([84171(8)])]. 84525 L(a(x,x * y,z),u,x * ((x \ y) * z)) * L(a(x,y,x \ z),u,y * z) = 1. [back_rewrite(54493),rewrite([84171(8)])]. 84641 a(x,y * x,z) = a(x,x * y,z). [back_rewrite(44128),rewrite([84069(2),7836(4),84171(2)])]. 84738 a(x,x * y,z) \ 1 = a(x,y,x \ z). [back_rewrite(24285),rewrite([84171(6)])]. 84799 a(x,y * x,z) \ 1 = a(y,x,x * z). [back_rewrite(4795),rewrite([84171(2)])]. 84975 a(x,(x * y) * z,L(x \ z,x,y)) = a(x,x * y,L(x \ z,x,y)). [back_rewrite(83865),rewrite([84171(5),72886(5),84171(9),3954(9)])]. 84982 L(x,y,a(z,y * (z * u),u)) = x. [back_rewrite(83854),rewrite([84171(3)])]. 85014 x * a(y,x * (y * z),z) = L(x,y,z). [back_rewrite(83819),rewrite([84171(3)])]. 85028 a(x,x * y,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(83804),rewrite([84171(5),84975(5)])]. 85167 ((x / y) * (z * u)) * a(z,y * x,u) = ((x / y) * z) * u. [back_rewrite(83423),rewrite([84171(5)])]. 85230 a(x,y * (z * y),u) = a(x,T(z,y),u). [back_rewrite(83292),rewrite([84171(5)])]. 85233 a(x,y,z * (z * u)) = a(x,y,u). [back_rewrite(83266),rewrite([84171(3),24596(3),84171(3)])]. 85235 a(x,y \ (z / y),u) = a(z,x,u). [back_rewrite(83255),rewrite([84171(3)])]. 85241 a(x,T(y,z \ y),u) = a(x,T(y,z),u). [back_rewrite(83245),rewrite([84171(5),85230(5),84171(5)])]. 85251 a(x,T(y \ z,z),u) = a(x,z * y,u). [back_rewrite(83221),rewrite([84171(4),85230(4),84171(5)])]. 85263 a(x,y / z,u) = a(x,y * z,u). [back_rewrite(83180),rewrite([84171(2),84171(4)])]. 85290 a(x,y * (z / y),u) = a(x,T(z,y),u). [back_rewrite(83038),rewrite([84171(3),85241(3),84171(5)]),flip(a)]. 85298 a(x,(y \ z) * z,u) = a(y,x,u). [back_rewrite(83003),rewrite([84171(3)])]. 85357 a(x \ y,z * (y \ x),y) \ 1 = a(z,x \ y,T(x,y)). [back_rewrite(82112),rewrite([84171(9)])]. 85392 (T(x,y) * z) / a(y,y * x,z) = T(y,x) \ ((y * x) * z). [back_rewrite(81564),rewrite([84171(6),85251(6),84267(5)])]. 85865 a(T(x,y),x * y,T(z,x * y)) = a(x,x * y,T(z,x * y)). [back_rewrite(72844),rewrite([84171(6),85251(6),84267(5)]),flip(a)]. 86937 T(x,y) \ ((x * y) * z) = (x \ y) * (x * z). [back_rewrite(29584),rewrite([84171(4),3954(4),85392(5)])]. 86984 ((x * y) \ z) * ((z \ x) * y) = a(x,z,y). [back_rewrite(24624),rewrite([84171(6)])]. 86989 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(y,z,T(x,y)). [back_rewrite(24566),rewrite([84171(8)])]. 86999 a(x,y \ 1,z) = a(y,x,z). [back_rewrite(24189),rewrite([84171(3)])]. 87019 a(x \ y,z * (x \ y),x) = a(z,x \ y,T(y,x)) \ 1. [back_rewrite(23629),rewrite([84171(7)])]. 87102 a(x \ y,z * (x \ y),T(x,y)) = a(z,x \ y,y) \ 1. [back_rewrite(15593),rewrite([84171(7)])]. 87185 a(x,T(y,x),z) = a(x,y,z). [back_rewrite(4582),rewrite([84171(3)])]. 87186 a(T(x,y),y \ x,z) = a(x,y * x,z). [back_rewrite(4537),rewrite([84171(5),84082(5)])]. 87206 R(x,y * (z * (z * y)),u) = x. [back_rewrite(20504),rewrite([84200(5),17(10)]),flip(a)]. 87367 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,x * u,u). [back_rewrite(83213),rewrite([85263(11)])]. 87375 a(x,y,x \ z) \ 1 = a(x,y * x,z). [back_rewrite(82129),rewrite([85263(6)])]. 87376 a(x,y * x,T(z,x \ z)) = a(x,y,z / x) \ 1. [back_rewrite(82123),rewrite([85263(4)])]. 87377 a(x,y * x,x * z) = a(x,y,z) \ 1. [back_rewrite(82121),rewrite([85263(3)])]. 87830 a(x,x * y,(y \ z) * u) = a(x,x * y,(y * z) * u). [back_rewrite(35865),rewrite([85263(4)]),flip(a)]. 87988 a(x,y * x,(y \ x) * z) = a(y,x,y \ z). [back_rewrite(84378),rewrite([85298(6),84082(4)])]. 88057 (T(x \ y,y) * z) * T(T(x * y,y),z) = (x \ y) * ((x * y) * z). [back_rewrite(81596),rewrite([86937(6),3204(4)]),flip(a)]. 88170 R(x,K(y,z),K(z,y) * u) = x. [back_rewrite(50423),rewrite([87206(8)]),flip(a)]. 88394 x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w)) = x \ w. [para(4714(a,1),15(a,1,2)),flip(a)]. 88400 R(x,y,((y \ z) * z) * u) = L(x,y,u). [para(4714(a,1),148(a,1,2,2,2)),rewrite([88394(16),38445(5),57097(8),2507(3),88394(16),38534(5)]),flip(a)]. 88449 L(x,y,(z \ (z \ y)) * u) = R(x,y,u). [back_rewrite(38644),rewrite([88400(7)])]. 88465 R(x,y * z,z \ 1) = R(x,y,z). [back_rewrite(56903),rewrite([88449(8)])]. 89358 a(x,K(y,z),z \ 1) = 1. [para(17913(a,1),82978(a,1,2))]. 90470 (x * y) \ (x * z) = x \ ((x / y) * z). [para(15(a,1),15943(a,1,2,1,1)),rewrite([1091(2),3143(5),1091(5),4209(8),35645(8)]),flip(a)]. 90726 x * (y * T(z,x * y)) = (z * x) * y. [back_rewrite(70983),rewrite([90470(12),39792(4),35648(11),101(2),90470(9),3691(2),3143(8),15(6),24002(5),55776(6),79977(3)]),flip(a)]. 90841 x \ ((x / (y * z)) * y) = L(z \ 1,x,y). [back_rewrite(58412),rewrite([90470(4)])]. 90887 x \ ((x / (y * (z * u))) * ((y * z) * u)) = L(a(y,z,u),x,y * (z * u)). [back_rewrite(56231),rewrite([90470(7)])]. 90904 x \ ((x / (y * (z * u))) * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),x,y * (z * u)). [back_rewrite(56136),rewrite([90470(8)])]. 90948 L(K(x,y) * z,u,K(y,x)) = u * ((u \ K(x,y)) * z). [back_rewrite(55915),rewrite([90470(8),5005(6),24002(8)])]. 91095 L(x,y,y / z) = L(x,z,y). [back_rewrite(53065),rewrite([90470(3),55568(4)])]. 91332 L(x * (y * (z * x)),x,z) = x * ((y * z) * x). [back_rewrite(80273),rewrite([90726(4)]),flip(a)]. 91469 (x * T(y,z)) / z = (x / z) * y. [back_rewrite(21500),rewrite([91095(4),56632(3)])]. 91534 ((x * (y * z)) \ z) * T(x * y,z) = a(z,y * z,T(x,y * z)). [back_rewrite(68958),rewrite([91332(7),90470(7),72954(7),2643(4)])]. 91628 (x * y) / T(z,y) = (x / z) * y. [back_rewrite(79946),rewrite([91469(3)]),flip(a)]. 92765 (x * (y * z)) * (y * ((z * y) \ u)) = (y * z) * (((y * z) \ x) * (y * u)). [para(16(a,1),418(a,1,2,2,2)),flip(a)]. 92871 R(x,y * z,y * ((z * y) \ u)) = L(x,y * z,y * u). [back_rewrite(73876),rewrite([92765(6),57097(8)]),flip(a)]. 92882 R(x,y \ z,(z \ y) * u) = L(x,u,y * z). [back_rewrite(38476),rewrite([92871(6),16(3),52858(2)]),flip(a)]. 92926 L(T(x,y),z,y * x) = L(T(x,y),y,z). [back_rewrite(58065),rewrite([92882(5)])]. 92946 K(a(x,x * y,z),x * (x * ((y * z) / (x * ((x * y) * z))))) = 1. [hyper(27,a,21676,a)]. 92952 T(T(a(x,x * y,z),u),x * (x * ((y * z) / (x * ((x * y) * z))))) = T(a(x,x * y,z),u). [para(21676(a,1),29(a,1,1)),flip(a)]. 92963 a(x,x * y,z) \ u = a(x,y,x \ z) * u. [para(21676(a,1),5226(a,1,1,1)),rewrite([21676(12),92952(17),30512(10),46(7),84738(4),21676(13)]),flip(a)]. 92967 ((a(x,y,x \ z) / u) * a(x,x * y,z)) * u = K(a(x,x * y,z),u). [para(21676(a,1),38815(a,1,1,1)),rewrite([21676(18),15452(13),1091(9),4407(5),92963(5),1014(5),92946(19),13(11)])]. 93030 (T(x,K(y,z)) * K(z,y)) * (x \ K(y,z)) = 1. [para(4993(a,1),27619(a,1,2,1,1)),rewrite([9037(4),45(10),5005(10),12830(10),4407(8),6144(7),14(7)])]. 93714 L(x,y * (z * u),(y * z) * u) = R(x,y * (z * u),a(y,z,u)). [para(597(a,1),57033(a,2,1)),rewrite([16(6),52858(6),79784(6),52858(5),592(13)])]. 94677 T(x,R(x,y,z)) = x. [para(48247(a,1),7769(a,1,1)),rewrite([4408(4),45(3),65951(2),1708(3)])]. 94843 T(R(x,y,z) \ x,x) = R(x,y,z) \ x. [para(94677(a,1),7967(a,1,2)),rewrite([4231(6,R)]),flip(a)]. 94910 ((x * R(y,z,u)) * y) / (y * R(y,z,u)) = R(x,R(y,z,u),y). [para(94677(a,1),516(a,1,1,2)),rewrite([94677(9)])]. 94948 (R(x,y,z) \ x) * (R(x,y,z) * u) = L(x * u,x,R(x,y,z)). [back_rewrite(42834),rewrite([94843(3)])]. 95623 T(x,K(y,z)) * K(z,y) = K(z,y) * x. [para(93030(a,1),17(a,1,1)),rewrite([4155(4),6144(3),13(4)]),flip(a)]. 95624 R(K(x,y) * z,z \ K(y,x),u) = K(x,y) * z. [para(93030(a,1),22(a,1,1,1)),rewrite([13(2),3691(4),4408(4),6144(2),14(4),95623(6)]),flip(a)]. 95626 R(x,K(y,z) * u,u \ K(z,y)) = L(x,K(y,z) * u,u \ K(z,y)). [para(93030(a,1),22(a,1,2)),rewrite([95623(4),55103(6),48(7),95623(9)]),flip(a)]. 95631 L(x,K(y,z) * u,u \ K(z,y)) = x. [para(93030(a,1),104(a,1,2,2)),rewrite([95623(4),95623(6),14(7),16(6),95623(4),55103(6)]),flip(a)]. 95652 x / (K(y,z) * u) = x * (u \ K(z,y)). [para(93030(a,1),85(a,2,2)),rewrite([95623(4),95623(7),95626(8),95631(8),48(8)])]. 95681 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(93030(a,1),166(a,1,2,1)),rewrite([95623(4),95624(5),13(4)])]. 95687 (x \ K(y,z)) * (K(z,y) * (x * (K(z,y) * (x * u)))) = (K(z,y) * x) * u. [para(93030(a,1),169(a,1,1)),rewrite([4408(4),6144(3),13(5),95623(11),4408(10),6144(7),189(10),101(9),24558(11)]),flip(a)]. 95798 R(x * K(y,z),K(z,y),u) = u * ((u \ x) * K(y,z)). [back_rewrite(70649),rewrite([95652(8),169(8)])]. 95979 ((x \ K(y,z)) * u) * K(z,T(y,u)) = x \ u. [back_rewrite(37402),rewrite([95681(3)])]. 98284 (x * (y * z)) * (a(x,y,z) * ((x * y) * z)) = (x * y) * (z * ((x * y) * z)). [para(601(a,1),209(a,1,2)),rewrite([84171(6),20692(6),45(9),54(13),189(12),101(11),84171(18),20692(18),88(14)])]. 98289 (x \ T(x \ 1,y * z)) * (((y * z) \ x) * (y * (z * x))) = a(y,z,x) \ 1. [para(601(a,1),1091(a,1,1)),rewrite([98284(7),23718(11),54309(5),6072(4,R)])]. 98840 (x * y) \ T(x,z) = y \ K(x,z). [para(52627(a,1),6591(a,1,1)),rewrite([52619(5),4408(4),45(2),14(2),16343(2),52619(8),4408(7),45(5),14(5)]),flip(a)]. 99352 L(x,y,z) * z = L(x * z,y,z). [para(2642(a,1),602(a,1,2,3)),rewrite([16(2),80766(5),52858(2),2642(6),80225(6)]),flip(a)]. 99651 x \ (y * (z * y)) = ((x \ y) * z) * y. [back_rewrite(81235),rewrite([99352(3),53170(4)])]. 99656 ((x \ y) * z) * x = T(y,x) * T(z,x). [back_rewrite(81224),rewrite([52858(2),80509(3),53170(4),72954(3)]),flip(a)]. 99742 K(a(x,y \ z,T(y,z)),x * z) = 1. [back_rewrite(80568),rewrite([99352(2),72562(8)]),flip(a)]. 100197 L(x \ y,x,y * z) = (((y * x) \ (y / z)) * z) * y. [back_rewrite(18690),rewrite([99651(8),82165(6)])]. 100284 T(x,y) * T(z * y,y) = T((x * y) * T(z,y),y). [back_rewrite(68763),rewrite([99656(4)])]. 100316 T((x * y) * z,x) = y * (z * x). [back_rewrite(23766),rewrite([99656(3),4525(4),90(2)]),flip(a)]. 101793 x * T(y \ 1,z) = x / T(y,z). [para(19049(a,1),16981(a,2,2)),rewrite([64241(15),52619(3),16(10)])]. 103664 x * (y \ (z \ 1)) = x / (z * y). [para(64186(a,1),85(a,1)),rewrite([189(7),4578(6),4613(8),39792(6),16(7)]),flip(a)]. 103756 x / (y * (z * x)) = (x * z) \ (x / y). [back_rewrite(82190),rewrite([103664(5)])]. 103820 R(x,y,z \ 1) = L(x,z,y). [back_rewrite(58091),rewrite([103664(4),10229(4),10279(4)])]. 103993 ((x * y) \ (x / z)) * z = L(y \ 1,x,z). [back_rewrite(52635),rewrite([103756(3)])]. 104117 R(x,y,z) = L(x,y,z). [back_rewrite(88465),rewrite([103820(4),16256(2),52858(1)]),flip(a)]. 104458 L(x \ y,x,y * z) = L(x \ y,y,z). [back_rewrite(100197),rewrite([103993(7),80509(7),3143(6)])]. 105327 L(x * K(y,z),u,K(z,y)) = u * ((u \ x) * K(y,z)). [back_rewrite(95798),rewrite([104117(4),52858(4)])]. 105371 (L(x,y,z) \ x) * (L(x,y,z) * u) = L(x * u,x,L(x,y,z)). [back_rewrite(94948),rewrite([104117(1),104117(3),104117(7)])]. 105379 L(x,y,L(y,z,u)) = x. [back_rewrite(94910),rewrite([104117(1),32180(3),104117(4),17(6),104117(1),104117(2),52858(2)]),flip(a)]. 105551 L(x,y * (z * u),(y * z) * u) = L(x,a(y,z,u),y * (z * u)). [back_rewrite(93714),rewrite([104117(9),52858(9)])]. 105587 L(x,y,z \ u) = L(x,y,z * u). [back_rewrite(92882),rewrite([104117(4),55725(4)])]. 105864 L(x,y,K(z,u)) = x. [back_rewrite(88170),rewrite([104117(4),53895(4)])]. 106927 x * (L(x,y,z) \ x) = L(x,y,z). [back_rewrite(70731),rewrite([104117(6),52858(6),57044(6),52858(5),57044(5)])]. 106960 (x * y) / (z * (T(z,u) * y)) = x / (z * T(z,u)). [back_rewrite(70674),rewrite([104117(6),52858(6),57670(6)]),flip(a)]. 107041 ((x * y) * a(z,x,y)) \ ((z * x) * y) = T(T(z,x * y),a(z,x,y)). [back_rewrite(69080),rewrite([104117(7),34275(7)]),flip(a)]. 107091 L(T(x,y * (z * x)),y * z,a(x,y,z)) = T(T(x,y * z),a(x,y,z)). [back_rewrite(68979),rewrite([104117(6),107041(12)])]. 107917 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = L(y \ (z \ (y \ x)),u,y * (z * y)). [back_rewrite(57428),rewrite([104117(14),52858(14)])]. 108469 (L(x / y,y,z) * (y * (z * y))) \ ((x * z) * y) = a(y * z,(y * z) * (x * z),y). [back_rewrite(46495),rewrite([104117(2)])]. 108634 (x * (y * z)) / ((z * x) * y) = K(x * y,L(z,x,y)). [back_rewrite(42662),rewrite([104117(2),56240(3),104117(7)])]. 109339 L(x,y,z) * (y * (z * y)) = (x * (y * z)) * y. [back_rewrite(18750),rewrite([104117(2),52858(2),53163(2)])]. 109537 (x * y) \ (z * y) = T(x \ z,y). [back_rewrite(10592),rewrite([104117(4),34275(4),92(2)]),flip(a)]. 109828 (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. [back_rewrite(105371),rewrite([105379(8)])]. 110184 (x * (y \ L(y,x,z))) * a(y,z * (y \ (x / y)),T(z,y \ (x / y)) \ y) = x. [back_rewrite(63757),rewrite([105587(3),57044(3),52858(2),52942(2)])]. 110241 x * ((x \ (y \ z)) * y) = L(T(z,y),y,x). [back_rewrite(55404),rewrite([105587(3),92926(3)]),flip(a)]. 110290 L(x,y,z / u) = L(x,y,u * z). [back_rewrite(53484),rewrite([105587(4),1014(3)])]. 110366 ((x \ y) * z) \ T(y,x) = L(z \ x,x,y). [back_rewrite(7982),rewrite([105587(3),104458(3)]),flip(a)]. 110378 x * ((x \ y) * K(z,u)) = y * K(z,u). [back_rewrite(105327),rewrite([105864(4)]),flip(a)]. 110402 x * ((x \ K(y,z)) * u) = K(y,z) * u. [back_rewrite(90948),rewrite([105864(4)]),flip(a)]. 110793 a(x * y,(x * y) * (z * y),x) = a(z,y,x). [back_rewrite(108469),rewrite([109339(5),23697(3),101(4),99656(3),4525(4),90(2),23718(5),86984(5),84171(1)]),flip(a)]. 110800 T(a(x,y,z),y) = a(z,x \ y,y). [back_rewrite(58458),rewrite([109339(6),3143(4),109537(7),4408(5),86984(5),84171(1),110793(8),84171(4)])]. 110804 (x \ (((y * (x * z)) \ x) * ((z * x) * y))) * K(L(y,x,z),x * (z * x)) = 1. [back_rewrite(57173),rewrite([109339(4),35803(7)])]. 110982 (x \ y) * T(z,y) = (x \ z) * y. [back_rewrite(68754),rewrite([109537(3),90(3)]),flip(a)]. 111960 a(x,x * K(y,z),K(z,y) * u) = 1. [back_rewrite(9444),rewrite([110402(6),8296(4),46(1)]),flip(a)]. 112152 a(x,y * x,T(z,y * x)) = L(x,z,y) \ x. [back_rewrite(91534),rewrite([110982(6),90470(4),90841(4),65748(4)]),flip(a)]. 112164 a(x,y,T(z,x)) = a(z,y,x). [back_rewrite(86989),rewrite([110982(5),86984(5)]),flip(a)]. 112420 ((x / y) * z) * y = x * T(z,y). [back_rewrite(81309),rewrite([112164(6),85167(6)])]. 112421 a(x \ y,(y \ x) * z,T(y,x)) = a(y,x * z,x). [back_rewrite(81016),rewrite([112164(8)])]. 112508 a(x,y,z * x) \ 1 = a(z,y * x,x). [back_rewrite(23663),rewrite([112164(3)]),flip(a)]. 112766 a(x,y,x \ z) * T(a(x,x * y,z),u) = K(a(x,x * y,z),u). [back_rewrite(92967),rewrite([112420(7)])]. 112951 (x * (y / z)) * z = z * ((z \ x) * y). [back_rewrite(10393),rewrite([112420(4),23697(4),110982(3)]),flip(a)]. 113434 a(x,y * z,z) = a(x,z,z * y). [back_rewrite(87367),rewrite([112951(8),41919(6),84365(9)]),flip(a)]. 113707 a(x,y,z * x) \ 1 = a(x,z,x * y). [back_rewrite(112508),rewrite([113434(6),84171(6)])]. 113933 (x * y) \ K(z,u) = y \ (x \ K(z,u)). [para(105864(a,1),6591(a,1,1)),rewrite([6144(3),14(3),6144(7),14(7)]),flip(a)]. 114859 (x * y) * T(T(z,y),u) = (x * T(z,u)) * y. [para(62444(a,1),136(a,2)),rewrite([110982(4),136(5)]),flip(a)]. 114936 (x * y) * T(z,y) = (x * z) * y. [para(64397(a,1),62444(a,1,2,1)),rewrite([114859(23),64397(20)])]. 115135 (x \ y) * ((x * y) * z) = y * (T(y,x) * z). [back_rewrite(88057),rewrite([114936(7),100284(5),114936(4),4505(2),547(2),4209(3),547(2),32749(3)]),flip(a)]. 115350 L(a(x,y,T(z,y)),u,x * (z * y)) = L(a(x,z,y),u,x * (z * y)). [back_rewrite(90904),rewrite([114936(6),90887(7)]),flip(a)]. 115440 K(x * (y * (z * z)),z) = K(x * y,z). [back_rewrite(68786),rewrite([114936(3),18043(3)]),flip(a)]. 115458 (x \ y) * (z * x) = T(y * z,x). [back_rewrite(68727),rewrite([114936(3),79991(7),115440(5),16716(4)]),flip(a)]. 115485 a(x,y,T(z,y)) = a(x,z,y). [back_rewrite(35536),rewrite([114936(7),105551(7),115350(6),6018(5)]),flip(a)]. 116274 L(x,y,z) \ x = a(x,z,y * x). [back_rewrite(112152),rewrite([115485(4),52858(3)]),flip(a)]. 116288 a(x,T(y,z),y * z) = a(y,x,y * z). [back_rewrite(85865),rewrite([115485(5),84171(3),115485(7)])]. 116749 a(x,y,z * x) * (L(x,z,y) * u) = x * u. [back_rewrite(109828),rewrite([116274(2)])]. 116751 x * a(x,y,z * x) = L(x,z,y). [back_rewrite(106927),rewrite([116274(2)])]. 116872 T(x,a(x,y,z * x)) = x. [back_rewrite(28511),rewrite([116274(2)])]. 118635 L(x,K(y,z),y * (u * y)) = x. [para(52858(a,1),54785(a,2)),rewrite([54785(5),105864(8)])]. 118636 L(x,y,z * T(y,u)) = L(x,z,T(y,u)). [para(54785(a,1),55660(a,1,1)),rewrite([118635(4)])]. 118653 L(x,K(y,z),T(y \ u,w)) = x. [para(625(a,1),54785(a,2,3,2)),rewrite([118636(9),55660(8),2507(6)]),flip(a)]. 118966 (x * T(x,y)) \ z = T(x,y) \ (x \ z). [para(16875(a,1),107917(a,1,1,1,2,2)),rewrite([547(2),33507(9),21062(7),106960(8),7616(6),6144(8),35223(8),16875(10),547(8),57670(9)])]. 118967 (x \ (x \ K(y,x))) * z = T(x,y) \ (x \ z). [para(16985(a,1),107917(a,1,1,1,2,2)),rewrite([33497(7),106960(8),7616(6),118966(3),6144(6),9490(7),12473(5),16985(9),57670(10)]),flip(a)]. 119011 (x \ T(x \ 1,y)) * z = T(x,y) \ (x \ z). [back_rewrite(17906),rewrite([118967(9)])]. 119022 T(x,y * z) \ (x \ (((y * z) \ x) * (y * (z * x)))) = a(y,z,x) \ 1. [back_rewrite(98289),rewrite([119011(11)])]. 119325 a(x,y,x \ K(z,x)) = 1. [para(23(a,1),75804(a,1,3,2)),rewrite([98840(3)])]. 121557 x \ (L(x,y,z) * (a(y,z,(y * z) \ x) * u)) = L(u,L(x,y,z),a(y,z,(y * z) \ x)). [para(16(a,1),588(a,1,1)),rewrite([53598(4),53598(14),52858(12)])]. 122955 x * (y \ K(z,y)) = x / T(y,z). [para(89358(a,1),209(a,1,1)),rewrite([1014(6),75750(4),45(4),1014(6),12473(4),89358(9),88(7)]),flip(a)]. 123069 T(x,y) \ (x \ z) = x \ (T(x,y) \ z). [para(634(a,1),50365(a,1)),rewrite([547(2),118966(3)])]. 123095 x \ (K(y,z) * u) = (x \ K(y,z)) * u. [para(634(a,1),105864(a,1)),rewrite([95681(3),6144(5)]),flip(a)]. 123146 a(x,y,z) \ 1 = z \ L(z,x,y). [back_rewrite(119022),rewrite([123069(9),26952(8),90470(4),23697(3),55776(4),6022(3)]),flip(a)]. 128856 x / (T(y,z) * ((y \ L(y,u,w)) * (T(y,z) \ x))) = a(y,w,u * y). [para(26839(a,1),19479(a,1,2,2,2,1,1)),rewrite([116274(10)])]. 129028 x / (T(y,z) * (a(y,u,w * y) * (T(y,z) \ x))) = y \ L(y,w,u). [para(26839(a,1),19536(a,1,2,1,1)),rewrite([116274(3)])]. 131120 T(x,a(x,y,z)) = x. [para(18(a,1),116872(a,1,2,3))]. 131121 a(x,y,z * x) \ L(x,y,z) = x. [para(116872(a,1),23(a,2)),rewrite([116751(5),52858(3)])]. 131133 T(x,a(y,z,x)) = x. [para(4505(a,1),116872(a,1,2,3)),rewrite([112164(2),84171(1)])]. 131212 T(a(x,y,z),x) = a(x,y,z). [hyper(26,a,131120,a)]. 131213 T(T(x,y),a(x,z,u)) = T(x,y). [para(131120(a,1),29(a,1,1)),flip(a)]. 131234 T(x,a(x,y,z) \ x) = x. [para(131120(a,1),7769(a,1,1))]. 131246 K(a(x,y,z),x) = 1. [para(131120(a,1),16687(a,1,2)),rewrite([47(1)]),flip(a)]. 131352 L(T(x,y * (z * x)),y * z,a(x,y,z)) = T(x,y * z). [back_rewrite(107091),rewrite([131213(10)])]. 133057 L(a(x,x * y,z),u,x * ((x \ y) * z)) = L(a(x,y * x,z),u,y * z). [para(84525(a,1),17(a,1,1)),rewrite([989(6),58434(6),87375(4)]),flip(a)]. 133073 a(x,y * x,z) * a(x,y,x \ z) = 1. [para(1607(a,1),84525(a,1,2)),rewrite([133057(7),1607(5)])]. 133580 x / a(y,z,x) = a(y,z,x) \ x. [para(131133(a,1),7616(a,1,1))]. 133716 K(a(x,y,z),y) = 1. [para(84171(a,1),131246(a,1,1))]. 133728 a(x,y \ z,z) = a(y,z,x). [hyper(28,a,133716,a),rewrite([110800(2)])]. 133748 a(x \ y,z * (x \ y),T(x,y)) = a(x,y,z) \ 1. [back_rewrite(87102),rewrite([133728(7)])]. 134004 (x * y) / T(x,z) = x * (y / T(x,z)). [para(119325(a,1),209(a,1,1)),rewrite([122955(5),45(5),122955(6),119325(9),88(8)])]. 134179 ((x \ y) * z) * L(z \ x,x,y) = T(y,x). [para(4505(a,1),1251(a,1,2,2)),rewrite([80501(4),81056(5),134004(9),2711(8),110366(6),4505(7)])]. 135160 T(x * (y / z),z) = (z \ x) * y. [para(4505(a,1),21316(a,1,1,2)),rewrite([90(4),10229(6),112420(7),15(7),110982(6)])]. 135282 x \ (L(x,y,z) * u) = (x \ L(x,y,z)) * u. [back_rewrite(57568),rewrite([135160(4)]),flip(a)]. 135292 (x \ L(x,y,z)) * (a(y,z,(y * z) \ x) * u) = L(u,L(x,y,z),a(y,z,(y * z) \ x)). [back_rewrite(121557),rewrite([135282(7)])]. 136169 a(x,y,x * z) \ 1 = a(x,y * x,z). [para(15(a,1),87019(a,1,1)),rewrite([15(2),15(4),4209(4),84171(4)]),flip(a)]. 136171 a(x \ y,z * (y \ x),T(y,x)) \ 1 = a(z,x \ y,x). [para(18(a,1),87019(a,1,2)),rewrite([84171(2),4155(4),84171(7)]),flip(a)]. 136177 a(x \ (y / x),z * (x \ (y / x)),x) = a(y,z,x \ y) \ 1. [para(92(a,1),87019(a,2,1,3)),rewrite([85235(10)])]. 136185 a(x \ 1,y * x,z * x) = a(y,z,x) \ 1. [para(1091(a,1),87019(a,1,1)),rewrite([1091(4),1014(5),85263(5),1091(7),1708(9),86999(9),112164(7),84171(6)])]. 136188 a(x \ 1,y * x,z) = a(x,y * x,z). [para(1829(a,1),87019(a,1,1)),rewrite([1829(4),1014(5),85263(4),1829(6),2643(8),86999(8),87375(8)])]. 136196 a(x,y * z,y) \ 1 = a(z,y \ x,y). [para(4505(a,1),87019(a,1,2)),rewrite([87185(4),84171(2),4408(4),84171(7),112421(7)]),flip(a)]. 136206 a(x * y,z * (x * y),y \ 1) = a(y,x \ z,x). [para(12372(a,1),87019(a,2,1,3)),rewrite([4408(4),45(2),90(2),4408(5),45(3),90(3),4408(10),45(8),90(8),136196(10)])]. 136217 a(T(x \ y,y),z * T(x \ y,y),T(x,y)) = a(z,y * x,T(y,x)) \ 1. [para(23380(a,1),87019(a,2,1,3)),rewrite([4278(2),4278(4),4278(9),85251(11)])]. 136223 a(x \ y,x * ((x \ z) * y),x) = a(z * x,x \ y,T(y,x)) \ 1. [para(169(a,1),87019(a,1,2))]. 136232 a(x,y,z * (x * x)) \ 1 = a(z,x,y) \ 1. [para(22354(a,1),87019(a,2,1,3)),rewrite([22283(6),15(3),15(2),89(1),22283(6),15(3),15(2),89(1),112164(4),113434(3),84171(3),87377(3),84171(1),22283(9),15(6),15(5),89(4),84171(6)]),flip(a)]. 136306 a(x,y * x,z * x) = a(y,z,x) \ 1. [back_rewrite(136185),rewrite([136188(5)])]. 138261 (T(T(x,y),z) * u) * y = T(T(x,z) * (y * u),y). [para(1466(a,1),4209(a,2)),rewrite([4525(4)]),flip(a)]. 138368 (T(x,y) * z) * y = T(x * (y * z),y). [para(64397(a,1),1466(a,1,1,1,1)),rewrite([138261(23),64397(20)])]. 139543 a(x,y,x \ z) = a(x,y,x * z). [para(133073(a,1),15(a,1,2)),rewrite([84799(4),84171(2)]),flip(a)]. 139565 T(a(x,y,x * z),a(x,y * x,z)) = a(x,y,x * z). [para(133073(a,1),12386(a,1,2,2)),rewrite([139543(2),48(6),139543(7)])]. 139577 a(a(x,y,x * z),a(x,y * x,z),u) \ u = a(x,y * x,z) * (a(x,y,x * z) * u). [para(133073(a,1),162(a,1,1,1)),rewrite([13(2),139543(4),84171(5),133580(6),139543(10)])]. 139595 T(a(x,y,x * z),(a(x,y * x,z) \ a(x,y,x * z)) * u) = T(a(x,y,x * z),u). [para(133073(a,1),6973(a,1,1,2)),rewrite([139543(2),4407(5),136169(4),139543(7),115458(10),16(8),139543(5),139543(9)]),flip(a)]. 139610 L(x,a(y,z,y * u),a(y,z * y,u)) = x. [para(133073(a,1),27459(a,1,3,2)),rewrite([139543(4),14(6),52858(5)])]. 139615 x / a(y,z,y * u) = x * a(y,z * y,u). [para(133073(a,1),57033(a,2,1,2)),rewrite([139543(7),52858(8),139610(8),14(5),139543(5)]),flip(a)]. 139762 a(x,y,x * z) * T(a(x,x * y,z),u) = K(a(x,x * y,z),u). [back_rewrite(112766),rewrite([139543(2)])]. 139811 a(x,y * x,(y \ x) * z) = a(x,y,y * z). [back_rewrite(87988),rewrite([84171(6),84069(6)])]. 141555 T(x,y) * ((z / (x * T(x,y))) * (x * (T(x,y) * u))) = x * ((K(x,y) * z) * u). [para(7416(a,1),15(a,1,2)),rewrite([24002(5),38208(3)]),flip(a)]. 141573 x * (((K(x,y) * z) * u) * x) = (T(x,y) * z) * (u * x). [para(7416(a,1),4209(a,1,1)),rewrite([100316(5),141555(13),101(9)]),flip(a)]. 146366 a(x,y,x * z) \ ((a(x,y * x,z) \ a(x,y,x * z)) * u) = a(x,y,x * z) * u. [para(139595(a,1),2711(a,1,2)),rewrite([91628(10),139615(8),4505(8),139565(5)]),flip(a)]. 147584 T(T(x,y),z) / L(x,u,w) = L(x,u,w) \ T(T(x,y),z). [para(26839(a,1),10402(a,1,1,1,1))]. 147739 L(x,y,z) \ T(T(x,y),z) = K(y * z,(x \ y) * z). [back_rewrite(58399),rewrite([147584(4)])]. 151591 x \ (a(x,y,z) \ x) = a(x,y,z) \ 1. [para(131234(a,1),2711(a,1,2)),rewrite([3666(3)]),flip(a)]. 151649 x / (T(y,z) * (a(y,u,w) * (T(y,z) \ x))) = a(y,u,w) \ 1. [para(131234(a,1),19536(a,1,2,1,1)),rewrite([4408(4),4505(4),131212(3),151591(10)])]. 151677 x \ L(x,y,z) = a(x,z,x * y). [back_rewrite(129028),rewrite([151649(8),113707(4),52858(3)]),flip(a)]. 151689 a(x,y,x * z) * (a(z,y,(z * y) \ x) * u) = L(u,L(x,z,y),a(z,y,(z * y) \ x)). [back_rewrite(135292),rewrite([151677(2)])]. 151698 a(x,y * x,z) = a(x,y,z * x). [back_rewrite(128856),rewrite([151677(3),151649(8),136169(4)])]. 151701 a(x,y,y * z) = a(z,x,y) \ 1. [back_rewrite(123146),rewrite([151677(5),84171(5)]),flip(a)]. 151723 (x * a(y,z,y * x)) * a(y,z * (y \ (x / y)),T(z,y \ (x / y)) \ y) = x. [back_rewrite(110184),rewrite([151677(2)])]. 151813 a(x,y,x * z) \ ((a(x,y,z * x) \ a(x,y,x * z)) * u) = a(x,y,x * z) * u. [back_rewrite(146366),rewrite([151698(4)])]. 151860 a(x,y,((y \ x) * z) * x) = a(x,y,y * z). [back_rewrite(139811),rewrite([151698(4)])]. 151925 a(a(x,y,x * z),a(x,y,z * x),u) \ u = a(x,y,z * x) * (a(x,y,x * z) * u). [back_rewrite(139577),rewrite([151698(4),151698(8)])]. 151954 a(x,y,z * (x * x)) = a(y,z,x) \ 1. [back_rewrite(136306),rewrite([151698(3),4578(2)])]. 152016 a(x,y * z,T(y,z)) \ 1 = a(x,y * z,y). [back_rewrite(136217),rewrite([151698(7),73156(6),89(3),6018(3),84171(3),85251(3)]),flip(a)]. 152025 a(x,y * z,T(y,z)) = a(z,y \ x,y). [back_rewrite(136206),rewrite([151698(6),115458(5),13(3),84171(3)])]. 152039 a(x,y,z * x) = a(y,z,x \ y) \ 1. [back_rewrite(136177),rewrite([151698(6),16(5),84171(4),133728(4),85263(2),151698(2)])]. 152050 a(x,y,z \ x) = a(z,x,y) \ 1. [back_rewrite(133748),rewrite([151698(5),37224(4),28991(3),84171(4),115485(4),84171(2)])]. 152277 a(x,y,z / x) \ 1 = a(x,y,x * z). [back_rewrite(87376),rewrite([151698(4),33781(3),16985(2),90(2)]),flip(a)]. 152280 a(T(x,y),y \ x,z) = a(x,y,z * x). [back_rewrite(87186),rewrite([151698(5)])]. 152337 a(x,x * y,z) = a(x,y,z * x). [back_rewrite(84641),rewrite([151698(2)]),flip(a)]. 152342 a(x,y \ x,z) = a(x,y,z * x). [back_rewrite(84082),rewrite([151698(4)])]. 152407 a(x,y,z) \ 1 = a(z,y,x). [back_rewrite(136232),rewrite([151954(3),4408(5),45(3),14(3),84171(2)]),flip(a)]. 152415 a(x,y * z,y) = a(x,y,z * y). [back_rewrite(152016),rewrite([152025(3),152407(4),3954(2),152337(2),84171(2)]),flip(a)]. 152485 a(x,y * (x * z),z) = a(z,x,(y * z) * x). [back_rewrite(136223),rewrite([152415(5),99656(4),84171(5),3954(5),152337(5),138368(4),90(2),112164(4),84171(3),152407(9),152280(7),84171(6)])]. 152683 a(x,y,x * z) * T(a(x,y,z * x),u) = K(a(x,y,z * x),u). [back_rewrite(139762),rewrite([152337(4),152337(8)])]. 153027 a(x,K(y,z),(K(z,y) * u) * x) = 1. [back_rewrite(111960),rewrite([152337(5)])]. 153030 a(x,y,y * (z * y)) = a(y,z,x). [back_rewrite(110793),rewrite([152337(5),85233(5),113434(3),84171(3),151698(3),101(2),84171(3),84171(4)])]. 153147 a(x,y,((y \ z) * u) * x) = a(x,y,((y * z) * u) * x). [back_rewrite(87830),rewrite([152337(4),152337(8)])]. 153242 a(x,y,z) = a(x,z,y). [back_rewrite(85028),rewrite([152337(4),80509(3),4505(2),56215(3),112164(2),84171(1),152407(3)])]. 153314 a(x,y,x * (z \ u)) = a(x,y,x * (z * u)). [back_rewrite(82939),rewrite([153242(3),153242(6)])]. 153371 a(x,K(y,z),K(z,y) * u) = a(x,K(y,z),K(y,z) * u). [back_rewrite(48772),rewrite([153242(4),84171(4),153242(8),84171(8)])]. 153473 a(x,y,z / x) = a(x,y,x * z). [back_rewrite(152277),rewrite([152407(4),84171(2),153242(2),84171(2)])]. 153478 a(x,y,z \ x) = a(x,y,z). [back_rewrite(152050),rewrite([84171(3),153242(3),152407(5),84171(3),153242(3),84171(3)])]. 153484 a(x,y,z * x) = a(x,y,z). [back_rewrite(152039),rewrite([153478(4),153242(3),84171(3),152407(5),84171(3),153242(3),84171(3)])]. 153502 a(x,y,y * z) = a(x,y,z). [back_rewrite(151701),rewrite([84171(3),153242(3),152407(5),84171(3),153242(3),84171(3)])]. 153528 a(x,y,x * z) = a(z,x,y). [back_rewrite(136196),rewrite([153242(2),153502(2),152407(3),84171(1),153242(1),84171(1),153242(3),84171(3),139543(3)]),flip(a)]. 153530 a(x,y,(z / y) * (x * y)) = a(x,y,z). [back_rewrite(136171),rewrite([153242(5),84171(5),152280(5),80501(3),84171(4),152407(6),84171(4),153242(4),84171(4),153242(6),84171(6),139543(6),153528(6),84171(5)])]. 153607 a(x,T(y,z),y \ z) = a(y,z,x). [back_rewrite(85357),rewrite([153242(4),84171(4),152342(4),80501(3),84171(4),153530(4),152407(3),84171(1),153242(1),84171(1),153242(4)]),flip(a)]. 153757 a(x,y,z) * (a(x,y,z) * u) = u. [back_rewrite(151925),rewrite([153528(2),84171(1),153242(1),153484(3),1300(3),45(2),153484(2),153528(3),84171(2),153242(2)]),flip(a)]. 153764 a(x,y,z) \ u = a(x,y,z) * u. [back_rewrite(151813),rewrite([153528(2),84171(1),153242(1),153484(3),153528(4),84171(3),153242(3),46(4),13(3),153528(4),84171(3),153242(3)])]. 153769 a(x,y,z) * L(x,y,z) = x. [back_rewrite(131121),rewrite([153484(2),153764(3)])]. 153777 a(x,y,(y \ x) * z) = a(x,y,z). [back_rewrite(151860),rewrite([153484(4),153502(5)])]. 153815 a(x,y,z * y) = a(x,y,z). [back_rewrite(153030),rewrite([153502(3),153242(3),84171(3)])]. 153874 a(x,y,z * (x * y)) = a(x,z,y). [back_rewrite(152485),rewrite([153242(3),84171(6),153484(6),153815(5),153242(4)])]. 156427 K(a(x,y,z),x * z) = 1. [back_rewrite(99742),rewrite([153242(3),153607(3),153242(1),84171(1)])]. 157152 a(x,y,z * (u / z)) = a(x,y,T(u,z)). [back_rewrite(85290),rewrite([153242(3),153242(5)])]. 157169 a(x,y,z \ (u / z)) = a(x,u,y). [back_rewrite(85235),rewrite([153242(3),84171(4)])]. 157230 x * a(x,y,z) = L(x,y,z). [back_rewrite(85014),rewrite([153242(3),153874(3),84171(1)])]. 157238 L(x,y,a(y,z,u)) = x. [back_rewrite(84982),rewrite([153242(3),153874(3),84171(1)])]. 157850 a(c22,c26,a(c23,c24,c25)) != 1 # answer("aa2"). [back_rewrite(43),rewrite([153242(7)])]. 157958 L(x,y,z) * a(x,y,z) = x. [back_rewrite(151723),rewrite([153528(2),157230(2),153478(9),153242(8),116288(8),84171(5),153502(5),139543(4),153528(4),84171(3),153242(3),153473(3),153528(3)])]. 158059 a(x,y,(y \ z) * u) = a(x,y,(y * z) * u). [back_rewrite(153147),rewrite([153484(4),153484(7)])]. 158117 a(x,K(y,z),K(z,y) * u) = 1. [back_rewrite(153027),rewrite([153484(5)])]. 158223 a(x,y,z) * T(a(x,y,z),u) = K(a(x,y,z),u). [back_rewrite(152683),rewrite([153528(2),84171(1),153242(1),153484(3),153484(6)])]. 158546 a(x,y,z) * (L(x,y,z) * u) = x * u. [back_rewrite(116749),rewrite([153484(2),52858(2)])]. 158552 L(x,y,z) \ x = a(x,y,z). [back_rewrite(116274),rewrite([153484(4),153242(3)])]. 158590 a(x,y,K(z,u)) = 1. [back_rewrite(153371),rewrite([158117(4),153502(5),153242(3)]),flip(a)]. 158938 a(x,y,z \ u) = a(x,y,z * u). [back_rewrite(153314),rewrite([153528(3),84171(2),153242(2),153528(5),84171(4),153242(4)])]. 158992 a(x,y,z) * (a(y,z,(z * y) * x) * u) = L(u,L(x,y,z),a(y,z,(z * y) * x)). [back_rewrite(151689),rewrite([153528(2),84171(1),153242(1),84171(4),158938(4),52858(7),84171(10),158938(10)])]. 160232 a(x,y,(y * x) * z) = a(x,y,z). [back_rewrite(153777),rewrite([158059(3)])]. 160751 a(x,y,T(z,u)) = a(x,y,z). [back_rewrite(157169),rewrite([158938(3),157152(3),153242(3)])]. 161700 L(x,a(y,z,u),L(y,z,u)) = x. [back_rewrite(158992),rewrite([160232(4),153242(2),84171(2),153757(4),160232(4),153242(2),84171(2),52858(3)]),flip(a)]. 163437 (x * y) * K(z,u) = x * (y * K(z,u)). [para(158590(a,1),54(a,1,2)),rewrite([14(5)]),flip(a)]. 163614 (x \ K(y,z)) * (K(z,y) * u) = x \ u. [back_rewrite(95979),rewrite([163437(6),65880(5)])]. 163693 (K(x,y) * z) * u = K(x,y) * (z * u). [back_rewrite(95687),rewrite([163614(9),15(5)]),flip(a)]. 163798 (T(x,y) * z) * (u * x) = T(x,y) * ((z * u) * x). [back_rewrite(141573),rewrite([163693(3),38770(4),90(5),33180(4)]),flip(a)]. 165291 a(x,y,z) * (u * L(x,y,z)) = x * T(u,L(x,y,z)). [para(90(a,1),158546(a,1,2))]. 167247 a(x,y,z) * (((u * x) \ a(x,y,z)) * (x * T(u,L(x,y,z)))) = 1. [para(158546(a,1),110804(a,1,2,2)),rewrite([153769(4),157958(7),153764(7),161700(10),157230(9),163437(10),163437(9),163437(8),16716(7)])]. 168431 K(a(x,y,z),T(y,x)) = 1. [para(4505(a,1),156427(a,1,2)),rewrite([84171(2),153242(2),84171(2),158938(2),153528(2),84171(1)])]. 170607 T(x / (x * y),K(y,x)) * (y * z) = K(y,x) * z. [para(24764(a,1),15(a,1,2)),rewrite([38208(3)]),flip(a)]. 170861 a(x,y,z) * (L(T(x,u),y,z) * w) = x * (K(L(x,y,z),u) * w). [para(24764(a,1),158546(a,1,2)),rewrite([30(3),170607(14)])]. 173117 K(a(x,y,z),T(y,u)) = 1. [para(13425(a,1),168431(a,1,2)),rewrite([153242(5),84171(5),160751(5),160751(4),153242(3),84171(3),158938(3),14(2),153242(1),84171(1)])]. 177098 K(x,T(a(x,y,z),u)) = 1. [para(173117(a,1),4993(a,1,1)),rewrite([84171(3),37242(4),13(5)])]. 181313 T(x,T(a(x,y,z),u)) = x. [hyper(28,a,177098,a)]. 181315 T(T(a(x,y,z),u),x) = T(a(x,y,z),u). [para(177098(a,1),16623(a,1,2)),rewrite([14(5)])]. 183896 K(x * (y * z),z) = K(x * y,L(z,x,y)). [para(136(a,1),2925(a,1,2)),rewrite([101(4),99656(3),4525(4),90(2),108634(5),16568(7),58035(6)]),flip(a)]. 184265 L(x,y,z * (u * z)) = L(x,y,T(u,z)). [para(90(a,1),2507(a,1,3,2))]. 184282 L(x,y,z * (u * (z * w))) = L(x,y,u * w). [para(169(a,1),2507(a,1,3,2)),rewrite([23711(5),115135(4),65408(4),105587(6)])]. 184298 L(x,y,T(z,u)) = L(x,y,z). [para(18848(a,1),2507(a,2)),rewrite([2507(7),184282(5),8679(3),184265(4)]),flip(a)]. 186144 L(x,K(y,z),y * u) = x. [back_rewrite(118653),rewrite([184298(4),105587(3)])]. 187171 T(T(x,y),z) / (x * y) = y \ K(x,z). [para(2644(a,1),7616(a,1,1)),rewrite([98840(7)])]. 193371 T(x,L(x,y,z) * u) = T(x,u). [para(2645(a,1),55660(a,1,1)),rewrite([55660(3)]),flip(a)]. 193392 x * (K(L(x,y,z),u) * w) = T(x,u) * w. [para(2645(a,1),158546(a,1,2,1)),rewrite([193371(3),84171(2),153242(2),160751(2),153242(1),84171(1),170861(5),193371(7)])]. 194121 L(x,y,a(x,z,u)) = x. [para(181313(a,1),134179(a,2)),rewrite([52858(10),184298(10),157238(9),169(8),110241(8),181313(3),52858(3),184298(3)])]. 196290 L(x,K(y,z),u * w) = x. [para(11282(a,1),186144(a,1,3)),rewrite([105587(5),1014(4),110290(3)])]. 196788 L(T(x,y),z,a(x,u,w)) = T(x,y). [para(194121(a,1),30(a,1,1)),flip(a)]. 196821 (x * y) \ a(y,z,u) = y \ (x \ a(y,z,u)). [para(194121(a,1),6591(a,1,1)),rewrite([153764(3),14(3),153764(7),14(7)]),flip(a)]. 196855 T(x,y * (z * x)) = T(x,y * z). [back_rewrite(131352),rewrite([196788(6)])]. 196856 a(x,y,z) * ((x \ (u \ a(x,y,z))) * (x * T(u,L(x,y,z)))) = 1. [back_rewrite(167247),rewrite([196821(4)])]. 196936 T(x,L(y,x,z)) = T(x,y). [back_rewrite(56831),rewrite([196855(4),16(2)]),flip(a)]. 197293 K(L(x,y,z),y) = K(x,y). [para(196936(a,1),16687(a,1,2)),rewrite([16687(2)]),flip(a)]. 198001 K(L(x,y,z),z) = K(x,z). [para(52858(a,1),197293(a,1,1))]. 198088 K(x * (y * z),z) = K(x * y,z). [back_rewrite(80004),rewrite([198001(3)]),flip(a)]. 198118 K(x * y,L(z,x,y)) = K(x * y,z). [back_rewrite(183896),rewrite([198088(3)]),flip(a)]. 198251 K(x * y,(z \ x) * y) = K(z,x * y). [back_rewrite(58518),rewrite([198118(5),17781(4)]),flip(a)]. 198284 L(x,y,z) \ T(T(x,y),z) = K(x,y * z). [back_rewrite(147739),rewrite([198251(8)])]. 204095 (x * K(y,z)) * u = x * (K(y,z) * u). [para(6144(a,1),104(a,1,2,1)),rewrite([163693(6),8296(7)]),flip(a)]. 208399 T(T(x,K(y,z)),u) = T(x,K(y,z) * u). [para(8296(a,1),2705(a,2,1)),rewrite([95681(3),52858(7),196290(7),123095(6),113933(5),4408(4),6144(2),163437(4),8310(4),4505(4)])]. 208429 T(T(x,y),K(z,u)) = T(x,K(z,u) * y). [para(517(a,1),8296(a,1,2)),rewrite([8310(5),208399(6)])]. 228215 (T(x,y) * z) \ T(x,y * y) = z \ K(x,y). [para(30881(a,1),17(a,1,1)),rewrite([187171(4)]),flip(a)]. 228407 T(x,T(y,L(x,z,u))) = T(x,y). [para(131120(a,1),30881(a,2,1)),rewrite([228215(6),153764(3),157230(5),204095(5),165291(5),37429(3),16716(4)])]. 230608 T(x,K(L(x,y,z),u)) = x. [para(16813(a,1),55660(a,1)),rewrite([55660(2)]),flip(a)]. 231489 K(L(x,y,z),u) * x = x * K(L(x,y,z),u). [para(230608(a,1),90(a,1,2))]. 231501 K(x,L(y,z,u)) * y = y * K(x,L(y,z,u)). [para(230608(a,1),7616(a,1,1)),rewrite([5005(3),6144(6)]),flip(a)]. 231502 T(x,K(y,L(x,z,u))) = x. [para(230608(a,1),7769(a,1,1)),rewrite([6144(3),231501(3),1708(4)])]. 231568 x * K(L(x,y,z),u) = T(x,u). [para(230608(a,1),25524(a,1,2,2)),rewrite([231489(5),204095(6),193392(6),95681(10),113933(9),163693(11),163798(10),16(8),4505(7),37429(6),30(5),89(4),8310(7),208429(4),16985(3),228407(3)]),flip(a)]. 231594 K(L(x,y,z),u) * x = T(x,u). [back_rewrite(231489),rewrite([231568(6)])]. 231954 K(x,L(y,z,u)) / y = y \ K(x,L(y,z,u)). [para(231502(a,1),2711(a,1,2))]. 231983 x \ K(y,L(x,z,u)) = T(x \ 1,y). [para(231502(a,1),19536(a,1,2,1,1)),rewrite([6144(4),231594(4),53195(7)]),flip(a)]. 232004 K(x,L(y,z,u)) = K(x,y). [para(231502(a,1),56531(a,1,2,1)),rewrite([110378(5),105864(6),19074(4),231954(3),231983(3),101793(4),16687(2)]),flip(a)]. 235046 T(x,L(y,z,u)) = T(x,y). [para(232004(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 235228 K(a(x,y,z),u) = 1. [back_rewrite(196856),rewrite([235046(6),90(6),115458(6),4505(4),181315(4),158223(4)])]. 258700 T(a(x,y,z),u) = a(x,y,z). [hyper(28,a,235228,a)]. 301066 a(x,y,a(z,u,w)) = 1. [para(235228(a,1),198284(a,2)),rewrite([258700(4),258700(4),158552(4),84171(2),153242(2)])]. 301067 $F # answer("aa2"). [resolve(301066,a,157850,a)]. ============================== end of proof ========================== -------- Proof 6 -------- "aa1". ============================== PROOF ================================= % Proof 6 at 186.39 (+ 0.64) seconds: "aa1". % Length of proof is 2026. % Level of proof is 80. % Maximum clause weight is 35. % Given clauses 2809. 1 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 2 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 3 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 4 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 5 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 10 a(a(x,y,z),u,w) = 1 # label("aa1") # label(non_clause) # label(goal). [goal]. 13 1 * x = x. [assumption]. 14 x * 1 = x. [assumption]. 15 x \ (x * y) = y. [assumption]. 16 x * (x \ y) = y. [assumption]. 17 (x * y) / y = x. [assumption]. 18 (x / y) * y = x. [assumption]. 19 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 20 (x * y) \ (y * x) = K(y,x). [assumption]. 21 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 22 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 23 x \ (y * x) = T(y,x). [assumption]. 24 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(1)]. 25 L(x,y,z) != x | a(z,y,x) = 1. [clausify(2)]. 26 T(x,y) != x | T(y,x) = y. [clausify(3)]. 27 T(x,y) != x | K(x,y) = 1. [clausify(4)]. 28 K(x,y) != 1 | T(x,y) = x. [clausify(5)]. 29 T(T(x,y),z) = T(T(x,z),y). [assumption]. 30 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 31 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 32 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 33 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(32),flip(a)]. 34 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 35 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 36 ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang (M1)"). [assumption]. 37 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 42 a(a(c17,c18,c19),c20,c21) != 1 # label("aa1") # answer("aa1"). [deny(10)]. 45 1 \ x = x. [para(13(a,1),15(a,1,2))]. 46 x \ x = 1. [para(14(a,1),15(a,1,2))]. 47 x / x = 1. [para(13(a,1),17(a,1,1))]. 48 x / 1 = x. [para(14(a,1),17(a,1,1))]. 49 x / (y \ x) = y. [para(16(a,1),17(a,1,1))]. 50 (x / y) \ x = y. [para(18(a,1),15(a,1,2))]. 51 a(x,1,y) = 1. [para(13(a,1),19(a,1,1,2)),rewrite([14(3),46(3)]),flip(a)]. 52 a(1,x,y) = 1. [para(13(a,1),19(a,1,1)),rewrite([13(3),46(3)]),flip(a)]. 54 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(19(a,1),16(a,1,2))]. 55 (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y). [para(16(a,1),19(a,1,1,2))]. 56 (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z). [para(16(a,1),19(a,1,2,1))]. 57 (x * (y * ((x * y) \ z))) \ z = a(x,y,(x * y) \ z). [para(16(a,1),19(a,1,2))]. 58 (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z). [para(18(a,1),19(a,1,1,2))]. 59 x \ (((x / (y * z)) * y) * z) = a(x / (y * z),y,z). [para(18(a,1),19(a,1,1))]. 60 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(18(a,1),19(a,1,2,1))]. 63 (x * y) * K(y,x) = y * x. [para(20(a,1),16(a,1,2))]. 64 x \ ((y \ x) * y) = K(y \ x,y). [para(16(a,1),20(a,1,1))]. 65 ((x \ y) * x) \ y = K(x,x \ y). [para(16(a,1),20(a,1,2))]. 66 x \ (y * (x / y)) = K(y,x / y). [para(18(a,1),20(a,1,1))]. 67 (x * (y / x)) \ y = K(y / x,x). [para(18(a,1),20(a,1,2))]. 68 K(x * x,x) = a(x,x,x). [para(20(a,1),19(a,1))]. 70 L(x,1,y) = x. [para(13(a,1),21(a,1,2,2)),rewrite([14(2),15(2)]),flip(a)]. 72 (x * y) * L(z,y,x) = x * (y * z). [para(21(a,1),16(a,1,2))]. 73 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(16(a,1),21(a,1,1))]. 74 L(x \ y,x,z) = (z * x) \ (z * y). [para(16(a,1),21(a,1,2,2)),flip(a)]. 75 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(18(a,1),21(a,1,1))]. 76 L(x,y / x,z) = (z * (y / x)) \ (z * y). [para(18(a,1),21(a,1,2,2)),flip(a)]. 80 R(x,y,1) = x. [para(14(a,1),22(a,1,1)),rewrite([14(3),17(2)]),flip(a)]. 81 R(x,x \ y,z) = (y * z) / ((x \ y) * z). [para(16(a,1),22(a,1,1,1)),flip(a)]. 82 R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z)). [para(16(a,1),22(a,1,1)),flip(a)]. 83 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(16(a,1),22(a,1,2))]. 84 R(x,y,z) * (y * z) = (x * y) * z. [para(22(a,1),18(a,1,1))]. 85 R(x / y,y,z) = (x * z) / (y * z). [para(18(a,1),22(a,1,1,1)),flip(a)]. 86 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(18(a,1),22(a,1,2))]. 87 T(1,x) = 1. [para(13(a,1),23(a,1,2)),rewrite([46(1)]),flip(a)]. 88 T(x,1) = x. [para(14(a,1),23(a,1,2)),rewrite([45(2)]),flip(a)]. 89 T(x,x) = x. [para(23(a,1),15(a,1))]. 90 x * T(y,x) = y * x. [para(23(a,1),16(a,1,2))]. 91 T(x,x \ y) = (x \ y) \ y. [para(16(a,1),23(a,1,2)),flip(a)]. 92 T(x / y,y) = y \ x. [para(18(a,1),23(a,1,2)),flip(a)]. 94 T(T(T(x,y),z),u) = T(T(T(x,u),y),z). [para(29(a,1),29(a,1,1)),flip(a)]. 97 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,v5,v6),y,z),u,w). [para(34(a,1),34(a,1,1)),flip(a)]. 100 (x * x) * y = x * (x * y). [para(13(a,1),36(a,2,2)),rewrite([14(2)])]. 101 (x * y) * x = x * (y * x). [para(36(a,1),14(a,1)),rewrite([14(2)]),flip(a)]. 103 x * (y * (x * ((x * (y * x)) \ z))) = z. [para(36(a,1),16(a,1)),rewrite([101(2)])]. 104 x * ((x \ y) * (x * z)) = (y * x) * z. [para(16(a,1),36(a,1,1,1)),flip(a)]. 106 (x * (y * (x * z))) / z = x * (y * x). [para(36(a,1),17(a,1,1)),rewrite([101(6)])]. 107 (x / y) * (y * ((x / y) * z)) = (x * (x / y)) * z. [para(18(a,1),36(a,1,1,1)),flip(a)]. 110 (x * (y * (z * (y * u)))) \ ((x * (y * (z * y))) * u) = a(x,y * (z * y),u). [para(36(a,1),19(a,1,1,2)),rewrite([101(6),101(11)])]. 112 ((x * (y * x)) * (z * u)) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [para(36(a,1),19(a,1,2,1)),rewrite([101(2),101(11)])]. 113 ((x * y) * (x * z)) \ (x * (y * (x * z))) = a(x * y,x,z). [para(36(a,1),19(a,1,2))]. 114 (x * (y * (x * z))) \ (z * (x * (y * x))) = K(z,x * (y * x)). [para(36(a,1),20(a,1,1)),rewrite([101(5),101(9)])]. 117 (x * (y * (z * y))) \ (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(36(a,1),21(a,1,2,2)),rewrite([101(2),101(10)])]. 118 ((x * (y * x)) * z) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(36(a,1),21(a,1,2)),rewrite([101(2),101(10)])]. 121 ((x * (y * (z * y))) * u) / (y * (z * (y * u))) = R(x,y * (z * y),u). [para(36(a,1),22(a,1,2)),rewrite([101(2),101(10)])]. 122 x \ (y * (z * (y * x))) = T(y * (z * y),x). [para(36(a,1),23(a,1,2)),rewrite([101(6)])]. 125 ((x * (y * x)) * (z * (x * (y * x)))) * u = (x * (y * x)) * (z * (x * (y * (x * u)))). [para(36(a,1),36(a,2,2,2)),rewrite([101(2),101(5),101(6),101(9)])]. 126 (x * ((y * (z * y)) * x)) * u = x * (y * (z * (y * (x * u)))). [para(36(a,1),36(a,2,2)),rewrite([101(2),101(4)])]. 128 (x * (y * x)) * z = x * (y * (x * z)). [back_rewrite(36),rewrite([101(2)])]. 129 (x * (y * (x * (z * (x * (y * x)))))) * u = x * (y * (x * (z * (x * (y * (x * u)))))). [back_rewrite(125),rewrite([128(6),128(14)])]. 130 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [back_rewrite(126),rewrite([128(3)])]. 132 (x * (y * (x * z))) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [back_rewrite(118),rewrite([128(3)])]. 133 (x * (y * (x * (z * u)))) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [back_rewrite(112),rewrite([128(4)])]. 134 (x * (x * y)) \ (x * (x * (y * z))) = z. [para(37(a,1),15(a,1,2))]. 136 x * (x * ((x \ y) * z)) = (x * y) * z. [para(16(a,1),37(a,1,1,2)),flip(a)]. 139 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(37(a,1),19(a,1,1,2))]. 140 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(37(a,1),19(a,1,1)),rewrite([37(7),37(8)])]. 141 (x * ((x * y) * z)) \ (x * (x * (y * z))) = a(x,x * y,z). [para(37(a,1),19(a,1,2))]. 143 (x * (y * (y * z))) \ (y * (y * (z * x))) = K(y * (y * z),x). [para(37(a,1),20(a,1,2))]. 144 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(37(a,1),21(a,1,1)),rewrite([37(7)])]. 145 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(37(a,1),21(a,1,2,2))]. 146 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(37(a,1),22(a,1,1,1)),rewrite([37(4)])]. 148 ((x * (y * (y * z))) * u) / (y * (y * (z * u))) = R(x,y * (y * z),u). [para(37(a,1),22(a,1,2))]. 150 x * (x * ((y * (x * (x * (y * z)))) * u)) = x * (x * (y * (x * (x * (y * (z * u)))))). [para(37(a,1),37(a,1,1,2)),rewrite([37(6),37(7),37(13),37(14)])]. 159 T(T(x,y),x) = T(x,y). [para(89(a,1),29(a,1,1)),flip(a)]. 160 L(T(x,L(x,y,z)),y,z) = L(x,y,z). [para(89(a,1),30(a,1)),flip(a)]. 162 ((x * y) * z) / a(x,y,z) = x * (y * z). [para(19(a,1),49(a,1,2))]. 164 (x * (y * z)) / L(z,y,x) = x * y. [para(21(a,1),49(a,1,2))]. 165 (x * y) / T(x,y) = y. [para(23(a,1),49(a,1,2))]. 166 R(x,y,z) \ ((x * y) * z) = y * z. [para(22(a,1),50(a,1,1))]. 168 x \ ((y * x) * z) = (x \ y) * (x * z). [para(104(a,1),15(a,1,2))]. 169 (x * y) * (y \ z) = y * ((y \ x) * z). [para(16(a,1),104(a,1,2,2)),flip(a)]. 170 ((x * y) * z) / ((y \ x) * (y * z)) = y. [para(104(a,1),17(a,1,1))]. 171 (x / y) * (((x / y) \ z) * x) = (z * (x / y)) * y. [para(18(a,1),104(a,1,2,2))]. 173 a(x,x \ y,x * z) = ((y * x) * z) \ (y * (x * z)). [para(104(a,1),19(a,1,1)),rewrite([16(4)]),flip(a)]. 175 (x * (y * z)) * (a(x,y,z) * ((x * (y * z)) * u)) = (((x * y) * z) * (x * (y * z))) * u. [para(19(a,1),104(a,1,2,1))]. 176 ((x * y) * z) \ (((y \ x) * (y * z)) * y) = K((y \ x) * (y * z),y). [para(104(a,1),20(a,1,1))]. 177 (((x \ y) * (x * z)) * x) \ ((y * x) * z) = K(x,(x \ y) * (x * z)). [para(104(a,1),20(a,1,2))]. 178 (x * y) * (K(y,x) * ((x * y) * z)) = ((y * x) * (x * y)) * z. [para(20(a,1),104(a,1,2,1))]. 179 ((x * y) * z) \ (y * (((y \ x) * (y * z)) * u)) = L(u,(y \ x) * (y * z),y). [para(104(a,1),21(a,1,1))]. 180 L((x \ y) * (x * z),x,u) = (u * x) \ (u * ((y * x) * z)). [para(104(a,1),21(a,1,2,2)),flip(a)]. 181 L(x * y,x \ z,x) = z \ ((z * x) * y). [para(104(a,1),21(a,1,2)),rewrite([16(2)]),flip(a)]. 182 (x * y) * (L(z,y,x) * ((x * y) * u)) = ((x * (y * z)) * (x * y)) * u. [para(21(a,1),104(a,1,2,1))]. 183 (((x * y) * z) * u) / (((y \ x) * (y * z)) * u) = R(y,(y \ x) * (y * z),u). [para(104(a,1),22(a,1,1,1))]. 185 ((x \ y) * (x * z)) \ ((y * x) * z) = T(x,(x \ y) * (x * z)). [para(104(a,1),23(a,1,2))]. 186 x * (T(y,x) * (x * z)) = ((y * x) * x) * z. [para(23(a,1),104(a,1,2,1))]. 187 x * (x * (((x \ y) * (x * z)) * u)) = (x * ((y * x) * z)) * u. [para(104(a,1),37(a,1,1,2)),flip(a)]. 188 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * (y * u)))))) = (z * (x * (x * y))) * u. [para(104(a,1),37(a,1)),rewrite([37(10)]),flip(a)]. 189 (x * y) * (x * z) = x * ((y * x) * z). [para(104(a,1),37(a,2,2)),rewrite([16(2)])]. 190 (x * y) * ((y \ z) * (y * u)) = y * ((y \ x) * ((z * y) * u)). [para(104(a,1),104(a,1,2,2)),flip(a)]. 191 (x * ((x \ y) * z)) / z = R(y,x,x \ z). [back_rewrite(83),rewrite([169(3)])]. 192 (x * y) \ (z * ((z \ x) * y)) = a(x,z,z \ y). [back_rewrite(55),rewrite([169(4)])]. 193 (x * y) * (L(z,y,x) * ((x * y) * u)) = (x * (((y * z) * x) * y)) * u. [back_rewrite(182),rewrite([189(10)])]. 196 (x * ((y * x) * z)) \ (x * (y * (x * z))) = a(x * y,x,z). [back_rewrite(113),rewrite([189(3)])]. 197 R(x,y,y \ 1) = x. [para(14(a,1),191(a,1,1,2)),rewrite([16(2),48(2)]),flip(a)]. 198 R(x * y,x,x \ z) = (x * (y * z)) / z. [para(15(a,1),191(a,1,1,2,1)),flip(a)]. 199 R(x,y,y \ ((y \ x) \ z)) = (y * z) / ((y \ x) \ z). [para(16(a,1),191(a,1,1,2)),flip(a)]. 200 R(x,y,y \ z) * z = y * ((y \ x) * z). [para(191(a,1),18(a,1,1))]. 201 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) = ((x * (y * z)) * (a(x,y,z) * u)) / u. [para(19(a,1),191(a,1,1,2,1)),flip(a)]. 202 R(x * y,y * x,(y * x) \ z) = ((y * x) * (K(x,y) * z)) / z. [para(20(a,1),191(a,1,1,2,1)),flip(a)]. 203 R(x * (y * z),x * y,(x * y) \ u) = ((x * y) * (L(z,y,x) * u)) / u. [para(21(a,1),191(a,1,1,2,1)),flip(a)]. 204 R(x * y,y,y \ z) = (y * (T(x,y) * z)) / z. [para(23(a,1),191(a,1,1,2,1)),flip(a)]. 205 (x * (x * (y * (((x * (x * y)) \ z) * u)))) / u = R(z,x * (x * y),(x * (x * y)) \ u). [para(37(a,1),191(a,1,1))]. 206 R(x,x,x \ y) = x. [para(46(a,1),191(a,1,1,2,1)),rewrite([13(2),17(2)]),flip(a)]. 208 R(x,x / y,(x / y) \ z) = ((x / y) * (y * z)) / z. [para(50(a,1),191(a,1,1,2,1)),flip(a)]. 209 a(x,y,z) \ ((x * y) * z) = T(x * (y * z),a(x,y,z)). [para(19(a,1),91(a,1,2)),rewrite([19(9)]),flip(a)]. 218 x / T(y,y \ x) = y \ x. [para(91(a,2),49(a,1,2))]. 220 R(x,y \ z,T(y,y \ z)) = R(x,y \ z,(y \ z) \ z). [para(91(a,2),191(a,2,3)),rewrite([191(6)]),flip(a)]. 221 T(x \ y,T(x,x \ y)) = ((x \ y) \ y) \ y. [para(91(a,2),91(a,1,2))]. 228 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,u,w),y,z),v5,v6). [para(97(a,1),34(a,1))]. 229 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v5,v6),y,z),v7,v8),u,w). [para(97(a,2),34(a,1,1))]. 260 T(x * ((x \ y) * z),a(x,x \ y,z)) = a(x,x \ y,z) \ (y * z). [para(16(a,1),209(a,1,2,1)),flip(a)]. 262 a(x,y,y \ z) \ (y * ((y \ x) * z)) = T(x * z,a(x,y,y \ z)). [para(16(a,1),209(a,2,1,2)),rewrite([169(5)])]. 263 T((x / y) * (y * z),a(x / y,y,z)) = a(x / y,y,z) \ (x * z). [para(18(a,1),209(a,1,2,1)),flip(a)]. 265 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(209(a,1),49(a,1,2))]. 268 ((x * (y \ z)) * T(y,y \ z)) / z = R(x,y \ z,(y \ z) \ z). [para(220(a,1),22(a,2)),rewrite([90(9),16(7)])]. 311 (x * (y * (y * z))) \ ((x * (y * y)) * z) = a(x,y * y,z). [para(13(a,1),110(a,1,1,2,2)),rewrite([13(5),13(9)])]. 312 (x * (y * (z * (y * u)))) * a(x,y * (z * y),u) = (x * (y * (z * y))) * u. [para(110(a,1),16(a,1,2))]. 314 (x * ((y \ z) * (y * ((y \ z) * u)))) \ ((x * ((y \ z) * z)) * u) = a(x,(y \ z) * z,u). [para(16(a,1),110(a,1,2,1,2,2)),rewrite([16(14)])]. 326 ((x / y) * (z * x)) \ (y * ((x / y) * (z * (x / y)))) = K(y,(x / y) * (z * (x / y))). [para(18(a,1),114(a,1,1,2,2))]. 338 ((x * (y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(13(a,1),148(a,1,2,2,2)),rewrite([14(2),14(8)])]. 340 ((x * (y * (y * z))) * (z \ u)) / (y * (y * u)) = R(x,y * (y * z),z \ u). [para(16(a,1),148(a,1,2,2,2))]. 341 R(x,y * (y * z),u) * (y * (y * (z * u))) = (x * (y * (y * z))) * u. [para(148(a,1),18(a,1,1))]. 342 R(x / (y * (y * z)),y * (y * z),u) = (x * u) / (y * (y * (z * u))). [para(18(a,1),148(a,1,1,1)),flip(a)]. 345 (x * (x * ((x * y) * z))) / (x * (x * (y * z))) = R(x,x * (x * y),z). [para(37(a,1),148(a,1,1))]. 346 ((x * (y * z)) * (y * u)) / (y * ((z * y) * u)) = R(x,y * z,y * u). [para(104(a,1),148(a,1,2,2)),rewrite([16(2),16(10)])]. 350 ((x * y) * z) * K((y \ x) * (y * z),y) = ((y \ x) * (y * z)) * y. [para(176(a,1),16(a,1,2))]. 354 ((x * (y / z)) * z) \ ((((y / z) \ x) * y) * (y / z)) = K(((y / z) \ x) * y,y / z). [para(18(a,1),176(a,1,2,1,2)),rewrite([18(13)])]. 356 (x * (x * y)) \ (x * (y * x)) = K(x * y,x). [para(46(a,1),176(a,1,2,1,1)),rewrite([100(2),13(5),101(4),46(6),13(8)])]. 357 ((x * (x / y)) * z) \ ((y * ((x / y) * z)) * (x / y)) = K(y * ((x / y) * z),x / y). [para(50(a,1),176(a,1,2,1,1)),rewrite([50(11)])]. 393 x * (x * ((x * (y * (x * (x * x)))) * z)) = x * (x * (x * (y * (x * (x * (x * z)))))). [para(129(a,1),37(a,1)),flip(a)]. 398 x * (x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u))))))) = x * (x * u). [para(16(a,1),150(a,1,2,2)),flip(a)]. 405 x * ((y * x) * (x * ((x \ y) * (z * u)))) = x * (x * (((x \ y) * ((x * y) * z)) * u)). [para(104(a,1),150(a,2,2)),rewrite([136(5)]),flip(a)]. 407 x * (x * (((x * x) \ y) * (x * (x * z)))) = (y * (x * x)) * z. [para(13(a,1),188(a,1,2,2,2,2,2,2)),rewrite([14(3),13(7),14(9)])]. 411 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [para(16(a,1),188(a,1,2,2,2,2,2,2))]. 418 (x * y) * (((x * y) \ z) * (x * ((y * x) * u))) = (z * (x * y)) * (x * u). [para(104(a,1),188(a,1,2,2,2,2,2)),rewrite([16(3),136(10),16(10)])]. 426 (x * (y * (x * y))) * z = (x * y) * ((x * y) * z). [para(13(a,1),175(a,1,1,2)),rewrite([51(3),13(4),13(5),14(6),13(7),189(7),101(6)]),flip(a)]. 435 R(x * ((x \ y) * z),y * z,(y * z) \ u) = ((y * z) * (a(y,x,x \ z) * u)) / u. [para(16(a,1),201(a,1,2,2)),rewrite([169(3),16(6),16(9)])]. 437 R(((x / (y * z)) * y) * z,x,x \ u) = (x * (a(x / (y * z),y,z) * u)) / u. [para(18(a,1),201(a,1,2)),rewrite([18(8),18(10)])]. 439 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) \ ((x * (y * z)) * (a(x,y,z) * u)) = u. [para(201(a,2),50(a,1,1))]. 463 x * (x * (x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))))) = x * (x * z). [para(16(a,1),393(a,1,2,2)),flip(a)]. 478 R(x,1 / y,y) = x. [para(50(a,1),197(a,1,3))]. 480 R(x,x,y) = x. [para(15(a,1),206(a,1,3))]. 493 R(T(x,y),x,z) = T(x,y). [para(480(a,1),31(a,1,1)),flip(a)]. 495 R(R(x,y,z),x,u) = R(x,y,z). [para(480(a,1),35(a,1,1)),flip(a)]. 506 (x * (1 / y)) * y = x. [para(478(a,1),22(a,2)),rewrite([18(7),48(6)])]. 507 (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z)). [para(90(a,1),19(a,1,1,2))]. 508 (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z). [para(90(a,1),19(a,1,2,1))]. 510 (x * y) \ (T(x,y) * y) = K(T(x,y),y). [para(90(a,1),20(a,1,1))]. 511 (T(x,y) * y) \ (x * y) = K(y,T(x,y)). [para(90(a,1),20(a,1,2))]. 512 (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y). [para(90(a,1),21(a,1,1))]. 516 ((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,y)). [para(90(a,1),22(a,1,2))]. 517 x * T(T(y,x),z) = T(y,z) * x. [para(29(a,1),90(a,1,2))]. 518 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(30(a,1),90(a,1,2))]. 519 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(31(a,1),90(a,1,2))]. 520 x * (x * (T(y,x) * z)) = x * (y * (x * z)). [para(90(a,1),37(a,1,1,2)),rewrite([128(3)]),flip(a)]. 521 x * (x * (y * T(z,x * (x * y)))) = z * (x * (x * y)). [para(90(a,1),37(a,1)),flip(a)]. 522 x * ((x \ y) * (z * x)) = (y * x) * T(z,x). [para(90(a,1),104(a,1,2,2))]. 536 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(22(a,1),92(a,1,1)),rewrite([31(3)]),flip(a)]. 537 T(T(x / y,z),y) = T(y \ x,z). [para(92(a,1),29(a,1,1)),flip(a)]. 538 x \ (y * ((y \ z) * x)) = R(T(z,x),y,y \ x). [para(191(a,1),92(a,1,1)),rewrite([31(3)]),flip(a)]. 540 K(T(x,y),x) = 1. [hyper(27,a,159,a)]. 541 T(x,T(x,y)) = x. [hyper(26,a,159,a)]. 547 T(x,y) * x = x * T(x,y). [para(159(a,1),90(a,1,2)),flip(a)]. 554 K(x \ y,y / x) = 1. [para(92(a,1),540(a,1,1))]. 555 K(x,T(x,y)) = 1. [hyper(27,a,541,a)]. 560 T(x,(x \ y) \ y) = x. [para(91(a,1),541(a,1,2))]. 568 K(x / y,y \ x) = 1. [para(92(a,1),555(a,1,2))]. 582 x * a(x / (y * z),y,z) = ((x / (y * z)) * y) * z. [para(18(a,1),54(a,1,1))]. 588 ((x * y) * z) \ ((x * (y * z)) * (a(x,y,z) * u)) = L(u,a(x,y,z),x * (y * z)). [para(54(a,1),21(a,1,1))]. 589 (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),y * (z * u),x). [para(54(a,1),21(a,1,2,2))]. 592 ((x * (y * (z * u))) * a(y,z,u)) / ((y * z) * u) = R(x,y * (z * u),a(y,z,u)). [para(54(a,1),22(a,1,2))]. 597 (x * (y * z)) * (((x * (y * z)) \ u) * ((x * y) * z)) = (u * (x * (y * z))) * a(x,y,z). [para(54(a,1),104(a,1,2,2))]. 601 (((x * y) * z) * (x * (y * z))) * a(x,y,z) = (x * (y * z)) * (a(x,y,z) * ((x * y) * z)). [para(54(a,1),175(a,1,2,2)),flip(a)]. 602 (x * (y * z)) * a(x,z,T(y,z)) = (x * z) * T(y,z). [para(90(a,1),54(a,1,1,2))]. 614 (x * ((x \ y) * ((y \ z) * (y * u)))) \ ((z * y) * u) = a(x,x \ y,(y \ z) * (y * u)). [para(104(a,1),56(a,1,2))]. 625 T(x / y,z) * y = y * T(y \ x,z). [para(537(a,1),90(a,1,2)),flip(a)]. 632 L(x \ 1,x,y) = (y * x) \ y. [para(14(a,1),74(a,2,2))]. 634 L(x \ (y \ z),x,y) = (y * x) \ z. [para(16(a,1),74(a,2,2))]. 637 (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x). [para(20(a,1),74(a,1,1)),flip(a)]. 638 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(21(a,1),74(a,1,1)),flip(a)]. 639 L(T(x,y),y,x) = T(x,x * y). [para(74(a,2),23(a,1)),rewrite([23(2)])]. 648 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(y * z) \ (y * u)). [para(74(a,2),191(a,2,3)),rewrite([191(8)]),flip(a)]. 650 T(x * y,(x * y) \ (x * z)) = L(y \ z,y,x) \ (x * z). [para(74(a,2),91(a,2,1))]. 659 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(90(a,1),74(a,2,2))]. 662 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,(x * y) \ (x * z),u). [para(74(a,2),56(a,1,1,2,1))]. 666 L(K(x,y),y * x,y) = K(y * x,y). [back_rewrite(356),rewrite([637(5)])]. 667 L(L(x,y,z),z * y,z) = x. [back_rewrite(134),rewrite([638(6)])]. 669 x * (T(y,x) * x) = (y * x) * x. [para(14(a,1),186(a,1,2,2)),rewrite([14(7)])]. 673 (((x * y) * y) * z) \ ((x * y) * (y * z)) = a(y,T(x,y),y * z). [para(186(a,1),19(a,1,1)),rewrite([90(5)])]. 674 (x * ((T(y,x) * (x * z)) * u)) \ ((((y * x) * x) * z) * u) = a(x,T(y,x) * (x * z),u). [para(186(a,1),19(a,1,2,1))]. 675 ((T(x,y) * (y * z)) * y) \ (((x * y) * y) * z) = K(y,T(x,y) * (y * z)). [para(186(a,1),20(a,1,2))]. 682 x * (T(T(y,x),z) * (x * u)) = ((T(y,z) * x) * x) * u. [para(29(a,1),186(a,1,2,1))]. 684 x * (R(T(y,x),z,u) * (x * w)) = ((R(y,z,u) * x) * x) * w. [para(31(a,1),186(a,1,2,1))]. 690 a((x * y) * y,T(x,y),z) = a(y,T(x,y) * (x * y),z). [para(186(a,1),110(a,1,2,1)),rewrite([186(6),19(11),90(7)])]. 729 ((x * (y / z)) * z) / T(x * y,a(x,y / z,z)) = a(x,y / z,z). [para(18(a,1),265(a,1,2,1,2))]. 732 (x * (y * z)) / T((x * y) * z,a(y,y \ x,y * z)) = a(y,y \ x,y * z). [para(104(a,1),265(a,1,2,1)),rewrite([16(2)])]. 777 x * (x * T(y,x * x)) = y * (x * x). [para(13(a,1),521(a,1,2,2)),rewrite([14(2),14(6)])]. 778 x * (y * T(z,x * (x * y))) = x \ (z * (x * (x * y))). [para(521(a,1),15(a,1,2)),flip(a)]. 780 L(x * T(y,z * (z * x)),z,z) = (z * z) \ (y * (z * (z * x))). [para(521(a,1),21(a,1,2)),flip(a)]. 788 x * (y * (x * T(z,x * (y * x)))) = z * (x * (y * x)). [para(90(a,1),521(a,1,2,2,2,2,2)),rewrite([520(7),90(8)])]. 831 (x * ((x \ y) * y)) \ ((y * x) * ((x \ y) * z)) = L(z,(x \ y) * y,x). [para(104(a,1),117(a,1,1)),rewrite([169(3),104(9),16(11)])]. 843 (((x * y) * y) * z) / K(y,T(x,y) * (y * z)) = (T(x,y) * (y * z)) * y. [para(675(a,1),49(a,1,2))]. 863 (T(T(x,y),z) * (z * u)) * z = (T(T(x,z),y) * (z * u)) * z. [para(29(a,1),843(a,2,1,1)),rewrite([843(10)])]. 874 x * K((y \ z) * (y * ((z * y) \ x)),y) = ((y \ z) * (y * ((z * y) \ x))) * y. [para(16(a,1),350(a,1,1))]. 888 ((1 / x) * y) \ (x * ((1 / x) * (y * (1 / x)))) = K(x,(1 / x) * (y * (1 / x))). [para(14(a,1),326(a,1,1,2))]. 960 (R(x,y,z) * u) / R(T(x,u),y,z) = u. [para(31(a,1),165(a,1,2))]. 961 (x * (x * (y * z))) / T(x * (x * y),z) = z. [para(37(a,1),165(a,1,1))]. 965 (x * y) / T(y,T(x,y)) = T(x,y). [para(90(a,1),165(a,1,1))]. 969 (((x \ y) * (x * z)) * x) / T((y * x) * z,K((x \ y) * (x * z),x)) = K((x \ y) * (x * z),x). [para(350(a,1),165(a,1,1))]. 974 x * (1 / y) = x / y. [para(506(a,1),17(a,1,1)),flip(a)]. 975 x / (1 / y) = x * y. [para(18(a,1),506(a,1,1)),flip(a)]. 976 a(x,1 / y,y) = 1. [para(506(a,1),19(a,1,2)),rewrite([18(3),14(2),46(1)]),flip(a)]. 980 (x / y) / K(1 / y,T(x,1 / y)) = T(x,1 / y) / y. [para(506(a,1),843(a,1,1)),rewrite([974(3),18(9),14(8),18(14),14(13),974(14)])]. 982 K(x,1 / x) = 1. [para(506(a,1),357(a,1,1)),rewrite([18(4),14(3),974(4),47(2),46(3),18(4),14(3)]),flip(a)]. 985 ((1 / x) * y) \ (x * ((1 / x) * (y / x))) = K(x,(1 / x) * (y / x)). [back_rewrite(888),rewrite([974(8),974(14)])]. 986 T(x,1 / x) = x. [hyper(28,a,982,a)]. 989 1 / x = x \ 1. [hyper(26,a,986,a),rewrite([92(3)]),flip(a)]. 990 (x \ 1) \ 1 = x. [para(986(a,1),23(a,2)),rewrite([989(2),989(4),16(5)])]. 996 T(x \ 1,x) = x \ 1. [para(49(a,1),986(a,1,2))]. 997 (x \ 1) * x = 1. [para(986(a,1),90(a,1,2)),rewrite([989(2),989(5),16(6)])]. 1004 ((x \ 1) * y) \ (x * ((x \ 1) * (y / x))) = K(x,(x \ 1) * (y / x)). [back_rewrite(985),rewrite([989(2),989(5),989(11)])]. 1009 (x / y) / K(y \ 1,T(x,y \ 1)) = T(x,y \ 1) / y. [back_rewrite(980),rewrite([989(3),989(5),989(10)])]. 1012 a(x,y \ 1,y) = 1. [back_rewrite(976),rewrite([989(2)])]. 1013 x / (y \ 1) = x * y. [back_rewrite(975),rewrite([989(2)])]. 1014 x * (y \ 1) = x / y. [back_rewrite(974),rewrite([989(2)])]. 1022 L(x,x \ 1,y) = x. [para(990(a,1),74(a,1,1)),rewrite([1014(6),14(6),50(5)])]. 1025 (x \ 1) * (x * y) = L(y,x,x \ 1). [para(997(a,1),21(a,1,1)),rewrite([45(6)])]. 1026 L(x,y,(y * x) \ 1) = (((y * x) \ 1) * y) \ 1. [para(997(a,1),21(a,1,2)),flip(a)]. 1027 R(x \ 1,x,y) = y / (x * y). [para(997(a,1),22(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1039 R((x * (x * y)) \ 1,x * (x * y),z) = z / (x * (x * (y * z))). [para(997(a,1),148(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1051 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x \ (y \ 1),y). [para(997(a,1),56(a,1,2))]. 1072 a(x,y,y \ 1) = 1. [para(50(a,1),1012(a,1,2)),rewrite([989(2)])]. 1077 L(x \ 1,x,y) = x \ 1. [para(50(a,1),1022(a,1,2)),rewrite([989(2),989(5)])]. 1078 L(L(L(x,y,z),u,w),L(x,u,w) \ 1,v5) = L(L(x,u,w),y,z). [para(1022(a,1),97(a,1,1)),flip(a)]. 1080 L(L(L(x,y,z),u,w),x \ 1,v5) = L(L(x,y,z),u,w). [para(1022(a,1),97(a,2,1,1))]. 1091 (x * y) \ x = y \ 1. [back_rewrite(632),rewrite([1077(3)]),flip(a)]. 1097 (x * (y * K(y,x))) \ (y * x) = a(x,y,K(y,x)). [para(20(a,1),57(a,1,1,2,2)),rewrite([20(8)])]. 1098 (x * (y * L(z,y,x))) \ (x * (y * z)) = a(x,y,L(z,y,x)). [para(21(a,1),57(a,1,1,2,2)),rewrite([21(10)])]. 1105 (x * (y * L(y \ z,y,x))) \ (x * z) = a(x,y,(x * y) \ (x * z)). [para(74(a,2),57(a,1,1,2,2))]. 1141 L(x,y,(y * x) \ 1) \ 1 = ((y * x) \ 1) * y. [para(1026(a,2),49(a,1,2)),rewrite([989(6)])]. 1180 L(x,x \ y,x) = x. [para(14(a,1),181(a,1,1)),rewrite([14(5),15(4)])]. 1201 T(x,L(y * z,y \ x,y)) = T(x,x \ ((x * y) * z)). [para(181(a,2),91(a,1,2)),rewrite([91(10,R)])]. 1227 L(x * y,x \ (x \ 1),x) = (x \ 1) \ y. [para(997(a,1),181(a,2,2,1)),rewrite([13(9)])]. 1246 (x * (x * y)) / T(x * (x * (y / z)),z) = z. [para(18(a,1),961(a,1,1,2,2))]. 1251 (x * ((y * x) * z)) / T(x * y,x * z) = x * z. [para(104(a,1),961(a,1,1,2)),rewrite([16(5)])]. 1252 (x * (x * (y * z))) / T(x * (x * z),T(y,z)) = T(y,z). [para(90(a,1),961(a,1,1,2,2))]. 1266 (((T(x,y) * z) * z) * u) / (T(T(x,z),y) * (z * u)) = z. [para(682(a,1),17(a,1,1))]. 1300 a(x,x,y) = 1. [para(13(a,1),690(a,1,1,1)),rewrite([87(3),51(3),87(3),13(4),13(3)]),flip(a)]. 1301 a(x * (y \ x),T(y,y \ x),z) = a(y \ x,T(y,y \ x) * x,z). [para(16(a,1),690(a,1,1,1)),rewrite([16(10)])]. 1316 K(x * x,x) = 1. [back_rewrite(68),rewrite([1300(3)])]. 1323 x \ (y * (x * x)) = x * T(y,x * x). [para(13(a,1),778(a,1,2)),rewrite([14(2),14(5)]),flip(a)]. 1324 x \ (x \ (y * (x * (x * z)))) = z * T(y,x * (x * z)). [para(778(a,1),15(a,1,2))]. 1346 (x \ (y * (x * z))) \ (z * T(y,x * z)) = a(x,x \ z,T(y,x * z)). [para(778(a,1),56(a,1,1)),rewrite([16(2),16(5),16(10)])]. 1353 x * (y / (x * (x * y))) = x \ 1. [para(997(a,1),778(a,2,2)),rewrite([996(7),1014(5)])]. 1359 x * (y * T(z,y * (x * y))) = y \ (z * (y * (x * y))). [para(788(a,1),15(a,1,2)),flip(a)]. 1448 R((x * (y * x)) \ 1,x * (y * x),z) = z / (x * (y * (x * z))). [para(997(a,1),121(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1452 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,x \ y). [para(268(a,1),18(a,1,1)),rewrite([200(5)])]. 1457 R(x,y \ z,(y \ z) \ z) \ ((x * (y \ z)) * T(y,y \ z)) = z. [para(268(a,1),50(a,1,1))]. 1466 (T(T(x,y),z) * u) * z = (T(T(x,z),y) * u) * z. [para(16(a,1),863(a,1,1,2)),rewrite([16(8)])]. 1479 x * (x * ((T(T(y,z),u) * (u * w)) * u)) = x * (x * ((T(T(y,u),z) * (u * w)) * u)). [para(863(a,1),37(a,2,2,2)),rewrite([37(7)])]. 1517 (x * (y * z)) / T((x * z) * T(y,z),a(z,z \ x,y * z)) = a(z,z \ x,y * z). [para(90(a,1),732(a,1,1,2)),rewrite([90(8),90(13)])]. 1524 L(x * ((y * (y * x)) \ z),y,y) = (y * y) \ z. [para(18(a,1),780(a,2,2)),rewrite([92(6)])]. 1534 L(x / (y * (y * x)),y,y) = (y * y) \ 1. [para(997(a,1),780(a,2,2)),rewrite([996(7),1014(5)])]. 1603 (x * (x * ((T(T(y,z),u) * (u * w)) * u))) / (x * (x * ((T(T(y,u),z) * (u * w)) * u))) = 1. [para(1479(a,1),265(a,1,2,1)),rewrite([100(7),1300(20),88(16),1300(21)])]. 1607 L(x,y,y) = x. [hyper(24,a,1300,a)]. 1609 x / (y * (y * x)) = (y * y) \ 1. [back_rewrite(1534),rewrite([1607(4)])]. 1619 x * ((y * (y * x)) \ z) = (y * y) \ z. [back_rewrite(1524),rewrite([1607(5)])]. 1649 x / (x * x) = x \ 1. [back_rewrite(1353),rewrite([1609(3),1014(4)])]. 1659 T(x * x,x) = x * x. [hyper(28,a,1316,a)]. 1667 L(x,y,x) = x. [para(15(a,1),1180(a,1,2))]. 1684 a(x,y,x) = 1. [hyper(25,a,1667,a)]. 1685 L(T(x,y),z,x) = T(x,y). [para(1667(a,1),30(a,1,1)),flip(a)]. 1689 L(L(L(x,y,z),u,w),v5,L(x,u,w)) = L(L(x,u,w),y,z). [para(1667(a,1),97(a,1,1)),flip(a)]. 1699 ((x \ y) * x) \ ((x \ y) * y) = x \ y. [para(1667(a,1),74(a,1)),flip(a)]. 1702 a((x \ y) * x,x \ y,z) = a(x \ y,y,z). [para(1667(a,1),662(a,1,1,2,1)),rewrite([189(5),16(3),19(7),1699(9)]),flip(a)]. 1708 T(x,x * y) = T(x,y). [back_rewrite(639),rewrite([1685(2)]),flip(a)]. 1723 K(x,(y * x) / y) = 1. [para(15(a,1),554(a,1,1))]. 1812 T(x * y,y \ 1) = (y \ 1) \ x. [para(1013(a,1),92(a,1,1))]. 1826 K(x * y,(y \ 1) \ x) = 1. [para(1013(a,1),568(a,1,1))]. 1829 x \ (x / y) = y \ 1. [para(1014(a,1),15(a,1,2))]. 1832 (x / y) \ ((y \ 1) * x) = K(y \ 1,x). [para(1014(a,1),20(a,1,1))]. 1833 ((x \ 1) * y) \ (y / x) = K(y,x \ 1). [para(1014(a,1),20(a,1,2))]. 1834 (x / y) \ (x * ((y \ 1) * z)) = L(z,y \ 1,x). [para(1014(a,1),21(a,1,1))]. 1836 ((x * y) / z) / (y / z) = R(x,y,z \ 1). [para(1014(a,1),22(a,1,1)),rewrite([1014(5)])]. 1837 (x \ 1) \ (y / x) = T(y,x \ 1). [para(1014(a,1),23(a,1,2))]. 1838 x * (x * ((y \ 1) * z)) = (x * (x / y)) * z. [para(1014(a,1),37(a,1,1,2)),flip(a)]. 1839 (x * (x * y)) / z = x * (x * (y / z)). [para(1014(a,1),37(a,1)),rewrite([1014(6)])]. 1840 x * ((x \ y) * (x / z)) = (y * x) / z. [para(1014(a,1),104(a,1,2,2)),rewrite([1014(8)])]. 1851 (x * (y * (x * (z * (x * (y * x)))))) / u = x * (y * (x * (z * (x * (y * (x / u)))))). [para(1014(a,1),129(a,1)),rewrite([1014(10)])]. 1859 x * (T(y,x) * (x / z)) = ((y * x) * x) / z. [para(1014(a,1),186(a,1,2,2)),rewrite([1014(9)])]. 1864 ((T(x,y) * (y / z)) * y) \ (((x * y) * y) / z) = K(y,T(x,y) * (y / z)). [para(1014(a,1),675(a,1,1,1,2)),rewrite([1014(9),1014(12)])]. 1870 x * (x * ((y * (((x * (x * y)) \ z) * u)) / u)) = R(z,x * (x * y),(x * (x * y)) \ u). [para(205(a,1),1014(a,2)),rewrite([1014(10),1839(8)])]. 1884 x * (x * ((y / z) / T(x * (x * y),z \ 1))) = z \ 1. [para(1014(a,1),961(a,1,1,2,2)),rewrite([1839(9)])]. 1885 x * (x * ((y * z) / T(x * (x * y),z))) = z. [para(961(a,1),1014(a,2)),rewrite([1014(9),1839(7)])]. 1888 x * ((y \ 1) * T(z,x * (x / y))) = x \ (z * (x * (x / y))). [para(1014(a,1),778(a,1,2,2,2,2)),rewrite([1014(10)])]. 1907 x * (x * (((T(T(y,z),u) * (u * w)) * u) / (x * (x * ((T(T(y,u),z) * (u * w)) * u))))) = 1. [back_rewrite(1603),rewrite([1839(15)])]. 1921 x * (x * ((y * z) / T(x * (x * z),T(y,z)))) = T(y,z). [back_rewrite(1252),rewrite([1839(8)])]. 1925 x * (x * (y / T(x * (x * (y / z)),z))) = z. [back_rewrite(1246),rewrite([1839(7)])]. 1932 x * (x * (((x * y) * z) / (x * (x * (y * z))))) = R(x,x * (x * y),z). [back_rewrite(345),rewrite([1839(8)])]. 1935 x * (x * R(y,z,u)) = R(x * (x * y),z,u). [back_rewrite(146),rewrite([1839(6),22(4)])]. 1952 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(x / (y * (y * z)),y * (y * z),u). [para(37(a,1),60(a,1,1,2))]. 1958 ((x / y) * (z * y)) \ (x * T(z,y)) = a(x / y,y,T(z,y)). [para(90(a,1),60(a,1,1,2))]. 1961 L(a(x / y,y,z),(x / y) * (y * z),u) = (u * ((x / y) * (y * z))) \ (u * (x * z)). [para(60(a,1),74(a,1,1))]. 1972 R(x,x / y,(x / y) \ (y \ z)) = ((x / y) * z) / (y \ z). [para(16(a,1),208(a,2,1,2))]. 1990 R(x,x / y,(x / y) \ T(z,y)) = ((x / y) * (z * y)) / T(z,y). [para(90(a,1),208(a,2,1,2))]. 2004 R(x,x * y,(x * y) \ z) = ((x * y) * ((y \ 1) * z)) / z. [para(1013(a,1),208(a,1,2)),rewrite([1013(4),1013(7)])]. 2009 (x / y) * ((x / y) * ((y * z) / T((x / y) * x,z))) = z. [para(18(a,1),1885(a,1,2,2,2,1,2))]. 2010 (x * y) / T(z * (z * x),y) = (z * z) \ y. [para(1885(a,1),21(a,1,2)),rewrite([1607(8)]),flip(a)]. 2012 x * (x * (((x * x) \ y) * z)) = y * z. [para(1885(a,1),37(a,1,1)),rewrite([2010(6)]),flip(a)]. 2032 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (((T(y,z) * x) * x) * u),w))) = w. [para(682(a,1),1885(a,1,2,2,2,1,2))]. 2040 (x * (y * y)) * z = x * (y * (y * z)). [back_rewrite(407),rewrite([2012(7)]),flip(a)]. 2044 R(x,y * y,z) = x. [back_rewrite(338),rewrite([2040(3),17(6)]),flip(a)]. 2045 a(x,y * y,z) = 1. [back_rewrite(311),rewrite([2040(6),46(7)]),flip(a)]. 2166 x / (T(T(y,z),u) * (z * (((T(y,u) * z) * z) \ x))) = z. [para(16(a,1),1266(a,1,1))]. 2213 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(13(a,1),130(a,1,1,2,2)),rewrite([13(8)])]. 2214 (x * (y * (z * (y * x)))) \ (x * (y * (z * (y * (x * u))))) = u. [para(130(a,1),15(a,1,2))]. 2215 x * (y * (z * (y * (x * ((x * (y * (z * (y * x)))) \ u))))) = u. [para(130(a,1),16(a,1))]. 2234 T(x,y) * (y * (z * (y * (T(x,y) * u)))) = (T(x,y) * (y * (z * (x * y)))) * u. [para(90(a,1),130(a,1,1,2,2,2)),flip(a)]. 2243 x * (y * (((y * x) \ 1) * (y * (x * z)))) = (x * y) * z. [para(997(a,1),130(a,1,1,2,2)),rewrite([14(2)]),flip(a)]. 2254 L(x,y,z * z) = x. [para(13(a,1),132(a,1,1,2)),rewrite([13(6),638(6),667(3),13(2)]),flip(a)]. 2276 L(x,y,z * (((z * y) \ 1) * z)) = ((z * y) \ 1) * (z * (y * x)). [para(997(a,1),132(a,1,1,2)),rewrite([14(2),15(8)]),flip(a)]. 2278 L(x,y,z * (((z * (y * x)) \ 1) * z)) = (((z * (y * x)) \ 1) * (z * y)) \ 1. [para(997(a,1),132(a,1,2,2)),rewrite([14(9),1091(8)]),flip(a)]. 2356 L(L(L(x,y,z),u,(u * x) \ 1),((u * x) \ 1) * u,w) = L(L(x,u,(u * x) \ 1),y,z). [para(1026(a,1),1078(a,1,2,1)),rewrite([990(13)])]. 2357 L(L(x,y,(y * x) \ 1),z,u) = L((((y * x) \ 1) * y) \ 1,z,u). [para(1026(a,1),1078(a,2,1)),rewrite([1141(11),2356(10)])]. 2445 ((x \ y) * (x * ((x \ y) * z))) \ (((x \ y) * y) * z) = 1. [para(13(a,1),314(a,1,1)),rewrite([13(9),52(13)])]. 2485 L(x,y * y,z) = x. [hyper(24,a,2045,a)]. 2486 a(x,y * (y * (z * (y * (y * z)))),u) = 1. [para(37(a,1),2045(a,1,2))]. 2495 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(2254(a,1),74(a,1)),rewrite([100(3),100(5)]),flip(a)]. 2497 L(x,y,(z \ 1) / z) = x. [para(1014(a,1),2254(a,1,3))]. 2507 L(x,y,z * (z * u)) = L(x,y,u). [back_rewrite(144),rewrite([2495(8),21(4)]),flip(a)]. 2508 a(x * (x * y),z,u) = a(y,z,u). [back_rewrite(140),rewrite([2495(9),19(5)]),flip(a)]. 2522 L(x,y * (y * (z * (y * (y * z)))),u) = x. [para(37(a,1),2485(a,1,2))]. 2528 L(x,(y \ 1) / y,z) = x. [para(1014(a,1),2485(a,1,2))]. 2538 (x \ y) \ 1 = y \ x. [para(16(a,1),1091(a,1,1)),flip(a)]. 2540 ((x \ y) * (x * z)) \ 1 = ((y * x) * z) \ x. [para(104(a,1),1091(a,1,1)),flip(a)]. 2548 ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. [para(54(a,1),1091(a,1,1))]. 2551 x * (x * ((y * z) * K((y \ 1) * ((x * y) * z),x * y))) = ((y \ 1) * ((x * y) * z)) * (x * y). [para(1091(a,1),350(a,1,2,1,1)),rewrite([37(3),37(11),1091(13)])]. 2556 ((x / y) * ((y \ 1) \ z)) / z = R(x,y \ 1,(y \ 1) \ z). [para(1091(a,1),268(a,1,1,1,2)),rewrite([1014(3),1091(4),1812(5),1091(8),1091(10)])]. 2560 T(x * y,(y \ 1) \ x) = x * y. [para(1091(a,1),560(a,1,2,1))]. 2574 a(x,T(y,x),x * z) = a(y * x,x,z) \ 1. [back_rewrite(673),rewrite([2548(7)]),flip(a)]. 2575 a(x,x \ y,x * z) = a(y,x,z) \ 1. [back_rewrite(173),rewrite([2548(8)])]. 2599 ((x / y) * (y * y)) / T(x * y,a(x,y \ 1,y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),729(a,1,1,1,2)),rewrite([1014(3),1649(6),1649(12)])]. 2601 ((x / y) * (y * y)) \ ((y \ 1) \ x) = K(((y \ 1) \ x) * y,y \ 1). [para(1649(a,1),354(a,1,1,1,2)),rewrite([1014(3),1649(5),1649(9),1014(10),17(8),1649(9),1649(13)])]. 2604 (x * y) \ ((x / y) * (y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),58(a,1,2,1,2)),rewrite([1014(4),1649(7)])]. 2635 T(T(x * x,y),x) = T(x * x,y). [para(1659(a,1),29(a,1,1)),flip(a)]. 2639 T((x \ 1) / x,x \ 1) = (x \ 1) / x. [para(1014(a,1),1659(a,1,1)),rewrite([1014(11)])]. 2640 x * (x * (y * (y * (z / (T(x * x,y) * (y * z)))))) = y. [para(1659(a,1),1266(a,1,1,1,1,1)),rewrite([100(2),37(3),37(4),100(2),2635(7),1839(9),1839(7)])]. 2642 T(x,x \ y) = T(x,y). [para(16(a,1),1708(a,1,2)),flip(a)]. 2643 T(x / y,x) = y \ x. [para(18(a,1),1708(a,1,2)),rewrite([92(4)])]. 2644 T(T(x,y),x * z) = T(T(x,z),y). [para(1708(a,1),29(a,1,1)),flip(a)]. 2645 L(T(x,L(x,y,z) * u),y,z) = L(T(x,u),y,z). [para(1708(a,1),30(a,1)),rewrite([30(2)]),flip(a)]. 2647 T(x * (x * y),x * (x * (y * z))) = T(x * (x * y),z). [para(37(a,1),1708(a,1,2))]. 2648 T(x,(x \ y) * (x * z)) = T(x,(y * x) * z). [para(104(a,1),1708(a,1,2)),flip(a)]. 2649 (x \ y) \ y = T(x,y). [para(91(a,1),1708(a,2)),rewrite([16(2)]),flip(a)]. 2652 T(x,y * x) = T(x,T(y,x)). [para(90(a,1),1708(a,1,2))]. 2690 (x \ y) * T(x,y) = y. [back_rewrite(1457),rewrite([2649(3),2642(7),166(8)])]. 2692 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(1452),rewrite([2642(9)])]. 2697 a(x * (y \ x),T(y,x),z) = a(y \ x,T(y,x) * x,z). [back_rewrite(1301),rewrite([2642(4),2642(7)])]. 2700 T(x,L(y * z,y \ x,y)) = T(x,(x * y) * z). [back_rewrite(1201),rewrite([2642(8)])]. 2705 L(x \ y,x,z) \ (z * y) = T(z * x,z * y). [back_rewrite(650),rewrite([2642(5)]),flip(a)]. 2708 ((x * (y \ z)) * T(y,z)) / z = R(x,y \ z,T(y,z)). [back_rewrite(268),rewrite([2642(4),2649(8)])]. 2709 T(x \ y,T(x,y)) = T(x,y) \ y. [back_rewrite(221),rewrite([2642(3),2649(5)])]. 2711 x / T(y,x) = y \ x. [back_rewrite(218),rewrite([2642(2)])]. 2712 (x \ 1) / x = x \ (x \ 1). [back_rewrite(2639),rewrite([2643(6)]),flip(a)]. 2713 ((x \ y) * (x * z)) \ ((y * x) * z) = T(x,(y * x) * z). [back_rewrite(185),rewrite([2648(10)])]. 2747 L(x,y \ (y \ 1),z) = x. [back_rewrite(2528),rewrite([2712(3)])]. 2748 L(x,y,z \ (z \ 1)) = x. [back_rewrite(2497),rewrite([2712(3)])]. 2755 (x \ 1) \ y = x * y. [back_rewrite(1227),rewrite([2747(5)]),flip(a)]. 2757 ((x / y) * (y * y)) \ (y * x) = K(y * (x * y),y \ 1). [back_rewrite(2601),rewrite([2755(6),2755(8),101(7)])]. 2759 T(x * y,y * x) = x * y. [back_rewrite(2560),rewrite([2755(4)])]. 2760 ((x / y) * (y * z)) / z = R(x,y \ 1,y * z). [back_rewrite(2556),rewrite([2755(4),2755(9)])]. 2771 T(x,y \ 1) = y * (x / y). [back_rewrite(1837),rewrite([2755(4)]),flip(a)]. 2772 K(x * y,y * x) = 1. [back_rewrite(1826),rewrite([2755(4)])]. 2774 T(x * y,y \ 1) = y * x. [back_rewrite(1812),rewrite([2755(7)])]. 2796 R(x,x / y,(x / y) \ z) = R(x,y \ 1,y * z). [back_rewrite(208),rewrite([2760(8)])]. 2802 ((x / y) * (z * y)) / T(z,y) = R(x,y \ 1,z * y). [back_rewrite(1990),rewrite([2796(5),90(4)]),flip(a)]. 2806 ((x / y) * z) / (y \ z) = R(x,y \ 1,z). [back_rewrite(1972),rewrite([2796(5),16(4)]),flip(a)]. 2810 T(x,(y * x) / y) = x. [hyper(28,a,1723,a)]. 2852 x * K(y \ x,y) = (y \ x) * y. [para(16(a,1),63(a,1,1))]. 2853 x * K(y,x / y) = y * (x / y). [para(18(a,1),63(a,1,1))]. 2855 (x * y) \ (K(x,y) * (y * x)) = K(K(x,y),y * x). [para(63(a,1),20(a,1,1))]. 2857 (x * y) \ ((y * x) * (K(x,y) * z)) = L(z,K(x,y),y * x). [para(63(a,1),21(a,1,1))]. 2858 ((x * y) * z) / (K(x,y) * z) = R(y * x,K(x,y),z). [para(63(a,1),22(a,1,1,1))]. 2880 ((x * (y * z)) * K(z,y)) / T(x * (z * y),a(x,y * z,K(z,y))) = a(x,y * z,K(z,y)). [para(63(a,1),265(a,1,2,1,2))]. 2887 (x * y) / T(y * x,K(x,y)) = K(x,y). [para(63(a,1),165(a,1,1))]. 2903 (x / y) * (y \ x) = (y \ x) * (x / y). [para(554(a,1),63(a,1,2)),rewrite([14(5)])]. 2917 K(x,y) \ 1 = K(y,x). [para(63(a,1),1091(a,1,1)),rewrite([20(3)]),flip(a)]. 2918 T(x * y,K(y,x)) = x * y. [para(63(a,1),1708(a,1,2)),rewrite([2759(3)]),flip(a)]. 2925 (x * y) / (y * x) = K(x,y). [back_rewrite(2887),rewrite([2918(4)])]. 2934 (x * (y * z)) \ (L(z,y,x) * (x * y)) = K(L(z,y,x),x * y). [para(21(a,1),64(a,1,2,1)),rewrite([21(10)])]. 2935 x * (K(y \ x,y) * (x * z)) = (((y \ x) * y) * x) * z. [para(64(a,1),104(a,1,2,1))]. 2962 x \ ((y \ 1) * (x * y)) = K(y \ 1,x * y). [para(1091(a,1),64(a,1,2,1)),rewrite([1091(7)])]. 2965 x * (((x \ y) * x) * z) = y * (x * z). [para(16(a,1),189(a,1,1)),flip(a)]. 2971 L(a(x,y,z),x * (y * z),y) = a(y,x,y * z). [para(189(a,1),19(a,1,2)),rewrite([589(7)])]. 2975 L(x,y * z,z) = L(x,z,z * y). [para(189(a,1),21(a,1,2)),rewrite([101(2),21(6)])]. 2993 x * ((T(y,x) * x) * z) = (y * x) * (x * z). [para(90(a,1),189(a,1,1)),flip(a)]. 3018 L(x * (y * z),x \ y,x) = (x * y) * z. [para(189(a,1),181(a,2,2)),rewrite([15(8)])]. 3031 x * (((y \ 1) * x) * z) = (x / y) * (x * z). [para(1014(a,1),189(a,1,1)),flip(a)]. 3032 (x * y) * (x / z) = x * ((y * x) / z). [para(1014(a,1),189(a,1,2)),rewrite([1014(7)])]. 3050 L(x,y * (z * (y * z)),u) = x. [para(189(a,1),2485(a,1,2)),rewrite([101(2)])]. 3078 x * (y * ((y * (x * y)) \ z)) = y \ z. [para(103(a,1),15(a,1,2)),flip(a)]. 3093 x * a(y,z,y * ((y * (z * y)) \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [para(103(a,1),54(a,1,1)),rewrite([189(12)])]. 3097 (x \ y) * (T(x,y) * ((x \ y) * z)) = (y * (x \ y)) * z. [para(103(a,1),186(a,2,1,1)),rewrite([3078(5),3078(6),2642(3),3078(7),3078(11)])]. 3103 x * ((x \ 1) * y) = y. [para(997(a,1),103(a,1,2,2,2,1,2)),rewrite([14(4),16(4)])]. 3118 L((x * (y * x)) \ z,x,y * (x * y)) = (y * (x * (y * x))) \ (y * z). [para(103(a,1),132(a,1,2,2)),flip(a)]. 3130 K(x,(x \ 1) * (y / x)) = K(y,x \ 1). [back_rewrite(1004),rewrite([3103(8),1833(5)]),flip(a)]. 3135 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(16(a,1),2495(a,1,1,2))]. 3136 (x * (x * y)) \ (x * z) = y \ (x \ z). [para(16(a,1),2495(a,1,2,2))]. 3139 T(x * (x * (y / (x * (x * z)))),x * (x * z)) = z \ y. [para(2495(a,1),92(a,2)),rewrite([1839(5)])]. 3141 L(x \ y,z * (z * x),u) = (u * (z * (z * x))) \ (u * (z * (z * y))). [para(2495(a,1),74(a,1,1))]. 3143 (x \ 1) * y = x \ y. [para(997(a,1),2495(a,1,1,2)),rewrite([14(4),15(9)])]. 3162 (x \ ((x * y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(141),rewrite([3135(7)])]. 3163 K(x,x \ (y / x)) = K(y,x \ 1). [back_rewrite(3130),rewrite([3143(4)])]. 3169 (x / y) * (x * z) = x * ((y \ x) * z). [back_rewrite(3031),rewrite([3143(3)]),flip(a)]. 3171 K(x \ 1,y * x) = y \ T(y,x). [back_rewrite(2962),rewrite([3143(4),23(2)]),flip(a)]. 3184 x * (x * ((y * z) * K((y \ x) * (y * z),x * y))) = ((y \ x) * (y * z)) * (x * y). [back_rewrite(2551),rewrite([3143(6),168(4),3143(14),168(12)])]. 3191 L(L(x,y,(y * x) \ 1),z,u) = L(x,z,u). [back_rewrite(2357),rewrite([3143(9),1091(7),2649(9),88(7)])]. 3192 L(L(x,y,z),u,(u * x) \ 1) = L(x,y,z). [back_rewrite(2356),rewrite([3143(9),1091(7),1080(8),3191(10)])]. 3199 L(x,y,z / (y * x)) = L(x,y,z). [back_rewrite(2278),rewrite([3143(5),1091(3),1014(4),3143(9),2538(9),21(7)])]. 3200 L(x,y,z / y) = L(x,y,z). [back_rewrite(2276),rewrite([3143(4),1091(2),1014(3),3143(8),21(6)])]. 3204 x * (y * L(z,x,y)) = (x * y) * z. [back_rewrite(2243),rewrite([3143(6),21(4)])]. 3213 R(x,x * y,(x * y) \ z) = R(x,y,y \ z). [back_rewrite(2004),rewrite([3143(8),169(7),191(8)])]. 3218 x * (y \ T(z,x * (x / y))) = x \ (z * (x * (x / y))). [back_rewrite(1888),rewrite([3143(6)])]. 3228 (x * (x / y)) * z = x * (x * (y \ z)). [back_rewrite(1838),rewrite([3143(3)]),flip(a)]. 3229 (x / y) \ (x * (y \ z)) = L(z,y \ 1,x). [back_rewrite(1834),rewrite([3143(4)])]. 3230 (x \ y) \ (y / x) = K(y,x \ 1). [back_rewrite(1833),rewrite([3143(3)])]. 3231 (x / y) \ (y \ x) = K(y \ 1,x). [back_rewrite(1832),rewrite([3143(4)])]. 3266 L(x,y,y \ 1) = x. [back_rewrite(1025),rewrite([3143(4),15(2)]),flip(a)]. 3276 x \ ((x / y) * (y * z)) = L(z,y,x). [back_rewrite(75),rewrite([3200(6)])]. 3286 (x / y) * (y * ((x / y) * z)) = x * (x * (y \ z)). [back_rewrite(107),rewrite([3228(8)])]. 3302 K(x * y,K(y,x)) = 1. [hyper(27,a,2918,a)]. 3304 T(x,K(y \ x,y)) = x. [para(16(a,1),2918(a,1,1)),rewrite([16(5)])]. 3305 T(x,K(y,x / y)) = x. [para(18(a,1),2918(a,1,1)),rewrite([18(5)])]. 3307 T((x * y) * z,K((y \ x) * (y * z),y)) = (x * y) * z. [para(104(a,1),2918(a,1,1)),rewrite([104(11)])]. 3308 K(x,y) * (y * x) = x * y. [para(2918(a,1),90(a,1,2)),rewrite([63(6)])]. 3323 (((x \ y) * (x * z)) * x) / ((y * x) * z) = K((x \ y) * (x * z),x). [back_rewrite(969),rewrite([3307(11)])]. 3327 K(K(x,y),y * x) = 1. [back_rewrite(2855),rewrite([3308(4),46(3)]),flip(a)]. 3382 T(T(T(x,y \ 1),z),u) / y = T(T(T(x,z),u),y \ 1) / y. [para(94(a,1),1009(a,2,1)),rewrite([1009(12)]),flip(a)]. 3436 (x * x) \ y = x \ (x \ y). [para(18(a,1),1324(a,1,2,2)),rewrite([92(8),1619(6)]),flip(a)]. 3476 x * T(y * z,y * (y * x)) = (y \ z) * (y * (y * x)). [para(181(a,2),1324(a,1,2)),rewrite([3018(5),168(4)]),flip(a)]. 3482 x \ T(y,z * (z / x)) = z \ (z \ (y * (z * (z / x)))). [para(1014(a,1),1324(a,1,2,2,2,2)),rewrite([1014(10),3143(11)]),flip(a)]. 3541 x \ (y \ (z * (y * (x * y)))) = y * T(z,y * (x * y)). [para(1359(a,1),15(a,1,2))]. 3544 (x \ (y * (x * (z * x)))) / (x * T(y,x * (z * x))) = z. [para(1359(a,1),17(a,1,1))]. 3575 x * (y \ T(z,y \ (x / y))) = y * (z * (y \ (x / y))). [para(1014(a,1),1359(a,1,2,2,2,2)),rewrite([3143(6),3143(6),1014(12),3143(11),2755(11)])]. 3576 a(x / y,y,T(z,y * x)) = a(y,y \ x,T(z,y * x)). [para(1359(a,1),60(a,1,1)),rewrite([18(2),18(5),1346(7),18(7)]),flip(a)]. 3640 x * (x * (((x \ y) / z) / T(x * y,z \ 1))) = z \ 1. [para(16(a,1),1884(a,1,2,2,2,1,2))]. 3641 x * (x * (y / T(x * (x * (y * z)),z \ 1))) = z \ 1. [para(17(a,1),1884(a,1,2,2,1))]. 3645 (x / y) / T(z * (z * x),y \ 1) = z \ (z \ (y \ 1)). [para(1884(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 3646 R(x,x \ (y \ 1),z) = (y \ z) / ((x \ (y \ 1)) * z). [para(1884(a,1),22(a,1,1,1)),rewrite([3143(3),3645(8),16(6),3645(13),16(11)]),flip(a)]. 3666 (x \ y) / y = x \ 1. [para(1884(a,1),201(a,1,2)),rewrite([3645(8),100(6),16(5),16(4),3645(11),16(9),16(8),2755(7),480(6),3645(9),16(7),16(6),3645(11),1300(9),13(6),3143(5)]),flip(a)]. 3670 x * (x * (((T(y,x) * (x * z)) / u) / T(x * (((y * x) * x) * z),u \ 1))) = u \ 1. [para(186(a,1),1884(a,1,2,2,2,1,2))]. 3683 x * ((x \ (y \ 1)) * T(z,x / y)) = x \ (z * (x / y)). [para(1884(a,1),778(a,1,2,2,2,2)),rewrite([3645(7),16(5),1014(6),3645(14),16(12),16(11),1014(10)])]. 3691 x / (y * x) = y \ 1. [para(1884(a,1),1013(a,2)),rewrite([3645(7),16(5),2538(5),2755(3)])]. 3709 x \ (x \ (y * (x / z))) = (x \ (z \ 1)) * T(y,x / z). [para(1884(a,1),1324(a,1,2,2,2,2)),rewrite([1014(3),3645(11),16(9),3645(14),16(12),16(11),1014(10)])]. 3710 (x \ (x \ (y \ 1))) * T(z,y \ 1) = x \ (x \ (z / y)). [para(1884(a,1),1324(a,1,2,2,2)),rewrite([1014(3),3645(10),3645(14),16(12),16(11)]),flip(a)]. 3723 R(x \ 1,x,y) = x \ 1. [back_rewrite(1027),rewrite([3691(5)])]. 3724 x / (y * (z * (y * x))) = (y * (z * y)) \ 1. [back_rewrite(1448),rewrite([3723(7)]),flip(a)]. 3725 x / (y * (y * (z * x))) = (y * (y * z)) \ 1. [back_rewrite(1039),rewrite([3723(7)]),flip(a)]. 3735 a(x * (y * x),y,z) = a(x,y * (x * y),z). [para(133(a,1),110(a,1))]. 3752 (x * (y * (y * z))) \ ((x * (y * (y * u))) * (u \ z)) = a(x,y * (y * u),u \ z). [para(16(a,1),139(a,1,1,2,2,2))]. 3753 (x * (y * (y * z))) \ ((x * (y * (y * (z / u)))) * u) = a(x,y * (y * (z / u)),u). [para(18(a,1),139(a,1,1,2,2,2))]. 3762 a(x * ((y * x) * x),z,u) = a(x * y,x * (x * z),u). [para(189(a,1),139(a,1,1)),rewrite([189(9),133(11)])]. 3794 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,w),y),z),v5),u \ 1) / u. [para(94(a,1),3382(a,2,1,1,1))]. 3933 x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u)))))) = x * u. [para(398(a,1),15(a,1,2)),rewrite([15(3)]),flip(a)]. 3934 K(x * y,x) = y \ T(y,x). [para(398(a,1),20(a,1,1)),rewrite([3933(13),101(4),3136(5),23(2),3933(13)]),flip(a)]. 3935 K(x,x * y) = T(y,x) \ y. [para(398(a,1),20(a,1,2)),rewrite([3933(11),101(2),3135(5),23(2),3933(13)]),flip(a)]. 3936 x * (y * (y * (x * (z * ((x * (y * (y * (x * z)))) \ u))))) = u. [para(398(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 3940 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(398(a,1),74(a,2,1)),rewrite([3936(10),3936(12),3136(8)])]. 3941 L(x \ (y * z),x,y) = (y \ x) \ z. [para(398(a,1),74(a,2,2)),rewrite([3936(10),3135(7)])]. 3947 x * (x * (y * (x * (x * (y * (z \ ((y * (x * (x * (y / z)))) \ u))))))) = x * (x * u). [para(1014(a,1),398(a,1,2,2,2,2,2,2,2,1,2,2,2)),rewrite([3143(8)])]. 3949 x * (x * (y * ((x * (x * (x * (x * y)))) \ z))) = x \ (x \ z). [para(398(a,1),132(a,1,2)),rewrite([3135(6),15(3),3436(2),2507(13),1607(11)]),flip(a)]. 3954 a(x,x \ y,z) = a(x,x * y,z). [para(398(a,1),133(a,1,2,1)),rewrite([3949(8),16(3),136(4),37(6),3135(7),3162(5),3949(12),16(7),2508(6)]),flip(a)]. 3968 a(x / y,y,T(z,y * x)) = a(y,y * x,T(z,y * x)). [back_rewrite(3576),rewrite([3954(8)])]. 3982 a(x,x * y,x * z) = a(y,x,z) \ 1. [back_rewrite(2575),rewrite([3954(3)])]. 4007 (x * (y * z)) / T((x * z) * T(y,z),a(z,z * x,y * z)) = a(z,z * x,y * z). [back_rewrite(1517),rewrite([3954(8),3954(13)])]. 4013 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x / y,y). [back_rewrite(1051),rewrite([3954(11),1014(10)])]. 4021 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,x * ((y * x) * z),u). [back_rewrite(662),rewrite([3954(13),189(12)])]. 4025 (x * ((x \ y) * ((y \ z) * (y * u)))) \ ((z * y) * u) = a(x,x * y,(y \ z) * (y * u)). [back_rewrite(614),rewrite([3954(14)])]. 4031 T(x * ((x \ y) * z),a(x,x * y,z)) = a(x,x * y,z) \ (y * z). [back_rewrite(260),rewrite([3954(5),3954(8)])]. 4032 (x * ((x \ y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(56),rewrite([3954(7)])]. 4097 T(T(T(T(T(x,y),z \ 1),u),w),v5) / z = T(T(T(T(T(x,w),u),y),v5),z \ 1) / z. [para(94(a,2),3794(a,1,1,1,1))]. 4108 K(x * y,K(x,y)) = 1. [para(1684(a,1),2880(a,1,2,2)),rewrite([3308(3),88(8),2925(7),1684(7)])]. 4114 ((x * y) * z) \ R(x,y,z) = (y * z) \ 1. [para(22(a,1),1829(a,1,2))]. 4115 ((x / y) * x) * z = x * (y \ (x * z)). [para(1829(a,1),104(a,1,2,1)),rewrite([3143(4)]),flip(a)]. 4137 (x \ y) * (y \ x) = 1. [para(2538(a,1),16(a,1,2))]. 4138 (x * (y * z)) \ (x * y) = L(z,y,x) \ 1. [para(21(a,1),2538(a,1,1)),flip(a)]. 4145 L(x \ y,y \ x,z) = x \ y. [para(2538(a,1),74(a,1,1)),rewrite([14(7),1091(6),2538(6)])]. 4151 a(x,y \ z,z \ y) = 1. [para(2538(a,1),1012(a,1,2))]. 4155 x / (y \ z) = x * (z \ y). [para(2538(a,1),1013(a,1,2))]. 4157 (x * y) \ ((x / z) * (z * y)) = a(x / z,z,y) \ 1. [para(60(a,1),2538(a,1,1)),flip(a)]. 4165 L(x,y \ z,z \ y) = x. [para(2538(a,1),3266(a,1,3))]. 4180 x * ((x \ (y / z)) * z) = R(y,z \ 1,x). [back_rewrite(2806),rewrite([4155(4),169(4)])]. 4186 R(x,y,y \ ((y \ x) \ z)) = z * ((z \ y) * (y \ x)). [back_rewrite(199),rewrite([4155(8),169(8)])]. 4187 a(x / y,y,y) \ 1 = a(x,y \ 1,y * y). [back_rewrite(2604),rewrite([4157(5)])]. 4206 T((x / y) * (y * z),x * z) = a(x / y,y,z) \ (x * z). [para(60(a,1),2642(a,1,2)),rewrite([263(6)]),flip(a)]. 4209 T(x * y,x) = y * x. [para(1091(a,1),2642(a,1,2)),rewrite([2774(4)]),flip(a)]. 4210 T(x,(y \ x) * y) = x. [para(64(a,1),2642(a,1,2)),rewrite([3304(3)]),flip(a)]. 4214 T(T(T(x,y),z),T(T(x,z),y) \ u) = T(T(T(x,z),y),u). [para(2642(a,1),94(a,2)),rewrite([29(6)])]. 4230 (x / y) * x = x * (y \ x). [para(2643(a,1),90(a,1,2)),flip(a)]. 4231 T(x \ y,y) = T(x \ y,x). [para(2643(a,1),537(a,1,1)),flip(a)]. 4247 (x * (y \ x)) * z = x * (y \ (x * z)). [back_rewrite(4115),rewrite([4230(2)])]. 4254 (x / y) * ((x / y) * ((y * z) / T(x * (y \ x),z))) = z. [back_rewrite(2009),rewrite([4230(5)])]. 4261 (x \ y) * (T(x,y) * ((x \ y) * z)) = y * (x \ (y * z)). [back_rewrite(3097),rewrite([4247(9)])]. 4278 T(x,y) \ y = T(x \ y,y). [para(2649(a,1),2642(a,1,2)),rewrite([2709(3)])]. 4281 T(x \ y,T(x,y)) = T(x \ y,y). [back_rewrite(2709),rewrite([4278(5)])]. 4304 T(x,y) * T(x \ y,y) = y. [para(2690(a,1),90(a,2)),rewrite([4281(4)])]. 4308 (x * y) * a(x,z \ y,T(z,y)) = (x * (z \ y)) * T(z,y). [para(2690(a,1),54(a,1,1,2))]. 4314 T(x,y) * (T(x \ y,y) * (T(x,y) * z)) = (x * y) * z. [para(2690(a,1),186(a,2,1,1)),rewrite([4281(4),90(9)])]. 4315 ((x * (y \ z)) * T(y,z)) / T(x * z,a(x,y \ z,T(y,z))) = a(x,y \ z,T(y,z)). [para(2690(a,1),265(a,1,2,1,2))]. 4335 a(x * (y \ z),z \ y,T(z,y)) = ((x * (y \ z)) * y) \ (x * T(z,y)). [para(2690(a,1),60(a,1,1,2)),rewrite([4155(2),4155(8)]),flip(a)]. 4344 (x \ y) * ((z * (x \ y)) * T(x,y)) = ((x \ y) * z) * y. [para(2690(a,1),189(a,1,2)),flip(a)]. 4357 (x \ (x \ y)) * T(x,y) = x \ y. [para(2642(a,1),2690(a,1,2))]. 4365 x / T(x,y) = T(x,y) \ x. [para(159(a,1),2711(a,1,2))]. 4366 T(x,y) / x = x \ T(x,y). [para(541(a,1),2711(a,1,2))]. 4379 ((x \ y) * x) / y = K(x \ y,x). [para(64(a,1),2711(a,2)),rewrite([4210(5)])]. 4404 x * T(y,z \ (z \ x)) = z * (z * (y * (z \ (z \ x)))). [para(2755(a,1),1324(a,1,2)),rewrite([3143(7),3143(6),2755(7),3143(10),3143(9)]),flip(a)]. 4407 (x * y) \ 1 = y \ (x \ 1). [para(2755(a,1),2538(a,1,1))]. 4408 (x \ y) \ z = (y \ x) * z. [para(2538(a,1),2755(a,1,1))]. 4417 ((x * y) * z) \ R(x,y,z) = z \ (y \ 1). [back_rewrite(4114),rewrite([4407(7)])]. 4419 ((x \ (y \ 1)) * y) \ (x \ 1) = a(x,x / y,y). [back_rewrite(4013),rewrite([4407(7)])]. 4420 x / (y * (y * (z * x))) = (y * z) \ (y \ 1). [back_rewrite(3725),rewrite([4407(8)])]. 4421 x / (y * (z * (y * x))) = (z * y) \ (y \ 1). [back_rewrite(3724),rewrite([4407(8)])]. 4445 L(L(x,y,z),u,x \ (u \ 1)) = L(x,y,z). [back_rewrite(3192),rewrite([4407(4)])]. 4458 ((x * y) * z) \ y = (y * z) \ (x \ y). [back_rewrite(2540),rewrite([4407(5),4408(4),14(4)]),flip(a)]. 4470 R(x,y,y \ ((x \ y) * z)) = z * ((z \ y) * (y \ x)). [back_rewrite(4186),rewrite([4408(2)])]. 4480 L(x \ (y * z),x,y) = (x \ y) * z. [back_rewrite(3941),rewrite([4408(5)])]. 4493 (x \ y) * (x / y) = K(x,y \ 1). [back_rewrite(3230),rewrite([4408(3)])]. 4498 (((x * y) * z) \ x) * (y * z) = a(x,x * y,z). [back_rewrite(3162),rewrite([4408(5)])]. 4501 (x * y) \ (x * (x * z)) = (y \ x) * z. [back_rewrite(3135),rewrite([4408(6)])]. 4504 (x \ y) * (((y \ x) * z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(2692),rewrite([4408(3)])]. 4505 (x \ y) * x = T(y,x). [back_rewrite(2649),rewrite([4408(2)])]. 4516 K(x \ y,x) = y \ T(y,x). [back_rewrite(4379),rewrite([4505(2),4366(2)]),flip(a)]. 4525 x * (T(y,x) * z) = y * (x * z). [back_rewrite(2965),rewrite([4505(2)])]. 4534 x * (K(y \ x,y) * (x * z)) = (x * T(x,y)) * z. [back_rewrite(2935),rewrite([4505(7),547(7)])]. 4535 x * K(y \ x,y) = T(x,y). [back_rewrite(2852),rewrite([4505(5)])]. 4537 a(T(x,y),y \ x,z) = a(y \ x,x,z). [back_rewrite(1702),rewrite([4505(2)])]. 4539 K(x,x \ y) = T(y,x) \ y. [back_rewrite(65),rewrite([4505(2)]),flip(a)]. 4559 (T(x,y) * (y * (z * (x * y)))) * u = T(x,y) * (y * (z * (x * (y * u)))). [back_rewrite(2234),rewrite([4525(4)]),flip(a)]. 4562 ((x * y) * y) / z = x * (y * (y / z)). [back_rewrite(1859),rewrite([4525(4)]),flip(a)]. 4578 (x * y) * y = x * (y * y). [back_rewrite(669),rewrite([4525(3)]),flip(a)]. 4581 L(x,T(y,z),z) = L(x,z,y). [back_rewrite(512),rewrite([4525(4),21(4)]),flip(a)]. 4582 a(x,T(y,x),z) = a(y,x,z). [back_rewrite(508),rewrite([4525(3),19(5)]),flip(a)]. 4583 R(x * y,y,y \ z) = (x * (y * z)) / z. [back_rewrite(204),rewrite([4525(6)])]. 4596 ((T(x,y) * (y / z)) * y) \ ((x * (y * y)) / z) = K(y,T(x,y) * (y / z)). [back_rewrite(1864),rewrite([4578(6)])]. 4613 (x * (y * y)) / z = x * (y * (y / z)). [back_rewrite(4562),rewrite([4578(2)])]. 4636 a(x * (y * (x * x)),z,u) = a(x * y,x * (x * z),u). [back_rewrite(3762),rewrite([4578(2)])]. 4640 x * (x * (((T(y,x) * (x * z)) / u) / T(x * (y * (x * (x * z))),u \ 1))) = u \ 1. [back_rewrite(3670),rewrite([4578(6),2040(7)])]. 4713 x / (T(T(y,z),u) * (z * ((T(y,u) * (z * z)) \ x))) = z. [back_rewrite(2166),rewrite([4578(5)])]. 4714 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w))) = w. [back_rewrite(2032),rewrite([4578(8),2040(9)])]. 4770 x * (R(T(y,x),z,u) * (x * w)) = R(y,z,u) * (x * (x * w)). [back_rewrite(684),rewrite([4578(8),2040(9)])]. 4778 (x * ((T(y,x) * (x * z)) * u)) \ ((y * (x * (x * z))) * u) = a(x,T(y,x) * (x * z),u). [back_rewrite(674),rewrite([4578(7),2040(8)])]. 4795 a(x * y,y,z) \ 1 = a(x,y,y * z). [back_rewrite(2574),rewrite([4582(3)]),flip(a)]. 4809 ((T(x,y) * (y / z)) * y) \ (x * (y * (y / z))) = K(y,T(x,y) * (y / z)). [back_rewrite(4596),rewrite([4613(7)])]. 4813 (x / y) * (y * (y / T(x * y,a(x,y \ 1,y * y)))) = a(x,y \ 1,y * y). [back_rewrite(2599),rewrite([4613(10)])]. 4915 K(x,y * (x / y)) = 1. [para(18(a,1),2772(a,1,1))]. 4950 T(a(x,y,z),((x * y) * z) / (x * (y * z))) = a(x,y,z). [para(54(a,1),2810(a,1,2,1))]. 4993 K(x,y) * K(y,x) = 1. [para(2917(a,1),16(a,1,2))]. 4996 R(x,K(y,z),K(z,y)) = x. [para(2917(a,1),191(a,2,3)),rewrite([14(5),16(4),48(2)]),flip(a)]. 5005 x / K(y,z) = x * K(z,y). [para(2917(a,1),1014(a,1,2)),flip(a)]. 5011 L(x,K(y,z),K(z,y)) = x. [para(2917(a,1),3266(a,1,3))]. 5067 T(x,y * (x / y)) = x. [para(66(a,1),2642(a,1,2)),rewrite([3305(3)]),flip(a)]. 5068 K(x,y / x) * y = x * (y / x). [para(66(a,1),2690(a,1,1)),rewrite([5067(5)])]. 5070 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(16(a,1),72(a,1,1))]. 5116 (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). [para(63(a,1),72(a,1,1))]. 5129 x * L(y,T(z,x),z \ x) = (z \ x) * (T(z,x) * y). [para(2690(a,1),72(a,1,1))]. 5134 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(15(a,1),3940(a,1,1)),flip(a)]. 5138 L(T(x,y * z),y * z,y) = z \ (y \ (x * (y * z))). [para(23(a,1),3940(a,1,1))]. 5147 L((x * y) \ z,y,y * x) = T(x,y) \ (y \ z). [para(90(a,1),3940(a,1,1,1)),rewrite([90(4),2975(4)])]. 5152 K(x * (y / x),x) = K(x \ 1,y). [para(67(a,1),3940(a,1,1)),rewrite([666(5),3231(6)])]. 5155 L((x / y) \ z,x / y,x) = y * (x \ z). [para(1014(a,1),3940(a,1,1,1)),rewrite([1014(5),4408(8),45(6)])]. 5162 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(3940(a,1),2254(a,1)),rewrite([3436(2),100(5)]),flip(a)]. 5163 L((x * y) \ z,x * y,y * x) = K(x,y) \ ((y * x) \ z). [para(63(a,1),3940(a,1,1,1)),rewrite([63(5)])]. 5194 R(x,y * (y * z),z \ (y \ (y \ u))) = R(x,z,z \ u). [back_rewrite(1870),rewrite([5162(3),191(6),1935(6),16(3),16(2),5162(7)]),flip(a)]. 5200 x * (x * (y * ((y \ (x \ (x \ z))) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [back_rewrite(411),rewrite([5162(3)])]. 5208 (x * (y \ z)) * (z \ y) = x. [para(4151(a,1),209(a,1,1)),rewrite([45(6),4137(7),14(6),4151(7),88(6)])]. 5226 (T(x,y) \ (T(x,y) \ z)) * T(T(x,z),y) = T(x,y) \ z. [para(29(a,1),4357(a,1,2))]. 5332 a(x,y,y) = 1. [para(89(a,1),507(a,1,2,2)),rewrite([4578(4),46(5),89(2)]),flip(a)]. 5337 (x * (y * (z * u))) \ (x * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),y * (z * u),x). [para(507(a,1),74(a,1,1)),flip(a)]. 5358 a(x,y \ 1,y * y) = 1. [back_rewrite(4187),rewrite([5332(2),46(3)]),flip(a)]. 5359 (x / y) * (y / x) = 1. [back_rewrite(4813),rewrite([5358(6),88(4),3691(3),1014(4),5358(7)])]. 5364 (x * y) / T(z * (z * y),T(x,y)) = z \ (z \ T(x,y)). [para(1921(a,1),21(a,1,2)),rewrite([3436(3),1607(10)]),flip(a)]. 5392 (x \ y) * (x * ((x \ y) * z)) = ((x \ y) * y) * z. [para(2445(a,1),16(a,1,2)),rewrite([14(7)])]. 5410 (x \ (y \ (y \ z))) * (((z \ y) * y) * x) = 1. [para(2445(a,1),4357(a,1,1,2)),rewrite([5392(5),4407(5),4407(4),4408(3),14(3),5392(8),89(10),5392(12),46(14)])]. 5428 x * (x * (y / (T(z * z,x) * (x * y)))) = z \ (z \ x). [para(2640(a,1),21(a,1,2)),rewrite([3436(2),1607(10)]),flip(a)]. 5444 L(x,y \ (y \ z),y) = L(x,z,y). [para(2640(a,1),132(a,1,1,2)),rewrite([5428(8),136(6),16(3),21(4),5428(8),2507(6)]),flip(a)]. 5452 x * (x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u))))))) = y * z. [para(189(a,1),2640(a,1,2,2,2,2,2,2))]. 5468 T(x * (x * y),y \ z) = T(x * (x * y),x * (x * z)). [para(16(a,1),2647(a,1,2,2,2)),flip(a)]. 5480 T(x * (x * y),x * (x * (y / z))) = T(x * (x * y),z \ 1). [para(1014(a,1),2647(a,1,2,2,2))]. 5515 a(x \ y,T(x,y) * y,z) = 1. [para(2697(a,1),19(a,2)),rewrite([4247(5),4525(3),15(3),4247(6),90(4),15(4),100(4),46(5)]),flip(a)]. 5524 a((x * y) * L(z \ y,z,x),T(x * z,x * y),u) = 1. [para(74(a,2),2697(a,1,1,2)),rewrite([5515(17)])]. 5560 ((x \ y) * (x / z)) \ ((y * x) / z) = T(x,(y * x) / z). [para(1014(a,1),2713(a,1,1,2)),rewrite([1014(7),1014(10)])]. 5569 (((x \ y) * z) * x) \ ((z * (y \ x)) * T(y,x)) = T(y \ x,(z * (y \ x)) * T(y,x)). [para(2690(a,1),2713(a,1,1,2)),rewrite([4408(2)])]. 5600 ((x * (y * (y * (y * x)))) \ y) * (x * (y * (x * y))) = 1. [para(2772(a,1),143(a,2)),rewrite([101(2),189(5),4578(2),2040(4),101(7),4501(11)])]. 5610 (x \ (y \ (y \ (z \ 1)))) * (z * (y * (y * (x * u)))) = L(u,y * (y * x),z). [para(37(a,1),145(a,1,1)),rewrite([37(11),4501(12),1091(5),4407(5),5162(5),2507(15)])]. 5614 L(x,y * (y * z),z) = x. [para(1607(a,1),145(a,2)),rewrite([189(5),101(2),189(4),4578(2),101(3),100(2),189(11),101(7),189(10),4578(7),189(9),100(7),37(8),4501(12),1091(5),4407(5),5162(5),5610(10)])]. 5657 x * (y * (x * (z * ((z * (x * (y * (x * z)))) \ u)))) = z \ u. [para(2215(a,1),15(a,1,2)),flip(a)]. 5665 R(x,y,y \ ((x \ y) * z)) = (y * z) / ((x \ y) * z). [para(2215(a,1),191(a,1,1,2)),rewrite([5657(13),4408(3),5657(16),4408(6)]),flip(a)]. 5674 x * (y * (z * (y * (x / (x * (y * (z * (y * x)))))))) = 1. [para(1014(a,1),2215(a,1,2,2,2,2))]. 5742 K(L(x * y,x \ z,x),z) = K(z * ((z * x) * y),z). [para(181(a,1),2934(a,1,2,1)),rewrite([104(4),16(7),4505(6),3934(6,R),16(9)]),flip(a)]. 5752 (x * ((y * x) * z)) \ (L(z,x,x * y) * (x * (y * x))) = K(L(z,x,x * y),x * (y * x)). [para(189(a,1),2934(a,1,1)),rewrite([101(7),101(13)])]. 5783 x * ((y * x) * (x * ((x \ y) * z))) = (x * y) * ((x * y) * z). [para(13(a,1),405(a,1,2,2,2,2)),rewrite([14(10),187(12),101(8),426(10)])]. 5816 R(x * ((x \ y) * (y \ z)),z,z \ u) = (z * (a(y,x,x \ (y \ z)) * u)) / u. [para(16(a,1),435(a,1,2)),rewrite([16(6),16(8)])]. 5817 (x * (a(x / y,z,z \ y) * u)) / u = R(x,y \ 1,z). [para(18(a,1),435(a,1,2)),rewrite([4180(4),18(5),495(5),18(5)]),flip(a)]. 5841 R(x * ((x \ (y \ z)) * T(y,z)),z,z \ u) = (z * (a(y \ z,x,x \ T(y,z)) * u)) / u. [para(2690(a,1),435(a,1,2)),rewrite([2690(8),2690(10)])]. 5879 x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))) = z. [para(463(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 5885 (x \ (y \ 1)) * (y * (x * z)) = L(z,x,y). [para(463(a,1),132(a,1,1,2)),rewrite([5879(13),4501(8),1091(3),4407(3),5879(16),2507(9)])]. 5921 a(x,T(y,x) * x,z) = a(y,x,x * z) \ 1. [para(14(a,1),4778(a,1,1,2,1,2)),rewrite([2993(4),14(5),2040(6),2548(7),14(7)]),flip(a)]. 6018 L(x,x,y) = x. [hyper(24,a,5332,a)]. 6020 L(T(x,y),x,z) = T(x,y). [para(6018(a,1),30(a,1,1)),flip(a)]. 6022 L(L(x,y,z),x,u) = L(x,y,z). [para(6018(a,1),34(a,1,1)),flip(a)]. 6024 L(L(L(x,y,z),u,w),L(x,u,w),v5) = L(L(x,u,w),y,z). [para(6018(a,1),97(a,1,1)),flip(a)]. 6068 ((x * y) \ z) * ((z \ x) * y) = a(z \ 1,x,y). [para(3143(a,1),19(a,1,1)),rewrite([3143(5),4408(5)])]. 6069 (x \ (y \ 1)) * (x * y) = K(x,y). [para(20(a,1),3143(a,2)),rewrite([4407(3)])]. 6070 (x \ y) * (y \ (x * z)) = L(z,x,y \ 1). [para(3143(a,1),21(a,1,1)),rewrite([3143(5),4408(4)])]. 6071 ((x \ y) * z) / (y * z) = R(x \ 1,y,z). [para(3143(a,1),22(a,1,1,1))]. 6072 T(x \ 1,y) = y \ (x \ y). [para(3143(a,1),23(a,1,2)),flip(a)]. 6073 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [para(3143(a,1),37(a,1,1,2)),rewrite([3143(4),3143(9),3143(8)]),flip(a)]. 6095 x \ T(y,x \ 1) = y / x. [para(3143(a,1),90(a,1)),rewrite([1014(7)])]. 6120 (x \ 1) / y = x \ (y \ 1). [para(3143(a,1),1014(a,1)),flip(a)]. 6128 ((x * (y * z)) \ (y \ 1)) * (y * (x * (y * (z * u)))) = L(u,z,y * (x * y)). [para(132(a,1),3143(a,2)),rewrite([4407(5)])]. 6132 (x \ (y \ 1)) * y = x \ 1. [para(1091(a,1),3143(a,2)),rewrite([4407(3)])]. 6134 T(x \ 1,x \ y) = T(x \ 1,y). [para(3143(a,1),1708(a,1,2))]. 6135 x \ ((y / x) * z) = (x \ y) * (x \ z). [para(3143(a,1),189(a,1,1)),rewrite([3143(4),1014(8),3143(8)]),flip(a)]. 6141 ((x * y) \ (z \ (z \ (u \ 1)))) * ((u * (z * (z * x))) * y) = a(u,z * (z * x),y). [para(139(a,1),3143(a,2)),rewrite([4407(6),5162(6)])]. 6144 K(x,y) \ z = K(y,x) * z. [para(2917(a,1),3143(a,1,1)),flip(a)]. 6145 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(3143(a,1),72(a,1,1)),rewrite([3143(9)])]. 6149 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(z \ 1,y,T(x,y)). [para(3143(a,1),507(a,1,1)),rewrite([3143(5),4408(6)])]. 6151 ((x \ (y \ 1)) * (x * z)) \ ((y \ x) * z) = T(x,(y \ x) * z). [para(3143(a,1),2713(a,1,2,1)),rewrite([3143(11)])]. 6152 ((x * y) \ (z \ x)) * ((z * x) * y) = T(x,(z * x) * y). [para(2713(a,1),3143(a,2)),rewrite([4407(5),4408(4),14(4)])]. 6185 (x \ (y \ 1)) * T(z,x / y) = (x \ (x \ z)) * (x / y). [back_rewrite(3709),rewrite([6073(4)]),flip(a)]. 6188 x \ T(y,z * (z / x)) = (z \ (z \ y)) * (z * (z / x)). [back_rewrite(3482),rewrite([6073(9)])]. 6233 a(x,x / y,y) = 1. [back_rewrite(4419),rewrite([6132(4),46(5)]),flip(a)]. 6238 L((x * y) \ z,x * y,y * x) = K(y,x) * ((y * x) \ z). [back_rewrite(5163),rewrite([6144(9)])]. 6257 L(x,y / x,y) = x. [hyper(24,a,6233,a)]. 6258 a(x * y,x,y) = 1. [para(17(a,1),6233(a,1,2))]. 6279 L(x,y,y * x) = x. [para(17(a,1),6257(a,1,2))]. 6335 a(x,y,y \ x) = 1. [para(16(a,1),6258(a,1,1))]. 6351 x * ((x \ y) * y) = y * y. [para(6258(a,1),435(a,2,1,2,1)),rewrite([16(2),16(5),16(6),3436(6),2044(7),16(5),13(6),100(5),1839(6),47(4),14(5)])]. 6353 (x \ y) * ((y \ x) * z) = L(z,(y \ x) * x,y). [back_rewrite(831),rewrite([6351(3),3436(6),6073(6),15(2)])]. 6368 L(x \ y,x,y) = x \ y. [para(16(a,1),6279(a,1,3))]. 6416 L(x,y \ 1,y \ x) = x. [para(3143(a,1),6279(a,1,3))]. 6438 a((x * y) * T(z,y),x * (z * y),a(x,y,T(z,y))) = 1. [para(507(a,1),6335(a,1,3))]. 6446 K(x,K(y,x / y)) = 1. [para(18(a,1),3302(a,1,1))]. 6557 K(K(L(x,y,z),z * y),z * (y * x)) = 1. [para(72(a,1),3327(a,1,2))]. 6562 K(x,y) / (x * y) = x \ (y \ 1). [para(20(a,1),3666(a,1,1)),rewrite([4407(6)])]. 6564 T(x,y) / (x * y) = y \ 1. [para(23(a,1),3666(a,1,1))]. 6565 (x / y) \ 1 = y / x. [para(50(a,1),3666(a,1,1)),flip(a)]. 6567 (x * (y * z)) \ (y \ 1) = z \ ((x * y) \ (y \ 1)). [para(114(a,1),3666(a,1,1)),rewrite([6562(7),4407(4),4407(10)]),flip(a)]. 6575 (x / y) \ (y \ 1) = K(x / y,y) / x. [para(67(a,1),3666(a,1,1)),rewrite([4407(7)]),flip(a)]. 6591 L(x,y,z) \ (y \ (z \ 1)) = (y * x) \ (z \ 1). [para(2934(a,1),3666(a,1,1)),rewrite([6562(7),4407(4),4407(9)])]. 6600 (x \ ((y * z) \ (z \ 1))) * (z * (y * (z * (x * u)))) = L(u,x,z * (y * z)). [back_rewrite(6128),rewrite([6567(5)])]. 6606 x * (L(y,z \ x,z) * (x * u)) = ((z * ((z \ x) * y)) * x) * u. [para(73(a,1),104(a,1,2,1))]. 6618 L(x,y \ 1,z * y) = L(x,y \ z,y). [para(73(a,1),181(a,2)),rewrite([1091(2),3143(3),16(2),1091(4)]),flip(a)]. 6623 (((x / (y * z)) * y) * z) \ (x * (a(x / (y * z),y,z) * u)) = L(u,a(x / (y * z),y,z),x). [para(59(a,1),73(a,1,2,2,1)),rewrite([59(15)])]. 6634 L(x,y * z,y \ 1) = L(x,y * z,y). [para(3143(a,1),73(a,1,2)),rewrite([4408(3),45(2),5134(4),4408(5),45(4)]),flip(a)]. 6663 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,u,w),y,z))) \ (v6 * v5). [para(76(a,1),228(a,1)),flip(a)]. 6676 L(x,y \ (x \ 1),z) = (z * (y \ (x \ 1))) \ (z / y). [para(1014(a,1),76(a,2,2)),rewrite([6120(3),6120(7)])]. 6694 T(x * (y / z),L(z,y / z,x)) = T(x * (y / z),x * y). [para(76(a,2),2642(a,1,2))]. 6696 L(x,T(y,z) / x,y \ z) = ((y \ z) * (T(y,z) / x)) \ z. [para(2690(a,1),76(a,2,2))]. 6697 L(x,L(y,z,u) / x,u * z) = ((u * z) * (L(y,z,u) / x)) \ (u * (z * y)). [para(72(a,1),76(a,2,2))]. 6707 L(x,y / x,z \ 1) = ((y / x) \ z) * (z \ y). [para(3143(a,1),76(a,2,1)),rewrite([3143(9),4408(8)])]. 6793 L(L(R(x,y,z),u,w),v5,x \ (v5 \ 1)) = L(R(x,y,z),u,w). [para(4445(a,1),33(a,1,1)),rewrite([33(2),33(4)]),flip(a)]. 6878 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(y * (x \ y),y \ 1). [para(1014(a,1),2757(a,1,2)),rewrite([6120(3),3143(10)])]. 6887 L(K(x * (y * x),x \ 1),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [para(2757(a,1),3940(a,1,1)),rewrite([3436(15)])]. 6890 K(x * (y * x),x \ 1) = K(x,y). [para(2757(a,1),3143(a,2)),rewrite([4407(5),6565(4),3436(3),1829(2),6069(5)]),flip(a)]. 6897 L(K(x,y),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [back_rewrite(6887),rewrite([6890(5)])]. 6946 T(x * (x * (y / (x * z))),x * z) = (z \ x) * y. [para(16(a,1),3139(a,1,1,2,2,2,2)),rewrite([16(6),4408(8)])]. 6951 ((x \ y) * (x * z)) \ u = ((x * z) \ (y \ x)) * u. [para(104(a,1),3139(a,1,1,2,2,2,2)),rewrite([104(10),6946(10),4458(3)]),flip(a)]. 6953 (x \ ((y * z) \ (y \ 1))) * u = (z * x) \ (y \ (y \ u)). [para(341(a,1),3139(a,1,1,2,2,2,2)),rewrite([341(27),6946(26),4417(8),4407(4),5162(10)])]. 6955 ((x * y) \ y) * z = T(x,y) \ z. [para(90(a,1),3139(a,1,1,2,2,2,2)),rewrite([90(7),6946(8)])]. 6968 (x \ (y \ x)) * z = T(y,x) \ z. [para(2690(a,1),3139(a,1,1,2,2,2,2)),rewrite([2690(11),6946(10)])]. 6973 ((x * y) \ (z * x)) * ((z \ x) * y) = T(x,(z \ x) * y). [back_rewrite(6151),rewrite([6951(8),4408(4),45(3)])]. 7004 x * (y \ ((x * (x / y)) \ z)) = x \ z. [para(18(a,1),3218(a,2,2)),rewrite([92(6)])]. 7047 T(x,K((y \ z) * (y * ((z * y) \ x)),y)) = x. [para(16(a,1),3307(a,1,1)),rewrite([16(11)])]. 7257 (T(x,y) * (y * (x * y))) * z = T(x,y) * (y * (x * (y * z))). [para(13(a,1),4559(a,1,1,2,2)),rewrite([13(10)])]. 7262 T(x,y) * (y * ((z / (x * y)) * (x * (y * u)))) = (T(x,y) * (y * z)) * u. [para(18(a,1),4559(a,1,1,2,2)),flip(a)]. 7353 R(x,y,z) * (x * (x * u)) = x * (R(x,y,z) * (x * u)). [para(89(a,1),4770(a,1,2,1,1)),flip(a)]. 7412 a(x / (y * y),y,y * z) = (x * z) \ (y \ ((y * x) * z)). [para(7262(a,1),110(a,1,1)),rewrite([89(1),37(3),89(4),189(10),101(8),4578(7),18(7),5162(7),15(5),89(6),3982(11),4795(11)]),flip(a)]. 7416 x * (T(x,y) * ((z / (x * T(x,y))) * (x * (T(x,y) * u)))) = (x * (T(x,y) * z)) * u. [para(541(a,1),7262(a,1,1)),rewrite([541(12)])]. 7488 x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u)))))) = x \ (y * z). [para(5452(a,1),15(a,1,2)),flip(a)]. 7490 (x * y) * ((x * y) * ((x * z) / (T(u * u,x * y) * (x * ((y * x) * z))))) = (u \ (u \ x)) * y. [para(5452(a,1),21(a,1,2)),rewrite([3436(3),6073(3),1607(17)]),flip(a)]. 7495 x * (x * (((x \ (x \ y)) * z) * u)) = (y * z) * u. [para(5452(a,1),37(a,1,1)),rewrite([7490(15)]),flip(a)]. 7513 L(x,(y \ (y \ z)) * u,y) = L(x,z * u,y). [para(5452(a,1),132(a,1,1,2)),rewrite([7490(15),7495(8),21(6),7490(15),2507(8)]),flip(a)]. 7550 x * ((x \ (x \ y)) * z) = x \ (y * z). [back_rewrite(7488),rewrite([7490(13)])]. 7607 a(x / y,y,z) \ 1 = a(x,y \ 1,y * z). [para(3691(a,1),58(a,1,2,1,2)),rewrite([1014(4),4157(5),3691(6)])]. 7616 T(x,y) / y = y \ x. [para(2690(a,1),3691(a,1,2)),rewrite([4408(5),14(5)])]. 7617 T(x,y) * (y \ x) = (y \ x) * x. [para(4357(a,1),3691(a,1,2)),rewrite([4155(3),4408(7),4408(5),14(7)])]. 7622 x * ((y * x) \ T(z,x / y)) = x \ (z * (x / y)). [para(3691(a,1),3218(a,1,2,2,2,2)),rewrite([1014(4),3691(7),1014(8)])]. 7628 (x * y) \ ((x / z) * (z * y)) = a(x,z \ 1,z * y). [back_rewrite(4157),rewrite([7607(9)])]. 7636 K(x,K(x / y,y)) = 1. [para(18(a,1),4108(a,1,1))]. 7656 L(x,(y \ z) * z,y) = x. [para(4137(a,1),21(a,1,1)),rewrite([6353(5),45(5),4165(6)])]. 7662 K(x \ y,(y \ x) * (z * (y \ x))) = K(z,y \ x). [para(4137(a,1),114(a,1,1,2,2)),rewrite([14(3),6353(8),7656(7),20(5)]),flip(a)]. 7679 L(x,y \ z,(z \ y) * (u * (z \ y))) = L(x,u,z \ y). [para(4137(a,1),132(a,1,1,2,2)),rewrite([14(3),6353(7),7656(6),21(6)]),flip(a)]. 7681 (x \ y) * (z * (y \ x)) = T(z,y \ x). [para(4137(a,1),1359(a,1,2,2,2,2)),rewrite([14(5),90(5),4137(9),14(8),23(8)])]. 7682 a((x \ y) * (z * (x \ y)),y \ x,u) = a(x \ y,z,u). [para(4137(a,1),133(a,1,2,1,2,2)),rewrite([6353(5),7656(4),14(6),19(7)]),flip(a)]. 7701 ((L(x,y,y * z) * (y * (z * y))) \ (y * ((z * y) * x))) * K(L(x,y,y * z),y * (z * y)) = 1. [para(5752(a,1),4137(a,1,2))]. 7707 K(K(x \ y,z * (y \ x)),z) = 1. [para(4137(a,1),6557(a,1,2,2)),rewrite([4145(3),14(6)])]. 7713 K(x \ y,(y \ x) * z) = K(x \ y,z). [para(4137(a,1),177(a,1,1,1,2)),rewrite([4408(2),14(4),5208(8),4458(5),4408(4),20(5),4408(5),4137(8),14(7)]),flip(a)]. 7715 (x \ y) * ((y \ x) * z) = z. [back_rewrite(6353),rewrite([7656(7)])]. 7719 K(x \ y,z * (y \ x)) = K(z,y \ x). [back_rewrite(7662),rewrite([7713(6)])]. 7726 K(K(x,y \ z),x) = 1. [back_rewrite(7707),rewrite([7719(4)])]. 7769 T(T(x,y),y \ x) = x. [para(16(a,1),4209(a,2)),rewrite([4505(2)])]. 7772 ((x \ y) * (x * z)) * x = T((y * x) * z,x). [para(104(a,1),4209(a,1,1)),flip(a)]. 7775 T(x,y) * y = T(x * y,y). [para(90(a,1),4209(a,1,1)),flip(a)]. 7789 T(x,y) * (x \ y) = T(y,x \ y). [para(2690(a,1),4209(a,1,1)),flip(a)]. 7820 K((x \ y) * (x * z),x) = K(x * ((y * x) * z),x). [back_rewrite(3323),rewrite([7772(4),4366(6),3934(6,R)]),flip(a)]. 7826 x * K(y * x,y) = T(x,y). [back_rewrite(874),rewrite([7820(6),16(4),7772(9),16(7)])]. 7836 a(x,y,y * z) \ 1 = a(x * y,y,z). [back_rewrite(5921),rewrite([7775(2),4582(3)]),flip(a)]. 7875 K(x,x * (y * x)) = K(x,T(y,x)). [back_rewrite(511),rewrite([7775(2),3935(4,R)])]. 7876 K(x * (y * x),x) = K(T(y,x),x). [back_rewrite(510),rewrite([7775(3),3934(4,R)])]. 7925 T(x,K(y * x,y)) = x. [back_rewrite(7047),rewrite([7820(6),16(4)])]. 7966 ((x * (y \ z)) * y) / T(z,y) = R(x,y \ z,y). [para(4505(a,1),22(a,1,2))]. 7967 x \ T(y,x) = T(x \ y,x). [para(4505(a,1),23(a,1,2))]. 7969 (x \ y) * (((y \ x) * z) * T(y,x)) = (z * (x \ y)) * x. [para(4505(a,1),104(a,1,2,2)),rewrite([4408(3)])]. 7981 L(x \ y,x,x \ z) = T(z,x) \ ((x \ z) * y). [para(4505(a,1),74(a,2,1))]. 7982 L(x \ y,x,y \ z) = ((y \ z) * x) \ T(z,y). [para(4505(a,1),74(a,2,2))]. 7996 L(T(x,y),(x \ y) * z,y \ x) = z \ ((z * (y \ x)) * y). [para(4505(a,1),181(a,1,1)),rewrite([4408(3)])]. 7997 (x \ y) * (T(x,y) * z) = L(y * z,x,y). [para(4505(a,1),181(a,2,2,1)),rewrite([5444(4),4408(6)]),flip(a)]. 8002 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = R((y * (z * y)) \ x,y * (z * y),u). [para(4505(a,1),121(a,1,1,1))]. 8018 T(x,y) \ (y \ x) = y \ 1. [para(4505(a,1),1091(a,1,1))]. 8020 (x \ y) * ((z * (x \ y)) * x) = ((x \ y) * z) * T(y,x). [para(4505(a,1),189(a,1,2)),flip(a)]. 8036 T(x * (x * (y \ z)),x * (x * T(z,y))) = T(x * (x * (y \ z)),y). [para(4505(a,1),2647(a,1,2,2,2))]. 8054 a(x \ y,y,x) = 1. [para(4505(a,1),6258(a,1,1)),rewrite([4537(3)])]. 8061 T(x * ((x \ y) * z),y) = L(z,x \ y,x) * y. [para(73(a,1),4505(a,1,1)),flip(a)]. 8078 K(T(x,y),K(y \ x,y)) = 1. [para(4505(a,1),4108(a,1,1))]. 8091 x * L(y,T(z,x),z \ x) = L(x * y,z,x). [back_rewrite(5129),rewrite([7997(8)])]. 8098 L(x * ((y \ x) * z),y,x) = x * (y \ (x * z)). [back_rewrite(4261),rewrite([7997(6)])]. 8105 L(x,y,x \ y) = x. [hyper(24,a,8054,a)]. 8106 a(x,y * x,y) = 1. [para(15(a,1),8054(a,1,1))]. 8255 (x * (y / x)) * y = y * (x * (y / x)). [para(4915(a,1),63(a,1,2)),rewrite([14(5)])]. 8296 K(x,y) * (K(y,x) * z) = z. [para(4993(a,1),21(a,1,1)),rewrite([45(6),5011(7)])]. 8298 (x * K(y,z)) * K(z,y) = x. [para(4993(a,1),22(a,1,2)),rewrite([48(6),4996(7)])]. 8302 L(x \ K(y,z),x,K(z,y)) = x \ K(y,z). [para(4993(a,1),74(a,2,2)),rewrite([4407(8),6144(7),14(7)])]. 8308 L(x,K(y,z),K(z,y) * (u * K(z,y))) = L(x,u,K(z,y)). [para(4993(a,1),132(a,1,1,2,2)),rewrite([14(3),8296(7),21(6)]),flip(a)]. 8310 K(x,y) * (z * K(y,x)) = T(z,K(y,x)). [para(4993(a,1),1359(a,1,2,2,2,2)),rewrite([14(5),90(5),4993(9),14(8),23(8)])]. 8311 a(K(x,y) * (z * K(x,y)),K(y,x),u) = a(K(x,y),z,u). [para(4993(a,1),133(a,1,2,1,2,2)),rewrite([8296(5),14(6),19(7)]),flip(a)]. 8328 R(x,x \ y,y \ z) = z / ((x \ y) * (y \ z)). [para(16(a,1),81(a,2,1))]. 8331 T((x * y) / ((z \ x) * y),u) = R(T(z,u),z \ x,y). [para(81(a,1),31(a,1,1))]. 8379 R(x,x \ y,z) = z * ((z \ y) * (y \ x)). [para(81(a,2),1014(a,2)),rewrite([4407(5),4408(4),14(4),169(4)]),flip(a)]. 8393 (x * y) \ R(z,z \ x,y) = y \ (x \ z). [para(81(a,2),1829(a,1,2)),rewrite([4407(8),4408(7),14(7)])]. 8394 R(T(x,y * z),x \ y,z) = ((x \ y) * z) \ (y * z). [para(81(a,2),2643(a,1,1)),rewrite([31(4)])]. 8463 R(x,y \ 1,(x / y) \ z) = R(x,y \ 1,z). [para(1014(a,1),82(a,1,3,1)),rewrite([1014(10),3143(10),4155(9),4408(8),4180(9)])]. 8497 R(x,y,(x * y) \ T(z,y / x)) = T(z,y / x) * ((z * (y / x)) \ y). [para(3218(a,1),82(a,2,2)),rewrite([3691(3),1014(4),3691(7),1014(8),3691(9),1014(10),4155(11)])]. 8532 T(x,y) \ x = K(x \ y,x). [para(2642(a,1),4539(a,2,1)),rewrite([4408(3),7713(4)]),flip(a)]. 8534 K(x \ y,x) = K(y,y \ x). [para(4539(a,2),2711(a,2)),rewrite([159(2),4365(2),8532(2)])]. 8593 x / T(x,y) = K(x \ y,x). [back_rewrite(4365),rewrite([8532(4)])]. 8594 K(x \ y,x) = K(y,y * x). [back_rewrite(3935),rewrite([8532(4)]),flip(a)]. 8609 x * (L(y,z \ x,z) * x) = (z * ((z \ x) * y)) * x. [para(8061(a,1),90(a,1,2))]. 8679 L(x,y,z * (y * x)) = L(x,y,z). [para(17(a,1),3199(a,1,3)),flip(a)]. 8681 L(x,y,(z * y) * x) = L(x,y,R(z,y,x)). [para(22(a,1),3199(a,1,3)),flip(a)]. 8684 L(L(x,y,z),u,w / (u * x)) = L(L(x,u,w),y,z). [para(3199(a,1),34(a,1,1)),flip(a)]. 8701 L(x \ y,x,z) = ((z / y) * x) \ z. [para(3199(a,1),74(a,1)),rewrite([16(4),16(6),18(6)])]. 8972 (x \ y) * (x * x) = T(x * y,x * x). [para(3476(a,1),13(a,1)),rewrite([14(3),14(6)])]. 8992 ((x \ y) * (x * (x * z))) / T(z,T(x * y,x * (x * z))) = T(x * y,x * (x * z)). [para(3476(a,1),165(a,1,1))]. 9001 T(x,(y \ z) * (y * (y * x))) = T(x,T(y * z,y * (y * x))). [para(3476(a,1),1708(a,1,2))]. 9018 (x * y) * T(z * (z * x),y) = x * (z * (z * (x * y))). [para(2647(a,1),3476(a,1,2)),rewrite([15(7)])]. 9031 ((x \ y) * z) * (y \ x) = T(z,y \ x). [para(4137(a,1),3476(a,1,2,2,2)),rewrite([14(6),4209(5),7681(4),4408(4),4137(8),14(7)]),flip(a)]. 9037 (K(x,y) * z) * K(y,x) = T(z,K(y,x)). [para(4993(a,1),3476(a,1,2,2,2)),rewrite([14(6),4209(5),8310(4),6144(4),4993(8),14(7)]),flip(a)]. 9050 x * ((x * (y * x)) \ z) = y \ (x \ z). [para(18(a,1),3541(a,1,2,2)),rewrite([92(8)]),flip(a)]. 9085 x * a(y,z,z \ (y \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [back_rewrite(3093),rewrite([9050(4)])]. 9101 (x * (((y * z) * (z * y)) * u)) * a(x,(z * y) * (y * z),u) = (x * ((z * y) * (y * z))) * u. [para(178(a,1),312(a,1,1,2)),rewrite([3308(9),3308(14)])]. 9104 ((x * y) * (y * x)) * T(z,y * x) = (y * x) * (K(x,y) * (z * (y * x))). [para(90(a,1),178(a,1,2,2)),flip(a)]. 9114 ((x * ((y * z) * (z * y))) * u) / (((z * y) * (y * z)) * u) = R(x,(y * z) * (z * y),u). [para(178(a,1),121(a,1,2)),rewrite([3308(4),3308(14)])]. 9186 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,(y \ z) * (y * x),y). [para(179(a,1),3143(a,2)),rewrite([4407(4),4407(3)])]. 9191 x \ ((y \ z) * (((z \ y) * x) * u)) = L(u,(z \ y) * x,y \ z). [para(4137(a,1),179(a,1,1,1)),rewrite([13(2),4408(4),100(7),7715(6),4408(9),100(12),7715(11)])]. 9195 (T(x,y) * z) \ (y * (((y \ (y \ x)) * (y * z)) * u)) = L(u,x * (y * z),y). [para(4505(a,1),179(a,1,1,1)),rewrite([7513(14)])]. 9198 x \ (K(y,z) * ((K(z,y) * x) * u)) = L(u,K(z,y) * x,K(y,z)). [para(4993(a,1),179(a,1,1,1)),rewrite([13(2),6144(4),100(7),8296(6),6144(9),100(12),8296(11)])]. 9423 (x * ((x \ (y \ 1)) * ((y * z) * (y \ u)))) \ ((z / y) * u) = a(x,x / y,(y * z) * (y \ u)). [para(1014(a,1),4025(a,1,2,1)),rewrite([4408(6),45(5),3143(7),1014(14),4408(15),45(14),3143(16)])]. 9444 (x * ((x \ K(y,z)) * (K(z,y) * u))) \ u = a(x,x * K(y,z),K(z,y) * u). [para(4993(a,1),4025(a,1,1,2,2,2)),rewrite([6144(4),14(6),8298(10),6144(11),4993(14),14(13)])]. 9484 ((T(T(x,y),z) * (z * u)) * z) / (w * (w * ((T(T(x,z),y) * (z * u)) * z))) = w \ (w \ 1). [para(1907(a,1),21(a,1,2)),rewrite([3436(3),1607(17)]),flip(a)]. 9490 x \ (y * (x \ z)) = (x \ (y / x)) * z. [para(1907(a,1),129(a,1,1,2,2,2,2,2)),rewrite([9484(13),16(4),9484(15),16(6),9484(17),16(8),14(8),1014(7),3143(6),16(5),3143(4),9484(16),16(7),9484(18),16(9),9484(20),16(11),9484(22),16(13),3143(12),16(11),3143(10),3143(10),16(9),3143(8)]),flip(a)]. 9548 x * (x * (y * (x * (x * (y * (z \ ((y / z) \ (x \ (x \ (y \ 1)))))))))) = x * x. [para(14(a,1),3947(a,2,2)),rewrite([4407(6),5162(6)])]. 9553 x * (y * (y * (x * (z \ ((x * (y * (y * (x / z)))) \ u))))) = u. [para(3947(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 9559 L(x,y \ z,y) = L(x,y * z,y). [para(3947(a,1),132(a,1,1)),rewrite([5162(7),7004(9),16(6),16(5),136(6),21(6),5162(7),7004(9),16(6),16(5),2507(6)]),flip(a)]. 9575 L(x,(y * z) / x,y) = (((y * z) / x) \ y) * z. [para(3947(a,1),76(a,2,2)),rewrite([9553(10),9553(13),4501(9)])]. 9640 x * (L(y,z * x,z) * x) = (z * ((z \ x) * y)) * x. [back_rewrite(8609),rewrite([9559(2)])]. 9719 L(x,y \ 1,z * y) = L(x,y * z,y). [back_rewrite(6618),rewrite([9559(6)])]. 9729 x * (L(y,z * x,z) * (x * u)) = ((z * ((z \ x) * y)) * x) * u. [back_rewrite(6606),rewrite([9559(2)])]. 9737 K(L(x * y,x * z,x),z) = K(z * ((z * x) * y),z). [back_rewrite(5742),rewrite([9559(3)])]. 9755 x * L(y,z * x,z) = z * ((z \ x) * y). [back_rewrite(5070),rewrite([9559(2)])]. 9786 L(x * (y * z),x * y,x) = (x * y) * z. [back_rewrite(3018),rewrite([9559(4)])]. 9791 T(x,L(y * z,y * x,y)) = T(x,(x * y) * z). [back_rewrite(2700),rewrite([9559(3)])]. 9832 x \ (y * ((y \ x) * z)) = L(z,y * x,y). [back_rewrite(73),rewrite([9559(6)])]. 10000 (x / y) * ((y / x) * z) = L(z,y / x,x / y). [para(5359(a,1),21(a,1,1)),rewrite([45(6)])]. 10094 R(x,y,(x * y) \ z) * ((y * ((x * y) \ z)) / z) = 1. [para(82(a,2),5359(a,1,1))]. 10140 (x * (y / x)) * ((x * (y / x)) * z) = (x * (y * (y / x))) * z. [para(6446(a,1),178(a,1,2,1)),rewrite([5068(3),5068(6),13(7),2853(9),5068(11),189(11),18(8)])]. 10215 x / (y / z) = x * (z / y). [para(6565(a,1),1014(a,1,2)),flip(a)]. 10221 L(x,y / z,z / y) = x. [para(6565(a,1),3266(a,1,3))]. 10229 (x / y) \ z = (y / x) * z. [para(6565(a,1),3143(a,1,1)),flip(a)]. 10233 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(81(a,2),6565(a,1,1)),rewrite([6071(8)])]. 10235 R(x,y,(x * y) \ z) \ 1 = (y * ((x * y) \ z)) / z. [para(82(a,2),6565(a,1,1))]. 10279 ((x * y) / z) * (z / y) = R(x,y,z \ 1). [back_rewrite(1836),rewrite([10215(4)])]. 10287 (x / y) * ((y / x) * z) = z. [back_rewrite(10000),rewrite([10221(7)])]. 10295 L(x,(y * z) / x,y) = ((x / (y * z)) * y) * z. [back_rewrite(9575),rewrite([10229(6)])]. 10296 x * (x * (y * (x * (x * (y * (z \ ((z / y) * (x \ (x \ (y \ 1)))))))))) = x * x. [back_rewrite(9548),rewrite([10229(6)])]. 10305 R(x,y \ 1,(y / x) * z) = R(x,y \ 1,z). [back_rewrite(8463),rewrite([10229(4)])]. 10321 L(K(x,y),(y / x) * (x * x),y / x) = x \ T(x,y). [back_rewrite(6897),rewrite([10229(9),3169(9),4505(8),15(9)])]. 10323 L(x,y / x,z \ 1) = R(x,y \ 1,z). [back_rewrite(6707),rewrite([10229(6),169(8),4180(8)])]. 10326 K(x / y,y) / x = (y / x) / y. [back_rewrite(6575),rewrite([10229(4),1014(4)]),flip(a)]. 10347 L((x / y) * z,y / x,y) = x * (y \ z). [back_rewrite(5155),rewrite([10229(2)])]. 10366 (x / y) * (x \ y) = K(x \ 1,y). [back_rewrite(3231),rewrite([10229(3)])]. 10367 (x / y) * (y * (x \ z)) = L(z,x \ 1,y). [back_rewrite(3229),rewrite([10229(4)])]. 10393 (x / y) * (((y / x) * z) * x) = (z * (x / y)) * y. [back_rewrite(171),rewrite([10229(3)])]. 10400 (x \ y) / x = x \ (y / x). [para(92(a,1),7616(a,1,1))]. 10401 T(x \ y,z) / x = x \ T(y / x,z). [para(537(a,1),7616(a,1,1))]. 10402 T(T(T(x,y),z),u) / y = y \ T(T(x,z),u). [para(94(a,1),7616(a,1,1))]. 10408 (x / (x * y)) * y = y * (x / (x * y)). [para(2810(a,1),7616(a,1,1)),rewrite([10215(3),10229(6)]),flip(a)]. 10461 T(x,K(x / y,y)) = x. [hyper(28,a,7636,a)]. 10537 R(x,y \ z,T(y,z)) * z = (x * (y \ z)) * T(y,z). [para(2690(a,1),84(a,1,2))]. 10561 T((x * y) * z,R(x,y,z)) = (y * z) * R(x,y,z). [para(84(a,1),4209(a,1,1))]. 10562 R(x,y \ z,y) * T(z,y) = (x * (y \ z)) * y. [para(4505(a,1),84(a,1,2))]. 10592 R(T(x / y,y * z),y,z) = (y * z) \ (x * z). [para(85(a,2),92(a,1,1)),rewrite([31(4)])]. 10670 L(x,y,R(z / y,y,x)) = L(x,y,z * x). [para(85(a,2),3199(a,1,3))]. 10690 ((x / y) * z) \ x = (x * z) \ (x * y). [para(8701(a,1),21(a,2)),rewrite([16(3)]),flip(a)]. 10700 a(x / y,z,(x * z) \ (x * y)) = a(x,z,(x * z) \ (x * y)). [para(8701(a,2),57(a,1,1,2,2)),rewrite([10690(6),1105(6),10690(8)]),flip(a)]. 10702 K(x * (y / x),x / y) = K(x \ 1,y). [para(8701(a,2),67(a,1)),rewrite([10215(2),67(3),10215(4),666(5),5152(3),10215(5)]),flip(a)]. 10707 ((x * (y / z)) * z) \ x = L(y \ 1,z,x). [para(1829(a,1),8701(a,1,1)),rewrite([10215(5)]),flip(a)]. 10710 ((x \ y) * z) \ y = (y * z) \ (x * y). [para(2711(a,1),8701(a,2,1,1)),rewrite([659(3)]),flip(a)]. 10725 L(x \ (y * z),x,z) = (x \ y) * z. [para(3691(a,1),8701(a,2,1,1)),rewrite([3143(6),4408(5)])]. 10748 L(x,T(y,z) / x,y \ z) = (z * (T(y,z) / x)) \ (y * z). [back_rewrite(6696),rewrite([10710(9)])]. 10809 (x \ y) * (x * (x * z)) = T(y * x,x) * z. [para(7967(a,1),104(a,1,2,1)),rewrite([4525(5),7775(6)])]. 10810 R(T(x,y),y,y \ z) = ((y \ x) * (y * z)) / z. [para(7967(a,1),191(a,1,1,2,1)),rewrite([4525(4)]),flip(a)]. 10885 T(x,T(y * z,y * (y * x))) = T(x,T(T(z * y,y),x)). [back_rewrite(9001),rewrite([10809(4),2652(4)]),flip(a)]. 10888 T(x * y,x * (x * z)) = T(T(y * x,x),z). [back_rewrite(8992),rewrite([10809(4),10885(8),965(8)]),flip(a)]. 10900 T((x \ y) * (z * z),T(y,x)) = T(z * (z * (x \ y)),x). [back_rewrite(8036),rewrite([10888(7),101(3),4209(4),4578(3)])]. 10920 T(x * (y * y),x / z) = T(y * (y * x),z \ 1). [back_rewrite(5480),rewrite([10888(6),101(2),4209(3),4578(2)])]. 10927 T(x * (x * y),y \ z) = T(y * (x * x),z). [back_rewrite(5468),rewrite([10888(9),101(6),4209(7),4578(6)])]. 11076 L(T(x * y,x * z),L(y \ z,y,x),u) = (u * L(y \ z,y,x)) \ (u * (x * z)). [para(2705(a,1),74(a,1,1))]. 11083 (x \ y) * (z * (z * x)) = T(y * (z * z),x). [para(2254(a,1),2705(a,1,1)),rewrite([100(3),4408(4),100(6),100(8),10888(9),101(6),4209(7),4578(6)])]. 11138 (x * (y * (x \ (z / x)))) * (T(y,x \ (z / x)) \ x) = z. [para(1014(a,1),3544(a,1,1,2,2,2)),rewrite([3143(6),4408(6),45(2),1014(11),3143(10),3143(10),4155(9)])]. 11215 x * (((x \ y) / z) / T(x * y,z \ 1)) = x \ (z \ 1). [para(3640(a,1),15(a,1,2)),flip(a)]. 11218 K(x * y,x \ 1) = K(y,y \ (x \ 1)). [para(3640(a,1),20(a,1,2)),rewrite([11215(8),4505(4),8532(6),4408(3),45(2),11215(12)])]. 11219 ((x \ y) / z) / T(x * y,z \ 1) = x \ (x \ (z \ 1)). [para(3640(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 11221 x * (x / T(x * y,y \ x)) = y \ x. [para(47(a,1),3640(a,1,2,2,1)),rewrite([4408(5),14(5),989(5),1014(6),4408(8),14(8)])]. 11253 R(x,x \ (y \ 1),y * z) = z / ((x \ (y \ 1)) * (y * z)). [para(3640(a,1),82(a,1,3,1)),rewrite([11219(7),16(5),4408(6),45(5),11219(12),16(10),11219(15),16(13),16(12),4408(11),45(10)])]. 11256 (x \ (K(y \ (x \ 1),y) / x)) * z = (x \ T(x \ 1,y)) * z. [para(3640(a,1),178(a,1,1)),rewrite([11219(9),16(7),11219(13),16(11),16(10),3143(9),3143(9),9490(7),11219(14),16(12),4505(11),11219(17),16(15),16(14),1014(13),10401(11),989(9)])]. 11276 x / T(y * (y * (x * z)),z \ 1) = y \ (y \ (z \ 1)). [para(3641(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 11282 x * (x * ((y * z) / T(x * (x * (y * ((z * y) * u))),u \ (y \ 1)))) = u \ (y \ 1). [para(189(a,1),3641(a,1,2,2,2,1,2,2)),rewrite([4407(9),4407(16)])]. 11295 x * (x * (x / T(x / y,y * (x * x)))) = y * (x * x). [para(3641(a,1),3641(a,1,2,2,2,1,2)),rewrite([1014(3),11276(8),4408(7),4408(5),4408(4),45(3),4578(3),14(5),11276(14),4408(13),4408(11),4408(10),45(9),4578(9),14(11)])]. 11597 L(K(x,y) * z,K(y,x),u) = (u * K(y,x)) \ (u * z). [para(4993(a,1),180(a,1,1,2)),rewrite([6144(2),14(4),8298(10)])]. 11625 R(x,(x \ (y / x)) * (x * z),u) = ((y * z) * u) / (((x \ (y / x)) * (x * z)) * u). [para(18(a,1),183(a,1,1,1,1)),flip(a)]. 11645 (((x \ y) * z) * u) / (((y \ (x \ 1)) * (y * z)) * u) = R(y,(y \ (x \ 1)) * (y * z),u). [para(3143(a,1),183(a,1,1,1,1))]. 11726 a((x \ y) / z,x,T(y,x) \ ((x \ y) * z)) = a(x \ y,x,T(y,x) \ ((x \ y) * z)). [para(4505(a,1),10700(a,1,3,1)),rewrite([4505(10)])]. 11803 (x * ((y \ z) * z)) \ (x * ((y \ z) * ((y \ z) * u))) = L(T(y,z) \ u,(y \ z) * z,x). [para(2690(a,1),3141(a,1,2,2)),rewrite([2690(9)]),flip(a)]. 11853 L(x,(y \ z) * u,z \ y) = L(x,y \ z,u * (z \ y)). [para(4505(a,1),7679(a,1,3,2)),rewrite([90(5),4408(6)]),flip(a)]. 11861 x \ ((y \ z) * (((z \ y) * x) * u)) = L(u,z \ y,x * (y \ z)). [back_rewrite(9191),rewrite([11853(10)])]. 11862 L(T(x,y),x \ y,z * (y \ x)) = z \ ((z * (y \ x)) * y). [back_rewrite(7996),rewrite([11853(5)])]. 12076 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,y,z),u,w))) \ (v6 * v5). [para(34(a,1),6663(a,2,1,2,2))]. 12077 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = ((L(L(x,u,w),y,z) / v5) / v6) * (v6 * v5). [para(37(a,1),6663(a,2,1)),rewrite([2507(8),37(15),4501(16),1091(12),4407(12),10229(12),1014(12)])]. 12303 K(K(x,y),x) = 1. [para(15(a,1),7726(a,1,1,2))]. 12307 T(K(x,y),x) = K(x,y). [hyper(28,a,12303,a)]. 12308 K(x,y) * x = x * K(x,y). [para(12303(a,1),63(a,1,2)),rewrite([14(4)]),flip(a)]. 12309 K(x,K(x,y)) = 1. [para(12303(a,1),4993(a,1,1)),rewrite([13(4)])]. 12310 (x * K(x,y)) * ((x * K(x,y)) * z) = x * (x * (K(x,y) * (K(x,y) * z))). [para(12303(a,1),178(a,1,2,1)),rewrite([13(7),12308(8),189(11),12308(8),4578(10),37(12),100(10)])]. 12312 T(x,K(x,y)) = x. [hyper(28,a,12309,a)]. 12328 K(x,y) / x = x \ K(x,y). [para(12312(a,1),2711(a,1,2))]. 12349 K(x,y) * y = y * K(x,y). [para(12312(a,1),7616(a,1,1)),rewrite([5005(2),6144(4)]),flip(a)]. 12372 T(T(x,y),y \ 1) = x. [para(1091(a,1),7769(a,1,2)),rewrite([1708(2)])]. 12386 T(x,y / (y * x)) = x. [para(2810(a,1),7769(a,1,1)),rewrite([10229(3),10408(3),1708(4)])]. 12432 T(x,K(y,x)) = x. [para(12312(a,1),7769(a,1,1)),rewrite([6144(2),12349(2),1708(3)])]. 12473 K(x,y) / y = y \ K(x,y). [para(12432(a,1),2711(a,1,2))]. 12504 K(x,x * y) * T(y,x) = y. [para(7925(a,1),23(a,2)),rewrite([7826(5),6144(4)])]. 12506 L(T(x,K(y * L(x,z,u),y)),z,u) = L(x,z,u). [para(7925(a,1),30(a,1)),flip(a)]. 12519 T(x * y,K(x * ((z * x) * y),x * z)) = x * y. [para(189(a,1),7925(a,1,2,1))]. 12671 x \ K(x / y,y) = (y / x) / y. [para(10461(a,1),2711(a,1,2)),rewrite([10326(3)]),flip(a)]. 12698 T(T(K(x,y),z),x) = T(K(x,y),z). [para(12307(a,1),29(a,1,1)),flip(a)]. 12705 x * ((x \ (y / x)) * K(x \ (y / x),z)) = y * (x \ K(x \ (y / x),z)). [para(12307(a,1),3575(a,1,2,2)),rewrite([12308(11)]),flip(a)]. 12809 R(T(x \ 1,(x \ y) * z),y,z) = (y * z) \ ((x \ y) * z). [para(6071(a,1),2643(a,1,1)),rewrite([31(6)])]. 12830 (x \ K(y,z)) * K(z,y) = x \ 1. [para(4993(a,1),6071(a,1,2)),rewrite([48(6),4996(9)])]. 12856 L(L(T(x,K(y * L(x,z,u),y)),w,v5),z,u) = L(L(x,z,u),w,v5). [para(12506(a,1),34(a,1,1)),flip(a)]. 12884 (x * R(y,z,(y * z) \ u)) * ((z * ((y * z) \ u)) / u) = x. [para(10094(a,1),104(a,1,2,2)),rewrite([14(9),16(8)]),flip(a)]. 12928 R(x,R(y,z,(y * z) \ u),(z * ((y * z) \ u)) / u) = x. [para(10094(a,1),84(a,1,2)),rewrite([14(10),12884(17)])]. 12931 x / R(y,z,(y * z) \ u) = x * ((z * ((y * z) \ u)) / u). [para(10094(a,1),85(a,2,2)),rewrite([12928(12),48(11)])]. 13311 a(x \ y,x,T(z,y * x)) = a(x,y * x,T(z,y * x)). [para(90(a,1),3968(a,1,3,2)),rewrite([7616(2),90(6),90(7)])]. 13425 T(T(T(x,y),z),y \ 1) = T(x,z). [para(7769(a,1),4214(a,2)),rewrite([8018(7)])]. 13457 L(x,(y \ z) * (y * u),y) = L(x,y * ((z * y) * u),y). [para(187(a,1),132(a,1,2,2)),rewrite([104(4),21(10),2507(10)]),flip(a)]. 13466 a(x,(x \ y) * (x * z),u) = a(x,x * ((y * x) * z),u). [para(187(a,1),133(a,1,1,2)),rewrite([104(9),37(10),4501(11),4498(9),2508(10)]),flip(a)]. 13523 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,y * ((z * y) * x),y). [back_rewrite(9186),rewrite([13457(14)])]. 13639 (x * (y \ z)) * ((z \ y) * u) = (y \ z) * (((z \ y) * x) * u). [para(4137(a,1),190(a,1,2,2)),rewrite([4408(4),14(6),4408(8),5208(12)])]. 13641 T(x,y) * ((y \ z) * (y * u)) = y \ (x * ((z * y) * u)). [para(4505(a,1),190(a,1,1)),rewrite([7550(11)])]. 13663 x / T(x / y,y * (x * x)) = T(y,x * x). [para(11295(a,1),21(a,1,2)),rewrite([23(4),1607(8)]),flip(a)]. 13668 x * (x * (T(y,x * x) * z)) = y * (x * (x * z)). [para(11295(a,1),37(a,1,1)),rewrite([2040(3),13663(8)]),flip(a)]. 13687 ((x / y) * (z * (y * y))) \ (x * (y * T(z,y * y))) = a(x / y,y,y * T(z,y * y)). [para(11295(a,1),60(a,1,1,2)),rewrite([13663(9),13663(15)])]. 13702 (x * (y * (z * (z * u)))) \ ((x * (y * (z * z))) * u) = a(x,y * (z * z),u). [para(11295(a,1),139(a,1,2,1,2)),rewrite([13663(5),13668(5),13663(14),777(13)])]. 13709 L((x * (y * y)) \ z,x * (y * y),y) = (y * T(x,y * y)) \ (y \ z). [para(11295(a,1),3940(a,1,1,1)),rewrite([13663(8),777(7),13663(11)])]. 13734 x * (T(y,x * x) * x) = T(y * (x * x),x). [para(11295(a,1),4209(a,1,1)),rewrite([13663(8),101(7)]),flip(a)]. 13735 T(T(x * (y * y),y),y * T(x,y * y)) = x * (y * y). [para(11295(a,1),4209(a,2)),rewrite([13663(5),101(4),13734(4),13663(8)])]. 13845 L(x,(y * ((y \ z) * u)) * z,L(u,y * z,y)) = L(x,z,L(u,y * z,y) * (y * ((y \ z) * u))). [para(9729(a,1),132(a,1,2,2)),rewrite([9640(6),21(16),9755(12)])]. 13884 L(x,y * (z * y),y) = L(x,y,z). [para(14(a,1),13523(a,1,2,2,1,2)),rewrite([45(5),4505(5),4525(6),5885(6),14(4)]),flip(a)]. 13929 L(x,(y \ z) * u,y \ z) = L(x,z \ y,u * (y \ z)). [para(4137(a,1),13523(a,1,2,2,1,2)),rewrite([4408(5),1014(5),1829(4),4408(5),14(7),3143(8),11861(6),5208(9)]),flip(a)]. 13932 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y) * u,K(z,y)). [para(4993(a,1),13523(a,1,2,2,1,2)),rewrite([6144(5),1014(5),1829(4),6144(5),14(7),3143(8),9198(6),8298(9)])]. 14038 (x * ((x \ (y \ 1)) * ((y * z) * u))) \ ((z / y) * (y * u)) = a(x,x / y,(y * z) * u). [para(15(a,1),9423(a,1,1,2,2,2)),rewrite([15(15)])]. 14083 (x / y) * (y * (x * T(x \ (x \ 1),x * x))) = 1. [para(996(a,1),13687(a,2,3,2)),rewrite([3436(4),8972(6),16(4),87(4),14(3),3436(4),10229(9),3436(13),16(14),1072(13)])]. 14102 T(x,T(x,y) \ 1) = x. [para(541(a,1),12372(a,1,1))]. 14123 T(x,(y / x) / y) = x. [para(5067(a,1),12372(a,1,1)),rewrite([4407(4),10229(4),1014(4)])]. 14124 (x \ (x \ (y \ 1))) * z = x \ (x \ (y \ z)). [para(12372(a,1),3710(a,1,2)),rewrite([7616(7)])]. 14154 K(x,y / (y * x)) = 1. [hyper(27,a,12386,a)]. 14430 T(x,y) * K(x \ y,x) = x. [para(14102(a,1),23(a,2)),rewrite([1014(7),8593(5),4408(6),45(3)])]. 14495 T(x,(T(T(T(y,z),u),x \ 1) / x) / T(T(T(y,x \ 1),z),u)) = x. [para(3382(a,1),14123(a,1,2,1))]. 14546 K(x \ y,x / y) = 1. [para(16(a,1),14154(a,1,2,2))]. 14868 (x * x) / y = x * (x / y). [para(100(a,1),1014(a,1)),rewrite([1014(3)]),flip(a)]. 14874 L(x,y * (y * z),u) = L(x,z,u * (y * y)). [para(100(a,1),132(a,1,1,2,2)),rewrite([100(5),100(9),100(11),4501(12),1091(5),4407(5),5162(5),5610(10),100(7),2507(8)])]. 14882 a(x * (y * y),z,u) = a(x,y * (y * z),u). [para(100(a,1),133(a,1,1,2,2)),rewrite([100(6),100(9),100(11),37(12),4501(13),1091(6),4407(6),5162(6),6141(11),100(7),2508(8)]),flip(a)]. 15035 L(x,y,y * (z * z)) = x. [back_rewrite(5614),rewrite([14874(3)])]. 15045 L(x,y * (z * (z * y)),u * (z * z)) = x. [back_rewrite(2522),rewrite([14874(6)])]. 15052 x * (y * T(y \ (y \ 1),y * y)) = x / y. [para(14083(a,1),15(a,1,2)),rewrite([10229(3),14(3)]),flip(a)]. 15056 L(x * T(x \ (x \ 1),x * x),y,x) = x \ 1. [para(14083(a,1),21(a,1,2)),rewrite([18(2),3200(10)]),flip(a)]. 15079 a((x / y) * (z * (x / y)),y / x,u) = a(x / y,z,u). [para(14083(a,1),133(a,1,2,1,2,2)),rewrite([15052(9),10287(5),14(6),19(7),15052(13)]),flip(a)]. 15120 L(x,y * ((y \ z) * T(z,y)),u * ((y \ z) * (y \ z))) = x. [para(4505(a,1),15045(a,1,2,2,2))]. 15137 K(T(x * y,y),y \ 1) = K(T(x,y) \ 1,x * y). [para(165(a,1),10702(a,1,1,2)),rewrite([7775(2),6564(5)])]. 15143 K(x \ 1,T(y,x)) = K(y,y \ x). [para(2711(a,1),10702(a,1,2)),rewrite([7616(2),16(2)]),flip(a)]. 15144 K(T(x,y),y \ (x \ 1)) = K(y,x). [para(3143(a,1),10702(a,1,1)),rewrite([4155(3),45(2),23(2),6120(4),4408(9),45(7),14(7)])]. 15148 K(x \ 1,y \ x) = K(x / y,y). [para(3666(a,1),10702(a,1,1,2)),rewrite([1014(3),4155(3),16(3)]),flip(a)]. 15149 K(T(x,y),y \ 1) = K(x \ y,x). [para(3666(a,1),10702(a,1,2)),rewrite([4155(3),16(3),4505(2),4408(7),14(7)])]. 15266 (x / y) * ((y * z) / T(x * (y \ x),z)) = (y / x) * z. [para(4254(a,1),15(a,1,2)),rewrite([10229(2)]),flip(a)]. 15271 ((x / y) * (((y / x) * z) * u)) \ (z * u) = a(x / y,(y / x) * z,u). [para(4254(a,1),19(a,1,2,1)),rewrite([15266(8),15266(15)])]. 15276 (x * y) / T(z * (x \ z),y) = (x / z) * ((x / z) * y). [para(4254(a,1),21(a,1,2)),rewrite([3436(4),10229(3),10229(4),1607(12)]),flip(a)]. 15308 a(x / y,(y / x) * ((y / x) * z),u) = a(x / y,z,u). [para(4254(a,1),133(a,1,2,1,2)),rewrite([15276(8),37(8),10287(9),10287(6),19(7),15276(12),2508(12)]),flip(a)]. 15408 T(x \ y,y) * (T(x,y) * z) = T(x,y) \ ((x * y) * z). [para(4314(a,1),15(a,1,2)),flip(a)]. 15409 T(x,y) * (T(x \ y,y) * z) = (x * y) * (T(x,y) \ z). [para(16(a,1),4314(a,1,2,2))]. 15411 a(T(x,y),T(x \ y,y),T(x,y) * z) = a(x,y,z) \ 1. [para(4314(a,1),19(a,1,1)),rewrite([4304(6),4525(5),2548(5)]),flip(a)]. 15452 x \ (y * (y * z)) = ((x \ y) * y) * z. [para(7769(a,1),4314(a,1,1)),rewrite([8018(3),6134(4),7769(6),4525(6),3143(5),7617(6)])]. 15454 x * (T((y / x) / y,K(x / y,y)) * (x * z)) = (x * K(x / y,y)) * z. [para(10461(a,1),4314(a,1,1)),rewrite([12671(3),10461(8)])]. 15593 a(x \ y,z * (x \ y),T(x,y)) = a(x \ y,z,y) \ 1. [para(4344(a,1),19(a,1,1)),rewrite([128(9),2690(7),2548(7)]),flip(a)]. 15621 (((x \ y) * z) * y) \ (x \ y) = T(x,y) \ ((y \ x) / z). [para(4344(a,1),1091(a,1,1)),rewrite([4407(11),4407(10),4408(10),1014(10)])]. 15622 T(x \ y,(z * (x \ y)) * T(x,y)) = T(x \ y,((x \ y) * z) * y). [para(4344(a,1),1708(a,1,2)),flip(a)]. 15645 ((x * (y \ z)) * T(y,z)) * (y \ z) = T(((y \ z) * x) * z,y \ z). [para(4344(a,1),4209(a,1,1)),flip(a)]. 15646 T(T(((x \ y) * z) * y,x \ y),(z * (x \ y)) * T(x,y)) = ((x \ y) * z) * y. [para(4344(a,1),4209(a,2)),rewrite([15645(6)])]. 15674 (((x \ y) * z) * x) \ ((z * (y \ x)) * T(y,x)) = T(y \ x,((y \ x) * z) * x). [back_rewrite(5569),rewrite([15622(14)])]. 15862 x * ((x \ y) * (x \ y)) = y * (x \ y). [para(7769(a,1),4404(a,1,2)),rewrite([7617(7),6351(7)]),flip(a)]. 15916 x \ ((x * y) * z) = (y / x) * (x * z). [para(15(a,1),4504(a,1,2,1,1)),rewrite([1091(2),3143(5),1091(5),1014(6),4209(6)])]. 15922 L(x,x \ y,z * (y \ x)) = ((y \ x) / z) * (z * T(y,x)). [para(4504(a,1),21(a,1,2)),rewrite([7715(4),15916(5),11853(9)]),flip(a)]. 15924 T(x \ y,((y \ x) * z) * y) = T(x \ y,((x \ y) * z) * y). [para(4504(a,1),23(a,1,2)),rewrite([15674(8)]),flip(a)]. 15928 T(x,y \ z) * T(y,z) = (z \ y) * (x * z). [para(37(a,1),4504(a,1,2)),rewrite([7715(7),9031(7)]),flip(a)]. 15940 ((x * (y \ z)) * T(y,z)) / T(y \ z,((z \ y) * x) * z) = ((z \ y) * x) * z. [para(4504(a,1),165(a,1,1))]. 15943 (x \ y) * (((y \ x) / z) * y) = (z \ (x \ y)) * T(x,y). [para(1014(a,1),4504(a,1,2,1)),rewrite([3143(9)])]. 15957 x * L(y,y \ z,x * (z \ y)) = (x * (z \ y)) * T(z,y). [para(4504(a,1),72(a,2)),rewrite([7715(4),11853(4)])]. 16020 L(T(x,y),x \ y,z * (y \ x)) = ((y \ x) / z) * (z * y). [back_rewrite(11862),rewrite([15916(9)])]. 16096 a(x / (y * y),y,y * z) = a(x,y \ 1,y * z). [back_rewrite(7412),rewrite([15916(8),7628(9)])]. 16103 L(x,y * z,y) = L(x,y,z). [back_rewrite(5134),rewrite([15916(3),3276(4)]),flip(a)]. 16229 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y),u). [back_rewrite(13932),rewrite([16103(8)])]. 16231 L(x,y \ z,u * (z \ y)) = L(x,z \ y,u). [back_rewrite(13929),rewrite([16103(4)]),flip(a)]. 16256 L(x,y,z * y) = L(x,y,z). [back_rewrite(13884),rewrite([16103(3)])]. 16286 L(x,(y * ((y \ z) * u)) * z,L(u,y,z)) = L(x,z,L(u,y,z) * (y * ((y \ z) * u))). [back_rewrite(13845),rewrite([16103(6),16103(8)])]. 16343 x \ T(x,y) = K(x,y). [back_rewrite(10321),rewrite([16103(6),2254(4)]),flip(a)]. 16348 x \ (y * ((y \ x) * z)) = L(z,y,x). [back_rewrite(9832),rewrite([16103(6)])]. 16362 T(x,L(y * z,y,x)) = T(x,(x * y) * z). [back_rewrite(9791),rewrite([16103(3)])]. 16364 L(x * (y * z),x,y) = (x * y) * z. [back_rewrite(9786),rewrite([16103(4)])]. 16387 K(L(x * y,x,z),z) = K(z * ((z * x) * y),z). [back_rewrite(9737),rewrite([16103(3)])]. 16398 L(x,y \ 1,z * y) = L(x,y,z). [back_rewrite(9719),rewrite([16103(6)])]. 16465 L(x,y \ z,y) = L(x,y,z). [back_rewrite(9559),rewrite([16103(4)])]. 16470 L(x,y * z,y \ 1) = L(x,y,z). [back_rewrite(6634),rewrite([16103(6)])]. 16484 x \ (y \ (z * (y * x))) = L(T(z,y * x),y,x). [back_rewrite(5138),rewrite([16103(4)]),flip(a)]. 16485 L((x * y) \ z,x,y) = y \ (x \ z). [back_rewrite(3940),rewrite([16103(4)])]. 16487 L(L(x,y,z),z,y) = x. [back_rewrite(667),rewrite([16103(3)])]. 16505 L(T(x,y),y \ x,z) = ((y \ x) / z) * (z * y). [back_rewrite(16020),rewrite([16231(5)])]. 16508 (x * (y \ z)) * T(y,z) = x * L(z,y \ z,x). [back_rewrite(15957),rewrite([16231(4)]),flip(a)]. 16509 ((x \ y) / z) * (z * T(x,y)) = L(y,x \ y,z). [back_rewrite(15922),rewrite([16231(4)]),flip(a)]. 16517 L(x,(y \ z) * u,z \ y) = L(x,z \ y,u). [back_rewrite(11853),rewrite([16231(8)])]. 16564 K(x \ y,x) = K(y,x). [back_rewrite(4516),rewrite([16343(4)])]. 16566 T(x,y) / x = K(x,y). [back_rewrite(4366),rewrite([16343(4)])]. 16568 K(x * y,x) = K(y,x). [back_rewrite(3934),rewrite([16343(4)])]. 16569 K(x \ 1,y * x) = K(y,x). [back_rewrite(3171),rewrite([16343(6)])]. 16603 K(T(x,y),y \ 1) = K(y,x). [back_rewrite(15149),rewrite([16564(6)])]. 16623 T(x,y) * K(y,x) = x. [back_rewrite(14430),rewrite([16564(3)])]. 16660 (x \ (K(x \ 1,y) / x)) * z = (x \ T(x \ 1,y)) * z. [back_rewrite(11256),rewrite([16564(4)])]. 16686 K(x,x * y) = K(x,y). [back_rewrite(8594),rewrite([16564(2)]),flip(a)]. 16687 x / T(x,y) = K(y,x). [back_rewrite(8593),rewrite([16564(4)])]. 16710 K(x,x \ y) = K(x,y). [back_rewrite(8534),rewrite([16564(2)]),flip(a)]. 16711 T(x,y) \ x = K(y,x). [back_rewrite(8532),rewrite([16564(4)])]. 16712 K(T(x,y),K(x,y)) = 1. [back_rewrite(8078),rewrite([16564(3)])]. 16716 x * K(x,y) = T(x,y). [back_rewrite(4535),rewrite([16564(2)])]. 16717 x * (K(x,y) * (x * z)) = (x * T(x,y)) * z. [back_rewrite(4534),rewrite([16564(2)])]. 16735 K(L(x * y,x,z),z) = K((z * x) * y,z). [back_rewrite(16387),rewrite([16568(7)])]. 16813 L(L(T(x,K(L(x,y,z),u)),w,v5),y,z) = L(L(x,y,z),w,v5). [back_rewrite(12856),rewrite([16568(3)])]. 16827 K(x * y,y) = K(T(x,y),y). [back_rewrite(7876),rewrite([16568(3)])]. 16839 K(T(x,y) \ 1,x * y) = K(y,x * y). [back_rewrite(15137),rewrite([16603(5)]),flip(a)]. 16875 K(x,y) * T(y,x) = y. [back_rewrite(12504),rewrite([16686(2)])]. 16909 K(x,y * x) = K(x,T(y,x)). [back_rewrite(7875),rewrite([16686(3)])]. 16936 K(x \ 1,T(y,x)) = K(y,x). [back_rewrite(15143),rewrite([16710(6)])]. 16950 K(x * y,x \ 1) = K(y,x \ 1). [back_rewrite(11218),rewrite([16710(8)])]. 16967 K(x,y \ 1) = K(y,x / y). [back_rewrite(3163),rewrite([16710(3)]),flip(a)]. 16981 x * (y \ K(y \ (x / y),z)) = y * T(y \ (x / y),z). [back_rewrite(12705),rewrite([16716(6)]),flip(a)]. 16984 x * (x * (K(x,y) * (K(x,y) * z))) = T(x,y) * (T(x,y) * z). [back_rewrite(12310),rewrite([16716(2),16716(3)]),flip(a)]. 16985 K(x,y) * x = T(x,y). [back_rewrite(12308),rewrite([16716(4)])]. 16999 a(x,y,K(y,x)) = 1. [back_rewrite(1097),rewrite([16716(2),90(2),46(3)]),flip(a)]. 17019 K(T(x,y) \ 1,x * y) = K(y,T(x,y)). [back_rewrite(16839),rewrite([16909(7)])]. 17040 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(x \ y,y \ 1). [back_rewrite(6878),rewrite([16950(12)])]. 17093 (x \ y) * (((y \ x) * z) * ((z * (x \ y)) * u)) = z * (z * ((x \ y) * u)). [para(4137(a,1),193(a,2,1,2,1,1)),rewrite([4145(5),13639(8),13(10),37(12)])]. 17291 K(x,y \ 1) = K(x,x / y). [para(89(a,1),4809(a,1,1,1,1)),rewrite([101(3),4230(2),15452(7),1091(4),4407(4),4408(4),1014(4),10400(2),4505(3),92(2),4493(3),89(4),16686(6)])]. 17387 (x * T(y,x * x)) \ T(z,x) = ((y * (x * x)) \ z) * x. [para(23(a,1),13709(a,2,2)),rewrite([10725(7)]),flip(a)]. 17666 L(K(x,y),x,y) = K(x,y). [hyper(24,a,16999,a)]. 17730 K(x \ 1,y) = K(x,y \ 1). [para(14546(a,1),63(a,1,2)),rewrite([10366(3),14(5),4493(6)])]. 17771 K(x,T(y,x)) = K(x,y). [back_rewrite(17019),rewrite([17730(5),4407(4),15144(5)]),flip(a)]. 17772 K(x,T(y,x) \ 1) = K(y,x). [back_rewrite(16936),rewrite([17730(4)])]. 17778 (x \ (x \ K(x,y \ 1))) * z = (x \ T(x \ 1,y)) * z. [back_rewrite(16660),rewrite([17730(3),12328(4)])]. 17781 K(x,y \ 1) = K(y,x). [back_rewrite(16569),rewrite([17730(4),4407(3),16710(4)])]. 17822 K(x / y,y) = K(x,y). [back_rewrite(15148),rewrite([17730(4),4408(3),14(3),16710(2)]),flip(a)]. 17906 (x \ T(x \ 1,y)) * z = (x \ (x \ K(y,x))) * z. [back_rewrite(17778),rewrite([17781(3)]),flip(a)]. 17910 K(T(x,y),y) = K(x,y). [back_rewrite(17772),rewrite([17781(4)])]. 17913 K(x \ 1,y) = K(y,x). [back_rewrite(17730),rewrite([17781(6)])]. 17914 K(x,x / y) = K(y,x). [back_rewrite(17291),rewrite([17781(3)]),flip(a)]. 17919 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(y,x \ y). [back_rewrite(17040),rewrite([17781(11)])]. 17924 K(x,y / x) = K(x,y). [back_rewrite(16967),rewrite([17781(3)]),flip(a)]. 17974 x * (T((y / x) / y,K(x,y)) * (x * z)) = T(x,y) * z. [back_rewrite(15454),rewrite([17822(4),17822(9),16716(9)])]. 18023 (x * (y / x)) \ y = K(y,x). [back_rewrite(67),rewrite([17822(5)])]. 18043 K(x * y,y) = K(x,y). [back_rewrite(16827),rewrite([17910(4)])]. 18156 x \ (y * (x / y)) = K(y,x). [back_rewrite(66),rewrite([17924(5)])]. 18422 (T(x,y) * z) / (K(x,y) * z) = R(x,K(x,y),z). [para(16343(a,1),81(a,1,2)),rewrite([16343(6)]),flip(a)]. 18454 L(x,y,x \ 1) = x. [para(1022(a,1),16487(a,1,1))]. 18461 L(x,y,L(x,z,u)) = x. [para(16487(a,1),1689(a,1,1)),rewrite([16487(4)])]. 18472 L(x,x \ y,y) = x. [para(8105(a,1),16487(a,1,1))]. 18473 L(L(x,y,z),z / (y * x),y) = x. [para(3199(a,1),16487(a,1,1))]. 18485 L(R(x,y,z),u,x \ 1) = R(x,y,z). [para(18454(a,1),33(a,1,1)),flip(a)]. 18604 a(x,y \ x,y) = 1. [hyper(25,a,18472,a)]. 18608 L(x,T(y,x),y * x) = x. [para(23(a,1),18472(a,1,2))]. 18650 L(x,y \ 1,x / y) = x. [para(1829(a,1),18472(a,1,2))]. 18689 (x * (y * x)) \ ((x * y) * z) = L(x \ z,x,x * y). [para(101(a,1),74(a,2,1)),flip(a)]. 18690 L(x \ y,x,y * z) = ((y * z) * x) \ (y * (z * y)). [para(101(a,1),74(a,2,2))]. 18703 ((x / (y * z)) * (y * (z * y))) \ (x * y) = a(x / (y * z),y * z,y). [para(101(a,1),60(a,1,1,2))]. 18718 T(x * y,x * x) = T(y * x,x). [para(2690(a,1),101(a,2,2)),rewrite([7789(3),15928(4),8972(3),7775(5)])]. 18724 a(x * y,x,T(z,x)) = a(x,y,z * x) \ 1. [para(101(a,1),507(a,1,2,1)),rewrite([128(7),90(5),2548(7)]),flip(a)]. 18742 a(x,y,y * x) = 1. [para(101(a,1),8106(a,1,2)),rewrite([3982(4),4795(4)])]. 18750 R(x,y * z,y) * (y * (z * y)) = (x * (y * z)) * y. [para(101(a,1),84(a,1,2))]. 18752 R((x * y) / z,z,x) = (x * (y * x)) / (z * x). [para(101(a,1),85(a,2,1))]. 18763 a((x * y) / z,x,L(x \ z,x,x * y)) = a(x * y,x,L(x \ z,x,x * y)). [para(101(a,1),10700(a,1,3,1)),rewrite([18689(7),101(9),18689(12)])]. 18809 (x \ y) * (x * x) = T(y * x,x). [back_rewrite(8972),rewrite([18718(6)])]. 18848 L(x,y,z * (u * (z * (y * x)))) = L(x,y,z * (u * z)). [para(106(a,1),3199(a,1,3)),flip(a)]. 18870 (((x \ y) * z) * ((z * (y \ x)) * T(y,x))) / x = (x \ y) * (z * z). [para(4504(a,1),106(a,1,1,2)),rewrite([7715(14),4578(11)])]. 18962 x / T(x * y,y \ x) = x \ (y \ x). [para(11221(a,1),15(a,1,2)),flip(a)]. 19049 T(T(x,y) \ z,K(T(x,y) \ ((x \ y) * z),T(x \ y,y))) = T(x,y) \ z. [para(11221(a,1),12519(a,1,2,1,2,1)),rewrite([18962(4),6968(3),18962(6),6968(7),18962(10),4505(9),18962(14),6968(13)])]. 19065 x * T(x \ (x \ 1),x * x) = x \ 1. [para(15056(a,1),70(a,1)),flip(a)]. 19074 (x * y) / x = x * (y / x). [para(15056(a,1),72(a,1,2)),rewrite([1014(4),19065(8),1014(5)])]. 19167 a(x,(x / y) * ((x / y) * z),u) = a(y \ (x / y),z,u). [para(18(a,1),4636(a,2,1)),rewrite([3286(6),2508(5)]),flip(a)]. 19178 a(x * (y \ (x * x)),z,u) = a(x / y,x * (x * z),u). [para(1014(a,1),4636(a,2,1)),rewrite([3143(4)])]. 19195 a(T(x,y),(y \ x) * ((y \ x) * z),u) = a((y \ x) * (x * (y \ x)),z,u). [para(4505(a,1),4636(a,2,1)),rewrite([15862(5)]),flip(a)]. 19450 (x * ((T(y,z) * (x * x)) \ u)) \ (T(T(y,x),z) \ 1) = u \ x. [para(4713(a,1),1829(a,1,2)),rewrite([4407(11)]),flip(a)]. 19451 x / (T(T(y,z),u) * ((y \ z) * ((T(y,u) * ((y \ z) * (y \ z))) \ x))) = y \ z. [para(2642(a,1),4713(a,1,2,1,1))]. 19474 (x * (y * y)) \ z = y \ (y \ (x \ z)). [para(4713(a,1),3645(a,1,1)),rewrite([4407(12),19450(12),10927(4),2711(4),4407(13),19450(13)])]. 19479 x / (T(y,z) * ((y \ u) * (T(T(y,u),z) \ x))) = u \ y. [para(7769(a,1),4713(a,1,2,1,1)),rewrite([19474(9),4408(8),4408(9),7715(10)])]. 19486 x / (T(K(y,z),u) * (u \ (K(z,y) * x))) = u. [para(12307(a,1),4713(a,1,2,2,2,1,1)),rewrite([12698(3),19474(6),6144(4),6073(6),7550(7)])]. 19496 x / (T(y,z) * ((u / (u * y)) * ((u * (y * (y / u))) * (T(y,z) \ x)))) = u / (u * y). [para(12386(a,1),4713(a,1,2,1,1)),rewrite([19474(11),10229(10),19074(7),10229(11),19074(5),10140(11)])]. 19499 x / (T(y,z) * (T(y,u) \ ((T(y,z) * (T(y,u) \ (T(y,u) \ 1))) \ x))) = T(y,u) \ 1. [para(14102(a,1),4713(a,1,2,1,1)),rewrite([1014(12),10400(10),989(9),3143(13)])]. 19502 x / (T(y,z) * (((u / y) / u) * ((u * (y * (y / u))) * (T(y,z) \ x)))) = (u / y) / u. [para(14123(a,1),4713(a,1,2,1,1)),rewrite([19474(11),10229(10),10215(7),10229(11),10215(5),10140(11)])]. 19536 x / (T(T(y,z),u) * ((z \ y) * (T(y,u) \ x))) = y \ z. [back_rewrite(19451),rewrite([19474(9),4408(8),4408(9),7715(10)])]. 19567 K(x,y \ x) = K(y,x). [back_rewrite(17919),rewrite([19474(7),4408(5),4408(3),45(2),3032(3),19074(2),15(4),18156(3)]),flip(a)]. 19570 (x * T(y,x * x)) \ T(z,x) = T(x \ (y \ z),x). [back_rewrite(17387),rewrite([19474(8),4505(9)])]. 19639 (x * (y * (z * x))) \ (x * (z * (x * T(y,z * x)))) = a(x * z,x,T(y,z * x)). [para(90(a,1),196(a,1,1,2))]. 19647 (x * ((y \ x) * z)) \ (x * (y \ (x * z))) = a(x / y,x,z). [para(1014(a,1),196(a,2,1)),rewrite([3143(3),3143(7)])]. 19659 a(x / y,x,z) = a(x,y \ x,z). [para(2690(a,1),196(a,2,1)),rewrite([7789(4),4525(5),7997(9),8098(7),19647(7)])]. 19660 (x * (y * (x * z))) \ (x * (y * (x * L(z,x,y)))) = a(x * y,x,L(z,x,y)). [para(72(a,1),196(a,1,1,2))]. 19674 a((x \ y) * z,x \ y,x) = a(x \ y,z,T(y,x)) \ 1. [para(4505(a,1),196(a,1,2,2,2)),rewrite([8020(5),2548(9)]),flip(a)]. 19707 R(x * y,y * x,(y * x) \ (K(y,x) * z)) = R(x * y,K(y,x),z). [para(16(a,1),202(a,2,1,2)),rewrite([6144(5),6144(11),2858(12)])]. 19771 T(x * (x / y),y) = y \ (x * x). [para(87(a,1),10900(a,1,2)),rewrite([3143(4),88(4),1014(5)]),flip(a)]. 19991 (x * (y * x)) / z = x * (y * (x / z)). [para(13(a,1),1851(a,1,1,2,2,2,2)),rewrite([14(4),13(4),13(4),989(8),1014(9),13(8),13(8),13(8)])]. 20016 R((x * y) / z,z,x) = x * (y / z). [back_rewrite(18752),rewrite([19991(7),3691(5),1014(6)])]. 20095 L(a(x / y,y,z),(x / y) * (y * z),u) * ((u * (x * z)) \ (u * ((x / y) * (y * z)))) = 1. [para(1961(a,2),4137(a,1,1))]. 20341 a(x * y,y,x) = 1. [para(15(a,1),18604(a,1,2))]. 20387 a(x,y / x,y) = 1. [para(18(a,1),18742(a,1,3))]. 20390 (x * y) * (y * x) = x * (y * (y * x)). [para(18742(a,1),209(a,1,1)),rewrite([45(5),18742(8),88(8)])]. 20397 a(T(x,y),y,x * y) = 1. [para(90(a,1),18742(a,1,3))]. 20504 ((x * (y * (z * (z * y)))) * u) / (z * (y * (y * (z * u)))) = R(x,y * (z * (z * y)),u). [back_rewrite(9114),rewrite([20390(3),20390(8),2213(9),20390(13)])]. 20509 (x * y) * (K(y,x) * (z * (x * y))) = y * (x * (x * (y * T(z,x * y)))). [back_rewrite(9104),rewrite([20390(3),2213(6)]),flip(a)]. 20510 (x * (y * (z * (z * (y * u))))) * a(x,z * (y * (y * z)),u) = (x * (z * (y * (y * z)))) * u. [back_rewrite(9101),rewrite([20390(3),2213(4),20390(8),20390(13)])]. 20551 a(x,y,x \ y) = 1. [para(2690(a,1),20341(a,1,1)),rewrite([4582(3)])]. 20620 (x * (y * (x / y))) / (y * (x * (y \ x))) = 1. [para(20387(a,1),265(a,1,2,2)),rewrite([8255(3),4230(5),88(8),20387(9)])]. 20692 a(x * (y * z),(x * y) * z,a(x,y,z)) = 1. [para(19(a,1),20551(a,1,3))]. 20939 T(T(x,y),z) / T(x,z) = K(T(x,z),y). [para(29(a,1),16566(a,1,1))]. 20967 ((x * K(y,z)) * y) / T(y,z) = R(x,K(y,z),y). [para(16566(a,1),86(a,1,1,1,2)),rewrite([16566(7)])]. 20994 K((x * y) * z,R(x,y,z)) = K(y * z,R(x,y,z)). [para(84(a,1),16568(a,1,1))]. 21045 L(K(x,y) * z,K(y,x),T(x,y)) = x \ (T(x,y) * z). [para(16623(a,1),74(a,2,1)),rewrite([6144(2)])]. 21062 T(x,y) * (x * z) = x * (T(x,y) * z). [para(16623(a,1),189(a,1,1)),rewrite([16875(7)]),flip(a)]. 21063 K(x,y) * (y * z) = y * (K(x,y) * z). [para(16623(a,1),189(a,2,2,1)),rewrite([16875(3)]),flip(a)]. 21070 x * L(y,K(z,x),T(x,z)) = T(x,z) * (K(z,x) * y). [para(16623(a,1),72(a,1,1))]. 21095 R(x / T(y,z),T(y,z),K(z,y)) = (x * K(z,y)) / y. [para(16623(a,1),85(a,2,2))]. 21316 T((x / y) * (z * (x / y)),y) = (y \ x) * (y \ (z * x)). [para(18(a,1),122(a,1,2,2,2)),rewrite([6135(4)]),flip(a)]. 21447 x * (y \ ((y / x) * z)) = L(z,y / x,y). [para(16(a,1),10347(a,1,1)),rewrite([10229(4)]),flip(a)]. 21463 T(x,y) * ((x * y) \ z) = L(y \ z,y,x). [para(165(a,1),10347(a,1,2)),rewrite([6564(3),3143(3),16256(3)]),flip(a)]. 21472 L((x \ y) * z,y \ x,x) = T(y,x) * (x \ z). [para(2711(a,1),10347(a,1,2)),rewrite([7616(2)])]. 21500 L(x * (y \ z),y,y / x) = (x / y) * z. [para(10347(a,1),16487(a,1,1))]. 21504 L(K(x,y) * z,K(y,x),x) = T(x,y) * (x \ z). [para(16566(a,1),10347(a,1,1,1)),rewrite([16687(4)])]. 21505 L(K(x,y) * z,K(y,x),T(y,x)) = y * (T(y,x) \ z). [para(16566(a,1),10347(a,1,2)),rewrite([16687(2)])]. 21507 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z / y,z))))) = x * x. [back_rewrite(10296),rewrite([21447(8)])]. 21510 R(x,y,(x * y) \ T(z,y / x)) = L(x,y / x,z). [back_rewrite(8497),rewrite([21463(11),10229(7),18(7)])]. 21676 T(a(x,x * y,z),x * (x * ((y * z) / (x * ((x * y) * z))))) = a(x,x * y,z). [para(37(a,1),4950(a,1,2,1)),rewrite([1839(9)])]. 21704 R(x,y * (y * z),z \ ((y \ (y \ z)) * u)) = R(x,z,u). [para(15(a,1),5194(a,2,3)),rewrite([6073(5)])]. 21705 R(x,y * z,(z \ y) * (y \ (y \ u))) = R(x,y \ z,(z \ y) * u). [para(16(a,1),5194(a,1,2,2)),rewrite([4408(5),4408(9)])]. 21708 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * (u * w))) = R(x,z * u,L(w,u,z)). [para(21(a,1),5194(a,2,3)),rewrite([6073(8)])]. 21713 (x * (y * (y * z))) * (z \ (y \ (y \ u))) = z * ((z \ x) * u). [para(5194(a,1),341(a,1,1)),rewrite([16(6),16(5),16(4),200(3)]),flip(a)]. 21715 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * w)) = R(x,z * u,L(u \ w,u,z)). [para(74(a,2),5194(a,2,3)),rewrite([6073(7)])]. 21721 R(x,(y \ (y \ z)) * u,((y \ (y \ z)) * u) \ z) = R(x,z * u,u \ 1). [para(1091(a,1),5194(a,1,3)),rewrite([7550(4),16(3)]),flip(a)]. 21722 R(x,y * (z * (z * y)),K(y,z) * ((y * z) \ ((y * z) \ u))) = R(x,K(z,y),K(y,z) * u). [para(63(a,1),5194(a,1,2,2)),rewrite([20390(3),6144(9),6144(13)])]. 21734 (x * ((x \ ((y \ z) * z)) * (z \ (z \ u)))) / u = R(y \ 1,x,x \ u). [para(5194(a,1),6071(a,2)),rewrite([15452(3),169(7),37(13),16(11),16(10),16(9)])]. 22110 R(T(x,y),y \ x,(x \ y) * z) = ((y \ x) * (y * z)) / z. [para(18454(a,1),203(a,2,1,2,1)),rewrite([3143(4),23(2),3143(4),3143(5),4408(4),3143(8)])]. 22202 ((x \ y) * z) * ((z * (y \ x)) * u) = (x \ y) * (z * (z * ((y \ x) * u))). [para(17093(a,1),15(a,1,2)),rewrite([15452(6),4408(2),4578(3),2040(6)]),flip(a)]. 22239 (x * y) * (T(x,y) \ (y * (x * z))) = y * ((y * x) * z). [para(17093(a,1),190(a,2,2)),rewrite([16(5),6968(6),136(10)])]. 22250 x \ (y * (z * z)) = (x \ y) * (z * z). [back_rewrite(18870),rewrite([22202(7),2690(4),11083(4),7616(4)])]. 22270 x * T(y,x * x) = T(y * x,x). [back_rewrite(1323),rewrite([22250(3),18809(3)]),flip(a)]. 22283 T(x * y,y) \ T(z,y) = T(y \ (x \ z),y). [back_rewrite(19570),rewrite([22270(3)])]. 22354 T(T(x * (y * y),y),T(x * y,y)) = x * (y * y). [back_rewrite(13735),rewrite([22270(6)])]. 22386 L(x,y / x,z) \ (z * y) = T(z * (y / x),z * y). [para(6694(a,1),23(a,2)),rewrite([72(7),18(4)])]. 22398 x \ (y * y) = (x \ y) * y. [para(6257(a,1),6694(a,1,2)),rewrite([19771(3),18718(6),4230(4),4209(5)])]. 22429 a(x * ((y \ x) * x),z,u) = a(x / y,x * (x * z),u). [back_rewrite(19178),rewrite([22398(2)])]. 22608 L(x,y * (z * y),z) = L(x,y,z * (y * z)). [para(13(a,1),16286(a,1,2,1)),rewrite([45(2),101(2),70(4),70(5),45(6),13(6)])]. 22726 T(x,y) / T(T(x,z),y) = K(z,T(x,y)). [para(29(a,1),16687(a,1,2))]. 22862 T(x,y) * K(x,y) = K(x,y) * T(x,y). [para(16712(a,1),63(a,1,2)),rewrite([14(5)]),flip(a)]. 22892 ((x * y) * K(y,z)) / T(y,z) = R(x,y,K(y,z)). [para(16716(a,1),22(a,1,2))]. 22893 x * (x * (K(x,y) * z)) = (x * T(x,y)) * z. [para(16716(a,1),37(a,1,1,2)),flip(a)]. 22906 L(K(x,y) * z,K(y,x),y) = T(y,x) \ (y * z). [para(16716(a,1),74(a,2,1)),rewrite([6144(2)])]. 22923 (x * (y * T(x,z))) \ (x * (y * (x * (K(x,z) * u)))) = L(u,K(x,z),x * (y * x)). [para(16716(a,1),132(a,1,1,2,2))]. 22925 x * ((y * x) * K(x,z)) = (x * y) * T(x,z). [para(16716(a,1),189(a,1,2)),flip(a)]. 22926 T(x,y) * (K(x,y) * z) = K(x,y) * (T(x,y) * z). [para(16716(a,1),189(a,2,2,1)),rewrite([16985(2)])]. 22931 T(x,y) * L(z,K(x,y),x) = x * (K(x,y) * z). [para(16716(a,1),72(a,1,1))]. 22947 R(x,K(x,y),T(x,y) \ z) = z / (K(x,y) * (T(x,y) \ z)). [para(16716(a,1),82(a,1,3,1)),rewrite([16716(7)])]. 22976 a(T(x,y),x * (x * z),u) = a(T(x,y),z,u). [para(16716(a,1),4636(a,2,1)),rewrite([16717(4),101(3),547(2),2508(4)]),flip(a)]. 22979 a(x * y,x,K(x,z)) = a(x,y,T(x,z)) \ 1. [para(16716(a,1),196(a,1,2,2,2)),rewrite([22925(4),2548(7)]),flip(a)]. 23000 (x * T(x,y)) * (K(x,y) * z) = T(x,y) * (T(x,y) * z). [back_rewrite(16984),rewrite([22893(6)])]. 23022 x \ (K(y,x) * (T(x,y) * z)) = L(z,T(x,y),K(y,x)). [para(16875(a,1),21(a,1,1))]. 23033 L(T(x,y) \ z,T(x,y),K(y,x)) = x \ (K(y,x) * z). [para(16875(a,1),74(a,2,1))]. 23108 T(x,y) \ (K(x,y) * (x * z)) = L(z,x,K(x,y)). [para(16985(a,1),21(a,1,1))]. 23144 (x * (y * (y * T(z,u)))) \ ((x * (y * (y * K(z,u)))) * z) = a(x,y * (y * K(z,u)),z). [para(16985(a,1),139(a,1,1,2,2,2))]. 23173 R(x,K(y,z),y) * T(y,z) = (x * K(y,z)) * y. [para(16985(a,1),84(a,1,2))]. 23380 T(x,T(y,x)) = T(x,y). [para(17771(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 23443 T(x,y * x) = T(x,y). [back_rewrite(2652),rewrite([23380(4)])]. 23494 a(x * y,x,z) = a(x,y * x,z). [para(128(a,1),19(a,1,2)),rewrite([196(7)])]. 23575 K(x,y) * (T(y,x) * (K(x,y) * z)) = (y * K(x,y)) * z. [para(16623(a,1),128(a,1,1,2)),rewrite([12349(2)]),flip(a)]. 23584 K(x,y) * (x * (K(x,y) * z)) = (K(x,y) * T(x,y)) * z. [para(16716(a,1),128(a,1,1,2)),flip(a)]. 23589 a(x,y * x,K(x,z)) = a(x,y,T(x,z)) \ 1. [back_rewrite(22979),rewrite([23494(3)])]. 23629 a(x \ y,z * (x \ y),x) = a(x \ y,z,T(y,x)) \ 1. [back_rewrite(19674),rewrite([23494(4)])]. 23643 (x * (y * (x * z))) \ (x * (y * (x * L(z,x,y)))) = a(x,y * x,L(z,x,y)). [back_rewrite(19660),rewrite([23494(11)])]. 23655 (x * (y * (z * x))) \ (x * (z * (x * T(y,z * x)))) = a(x,z * x,T(y,z * x)). [back_rewrite(19639),rewrite([23494(13)])]. 23662 a((x * y) / z,x,L(x \ z,x,x * y)) = a(x,y * x,L(x \ z,x,x * y)). [back_rewrite(18763),rewrite([23494(11)])]. 23663 a(x,y * x,T(z,x)) = a(x,y,z * x) \ 1. [back_rewrite(18724),rewrite([23494(3)])]. 23697 (x / y) * (y * z) = y * ((y \ x) * z). [para(136(a,1),15(a,1,2)),rewrite([15916(3)])]. 23711 (x * y) * (y * ((y \ z) * u)) = y * ((y \ x) * ((y * z) * u)). [para(136(a,1),104(a,1,2,2)),flip(a)]. 23717 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(136(a,1),74(a,2,1)),rewrite([16103(8),16485(7)])]. 23718 (x * y) \ ((x * z) * u) = (y \ x) * ((x \ z) * u). [para(136(a,1),74(a,2,2)),rewrite([4480(5)]),flip(a)]. 23735 x * ((x \ y) * ((x * y) * z)) = y * (x * (y * z)). [para(1091(a,1),136(a,1,2,2,1)),rewrite([3143(5),169(4),23711(5),101(7),128(8)])]. 23736 T(x,(x \ y) * z) = T(x,(x * y) * z). [para(136(a,1),1708(a,1,2)),rewrite([1708(7)]),flip(a)]. 23766 x * (((x \ y) * z) * x) = T((x * y) * z,x). [para(136(a,1),4209(a,1,1)),rewrite([101(7)]),flip(a)]. 23819 K((x \ y) * z,x) = K((x * y) * z,x). [para(136(a,1),16568(a,1,1)),rewrite([16568(7)]),flip(a)]. 23885 L(a(x / y,y,z),y * ((y \ x) * z),u) * ((u * (x * z)) \ (u * (y * ((y \ x) * z)))) = 1. [back_rewrite(20095),rewrite([23697(5),23697(11)])]. 23926 x * ((x \ (y \ z)) * T(y,z)) = L(z,y \ z,x). [back_rewrite(16509),rewrite([23697(5)])]. 23927 L(T(x,y),y \ x,z) = z * ((z \ (y \ x)) * y). [back_rewrite(16505),rewrite([23697(7)])]. 24002 x \ ((x * y) * z) = x * ((x \ y) * z). [back_rewrite(15916),rewrite([23697(6)])]. 24009 (x * ((x \ (y \ 1)) * ((y * z) * u))) \ (y * ((y \ z) * u)) = a(x,x / y,(y * z) * u). [back_rewrite(14038),rewrite([23697(10)])]. 24016 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = L(L(R(x,v5 \ 1,v6),u,w),y,z). [back_rewrite(12077),rewrite([23697(12),4180(12),33(11),33(10)])]. 24021 x * ((x \ y) * (y \ z)) = L(z,y \ 1,x). [back_rewrite(10367),rewrite([23697(4)])]. 24030 a(x,y \ 1,y * z) = a(x,y,y \ z). [back_rewrite(7628),rewrite([23697(4),192(5)]),flip(a)]. 24034 T(x * ((x \ y) * z),y * z) = a(y / x,x,z) \ (y * z). [back_rewrite(4206),rewrite([23697(3)])]. 24035 x * ((x \ y) * ((y / x) * z)) = y * (y * (x \ z)). [back_rewrite(3286),rewrite([23697(5)])]. 24043 R(x,y \ 1,y * z) = R(x,y,y \ z). [back_rewrite(2760),rewrite([23697(3),191(4)]),flip(a)]. 24057 a(x / y,y,z) = a(y,y * x,z). [back_rewrite(60),rewrite([23697(3),4032(5)]),flip(a)]. 24066 (x * y) * ((x * y) * z) = x * (y * (x * (y * z))). [back_rewrite(5783),rewrite([23711(5),23735(5)]),flip(a)]. 24075 (T(x,y) \ (z \ (z \ u))) * ((((u \ z) * z) * K(x,y)) * x) = a(u,z * (z * K(x,y)),x). [back_rewrite(23144),rewrite([23718(10),5162(4),15452(8)])]. 24100 L(x \ y,x,x * z) = T(z,x) \ ((x \ z) * y). [back_rewrite(18689),rewrite([23718(5),6955(5)]),flip(a)]. 24114 a(x \ 1,y,z * (z * u)) = a(x,y * (z * z),u). [back_rewrite(13702),rewrite([23718(9),22250(7),2040(8),6068(9)])]. 24163 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,y * (y * (x / u)),u). [back_rewrite(3753),rewrite([23718(9),5162(3),15452(7)])]. 24164 (x \ (y \ (y \ z))) * (u * ((u \ ((z \ y) * y)) * x)) = a(z,y * (y * u),u \ x). [back_rewrite(3752),rewrite([23718(9),5162(3),15452(6),169(8)])]. 24189 a(x \ 1,y,z) = a(x,y,z). [back_rewrite(19),rewrite([23718(5),6068(5)])]. 24229 (x * (a(y \ x,z,z \ T(y,x)) * u)) / u = L(x,y \ x,z). [back_rewrite(5841),rewrite([23926(5),33(4),480(2)]),flip(a)]. 24261 (x * (y / L(L(z,u,w),v5,v6))) \ (x * y) = L(L(R(z,y \ 1,x),v5,v6),u,w). [back_rewrite(12076),rewrite([24016(6)]),flip(a)]. 24264 R(x,x \ y,z) = L(x,y \ 1,z). [back_rewrite(8379),rewrite([24021(6)])]. 24267 (x * (a(y,z,z \ (y \ x)) * u)) / u = L(x,y \ 1,z). [back_rewrite(5816),rewrite([24021(4),33(5),480(2)]),flip(a)]. 24268 R(x,y,y \ ((x \ y) * z)) = L(x,y \ 1,z). [back_rewrite(4470),rewrite([24021(8)])]. 24279 a(x / (y * y),y,y * z) = a(x,y,y \ z). [back_rewrite(16096),rewrite([24030(8)])]. 24285 a(x,x * y,z) \ 1 = a(y,x,x \ z). [back_rewrite(7607),rewrite([24057(2),24030(8)])]. 24305 T(x * ((x \ y) * z),y * z) = a(x,x * y,z) \ (y * z). [back_rewrite(24034),rewrite([24057(7)])]. 24350 L(a(x,x * y,z),x * ((x \ y) * z),u) * ((u * (y * z)) \ (u * (x * ((x \ y) * z)))) = 1. [back_rewrite(23885),rewrite([24057(2)])]. 24428 ((x / (y * z)) * (y * (z * y))) \ (x * y) = a(y * z,(y * z) * x,y). [back_rewrite(18703),rewrite([24057(11)])]. 24477 ((x / y) * (z * y)) \ (x * T(z,y)) = a(y,y * x,T(z,y)). [back_rewrite(1958),rewrite([24057(9)])]. 24479 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(z,y * (y * (z * x)),u). [back_rewrite(1952),rewrite([24057(15),37(14),2508(15)])]. 24531 (x * (y * (y / x))) * z = x * (y * (y * (x \ z))). [back_rewrite(10140),rewrite([24066(6),23697(5),24035(5)]),flip(a)]. 24558 (x * (y * (x * y))) * z = x * (y * (x * (y * z))). [back_rewrite(426),rewrite([24066(8)])]. 24566 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(z,y,T(x,y)). [back_rewrite(6149),rewrite([24189(10)])]. 24596 a(x,y * (z * z),u) = a(x,y,z * (z * u)). [back_rewrite(24114),rewrite([24189(5)]),flip(a)]. 24624 ((x * y) \ z) * ((z \ x) * y) = a(z,x,y). [back_rewrite(6068),rewrite([24189(8)])]. 24638 (x * y) / ((z \ x) * y) = L(z,x \ 1,y). [back_rewrite(5665),rewrite([24268(4)]),flip(a)]. 24644 x / (T(y,z) * (u * (y * (u \ (T(y,z) \ x))))) = (u / y) / u. [back_rewrite(19502),rewrite([24531(9),23697(10),1829(3),10809(9),13(3),89(2)])]. 24645 (x / y) / x = x / (x * y). [back_rewrite(19496),rewrite([24531(9),3169(10),1091(3),10809(9),13(3),89(2),24644(8)])]. 24749 R(T(x,y),x \ z,u) = L(T(x,y),z \ 1,u). [back_rewrite(8331),rewrite([24638(4),30(4)]),flip(a)]. 24764 x * (T(y / (y * x),K(x,y)) * (x * z)) = T(x,y) * z. [back_rewrite(17974),rewrite([24645(2)])]. 24890 ((K(x,y) * z) \ u) / T(K(y,x),u) = z \ u. [para(19486(a,1),1829(a,1,2)),rewrite([4407(9),4408(9),1014(9)]),flip(a)]. 24897 x * ((T(K(y,z),u) * (u \ (K(z,y) * x))) \ T(w,x * u)) = x \ (w * (x * u)). [para(19486(a,1),3218(a,1,2,2,2,2)),rewrite([19486(17)])]. 24915 x / (K(y,z) * (y \ (K(z,y) * x))) = y. [para(12307(a,1),19486(a,1,2,1))]. 25093 (x \ y) / T(z * (z / x),y) = z \ (z \ y). [para(12372(a,1),5364(a,1,2,2)),rewrite([1014(4),7616(2),1014(4),12372(9)])]. 25357 a(x,y * (x * y),z) = 1. [para(14(a,1),5524(a,1,2,1)),rewrite([45(3),70(3),4578(2),1708(4),14882(4),90(2)])]. 25410 a(x * (y * x),y,z) = 1. [back_rewrite(3735),rewrite([25357(6)])]. 25524 (x * ((x * y) * z)) * ((x * (y * z)) \ T(y,x)) = y * x. [para(22239(a,1),17(a,1,1)),rewrite([4155(8)])]. 26340 (x * (y / x)) * K(y,x) = y. [para(17822(a,1),63(a,1,2)),rewrite([18(6)])]. 26495 K(x,y) * T(x,y) = T(T(x,y),y). [para(17910(a,1),16716(a,1,2)),rewrite([22862(3)])]. 26526 K(x,y) * (x * (K(x,y) * z)) = T(T(x,y),y) * z. [back_rewrite(23584),rewrite([26495(8)])]. 26628 K((x \ y) * z,R(x \ 1,y,z)) = K(y * z,(x \ y) * z). [para(6071(a,1),17914(a,1,2))]. 26642 x * K(y,x) = T(x,x / y). [para(17914(a,1),16716(a,1,2))]. 26699 K(x,y) * (T(y,x) * (K(x,y) * z)) = T(y,y / x) * z. [back_rewrite(23575),rewrite([26642(8)])]. 26745 K(x,y) * y = T(y,y / x). [back_rewrite(12349),rewrite([26642(4)])]. 26753 K(x * y,R(z \ 1,x,y)) = K(x * y,(z \ x) * y). [para(6071(a,1),17924(a,1,2))]. 26764 T(x,y / x) = T(x,y). [para(17924(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 26839 T(x,L(x,y,z)) = x. [para(160(a,1),16487(a,1,1)),rewrite([16487(2)]),flip(a)]. 26897 x / T(y * (y * (x / z)),z) = y \ (y \ z). [para(1925(a,1),21(a,1,2)),rewrite([3436(2),1607(8)]),flip(a)]. 26903 L(x,y,y \ z) = L(x,z,y). [para(1925(a,1),132(a,1,1,2)),rewrite([26897(6),7550(5),16(4),21(4),26897(6),2507(6),16465(4)]),flip(a)]. 26952 T(x,y) \ ((y \ x) * z) = L(y \ z,x,y). [back_rewrite(7981),rewrite([26903(3)]),flip(a)]. 26963 L(x \ y,x,x * z) = L(x \ y,z,x). [back_rewrite(24100),rewrite([26952(7)])]. 26968 a((x \ y) / z,x,L(x \ z,y,x)) = a(x \ y,x,L(x \ z,y,x)). [back_rewrite(11726),rewrite([26952(6),26952(10)])]. 26973 a((x * y) / z,x,L(x \ z,y,x)) = a(x,y * x,L(x \ z,y,x)). [back_rewrite(23662),rewrite([26963(5),26963(9)])]. 27047 x * ((x \ y) * T(z,x)) = (y / x) * (z * x). [para(165(a,1),10393(a,1,2,1,1)),rewrite([6564(3),3143(6),24002(4),6564(7),1014(7)])]. 27119 L(x,y * T(y,z),u * ((z \ y) * (z \ y))) = x. [back_rewrite(15120),rewrite([27047(4),3169(3),4505(2)])]. 27447 ((x * (y * (x \ y))) / (x * (y / x))) * K(x,y) = x * (y / x). [para(20620(a,1),5560(a,1,2)),rewrite([18023(3),4407(10),6144(9),14(9),10229(8),20620(17),88(12)])]. 27454 (x * (y * (y * (y * x)))) \ y = y \ ((y * x) \ (x \ 1)). [para(5600(a,1),17(a,1,1)),rewrite([989(5),4407(5),6567(5)]),flip(a)]. 27459 L(x,y,z * (y * z)) = x. [para(5600(a,1),21(a,1,1)),rewrite([27454(6),24558(10),6600(11),45(5),27454(11),3050(12)])]. 27549 L(x,y * (z * y),z) = x. [back_rewrite(22608),rewrite([27459(6)])]. 27556 (x * (y * (x * y))) \ (x * z) = (y * (x * y)) \ z. [back_rewrite(3118),rewrite([27459(6)]),flip(a)]. 27573 x * (y * (x * (z / (z * (x * (y * (x * z))))))) = z \ 1. [para(5674(a,1),15(a,1,2)),flip(a)]. 27619 (((x * y) * z) * x) * (((z * x) \ ((x * y) \ z)) / z) = 1. [para(5674(a,1),193(a,2)),rewrite([27573(23),4407(9),193(12),169(11),4458(7),1014(10)])]. 27689 (x * (a(x / (y * z),y,z) * u)) / u = R(x,z \ (y \ 1),y). [para(15(a,1),5817(a,1,1,2,1,3)),rewrite([4407(9)])]. 27706 R(x,T(y,x) \ 1,z) = L(x,y \ x,z). [para(2711(a,1),5817(a,1,1,2,1,1)),rewrite([24229(7)]),flip(a)]. 27732 R(((x / (y * z)) * y) * z,x,x \ u) = R(x,z \ (y \ 1),y). [back_rewrite(437),rewrite([27689(12)])]. 27871 L(x,L(x,y,z),u) = x. [para(16487(a,1),6024(a,1,1)),rewrite([16487(4)])]. 28029 L(x,((y * z) \ (y * u)) / x,y * z) = ((y * z) * (L(z \ u,z,y) / x)) \ (y * u). [para(74(a,1),6697(a,1,2,1)),rewrite([16(13)])]. 28379 L(x,(y \ K(z,u)) / x,K(u,z) * y) = (x * (K(u,z) * y)) * (y \ K(z,u)). [para(4993(a,1),28029(a,1,2,1,2)),rewrite([4407(4),6144(3),14(3),8302(12),4993(15),4407(14),4407(13),6144(12),14(12),10229(12),4155(9),6144(8)])]. 28464 T(T(x,y),L(x,z,u)) = T(x,y). [para(26839(a,1),29(a,1,1)),flip(a)]. 28473 L(x,y,z) * x = x * L(x,y,z). [para(26839(a,1),90(a,1,2))]. 28505 x / L(x,y,z) = L(x,y,z) \ x. [para(26839(a,1),7616(a,1,1))]. 28511 T(x,L(x,y,z) \ x) = x. [para(26839(a,1),7769(a,1,1))]. 28851 T(L(x,y,z) * (u / x),L(x,y,z) * u) = T(L(x,y,z) * (u / x),x). [para(18461(a,1),6694(a,1,2)),flip(a)]. 28965 T(x,x / y) = T(x,y \ x). [para(19567(a,1),16716(a,1,2)),rewrite([26642(2)])]. 28991 K(x,y) * y = T(y,x \ y). [back_rewrite(26745),rewrite([28965(4)])]. 29035 K(x,y) * (T(y,x) * (K(x,y) * z)) = T(y,x \ y) * z. [back_rewrite(26699),rewrite([28965(8)])]. 29216 T(x \ y,y) * T(x,y) = T(y,x). [para(23380(a,1),4505(a,2)),rewrite([4278(2)])]. 29325 (x \ y) * (y / x) = y * (x \ (x \ y)). [para(23443(a,1),3218(a,1,2,2)),rewrite([2643(2),3169(7),15(8)]),flip(a)]. 29339 T(x,y) / (y * x) = (y * x) \ x. [para(23443(a,1),7616(a,1,1))]. 29418 (x / y) * (y \ x) = x * (y \ (y \ x)). [back_rewrite(2903),rewrite([29325(6)])]. 29466 T(x,y * ((y \ z) * x)) = T(x,R(z,y,y \ x)). [para(191(a,1),26764(a,1,2)),flip(a)]. 29584 (T(x,y) * z) / a(y \ x,y,z) = (y \ x) * (y * z). [para(4505(a,1),162(a,1,1,1))]. 30202 ((T(x,y) * z) \ T(T(x,y),y)) * (x * z) = T(T(x,z),y). [para(16875(a,1),6152(a,1,2,1)),rewrite([6144(5),26495(5),16875(11),2644(10)])]. 30410 (x \ (T(y,x) \ 1)) * T(z,y \ x) = (x \ (x \ z)) * (y \ x). [para(2711(a,1),6185(a,1,2,2)),rewrite([2711(11)])]. 30432 (x \ (x \ y)) / z = x \ (x \ (y / z)). [para(3691(a,1),6185(a,1,2,2)),rewrite([4407(3),14124(8),6095(4),3691(7),1014(8)]),flip(a)]. 30455 x \ (y * (x / z)) = T(y,x) / z. [para(6185(a,1),3683(a,1,2)),rewrite([1840(5),4505(2)]),flip(a)]. 30508 x * (T(y,x) / z) = y * (x / z). [para(6185(a,1),136(a,1,2,2)),rewrite([1840(5),4505(2),1014(6),90(7)])]. 30512 (x \ (x \ y)) * T(z,y) = (x \ (x \ z)) * y. [para(19486(a,1),6185(a,1,2,2)),rewrite([4407(8),4408(8),1014(8),24890(6),19486(13)])]. 30627 x * ((y * x) \ T(z,x / y)) = T(z,x) / y. [back_rewrite(7622),rewrite([30455(8)])]. 30654 L(x,T(y,z) / x,y \ z) = (y * (z / x)) \ (y * z). [back_rewrite(10748),rewrite([30508(7)])]. 30703 T(T(x,y),y) = T(x,y * y). [para(6188(a,1),45(a,1)),rewrite([48(4),18809(4),4505(2),48(4)])]. 30840 (T(K(x,y),z) * (z \ (K(y,x) * u))) \ T(w,u * z) = (u \ (u \ w)) * (u * z). [para(19486(a,1),6188(a,1,2,2,2)),rewrite([19486(18)])]. 30881 ((T(x,y) * z) \ T(x,y * y)) * (x * z) = T(T(x,z),y). [back_rewrite(30202),rewrite([30703(4)])]. 30944 K(x,y) * (x * (K(x,y) * z)) = T(x,y * y) * z. [back_rewrite(26526),rewrite([30703(7)])]. 30953 K(x,y) * T(x,y) = T(x,y * y). [back_rewrite(26495),rewrite([30703(5)])]. 32180 (x * L(y,z,u)) * y = x * (y * L(y,z,u)). [para(27871(a,1),72(a,1,2)),rewrite([28473(5)])]. 32743 R(x * y,y * x,z) = x * y. [para(4209(a,1),493(a,1,1)),rewrite([4209(5)])]. 32749 (x * T(x,y)) * z = x * (T(x,y) * z). [para(493(a,1),84(a,1,1)),rewrite([21062(3),547(5)]),flip(a)]. 32816 R(x * y,K(y,x),z) = x * y. [back_rewrite(19707),rewrite([32743(7)]),flip(a)]. 32894 x * (K(x,y) * (T(x,y) * z)) = T(x,y) * (T(x,y) * z). [back_rewrite(23000),rewrite([32749(5),22926(4)])]. 33039 L(T(x \ 1,y),x,z) = T(x \ 1,y). [para(1077(a,1),30(a,1,1)),flip(a)]. 33049 a(x,y,T(x,z)) = 1. [hyper(25,a,1685,a)]. 33075 L(x,y,T(x,z)) = x. [para(7769(a,1),1685(a,1,1)),rewrite([7769(5)])]. 33091 a(x,y * x,K(x,z)) = 1. [back_rewrite(23589),rewrite([33049(5),46(6)])]. 33119 a(x / y,z,y \ x) = 1. [para(92(a,1),33049(a,1,3))]. 33180 (T(x,y) * z) * x = T(x,y) * (z * x). [para(33075(a,1),72(a,1,2))]. 33181 (T(x,y) * (z * x)) \ (x * (T(x,y) * z)) = K(x,T(x,y) * z). [para(33075(a,1),2934(a,1,2,1)),rewrite([33075(9)])]. 33249 R(x,y * z,a(x,y,z)) \ ((x * y) * z) = (y * z) * a(x,y,z). [para(54(a,1),166(a,1,2))]. 33258 (x * y) \ ((y * x) * z) = K(y,x) * z. [para(63(a,1),166(a,1,2,1)),rewrite([32816(3)])]. 33300 R(x,K(x,y),z) \ (T(x,y) * z) = K(x,y) * z. [para(16716(a,1),166(a,1,2,1))]. 33324 T(x,y) \ (x * (T(x,y) * z)) = x * z. [para(493(a,1),166(a,1,1)),rewrite([547(3),32749(4)])]. 33334 L(x,K(y,z),z * y) = x. [back_rewrite(2857),rewrite([33258(6),8296(4)]),flip(a)]. 33346 (x * y) * (K(y,x) * z) = (y * x) * z. [back_rewrite(5116),rewrite([33334(4)]),flip(a)]. 33415 x * (y * (y * (x * T(z,y * x)))) = (x * y) * (z * (y * x)). [back_rewrite(20509),rewrite([33346(6)]),flip(a)]. 33450 (x \ (y / x)) * (x * z) = x \ (y * z). [para(18(a,1),168(a,1,2,1)),flip(a)]. 33472 (x \ (y \ 1)) * (x * z) = x \ ((y \ x) * z). [para(3143(a,1),168(a,1,2,1)),flip(a)]. 33476 (x \ (x \ y)) * (x * z) = x \ (T(y,x) * z). [para(4505(a,1),168(a,1,2,1)),flip(a)]. 33497 K(x,y) * (x * z) = T(x,y) * z. [para(16343(a,1),168(a,2,1)),rewrite([547(2),32749(3),15(4)]),flip(a)]. 33507 K(x,y) * (T(y,x) * z) = y * z. [para(16711(a,1),168(a,2,1)),rewrite([32749(4),33324(5)]),flip(a)]. 33511 (x \ K(x,y)) * (x * z) = x \ (T(x,y) * z). [para(16985(a,1),168(a,1,2,1)),flip(a)]. 33545 R(x,x \ (y * z),u) = L(x,z \ (y \ 1),u). [back_rewrite(11625),rewrite([33450(4),33450(9),24638(9),4407(6)])]. 33575 R(x,x \ ((y \ x) * z),u) = L(x,z \ (x \ y),u). [back_rewrite(11645),rewrite([33472(8),24638(8),4407(4),4408(3),14(3),33472(8)]),flip(a)]. 33590 (T(K(x,y),z) * (z \ (K(y,x) * u))) \ T(w,u * z) = u \ (T(w,u) * z). [back_rewrite(30840),rewrite([33476(13)])]. 33664 L(x,y * (z * u),z) = L(x,z,T(y,z) * u). [back_rewrite(9195),rewrite([33476(6),16348(8)]),flip(a)]. 33705 K(x,y) * (T(x,y) * z) = T(x,y * y) * z. [back_rewrite(30944),rewrite([33497(5),22926(4)])]. 33734 L(x,y,K(y,z)) = x. [back_rewrite(23108),rewrite([33497(4),15(4)]),flip(a)]. 33781 T(x,y \ x) * z = x * (K(y,x) * z). [back_rewrite(29035),rewrite([33507(6)]),flip(a)]. 33796 L(x,T(y,z),K(z,y)) = x. [back_rewrite(23022),rewrite([33507(4),15(2)]),flip(a)]. 33957 x \ (y * (x * z)) = T(y,x) * z. [back_rewrite(24897),rewrite([33590(9),16(4)]),flip(a)]. 33969 L(x,y,z * T(z,y)) = x. [back_rewrite(27549),rewrite([33664(3),547(2)])]. 33981 L(a(x,y,z),y,T(x,y) * z) = a(y,x,y * z). [back_rewrite(2971),rewrite([33664(4)])]. 33992 T(x,y) * (T(x,y) * z) = x * (T(x,y * y) * z). [back_rewrite(32894),rewrite([33705(4)]),flip(a)]. 34091 x \ (K(y,x) * z) = T(x,y) \ z. [back_rewrite(23033),rewrite([33796(5)]),flip(a)]. 34275 L(T(x,y * z),y,z) = T(T(x,y),z). [back_rewrite(16484),rewrite([33957(3),23(3)]),flip(a)]. 34415 x / (K(y,z) * (T(y,z) \ x)) = y. [back_rewrite(24915),rewrite([34091(4)])]. 34554 R(x,K(x,y),T(x,y) \ z) = x. [back_rewrite(22947),rewrite([34415(9)])]. 34768 (x * y) \ T(z,y / x) = y \ (T(z,y) / x). [para(30627(a,1),15(a,1,2)),flip(a)]. 34798 x * (T(y * x,x) \ T(z,y \ x)) = T(z,x) / T(y,x). [para(2711(a,1),30627(a,1,2,2,2)),rewrite([7775(2)])]. 34823 (x * y) \ y = y \ (x \ y). [para(12386(a,1),30627(a,1,2,2)),rewrite([101(2),9050(4),29339(5)]),flip(a)]. 34860 R(x,y,y \ (T(z,y) / x)) = L(x,y / x,z). [back_rewrite(21510),rewrite([34768(4)])]. 35223 K(x,y) * (T(x,y) \ z) = x \ z. [para(16(a,1),33300(a,1,2)),rewrite([34554(4)]),flip(a)]. 35247 (K(x,y) * z) * R(x,K(x,y),z) = T(T(x,y) * z,R(x,K(x,y),z)). [para(33300(a,1),4505(a,1,1))]. 35274 K(R(x,K(x,y),z),T(x,y) * z) = K(R(x,K(x,y),z),K(x,y) * z). [para(33300(a,1),16710(a,1,2)),flip(a)]. 35287 K(R(x,K(x,y),z),K(x,y) * z) = K(T(x,y) * z,K(x,y) * z). [para(33300(a,1),19567(a,1,2)),rewrite([35274(10)]),flip(a)]. 35301 K(R(x,K(x,y),z),T(x,y) * z) = K(T(x,y) * z,K(x,y) * z). [back_rewrite(35274),rewrite([35287(10)])]. 35536 L(a(x,y,T(z,y)),x * (z * y),(x * y) * T(z,y)) = a(x,y,T(z,y)). [hyper(24,a,6438,a)]. 35645 (x \ (y \ 1)) * z = (y * x) \ z. [para(13(a,1),6953(a,1,1,2,1)),rewrite([46(3),45(8),45(7)])]. 35648 (x \ (y \ (z \ 1))) * u = ((z * y) * x) \ u. [para(16(a,1),6953(a,1,1,2,1)),rewrite([23717(10),16(9)])]. 35675 (x * ((y * z) \ (y \ 1))) * u = (x / z) * (y \ (y \ u)). [para(1014(a,1),6953(a,2,1)),rewrite([4408(7),45(2),10229(10)])]. 35683 x * (T(y,x) \ (x \ z)) = y \ z. [para(1091(a,1),6953(a,1,1)),rewrite([3143(3),35645(6),5162(4),16(5),4408(6),4408(3),169(6),6968(5)]),flip(a)]. 35698 (x \ ((y \ z) * z)) * u = (((y * x) \ z) * z) * u. [para(3143(a,1),6953(a,1,1,2,1)),rewrite([4408(5),45(3),14(3),4408(2),4408(10),45(9),4408(9),45(7),15452(8)])]. 35803 (x * y) \ (y * z) = y \ ((x \ y) * z). [back_rewrite(33472),rewrite([35645(5)])]. 35829 T(x * y,y) \ T(z,x \ y) = (y \ (y \ z)) * (x \ y). [back_rewrite(30410),rewrite([35645(7),7775(2)])]. 35865 a(x,x / y,(y * z) * u) = a(x,x * y,(y \ z) * u). [back_rewrite(24009),rewrite([35645(6),23718(4),4032(9)]),flip(a)]. 35905 R(x,x \ (y \ 1),y * z) = z * ((y * z) \ (y * x)). [back_rewrite(11253),rewrite([35645(10),4155(9)])]. 35922 R(x,x \ (y \ 1),z) = L(x,y,z \ 1). [back_rewrite(3646),rewrite([35645(9),4155(8),6070(8)])]. 35944 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,y * (y * u),u \ x). [back_rewrite(24164),rewrite([35698(7)])]. 35945 (x * ((y * x) \ z)) / z = R(y \ 1,x,x \ z). [back_rewrite(21734),rewrite([35698(6),169(6),6968(5),35683(5)])]. 35978 T(x,y) / T(z,y) = y \ (x * (z \ y)). [back_rewrite(34798),rewrite([35829(5),7550(5)]),flip(a)]. 36021 x * ((y * x) \ (y * z)) = L(z,y,x \ (y \ 1)). [back_rewrite(35905),rewrite([35922(5),4407(3)]),flip(a)]. 36043 x / R(y,z,(y * z) \ u) = x * R(y \ 1,z,z \ u). [back_rewrite(12931),rewrite([35945(8)])]. 36066 R(x,y,(x * y) \ z) \ 1 = R(x \ 1,y,y \ z). [back_rewrite(10235),rewrite([35945(9)])]. 36081 x \ (y * (T(y,z) \ x)) = K(z,T(y,x)). [back_rewrite(22726),rewrite([35978(4)])]. 36084 x \ (T(y,z) * (y \ x)) = K(T(y,x),z). [back_rewrite(20939),rewrite([35978(4)])]. 36652 (x * y) * T(x * y,y) = x * (x * (y * y)). [para(100(a,1),3184(a,1,2,2)),rewrite([18809(3),540(4),14(2),18809(6),547(7)]),flip(a)]. 37107 L(x,K(y,z),y) = x. [para(33734(a,1),16487(a,1,1))]. 37125 x * (K(x,y) * z) = T(x,y) * z. [back_rewrite(22931),rewrite([37107(3)]),flip(a)]. 37126 T(x,y) \ (x * z) = K(y,x) * z. [back_rewrite(22906),rewrite([37107(4)]),flip(a)]. 37146 L(L(x,T(y,z),u),u * T(y,z),y) = L(x,K(y,z),y * (u * y)). [back_rewrite(22923),rewrite([37125(6),638(8)])]. 37216 L(x,K(y,z),z) = x. [para(17781(a,1),37107(a,1,2))]. 37218 L(x,K(y,z),T(y,z)) = x. [para(17910(a,1),37107(a,1,2))]. 37224 T(x,y) * (x \ z) = K(x,y) * z. [back_rewrite(21504),rewrite([37216(4)]),flip(a)]. 37229 x * (T(x,y) \ z) = K(y,x) * z. [back_rewrite(21505),rewrite([37218(5)]),flip(a)]. 37231 T(K(x,y),z) = K(T(x,z),y). [back_rewrite(36084),rewrite([37224(3),23(3)])]. 37242 K(T(x,y),z) = K(x,T(z,y)). [back_rewrite(36081),rewrite([37229(3),23(3),37231(2)])]. 37402 ((K(x,y) * z) \ u) * K(x,T(y,u)) = z \ u. [back_rewrite(24890),rewrite([37231(5),37242(5),5005(6),37242(5)])]. 37429 T(K(x,y),z) = K(x,T(y,z)). [back_rewrite(37231),rewrite([37242(4)])]. 38196 L(x,K(y,z),T(z,y)) = x. [para(17771(a,1),37216(a,1,2))]. 38207 T(x,y) * (K(y,x) * z) = x * z. [back_rewrite(21070),rewrite([38196(3)]),flip(a)]. 38208 x \ (T(x,y) * z) = K(x,y) * z. [back_rewrite(21045),rewrite([38196(5)]),flip(a)]. 38223 (x \ K(x,y)) * (x * z) = K(x,y) * z. [back_rewrite(33511),rewrite([38208(7)])]. 38305 x * ((x \ (y / x)) * z) = y * (x \ z). [para(18(a,1),169(a,1,1)),flip(a)]. 38314 x * (x * (y * ((y \ (x \ (x \ z))) * u))) = y * ((y \ z) * u). [para(37(a,1),169(a,2)),rewrite([5162(6),21713(7),5162(6)]),flip(a)]. 38342 (x \ y) * (y \ z) = y * ((x * y) \ z). [para(3143(a,1),169(a,1,1)),rewrite([35645(7)])]. 38356 T(x,y) * (y \ z) = y \ (x * z). [para(4505(a,1),169(a,1,1)),rewrite([7550(7)])]. 38365 (x * y) * T(y \ z,y) = (x / y) * (z * y). [para(7967(a,1),169(a,1,2)),rewrite([27047(8)])]. 38393 K(x,y) * (T(y,x * x) * z) = T(y,x) * z. [para(16623(a,1),169(a,1,1)),rewrite([6144(2),37125(3),6144(6),30953(6)]),flip(a)]. 38402 x * (y * (x * ((y * x) \ z))) = (y * x) * (T(y,x) \ z). [para(169(a,1),128(a,1)),rewrite([34823(3),6968(4)]),flip(a)]. 38445 (x * (y * (y * z))) * (z \ u) = z * ((z \ x) * (y * (y * u))). [back_rewrite(5200),rewrite([38314(9)]),flip(a)]. 38475 x * (y * ((x * y) \ z)) = L(z,y \ 1,x). [back_rewrite(24021),rewrite([38342(3)])]. 38476 R(x,y * z,y * ((z * y) \ (y \ u))) = R(x,y \ z,(z \ y) * u). [back_rewrite(21705),rewrite([38342(5)])]. 38485 R(x,x \ y,y \ z) = z / (y * ((x * y) \ z)). [back_rewrite(8328),rewrite([38342(6)])]. 38488 L(x,y,z \ (y \ 1)) = L(x,y,z \ 1). [back_rewrite(6070),rewrite([38342(4),36021(4)])]. 38503 L((x \ y) * z,y \ x,x) = x \ (y * z). [back_rewrite(21472),rewrite([38356(7)])]. 38534 R(x,y * (y * z),z \ u) = R(x,z,((z \ y) * y) * u). [back_rewrite(340),rewrite([38445(5),191(8),15452(3)]),flip(a)]. 38535 (x * y) * (T(x,y) \ z) = y * L(z,y \ 1,x). [back_rewrite(38402),rewrite([38475(4)]),flip(a)]. 38568 x * a(y,z,z \ (y \ x)) = L(x,y,z \ 1). [back_rewrite(9085),rewrite([38475(10),4407(7),16465(8)])]. 38590 x * ((y * x) \ (y * z)) = L(z,y,x \ 1). [back_rewrite(36021),rewrite([38488(8)])]. 38623 L(L(R(x,y,z),u,w),v5,x \ 1) = L(R(x,y,z),u,w). [back_rewrite(6793),rewrite([38488(6)])]. 38642 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(21715),rewrite([38534(9)]),flip(a)]. 38643 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,z,y)). [back_rewrite(21708),rewrite([38534(10)])]. 38644 R(x,y,((y \ z) * z) * ((z \ (z \ y)) * u)) = R(x,y,u). [back_rewrite(21704),rewrite([38534(7)])]. 38658 T(x,y) * (T(x \ y,y) * z) = y * L(z,y \ 1,x). [back_rewrite(15409),rewrite([38535(9)])]. 38713 R(x,K(x,y),z) = x. [para(16985(a,1),170(a,1,1,1)),rewrite([38223(6),18422(5)])]. 38747 K(T(x,y) * z,K(x,y) * z) = K(x,T(x,y) * z). [back_rewrite(35301),rewrite([38713(2)]),flip(a)]. 38752 K(x,T(x,y) * z) = K(x,K(x,y) * z). [back_rewrite(35287),rewrite([38713(2),38747(8)]),flip(a)]. 38770 (K(x,y) * z) * x = T(T(x,y) * z,x). [back_rewrite(35247),rewrite([38713(4),38713(7)])]. 38815 (T(x,y) * (z * x)) \ (x * (T(x,y) * z)) = K(x,K(x,y) * z). [back_rewrite(33181),rewrite([38752(10)])]. 39396 a(x / y,y * (y * z),u) = a(x * y,z,u). [para(33450(a,1),4636(a,1,1,2)),rewrite([23(2),90(2),16(5)]),flip(a)]. 39505 (x * y) \ (x \ 1) = y \ (x \ (x \ 1)). [para(1607(a,1),6591(a,1,1)),flip(a)]. 39506 (x * y) \ (y \ 1) = y \ (x \ (y \ 1)). [para(1667(a,1),6591(a,1,1)),flip(a)]. 39650 (x * (y \ (z \ (z \ 1)))) * u = (x / y) * (z \ (z \ u)). [back_rewrite(35675),rewrite([39505(4)])]. 39699 x / (y * (y * (z * x))) = z \ (y \ (y \ 1)). [back_rewrite(4420),rewrite([39505(8)])]. 39792 x / (y * (z * (y * x))) = y \ (z \ (y \ 1)). [back_rewrite(4421),rewrite([39506(8)])]. 40866 (((x \ y) * z) \ (y * z)) * R(x \ 1,y,z) = K(y * z,(x \ y) * z). [para(26628(a,1),16711(a,2)),rewrite([31(6),12809(6),4408(8)])]. 41620 T(x \ 1,y) * z = T(x,y) \ z. [para(104(a,1),11803(a,1,1)),rewrite([101(2),128(3),15(5),15(5),27556(7),15452(5),1091(3),4407(3),4505(4),1708(6),15(8),33664(9),547(8),33969(9)])]. 41919 x \ ((y \ z) * z) = ((y * x) \ z) * z. [para(2748(a,1),6591(a,1,1)),rewrite([4408(5),4408(3),45(2),14(3),22398(2),4408(9),4408(7),45(6),14(7),22398(6)])]. 42192 (x * (y * z)) \ (x * (u * ((u \ y) * z))) = L(a(y,u,u \ z),y * z,x). [para(192(a,1),74(a,1,1)),flip(a)]. 42198 a(x,x * y,(x * y) \ z) = a(x,y,y \ z). [para(1091(a,1),192(a,1,2,2,1)),rewrite([3143(5),169(4),192(5)]),flip(a)]. 42212 a(x,x * y,z) \ (y * z) = a(y,x,x \ z) * (y * z). [para(192(a,1),4505(a,1,1)),rewrite([24305(9)]),flip(a)]. 42284 L(a(x,x * y,z),x * ((x \ y) * z),u) * L(a(y,x,x \ z),y * z,u) = 1. [back_rewrite(24350),rewrite([42192(13)])]. 42295 T(x * ((x \ y) * z),a(x,x * y,z)) = a(y,x,x \ z) * (y * z). [back_rewrite(4031),rewrite([42212(10)])]. 42314 R(x * y,x,x \ T(z,y)) = (x * (z * y)) / T(z,y). [para(90(a,1),198(a,2,1,2))]. 42356 R(x * (y \ z),x,x \ y) = (x * T(z,y)) / y. [para(4505(a,1),198(a,2,1,2))]. 42387 R(x * (y * z),x,x \ y) = (x * (y * (z * y))) / y. [para(101(a,1),198(a,2,1,2))]. 42416 K(R(x * y,x,x \ z),z) = K(x * (y * z),z). [para(198(a,2),17822(a,1,1))]. 42429 T(x,R(y * z,y,y \ x)) = T(x,y * (z * x)). [para(198(a,2),26764(a,1,2))]. 42662 ((x * y) * R(z,x,y)) / ((z * x) * y) = K(x * y,R(z,x,y)). [para(20994(a,1),16566(a,2)),rewrite([10561(4)])]. 42829 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(16(a,1),7353(a,1,2,2)),rewrite([16(6)])]. 42834 T(R(x,y,z) \ x,x) * (R(x,y,z) * u) = L(x * u,x,R(x,y,z)). [para(7353(a,1),21(a,1,2)),rewrite([42829(5),15452(7),34823(3),4505(4)])]. 42930 a(x \ (y / x),x,z) = a(x,y,z). [para(15(a,1),7682(a,1,2)),rewrite([1091(2),1091(4),1014(5),3143(4),1091(5),24189(6)])]. 42940 a(x * (y \ z),z \ y,u) = a(y \ z,(z \ y) * x,u). [para(4505(a,1),7682(a,1,1,2)),rewrite([90(4),4408(7)])]. 42971 a(x \ y,(y \ x) * z,T(y,x)) = ((z * (x \ y)) * x) \ (z * T(y,x)). [back_rewrite(4335),rewrite([42940(5)])]. 43418 ((x * (y \ z)) * y) * a(y \ z,(z \ y) * x,T(z,y)) = x * T(z,y). [para(7969(a,1),54(a,1,1)),rewrite([7715(13)])]. 44128 a(x,y,y \ z) \ 1 = a(y,y * x,z). [para(18(a,1),4007(a,1,1,2)),rewrite([92(4),169(4),18(7),42295(7),3691(6),18(7)])]. 44649 L(L(x,y / x,z),z * (y / x),z * y) = (z * (y / x)) \ (z * y). [para(76(a,2),6368(a,1,1))]. 44671 L(L(L(x,y,z),u,w),v5 \ 1,v5 \ x) = L(L(x,y,z),u,w). [para(6416(a,1),97(a,2,1,1))]. 44709 L(L(L(L(x,y,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(L(x,u,w),y,z),v5,v6). [para(6416(a,1),229(a,1,1,1)),flip(a)]. 45267 (x * ((x \ y) * z)) / R(T(y,z),x,x \ z) = z. [para(200(a,1),165(a,1,1)),rewrite([31(6)])]. 45271 x * (a(x / (y * z),y,z) * u) = R(x,z \ (y \ 1),y) * u. [para(59(a,1),200(a,2,2,1)),rewrite([27732(6)]),flip(a)]. 45295 R(x,y,T(y \ z,y)) * T(z,y) = (x / y) * (z * y). [para(7967(a,1),200(a,1,1,3)),rewrite([27047(9)])]. 45359 (((x / (y * z)) * y) * z) \ (R(x,z \ (y \ 1),y) * u) = L(u,a(x / (y * z),y,z),x). [back_rewrite(6623),rewrite([45271(9)])]. 45676 (x * y) \ L(y \ z,y,x) = (y * (x * y)) \ z. [para(74(a,2),25093(a,2,2)),rewrite([25093(9),6073(5),1091(3),39506(4),35648(5),101(2)]),flip(a)]. 46495 (R(x / y,y,z) * (y * (z * y))) \ ((x * z) * y) = a(y * z,(y * z) * (x * z),y). [para(85(a,2),24428(a,1,1,1))]. 46497 (R(x \ 1,y,z) * (y * (z * y))) \ (((x \ y) * z) * y) = a(y * z,(y * z) * ((x \ y) * z),y). [para(6071(a,1),24428(a,1,1,1))]. 46810 a(x * y,x * (y * x),z) = a(y,y * x,z). [para(14(a,1),4021(a,1,2,1)),rewrite([1077(4),3143(4),169(3),4032(5),14(6)]),flip(a)]. 46815 a(x,y * (y * (x * (y * z))),u) = a(x,x * (y \ z),u). [para(37(a,1),4021(a,1,1)),rewrite([16103(4),16485(3),23718(9),1091(6),4407(6),23717(6),14(5),4498(7),101(7),128(8),2508(10)]),flip(a)]. 47034 L(L(L(R(x,y \ 1,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(R(x,y \ 1,z),v5,v6),u,w). [para(76(a,1),44709(a,1,1)),rewrite([24261(6),24016(16)])]. 47036 L(L(x,y,z),u \ 1,u \ L(x,w,v5)) = L(x,y,z). [para(16487(a,1),44709(a,1,1,1)),rewrite([16487(8)])]. 47734 L(x,y * z,y * (z * (y * y))) = x. [para(189(a,1),15035(a,1,3)),rewrite([4578(3)])]. 47883 L(K(x,T(y,z)),x,y) = K(x,T(y,z)). [para(17666(a,1),30(a,1,1)),rewrite([37429(2),37429(4)]),flip(a)]. 48247 T(x,R(x,y,z) \ 1) = x. [para(89(a,1),960(a,1,2,1)),rewrite([19074(4),2771(4,R)])]. 48405 T(x,y) \ (y \ z) = y \ (x \ z). [para(3143(a,1),38503(a,2,2)),rewrite([35645(4),4408(5),45(4),2975(4),5147(4)])]. 48721 L(x,y * K(z,u),K(u,z)) = L(x,K(z,u),K(u,z) * y). [para(18(a,1),8308(a,1,3,2)),rewrite([5005(6)]),flip(a)]. 48733 L(x,K(y,z),u * K(z,y)) = L(x,K(z,y),u). [para(4505(a,1),8308(a,1,3,2)),rewrite([90(5),6144(6),16229(8)])]. 48767 a(x * K(y,z),K(z,y),u) = a(K(y,z),K(z,y) * x,u). [para(4505(a,1),8311(a,1,1,2)),rewrite([90(4),6144(7)])]. 48772 a(K(x,y),K(y,x) * z,u) = a(K(x,y),K(x,y) * z,u). [para(101(a,1),8311(a,1,1,2)),rewrite([2508(8),48767(4)])]. 49860 L(x,T(y,z),y) = x. [para(18604(a,1),439(a,1,2,2,1)),rewrite([4247(3),23(2),4505(4),4505(6),480(8),4505(4),13(6),32749(5),21(6)])]. 50186 L(L(R(x,y \ 1,z),u,w),v5,v6) = L(L(L(x,y,z \ 1),u,w),v5,v6). [para(82(a,1),47034(a,2,1,1)),rewrite([1014(5),10229(4),10305(5),47034(10),1014(10),10229(9),3143(10),4155(9),10690(8),38590(9)])]. 50188 L(R(x,y \ 1,z),u \ 1,u \ L(x,w,v5)) = R(x,y \ 1,z). [para(16487(a,1),47034(a,1,1)),rewrite([16487(13)])]. 50190 L(R(x,y \ 1,z),u,w) = L(L(x,y,z \ 1),u,w). [para(18454(a,1),47034(a,1,3,2)),rewrite([18485(6),50186(8),44671(8),38623(11)]),flip(a)]. 50224 R(x,y \ 1,z) = L(x,y,z \ 1). [back_rewrite(50188),rewrite([50190(8),47036(8)]),flip(a)]. 50298 L(x,T(y,x),z \ 1) = L(x,y \ x,z). [back_rewrite(27706),rewrite([50224(4)])]. 50308 R(x,y,y \ z) = L(x,y,z \ 1). [back_rewrite(24043),rewrite([50224(4),4407(3),38488(4)]),flip(a)]. 50323 L(x,y / x,z \ 1) = L(x,y,z \ 1). [back_rewrite(10323),rewrite([50224(7)])]. 50345 ((x / y) * (z * y)) / T(z,y) = L(x,z \ 1,y). [back_rewrite(2802),rewrite([50224(9),4407(8),26903(9)])]. 50347 a(x,T(x,y),z) = 1. [hyper(25,a,49860,a)]. 50359 L(x,y * z,z * y) = x. [para(4209(a,1),49860(a,1,2))]. 50365 L(x,y,T(y,z)) = x. [para(7769(a,1),49860(a,1,2))]. 50404 K(x,y) * ((x * y) \ z) = (y * x) \ z. [back_rewrite(6238),rewrite([50359(5)]),flip(a)]. 50423 R(x,y * (z * (z * y)),(z * y) \ ((y * z) \ u)) = R(x,K(z,y),K(y,z) * u). [back_rewrite(21722),rewrite([50404(9)])]. 50785 L(L(x,y / x,z),z * y,z * (y / x)) = L(x,y / x,z). [para(6694(a,1),18608(a,1,2)),rewrite([72(11),18(8),4581(8)])]. 50886 x * (y \ (y \ 1)) = (x / y) / y. [para(18650(a,1),164(a,1,2)),rewrite([3143(4),29418(3),19074(4),30432(3),47(1),1014(8)])]. 51015 x / (T(y,z) * (T(y,u) * (T(y,z) \ x))) = T(y,u) \ 1. [back_rewrite(19499),rewrite([50886(9),10229(8),10215(7),3228(8),33992(8),37126(9),38393(8)])]. 51318 T(x,y) * (y * (x * y)) = x * (x * (y * y)). [para(20397(a,1),209(a,1,1)),rewrite([7775(3),547(5),36652(5),15452(5),45(2),100(3),20397(10),88(9)]),flip(a)]. 51385 T(x,y) * (y * (x * (y * z))) = x * (x * (y * (y * z))). [back_rewrite(7257),rewrite([51318(4),37(4),100(2)]),flip(a)]. 51470 R(x / (y * ((z * y) \ x)),z,u) = R(z,y,(z * y) \ x). [para(82(a,1),495(a,1,1))]. 51780 (x / (y * (z * x))) * y = L(z \ 1,x \ 1,y). [para(1014(a,1),10707(a,1,1)),rewrite([4155(3),45(2),10229(4)])]. 52573 L(x,y \ 1,z) = L(x,y,z \ 1). [para(14(a,1),24267(a,1,1,2)),rewrite([38568(4),48(5)]),flip(a)]. 52576 x * (a(y,z,z \ (y \ x)) * u) = L(x,y,z \ 1) * u. [para(24267(a,1),18(a,1,1)),rewrite([52573(3)]),flip(a)]. 52596 L(x,y,z \ 1) = L(x,y,z). [para(7679(a,1),24267(a,2)),rewrite([45(2),45(2),45(4),45(4),42198(7),52576(7),4407(3),26903(4),52573(3),17(5),45(5)])]. 52619 T(x,y) \ 1 = T(x \ 1,y). [para(6020(a,1),24267(a,2)),rewrite([52576(11),52596(6),33039(4),41620(4),3666(3)])]. 52627 L(x,y,T(y \ 1,z)) = x. [para(50347(a,1),24267(a,1,1,2,1)),rewrite([13(2),17(2),52573(4),52619(3)]),flip(a)]. 52635 (x / (y * (z * x))) * y = L(z \ 1,x,y). [back_rewrite(51780),rewrite([52573(9),52596(9)])]. 52653 ((x / y) * (z * y)) / T(z,y) = L(x,z,y). [back_rewrite(50345),rewrite([52573(8),52596(8)])]. 52724 T(x,y) * (T(x \ y,y) * z) = y * L(z,y,x). [back_rewrite(38658),rewrite([52573(8),52596(8)])]. 52760 (x * y) * (T(x,y) \ z) = y * L(z,y,x). [back_rewrite(38535),rewrite([52573(7),52596(7)])]. 52764 x * (y * ((x * y) \ z)) = L(z,y,x). [back_rewrite(38475),rewrite([52573(7),52596(7)])]. 52794 R(T(x,y),x \ z,u) = L(T(x,y),z,u). [back_rewrite(24749),rewrite([52573(7),52596(7)])]. 52843 R(x,x \ y,z) = L(x,y,z). [back_rewrite(24264),rewrite([52573(5),52596(5)])]. 52858 L(x,y,z) = L(x,z,y). [back_rewrite(16398),rewrite([52573(4),4407(3),26903(4),52573(3),52596(3)])]. 52942 L(x,y,z / x) = L(x,z,y). [back_rewrite(50323),rewrite([52596(4),52858(2),52596(5)])]. 52953 R(x,y,y \ z) = L(x,y,z). [back_rewrite(50308),rewrite([52596(5)])]. 52963 L(x,y,z \ x) = L(x,y,T(z,x)). [back_rewrite(50298),rewrite([52596(4),52858(2),52858(4)]),flip(a)]. 53065 x * ((y * x) \ (y * z)) = L(z,x,y). [back_rewrite(38590),rewrite([52596(7),52858(5)])]. 53163 L(x,y,y * z) = L(x,y,z). [back_rewrite(16470),rewrite([52596(4),52858(2)])]. 53170 (x \ y) * L(z,x,y) = x \ (y * z). [back_rewrite(6145),rewrite([52596(4),52858(2)])]. 53195 x / (T(y,z) * (T(y,u) * (T(y,z) \ x))) = T(y \ 1,u). [back_rewrite(51015),rewrite([52619(10)])]. 53431 ((x \ y) * z) \ (y * z) = T(T(x,y),z). [back_rewrite(8394),rewrite([52794(4),34275(3)]),flip(a)]. 53473 x / (y * ((z * y) \ x)) = L(z,y,x). [back_rewrite(38485),rewrite([52843(3),26903(2),52858(1)]),flip(a)]. 53483 L(x,y,z \ (x \ u)) = L(x,y,(u \ x) * z). [back_rewrite(33575),rewrite([52843(4),52858(3),52858(6)]),flip(a)]. 53484 L(x,y,z \ (u \ 1)) = L(x,y,u * z). [back_rewrite(33545),rewrite([52843(3),52858(2),52858(6)]),flip(a)]. 53550 L(x,y,z) \ 1 = R(x \ 1,y,z). [back_rewrite(10233),rewrite([52843(2)])]. 53564 (x * y) \ L(z,x,y) = y \ (x \ z). [back_rewrite(8393),rewrite([52843(3)])]. 53598 x * (y * ((x * y) \ z)) = L(z,x,y). [back_rewrite(52764),rewrite([52858(5)])]. 53600 (x * y) * (T(x,y) \ z) = y * L(z,x,y). [back_rewrite(52760),rewrite([52858(5)])]. 53617 T(x,y) * (T(x \ y,y) * z) = y * L(z,x,y). [back_rewrite(52724),rewrite([52858(6)])]. 53634 ((x / y) * (z * y)) / T(z,y) = L(x,y,z). [back_rewrite(52653),rewrite([52858(6)])]. 53804 L(L(x,y,z),z * y,z * (y / x)) = L(x,y,z). [back_rewrite(50785),rewrite([52858(2),52942(2),52858(7),52942(7)])]. 53894 L(x,K(y,z),u * K(z,y)) = L(x,u,K(z,y)). [back_rewrite(48733),rewrite([52858(6)])]. 53895 L(x,K(y,z),K(z,y) * u) = L(x,u,K(y,z)). [back_rewrite(48721),rewrite([52858(4),53894(4)]),flip(a)]. 54309 (x * (y * x)) \ z = x \ (y \ (x \ z)). [back_rewrite(45676),rewrite([52858(3),53564(4)]),flip(a)]. 54321 (((x / (y * z)) * y) * z) \ (R(x,z \ (y \ 1),y) * u) = L(u,x,a(x / (y * z),y,z)). [back_rewrite(45359),rewrite([52858(14)])]. 54371 (x * (y / z)) \ (x * y) = L(z,y,x). [back_rewrite(44649),rewrite([52858(2),52942(2),52858(5),53804(5)]),flip(a)]. 54493 L(a(x,x * y,z),u,x * ((x \ y) * z)) * L(a(y,x,x \ z),u,y * z) = 1. [back_rewrite(42284),rewrite([52858(6),52858(10)])]. 54757 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,y,z)). [back_rewrite(38643),rewrite([52858(12)])]. 54758 R(x,y * z,L(z \ u,y,z)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(38642),rewrite([52858(3)])]. 54785 L(L(x,y,T(z,u)),z,y * T(z,u)) = L(x,K(z,u),z * (y * z)). [back_rewrite(37146),rewrite([52858(2),52858(5)])]. 54855 L(x,y,T(z,y)) = L(x,y,z). [back_rewrite(34860),rewrite([52953(4),52942(3),52858(2),52858(4),52942(4)])]. 54918 L(x,y,T(z,y) * u) = L(x,y,z * (y * u)). [back_rewrite(33664),rewrite([52858(3)]),flip(a)]. 54976 L(x,T(y,z),y \ z) = L(x,y,z). [back_rewrite(30654),rewrite([52858(4),52942(4),54371(7),52858(4)])]. 55103 (x * (K(y,z) * u)) * (u \ K(z,y)) = L(x,K(y,z) * u,u \ K(z,y)). [back_rewrite(28379),rewrite([52858(6),52942(6),52858(5)]),flip(a)]. 55235 a((x * y) / z,x,L(x \ z,x,y)) = a(x,y * x,L(x \ z,x,y)). [back_rewrite(26973),rewrite([52858(4),52858(8)])]. 55237 a((x \ y) / z,x,L(x \ z,x,y)) = a(x \ y,x,L(x \ z,x,y)). [back_rewrite(26968),rewrite([52858(4),52858(8)])]. 55249 L(x,y,y \ z) = L(x,y,z). [back_rewrite(26903),rewrite([52858(3)])]. 55404 L(T(x,y),z,y \ x) = z * ((z \ (y \ x)) * y). [back_rewrite(23927),rewrite([52858(3)])]. 55494 T(x * (y / z),x * y) = L(z,y,x) \ (x * y). [back_rewrite(22386),rewrite([52858(2),52942(2)]),flip(a)]. 55548 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y))))) = x * x. [back_rewrite(21507),rewrite([52858(6)])]. 55568 x * (y \ ((y / x) * z)) = L(z,y,y / x). [back_rewrite(21447),rewrite([52858(6)])]. 55660 L(L(x,y,z),y,z) = x. [back_rewrite(18473),rewrite([52858(4),8684(4)])]. 55725 L(x,y \ z,(z \ y) * u) = L(x,u,y \ z). [back_rewrite(16517),rewrite([52858(4),52858(6)])]. 55731 (x * (y \ z)) * T(y,z) = x * L(z,x,T(y,z)). [back_rewrite(16508),rewrite([52858(6),52963(6)])]. 55771 T(x,L(y * z,x,y)) = T(x,(x * y) * z). [back_rewrite(16362),rewrite([52858(2)])]. 55776 x \ (y * ((y \ x) * z)) = L(z,x,y). [back_rewrite(16348),rewrite([52858(5)])]. 55819 L(x,y,z * (u * u)) = L(x,y,z). [back_rewrite(14874),rewrite([52858(3),2507(3),52858(1)]),flip(a)]. 55915 L(K(x,y) * z,u,K(y,x)) = (u * K(y,x)) \ (u * z). [back_rewrite(11597),rewrite([52858(4)])]. 55954 L(T(x * y,x * z),u,L(y \ z,x,y)) = (u * L(y \ z,x,y)) \ (u * (x * z)). [back_rewrite(11076),rewrite([52858(5),52858(6),52858(8)])]. 56000 ((x / (y * z)) * y) * z = L(x,y,z). [back_rewrite(10295),rewrite([52858(3),52942(3),52858(2),53163(2)]),flip(a)]. 56040 x * L(y,x,z) = L(x * y,x,z). [back_rewrite(8091),rewrite([54976(3),52858(1),52858(4)])]. 56084 L(x,y,x * z) = (y * (z \ (x \ 1))) \ (y / z). [back_rewrite(6676),rewrite([52858(4),53483(4),45(2)])]. 56136 (x * (y * (z * u))) \ (x * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),x,y * (z * u)). [back_rewrite(5337),rewrite([52858(13)])]. 56176 (x * (y * z)) \ (x * y) = R(z \ 1,x,y). [back_rewrite(4138),rewrite([52858(5),53550(7)])]. 56215 a(x,y,L(z,x,y)) = a(x,y,z) \ 1. [back_rewrite(1098),rewrite([52858(1),3204(3),2548(5),52858(4)]),flip(a)]. 56223 R(x,y * z,L(z \ u,y,z)) = L(x,y * z,y * u). [back_rewrite(648),rewrite([52858(3),52953(9)])]. 56231 (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),x,y * (z * u)). [back_rewrite(589),rewrite([52858(11)])]. 56240 (x * y) * L(z,x,y) = x * (y * z). [back_rewrite(72),rewrite([52858(2)])]. 56531 (x * ((x \ y) * z)) / L(T(y,z),x,z) = z. [back_rewrite(45267),rewrite([52953(6)])]. 56576 T(x,(x * y) * z) = T(x,y * (z * x)). [back_rewrite(42429),rewrite([52953(3),52858(2),55771(3)])]. 56588 K((x * y) * z,x) = K(y * (z * x),x). [back_rewrite(42416),rewrite([52953(3),16735(3)])]. 56609 (x * (y * (z * y))) / y = (x * y) * z. [back_rewrite(42387),rewrite([52953(4),16364(3)]),flip(a)]. 56632 L(x * (y \ z),x,y) = (x * T(z,y)) / y. [back_rewrite(42356),rewrite([52953(4)])]. 56659 L(x * y,x,T(z,y)) = (x * (z * y)) / T(z,y). [back_rewrite(42314),rewrite([52953(4)])]. 56731 R(x,y,(x * y) \ z) \ 1 = L(x \ 1,y,z). [back_rewrite(36066),rewrite([52953(9)])]. 56746 x / R(y,z,(y * z) \ u) = x * L(y \ 1,z,u). [back_rewrite(36043),rewrite([52953(8)])]. 56831 T(x,y * ((y \ z) * x)) = T(x,L(z,x,y)). [back_rewrite(29466),rewrite([52953(6),52858(5)])]. 56835 R(x,y \ (z \ 1),z) = L(x,z,y). [back_rewrite(27732),rewrite([56000(4),52953(3),6022(2)]),flip(a)]. 56903 R(x,y * z,z \ 1) = L(x,y,(u \ (u \ y)) * z). [back_rewrite(21721),rewrite([52953(8),52858(4)]),flip(a)]. 56973 ((x \ y) * (x * z)) / z = L(T(y,x),x,z). [back_rewrite(10810),rewrite([52953(3)]),flip(a)]. 57033 L(x * y,y,z) = (x * (y * z)) / z. [back_rewrite(4583),rewrite([52953(3)])]. 57044 L(x,y,x * z) = L(x,z,y). [back_rewrite(3213),rewrite([52953(4),52858(2),52953(4)])]. 57089 x \ (y * ((y \ z) * x)) = L(T(z,x),x,y). [back_rewrite(538),rewrite([52953(7),52858(6)])]. 57097 (x * ((x \ y) * z)) / z = L(y,x,z). [back_rewrite(191),rewrite([52953(6)])]. 57173 ((L(x,y,z) * (y * (z * y))) \ (y * ((z * y) * x))) * K(L(x,y,z),y * (z * y)) = 1. [back_rewrite(7701),rewrite([53163(2),53163(10)])]. 57197 T(T(x,y),z) * R(x \ 1,y,z) = K(y * z,(x \ y) * z). [back_rewrite(40866),rewrite([53431(4)])]. 57210 R(x,y,(x * y) \ z) = L(x,z,y). [back_rewrite(51470),rewrite([53473(4),52858(1),33(2),480(1)]),flip(a)]. 57428 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = R(y \ (z \ (y \ x)),y * (z * y),u). [back_rewrite(8002),rewrite([54309(11)])]. 57506 L(a(x,y,z),y,x * (y * z)) = a(y,x,y * z). [back_rewrite(33981),rewrite([54918(4)])]. 57568 T(L(x,y,z) * (u / x),x) = x \ (L(x,y,z) * u). [back_rewrite(28851),rewrite([55494(6),18461(2)]),flip(a)]. 57670 L(x,y,z * T(z,u)) = x. [back_rewrite(27119),rewrite([55819(7),52858(3)])]. 57764 L(x,y,a(y / (z * u),z,u)) = x. [back_rewrite(54321),rewrite([56000(4),56835(5),15(4)]),flip(a)]. 57831 x * a(x / (y * z),y,z) = L(x,y,z). [back_rewrite(582),rewrite([56000(8)])]. 57837 L(x * y,x,T(z,y)) = (x * (z \ y)) * T(z,y). [back_rewrite(55731),rewrite([56040(7)]),flip(a)]. 57867 a(x,y * x,L(z,x,y)) = a(x,y,x * z). [back_rewrite(23643),rewrite([56040(5),3204(7),189(6),56231(7),57506(4)]),flip(a)]. 57908 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * w)) = L(x,y * z,y * w). [back_rewrite(54758),rewrite([56223(4)]),flip(a)]. 57969 T(x,(x \ y) * z) = T(x,y * (z * x)). [back_rewrite(23736),rewrite([56576(6)])]. 57975 T(x \ y,((y \ x) * z) * y) = T(x \ y,z * (y * (x \ y))). [back_rewrite(15924),rewrite([56576(10)])]. 57979 T(x \ y,(z * (x \ y)) * T(x,y)) = T(x \ y,z * (y * (x \ y))). [back_rewrite(15622),rewrite([56576(11)])]. 58035 K((x \ y) * z,x) = K(y * (z * x),x). [back_rewrite(23819),rewrite([56588(6)])]. 58065 R(T(x,y),y \ x,(x \ y) * z) = L(T(x,y),y,z). [back_rewrite(22110),rewrite([56973(9)])]. 58091 (x * (y \ (z \ 1))) \ (x / y) = L(z,x,y). [back_rewrite(56084),rewrite([57044(2),52858(1)]),flip(a)]. 58133 x * L(y \ 1,z,u) = x / L(y,z,u). [back_rewrite(56746),rewrite([57210(3),52858(1)]),flip(a)]. 58139 R(x \ 1,y,z) = L(x \ 1,y,z). [back_rewrite(56731),rewrite([57210(3),52858(1),53550(3)])]. 58268 a((x * y) / z,x,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(55235),rewrite([57867(9),16(7)])]. 58275 L(x,y * z,y * (z * u)) = R(x,y * z,L(u,y,z)). [back_rewrite(54757),rewrite([57908(10)])]. 58306 ((x * (y \ z)) * T(y,z)) / T(y \ z,x * (z * (y \ z))) = ((z \ y) * x) * z. [back_rewrite(15940),rewrite([57975(9)])]. 58399 T(T(x,y),z) / L(x,y,z) = K(y * z,(x \ y) * z). [back_rewrite(57197),rewrite([58139(5),58133(6)])]. 58412 (x * (y * z)) \ (x * y) = L(z \ 1,x,y). [back_rewrite(56176),rewrite([58139(7)])]. 58434 L(x,y,z) \ 1 = L(x \ 1,y,z). [back_rewrite(53550),rewrite([58139(6)])]. 58458 (L(x \ 1,y,z) * (y * (z * y))) \ (((x \ y) * z) * y) = a(y * z,(y * z) * ((x \ y) * z),y). [back_rewrite(46497),rewrite([58139(3)])]. 58518 K(x * y,L(z \ 1,x,y)) = K(x * y,(z \ x) * y). [back_rewrite(26753),rewrite([58139(4)])]. 58601 R(x,y * z,L(y * y,y,z)) = x. [back_rewrite(47734),rewrite([58275(5)])]. 58647 R(T(x,(y * z) * a(x,y,z)),y * z,a(x,y,z)) = R(T(x,y * (z * x)),y * z,a(x,y,z)). [para(33249(a,1),2642(a,1,2)),rewrite([31(7),31(13),56576(10)])]. 62320 R(x,y,T(y \ z,y)) = L(x,y,z). [para(4505(a,1),516(a,1,2)),rewrite([38365(4),53634(5)]),flip(a)]. 62433 L(x,y,z) * T(z,y) = (x / y) * (z * y). [back_rewrite(45295),rewrite([62320(3)])]. 62444 (x * y) * T(T(z,u),y) = (x * y) * T(T(z,y),u). [para(517(a,1),104(a,1,2,2)),rewrite([522(5)])]. 63757 (x * (y \ L(y,z,y \ (x / y)))) * a(y,z * (y \ (x / y)),T(z,y \ (x / y)) \ y) = x. [para(11138(a,1),54(a,2)),rewrite([53600(8),38305(7)])]. 64162 L(x * x,x,y) = x * x. [para(1077(a,1),55954(a,1,3)),rewrite([14(3),4209(2),52596(4),52858(2),1607(5),1014(5),14(5),10229(5),23697(5),6351(5)])]. 64186 R(x,y * z,y * y) = x. [back_rewrite(58601),rewrite([64162(3)])]. 64241 K(T(x,y) \ z,K(T(x,y) \ ((x \ y) * z),T(x \ y,y))) = 1. [hyper(27,a,19049,a)]. 64397 T(x,(T(T(T(T(T(y,z),x \ 1),u),w),v5) / x) / T(T(T(T(T(y,w),u),x \ 1),z),v5)) = x. [para(4097(a,2),14495(a,1,2,1))]. 65408 x * (y * (T(y,x) * z)) = y * (x * (y * z)). [para(25410(a,1),262(a,1,1)),rewrite([33957(4),547(3),32749(4),45(6),128(7),25410(11),88(9)])]. 65748 L(x \ 1,y,z) * x = L(x,y,z) \ x. [para(996(a,1),518(a,1,2,1)),rewrite([58133(4),28505(2)]),flip(a)]. 65880 x * K(y,T(z,x)) = K(y,z) * x. [para(17666(a,1),518(a,2,1)),rewrite([37429(2),47883(3)])]. 65951 R(x,y,z) * x = x * R(x,y,z). [para(89(a,1),519(a,1,2,1)),flip(a)]. 67485 a(x \ (y \ (x \ 1)),x * (y * (x * z)),u) = a(T(y,x),T(y,x) * z,u). [para(106(a,1),15271(a,1,1,2,1,1)),rewrite([39792(4),128(7),35648(9),101(2),23718(7),34823(2),33957(5),6968(6),24002(5),4032(7),39792(8),106(12),128(11)]),flip(a)]. 68727 ((x * y) * T(z,y)) / T(y,x * (z * (y * y))) = (y \ x) * (z * y). [para(522(a,1),165(a,1,1)),rewrite([57969(7),4578(5)])]. 68754 x * ((y * x) \ (z * x)) = (y \ x) * T(z,x). [para(3143(a,1),522(a,2,1)),rewrite([35645(5)])]. 68763 ((x \ y) * (z * x)) * x = T((y * x) * T(z,x),x). [para(522(a,1),4209(a,1,1)),flip(a)]. 68786 K((x * y) * T(z,y),y) = K(x * (z * (y * y)),y). [para(522(a,1),16568(a,1,1)),rewrite([58035(8),4578(6)])]. 68796 x * (y * (x * T(z,y * x))) = x * L(z * (y * x),y,x). [para(128(a,1),522(a,2)),rewrite([34823(3),6968(6),53600(6)]),flip(a)]. 68958 (x * (y * (z * x))) \ L(x * (y * (z * x)),x,z) = a(x,z * x,T(y,z * x)). [back_rewrite(23655),rewrite([68796(8),52858(6),56040(7)])]. 68979 R(T(x,y * (z * x)),y * z,a(x,y,z)) = ((y * z) * a(x,y,z)) \ ((x * y) * z). [para(54(a,1),536(a,1,2)),rewrite([58647(13)]),flip(a)]. 69080 R(T(x,(y * z) * a(x,y,z)),y * z,a(x,y,z)) = ((y * z) * a(x,y,z)) \ ((x * y) * z). [back_rewrite(58647),rewrite([68979(13)])]. 70643 ((x * y) * z) / (x * (x * (y * z))) = L(x \ 1,y,z). [para(3691(a,1),342(a,1,1)),rewrite([58139(5),52858(5),2507(5),52858(3)]),flip(a)]. 70649 R(x * K(y,z),K(z,y),u) = (x * u) / (K(z,y) * u). [para(4993(a,1),342(a,1,1,2,2)),rewrite([14(3),5005(2),4993(6),14(5),8296(10)])]. 70674 R(x / (y * T(y,z)),y * T(y,z),u) = (x * u) / (y * (T(y,z) * u)). [para(16623(a,1),342(a,1,1,2,2)),rewrite([547(2),16623(7),547(5),38207(12),21062(10)])]. 70731 x * (L(x,y,z) \ x) = R(x,x * (x * y),z). [back_rewrite(1932),rewrite([70643(6),58133(4),28505(2)])]. 70983 (x * (y * (z * (y * x)))) \ (x * (y * (z * ((y * x) * (u * (x * y)))))) = x * (y * T(u,x * y)). [para(33415(a,1),2214(a,1,2,2,2,2))]. 72562 K(L(x,y,z),T(x,u)) = 1. [para(28464(a,1),16687(a,1,2)),rewrite([47(3)]),flip(a)]. 72844 a(T(x \ y,y),T(x,y),T(z,x * y)) = a(T(x,y),x * y,T(z,x * y)). [para(90(a,1),13311(a,1,3,2)),rewrite([4278(2),90(9),90(10)])]. 72886 a(x,(x \ y) * z,u) = a(x,(x * y) * z,u). [para(16(a,1),13466(a,1,2,2)),rewrite([169(6),136(7)])]. 72954 x \ (y * (z * x)) = T(y,x) * T(z,x). [para(14(a,1),13641(a,1,2,2)),rewrite([4505(3),14(6)]),flip(a)]. 73156 T(x,y) * T(x \ z,y) = L(T(z,y),y,x). [back_rewrite(57089),rewrite([72954(4)])]. 73876 ((x * (y * z)) * (y * ((z * y) \ u))) / (y * u) = R(x,y * z,y * ((z * y) \ u)). [para(16(a,1),346(a,1,2,2))]. 74086 (x * (y * (x \ y))) / (x * (y / x)) = y. [para(27447(a,1),17(a,1,1)),rewrite([5005(4),26340(4)]),flip(a)]. 74176 a(x * (y / x),y * (y * z),u) = a(T(y,x \ y),z,u). [para(27447(a,1),4636(a,2,1)),rewrite([74086(6),74086(7),74086(7),21063(3),28991(2),2508(5),74086(11),74086(11)]),flip(a)]. 74728 K((x * (y \ z)) * T(y,z),T(x * z,a(x,y \ z,T(y,z)))) = K(a(x,y \ z,T(y,z)),x * z). [para(4315(a,1),17822(a,1,1)),rewrite([17771(9)]),flip(a)]. 75476 a(x,y,K(x,z)) = 1. [para(18(a,1),33091(a,1,2))]. 75493 (x * y) * K(y,z) = x * T(y,z). [para(33091(a,1),33249(a,1,1,3)),rewrite([80(5),128(4),16716(2),15(4),75476(8),14(7)]),flip(a)]. 75570 R(x,y,K(y,z)) = x. [back_rewrite(22892),rewrite([75493(3),17(4)]),flip(a)]. 75628 R(x,y,K(z,y)) = x. [para(17781(a,1),75570(a,1,3))]. 75689 R(x,T(y,z),K(z,y)) = x. [para(17771(a,1),75628(a,1,3))]. 75750 (x * K(y,z)) / z = x / T(z,y). [back_rewrite(21095),rewrite([75689(5)]),flip(a)]. 75804 a(x,y,z \ (x \ z)) = 1. [para(3666(a,1),33119(a,1,1)),rewrite([24189(5)])]. 76377 T(x * (x * y),z \ 1) * (z / y) = z * (x * x). [para(10920(a,1),7616(a,1,1)),rewrite([10215(7),22250(11),10229(9),18(9)])]. 77305 a(x \ ((y \ ((x \ (z / x)) / y)) / x),x * (y * x),u) = a(x \ (y \ (x \ 1)),z,u). [para(106(a,1),15079(a,1,2)),rewrite([39792(4),39792(8),35648(10),101(2),54309(8),9490(6),9490(7),1014(7),39792(13)])]. 77469 ((x / y) * (z * u)) * a(y / x,z,u) = ((x / y) * z) * u. [para(15308(a,1),54(a,1,2)),rewrite([37(6),10287(7),10287(12)])]. 77479 a(x,x * (y \ (y \ (x \ z))),u) = a(x,y * (y * z),u). [para(3645(a,1),15308(a,1,2,1)),rewrite([10215(7),76377(7),3645(13),35648(11),4578(8),19474(9),35648(10),4578(4),19474(8),14882(9),16(7),16(6),3954(5),10215(12),76377(12),14882(8)])]. 77481 a(T(x,y),y * (y * z),u) = a(y \ (x \ (y \ 1)),z,u). [para(106(a,1),15308(a,1,2,1)),rewrite([39792(4),106(10),128(9),189(10),4578(6),189(9),100(6),189(8),101(6),128(7),67485(11),51385(6),22976(6),39792(8)])]. 78102 x * (((T(y,x) * (x * z)) / u) / T(x * (y * (x * (x * z))),u \ 1)) = x \ (u \ 1). [para(4640(a,1),15(a,1,2)),flip(a)]. 78147 a((x \ y) * y,z,u) = a(x,y * (y * z),u). [para(4640(a,1),4636(a,2,1)),rewrite([78102(13),18809(5),3143(3),90(3),24189(8)])]. 79623 L(x,y,R(z \ (y \ 1),y,x)) = L(x,y,T(z,x)). [para(3143(a,1),10670(a,2,3)),rewrite([6120(3),52963(7)])]. 79632 L(x,y,z * x) = L(x,y,z). [para(101(a,1),10670(a,2,3)),rewrite([20016(3),57044(3),52858(2),3200(2),57044(4),52858(3)]),flip(a)]. 79704 L(x,y,R(z,y,x)) = L(x,y,z). [back_rewrite(8681),rewrite([79632(3),16256(2)]),flip(a)]. 79714 L(x,y,T(z,x)) = L(x,y,z). [back_rewrite(79623),rewrite([79704(5),53484(4),53163(2)]),flip(a)]. 79784 L(x,y,z \ x) = L(x,y,z). [back_rewrite(52963),rewrite([79714(4)])]. 79922 (x * (y * z)) / T(y,z) = L(x * z,z,y). [para(90(a,1),57033(a,2,1,2)),rewrite([54855(3)]),flip(a)]. 79940 L(x * (y \ z),y,z) = (x * z) / T(y,z). [para(2690(a,1),57033(a,2,1,2)),rewrite([52858(5),54976(5)])]. 79946 (x * T(y,z)) / z = (x * y) / T(z,y). [para(4505(a,1),57033(a,2,1,2)),rewrite([52858(4),55249(4),79940(3)]),flip(a)]. 79974 R(x,y \ z,T(y,z)) = L(x,y,z). [para(4504(a,1),57033(a,2,1)),rewrite([7715(4),52858(3),79632(3),55249(2),52858(1),2708(6)]),flip(a)]. 79977 L(x * (y * z),y,z) = (x * y) * z. [para(101(a,1),57033(a,2,1,2)),rewrite([52858(4),53163(4),56609(7)])]. 79991 (x * y) / T(y,z) = x * K(z,y). [para(16875(a,1),57033(a,2,1,2)),rewrite([38196(5)]),flip(a)]. 80004 K(L(x * y,y,z),z) = K(x * (y * z),z). [para(57033(a,2),17822(a,1,1))]. 80058 R(x,y \ z,y) = L(x,y,z). [para(7969(a,1),57033(a,2,1)),rewrite([7715(4),52858(4),79632(4),54976(3),52858(1),7966(6)]),flip(a)]. 80171 L(x * y,x,T(z,y)) = L(x * y,y,z). [back_rewrite(56659),rewrite([79922(7)])]. 80225 (x * (y \ z)) * T(y,z) = L(x,y,z) * z. [back_rewrite(10537),rewrite([79974(3)]),flip(a)]. 80273 x * (y * (x * T(z,y * x))) = L(x * (z * (y * x)),x,y). [back_rewrite(68796),rewrite([52858(8),56040(9)])]. 80289 R(x,K(y,z),y) = x. [back_rewrite(20967),rewrite([79991(5),8298(4)]),flip(a)]. 80501 (x * (y \ z)) * y = (x / y) * (z * y). [back_rewrite(10562),rewrite([80058(2),62433(3)]),flip(a)]. 80509 L(x,y,z) * y = L(x * y,y,z). [back_rewrite(57837),rewrite([80171(3),80225(6),52858(3)]),flip(a)]. 80568 K(L(x,y,z) * z,T(x * z,a(x,y \ z,T(y,z)))) = K(a(x,y \ z,T(y,z)),x * z). [back_rewrite(74728),rewrite([80225(4)])]. 80615 (L(x,y,z) * z) / T(y \ z,x * (z * (y \ z))) = ((z \ y) * x) * z. [back_rewrite(58306),rewrite([80225(4)])]. 80627 T(x \ y,z * (y * (x \ y))) = T(x \ y,L(z,x,y) * y). [back_rewrite(57979),rewrite([80225(5)]),flip(a)]. 80744 T(T(((x \ y) * z) * y,x \ y),L(z,x,y) * y) = ((x \ y) * z) * y. [back_rewrite(15646),rewrite([80225(9)])]. 80745 T(((x \ y) * z) * y,x \ y) = (L(z,x,y) * y) * (x \ y). [back_rewrite(15645),rewrite([80225(4)]),flip(a)]. 80766 (x * y) * a(x,z \ y,T(z,y)) = L(x * y,y,z). [back_rewrite(4308),rewrite([80225(9),52858(6),80509(7)])]. 80776 (x * K(y,z)) * y = x * T(y,z). [back_rewrite(23173),rewrite([80289(2)]),flip(a)]. 81010 ((x / y) * (z * y)) * a(y \ z,(z \ y) * x,T(z,y)) = x * T(z,y). [back_rewrite(43418),rewrite([80501(3)])]. 81016 a(x \ y,(y \ x) * z,T(y,x)) = a(x,x * z,T(y,x)). [back_rewrite(42971),rewrite([80501(8),24477(11)])]. 81056 (x \ y) * ((z / x) * (y * x)) = ((x \ y) * z) * T(y,x). [back_rewrite(8020),rewrite([80501(4)])]. 81224 (x \ y) * (L(z,y,x) * x) = ((x \ y) * z) * x. [back_rewrite(80615),rewrite([80627(7),2711(7),4408(4)])]. 81235 (x \ y) * (L(z,x,y) * y) = ((x \ y) * z) * y. [back_rewrite(80744),rewrite([80745(5),4209(7)])]. 81262 a(x,y * (y * K(z,u)),z) = 1. [back_rewrite(24075),rewrite([80776(9),5410(9)]),flip(a)]. 81309 ((x / y) * (z * y)) * a(y,y * x,T(z,y)) = x * T(z,y). [back_rewrite(81010),rewrite([81016(8)])]. 81564 (T(x,y) * z) / a(T(y \ x,x),T(y,x),z) = T(y,x) \ ((y * x) * z). [para(15408(a,1),162(a,2)),rewrite([29216(4)])]. 81596 T(x,y) \ ((x * y) * (y * L(z,x,y))) = (T(x \ y,y) * z) * T(T(x * y,y),z). [para(15408(a,1),9018(a,2)),rewrite([73156(8),89(5),6018(5),7775(5),53617(14)]),flip(a)]. 81698 a(x \ y,(y \ x) * x,(x \ y) * z) = a(y,x,x \ z). [para(92(a,1),15411(a,1,1)),rewrite([10229(3),4230(3),4209(4),92(5),24057(8),24285(10)])]. 82112 a(x \ y,z * (y \ x),y) \ 1 = a(x \ y,z,T(x,y)). [para(18(a,1),15593(a,1,2)),rewrite([4155(6)]),flip(a)]. 82121 a(x,y / x,x * z) = a(x,y,z) \ 1. [para(1091(a,1),15593(a,1,1)),rewrite([1091(4),1014(5),4209(5),24189(5),1091(5),24189(6)])]. 82123 a(x,y / x,T(z,x \ z)) = a(x,y,z / x) \ 1. [para(1829(a,1),15593(a,1,1)),rewrite([1829(4),1014(5),28965(5),24189(6),1829(6),24189(8)])]. 82129 a(x,y,x \ z) \ 1 = a(x,y / x,z). [para(7769(a,1),15593(a,1,3)),rewrite([48405(3),46(1),48405(5),46(3),1014(5),24189(4),48405(5),46(3),24189(6)]),flip(a)]. 82165 ((x * y) * z) \ x = (x * z) \ (x / y). [para(15(a,1),15621(a,2,2,1)),rewrite([1091(2),3143(3),1091(4),23717(5),14(4),4209(5)])]. 82190 x * ((y * x) \ (z \ 1)) = (x * y) \ (x / z). [para(1829(a,1),15621(a,2,2,1)),rewrite([10229(2),18(2),10229(4),18(4),82165(3),2643(5),6120(7),4408(8),38342(8)]),flip(a)]. 82774 x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y)))) = x. [para(55548(a,1),15(a,1,2)),rewrite([15(2)]),flip(a)]. 82800 R(x / y,y,x) = x / y. [para(55548(a,1),85(a,2,1)),rewrite([82774(11),82774(13),14868(5),3691(4),1014(5)])]. 82841 x * (y \ (z \ (z \ 1))) = x / (z * (z * y)). [para(55548(a,1),342(a,2,1)),rewrite([82774(15),82800(6),82774(14),14868(8),39699(7)]),flip(a)]. 82892 (x / (y * (y * z))) * u = (x / z) * (y \ (y \ u)). [back_rewrite(39650),rewrite([82841(5)])]. 82924 a(x,y * (y * (x * z)),u) = a(x,x * z,u). [back_rewrite(24479),rewrite([82892(7),15(5),15(4),23697(3),4032(5)]),flip(a)]. 82939 a(x,x * (y \ z),u) = a(x,x * (y * z),u). [back_rewrite(46815),rewrite([82924(5)]),flip(a)]. 82951 a(x,y * (y * z),u) = a(x,z,u). [back_rewrite(77479),rewrite([82939(5),16(3),16(2)]),flip(a)]. 82978 a(x,K(y,z),y) = 1. [back_rewrite(81262),rewrite([82951(4)])]. 83003 a((x \ y) * y,z,u) = a(x,z,u). [back_rewrite(78147),rewrite([82951(6)])]. 83005 a(x \ (y \ (x \ 1)),z,u) = a(T(y,x),z,u). [back_rewrite(77481),rewrite([82951(4)]),flip(a)]. 83038 a(T(x,y \ x),z,u) = a(y * (x / y),z,u). [back_rewrite(74176),rewrite([82951(5)]),flip(a)]. 83180 a(x / y,z,u) = a(x * y,z,u). [back_rewrite(39396),rewrite([82951(4)])]. 83185 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,u,u \ x). [back_rewrite(35944),rewrite([82951(13)])]. 83213 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,x / u,u). [back_rewrite(24163),rewrite([82951(13)])]. 83221 a(x * ((y \ x) * x),z,u) = a(x * y,z,u). [back_rewrite(22429),rewrite([82951(8),83180(6)])]. 83245 a((x \ y) * (y * (x \ y)),z,u) = a(T(y,x),z,u). [back_rewrite(19195),rewrite([82951(6)]),flip(a)]. 83255 a(x \ (y / x),z,u) = a(y,z,u). [back_rewrite(19167),rewrite([82951(5)]),flip(a)]. 83266 a(x * (y * y),z,u) = a(x,z,u). [back_rewrite(14882),rewrite([82951(6)])]. 83285 a(x,y * (z * (z * y)),u) = 1. [back_rewrite(2486),rewrite([82951(6)])]. 83292 a(x,y * (z * y),u) = a(T(z,y),x,u). [back_rewrite(77305),rewrite([83255(9),83255(7),83255(5),83005(8)])]. 83423 ((x / y) * (z * u)) * a(y * x,z,u) = ((x / y) * z) * u. [back_rewrite(77469),rewrite([83180(5)])]. 83804 a((x * y) * z,x,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(58268),rewrite([83180(5)])]. 83819 x * a(x * (y * z),y,z) = L(x,y,z). [back_rewrite(57831),rewrite([83180(3)])]. 83854 L(x,y,a(y * (z * u),z,u)) = x. [back_rewrite(57764),rewrite([83180(3)])]. 83865 a((x \ y) * z,x,L(x \ z,x,y)) = a(x \ y,x,L(x \ z,x,y)). [back_rewrite(55237),rewrite([83180(5)])]. 84069 a(x,y,y \ z) = a(x,y,y * z). [back_rewrite(24279),rewrite([83180(4),83266(4)]),flip(a)]. 84082 a(x,y \ x,z) = a(x,y * x,z). [back_rewrite(19659),rewrite([83180(2),23494(2)]),flip(a)]. 84171 a(x,y,z) = a(y,x,z). [back_rewrite(42930),rewrite([83255(3)])]. 84200 (x * (y * (z * (z * y)))) * u = x * (z * (y * (y * (z * u)))). [back_rewrite(20510),rewrite([83285(9),14(7)]),flip(a)]. 84267 a(T(x,y),y * x,z) = a(x,x * y,z). [back_rewrite(46810),rewrite([83292(4)])]. 84365 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,u,u * x). [back_rewrite(83185),rewrite([84069(11)])]. 84378 a(x \ y,(y \ x) * x,(x \ y) * z) = a(x,y,x \ z). [back_rewrite(81698),rewrite([84171(8)])]. 84525 L(a(x,x * y,z),u,x * ((x \ y) * z)) * L(a(x,y,x \ z),u,y * z) = 1. [back_rewrite(54493),rewrite([84171(8)])]. 84641 a(x,y * x,z) = a(x,x * y,z). [back_rewrite(44128),rewrite([84069(2),7836(4),84171(2)])]. 84738 a(x,x * y,z) \ 1 = a(x,y,x \ z). [back_rewrite(24285),rewrite([84171(6)])]. 84799 a(x,y * x,z) \ 1 = a(y,x,x * z). [back_rewrite(4795),rewrite([84171(2)])]. 84975 a(x,(x * y) * z,L(x \ z,x,y)) = a(x,x * y,L(x \ z,x,y)). [back_rewrite(83865),rewrite([84171(5),72886(5),84171(9),3954(9)])]. 84982 L(x,y,a(z,y * (z * u),u)) = x. [back_rewrite(83854),rewrite([84171(3)])]. 85014 x * a(y,x * (y * z),z) = L(x,y,z). [back_rewrite(83819),rewrite([84171(3)])]. 85028 a(x,x * y,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(83804),rewrite([84171(5),84975(5)])]. 85167 ((x / y) * (z * u)) * a(z,y * x,u) = ((x / y) * z) * u. [back_rewrite(83423),rewrite([84171(5)])]. 85230 a(x,y * (z * y),u) = a(x,T(z,y),u). [back_rewrite(83292),rewrite([84171(5)])]. 85233 a(x,y,z * (z * u)) = a(x,y,u). [back_rewrite(83266),rewrite([84171(3),24596(3),84171(3)])]. 85235 a(x,y \ (z / y),u) = a(z,x,u). [back_rewrite(83255),rewrite([84171(3)])]. 85241 a(x,T(y,z \ y),u) = a(x,T(y,z),u). [back_rewrite(83245),rewrite([84171(5),85230(5),84171(5)])]. 85251 a(x,T(y \ z,z),u) = a(x,z * y,u). [back_rewrite(83221),rewrite([84171(4),85230(4),84171(5)])]. 85263 a(x,y / z,u) = a(x,y * z,u). [back_rewrite(83180),rewrite([84171(2),84171(4)])]. 85290 a(x,y * (z / y),u) = a(x,T(z,y),u). [back_rewrite(83038),rewrite([84171(3),85241(3),84171(5)]),flip(a)]. 85298 a(x,(y \ z) * z,u) = a(y,x,u). [back_rewrite(83003),rewrite([84171(3)])]. 85357 a(x \ y,z * (y \ x),y) \ 1 = a(z,x \ y,T(x,y)). [back_rewrite(82112),rewrite([84171(9)])]. 85392 (T(x,y) * z) / a(y,y * x,z) = T(y,x) \ ((y * x) * z). [back_rewrite(81564),rewrite([84171(6),85251(6),84267(5)])]. 85865 a(T(x,y),x * y,T(z,x * y)) = a(x,x * y,T(z,x * y)). [back_rewrite(72844),rewrite([84171(6),85251(6),84267(5)]),flip(a)]. 86937 T(x,y) \ ((x * y) * z) = (x \ y) * (x * z). [back_rewrite(29584),rewrite([84171(4),3954(4),85392(5)])]. 86984 ((x * y) \ z) * ((z \ x) * y) = a(x,z,y). [back_rewrite(24624),rewrite([84171(6)])]. 86989 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(y,z,T(x,y)). [back_rewrite(24566),rewrite([84171(8)])]. 86999 a(x,y \ 1,z) = a(y,x,z). [back_rewrite(24189),rewrite([84171(3)])]. 87019 a(x \ y,z * (x \ y),x) = a(z,x \ y,T(y,x)) \ 1. [back_rewrite(23629),rewrite([84171(7)])]. 87102 a(x \ y,z * (x \ y),T(x,y)) = a(z,x \ y,y) \ 1. [back_rewrite(15593),rewrite([84171(7)])]. 87185 a(x,T(y,x),z) = a(x,y,z). [back_rewrite(4582),rewrite([84171(3)])]. 87186 a(T(x,y),y \ x,z) = a(x,y * x,z). [back_rewrite(4537),rewrite([84171(5),84082(5)])]. 87200 a(c20,a(c17,c18,c19),c21) != 1 # answer("aa1"). [back_rewrite(42),rewrite([84171(7)])]. 87206 R(x,y * (z * (z * y)),u) = x. [back_rewrite(20504),rewrite([84200(5),17(10)]),flip(a)]. 87367 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,x * u,u). [back_rewrite(83213),rewrite([85263(11)])]. 87375 a(x,y,x \ z) \ 1 = a(x,y * x,z). [back_rewrite(82129),rewrite([85263(6)])]. 87376 a(x,y * x,T(z,x \ z)) = a(x,y,z / x) \ 1. [back_rewrite(82123),rewrite([85263(4)])]. 87377 a(x,y * x,x * z) = a(x,y,z) \ 1. [back_rewrite(82121),rewrite([85263(3)])]. 87830 a(x,x * y,(y \ z) * u) = a(x,x * y,(y * z) * u). [back_rewrite(35865),rewrite([85263(4)]),flip(a)]. 87988 a(x,y * x,(y \ x) * z) = a(y,x,y \ z). [back_rewrite(84378),rewrite([85298(6),84082(4)])]. 88057 (T(x \ y,y) * z) * T(T(x * y,y),z) = (x \ y) * ((x * y) * z). [back_rewrite(81596),rewrite([86937(6),3204(4)]),flip(a)]. 88170 R(x,K(y,z),K(z,y) * u) = x. [back_rewrite(50423),rewrite([87206(8)]),flip(a)]. 88394 x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w)) = x \ w. [para(4714(a,1),15(a,1,2)),flip(a)]. 88400 R(x,y,((y \ z) * z) * u) = L(x,y,u). [para(4714(a,1),148(a,1,2,2,2)),rewrite([88394(16),38445(5),57097(8),2507(3),88394(16),38534(5)]),flip(a)]. 88449 L(x,y,(z \ (z \ y)) * u) = R(x,y,u). [back_rewrite(38644),rewrite([88400(7)])]. 88465 R(x,y * z,z \ 1) = R(x,y,z). [back_rewrite(56903),rewrite([88449(8)])]. 89358 a(x,K(y,z),z \ 1) = 1. [para(17913(a,1),82978(a,1,2))]. 90470 (x * y) \ (x * z) = x \ ((x / y) * z). [para(15(a,1),15943(a,1,2,1,1)),rewrite([1091(2),3143(5),1091(5),4209(8),35645(8)]),flip(a)]. 90726 x * (y * T(z,x * y)) = (z * x) * y. [back_rewrite(70983),rewrite([90470(12),39792(4),35648(11),101(2),90470(9),3691(2),3143(8),15(6),24002(5),55776(6),79977(3)]),flip(a)]. 90841 x \ ((x / (y * z)) * y) = L(z \ 1,x,y). [back_rewrite(58412),rewrite([90470(4)])]. 90887 x \ ((x / (y * (z * u))) * ((y * z) * u)) = L(a(y,z,u),x,y * (z * u)). [back_rewrite(56231),rewrite([90470(7)])]. 90904 x \ ((x / (y * (z * u))) * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),x,y * (z * u)). [back_rewrite(56136),rewrite([90470(8)])]. 90948 L(K(x,y) * z,u,K(y,x)) = u * ((u \ K(x,y)) * z). [back_rewrite(55915),rewrite([90470(8),5005(6),24002(8)])]. 91095 L(x,y,y / z) = L(x,z,y). [back_rewrite(53065),rewrite([90470(3),55568(4)])]. 91332 L(x * (y * (z * x)),x,z) = x * ((y * z) * x). [back_rewrite(80273),rewrite([90726(4)]),flip(a)]. 91469 (x * T(y,z)) / z = (x / z) * y. [back_rewrite(21500),rewrite([91095(4),56632(3)])]. 91534 ((x * (y * z)) \ z) * T(x * y,z) = a(z,y * z,T(x,y * z)). [back_rewrite(68958),rewrite([91332(7),90470(7),72954(7),2643(4)])]. 91628 (x * y) / T(z,y) = (x / z) * y. [back_rewrite(79946),rewrite([91469(3)]),flip(a)]. 92765 (x * (y * z)) * (y * ((z * y) \ u)) = (y * z) * (((y * z) \ x) * (y * u)). [para(16(a,1),418(a,1,2,2,2)),flip(a)]. 92871 R(x,y * z,y * ((z * y) \ u)) = L(x,y * z,y * u). [back_rewrite(73876),rewrite([92765(6),57097(8)]),flip(a)]. 92882 R(x,y \ z,(z \ y) * u) = L(x,u,y * z). [back_rewrite(38476),rewrite([92871(6),16(3),52858(2)]),flip(a)]. 92926 L(T(x,y),z,y * x) = L(T(x,y),y,z). [back_rewrite(58065),rewrite([92882(5)])]. 92946 K(a(x,x * y,z),x * (x * ((y * z) / (x * ((x * y) * z))))) = 1. [hyper(27,a,21676,a)]. 92952 T(T(a(x,x * y,z),u),x * (x * ((y * z) / (x * ((x * y) * z))))) = T(a(x,x * y,z),u). [para(21676(a,1),29(a,1,1)),flip(a)]. 92963 a(x,x * y,z) \ u = a(x,y,x \ z) * u. [para(21676(a,1),5226(a,1,1,1)),rewrite([21676(12),92952(17),30512(10),46(7),84738(4),21676(13)]),flip(a)]. 92967 ((a(x,y,x \ z) / u) * a(x,x * y,z)) * u = K(a(x,x * y,z),u). [para(21676(a,1),38815(a,1,1,1)),rewrite([21676(18),15452(13),1091(9),4407(5),92963(5),1014(5),92946(19),13(11)])]. 93030 (T(x,K(y,z)) * K(z,y)) * (x \ K(y,z)) = 1. [para(4993(a,1),27619(a,1,2,1,1)),rewrite([9037(4),45(10),5005(10),12830(10),4407(8),6144(7),14(7)])]. 93714 L(x,y * (z * u),(y * z) * u) = R(x,y * (z * u),a(y,z,u)). [para(597(a,1),57033(a,2,1)),rewrite([16(6),52858(6),79784(6),52858(5),592(13)])]. 94677 T(x,R(x,y,z)) = x. [para(48247(a,1),7769(a,1,1)),rewrite([4408(4),45(3),65951(2),1708(3)])]. 94843 T(R(x,y,z) \ x,x) = R(x,y,z) \ x. [para(94677(a,1),7967(a,1,2)),rewrite([4231(6,R)]),flip(a)]. 94910 ((x * R(y,z,u)) * y) / (y * R(y,z,u)) = R(x,R(y,z,u),y). [para(94677(a,1),516(a,1,1,2)),rewrite([94677(9)])]. 94948 (R(x,y,z) \ x) * (R(x,y,z) * u) = L(x * u,x,R(x,y,z)). [back_rewrite(42834),rewrite([94843(3)])]. 95623 T(x,K(y,z)) * K(z,y) = K(z,y) * x. [para(93030(a,1),17(a,1,1)),rewrite([4155(4),6144(3),13(4)]),flip(a)]. 95624 R(K(x,y) * z,z \ K(y,x),u) = K(x,y) * z. [para(93030(a,1),22(a,1,1,1)),rewrite([13(2),3691(4),4408(4),6144(2),14(4),95623(6)]),flip(a)]. 95626 R(x,K(y,z) * u,u \ K(z,y)) = L(x,K(y,z) * u,u \ K(z,y)). [para(93030(a,1),22(a,1,2)),rewrite([95623(4),55103(6),48(7),95623(9)]),flip(a)]. 95631 L(x,K(y,z) * u,u \ K(z,y)) = x. [para(93030(a,1),104(a,1,2,2)),rewrite([95623(4),95623(6),14(7),16(6),95623(4),55103(6)]),flip(a)]. 95652 x / (K(y,z) * u) = x * (u \ K(z,y)). [para(93030(a,1),85(a,2,2)),rewrite([95623(4),95623(7),95626(8),95631(8),48(8)])]. 95681 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(93030(a,1),166(a,1,2,1)),rewrite([95623(4),95624(5),13(4)])]. 95687 (x \ K(y,z)) * (K(z,y) * (x * (K(z,y) * (x * u)))) = (K(z,y) * x) * u. [para(93030(a,1),169(a,1,1)),rewrite([4408(4),6144(3),13(5),95623(11),4408(10),6144(7),189(10),101(9),24558(11)]),flip(a)]. 95798 R(x * K(y,z),K(z,y),u) = u * ((u \ x) * K(y,z)). [back_rewrite(70649),rewrite([95652(8),169(8)])]. 95979 ((x \ K(y,z)) * u) * K(z,T(y,u)) = x \ u. [back_rewrite(37402),rewrite([95681(3)])]. 98284 (x * (y * z)) * (a(x,y,z) * ((x * y) * z)) = (x * y) * (z * ((x * y) * z)). [para(601(a,1),209(a,1,2)),rewrite([84171(6),20692(6),45(9),54(13),189(12),101(11),84171(18),20692(18),88(14)])]. 98289 (x \ T(x \ 1,y * z)) * (((y * z) \ x) * (y * (z * x))) = a(y,z,x) \ 1. [para(601(a,1),1091(a,1,1)),rewrite([98284(7),23718(11),54309(5),6072(4,R)])]. 98840 (x * y) \ T(x,z) = y \ K(x,z). [para(52627(a,1),6591(a,1,1)),rewrite([52619(5),4408(4),45(2),14(2),16343(2),52619(8),4408(7),45(5),14(5)]),flip(a)]. 99352 L(x,y,z) * z = L(x * z,y,z). [para(2642(a,1),602(a,1,2,3)),rewrite([16(2),80766(5),52858(2),2642(6),80225(6)]),flip(a)]. 99651 x \ (y * (z * y)) = ((x \ y) * z) * y. [back_rewrite(81235),rewrite([99352(3),53170(4)])]. 99656 ((x \ y) * z) * x = T(y,x) * T(z,x). [back_rewrite(81224),rewrite([52858(2),80509(3),53170(4),72954(3)]),flip(a)]. 99742 K(a(x,y \ z,T(y,z)),x * z) = 1. [back_rewrite(80568),rewrite([99352(2),72562(8)]),flip(a)]. 100197 L(x \ y,x,y * z) = (((y * x) \ (y / z)) * z) * y. [back_rewrite(18690),rewrite([99651(8),82165(6)])]. 100284 T(x,y) * T(z * y,y) = T((x * y) * T(z,y),y). [back_rewrite(68763),rewrite([99656(4)])]. 100316 T((x * y) * z,x) = y * (z * x). [back_rewrite(23766),rewrite([99656(3),4525(4),90(2)]),flip(a)]. 101793 x * T(y \ 1,z) = x / T(y,z). [para(19049(a,1),16981(a,2,2)),rewrite([64241(15),52619(3),16(10)])]. 103664 x * (y \ (z \ 1)) = x / (z * y). [para(64186(a,1),85(a,1)),rewrite([189(7),4578(6),4613(8),39792(6),16(7)]),flip(a)]. 103756 x / (y * (z * x)) = (x * z) \ (x / y). [back_rewrite(82190),rewrite([103664(5)])]. 103820 R(x,y,z \ 1) = L(x,z,y). [back_rewrite(58091),rewrite([103664(4),10229(4),10279(4)])]. 103993 ((x * y) \ (x / z)) * z = L(y \ 1,x,z). [back_rewrite(52635),rewrite([103756(3)])]. 104117 R(x,y,z) = L(x,y,z). [back_rewrite(88465),rewrite([103820(4),16256(2),52858(1)]),flip(a)]. 104458 L(x \ y,x,y * z) = L(x \ y,y,z). [back_rewrite(100197),rewrite([103993(7),80509(7),3143(6)])]. 105327 L(x * K(y,z),u,K(z,y)) = u * ((u \ x) * K(y,z)). [back_rewrite(95798),rewrite([104117(4),52858(4)])]. 105371 (L(x,y,z) \ x) * (L(x,y,z) * u) = L(x * u,x,L(x,y,z)). [back_rewrite(94948),rewrite([104117(1),104117(3),104117(7)])]. 105379 L(x,y,L(y,z,u)) = x. [back_rewrite(94910),rewrite([104117(1),32180(3),104117(4),17(6),104117(1),104117(2),52858(2)]),flip(a)]. 105551 L(x,y * (z * u),(y * z) * u) = L(x,a(y,z,u),y * (z * u)). [back_rewrite(93714),rewrite([104117(9),52858(9)])]. 105587 L(x,y,z \ u) = L(x,y,z * u). [back_rewrite(92882),rewrite([104117(4),55725(4)])]. 105864 L(x,y,K(z,u)) = x. [back_rewrite(88170),rewrite([104117(4),53895(4)])]. 106927 x * (L(x,y,z) \ x) = L(x,y,z). [back_rewrite(70731),rewrite([104117(6),52858(6),57044(6),52858(5),57044(5)])]. 106960 (x * y) / (z * (T(z,u) * y)) = x / (z * T(z,u)). [back_rewrite(70674),rewrite([104117(6),52858(6),57670(6)]),flip(a)]. 107041 ((x * y) * a(z,x,y)) \ ((z * x) * y) = T(T(z,x * y),a(z,x,y)). [back_rewrite(69080),rewrite([104117(7),34275(7)]),flip(a)]. 107091 L(T(x,y * (z * x)),y * z,a(x,y,z)) = T(T(x,y * z),a(x,y,z)). [back_rewrite(68979),rewrite([104117(6),107041(12)])]. 107917 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = L(y \ (z \ (y \ x)),u,y * (z * y)). [back_rewrite(57428),rewrite([104117(14),52858(14)])]. 108469 (L(x / y,y,z) * (y * (z * y))) \ ((x * z) * y) = a(y * z,(y * z) * (x * z),y). [back_rewrite(46495),rewrite([104117(2)])]. 108634 (x * (y * z)) / ((z * x) * y) = K(x * y,L(z,x,y)). [back_rewrite(42662),rewrite([104117(2),56240(3),104117(7)])]. 109339 L(x,y,z) * (y * (z * y)) = (x * (y * z)) * y. [back_rewrite(18750),rewrite([104117(2),52858(2),53163(2)])]. 109537 (x * y) \ (z * y) = T(x \ z,y). [back_rewrite(10592),rewrite([104117(4),34275(4),92(2)]),flip(a)]. 109828 (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. [back_rewrite(105371),rewrite([105379(8)])]. 110184 (x * (y \ L(y,x,z))) * a(y,z * (y \ (x / y)),T(z,y \ (x / y)) \ y) = x. [back_rewrite(63757),rewrite([105587(3),57044(3),52858(2),52942(2)])]. 110241 x * ((x \ (y \ z)) * y) = L(T(z,y),y,x). [back_rewrite(55404),rewrite([105587(3),92926(3)]),flip(a)]. 110290 L(x,y,z / u) = L(x,y,u * z). [back_rewrite(53484),rewrite([105587(4),1014(3)])]. 110366 ((x \ y) * z) \ T(y,x) = L(z \ x,x,y). [back_rewrite(7982),rewrite([105587(3),104458(3)]),flip(a)]. 110378 x * ((x \ y) * K(z,u)) = y * K(z,u). [back_rewrite(105327),rewrite([105864(4)]),flip(a)]. 110402 x * ((x \ K(y,z)) * u) = K(y,z) * u. [back_rewrite(90948),rewrite([105864(4)]),flip(a)]. 110793 a(x * y,(x * y) * (z * y),x) = a(z,y,x). [back_rewrite(108469),rewrite([109339(5),23697(3),101(4),99656(3),4525(4),90(2),23718(5),86984(5),84171(1)]),flip(a)]. 110800 T(a(x,y,z),y) = a(z,x \ y,y). [back_rewrite(58458),rewrite([109339(6),3143(4),109537(7),4408(5),86984(5),84171(1),110793(8),84171(4)])]. 110804 (x \ (((y * (x * z)) \ x) * ((z * x) * y))) * K(L(y,x,z),x * (z * x)) = 1. [back_rewrite(57173),rewrite([109339(4),35803(7)])]. 110982 (x \ y) * T(z,y) = (x \ z) * y. [back_rewrite(68754),rewrite([109537(3),90(3)]),flip(a)]. 111960 a(x,x * K(y,z),K(z,y) * u) = 1. [back_rewrite(9444),rewrite([110402(6),8296(4),46(1)]),flip(a)]. 112152 a(x,y * x,T(z,y * x)) = L(x,z,y) \ x. [back_rewrite(91534),rewrite([110982(6),90470(4),90841(4),65748(4)]),flip(a)]. 112164 a(x,y,T(z,x)) = a(z,y,x). [back_rewrite(86989),rewrite([110982(5),86984(5)]),flip(a)]. 112420 ((x / y) * z) * y = x * T(z,y). [back_rewrite(81309),rewrite([112164(6),85167(6)])]. 112421 a(x \ y,(y \ x) * z,T(y,x)) = a(y,x * z,x). [back_rewrite(81016),rewrite([112164(8)])]. 112508 a(x,y,z * x) \ 1 = a(z,y * x,x). [back_rewrite(23663),rewrite([112164(3)]),flip(a)]. 112766 a(x,y,x \ z) * T(a(x,x * y,z),u) = K(a(x,x * y,z),u). [back_rewrite(92967),rewrite([112420(7)])]. 112951 (x * (y / z)) * z = z * ((z \ x) * y). [back_rewrite(10393),rewrite([112420(4),23697(4),110982(3)]),flip(a)]. 113434 a(x,y * z,z) = a(x,z,z * y). [back_rewrite(87367),rewrite([112951(8),41919(6),84365(9)]),flip(a)]. 113707 a(x,y,z * x) \ 1 = a(x,z,x * y). [back_rewrite(112508),rewrite([113434(6),84171(6)])]. 113933 (x * y) \ K(z,u) = y \ (x \ K(z,u)). [para(105864(a,1),6591(a,1,1)),rewrite([6144(3),14(3),6144(7),14(7)]),flip(a)]. 114859 (x * y) * T(T(z,y),u) = (x * T(z,u)) * y. [para(62444(a,1),136(a,2)),rewrite([110982(4),136(5)]),flip(a)]. 114936 (x * y) * T(z,y) = (x * z) * y. [para(64397(a,1),62444(a,1,2,1)),rewrite([114859(23),64397(20)])]. 115135 (x \ y) * ((x * y) * z) = y * (T(y,x) * z). [back_rewrite(88057),rewrite([114936(7),100284(5),114936(4),4505(2),547(2),4209(3),547(2),32749(3)]),flip(a)]. 115350 L(a(x,y,T(z,y)),u,x * (z * y)) = L(a(x,z,y),u,x * (z * y)). [back_rewrite(90904),rewrite([114936(6),90887(7)]),flip(a)]. 115440 K(x * (y * (z * z)),z) = K(x * y,z). [back_rewrite(68786),rewrite([114936(3),18043(3)]),flip(a)]. 115458 (x \ y) * (z * x) = T(y * z,x). [back_rewrite(68727),rewrite([114936(3),79991(7),115440(5),16716(4)]),flip(a)]. 115485 a(x,y,T(z,y)) = a(x,z,y). [back_rewrite(35536),rewrite([114936(7),105551(7),115350(6),6018(5)]),flip(a)]. 116274 L(x,y,z) \ x = a(x,z,y * x). [back_rewrite(112152),rewrite([115485(4),52858(3)]),flip(a)]. 116288 a(x,T(y,z),y * z) = a(y,x,y * z). [back_rewrite(85865),rewrite([115485(5),84171(3),115485(7)])]. 116749 a(x,y,z * x) * (L(x,z,y) * u) = x * u. [back_rewrite(109828),rewrite([116274(2)])]. 116751 x * a(x,y,z * x) = L(x,z,y). [back_rewrite(106927),rewrite([116274(2)])]. 116872 T(x,a(x,y,z * x)) = x. [back_rewrite(28511),rewrite([116274(2)])]. 118635 L(x,K(y,z),y * (u * y)) = x. [para(52858(a,1),54785(a,2)),rewrite([54785(5),105864(8)])]. 118636 L(x,y,z * T(y,u)) = L(x,z,T(y,u)). [para(54785(a,1),55660(a,1,1)),rewrite([118635(4)])]. 118653 L(x,K(y,z),T(y \ u,w)) = x. [para(625(a,1),54785(a,2,3,2)),rewrite([118636(9),55660(8),2507(6)]),flip(a)]. 118966 (x * T(x,y)) \ z = T(x,y) \ (x \ z). [para(16875(a,1),107917(a,1,1,1,2,2)),rewrite([547(2),33507(9),21062(7),106960(8),7616(6),6144(8),35223(8),16875(10),547(8),57670(9)])]. 118967 (x \ (x \ K(y,x))) * z = T(x,y) \ (x \ z). [para(16985(a,1),107917(a,1,1,1,2,2)),rewrite([33497(7),106960(8),7616(6),118966(3),6144(6),9490(7),12473(5),16985(9),57670(10)]),flip(a)]. 119011 (x \ T(x \ 1,y)) * z = T(x,y) \ (x \ z). [back_rewrite(17906),rewrite([118967(9)])]. 119022 T(x,y * z) \ (x \ (((y * z) \ x) * (y * (z * x)))) = a(y,z,x) \ 1. [back_rewrite(98289),rewrite([119011(11)])]. 119325 a(x,y,x \ K(z,x)) = 1. [para(23(a,1),75804(a,1,3,2)),rewrite([98840(3)])]. 121557 x \ (L(x,y,z) * (a(y,z,(y * z) \ x) * u)) = L(u,L(x,y,z),a(y,z,(y * z) \ x)). [para(16(a,1),588(a,1,1)),rewrite([53598(4),53598(14),52858(12)])]. 122955 x * (y \ K(z,y)) = x / T(y,z). [para(89358(a,1),209(a,1,1)),rewrite([1014(6),75750(4),45(4),1014(6),12473(4),89358(9),88(7)]),flip(a)]. 123069 T(x,y) \ (x \ z) = x \ (T(x,y) \ z). [para(634(a,1),50365(a,1)),rewrite([547(2),118966(3)])]. 123095 x \ (K(y,z) * u) = (x \ K(y,z)) * u. [para(634(a,1),105864(a,1)),rewrite([95681(3),6144(5)]),flip(a)]. 123146 a(x,y,z) \ 1 = z \ L(z,x,y). [back_rewrite(119022),rewrite([123069(9),26952(8),90470(4),23697(3),55776(4),6022(3)]),flip(a)]. 128856 x / (T(y,z) * ((y \ L(y,u,w)) * (T(y,z) \ x))) = a(y,w,u * y). [para(26839(a,1),19479(a,1,2,2,2,1,1)),rewrite([116274(10)])]. 129028 x / (T(y,z) * (a(y,u,w * y) * (T(y,z) \ x))) = y \ L(y,w,u). [para(26839(a,1),19536(a,1,2,1,1)),rewrite([116274(3)])]. 131120 T(x,a(x,y,z)) = x. [para(18(a,1),116872(a,1,2,3))]. 131121 a(x,y,z * x) \ L(x,y,z) = x. [para(116872(a,1),23(a,2)),rewrite([116751(5),52858(3)])]. 131133 T(x,a(y,z,x)) = x. [para(4505(a,1),116872(a,1,2,3)),rewrite([112164(2),84171(1)])]. 131212 T(a(x,y,z),x) = a(x,y,z). [hyper(26,a,131120,a)]. 131213 T(T(x,y),a(x,z,u)) = T(x,y). [para(131120(a,1),29(a,1,1)),flip(a)]. 131234 T(x,a(x,y,z) \ x) = x. [para(131120(a,1),7769(a,1,1))]. 131246 K(a(x,y,z),x) = 1. [para(131120(a,1),16687(a,1,2)),rewrite([47(1)]),flip(a)]. 131352 L(T(x,y * (z * x)),y * z,a(x,y,z)) = T(x,y * z). [back_rewrite(107091),rewrite([131213(10)])]. 133057 L(a(x,x * y,z),u,x * ((x \ y) * z)) = L(a(x,y * x,z),u,y * z). [para(84525(a,1),17(a,1,1)),rewrite([989(6),58434(6),87375(4)]),flip(a)]. 133073 a(x,y * x,z) * a(x,y,x \ z) = 1. [para(1607(a,1),84525(a,1,2)),rewrite([133057(7),1607(5)])]. 133580 x / a(y,z,x) = a(y,z,x) \ x. [para(131133(a,1),7616(a,1,1))]. 133716 K(a(x,y,z),y) = 1. [para(84171(a,1),131246(a,1,1))]. 133728 a(x,y \ z,z) = a(y,z,x). [hyper(28,a,133716,a),rewrite([110800(2)])]. 133748 a(x \ y,z * (x \ y),T(x,y)) = a(x,y,z) \ 1. [back_rewrite(87102),rewrite([133728(7)])]. 134004 (x * y) / T(x,z) = x * (y / T(x,z)). [para(119325(a,1),209(a,1,1)),rewrite([122955(5),45(5),122955(6),119325(9),88(8)])]. 134179 ((x \ y) * z) * L(z \ x,x,y) = T(y,x). [para(4505(a,1),1251(a,1,2,2)),rewrite([80501(4),81056(5),134004(9),2711(8),110366(6),4505(7)])]. 135160 T(x * (y / z),z) = (z \ x) * y. [para(4505(a,1),21316(a,1,1,2)),rewrite([90(4),10229(6),112420(7),15(7),110982(6)])]. 135282 x \ (L(x,y,z) * u) = (x \ L(x,y,z)) * u. [back_rewrite(57568),rewrite([135160(4)]),flip(a)]. 135292 (x \ L(x,y,z)) * (a(y,z,(y * z) \ x) * u) = L(u,L(x,y,z),a(y,z,(y * z) \ x)). [back_rewrite(121557),rewrite([135282(7)])]. 136169 a(x,y,x * z) \ 1 = a(x,y * x,z). [para(15(a,1),87019(a,1,1)),rewrite([15(2),15(4),4209(4),84171(4)]),flip(a)]. 136171 a(x \ y,z * (y \ x),T(y,x)) \ 1 = a(z,x \ y,x). [para(18(a,1),87019(a,1,2)),rewrite([84171(2),4155(4),84171(7)]),flip(a)]. 136177 a(x \ (y / x),z * (x \ (y / x)),x) = a(y,z,x \ y) \ 1. [para(92(a,1),87019(a,2,1,3)),rewrite([85235(10)])]. 136185 a(x \ 1,y * x,z * x) = a(y,z,x) \ 1. [para(1091(a,1),87019(a,1,1)),rewrite([1091(4),1014(5),85263(5),1091(7),1708(9),86999(9),112164(7),84171(6)])]. 136188 a(x \ 1,y * x,z) = a(x,y * x,z). [para(1829(a,1),87019(a,1,1)),rewrite([1829(4),1014(5),85263(4),1829(6),2643(8),86999(8),87375(8)])]. 136196 a(x,y * z,y) \ 1 = a(z,y \ x,y). [para(4505(a,1),87019(a,1,2)),rewrite([87185(4),84171(2),4408(4),84171(7),112421(7)]),flip(a)]. 136206 a(x * y,z * (x * y),y \ 1) = a(y,x \ z,x). [para(12372(a,1),87019(a,2,1,3)),rewrite([4408(4),45(2),90(2),4408(5),45(3),90(3),4408(10),45(8),90(8),136196(10)])]. 136217 a(T(x \ y,y),z * T(x \ y,y),T(x,y)) = a(z,y * x,T(y,x)) \ 1. [para(23380(a,1),87019(a,2,1,3)),rewrite([4278(2),4278(4),4278(9),85251(11)])]. 136223 a(x \ y,x * ((x \ z) * y),x) = a(z * x,x \ y,T(y,x)) \ 1. [para(169(a,1),87019(a,1,2))]. 136232 a(x,y,z * (x * x)) \ 1 = a(z,x,y) \ 1. [para(22354(a,1),87019(a,2,1,3)),rewrite([22283(6),15(3),15(2),89(1),22283(6),15(3),15(2),89(1),112164(4),113434(3),84171(3),87377(3),84171(1),22283(9),15(6),15(5),89(4),84171(6)]),flip(a)]. 136306 a(x,y * x,z * x) = a(y,z,x) \ 1. [back_rewrite(136185),rewrite([136188(5)])]. 138261 (T(T(x,y),z) * u) * y = T(T(x,z) * (y * u),y). [para(1466(a,1),4209(a,2)),rewrite([4525(4)]),flip(a)]. 138368 (T(x,y) * z) * y = T(x * (y * z),y). [para(64397(a,1),1466(a,1,1,1,1)),rewrite([138261(23),64397(20)])]. 139543 a(x,y,x \ z) = a(x,y,x * z). [para(133073(a,1),15(a,1,2)),rewrite([84799(4),84171(2)]),flip(a)]. 139565 T(a(x,y,x * z),a(x,y * x,z)) = a(x,y,x * z). [para(133073(a,1),12386(a,1,2,2)),rewrite([139543(2),48(6),139543(7)])]. 139577 a(a(x,y,x * z),a(x,y * x,z),u) \ u = a(x,y * x,z) * (a(x,y,x * z) * u). [para(133073(a,1),162(a,1,1,1)),rewrite([13(2),139543(4),84171(5),133580(6),139543(10)])]. 139595 T(a(x,y,x * z),(a(x,y * x,z) \ a(x,y,x * z)) * u) = T(a(x,y,x * z),u). [para(133073(a,1),6973(a,1,1,2)),rewrite([139543(2),4407(5),136169(4),139543(7),115458(10),16(8),139543(5),139543(9)]),flip(a)]. 139610 L(x,a(y,z,y * u),a(y,z * y,u)) = x. [para(133073(a,1),27459(a,1,3,2)),rewrite([139543(4),14(6),52858(5)])]. 139615 x / a(y,z,y * u) = x * a(y,z * y,u). [para(133073(a,1),57033(a,2,1,2)),rewrite([139543(7),52858(8),139610(8),14(5),139543(5)]),flip(a)]. 139762 a(x,y,x * z) * T(a(x,x * y,z),u) = K(a(x,x * y,z),u). [back_rewrite(112766),rewrite([139543(2)])]. 139811 a(x,y * x,(y \ x) * z) = a(x,y,y * z). [back_rewrite(87988),rewrite([84171(6),84069(6)])]. 141555 T(x,y) * ((z / (x * T(x,y))) * (x * (T(x,y) * u))) = x * ((K(x,y) * z) * u). [para(7416(a,1),15(a,1,2)),rewrite([24002(5),38208(3)]),flip(a)]. 141573 x * (((K(x,y) * z) * u) * x) = (T(x,y) * z) * (u * x). [para(7416(a,1),4209(a,1,1)),rewrite([100316(5),141555(13),101(9)]),flip(a)]. 146366 a(x,y,x * z) \ ((a(x,y * x,z) \ a(x,y,x * z)) * u) = a(x,y,x * z) * u. [para(139595(a,1),2711(a,1,2)),rewrite([91628(10),139615(8),4505(8),139565(5)]),flip(a)]. 147584 T(T(x,y),z) / L(x,u,w) = L(x,u,w) \ T(T(x,y),z). [para(26839(a,1),10402(a,1,1,1,1))]. 147739 L(x,y,z) \ T(T(x,y),z) = K(y * z,(x \ y) * z). [back_rewrite(58399),rewrite([147584(4)])]. 151591 x \ (a(x,y,z) \ x) = a(x,y,z) \ 1. [para(131234(a,1),2711(a,1,2)),rewrite([3666(3)]),flip(a)]. 151649 x / (T(y,z) * (a(y,u,w) * (T(y,z) \ x))) = a(y,u,w) \ 1. [para(131234(a,1),19536(a,1,2,1,1)),rewrite([4408(4),4505(4),131212(3),151591(10)])]. 151677 x \ L(x,y,z) = a(x,z,x * y). [back_rewrite(129028),rewrite([151649(8),113707(4),52858(3)]),flip(a)]. 151689 a(x,y,x * z) * (a(z,y,(z * y) \ x) * u) = L(u,L(x,z,y),a(z,y,(z * y) \ x)). [back_rewrite(135292),rewrite([151677(2)])]. 151698 a(x,y * x,z) = a(x,y,z * x). [back_rewrite(128856),rewrite([151677(3),151649(8),136169(4)])]. 151701 a(x,y,y * z) = a(z,x,y) \ 1. [back_rewrite(123146),rewrite([151677(5),84171(5)]),flip(a)]. 151723 (x * a(y,z,y * x)) * a(y,z * (y \ (x / y)),T(z,y \ (x / y)) \ y) = x. [back_rewrite(110184),rewrite([151677(2)])]. 151813 a(x,y,x * z) \ ((a(x,y,z * x) \ a(x,y,x * z)) * u) = a(x,y,x * z) * u. [back_rewrite(146366),rewrite([151698(4)])]. 151860 a(x,y,((y \ x) * z) * x) = a(x,y,y * z). [back_rewrite(139811),rewrite([151698(4)])]. 151925 a(a(x,y,x * z),a(x,y,z * x),u) \ u = a(x,y,z * x) * (a(x,y,x * z) * u). [back_rewrite(139577),rewrite([151698(4),151698(8)])]. 151954 a(x,y,z * (x * x)) = a(y,z,x) \ 1. [back_rewrite(136306),rewrite([151698(3),4578(2)])]. 152016 a(x,y * z,T(y,z)) \ 1 = a(x,y * z,y). [back_rewrite(136217),rewrite([151698(7),73156(6),89(3),6018(3),84171(3),85251(3)]),flip(a)]. 152025 a(x,y * z,T(y,z)) = a(z,y \ x,y). [back_rewrite(136206),rewrite([151698(6),115458(5),13(3),84171(3)])]. 152039 a(x,y,z * x) = a(y,z,x \ y) \ 1. [back_rewrite(136177),rewrite([151698(6),16(5),84171(4),133728(4),85263(2),151698(2)])]. 152050 a(x,y,z \ x) = a(z,x,y) \ 1. [back_rewrite(133748),rewrite([151698(5),37224(4),28991(3),84171(4),115485(4),84171(2)])]. 152277 a(x,y,z / x) \ 1 = a(x,y,x * z). [back_rewrite(87376),rewrite([151698(4),33781(3),16985(2),90(2)]),flip(a)]. 152280 a(T(x,y),y \ x,z) = a(x,y,z * x). [back_rewrite(87186),rewrite([151698(5)])]. 152337 a(x,x * y,z) = a(x,y,z * x). [back_rewrite(84641),rewrite([151698(2)]),flip(a)]. 152342 a(x,y \ x,z) = a(x,y,z * x). [back_rewrite(84082),rewrite([151698(4)])]. 152407 a(x,y,z) \ 1 = a(z,y,x). [back_rewrite(136232),rewrite([151954(3),4408(5),45(3),14(3),84171(2)]),flip(a)]. 152415 a(x,y * z,y) = a(x,y,z * y). [back_rewrite(152016),rewrite([152025(3),152407(4),3954(2),152337(2),84171(2)]),flip(a)]. 152485 a(x,y * (x * z),z) = a(z,x,(y * z) * x). [back_rewrite(136223),rewrite([152415(5),99656(4),84171(5),3954(5),152337(5),138368(4),90(2),112164(4),84171(3),152407(9),152280(7),84171(6)])]. 152683 a(x,y,x * z) * T(a(x,y,z * x),u) = K(a(x,y,z * x),u). [back_rewrite(139762),rewrite([152337(4),152337(8)])]. 153027 a(x,K(y,z),(K(z,y) * u) * x) = 1. [back_rewrite(111960),rewrite([152337(5)])]. 153030 a(x,y,y * (z * y)) = a(y,z,x). [back_rewrite(110793),rewrite([152337(5),85233(5),113434(3),84171(3),151698(3),101(2),84171(3),84171(4)])]. 153147 a(x,y,((y \ z) * u) * x) = a(x,y,((y * z) * u) * x). [back_rewrite(87830),rewrite([152337(4),152337(8)])]. 153242 a(x,y,z) = a(x,z,y). [back_rewrite(85028),rewrite([152337(4),80509(3),4505(2),56215(3),112164(2),84171(1),152407(3)])]. 153314 a(x,y,x * (z \ u)) = a(x,y,x * (z * u)). [back_rewrite(82939),rewrite([153242(3),153242(6)])]. 153371 a(x,K(y,z),K(z,y) * u) = a(x,K(y,z),K(y,z) * u). [back_rewrite(48772),rewrite([153242(4),84171(4),153242(8),84171(8)])]. 153473 a(x,y,z / x) = a(x,y,x * z). [back_rewrite(152277),rewrite([152407(4),84171(2),153242(2),84171(2)])]. 153478 a(x,y,z \ x) = a(x,y,z). [back_rewrite(152050),rewrite([84171(3),153242(3),152407(5),84171(3),153242(3),84171(3)])]. 153484 a(x,y,z * x) = a(x,y,z). [back_rewrite(152039),rewrite([153478(4),153242(3),84171(3),152407(5),84171(3),153242(3),84171(3)])]. 153502 a(x,y,y * z) = a(x,y,z). [back_rewrite(151701),rewrite([84171(3),153242(3),152407(5),84171(3),153242(3),84171(3)])]. 153528 a(x,y,x * z) = a(z,x,y). [back_rewrite(136196),rewrite([153242(2),153502(2),152407(3),84171(1),153242(1),84171(1),153242(3),84171(3),139543(3)]),flip(a)]. 153530 a(x,y,(z / y) * (x * y)) = a(x,y,z). [back_rewrite(136171),rewrite([153242(5),84171(5),152280(5),80501(3),84171(4),152407(6),84171(4),153242(4),84171(4),153242(6),84171(6),139543(6),153528(6),84171(5)])]. 153607 a(x,T(y,z),y \ z) = a(y,z,x). [back_rewrite(85357),rewrite([153242(4),84171(4),152342(4),80501(3),84171(4),153530(4),152407(3),84171(1),153242(1),84171(1),153242(4)]),flip(a)]. 153757 a(x,y,z) * (a(x,y,z) * u) = u. [back_rewrite(151925),rewrite([153528(2),84171(1),153242(1),153484(3),1300(3),45(2),153484(2),153528(3),84171(2),153242(2)]),flip(a)]. 153764 a(x,y,z) \ u = a(x,y,z) * u. [back_rewrite(151813),rewrite([153528(2),84171(1),153242(1),153484(3),153528(4),84171(3),153242(3),46(4),13(3),153528(4),84171(3),153242(3)])]. 153769 a(x,y,z) * L(x,y,z) = x. [back_rewrite(131121),rewrite([153484(2),153764(3)])]. 153777 a(x,y,(y \ x) * z) = a(x,y,z). [back_rewrite(151860),rewrite([153484(4),153502(5)])]. 153815 a(x,y,z * y) = a(x,y,z). [back_rewrite(153030),rewrite([153502(3),153242(3),84171(3)])]. 153874 a(x,y,z * (x * y)) = a(x,z,y). [back_rewrite(152485),rewrite([153242(3),84171(6),153484(6),153815(5),153242(4)])]. 156427 K(a(x,y,z),x * z) = 1. [back_rewrite(99742),rewrite([153242(3),153607(3),153242(1),84171(1)])]. 156787 a(c20,c21,a(c17,c18,c19)) != 1 # answer("aa1"). [back_rewrite(87200),rewrite([153242(7)])]. 157152 a(x,y,z * (u / z)) = a(x,y,T(u,z)). [back_rewrite(85290),rewrite([153242(3),153242(5)])]. 157169 a(x,y,z \ (u / z)) = a(x,u,y). [back_rewrite(85235),rewrite([153242(3),84171(4)])]. 157230 x * a(x,y,z) = L(x,y,z). [back_rewrite(85014),rewrite([153242(3),153874(3),84171(1)])]. 157238 L(x,y,a(y,z,u)) = x. [back_rewrite(84982),rewrite([153242(3),153874(3),84171(1)])]. 157958 L(x,y,z) * a(x,y,z) = x. [back_rewrite(151723),rewrite([153528(2),157230(2),153478(9),153242(8),116288(8),84171(5),153502(5),139543(4),153528(4),84171(3),153242(3),153473(3),153528(3)])]. 158059 a(x,y,(y \ z) * u) = a(x,y,(y * z) * u). [back_rewrite(153147),rewrite([153484(4),153484(7)])]. 158117 a(x,K(y,z),K(z,y) * u) = 1. [back_rewrite(153027),rewrite([153484(5)])]. 158223 a(x,y,z) * T(a(x,y,z),u) = K(a(x,y,z),u). [back_rewrite(152683),rewrite([153528(2),84171(1),153242(1),153484(3),153484(6)])]. 158546 a(x,y,z) * (L(x,y,z) * u) = x * u. [back_rewrite(116749),rewrite([153484(2),52858(2)])]. 158552 L(x,y,z) \ x = a(x,y,z). [back_rewrite(116274),rewrite([153484(4),153242(3)])]. 158590 a(x,y,K(z,u)) = 1. [back_rewrite(153371),rewrite([158117(4),153502(5),153242(3)]),flip(a)]. 158938 a(x,y,z \ u) = a(x,y,z * u). [back_rewrite(153314),rewrite([153528(3),84171(2),153242(2),153528(5),84171(4),153242(4)])]. 158992 a(x,y,z) * (a(y,z,(z * y) * x) * u) = L(u,L(x,y,z),a(y,z,(z * y) * x)). [back_rewrite(151689),rewrite([153528(2),84171(1),153242(1),84171(4),158938(4),52858(7),84171(10),158938(10)])]. 160232 a(x,y,(y * x) * z) = a(x,y,z). [back_rewrite(153777),rewrite([158059(3)])]. 160751 a(x,y,T(z,u)) = a(x,y,z). [back_rewrite(157169),rewrite([158938(3),157152(3),153242(3)])]. 161700 L(x,a(y,z,u),L(y,z,u)) = x. [back_rewrite(158992),rewrite([160232(4),153242(2),84171(2),153757(4),160232(4),153242(2),84171(2),52858(3)]),flip(a)]. 163437 (x * y) * K(z,u) = x * (y * K(z,u)). [para(158590(a,1),54(a,1,2)),rewrite([14(5)]),flip(a)]. 163614 (x \ K(y,z)) * (K(z,y) * u) = x \ u. [back_rewrite(95979),rewrite([163437(6),65880(5)])]. 163693 (K(x,y) * z) * u = K(x,y) * (z * u). [back_rewrite(95687),rewrite([163614(9),15(5)]),flip(a)]. 163798 (T(x,y) * z) * (u * x) = T(x,y) * ((z * u) * x). [back_rewrite(141573),rewrite([163693(3),38770(4),90(5),33180(4)]),flip(a)]. 165291 a(x,y,z) * (u * L(x,y,z)) = x * T(u,L(x,y,z)). [para(90(a,1),158546(a,1,2))]. 167247 a(x,y,z) * (((u * x) \ a(x,y,z)) * (x * T(u,L(x,y,z)))) = 1. [para(158546(a,1),110804(a,1,2,2)),rewrite([153769(4),157958(7),153764(7),161700(10),157230(9),163437(10),163437(9),163437(8),16716(7)])]. 168431 K(a(x,y,z),T(y,x)) = 1. [para(4505(a,1),156427(a,1,2)),rewrite([84171(2),153242(2),84171(2),158938(2),153528(2),84171(1)])]. 170607 T(x / (x * y),K(y,x)) * (y * z) = K(y,x) * z. [para(24764(a,1),15(a,1,2)),rewrite([38208(3)]),flip(a)]. 170861 a(x,y,z) * (L(T(x,u),y,z) * w) = x * (K(L(x,y,z),u) * w). [para(24764(a,1),158546(a,1,2)),rewrite([30(3),170607(14)])]. 173117 K(a(x,y,z),T(y,u)) = 1. [para(13425(a,1),168431(a,1,2)),rewrite([153242(5),84171(5),160751(5),160751(4),153242(3),84171(3),158938(3),14(2),153242(1),84171(1)])]. 177098 K(x,T(a(x,y,z),u)) = 1. [para(173117(a,1),4993(a,1,1)),rewrite([84171(3),37242(4),13(5)])]. 181313 T(x,T(a(x,y,z),u)) = x. [hyper(28,a,177098,a)]. 181315 T(T(a(x,y,z),u),x) = T(a(x,y,z),u). [para(177098(a,1),16623(a,1,2)),rewrite([14(5)])]. 183896 K(x * (y * z),z) = K(x * y,L(z,x,y)). [para(136(a,1),2925(a,1,2)),rewrite([101(4),99656(3),4525(4),90(2),108634(5),16568(7),58035(6)]),flip(a)]. 184265 L(x,y,z * (u * z)) = L(x,y,T(u,z)). [para(90(a,1),2507(a,1,3,2))]. 184282 L(x,y,z * (u * (z * w))) = L(x,y,u * w). [para(169(a,1),2507(a,1,3,2)),rewrite([23711(5),115135(4),65408(4),105587(6)])]. 184298 L(x,y,T(z,u)) = L(x,y,z). [para(18848(a,1),2507(a,2)),rewrite([2507(7),184282(5),8679(3),184265(4)]),flip(a)]. 186144 L(x,K(y,z),y * u) = x. [back_rewrite(118653),rewrite([184298(4),105587(3)])]. 187171 T(T(x,y),z) / (x * y) = y \ K(x,z). [para(2644(a,1),7616(a,1,1)),rewrite([98840(7)])]. 193371 T(x,L(x,y,z) * u) = T(x,u). [para(2645(a,1),55660(a,1,1)),rewrite([55660(3)]),flip(a)]. 193392 x * (K(L(x,y,z),u) * w) = T(x,u) * w. [para(2645(a,1),158546(a,1,2,1)),rewrite([193371(3),84171(2),153242(2),160751(2),153242(1),84171(1),170861(5),193371(7)])]. 194121 L(x,y,a(x,z,u)) = x. [para(181313(a,1),134179(a,2)),rewrite([52858(10),184298(10),157238(9),169(8),110241(8),181313(3),52858(3),184298(3)])]. 196290 L(x,K(y,z),u * w) = x. [para(11282(a,1),186144(a,1,3)),rewrite([105587(5),1014(4),110290(3)])]. 196788 L(T(x,y),z,a(x,u,w)) = T(x,y). [para(194121(a,1),30(a,1,1)),flip(a)]. 196821 (x * y) \ a(y,z,u) = y \ (x \ a(y,z,u)). [para(194121(a,1),6591(a,1,1)),rewrite([153764(3),14(3),153764(7),14(7)]),flip(a)]. 196855 T(x,y * (z * x)) = T(x,y * z). [back_rewrite(131352),rewrite([196788(6)])]. 196856 a(x,y,z) * ((x \ (u \ a(x,y,z))) * (x * T(u,L(x,y,z)))) = 1. [back_rewrite(167247),rewrite([196821(4)])]. 196936 T(x,L(y,x,z)) = T(x,y). [back_rewrite(56831),rewrite([196855(4),16(2)]),flip(a)]. 197293 K(L(x,y,z),y) = K(x,y). [para(196936(a,1),16687(a,1,2)),rewrite([16687(2)]),flip(a)]. 198001 K(L(x,y,z),z) = K(x,z). [para(52858(a,1),197293(a,1,1))]. 198088 K(x * (y * z),z) = K(x * y,z). [back_rewrite(80004),rewrite([198001(3)]),flip(a)]. 198118 K(x * y,L(z,x,y)) = K(x * y,z). [back_rewrite(183896),rewrite([198088(3)]),flip(a)]. 198251 K(x * y,(z \ x) * y) = K(z,x * y). [back_rewrite(58518),rewrite([198118(5),17781(4)]),flip(a)]. 198284 L(x,y,z) \ T(T(x,y),z) = K(x,y * z). [back_rewrite(147739),rewrite([198251(8)])]. 204095 (x * K(y,z)) * u = x * (K(y,z) * u). [para(6144(a,1),104(a,1,2,1)),rewrite([163693(6),8296(7)]),flip(a)]. 208399 T(T(x,K(y,z)),u) = T(x,K(y,z) * u). [para(8296(a,1),2705(a,2,1)),rewrite([95681(3),52858(7),196290(7),123095(6),113933(5),4408(4),6144(2),163437(4),8310(4),4505(4)])]. 208429 T(T(x,y),K(z,u)) = T(x,K(z,u) * y). [para(517(a,1),8296(a,1,2)),rewrite([8310(5),208399(6)])]. 228215 (T(x,y) * z) \ T(x,y * y) = z \ K(x,y). [para(30881(a,1),17(a,1,1)),rewrite([187171(4)]),flip(a)]. 228407 T(x,T(y,L(x,z,u))) = T(x,y). [para(131120(a,1),30881(a,2,1)),rewrite([228215(6),153764(3),157230(5),204095(5),165291(5),37429(3),16716(4)])]. 230608 T(x,K(L(x,y,z),u)) = x. [para(16813(a,1),55660(a,1)),rewrite([55660(2)]),flip(a)]. 231489 K(L(x,y,z),u) * x = x * K(L(x,y,z),u). [para(230608(a,1),90(a,1,2))]. 231501 K(x,L(y,z,u)) * y = y * K(x,L(y,z,u)). [para(230608(a,1),7616(a,1,1)),rewrite([5005(3),6144(6)]),flip(a)]. 231502 T(x,K(y,L(x,z,u))) = x. [para(230608(a,1),7769(a,1,1)),rewrite([6144(3),231501(3),1708(4)])]. 231568 x * K(L(x,y,z),u) = T(x,u). [para(230608(a,1),25524(a,1,2,2)),rewrite([231489(5),204095(6),193392(6),95681(10),113933(9),163693(11),163798(10),16(8),4505(7),37429(6),30(5),89(4),8310(7),208429(4),16985(3),228407(3)]),flip(a)]. 231594 K(L(x,y,z),u) * x = T(x,u). [back_rewrite(231489),rewrite([231568(6)])]. 231954 K(x,L(y,z,u)) / y = y \ K(x,L(y,z,u)). [para(231502(a,1),2711(a,1,2))]. 231983 x \ K(y,L(x,z,u)) = T(x \ 1,y). [para(231502(a,1),19536(a,1,2,1,1)),rewrite([6144(4),231594(4),53195(7)]),flip(a)]. 232004 K(x,L(y,z,u)) = K(x,y). [para(231502(a,1),56531(a,1,2,1)),rewrite([110378(5),105864(6),19074(4),231954(3),231983(3),101793(4),16687(2)]),flip(a)]. 235046 T(x,L(y,z,u)) = T(x,y). [para(232004(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 235228 K(a(x,y,z),u) = 1. [back_rewrite(196856),rewrite([235046(6),90(6),115458(6),4505(4),181315(4),158223(4)])]. 258700 T(a(x,y,z),u) = a(x,y,z). [hyper(28,a,235228,a)]. 301066 a(x,y,a(z,u,w)) = 1. [para(235228(a,1),198284(a,2)),rewrite([258700(4),258700(4),158552(4),84171(2),153242(2)])]. 301068 $F # answer("aa1"). [resolve(301066,a,156787,a)]. ============================== end of proof ========================== -------- Proof 7 -------- "aa3". ============================== PROOF ================================= % Proof 7 at 186.47 (+ 0.64) seconds: "aa3". % Length of proof is 2024. % Level of proof is 80. % Maximum clause weight is 35. % Given clauses 2809. 1 a(x,y,z) = 1 -> L(z,y,x) = z # label(non_clause). [assumption]. 2 L(x,y,z) = x -> a(z,y,x) = 1 # label(non_clause). [assumption]. 3 T(x,y) = x -> T(y,x) = y # label(non_clause). [assumption]. 4 T(x,y) = x -> K(x,y) = 1 # label(non_clause). [assumption]. 5 K(x,y) = 1 -> T(x,y) = x # label(non_clause). [assumption]. 12 a(x,y,a(z,u,w)) = 1 # label("aa3") # label(non_clause) # label(goal). [goal]. 13 1 * x = x. [assumption]. 14 x * 1 = x. [assumption]. 15 x \ (x * y) = y. [assumption]. 16 x * (x \ y) = y. [assumption]. 17 (x * y) / y = x. [assumption]. 18 (x / y) * y = x. [assumption]. 19 (x * (y * z)) \ ((x * y) * z) = a(x,y,z). [assumption]. 20 (x * y) \ (y * x) = K(y,x). [assumption]. 21 (x * y) \ (x * (y * z)) = L(z,y,x). [assumption]. 22 ((x * y) * z) / (y * z) = R(x,y,z). [assumption]. 23 x \ (y * x) = T(y,x). [assumption]. 24 a(x,y,z) != 1 | L(z,y,x) = z. [clausify(1)]. 25 L(x,y,z) != x | a(z,y,x) = 1. [clausify(2)]. 26 T(x,y) != x | T(y,x) = y. [clausify(3)]. 27 T(x,y) != x | K(x,y) = 1. [clausify(4)]. 28 K(x,y) != 1 | T(x,y) = x. [clausify(5)]. 29 T(T(x,y),z) = T(T(x,z),y). [assumption]. 30 T(L(x,y,z),u) = L(T(x,u),y,z). [assumption]. 31 T(R(x,y,z),u) = R(T(x,u),y,z). [assumption]. 32 L(R(x,y,z),u,w) = R(L(x,u,w),y,z). [assumption]. 33 R(L(x,y,z),u,w) = L(R(x,u,w),y,z). [copy(32),flip(a)]. 34 L(L(x,y,z),u,w) = L(L(x,u,w),y,z). [assumption]. 35 R(R(x,y,z),u,w) = R(R(x,u,w),y,z). [assumption]. 36 ((x * y) * x) * z = x * (y * (x * z)) # label("Moufang (M1)"). [assumption]. 37 (x * (x * y)) * z = x * (x * (y * z)) # label("LC"). [assumption]. 44 a(c27,c28,a(c29,c30,c31)) != 1 # label("aa3") # answer("aa3"). [deny(12)]. 45 1 \ x = x. [para(13(a,1),15(a,1,2))]. 46 x \ x = 1. [para(14(a,1),15(a,1,2))]. 47 x / x = 1. [para(13(a,1),17(a,1,1))]. 48 x / 1 = x. [para(14(a,1),17(a,1,1))]. 49 x / (y \ x) = y. [para(16(a,1),17(a,1,1))]. 50 (x / y) \ x = y. [para(18(a,1),15(a,1,2))]. 51 a(x,1,y) = 1. [para(13(a,1),19(a,1,1,2)),rewrite([14(3),46(3)]),flip(a)]. 52 a(1,x,y) = 1. [para(13(a,1),19(a,1,1)),rewrite([13(3),46(3)]),flip(a)]. 54 (x * (y * z)) * a(x,y,z) = (x * y) * z. [para(19(a,1),16(a,1,2))]. 55 (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y). [para(16(a,1),19(a,1,1,2))]. 56 (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z). [para(16(a,1),19(a,1,2,1))]. 57 (x * (y * ((x * y) \ z))) \ z = a(x,y,(x * y) \ z). [para(16(a,1),19(a,1,2))]. 58 (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z). [para(18(a,1),19(a,1,1,2))]. 59 x \ (((x / (y * z)) * y) * z) = a(x / (y * z),y,z). [para(18(a,1),19(a,1,1))]. 60 ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z). [para(18(a,1),19(a,1,2,1))]. 63 (x * y) * K(y,x) = y * x. [para(20(a,1),16(a,1,2))]. 64 x \ ((y \ x) * y) = K(y \ x,y). [para(16(a,1),20(a,1,1))]. 65 ((x \ y) * x) \ y = K(x,x \ y). [para(16(a,1),20(a,1,2))]. 66 x \ (y * (x / y)) = K(y,x / y). [para(18(a,1),20(a,1,1))]. 67 (x * (y / x)) \ y = K(y / x,x). [para(18(a,1),20(a,1,2))]. 68 K(x * x,x) = a(x,x,x). [para(20(a,1),19(a,1))]. 70 L(x,1,y) = x. [para(13(a,1),21(a,1,2,2)),rewrite([14(2),15(2)]),flip(a)]. 72 (x * y) * L(z,y,x) = x * (y * z). [para(21(a,1),16(a,1,2))]. 73 x \ (y * ((y \ x) * z)) = L(z,y \ x,y). [para(16(a,1),21(a,1,1))]. 74 L(x \ y,x,z) = (z * x) \ (z * y). [para(16(a,1),21(a,1,2,2)),flip(a)]. 75 x \ ((x / y) * (y * z)) = L(z,y,x / y). [para(18(a,1),21(a,1,1))]. 76 L(x,y / x,z) = (z * (y / x)) \ (z * y). [para(18(a,1),21(a,1,2,2)),flip(a)]. 80 R(x,y,1) = x. [para(14(a,1),22(a,1,1)),rewrite([14(3),17(2)]),flip(a)]. 81 R(x,x \ y,z) = (y * z) / ((x \ y) * z). [para(16(a,1),22(a,1,1,1)),flip(a)]. 82 R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z)). [para(16(a,1),22(a,1,1)),flip(a)]. 83 ((x * y) * (y \ z)) / z = R(x,y,y \ z). [para(16(a,1),22(a,1,2))]. 84 R(x,y,z) * (y * z) = (x * y) * z. [para(22(a,1),18(a,1,1))]. 85 R(x / y,y,z) = (x * z) / (y * z). [para(18(a,1),22(a,1,1,1)),flip(a)]. 86 ((x * (y / z)) * z) / y = R(x,y / z,z). [para(18(a,1),22(a,1,2))]. 87 T(1,x) = 1. [para(13(a,1),23(a,1,2)),rewrite([46(1)]),flip(a)]. 88 T(x,1) = x. [para(14(a,1),23(a,1,2)),rewrite([45(2)]),flip(a)]. 89 T(x,x) = x. [para(23(a,1),15(a,1))]. 90 x * T(y,x) = y * x. [para(23(a,1),16(a,1,2))]. 91 T(x,x \ y) = (x \ y) \ y. [para(16(a,1),23(a,1,2)),flip(a)]. 92 T(x / y,y) = y \ x. [para(18(a,1),23(a,1,2)),flip(a)]. 94 T(T(T(x,y),z),u) = T(T(T(x,u),y),z). [para(29(a,1),29(a,1,1)),flip(a)]. 97 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,v5,v6),y,z),u,w). [para(34(a,1),34(a,1,1)),flip(a)]. 100 (x * x) * y = x * (x * y). [para(13(a,1),36(a,2,2)),rewrite([14(2)])]. 101 (x * y) * x = x * (y * x). [para(36(a,1),14(a,1)),rewrite([14(2)]),flip(a)]. 103 x * (y * (x * ((x * (y * x)) \ z))) = z. [para(36(a,1),16(a,1)),rewrite([101(2)])]. 104 x * ((x \ y) * (x * z)) = (y * x) * z. [para(16(a,1),36(a,1,1,1)),flip(a)]. 106 (x * (y * (x * z))) / z = x * (y * x). [para(36(a,1),17(a,1,1)),rewrite([101(6)])]. 107 (x / y) * (y * ((x / y) * z)) = (x * (x / y)) * z. [para(18(a,1),36(a,1,1,1)),flip(a)]. 110 (x * (y * (z * (y * u)))) \ ((x * (y * (z * y))) * u) = a(x,y * (z * y),u). [para(36(a,1),19(a,1,1,2)),rewrite([101(6),101(11)])]. 112 ((x * (y * x)) * (z * u)) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [para(36(a,1),19(a,1,2,1)),rewrite([101(2),101(11)])]. 113 ((x * y) * (x * z)) \ (x * (y * (x * z))) = a(x * y,x,z). [para(36(a,1),19(a,1,2))]. 114 (x * (y * (x * z))) \ (z * (x * (y * x))) = K(z,x * (y * x)). [para(36(a,1),20(a,1,1)),rewrite([101(5),101(9)])]. 117 (x * (y * (z * y))) \ (x * (y * (z * (y * u)))) = L(u,y * (z * y),x). [para(36(a,1),21(a,1,2,2)),rewrite([101(2),101(10)])]. 118 ((x * (y * x)) * z) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [para(36(a,1),21(a,1,2)),rewrite([101(2),101(10)])]. 121 ((x * (y * (z * y))) * u) / (y * (z * (y * u))) = R(x,y * (z * y),u). [para(36(a,1),22(a,1,2)),rewrite([101(2),101(10)])]. 122 x \ (y * (z * (y * x))) = T(y * (z * y),x). [para(36(a,1),23(a,1,2)),rewrite([101(6)])]. 125 ((x * (y * x)) * (z * (x * (y * x)))) * u = (x * (y * x)) * (z * (x * (y * (x * u)))). [para(36(a,1),36(a,2,2,2)),rewrite([101(2),101(5),101(6),101(9)])]. 126 (x * ((y * (z * y)) * x)) * u = x * (y * (z * (y * (x * u)))). [para(36(a,1),36(a,2,2)),rewrite([101(2),101(4)])]. 128 (x * (y * x)) * z = x * (y * (x * z)). [back_rewrite(36),rewrite([101(2)])]. 129 (x * (y * (x * (z * (x * (y * x)))))) * u = x * (y * (x * (z * (x * (y * (x * u)))))). [back_rewrite(125),rewrite([128(6),128(14)])]. 130 (x * (y * (z * (y * x)))) * u = x * (y * (z * (y * (x * u)))). [back_rewrite(126),rewrite([128(3)])]. 132 (x * (y * (x * z))) \ (x * (y * (x * (z * u)))) = L(u,z,x * (y * x)). [back_rewrite(118),rewrite([128(3)])]. 133 (x * (y * (x * (z * u)))) \ ((x * (y * (x * z))) * u) = a(x * (y * x),z,u). [back_rewrite(112),rewrite([128(4)])]. 134 (x * (x * y)) \ (x * (x * (y * z))) = z. [para(37(a,1),15(a,1,2))]. 136 x * (x * ((x \ y) * z)) = (x * y) * z. [para(16(a,1),37(a,1,1,2)),flip(a)]. 139 (x * (y * (y * (z * u)))) \ ((x * (y * (y * z))) * u) = a(x,y * (y * z),u). [para(37(a,1),19(a,1,1,2))]. 140 (x * (x * (y * (z * u)))) \ (x * (x * ((y * z) * u))) = a(x * (x * y),z,u). [para(37(a,1),19(a,1,1)),rewrite([37(7),37(8)])]. 141 (x * ((x * y) * z)) \ (x * (x * (y * z))) = a(x,x * y,z). [para(37(a,1),19(a,1,2))]. 143 (x * (y * (y * z))) \ (y * (y * (z * x))) = K(y * (y * z),x). [para(37(a,1),20(a,1,2))]. 144 (x * (x * (y * z))) \ (x * (x * (y * (z * u)))) = L(u,z,x * (x * y)). [para(37(a,1),21(a,1,1)),rewrite([37(7)])]. 145 (x * (y * (y * z))) \ (x * (y * (y * (z * u)))) = L(u,y * (y * z),x). [para(37(a,1),21(a,1,2,2))]. 146 (x * (x * ((y * z) * u))) / (z * u) = R(x * (x * y),z,u). [para(37(a,1),22(a,1,1,1)),rewrite([37(4)])]. 148 ((x * (y * (y * z))) * u) / (y * (y * (z * u))) = R(x,y * (y * z),u). [para(37(a,1),22(a,1,2))]. 150 x * (x * ((y * (x * (x * (y * z)))) * u)) = x * (x * (y * (x * (x * (y * (z * u)))))). [para(37(a,1),37(a,1,1,2)),rewrite([37(6),37(7),37(13),37(14)])]. 159 T(T(x,y),x) = T(x,y). [para(89(a,1),29(a,1,1)),flip(a)]. 160 L(T(x,L(x,y,z)),y,z) = L(x,y,z). [para(89(a,1),30(a,1)),flip(a)]. 162 ((x * y) * z) / a(x,y,z) = x * (y * z). [para(19(a,1),49(a,1,2))]. 164 (x * (y * z)) / L(z,y,x) = x * y. [para(21(a,1),49(a,1,2))]. 165 (x * y) / T(x,y) = y. [para(23(a,1),49(a,1,2))]. 166 R(x,y,z) \ ((x * y) * z) = y * z. [para(22(a,1),50(a,1,1))]. 168 x \ ((y * x) * z) = (x \ y) * (x * z). [para(104(a,1),15(a,1,2))]. 169 (x * y) * (y \ z) = y * ((y \ x) * z). [para(16(a,1),104(a,1,2,2)),flip(a)]. 170 ((x * y) * z) / ((y \ x) * (y * z)) = y. [para(104(a,1),17(a,1,1))]. 171 (x / y) * (((x / y) \ z) * x) = (z * (x / y)) * y. [para(18(a,1),104(a,1,2,2))]. 173 a(x,x \ y,x * z) = ((y * x) * z) \ (y * (x * z)). [para(104(a,1),19(a,1,1)),rewrite([16(4)]),flip(a)]. 175 (x * (y * z)) * (a(x,y,z) * ((x * (y * z)) * u)) = (((x * y) * z) * (x * (y * z))) * u. [para(19(a,1),104(a,1,2,1))]. 176 ((x * y) * z) \ (((y \ x) * (y * z)) * y) = K((y \ x) * (y * z),y). [para(104(a,1),20(a,1,1))]. 177 (((x \ y) * (x * z)) * x) \ ((y * x) * z) = K(x,(x \ y) * (x * z)). [para(104(a,1),20(a,1,2))]. 178 (x * y) * (K(y,x) * ((x * y) * z)) = ((y * x) * (x * y)) * z. [para(20(a,1),104(a,1,2,1))]. 179 ((x * y) * z) \ (y * (((y \ x) * (y * z)) * u)) = L(u,(y \ x) * (y * z),y). [para(104(a,1),21(a,1,1))]. 180 L((x \ y) * (x * z),x,u) = (u * x) \ (u * ((y * x) * z)). [para(104(a,1),21(a,1,2,2)),flip(a)]. 181 L(x * y,x \ z,x) = z \ ((z * x) * y). [para(104(a,1),21(a,1,2)),rewrite([16(2)]),flip(a)]. 182 (x * y) * (L(z,y,x) * ((x * y) * u)) = ((x * (y * z)) * (x * y)) * u. [para(21(a,1),104(a,1,2,1))]. 183 (((x * y) * z) * u) / (((y \ x) * (y * z)) * u) = R(y,(y \ x) * (y * z),u). [para(104(a,1),22(a,1,1,1))]. 185 ((x \ y) * (x * z)) \ ((y * x) * z) = T(x,(x \ y) * (x * z)). [para(104(a,1),23(a,1,2))]. 186 x * (T(y,x) * (x * z)) = ((y * x) * x) * z. [para(23(a,1),104(a,1,2,1))]. 187 x * (x * (((x \ y) * (x * z)) * u)) = (x * ((y * x) * z)) * u. [para(104(a,1),37(a,1,1,2)),flip(a)]. 188 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * (y * u)))))) = (z * (x * (x * y))) * u. [para(104(a,1),37(a,1)),rewrite([37(10)]),flip(a)]. 189 (x * y) * (x * z) = x * ((y * x) * z). [para(104(a,1),37(a,2,2)),rewrite([16(2)])]. 190 (x * y) * ((y \ z) * (y * u)) = y * ((y \ x) * ((z * y) * u)). [para(104(a,1),104(a,1,2,2)),flip(a)]. 191 (x * ((x \ y) * z)) / z = R(y,x,x \ z). [back_rewrite(83),rewrite([169(3)])]. 192 (x * y) \ (z * ((z \ x) * y)) = a(x,z,z \ y). [back_rewrite(55),rewrite([169(4)])]. 193 (x * y) * (L(z,y,x) * ((x * y) * u)) = (x * (((y * z) * x) * y)) * u. [back_rewrite(182),rewrite([189(10)])]. 196 (x * ((y * x) * z)) \ (x * (y * (x * z))) = a(x * y,x,z). [back_rewrite(113),rewrite([189(3)])]. 197 R(x,y,y \ 1) = x. [para(14(a,1),191(a,1,1,2)),rewrite([16(2),48(2)]),flip(a)]. 198 R(x * y,x,x \ z) = (x * (y * z)) / z. [para(15(a,1),191(a,1,1,2,1)),flip(a)]. 199 R(x,y,y \ ((y \ x) \ z)) = (y * z) / ((y \ x) \ z). [para(16(a,1),191(a,1,1,2)),flip(a)]. 200 R(x,y,y \ z) * z = y * ((y \ x) * z). [para(191(a,1),18(a,1,1))]. 201 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) = ((x * (y * z)) * (a(x,y,z) * u)) / u. [para(19(a,1),191(a,1,1,2,1)),flip(a)]. 202 R(x * y,y * x,(y * x) \ z) = ((y * x) * (K(x,y) * z)) / z. [para(20(a,1),191(a,1,1,2,1)),flip(a)]. 203 R(x * (y * z),x * y,(x * y) \ u) = ((x * y) * (L(z,y,x) * u)) / u. [para(21(a,1),191(a,1,1,2,1)),flip(a)]. 204 R(x * y,y,y \ z) = (y * (T(x,y) * z)) / z. [para(23(a,1),191(a,1,1,2,1)),flip(a)]. 205 (x * (x * (y * (((x * (x * y)) \ z) * u)))) / u = R(z,x * (x * y),(x * (x * y)) \ u). [para(37(a,1),191(a,1,1))]. 206 R(x,x,x \ y) = x. [para(46(a,1),191(a,1,1,2,1)),rewrite([13(2),17(2)]),flip(a)]. 208 R(x,x / y,(x / y) \ z) = ((x / y) * (y * z)) / z. [para(50(a,1),191(a,1,1,2,1)),flip(a)]. 209 a(x,y,z) \ ((x * y) * z) = T(x * (y * z),a(x,y,z)). [para(19(a,1),91(a,1,2)),rewrite([19(9)]),flip(a)]. 218 x / T(y,y \ x) = y \ x. [para(91(a,2),49(a,1,2))]. 220 R(x,y \ z,T(y,y \ z)) = R(x,y \ z,(y \ z) \ z). [para(91(a,2),191(a,2,3)),rewrite([191(6)]),flip(a)]. 221 T(x \ y,T(x,x \ y)) = ((x \ y) \ y) \ y. [para(91(a,2),91(a,1,2))]. 228 L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,u,w),y,z),v5,v6). [para(97(a,1),34(a,1))]. 229 L(L(L(L(x,y,z),u,w),v5,v6),v7,v8) = L(L(L(L(x,v5,v6),y,z),v7,v8),u,w). [para(97(a,2),34(a,1,1))]. 260 T(x * ((x \ y) * z),a(x,x \ y,z)) = a(x,x \ y,z) \ (y * z). [para(16(a,1),209(a,1,2,1)),flip(a)]. 262 a(x,y,y \ z) \ (y * ((y \ x) * z)) = T(x * z,a(x,y,y \ z)). [para(16(a,1),209(a,2,1,2)),rewrite([169(5)])]. 263 T((x / y) * (y * z),a(x / y,y,z)) = a(x / y,y,z) \ (x * z). [para(18(a,1),209(a,1,2,1)),flip(a)]. 265 ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z). [para(209(a,1),49(a,1,2))]. 268 ((x * (y \ z)) * T(y,y \ z)) / z = R(x,y \ z,(y \ z) \ z). [para(220(a,1),22(a,2)),rewrite([90(9),16(7)])]. 311 (x * (y * (y * z))) \ ((x * (y * y)) * z) = a(x,y * y,z). [para(13(a,1),110(a,1,1,2,2)),rewrite([13(5),13(9)])]. 312 (x * (y * (z * (y * u)))) * a(x,y * (z * y),u) = (x * (y * (z * y))) * u. [para(110(a,1),16(a,1,2))]. 314 (x * ((y \ z) * (y * ((y \ z) * u)))) \ ((x * ((y \ z) * z)) * u) = a(x,(y \ z) * z,u). [para(16(a,1),110(a,1,2,1,2,2)),rewrite([16(14)])]. 326 ((x / y) * (z * x)) \ (y * ((x / y) * (z * (x / y)))) = K(y,(x / y) * (z * (x / y))). [para(18(a,1),114(a,1,1,2,2))]. 338 ((x * (y * y)) * z) / (y * (y * z)) = R(x,y * y,z). [para(13(a,1),148(a,1,2,2,2)),rewrite([14(2),14(8)])]. 340 ((x * (y * (y * z))) * (z \ u)) / (y * (y * u)) = R(x,y * (y * z),z \ u). [para(16(a,1),148(a,1,2,2,2))]. 341 R(x,y * (y * z),u) * (y * (y * (z * u))) = (x * (y * (y * z))) * u. [para(148(a,1),18(a,1,1))]. 342 R(x / (y * (y * z)),y * (y * z),u) = (x * u) / (y * (y * (z * u))). [para(18(a,1),148(a,1,1,1)),flip(a)]. 345 (x * (x * ((x * y) * z))) / (x * (x * (y * z))) = R(x,x * (x * y),z). [para(37(a,1),148(a,1,1))]. 346 ((x * (y * z)) * (y * u)) / (y * ((z * y) * u)) = R(x,y * z,y * u). [para(104(a,1),148(a,1,2,2)),rewrite([16(2),16(10)])]. 350 ((x * y) * z) * K((y \ x) * (y * z),y) = ((y \ x) * (y * z)) * y. [para(176(a,1),16(a,1,2))]. 354 ((x * (y / z)) * z) \ ((((y / z) \ x) * y) * (y / z)) = K(((y / z) \ x) * y,y / z). [para(18(a,1),176(a,1,2,1,2)),rewrite([18(13)])]. 356 (x * (x * y)) \ (x * (y * x)) = K(x * y,x). [para(46(a,1),176(a,1,2,1,1)),rewrite([100(2),13(5),101(4),46(6),13(8)])]. 357 ((x * (x / y)) * z) \ ((y * ((x / y) * z)) * (x / y)) = K(y * ((x / y) * z),x / y). [para(50(a,1),176(a,1,2,1,1)),rewrite([50(11)])]. 393 x * (x * ((x * (y * (x * (x * x)))) * z)) = x * (x * (x * (y * (x * (x * (x * z)))))). [para(129(a,1),37(a,1)),flip(a)]. 398 x * (x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u))))))) = x * (x * u). [para(16(a,1),150(a,1,2,2)),flip(a)]. 405 x * ((y * x) * (x * ((x \ y) * (z * u)))) = x * (x * (((x \ y) * ((x * y) * z)) * u)). [para(104(a,1),150(a,2,2)),rewrite([136(5)]),flip(a)]. 407 x * (x * (((x * x) \ y) * (x * (x * z)))) = (y * (x * x)) * z. [para(13(a,1),188(a,1,2,2,2,2,2,2)),rewrite([14(3),13(7),14(9)])]. 411 x * (x * (y * (((x * (x * y)) \ z) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [para(16(a,1),188(a,1,2,2,2,2,2,2))]. 418 (x * y) * (((x * y) \ z) * (x * ((y * x) * u))) = (z * (x * y)) * (x * u). [para(104(a,1),188(a,1,2,2,2,2,2)),rewrite([16(3),136(10),16(10)])]. 426 (x * (y * (x * y))) * z = (x * y) * ((x * y) * z). [para(13(a,1),175(a,1,1,2)),rewrite([51(3),13(4),13(5),14(6),13(7),189(7),101(6)]),flip(a)]. 435 R(x * ((x \ y) * z),y * z,(y * z) \ u) = ((y * z) * (a(y,x,x \ z) * u)) / u. [para(16(a,1),201(a,1,2,2)),rewrite([169(3),16(6),16(9)])]. 437 R(((x / (y * z)) * y) * z,x,x \ u) = (x * (a(x / (y * z),y,z) * u)) / u. [para(18(a,1),201(a,1,2)),rewrite([18(8),18(10)])]. 439 R((x * y) * z,x * (y * z),(x * (y * z)) \ u) \ ((x * (y * z)) * (a(x,y,z) * u)) = u. [para(201(a,2),50(a,1,1))]. 463 x * (x * (x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))))) = x * (x * z). [para(16(a,1),393(a,1,2,2)),flip(a)]. 478 R(x,1 / y,y) = x. [para(50(a,1),197(a,1,3))]. 480 R(x,x,y) = x. [para(15(a,1),206(a,1,3))]. 493 R(T(x,y),x,z) = T(x,y). [para(480(a,1),31(a,1,1)),flip(a)]. 495 R(R(x,y,z),x,u) = R(x,y,z). [para(480(a,1),35(a,1,1)),flip(a)]. 506 (x * (1 / y)) * y = x. [para(478(a,1),22(a,2)),rewrite([18(7),48(6)])]. 507 (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z)). [para(90(a,1),19(a,1,1,2))]. 508 (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z). [para(90(a,1),19(a,1,2,1))]. 510 (x * y) \ (T(x,y) * y) = K(T(x,y),y). [para(90(a,1),20(a,1,1))]. 511 (T(x,y) * y) \ (x * y) = K(y,T(x,y)). [para(90(a,1),20(a,1,2))]. 512 (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y). [para(90(a,1),21(a,1,1))]. 516 ((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,y)). [para(90(a,1),22(a,1,2))]. 517 x * T(T(y,x),z) = T(y,z) * x. [para(29(a,1),90(a,1,2))]. 518 x * L(T(y,x),z,u) = L(y,z,u) * x. [para(30(a,1),90(a,1,2))]. 519 x * R(T(y,x),z,u) = R(y,z,u) * x. [para(31(a,1),90(a,1,2))]. 520 x * (x * (T(y,x) * z)) = x * (y * (x * z)). [para(90(a,1),37(a,1,1,2)),rewrite([128(3)]),flip(a)]. 521 x * (x * (y * T(z,x * (x * y)))) = z * (x * (x * y)). [para(90(a,1),37(a,1)),flip(a)]. 522 x * ((x \ y) * (z * x)) = (y * x) * T(z,x). [para(90(a,1),104(a,1,2,2))]. 536 (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y). [para(22(a,1),92(a,1,1)),rewrite([31(3)]),flip(a)]. 537 T(T(x / y,z),y) = T(y \ x,z). [para(92(a,1),29(a,1,1)),flip(a)]. 538 x \ (y * ((y \ z) * x)) = R(T(z,x),y,y \ x). [para(191(a,1),92(a,1,1)),rewrite([31(3)]),flip(a)]. 540 K(T(x,y),x) = 1. [hyper(27,a,159,a)]. 541 T(x,T(x,y)) = x. [hyper(26,a,159,a)]. 547 T(x,y) * x = x * T(x,y). [para(159(a,1),90(a,1,2)),flip(a)]. 554 K(x \ y,y / x) = 1. [para(92(a,1),540(a,1,1))]. 555 K(x,T(x,y)) = 1. [hyper(27,a,541,a)]. 560 T(x,(x \ y) \ y) = x. [para(91(a,1),541(a,1,2))]. 568 K(x / y,y \ x) = 1. [para(92(a,1),555(a,1,2))]. 582 x * a(x / (y * z),y,z) = ((x / (y * z)) * y) * z. [para(18(a,1),54(a,1,1))]. 588 ((x * y) * z) \ ((x * (y * z)) * (a(x,y,z) * u)) = L(u,a(x,y,z),x * (y * z)). [para(54(a,1),21(a,1,1))]. 589 (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),y * (z * u),x). [para(54(a,1),21(a,1,2,2))]. 592 ((x * (y * (z * u))) * a(y,z,u)) / ((y * z) * u) = R(x,y * (z * u),a(y,z,u)). [para(54(a,1),22(a,1,2))]. 597 (x * (y * z)) * (((x * (y * z)) \ u) * ((x * y) * z)) = (u * (x * (y * z))) * a(x,y,z). [para(54(a,1),104(a,1,2,2))]. 601 (((x * y) * z) * (x * (y * z))) * a(x,y,z) = (x * (y * z)) * (a(x,y,z) * ((x * y) * z)). [para(54(a,1),175(a,1,2,2)),flip(a)]. 602 (x * (y * z)) * a(x,z,T(y,z)) = (x * z) * T(y,z). [para(90(a,1),54(a,1,1,2))]. 614 (x * ((x \ y) * ((y \ z) * (y * u)))) \ ((z * y) * u) = a(x,x \ y,(y \ z) * (y * u)). [para(104(a,1),56(a,1,2))]. 625 T(x / y,z) * y = y * T(y \ x,z). [para(537(a,1),90(a,1,2)),flip(a)]. 632 L(x \ 1,x,y) = (y * x) \ y. [para(14(a,1),74(a,2,2))]. 634 L(x \ (y \ z),x,y) = (y * x) \ z. [para(16(a,1),74(a,2,2))]. 637 (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x). [para(20(a,1),74(a,1,1)),flip(a)]. 638 (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x). [para(21(a,1),74(a,1,1)),flip(a)]. 639 L(T(x,y),y,x) = T(x,x * y). [para(74(a,2),23(a,1)),rewrite([23(2)])]. 648 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(y * z) \ (y * u)). [para(74(a,2),191(a,2,3)),rewrite([191(8)]),flip(a)]. 650 T(x * y,(x * y) \ (x * z)) = L(y \ z,y,x) \ (x * z). [para(74(a,2),91(a,2,1))]. 659 L(x \ T(y,z),x,z) = (z * x) \ (y * z). [para(90(a,1),74(a,2,2))]. 662 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,(x * y) \ (x * z),u). [para(74(a,2),56(a,1,1,2,1))]. 666 L(K(x,y),y * x,y) = K(y * x,y). [back_rewrite(356),rewrite([637(5)])]. 667 L(L(x,y,z),z * y,z) = x. [back_rewrite(134),rewrite([638(6)])]. 669 x * (T(y,x) * x) = (y * x) * x. [para(14(a,1),186(a,1,2,2)),rewrite([14(7)])]. 673 (((x * y) * y) * z) \ ((x * y) * (y * z)) = a(y,T(x,y),y * z). [para(186(a,1),19(a,1,1)),rewrite([90(5)])]. 674 (x * ((T(y,x) * (x * z)) * u)) \ ((((y * x) * x) * z) * u) = a(x,T(y,x) * (x * z),u). [para(186(a,1),19(a,1,2,1))]. 675 ((T(x,y) * (y * z)) * y) \ (((x * y) * y) * z) = K(y,T(x,y) * (y * z)). [para(186(a,1),20(a,1,2))]. 682 x * (T(T(y,x),z) * (x * u)) = ((T(y,z) * x) * x) * u. [para(29(a,1),186(a,1,2,1))]. 684 x * (R(T(y,x),z,u) * (x * w)) = ((R(y,z,u) * x) * x) * w. [para(31(a,1),186(a,1,2,1))]. 690 a((x * y) * y,T(x,y),z) = a(y,T(x,y) * (x * y),z). [para(186(a,1),110(a,1,2,1)),rewrite([186(6),19(11),90(7)])]. 729 ((x * (y / z)) * z) / T(x * y,a(x,y / z,z)) = a(x,y / z,z). [para(18(a,1),265(a,1,2,1,2))]. 732 (x * (y * z)) / T((x * y) * z,a(y,y \ x,y * z)) = a(y,y \ x,y * z). [para(104(a,1),265(a,1,2,1)),rewrite([16(2)])]. 777 x * (x * T(y,x * x)) = y * (x * x). [para(13(a,1),521(a,1,2,2)),rewrite([14(2),14(6)])]. 778 x * (y * T(z,x * (x * y))) = x \ (z * (x * (x * y))). [para(521(a,1),15(a,1,2)),flip(a)]. 780 L(x * T(y,z * (z * x)),z,z) = (z * z) \ (y * (z * (z * x))). [para(521(a,1),21(a,1,2)),flip(a)]. 788 x * (y * (x * T(z,x * (y * x)))) = z * (x * (y * x)). [para(90(a,1),521(a,1,2,2,2,2,2)),rewrite([520(7),90(8)])]. 831 (x * ((x \ y) * y)) \ ((y * x) * ((x \ y) * z)) = L(z,(x \ y) * y,x). [para(104(a,1),117(a,1,1)),rewrite([169(3),104(9),16(11)])]. 843 (((x * y) * y) * z) / K(y,T(x,y) * (y * z)) = (T(x,y) * (y * z)) * y. [para(675(a,1),49(a,1,2))]. 863 (T(T(x,y),z) * (z * u)) * z = (T(T(x,z),y) * (z * u)) * z. [para(29(a,1),843(a,2,1,1)),rewrite([843(10)])]. 874 x * K((y \ z) * (y * ((z * y) \ x)),y) = ((y \ z) * (y * ((z * y) \ x))) * y. [para(16(a,1),350(a,1,1))]. 888 ((1 / x) * y) \ (x * ((1 / x) * (y * (1 / x)))) = K(x,(1 / x) * (y * (1 / x))). [para(14(a,1),326(a,1,1,2))]. 960 (R(x,y,z) * u) / R(T(x,u),y,z) = u. [para(31(a,1),165(a,1,2))]. 961 (x * (x * (y * z))) / T(x * (x * y),z) = z. [para(37(a,1),165(a,1,1))]. 965 (x * y) / T(y,T(x,y)) = T(x,y). [para(90(a,1),165(a,1,1))]. 969 (((x \ y) * (x * z)) * x) / T((y * x) * z,K((x \ y) * (x * z),x)) = K((x \ y) * (x * z),x). [para(350(a,1),165(a,1,1))]. 974 x * (1 / y) = x / y. [para(506(a,1),17(a,1,1)),flip(a)]. 975 x / (1 / y) = x * y. [para(18(a,1),506(a,1,1)),flip(a)]. 976 a(x,1 / y,y) = 1. [para(506(a,1),19(a,1,2)),rewrite([18(3),14(2),46(1)]),flip(a)]. 980 (x / y) / K(1 / y,T(x,1 / y)) = T(x,1 / y) / y. [para(506(a,1),843(a,1,1)),rewrite([974(3),18(9),14(8),18(14),14(13),974(14)])]. 982 K(x,1 / x) = 1. [para(506(a,1),357(a,1,1)),rewrite([18(4),14(3),974(4),47(2),46(3),18(4),14(3)]),flip(a)]. 985 ((1 / x) * y) \ (x * ((1 / x) * (y / x))) = K(x,(1 / x) * (y / x)). [back_rewrite(888),rewrite([974(8),974(14)])]. 986 T(x,1 / x) = x. [hyper(28,a,982,a)]. 989 1 / x = x \ 1. [hyper(26,a,986,a),rewrite([92(3)]),flip(a)]. 990 (x \ 1) \ 1 = x. [para(986(a,1),23(a,2)),rewrite([989(2),989(4),16(5)])]. 996 T(x \ 1,x) = x \ 1. [para(49(a,1),986(a,1,2))]. 997 (x \ 1) * x = 1. [para(986(a,1),90(a,1,2)),rewrite([989(2),989(5),16(6)])]. 1004 ((x \ 1) * y) \ (x * ((x \ 1) * (y / x))) = K(x,(x \ 1) * (y / x)). [back_rewrite(985),rewrite([989(2),989(5),989(11)])]. 1009 (x / y) / K(y \ 1,T(x,y \ 1)) = T(x,y \ 1) / y. [back_rewrite(980),rewrite([989(3),989(5),989(10)])]. 1012 a(x,y \ 1,y) = 1. [back_rewrite(976),rewrite([989(2)])]. 1013 x / (y \ 1) = x * y. [back_rewrite(975),rewrite([989(2)])]. 1014 x * (y \ 1) = x / y. [back_rewrite(974),rewrite([989(2)])]. 1022 L(x,x \ 1,y) = x. [para(990(a,1),74(a,1,1)),rewrite([1014(6),14(6),50(5)])]. 1025 (x \ 1) * (x * y) = L(y,x,x \ 1). [para(997(a,1),21(a,1,1)),rewrite([45(6)])]. 1026 L(x,y,(y * x) \ 1) = (((y * x) \ 1) * y) \ 1. [para(997(a,1),21(a,1,2)),flip(a)]. 1027 R(x \ 1,x,y) = y / (x * y). [para(997(a,1),22(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1039 R((x * (x * y)) \ 1,x * (x * y),z) = z / (x * (x * (y * z))). [para(997(a,1),148(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1051 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x \ (y \ 1),y). [para(997(a,1),56(a,1,2))]. 1072 a(x,y,y \ 1) = 1. [para(50(a,1),1012(a,1,2)),rewrite([989(2)])]. 1077 L(x \ 1,x,y) = x \ 1. [para(50(a,1),1022(a,1,2)),rewrite([989(2),989(5)])]. 1078 L(L(L(x,y,z),u,w),L(x,u,w) \ 1,v5) = L(L(x,u,w),y,z). [para(1022(a,1),97(a,1,1)),flip(a)]. 1080 L(L(L(x,y,z),u,w),x \ 1,v5) = L(L(x,y,z),u,w). [para(1022(a,1),97(a,2,1,1))]. 1091 (x * y) \ x = y \ 1. [back_rewrite(632),rewrite([1077(3)]),flip(a)]. 1097 (x * (y * K(y,x))) \ (y * x) = a(x,y,K(y,x)). [para(20(a,1),57(a,1,1,2,2)),rewrite([20(8)])]. 1098 (x * (y * L(z,y,x))) \ (x * (y * z)) = a(x,y,L(z,y,x)). [para(21(a,1),57(a,1,1,2,2)),rewrite([21(10)])]. 1105 (x * (y * L(y \ z,y,x))) \ (x * z) = a(x,y,(x * y) \ (x * z)). [para(74(a,2),57(a,1,1,2,2))]. 1141 L(x,y,(y * x) \ 1) \ 1 = ((y * x) \ 1) * y. [para(1026(a,2),49(a,1,2)),rewrite([989(6)])]. 1180 L(x,x \ y,x) = x. [para(14(a,1),181(a,1,1)),rewrite([14(5),15(4)])]. 1201 T(x,L(y * z,y \ x,y)) = T(x,x \ ((x * y) * z)). [para(181(a,2),91(a,1,2)),rewrite([91(10,R)])]. 1227 L(x * y,x \ (x \ 1),x) = (x \ 1) \ y. [para(997(a,1),181(a,2,2,1)),rewrite([13(9)])]. 1246 (x * (x * y)) / T(x * (x * (y / z)),z) = z. [para(18(a,1),961(a,1,1,2,2))]. 1251 (x * ((y * x) * z)) / T(x * y,x * z) = x * z. [para(104(a,1),961(a,1,1,2)),rewrite([16(5)])]. 1252 (x * (x * (y * z))) / T(x * (x * z),T(y,z)) = T(y,z). [para(90(a,1),961(a,1,1,2,2))]. 1266 (((T(x,y) * z) * z) * u) / (T(T(x,z),y) * (z * u)) = z. [para(682(a,1),17(a,1,1))]. 1300 a(x,x,y) = 1. [para(13(a,1),690(a,1,1,1)),rewrite([87(3),51(3),87(3),13(4),13(3)]),flip(a)]. 1301 a(x * (y \ x),T(y,y \ x),z) = a(y \ x,T(y,y \ x) * x,z). [para(16(a,1),690(a,1,1,1)),rewrite([16(10)])]. 1316 K(x * x,x) = 1. [back_rewrite(68),rewrite([1300(3)])]. 1323 x \ (y * (x * x)) = x * T(y,x * x). [para(13(a,1),778(a,1,2)),rewrite([14(2),14(5)]),flip(a)]. 1324 x \ (x \ (y * (x * (x * z)))) = z * T(y,x * (x * z)). [para(778(a,1),15(a,1,2))]. 1346 (x \ (y * (x * z))) \ (z * T(y,x * z)) = a(x,x \ z,T(y,x * z)). [para(778(a,1),56(a,1,1)),rewrite([16(2),16(5),16(10)])]. 1353 x * (y / (x * (x * y))) = x \ 1. [para(997(a,1),778(a,2,2)),rewrite([996(7),1014(5)])]. 1359 x * (y * T(z,y * (x * y))) = y \ (z * (y * (x * y))). [para(788(a,1),15(a,1,2)),flip(a)]. 1448 R((x * (y * x)) \ 1,x * (y * x),z) = z / (x * (y * (x * z))). [para(997(a,1),121(a,1,1,1)),rewrite([13(2)]),flip(a)]. 1452 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,x \ y). [para(268(a,1),18(a,1,1)),rewrite([200(5)])]. 1457 R(x,y \ z,(y \ z) \ z) \ ((x * (y \ z)) * T(y,y \ z)) = z. [para(268(a,1),50(a,1,1))]. 1466 (T(T(x,y),z) * u) * z = (T(T(x,z),y) * u) * z. [para(16(a,1),863(a,1,1,2)),rewrite([16(8)])]. 1479 x * (x * ((T(T(y,z),u) * (u * w)) * u)) = x * (x * ((T(T(y,u),z) * (u * w)) * u)). [para(863(a,1),37(a,2,2,2)),rewrite([37(7)])]. 1517 (x * (y * z)) / T((x * z) * T(y,z),a(z,z \ x,y * z)) = a(z,z \ x,y * z). [para(90(a,1),732(a,1,1,2)),rewrite([90(8),90(13)])]. 1524 L(x * ((y * (y * x)) \ z),y,y) = (y * y) \ z. [para(18(a,1),780(a,2,2)),rewrite([92(6)])]. 1534 L(x / (y * (y * x)),y,y) = (y * y) \ 1. [para(997(a,1),780(a,2,2)),rewrite([996(7),1014(5)])]. 1603 (x * (x * ((T(T(y,z),u) * (u * w)) * u))) / (x * (x * ((T(T(y,u),z) * (u * w)) * u))) = 1. [para(1479(a,1),265(a,1,2,1)),rewrite([100(7),1300(20),88(16),1300(21)])]. 1607 L(x,y,y) = x. [hyper(24,a,1300,a)]. 1609 x / (y * (y * x)) = (y * y) \ 1. [back_rewrite(1534),rewrite([1607(4)])]. 1619 x * ((y * (y * x)) \ z) = (y * y) \ z. [back_rewrite(1524),rewrite([1607(5)])]. 1649 x / (x * x) = x \ 1. [back_rewrite(1353),rewrite([1609(3),1014(4)])]. 1659 T(x * x,x) = x * x. [hyper(28,a,1316,a)]. 1667 L(x,y,x) = x. [para(15(a,1),1180(a,1,2))]. 1684 a(x,y,x) = 1. [hyper(25,a,1667,a)]. 1685 L(T(x,y),z,x) = T(x,y). [para(1667(a,1),30(a,1,1)),flip(a)]. 1689 L(L(L(x,y,z),u,w),v5,L(x,u,w)) = L(L(x,u,w),y,z). [para(1667(a,1),97(a,1,1)),flip(a)]. 1699 ((x \ y) * x) \ ((x \ y) * y) = x \ y. [para(1667(a,1),74(a,1)),flip(a)]. 1702 a((x \ y) * x,x \ y,z) = a(x \ y,y,z). [para(1667(a,1),662(a,1,1,2,1)),rewrite([189(5),16(3),19(7),1699(9)]),flip(a)]. 1708 T(x,x * y) = T(x,y). [back_rewrite(639),rewrite([1685(2)]),flip(a)]. 1723 K(x,(y * x) / y) = 1. [para(15(a,1),554(a,1,1))]. 1812 T(x * y,y \ 1) = (y \ 1) \ x. [para(1013(a,1),92(a,1,1))]. 1826 K(x * y,(y \ 1) \ x) = 1. [para(1013(a,1),568(a,1,1))]. 1829 x \ (x / y) = y \ 1. [para(1014(a,1),15(a,1,2))]. 1832 (x / y) \ ((y \ 1) * x) = K(y \ 1,x). [para(1014(a,1),20(a,1,1))]. 1833 ((x \ 1) * y) \ (y / x) = K(y,x \ 1). [para(1014(a,1),20(a,1,2))]. 1834 (x / y) \ (x * ((y \ 1) * z)) = L(z,y \ 1,x). [para(1014(a,1),21(a,1,1))]. 1836 ((x * y) / z) / (y / z) = R(x,y,z \ 1). [para(1014(a,1),22(a,1,1)),rewrite([1014(5)])]. 1837 (x \ 1) \ (y / x) = T(y,x \ 1). [para(1014(a,1),23(a,1,2))]. 1838 x * (x * ((y \ 1) * z)) = (x * (x / y)) * z. [para(1014(a,1),37(a,1,1,2)),flip(a)]. 1839 (x * (x * y)) / z = x * (x * (y / z)). [para(1014(a,1),37(a,1)),rewrite([1014(6)])]. 1840 x * ((x \ y) * (x / z)) = (y * x) / z. [para(1014(a,1),104(a,1,2,2)),rewrite([1014(8)])]. 1851 (x * (y * (x * (z * (x * (y * x)))))) / u = x * (y * (x * (z * (x * (y * (x / u)))))). [para(1014(a,1),129(a,1)),rewrite([1014(10)])]. 1859 x * (T(y,x) * (x / z)) = ((y * x) * x) / z. [para(1014(a,1),186(a,1,2,2)),rewrite([1014(9)])]. 1864 ((T(x,y) * (y / z)) * y) \ (((x * y) * y) / z) = K(y,T(x,y) * (y / z)). [para(1014(a,1),675(a,1,1,1,2)),rewrite([1014(9),1014(12)])]. 1870 x * (x * ((y * (((x * (x * y)) \ z) * u)) / u)) = R(z,x * (x * y),(x * (x * y)) \ u). [para(205(a,1),1014(a,2)),rewrite([1014(10),1839(8)])]. 1884 x * (x * ((y / z) / T(x * (x * y),z \ 1))) = z \ 1. [para(1014(a,1),961(a,1,1,2,2)),rewrite([1839(9)])]. 1885 x * (x * ((y * z) / T(x * (x * y),z))) = z. [para(961(a,1),1014(a,2)),rewrite([1014(9),1839(7)])]. 1888 x * ((y \ 1) * T(z,x * (x / y))) = x \ (z * (x * (x / y))). [para(1014(a,1),778(a,1,2,2,2,2)),rewrite([1014(10)])]. 1907 x * (x * (((T(T(y,z),u) * (u * w)) * u) / (x * (x * ((T(T(y,u),z) * (u * w)) * u))))) = 1. [back_rewrite(1603),rewrite([1839(15)])]. 1921 x * (x * ((y * z) / T(x * (x * z),T(y,z)))) = T(y,z). [back_rewrite(1252),rewrite([1839(8)])]. 1925 x * (x * (y / T(x * (x * (y / z)),z))) = z. [back_rewrite(1246),rewrite([1839(7)])]. 1932 x * (x * (((x * y) * z) / (x * (x * (y * z))))) = R(x,x * (x * y),z). [back_rewrite(345),rewrite([1839(8)])]. 1935 x * (x * R(y,z,u)) = R(x * (x * y),z,u). [back_rewrite(146),rewrite([1839(6),22(4)])]. 1952 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(x / (y * (y * z)),y * (y * z),u). [para(37(a,1),60(a,1,1,2))]. 1958 ((x / y) * (z * y)) \ (x * T(z,y)) = a(x / y,y,T(z,y)). [para(90(a,1),60(a,1,1,2))]. 1961 L(a(x / y,y,z),(x / y) * (y * z),u) = (u * ((x / y) * (y * z))) \ (u * (x * z)). [para(60(a,1),74(a,1,1))]. 1972 R(x,x / y,(x / y) \ (y \ z)) = ((x / y) * z) / (y \ z). [para(16(a,1),208(a,2,1,2))]. 1990 R(x,x / y,(x / y) \ T(z,y)) = ((x / y) * (z * y)) / T(z,y). [para(90(a,1),208(a,2,1,2))]. 2004 R(x,x * y,(x * y) \ z) = ((x * y) * ((y \ 1) * z)) / z. [para(1013(a,1),208(a,1,2)),rewrite([1013(4),1013(7)])]. 2009 (x / y) * ((x / y) * ((y * z) / T((x / y) * x,z))) = z. [para(18(a,1),1885(a,1,2,2,2,1,2))]. 2010 (x * y) / T(z * (z * x),y) = (z * z) \ y. [para(1885(a,1),21(a,1,2)),rewrite([1607(8)]),flip(a)]. 2012 x * (x * (((x * x) \ y) * z)) = y * z. [para(1885(a,1),37(a,1,1)),rewrite([2010(6)]),flip(a)]. 2032 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (((T(y,z) * x) * x) * u),w))) = w. [para(682(a,1),1885(a,1,2,2,2,1,2))]. 2040 (x * (y * y)) * z = x * (y * (y * z)). [back_rewrite(407),rewrite([2012(7)]),flip(a)]. 2044 R(x,y * y,z) = x. [back_rewrite(338),rewrite([2040(3),17(6)]),flip(a)]. 2045 a(x,y * y,z) = 1. [back_rewrite(311),rewrite([2040(6),46(7)]),flip(a)]. 2166 x / (T(T(y,z),u) * (z * (((T(y,u) * z) * z) \ x))) = z. [para(16(a,1),1266(a,1,1))]. 2213 (x * (y * (y * x))) * z = x * (y * (y * (x * z))). [para(13(a,1),130(a,1,1,2,2)),rewrite([13(8)])]. 2214 (x * (y * (z * (y * x)))) \ (x * (y * (z * (y * (x * u))))) = u. [para(130(a,1),15(a,1,2))]. 2215 x * (y * (z * (y * (x * ((x * (y * (z * (y * x)))) \ u))))) = u. [para(130(a,1),16(a,1))]. 2234 T(x,y) * (y * (z * (y * (T(x,y) * u)))) = (T(x,y) * (y * (z * (x * y)))) * u. [para(90(a,1),130(a,1,1,2,2,2)),flip(a)]. 2243 x * (y * (((y * x) \ 1) * (y * (x * z)))) = (x * y) * z. [para(997(a,1),130(a,1,1,2,2)),rewrite([14(2)]),flip(a)]. 2254 L(x,y,z * z) = x. [para(13(a,1),132(a,1,1,2)),rewrite([13(6),638(6),667(3),13(2)]),flip(a)]. 2276 L(x,y,z * (((z * y) \ 1) * z)) = ((z * y) \ 1) * (z * (y * x)). [para(997(a,1),132(a,1,1,2)),rewrite([14(2),15(8)]),flip(a)]. 2278 L(x,y,z * (((z * (y * x)) \ 1) * z)) = (((z * (y * x)) \ 1) * (z * y)) \ 1. [para(997(a,1),132(a,1,2,2)),rewrite([14(9),1091(8)]),flip(a)]. 2356 L(L(L(x,y,z),u,(u * x) \ 1),((u * x) \ 1) * u,w) = L(L(x,u,(u * x) \ 1),y,z). [para(1026(a,1),1078(a,1,2,1)),rewrite([990(13)])]. 2357 L(L(x,y,(y * x) \ 1),z,u) = L((((y * x) \ 1) * y) \ 1,z,u). [para(1026(a,1),1078(a,2,1)),rewrite([1141(11),2356(10)])]. 2445 ((x \ y) * (x * ((x \ y) * z))) \ (((x \ y) * y) * z) = 1. [para(13(a,1),314(a,1,1)),rewrite([13(9),52(13)])]. 2485 L(x,y * y,z) = x. [hyper(24,a,2045,a)]. 2486 a(x,y * (y * (z * (y * (y * z)))),u) = 1. [para(37(a,1),2045(a,1,2))]. 2495 (x * (x * y)) \ (x * (x * z)) = y \ z. [para(2254(a,1),74(a,1)),rewrite([100(3),100(5)]),flip(a)]. 2497 L(x,y,(z \ 1) / z) = x. [para(1014(a,1),2254(a,1,3))]. 2507 L(x,y,z * (z * u)) = L(x,y,u). [back_rewrite(144),rewrite([2495(8),21(4)]),flip(a)]. 2508 a(x * (x * y),z,u) = a(y,z,u). [back_rewrite(140),rewrite([2495(9),19(5)]),flip(a)]. 2522 L(x,y * (y * (z * (y * (y * z)))),u) = x. [para(37(a,1),2485(a,1,2))]. 2528 L(x,(y \ 1) / y,z) = x. [para(1014(a,1),2485(a,1,2))]. 2538 (x \ y) \ 1 = y \ x. [para(16(a,1),1091(a,1,1)),flip(a)]. 2540 ((x \ y) * (x * z)) \ 1 = ((y * x) * z) \ x. [para(104(a,1),1091(a,1,1)),flip(a)]. 2548 ((x * y) * z) \ (x * (y * z)) = a(x,y,z) \ 1. [para(54(a,1),1091(a,1,1))]. 2551 x * (x * ((y * z) * K((y \ 1) * ((x * y) * z),x * y))) = ((y \ 1) * ((x * y) * z)) * (x * y). [para(1091(a,1),350(a,1,2,1,1)),rewrite([37(3),37(11),1091(13)])]. 2556 ((x / y) * ((y \ 1) \ z)) / z = R(x,y \ 1,(y \ 1) \ z). [para(1091(a,1),268(a,1,1,1,2)),rewrite([1014(3),1091(4),1812(5),1091(8),1091(10)])]. 2560 T(x * y,(y \ 1) \ x) = x * y. [para(1091(a,1),560(a,1,2,1))]. 2574 a(x,T(y,x),x * z) = a(y * x,x,z) \ 1. [back_rewrite(673),rewrite([2548(7)]),flip(a)]. 2575 a(x,x \ y,x * z) = a(y,x,z) \ 1. [back_rewrite(173),rewrite([2548(8)])]. 2599 ((x / y) * (y * y)) / T(x * y,a(x,y \ 1,y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),729(a,1,1,1,2)),rewrite([1014(3),1649(6),1649(12)])]. 2601 ((x / y) * (y * y)) \ ((y \ 1) \ x) = K(((y \ 1) \ x) * y,y \ 1). [para(1649(a,1),354(a,1,1,1,2)),rewrite([1014(3),1649(5),1649(9),1014(10),17(8),1649(9),1649(13)])]. 2604 (x * y) \ ((x / y) * (y * y)) = a(x,y \ 1,y * y). [para(1649(a,1),58(a,1,2,1,2)),rewrite([1014(4),1649(7)])]. 2635 T(T(x * x,y),x) = T(x * x,y). [para(1659(a,1),29(a,1,1)),flip(a)]. 2639 T((x \ 1) / x,x \ 1) = (x \ 1) / x. [para(1014(a,1),1659(a,1,1)),rewrite([1014(11)])]. 2640 x * (x * (y * (y * (z / (T(x * x,y) * (y * z)))))) = y. [para(1659(a,1),1266(a,1,1,1,1,1)),rewrite([100(2),37(3),37(4),100(2),2635(7),1839(9),1839(7)])]. 2642 T(x,x \ y) = T(x,y). [para(16(a,1),1708(a,1,2)),flip(a)]. 2643 T(x / y,x) = y \ x. [para(18(a,1),1708(a,1,2)),rewrite([92(4)])]. 2644 T(T(x,y),x * z) = T(T(x,z),y). [para(1708(a,1),29(a,1,1)),flip(a)]. 2645 L(T(x,L(x,y,z) * u),y,z) = L(T(x,u),y,z). [para(1708(a,1),30(a,1)),rewrite([30(2)]),flip(a)]. 2647 T(x * (x * y),x * (x * (y * z))) = T(x * (x * y),z). [para(37(a,1),1708(a,1,2))]. 2648 T(x,(x \ y) * (x * z)) = T(x,(y * x) * z). [para(104(a,1),1708(a,1,2)),flip(a)]. 2649 (x \ y) \ y = T(x,y). [para(91(a,1),1708(a,2)),rewrite([16(2)]),flip(a)]. 2652 T(x,y * x) = T(x,T(y,x)). [para(90(a,1),1708(a,1,2))]. 2690 (x \ y) * T(x,y) = y. [back_rewrite(1457),rewrite([2649(3),2642(7),166(8)])]. 2692 (x \ y) * (((x \ y) \ z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(1452),rewrite([2642(9)])]. 2697 a(x * (y \ x),T(y,x),z) = a(y \ x,T(y,x) * x,z). [back_rewrite(1301),rewrite([2642(4),2642(7)])]. 2700 T(x,L(y * z,y \ x,y)) = T(x,(x * y) * z). [back_rewrite(1201),rewrite([2642(8)])]. 2705 L(x \ y,x,z) \ (z * y) = T(z * x,z * y). [back_rewrite(650),rewrite([2642(5)]),flip(a)]. 2708 ((x * (y \ z)) * T(y,z)) / z = R(x,y \ z,T(y,z)). [back_rewrite(268),rewrite([2642(4),2649(8)])]. 2709 T(x \ y,T(x,y)) = T(x,y) \ y. [back_rewrite(221),rewrite([2642(3),2649(5)])]. 2711 x / T(y,x) = y \ x. [back_rewrite(218),rewrite([2642(2)])]. 2712 (x \ 1) / x = x \ (x \ 1). [back_rewrite(2639),rewrite([2643(6)]),flip(a)]. 2713 ((x \ y) * (x * z)) \ ((y * x) * z) = T(x,(y * x) * z). [back_rewrite(185),rewrite([2648(10)])]. 2747 L(x,y \ (y \ 1),z) = x. [back_rewrite(2528),rewrite([2712(3)])]. 2748 L(x,y,z \ (z \ 1)) = x. [back_rewrite(2497),rewrite([2712(3)])]. 2755 (x \ 1) \ y = x * y. [back_rewrite(1227),rewrite([2747(5)]),flip(a)]. 2757 ((x / y) * (y * y)) \ (y * x) = K(y * (x * y),y \ 1). [back_rewrite(2601),rewrite([2755(6),2755(8),101(7)])]. 2759 T(x * y,y * x) = x * y. [back_rewrite(2560),rewrite([2755(4)])]. 2760 ((x / y) * (y * z)) / z = R(x,y \ 1,y * z). [back_rewrite(2556),rewrite([2755(4),2755(9)])]. 2771 T(x,y \ 1) = y * (x / y). [back_rewrite(1837),rewrite([2755(4)]),flip(a)]. 2772 K(x * y,y * x) = 1. [back_rewrite(1826),rewrite([2755(4)])]. 2774 T(x * y,y \ 1) = y * x. [back_rewrite(1812),rewrite([2755(7)])]. 2796 R(x,x / y,(x / y) \ z) = R(x,y \ 1,y * z). [back_rewrite(208),rewrite([2760(8)])]. 2802 ((x / y) * (z * y)) / T(z,y) = R(x,y \ 1,z * y). [back_rewrite(1990),rewrite([2796(5),90(4)]),flip(a)]. 2806 ((x / y) * z) / (y \ z) = R(x,y \ 1,z). [back_rewrite(1972),rewrite([2796(5),16(4)]),flip(a)]. 2810 T(x,(y * x) / y) = x. [hyper(28,a,1723,a)]. 2852 x * K(y \ x,y) = (y \ x) * y. [para(16(a,1),63(a,1,1))]. 2853 x * K(y,x / y) = y * (x / y). [para(18(a,1),63(a,1,1))]. 2855 (x * y) \ (K(x,y) * (y * x)) = K(K(x,y),y * x). [para(63(a,1),20(a,1,1))]. 2857 (x * y) \ ((y * x) * (K(x,y) * z)) = L(z,K(x,y),y * x). [para(63(a,1),21(a,1,1))]. 2858 ((x * y) * z) / (K(x,y) * z) = R(y * x,K(x,y),z). [para(63(a,1),22(a,1,1,1))]. 2880 ((x * (y * z)) * K(z,y)) / T(x * (z * y),a(x,y * z,K(z,y))) = a(x,y * z,K(z,y)). [para(63(a,1),265(a,1,2,1,2))]. 2887 (x * y) / T(y * x,K(x,y)) = K(x,y). [para(63(a,1),165(a,1,1))]. 2903 (x / y) * (y \ x) = (y \ x) * (x / y). [para(554(a,1),63(a,1,2)),rewrite([14(5)])]. 2917 K(x,y) \ 1 = K(y,x). [para(63(a,1),1091(a,1,1)),rewrite([20(3)]),flip(a)]. 2918 T(x * y,K(y,x)) = x * y. [para(63(a,1),1708(a,1,2)),rewrite([2759(3)]),flip(a)]. 2925 (x * y) / (y * x) = K(x,y). [back_rewrite(2887),rewrite([2918(4)])]. 2934 (x * (y * z)) \ (L(z,y,x) * (x * y)) = K(L(z,y,x),x * y). [para(21(a,1),64(a,1,2,1)),rewrite([21(10)])]. 2935 x * (K(y \ x,y) * (x * z)) = (((y \ x) * y) * x) * z. [para(64(a,1),104(a,1,2,1))]. 2962 x \ ((y \ 1) * (x * y)) = K(y \ 1,x * y). [para(1091(a,1),64(a,1,2,1)),rewrite([1091(7)])]. 2965 x * (((x \ y) * x) * z) = y * (x * z). [para(16(a,1),189(a,1,1)),flip(a)]. 2971 L(a(x,y,z),x * (y * z),y) = a(y,x,y * z). [para(189(a,1),19(a,1,2)),rewrite([589(7)])]. 2975 L(x,y * z,z) = L(x,z,z * y). [para(189(a,1),21(a,1,2)),rewrite([101(2),21(6)])]. 2993 x * ((T(y,x) * x) * z) = (y * x) * (x * z). [para(90(a,1),189(a,1,1)),flip(a)]. 3018 L(x * (y * z),x \ y,x) = (x * y) * z. [para(189(a,1),181(a,2,2)),rewrite([15(8)])]. 3031 x * (((y \ 1) * x) * z) = (x / y) * (x * z). [para(1014(a,1),189(a,1,1)),flip(a)]. 3032 (x * y) * (x / z) = x * ((y * x) / z). [para(1014(a,1),189(a,1,2)),rewrite([1014(7)])]. 3050 L(x,y * (z * (y * z)),u) = x. [para(189(a,1),2485(a,1,2)),rewrite([101(2)])]. 3078 x * (y * ((y * (x * y)) \ z)) = y \ z. [para(103(a,1),15(a,1,2)),flip(a)]. 3093 x * a(y,z,y * ((y * (z * y)) \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [para(103(a,1),54(a,1,1)),rewrite([189(12)])]. 3097 (x \ y) * (T(x,y) * ((x \ y) * z)) = (y * (x \ y)) * z. [para(103(a,1),186(a,2,1,1)),rewrite([3078(5),3078(6),2642(3),3078(7),3078(11)])]. 3103 x * ((x \ 1) * y) = y. [para(997(a,1),103(a,1,2,2,2,1,2)),rewrite([14(4),16(4)])]. 3118 L((x * (y * x)) \ z,x,y * (x * y)) = (y * (x * (y * x))) \ (y * z). [para(103(a,1),132(a,1,2,2)),flip(a)]. 3130 K(x,(x \ 1) * (y / x)) = K(y,x \ 1). [back_rewrite(1004),rewrite([3103(8),1833(5)]),flip(a)]. 3135 (x * y) \ (x * (x * z)) = (x \ y) \ z. [para(16(a,1),2495(a,1,1,2))]. 3136 (x * (x * y)) \ (x * z) = y \ (x \ z). [para(16(a,1),2495(a,1,2,2))]. 3139 T(x * (x * (y / (x * (x * z)))),x * (x * z)) = z \ y. [para(2495(a,1),92(a,2)),rewrite([1839(5)])]. 3141 L(x \ y,z * (z * x),u) = (u * (z * (z * x))) \ (u * (z * (z * y))). [para(2495(a,1),74(a,1,1))]. 3143 (x \ 1) * y = x \ y. [para(997(a,1),2495(a,1,1,2)),rewrite([14(4),15(9)])]. 3162 (x \ ((x * y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(141),rewrite([3135(7)])]. 3163 K(x,x \ (y / x)) = K(y,x \ 1). [back_rewrite(3130),rewrite([3143(4)])]. 3169 (x / y) * (x * z) = x * ((y \ x) * z). [back_rewrite(3031),rewrite([3143(3)]),flip(a)]. 3171 K(x \ 1,y * x) = y \ T(y,x). [back_rewrite(2962),rewrite([3143(4),23(2)]),flip(a)]. 3184 x * (x * ((y * z) * K((y \ x) * (y * z),x * y))) = ((y \ x) * (y * z)) * (x * y). [back_rewrite(2551),rewrite([3143(6),168(4),3143(14),168(12)])]. 3191 L(L(x,y,(y * x) \ 1),z,u) = L(x,z,u). [back_rewrite(2357),rewrite([3143(9),1091(7),2649(9),88(7)])]. 3192 L(L(x,y,z),u,(u * x) \ 1) = L(x,y,z). [back_rewrite(2356),rewrite([3143(9),1091(7),1080(8),3191(10)])]. 3199 L(x,y,z / (y * x)) = L(x,y,z). [back_rewrite(2278),rewrite([3143(5),1091(3),1014(4),3143(9),2538(9),21(7)])]. 3200 L(x,y,z / y) = L(x,y,z). [back_rewrite(2276),rewrite([3143(4),1091(2),1014(3),3143(8),21(6)])]. 3204 x * (y * L(z,x,y)) = (x * y) * z. [back_rewrite(2243),rewrite([3143(6),21(4)])]. 3213 R(x,x * y,(x * y) \ z) = R(x,y,y \ z). [back_rewrite(2004),rewrite([3143(8),169(7),191(8)])]. 3218 x * (y \ T(z,x * (x / y))) = x \ (z * (x * (x / y))). [back_rewrite(1888),rewrite([3143(6)])]. 3228 (x * (x / y)) * z = x * (x * (y \ z)). [back_rewrite(1838),rewrite([3143(3)]),flip(a)]. 3229 (x / y) \ (x * (y \ z)) = L(z,y \ 1,x). [back_rewrite(1834),rewrite([3143(4)])]. 3230 (x \ y) \ (y / x) = K(y,x \ 1). [back_rewrite(1833),rewrite([3143(3)])]. 3231 (x / y) \ (y \ x) = K(y \ 1,x). [back_rewrite(1832),rewrite([3143(4)])]. 3266 L(x,y,y \ 1) = x. [back_rewrite(1025),rewrite([3143(4),15(2)]),flip(a)]. 3276 x \ ((x / y) * (y * z)) = L(z,y,x). [back_rewrite(75),rewrite([3200(6)])]. 3286 (x / y) * (y * ((x / y) * z)) = x * (x * (y \ z)). [back_rewrite(107),rewrite([3228(8)])]. 3302 K(x * y,K(y,x)) = 1. [hyper(27,a,2918,a)]. 3304 T(x,K(y \ x,y)) = x. [para(16(a,1),2918(a,1,1)),rewrite([16(5)])]. 3305 T(x,K(y,x / y)) = x. [para(18(a,1),2918(a,1,1)),rewrite([18(5)])]. 3307 T((x * y) * z,K((y \ x) * (y * z),y)) = (x * y) * z. [para(104(a,1),2918(a,1,1)),rewrite([104(11)])]. 3308 K(x,y) * (y * x) = x * y. [para(2918(a,1),90(a,1,2)),rewrite([63(6)])]. 3323 (((x \ y) * (x * z)) * x) / ((y * x) * z) = K((x \ y) * (x * z),x). [back_rewrite(969),rewrite([3307(11)])]. 3327 K(K(x,y),y * x) = 1. [back_rewrite(2855),rewrite([3308(4),46(3)]),flip(a)]. 3382 T(T(T(x,y \ 1),z),u) / y = T(T(T(x,z),u),y \ 1) / y. [para(94(a,1),1009(a,2,1)),rewrite([1009(12)]),flip(a)]. 3436 (x * x) \ y = x \ (x \ y). [para(18(a,1),1324(a,1,2,2)),rewrite([92(8),1619(6)]),flip(a)]. 3476 x * T(y * z,y * (y * x)) = (y \ z) * (y * (y * x)). [para(181(a,2),1324(a,1,2)),rewrite([3018(5),168(4)]),flip(a)]. 3482 x \ T(y,z * (z / x)) = z \ (z \ (y * (z * (z / x)))). [para(1014(a,1),1324(a,1,2,2,2,2)),rewrite([1014(10),3143(11)]),flip(a)]. 3541 x \ (y \ (z * (y * (x * y)))) = y * T(z,y * (x * y)). [para(1359(a,1),15(a,1,2))]. 3544 (x \ (y * (x * (z * x)))) / (x * T(y,x * (z * x))) = z. [para(1359(a,1),17(a,1,1))]. 3575 x * (y \ T(z,y \ (x / y))) = y * (z * (y \ (x / y))). [para(1014(a,1),1359(a,1,2,2,2,2)),rewrite([3143(6),3143(6),1014(12),3143(11),2755(11)])]. 3576 a(x / y,y,T(z,y * x)) = a(y,y \ x,T(z,y * x)). [para(1359(a,1),60(a,1,1)),rewrite([18(2),18(5),1346(7),18(7)]),flip(a)]. 3640 x * (x * (((x \ y) / z) / T(x * y,z \ 1))) = z \ 1. [para(16(a,1),1884(a,1,2,2,2,1,2))]. 3641 x * (x * (y / T(x * (x * (y * z)),z \ 1))) = z \ 1. [para(17(a,1),1884(a,1,2,2,1))]. 3645 (x / y) / T(z * (z * x),y \ 1) = z \ (z \ (y \ 1)). [para(1884(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 3646 R(x,x \ (y \ 1),z) = (y \ z) / ((x \ (y \ 1)) * z). [para(1884(a,1),22(a,1,1,1)),rewrite([3143(3),3645(8),16(6),3645(13),16(11)]),flip(a)]. 3666 (x \ y) / y = x \ 1. [para(1884(a,1),201(a,1,2)),rewrite([3645(8),100(6),16(5),16(4),3645(11),16(9),16(8),2755(7),480(6),3645(9),16(7),16(6),3645(11),1300(9),13(6),3143(5)]),flip(a)]. 3670 x * (x * (((T(y,x) * (x * z)) / u) / T(x * (((y * x) * x) * z),u \ 1))) = u \ 1. [para(186(a,1),1884(a,1,2,2,2,1,2))]. 3683 x * ((x \ (y \ 1)) * T(z,x / y)) = x \ (z * (x / y)). [para(1884(a,1),778(a,1,2,2,2,2)),rewrite([3645(7),16(5),1014(6),3645(14),16(12),16(11),1014(10)])]. 3691 x / (y * x) = y \ 1. [para(1884(a,1),1013(a,2)),rewrite([3645(7),16(5),2538(5),2755(3)])]. 3709 x \ (x \ (y * (x / z))) = (x \ (z \ 1)) * T(y,x / z). [para(1884(a,1),1324(a,1,2,2,2,2)),rewrite([1014(3),3645(11),16(9),3645(14),16(12),16(11),1014(10)])]. 3710 (x \ (x \ (y \ 1))) * T(z,y \ 1) = x \ (x \ (z / y)). [para(1884(a,1),1324(a,1,2,2,2)),rewrite([1014(3),3645(10),3645(14),16(12),16(11)]),flip(a)]. 3723 R(x \ 1,x,y) = x \ 1. [back_rewrite(1027),rewrite([3691(5)])]. 3724 x / (y * (z * (y * x))) = (y * (z * y)) \ 1. [back_rewrite(1448),rewrite([3723(7)]),flip(a)]. 3725 x / (y * (y * (z * x))) = (y * (y * z)) \ 1. [back_rewrite(1039),rewrite([3723(7)]),flip(a)]. 3735 a(x * (y * x),y,z) = a(x,y * (x * y),z). [para(133(a,1),110(a,1))]. 3752 (x * (y * (y * z))) \ ((x * (y * (y * u))) * (u \ z)) = a(x,y * (y * u),u \ z). [para(16(a,1),139(a,1,1,2,2,2))]. 3753 (x * (y * (y * z))) \ ((x * (y * (y * (z / u)))) * u) = a(x,y * (y * (z / u)),u). [para(18(a,1),139(a,1,1,2,2,2))]. 3762 a(x * ((y * x) * x),z,u) = a(x * y,x * (x * z),u). [para(189(a,1),139(a,1,1)),rewrite([189(9),133(11)])]. 3794 T(T(T(T(T(x,y),z),u \ 1),w),v5) / u = T(T(T(T(T(x,w),y),z),v5),u \ 1) / u. [para(94(a,1),3382(a,2,1,1,1))]. 3933 x * (y * (x * (x * (y * (z * ((y * (x * (x * (y * z)))) \ u)))))) = x * u. [para(398(a,1),15(a,1,2)),rewrite([15(3)]),flip(a)]. 3934 K(x * y,x) = y \ T(y,x). [para(398(a,1),20(a,1,1)),rewrite([3933(13),101(4),3136(5),23(2),3933(13)]),flip(a)]. 3935 K(x,x * y) = T(y,x) \ y. [para(398(a,1),20(a,1,2)),rewrite([3933(11),101(2),3135(5),23(2),3933(13)]),flip(a)]. 3936 x * (y * (y * (x * (z * ((x * (y * (y * (x * z)))) \ u))))) = u. [para(398(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 3940 L((x * y) \ z,x * y,x) = y \ (x \ z). [para(398(a,1),74(a,2,1)),rewrite([3936(10),3936(12),3136(8)])]. 3941 L(x \ (y * z),x,y) = (y \ x) \ z. [para(398(a,1),74(a,2,2)),rewrite([3936(10),3135(7)])]. 3947 x * (x * (y * (x * (x * (y * (z \ ((y * (x * (x * (y / z)))) \ u))))))) = x * (x * u). [para(1014(a,1),398(a,1,2,2,2,2,2,2,2,1,2,2,2)),rewrite([3143(8)])]. 3949 x * (x * (y * ((x * (x * (x * (x * y)))) \ z))) = x \ (x \ z). [para(398(a,1),132(a,1,2)),rewrite([3135(6),15(3),3436(2),2507(13),1607(11)]),flip(a)]. 3954 a(x,x \ y,z) = a(x,x * y,z). [para(398(a,1),133(a,1,2,1)),rewrite([3949(8),16(3),136(4),37(6),3135(7),3162(5),3949(12),16(7),2508(6)]),flip(a)]. 3968 a(x / y,y,T(z,y * x)) = a(y,y * x,T(z,y * x)). [back_rewrite(3576),rewrite([3954(8)])]. 3982 a(x,x * y,x * z) = a(y,x,z) \ 1. [back_rewrite(2575),rewrite([3954(3)])]. 4007 (x * (y * z)) / T((x * z) * T(y,z),a(z,z * x,y * z)) = a(z,z * x,y * z). [back_rewrite(1517),rewrite([3954(8),3954(13)])]. 4013 (x * ((x \ (y \ 1)) * y)) \ 1 = a(x,x / y,y). [back_rewrite(1051),rewrite([3954(11),1014(10)])]. 4021 ((x * y) * (L(y \ z,y,x) * u)) \ ((x * z) * u) = a(x * y,x * ((y * x) * z),u). [back_rewrite(662),rewrite([3954(13),189(12)])]. 4025 (x * ((x \ y) * ((y \ z) * (y * u)))) \ ((z * y) * u) = a(x,x * y,(y \ z) * (y * u)). [back_rewrite(614),rewrite([3954(14)])]. 4031 T(x * ((x \ y) * z),a(x,x * y,z)) = a(x,x * y,z) \ (y * z). [back_rewrite(260),rewrite([3954(5),3954(8)])]. 4032 (x * ((x \ y) * z)) \ (y * z) = a(x,x * y,z). [back_rewrite(56),rewrite([3954(7)])]. 4097 T(T(T(T(T(x,y),z \ 1),u),w),v5) / z = T(T(T(T(T(x,w),u),y),v5),z \ 1) / z. [para(94(a,2),3794(a,1,1,1,1))]. 4108 K(x * y,K(x,y)) = 1. [para(1684(a,1),2880(a,1,2,2)),rewrite([3308(3),88(8),2925(7),1684(7)])]. 4114 ((x * y) * z) \ R(x,y,z) = (y * z) \ 1. [para(22(a,1),1829(a,1,2))]. 4115 ((x / y) * x) * z = x * (y \ (x * z)). [para(1829(a,1),104(a,1,2,1)),rewrite([3143(4)]),flip(a)]. 4137 (x \ y) * (y \ x) = 1. [para(2538(a,1),16(a,1,2))]. 4138 (x * (y * z)) \ (x * y) = L(z,y,x) \ 1. [para(21(a,1),2538(a,1,1)),flip(a)]. 4145 L(x \ y,y \ x,z) = x \ y. [para(2538(a,1),74(a,1,1)),rewrite([14(7),1091(6),2538(6)])]. 4151 a(x,y \ z,z \ y) = 1. [para(2538(a,1),1012(a,1,2))]. 4155 x / (y \ z) = x * (z \ y). [para(2538(a,1),1013(a,1,2))]. 4157 (x * y) \ ((x / z) * (z * y)) = a(x / z,z,y) \ 1. [para(60(a,1),2538(a,1,1)),flip(a)]. 4165 L(x,y \ z,z \ y) = x. [para(2538(a,1),3266(a,1,3))]. 4180 x * ((x \ (y / z)) * z) = R(y,z \ 1,x). [back_rewrite(2806),rewrite([4155(4),169(4)])]. 4186 R(x,y,y \ ((y \ x) \ z)) = z * ((z \ y) * (y \ x)). [back_rewrite(199),rewrite([4155(8),169(8)])]. 4187 a(x / y,y,y) \ 1 = a(x,y \ 1,y * y). [back_rewrite(2604),rewrite([4157(5)])]. 4206 T((x / y) * (y * z),x * z) = a(x / y,y,z) \ (x * z). [para(60(a,1),2642(a,1,2)),rewrite([263(6)]),flip(a)]. 4209 T(x * y,x) = y * x. [para(1091(a,1),2642(a,1,2)),rewrite([2774(4)]),flip(a)]. 4210 T(x,(y \ x) * y) = x. [para(64(a,1),2642(a,1,2)),rewrite([3304(3)]),flip(a)]. 4214 T(T(T(x,y),z),T(T(x,z),y) \ u) = T(T(T(x,z),y),u). [para(2642(a,1),94(a,2)),rewrite([29(6)])]. 4230 (x / y) * x = x * (y \ x). [para(2643(a,1),90(a,1,2)),flip(a)]. 4231 T(x \ y,y) = T(x \ y,x). [para(2643(a,1),537(a,1,1)),flip(a)]. 4247 (x * (y \ x)) * z = x * (y \ (x * z)). [back_rewrite(4115),rewrite([4230(2)])]. 4254 (x / y) * ((x / y) * ((y * z) / T(x * (y \ x),z))) = z. [back_rewrite(2009),rewrite([4230(5)])]. 4261 (x \ y) * (T(x,y) * ((x \ y) * z)) = y * (x \ (y * z)). [back_rewrite(3097),rewrite([4247(9)])]. 4278 T(x,y) \ y = T(x \ y,y). [para(2649(a,1),2642(a,1,2)),rewrite([2709(3)])]. 4281 T(x \ y,T(x,y)) = T(x \ y,y). [back_rewrite(2709),rewrite([4278(5)])]. 4304 T(x,y) * T(x \ y,y) = y. [para(2690(a,1),90(a,2)),rewrite([4281(4)])]. 4308 (x * y) * a(x,z \ y,T(z,y)) = (x * (z \ y)) * T(z,y). [para(2690(a,1),54(a,1,1,2))]. 4314 T(x,y) * (T(x \ y,y) * (T(x,y) * z)) = (x * y) * z. [para(2690(a,1),186(a,2,1,1)),rewrite([4281(4),90(9)])]. 4315 ((x * (y \ z)) * T(y,z)) / T(x * z,a(x,y \ z,T(y,z))) = a(x,y \ z,T(y,z)). [para(2690(a,1),265(a,1,2,1,2))]. 4335 a(x * (y \ z),z \ y,T(z,y)) = ((x * (y \ z)) * y) \ (x * T(z,y)). [para(2690(a,1),60(a,1,1,2)),rewrite([4155(2),4155(8)]),flip(a)]. 4344 (x \ y) * ((z * (x \ y)) * T(x,y)) = ((x \ y) * z) * y. [para(2690(a,1),189(a,1,2)),flip(a)]. 4357 (x \ (x \ y)) * T(x,y) = x \ y. [para(2642(a,1),2690(a,1,2))]. 4365 x / T(x,y) = T(x,y) \ x. [para(159(a,1),2711(a,1,2))]. 4366 T(x,y) / x = x \ T(x,y). [para(541(a,1),2711(a,1,2))]. 4379 ((x \ y) * x) / y = K(x \ y,x). [para(64(a,1),2711(a,2)),rewrite([4210(5)])]. 4404 x * T(y,z \ (z \ x)) = z * (z * (y * (z \ (z \ x)))). [para(2755(a,1),1324(a,1,2)),rewrite([3143(7),3143(6),2755(7),3143(10),3143(9)]),flip(a)]. 4407 (x * y) \ 1 = y \ (x \ 1). [para(2755(a,1),2538(a,1,1))]. 4408 (x \ y) \ z = (y \ x) * z. [para(2538(a,1),2755(a,1,1))]. 4417 ((x * y) * z) \ R(x,y,z) = z \ (y \ 1). [back_rewrite(4114),rewrite([4407(7)])]. 4419 ((x \ (y \ 1)) * y) \ (x \ 1) = a(x,x / y,y). [back_rewrite(4013),rewrite([4407(7)])]. 4420 x / (y * (y * (z * x))) = (y * z) \ (y \ 1). [back_rewrite(3725),rewrite([4407(8)])]. 4421 x / (y * (z * (y * x))) = (z * y) \ (y \ 1). [back_rewrite(3724),rewrite([4407(8)])]. 4445 L(L(x,y,z),u,x \ (u \ 1)) = L(x,y,z). [back_rewrite(3192),rewrite([4407(4)])]. 4458 ((x * y) * z) \ y = (y * z) \ (x \ y). [back_rewrite(2540),rewrite([4407(5),4408(4),14(4)]),flip(a)]. 4470 R(x,y,y \ ((x \ y) * z)) = z * ((z \ y) * (y \ x)). [back_rewrite(4186),rewrite([4408(2)])]. 4480 L(x \ (y * z),x,y) = (x \ y) * z. [back_rewrite(3941),rewrite([4408(5)])]. 4493 (x \ y) * (x / y) = K(x,y \ 1). [back_rewrite(3230),rewrite([4408(3)])]. 4498 (((x * y) * z) \ x) * (y * z) = a(x,x * y,z). [back_rewrite(3162),rewrite([4408(5)])]. 4501 (x * y) \ (x * (x * z)) = (y \ x) * z. [back_rewrite(3135),rewrite([4408(6)])]. 4504 (x \ y) * (((y \ x) * z) * y) = (z * (x \ y)) * T(x,y). [back_rewrite(2692),rewrite([4408(3)])]. 4505 (x \ y) * x = T(y,x). [back_rewrite(2649),rewrite([4408(2)])]. 4516 K(x \ y,x) = y \ T(y,x). [back_rewrite(4379),rewrite([4505(2),4366(2)]),flip(a)]. 4525 x * (T(y,x) * z) = y * (x * z). [back_rewrite(2965),rewrite([4505(2)])]. 4534 x * (K(y \ x,y) * (x * z)) = (x * T(x,y)) * z. [back_rewrite(2935),rewrite([4505(7),547(7)])]. 4535 x * K(y \ x,y) = T(x,y). [back_rewrite(2852),rewrite([4505(5)])]. 4537 a(T(x,y),y \ x,z) = a(y \ x,x,z). [back_rewrite(1702),rewrite([4505(2)])]. 4539 K(x,x \ y) = T(y,x) \ y. [back_rewrite(65),rewrite([4505(2)]),flip(a)]. 4559 (T(x,y) * (y * (z * (x * y)))) * u = T(x,y) * (y * (z * (x * (y * u)))). [back_rewrite(2234),rewrite([4525(4)]),flip(a)]. 4562 ((x * y) * y) / z = x * (y * (y / z)). [back_rewrite(1859),rewrite([4525(4)]),flip(a)]. 4578 (x * y) * y = x * (y * y). [back_rewrite(669),rewrite([4525(3)]),flip(a)]. 4581 L(x,T(y,z),z) = L(x,z,y). [back_rewrite(512),rewrite([4525(4),21(4)]),flip(a)]. 4582 a(x,T(y,x),z) = a(y,x,z). [back_rewrite(508),rewrite([4525(3),19(5)]),flip(a)]. 4583 R(x * y,y,y \ z) = (x * (y * z)) / z. [back_rewrite(204),rewrite([4525(6)])]. 4596 ((T(x,y) * (y / z)) * y) \ ((x * (y * y)) / z) = K(y,T(x,y) * (y / z)). [back_rewrite(1864),rewrite([4578(6)])]. 4613 (x * (y * y)) / z = x * (y * (y / z)). [back_rewrite(4562),rewrite([4578(2)])]. 4636 a(x * (y * (x * x)),z,u) = a(x * y,x * (x * z),u). [back_rewrite(3762),rewrite([4578(2)])]. 4640 x * (x * (((T(y,x) * (x * z)) / u) / T(x * (y * (x * (x * z))),u \ 1))) = u \ 1. [back_rewrite(3670),rewrite([4578(6),2040(7)])]. 4713 x / (T(T(y,z),u) * (z * ((T(y,u) * (z * z)) \ x))) = z. [back_rewrite(2166),rewrite([4578(5)])]. 4714 x * (x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w))) = w. [back_rewrite(2032),rewrite([4578(8),2040(9)])]. 4770 x * (R(T(y,x),z,u) * (x * w)) = R(y,z,u) * (x * (x * w)). [back_rewrite(684),rewrite([4578(8),2040(9)])]. 4778 (x * ((T(y,x) * (x * z)) * u)) \ ((y * (x * (x * z))) * u) = a(x,T(y,x) * (x * z),u). [back_rewrite(674),rewrite([4578(7),2040(8)])]. 4795 a(x * y,y,z) \ 1 = a(x,y,y * z). [back_rewrite(2574),rewrite([4582(3)]),flip(a)]. 4809 ((T(x,y) * (y / z)) * y) \ (x * (y * (y / z))) = K(y,T(x,y) * (y / z)). [back_rewrite(4596),rewrite([4613(7)])]. 4813 (x / y) * (y * (y / T(x * y,a(x,y \ 1,y * y)))) = a(x,y \ 1,y * y). [back_rewrite(2599),rewrite([4613(10)])]. 4915 K(x,y * (x / y)) = 1. [para(18(a,1),2772(a,1,1))]. 4950 T(a(x,y,z),((x * y) * z) / (x * (y * z))) = a(x,y,z). [para(54(a,1),2810(a,1,2,1))]. 4993 K(x,y) * K(y,x) = 1. [para(2917(a,1),16(a,1,2))]. 4996 R(x,K(y,z),K(z,y)) = x. [para(2917(a,1),191(a,2,3)),rewrite([14(5),16(4),48(2)]),flip(a)]. 5005 x / K(y,z) = x * K(z,y). [para(2917(a,1),1014(a,1,2)),flip(a)]. 5011 L(x,K(y,z),K(z,y)) = x. [para(2917(a,1),3266(a,1,3))]. 5067 T(x,y * (x / y)) = x. [para(66(a,1),2642(a,1,2)),rewrite([3305(3)]),flip(a)]. 5068 K(x,y / x) * y = x * (y / x). [para(66(a,1),2690(a,1,1)),rewrite([5067(5)])]. 5070 x * L(y,z \ x,z) = z * ((z \ x) * y). [para(16(a,1),72(a,1,1))]. 5116 (x * y) * L(z,K(x,y),y * x) = (y * x) * (K(x,y) * z). [para(63(a,1),72(a,1,1))]. 5129 x * L(y,T(z,x),z \ x) = (z \ x) * (T(z,x) * y). [para(2690(a,1),72(a,1,1))]. 5134 x \ (y \ ((y * x) * z)) = L(z,y * x,y). [para(15(a,1),3940(a,1,1)),flip(a)]. 5138 L(T(x,y * z),y * z,y) = z \ (y \ (x * (y * z))). [para(23(a,1),3940(a,1,1))]. 5147 L((x * y) \ z,y,y * x) = T(x,y) \ (y \ z). [para(90(a,1),3940(a,1,1,1)),rewrite([90(4),2975(4)])]. 5152 K(x * (y / x),x) = K(x \ 1,y). [para(67(a,1),3940(a,1,1)),rewrite([666(5),3231(6)])]. 5155 L((x / y) \ z,x / y,x) = y * (x \ z). [para(1014(a,1),3940(a,1,1,1)),rewrite([1014(5),4408(8),45(6)])]. 5162 (x * (x * y)) \ z = y \ (x \ (x \ z)). [para(3940(a,1),2254(a,1)),rewrite([3436(2),100(5)]),flip(a)]. 5163 L((x * y) \ z,x * y,y * x) = K(x,y) \ ((y * x) \ z). [para(63(a,1),3940(a,1,1,1)),rewrite([63(5)])]. 5194 R(x,y * (y * z),z \ (y \ (y \ u))) = R(x,z,z \ u). [back_rewrite(1870),rewrite([5162(3),191(6),1935(6),16(3),16(2),5162(7)]),flip(a)]. 5200 x * (x * (y * ((y \ (x \ (x \ z))) * (x * (x * u))))) = (z * (x * (x * y))) * (y \ u). [back_rewrite(411),rewrite([5162(3)])]. 5208 (x * (y \ z)) * (z \ y) = x. [para(4151(a,1),209(a,1,1)),rewrite([45(6),4137(7),14(6),4151(7),88(6)])]. 5226 (T(x,y) \ (T(x,y) \ z)) * T(T(x,z),y) = T(x,y) \ z. [para(29(a,1),4357(a,1,2))]. 5332 a(x,y,y) = 1. [para(89(a,1),507(a,1,2,2)),rewrite([4578(4),46(5),89(2)]),flip(a)]. 5337 (x * (y * (z * u))) \ (x * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),y * (z * u),x). [para(507(a,1),74(a,1,1)),flip(a)]. 5358 a(x,y \ 1,y * y) = 1. [back_rewrite(4187),rewrite([5332(2),46(3)]),flip(a)]. 5359 (x / y) * (y / x) = 1. [back_rewrite(4813),rewrite([5358(6),88(4),3691(3),1014(4),5358(7)])]. 5364 (x * y) / T(z * (z * y),T(x,y)) = z \ (z \ T(x,y)). [para(1921(a,1),21(a,1,2)),rewrite([3436(3),1607(10)]),flip(a)]. 5392 (x \ y) * (x * ((x \ y) * z)) = ((x \ y) * y) * z. [para(2445(a,1),16(a,1,2)),rewrite([14(7)])]. 5410 (x \ (y \ (y \ z))) * (((z \ y) * y) * x) = 1. [para(2445(a,1),4357(a,1,1,2)),rewrite([5392(5),4407(5),4407(4),4408(3),14(3),5392(8),89(10),5392(12),46(14)])]. 5428 x * (x * (y / (T(z * z,x) * (x * y)))) = z \ (z \ x). [para(2640(a,1),21(a,1,2)),rewrite([3436(2),1607(10)]),flip(a)]. 5444 L(x,y \ (y \ z),y) = L(x,z,y). [para(2640(a,1),132(a,1,1,2)),rewrite([5428(8),136(6),16(3),21(4),5428(8),2507(6)]),flip(a)]. 5452 x * (x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u))))))) = y * z. [para(189(a,1),2640(a,1,2,2,2,2,2,2))]. 5468 T(x * (x * y),y \ z) = T(x * (x * y),x * (x * z)). [para(16(a,1),2647(a,1,2,2,2)),flip(a)]. 5480 T(x * (x * y),x * (x * (y / z))) = T(x * (x * y),z \ 1). [para(1014(a,1),2647(a,1,2,2,2))]. 5515 a(x \ y,T(x,y) * y,z) = 1. [para(2697(a,1),19(a,2)),rewrite([4247(5),4525(3),15(3),4247(6),90(4),15(4),100(4),46(5)]),flip(a)]. 5524 a((x * y) * L(z \ y,z,x),T(x * z,x * y),u) = 1. [para(74(a,2),2697(a,1,1,2)),rewrite([5515(17)])]. 5560 ((x \ y) * (x / z)) \ ((y * x) / z) = T(x,(y * x) / z). [para(1014(a,1),2713(a,1,1,2)),rewrite([1014(7),1014(10)])]. 5569 (((x \ y) * z) * x) \ ((z * (y \ x)) * T(y,x)) = T(y \ x,(z * (y \ x)) * T(y,x)). [para(2690(a,1),2713(a,1,1,2)),rewrite([4408(2)])]. 5600 ((x * (y * (y * (y * x)))) \ y) * (x * (y * (x * y))) = 1. [para(2772(a,1),143(a,2)),rewrite([101(2),189(5),4578(2),2040(4),101(7),4501(11)])]. 5610 (x \ (y \ (y \ (z \ 1)))) * (z * (y * (y * (x * u)))) = L(u,y * (y * x),z). [para(37(a,1),145(a,1,1)),rewrite([37(11),4501(12),1091(5),4407(5),5162(5),2507(15)])]. 5614 L(x,y * (y * z),z) = x. [para(1607(a,1),145(a,2)),rewrite([189(5),101(2),189(4),4578(2),101(3),100(2),189(11),101(7),189(10),4578(7),189(9),100(7),37(8),4501(12),1091(5),4407(5),5162(5),5610(10)])]. 5657 x * (y * (x * (z * ((z * (x * (y * (x * z)))) \ u)))) = z \ u. [para(2215(a,1),15(a,1,2)),flip(a)]. 5665 R(x,y,y \ ((x \ y) * z)) = (y * z) / ((x \ y) * z). [para(2215(a,1),191(a,1,1,2)),rewrite([5657(13),4408(3),5657(16),4408(6)]),flip(a)]. 5674 x * (y * (z * (y * (x / (x * (y * (z * (y * x)))))))) = 1. [para(1014(a,1),2215(a,1,2,2,2,2))]. 5742 K(L(x * y,x \ z,x),z) = K(z * ((z * x) * y),z). [para(181(a,1),2934(a,1,2,1)),rewrite([104(4),16(7),4505(6),3934(6,R),16(9)]),flip(a)]. 5752 (x * ((y * x) * z)) \ (L(z,x,x * y) * (x * (y * x))) = K(L(z,x,x * y),x * (y * x)). [para(189(a,1),2934(a,1,1)),rewrite([101(7),101(13)])]. 5783 x * ((y * x) * (x * ((x \ y) * z))) = (x * y) * ((x * y) * z). [para(13(a,1),405(a,1,2,2,2,2)),rewrite([14(10),187(12),101(8),426(10)])]. 5816 R(x * ((x \ y) * (y \ z)),z,z \ u) = (z * (a(y,x,x \ (y \ z)) * u)) / u. [para(16(a,1),435(a,1,2)),rewrite([16(6),16(8)])]. 5817 (x * (a(x / y,z,z \ y) * u)) / u = R(x,y \ 1,z). [para(18(a,1),435(a,1,2)),rewrite([4180(4),18(5),495(5),18(5)]),flip(a)]. 5841 R(x * ((x \ (y \ z)) * T(y,z)),z,z \ u) = (z * (a(y \ z,x,x \ T(y,z)) * u)) / u. [para(2690(a,1),435(a,1,2)),rewrite([2690(8),2690(10)])]. 5879 x * (y * (x * (x * (x * ((x * (y * (x * (x * x)))) \ z))))) = z. [para(463(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 5885 (x \ (y \ 1)) * (y * (x * z)) = L(z,x,y). [para(463(a,1),132(a,1,1,2)),rewrite([5879(13),4501(8),1091(3),4407(3),5879(16),2507(9)])]. 5921 a(x,T(y,x) * x,z) = a(y,x,x * z) \ 1. [para(14(a,1),4778(a,1,1,2,1,2)),rewrite([2993(4),14(5),2040(6),2548(7),14(7)]),flip(a)]. 6018 L(x,x,y) = x. [hyper(24,a,5332,a)]. 6020 L(T(x,y),x,z) = T(x,y). [para(6018(a,1),30(a,1,1)),flip(a)]. 6022 L(L(x,y,z),x,u) = L(x,y,z). [para(6018(a,1),34(a,1,1)),flip(a)]. 6024 L(L(L(x,y,z),u,w),L(x,u,w),v5) = L(L(x,u,w),y,z). [para(6018(a,1),97(a,1,1)),flip(a)]. 6068 ((x * y) \ z) * ((z \ x) * y) = a(z \ 1,x,y). [para(3143(a,1),19(a,1,1)),rewrite([3143(5),4408(5)])]. 6069 (x \ (y \ 1)) * (x * y) = K(x,y). [para(20(a,1),3143(a,2)),rewrite([4407(3)])]. 6070 (x \ y) * (y \ (x * z)) = L(z,x,y \ 1). [para(3143(a,1),21(a,1,1)),rewrite([3143(5),4408(4)])]. 6071 ((x \ y) * z) / (y * z) = R(x \ 1,y,z). [para(3143(a,1),22(a,1,1,1))]. 6072 T(x \ 1,y) = y \ (x \ y). [para(3143(a,1),23(a,1,2)),flip(a)]. 6073 x \ (x \ (y * z)) = (x \ (x \ y)) * z. [para(3143(a,1),37(a,1,1,2)),rewrite([3143(4),3143(9),3143(8)]),flip(a)]. 6095 x \ T(y,x \ 1) = y / x. [para(3143(a,1),90(a,1)),rewrite([1014(7)])]. 6120 (x \ 1) / y = x \ (y \ 1). [para(3143(a,1),1014(a,1)),flip(a)]. 6128 ((x * (y * z)) \ (y \ 1)) * (y * (x * (y * (z * u)))) = L(u,z,y * (x * y)). [para(132(a,1),3143(a,2)),rewrite([4407(5)])]. 6132 (x \ (y \ 1)) * y = x \ 1. [para(1091(a,1),3143(a,2)),rewrite([4407(3)])]. 6134 T(x \ 1,x \ y) = T(x \ 1,y). [para(3143(a,1),1708(a,1,2))]. 6135 x \ ((y / x) * z) = (x \ y) * (x \ z). [para(3143(a,1),189(a,1,1)),rewrite([3143(4),1014(8),3143(8)]),flip(a)]. 6141 ((x * y) \ (z \ (z \ (u \ 1)))) * ((u * (z * (z * x))) * y) = a(u,z * (z * x),y). [para(139(a,1),3143(a,2)),rewrite([4407(6),5162(6)])]. 6144 K(x,y) \ z = K(y,x) * z. [para(2917(a,1),3143(a,1,1)),flip(a)]. 6145 (x \ y) * L(z,y,x \ 1) = x \ (y * z). [para(3143(a,1),72(a,1,1)),rewrite([3143(9)])]. 6149 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(z \ 1,y,T(x,y)). [para(3143(a,1),507(a,1,1)),rewrite([3143(5),4408(6)])]. 6151 ((x \ (y \ 1)) * (x * z)) \ ((y \ x) * z) = T(x,(y \ x) * z). [para(3143(a,1),2713(a,1,2,1)),rewrite([3143(11)])]. 6152 ((x * y) \ (z \ x)) * ((z * x) * y) = T(x,(z * x) * y). [para(2713(a,1),3143(a,2)),rewrite([4407(5),4408(4),14(4)])]. 6185 (x \ (y \ 1)) * T(z,x / y) = (x \ (x \ z)) * (x / y). [back_rewrite(3709),rewrite([6073(4)]),flip(a)]. 6188 x \ T(y,z * (z / x)) = (z \ (z \ y)) * (z * (z / x)). [back_rewrite(3482),rewrite([6073(9)])]. 6233 a(x,x / y,y) = 1. [back_rewrite(4419),rewrite([6132(4),46(5)]),flip(a)]. 6238 L((x * y) \ z,x * y,y * x) = K(y,x) * ((y * x) \ z). [back_rewrite(5163),rewrite([6144(9)])]. 6257 L(x,y / x,y) = x. [hyper(24,a,6233,a)]. 6258 a(x * y,x,y) = 1. [para(17(a,1),6233(a,1,2))]. 6279 L(x,y,y * x) = x. [para(17(a,1),6257(a,1,2))]. 6335 a(x,y,y \ x) = 1. [para(16(a,1),6258(a,1,1))]. 6351 x * ((x \ y) * y) = y * y. [para(6258(a,1),435(a,2,1,2,1)),rewrite([16(2),16(5),16(6),3436(6),2044(7),16(5),13(6),100(5),1839(6),47(4),14(5)])]. 6353 (x \ y) * ((y \ x) * z) = L(z,(y \ x) * x,y). [back_rewrite(831),rewrite([6351(3),3436(6),6073(6),15(2)])]. 6368 L(x \ y,x,y) = x \ y. [para(16(a,1),6279(a,1,3))]. 6416 L(x,y \ 1,y \ x) = x. [para(3143(a,1),6279(a,1,3))]. 6438 a((x * y) * T(z,y),x * (z * y),a(x,y,T(z,y))) = 1. [para(507(a,1),6335(a,1,3))]. 6446 K(x,K(y,x / y)) = 1. [para(18(a,1),3302(a,1,1))]. 6557 K(K(L(x,y,z),z * y),z * (y * x)) = 1. [para(72(a,1),3327(a,1,2))]. 6562 K(x,y) / (x * y) = x \ (y \ 1). [para(20(a,1),3666(a,1,1)),rewrite([4407(6)])]. 6564 T(x,y) / (x * y) = y \ 1. [para(23(a,1),3666(a,1,1))]. 6565 (x / y) \ 1 = y / x. [para(50(a,1),3666(a,1,1)),flip(a)]. 6567 (x * (y * z)) \ (y \ 1) = z \ ((x * y) \ (y \ 1)). [para(114(a,1),3666(a,1,1)),rewrite([6562(7),4407(4),4407(10)]),flip(a)]. 6575 (x / y) \ (y \ 1) = K(x / y,y) / x. [para(67(a,1),3666(a,1,1)),rewrite([4407(7)]),flip(a)]. 6591 L(x,y,z) \ (y \ (z \ 1)) = (y * x) \ (z \ 1). [para(2934(a,1),3666(a,1,1)),rewrite([6562(7),4407(4),4407(9)])]. 6600 (x \ ((y * z) \ (z \ 1))) * (z * (y * (z * (x * u)))) = L(u,x,z * (y * z)). [back_rewrite(6128),rewrite([6567(5)])]. 6606 x * (L(y,z \ x,z) * (x * u)) = ((z * ((z \ x) * y)) * x) * u. [para(73(a,1),104(a,1,2,1))]. 6618 L(x,y \ 1,z * y) = L(x,y \ z,y). [para(73(a,1),181(a,2)),rewrite([1091(2),3143(3),16(2),1091(4)]),flip(a)]. 6623 (((x / (y * z)) * y) * z) \ (x * (a(x / (y * z),y,z) * u)) = L(u,a(x / (y * z),y,z),x). [para(59(a,1),73(a,1,2,2,1)),rewrite([59(15)])]. 6634 L(x,y * z,y \ 1) = L(x,y * z,y). [para(3143(a,1),73(a,1,2)),rewrite([4408(3),45(2),5134(4),4408(5),45(4)]),flip(a)]. 6663 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,u,w),y,z))) \ (v6 * v5). [para(76(a,1),228(a,1)),flip(a)]. 6676 L(x,y \ (x \ 1),z) = (z * (y \ (x \ 1))) \ (z / y). [para(1014(a,1),76(a,2,2)),rewrite([6120(3),6120(7)])]. 6694 T(x * (y / z),L(z,y / z,x)) = T(x * (y / z),x * y). [para(76(a,2),2642(a,1,2))]. 6696 L(x,T(y,z) / x,y \ z) = ((y \ z) * (T(y,z) / x)) \ z. [para(2690(a,1),76(a,2,2))]. 6697 L(x,L(y,z,u) / x,u * z) = ((u * z) * (L(y,z,u) / x)) \ (u * (z * y)). [para(72(a,1),76(a,2,2))]. 6707 L(x,y / x,z \ 1) = ((y / x) \ z) * (z \ y). [para(3143(a,1),76(a,2,1)),rewrite([3143(9),4408(8)])]. 6793 L(L(R(x,y,z),u,w),v5,x \ (v5 \ 1)) = L(R(x,y,z),u,w). [para(4445(a,1),33(a,1,1)),rewrite([33(2),33(4)]),flip(a)]. 6878 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(y * (x \ y),y \ 1). [para(1014(a,1),2757(a,1,2)),rewrite([6120(3),3143(10)])]. 6887 L(K(x * (y * x),x \ 1),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [para(2757(a,1),3940(a,1,1)),rewrite([3436(15)])]. 6890 K(x * (y * x),x \ 1) = K(x,y). [para(2757(a,1),3143(a,2)),rewrite([4407(5),6565(4),3436(3),1829(2),6069(5)]),flip(a)]. 6897 L(K(x,y),(y / x) * (x * x),y / x) = x \ (x \ ((y / x) \ (x * y))). [back_rewrite(6887),rewrite([6890(5)])]. 6946 T(x * (x * (y / (x * z))),x * z) = (z \ x) * y. [para(16(a,1),3139(a,1,1,2,2,2,2)),rewrite([16(6),4408(8)])]. 6951 ((x \ y) * (x * z)) \ u = ((x * z) \ (y \ x)) * u. [para(104(a,1),3139(a,1,1,2,2,2,2)),rewrite([104(10),6946(10),4458(3)]),flip(a)]. 6953 (x \ ((y * z) \ (y \ 1))) * u = (z * x) \ (y \ (y \ u)). [para(341(a,1),3139(a,1,1,2,2,2,2)),rewrite([341(27),6946(26),4417(8),4407(4),5162(10)])]. 6955 ((x * y) \ y) * z = T(x,y) \ z. [para(90(a,1),3139(a,1,1,2,2,2,2)),rewrite([90(7),6946(8)])]. 6968 (x \ (y \ x)) * z = T(y,x) \ z. [para(2690(a,1),3139(a,1,1,2,2,2,2)),rewrite([2690(11),6946(10)])]. 6973 ((x * y) \ (z * x)) * ((z \ x) * y) = T(x,(z \ x) * y). [back_rewrite(6151),rewrite([6951(8),4408(4),45(3)])]. 7004 x * (y \ ((x * (x / y)) \ z)) = x \ z. [para(18(a,1),3218(a,2,2)),rewrite([92(6)])]. 7047 T(x,K((y \ z) * (y * ((z * y) \ x)),y)) = x. [para(16(a,1),3307(a,1,1)),rewrite([16(11)])]. 7257 (T(x,y) * (y * (x * y))) * z = T(x,y) * (y * (x * (y * z))). [para(13(a,1),4559(a,1,1,2,2)),rewrite([13(10)])]. 7262 T(x,y) * (y * ((z / (x * y)) * (x * (y * u)))) = (T(x,y) * (y * z)) * u. [para(18(a,1),4559(a,1,1,2,2)),flip(a)]. 7353 R(x,y,z) * (x * (x * u)) = x * (R(x,y,z) * (x * u)). [para(89(a,1),4770(a,1,2,1,1)),flip(a)]. 7412 a(x / (y * y),y,y * z) = (x * z) \ (y \ ((y * x) * z)). [para(7262(a,1),110(a,1,1)),rewrite([89(1),37(3),89(4),189(10),101(8),4578(7),18(7),5162(7),15(5),89(6),3982(11),4795(11)]),flip(a)]. 7416 x * (T(x,y) * ((z / (x * T(x,y))) * (x * (T(x,y) * u)))) = (x * (T(x,y) * z)) * u. [para(541(a,1),7262(a,1,1)),rewrite([541(12)])]. 7488 x * ((y * z) * ((y * z) * ((y * u) / (T(x * x,y * z) * (y * ((z * y) * u)))))) = x \ (y * z). [para(5452(a,1),15(a,1,2)),flip(a)]. 7490 (x * y) * ((x * y) * ((x * z) / (T(u * u,x * y) * (x * ((y * x) * z))))) = (u \ (u \ x)) * y. [para(5452(a,1),21(a,1,2)),rewrite([3436(3),6073(3),1607(17)]),flip(a)]. 7495 x * (x * (((x \ (x \ y)) * z) * u)) = (y * z) * u. [para(5452(a,1),37(a,1,1)),rewrite([7490(15)]),flip(a)]. 7513 L(x,(y \ (y \ z)) * u,y) = L(x,z * u,y). [para(5452(a,1),132(a,1,1,2)),rewrite([7490(15),7495(8),21(6),7490(15),2507(8)]),flip(a)]. 7550 x * ((x \ (x \ y)) * z) = x \ (y * z). [back_rewrite(7488),rewrite([7490(13)])]. 7607 a(x / y,y,z) \ 1 = a(x,y \ 1,y * z). [para(3691(a,1),58(a,1,2,1,2)),rewrite([1014(4),4157(5),3691(6)])]. 7616 T(x,y) / y = y \ x. [para(2690(a,1),3691(a,1,2)),rewrite([4408(5),14(5)])]. 7617 T(x,y) * (y \ x) = (y \ x) * x. [para(4357(a,1),3691(a,1,2)),rewrite([4155(3),4408(7),4408(5),14(7)])]. 7622 x * ((y * x) \ T(z,x / y)) = x \ (z * (x / y)). [para(3691(a,1),3218(a,1,2,2,2,2)),rewrite([1014(4),3691(7),1014(8)])]. 7628 (x * y) \ ((x / z) * (z * y)) = a(x,z \ 1,z * y). [back_rewrite(4157),rewrite([7607(9)])]. 7636 K(x,K(x / y,y)) = 1. [para(18(a,1),4108(a,1,1))]. 7656 L(x,(y \ z) * z,y) = x. [para(4137(a,1),21(a,1,1)),rewrite([6353(5),45(5),4165(6)])]. 7662 K(x \ y,(y \ x) * (z * (y \ x))) = K(z,y \ x). [para(4137(a,1),114(a,1,1,2,2)),rewrite([14(3),6353(8),7656(7),20(5)]),flip(a)]. 7679 L(x,y \ z,(z \ y) * (u * (z \ y))) = L(x,u,z \ y). [para(4137(a,1),132(a,1,1,2,2)),rewrite([14(3),6353(7),7656(6),21(6)]),flip(a)]. 7681 (x \ y) * (z * (y \ x)) = T(z,y \ x). [para(4137(a,1),1359(a,1,2,2,2,2)),rewrite([14(5),90(5),4137(9),14(8),23(8)])]. 7682 a((x \ y) * (z * (x \ y)),y \ x,u) = a(x \ y,z,u). [para(4137(a,1),133(a,1,2,1,2,2)),rewrite([6353(5),7656(4),14(6),19(7)]),flip(a)]. 7701 ((L(x,y,y * z) * (y * (z * y))) \ (y * ((z * y) * x))) * K(L(x,y,y * z),y * (z * y)) = 1. [para(5752(a,1),4137(a,1,2))]. 7707 K(K(x \ y,z * (y \ x)),z) = 1. [para(4137(a,1),6557(a,1,2,2)),rewrite([4145(3),14(6)])]. 7713 K(x \ y,(y \ x) * z) = K(x \ y,z). [para(4137(a,1),177(a,1,1,1,2)),rewrite([4408(2),14(4),5208(8),4458(5),4408(4),20(5),4408(5),4137(8),14(7)]),flip(a)]. 7715 (x \ y) * ((y \ x) * z) = z. [back_rewrite(6353),rewrite([7656(7)])]. 7719 K(x \ y,z * (y \ x)) = K(z,y \ x). [back_rewrite(7662),rewrite([7713(6)])]. 7726 K(K(x,y \ z),x) = 1. [back_rewrite(7707),rewrite([7719(4)])]. 7769 T(T(x,y),y \ x) = x. [para(16(a,1),4209(a,2)),rewrite([4505(2)])]. 7772 ((x \ y) * (x * z)) * x = T((y * x) * z,x). [para(104(a,1),4209(a,1,1)),flip(a)]. 7775 T(x,y) * y = T(x * y,y). [para(90(a,1),4209(a,1,1)),flip(a)]. 7789 T(x,y) * (x \ y) = T(y,x \ y). [para(2690(a,1),4209(a,1,1)),flip(a)]. 7820 K((x \ y) * (x * z),x) = K(x * ((y * x) * z),x). [back_rewrite(3323),rewrite([7772(4),4366(6),3934(6,R)]),flip(a)]. 7826 x * K(y * x,y) = T(x,y). [back_rewrite(874),rewrite([7820(6),16(4),7772(9),16(7)])]. 7836 a(x,y,y * z) \ 1 = a(x * y,y,z). [back_rewrite(5921),rewrite([7775(2),4582(3)]),flip(a)]. 7875 K(x,x * (y * x)) = K(x,T(y,x)). [back_rewrite(511),rewrite([7775(2),3935(4,R)])]. 7876 K(x * (y * x),x) = K(T(y,x),x). [back_rewrite(510),rewrite([7775(3),3934(4,R)])]. 7925 T(x,K(y * x,y)) = x. [back_rewrite(7047),rewrite([7820(6),16(4)])]. 7966 ((x * (y \ z)) * y) / T(z,y) = R(x,y \ z,y). [para(4505(a,1),22(a,1,2))]. 7967 x \ T(y,x) = T(x \ y,x). [para(4505(a,1),23(a,1,2))]. 7969 (x \ y) * (((y \ x) * z) * T(y,x)) = (z * (x \ y)) * x. [para(4505(a,1),104(a,1,2,2)),rewrite([4408(3)])]. 7981 L(x \ y,x,x \ z) = T(z,x) \ ((x \ z) * y). [para(4505(a,1),74(a,2,1))]. 7982 L(x \ y,x,y \ z) = ((y \ z) * x) \ T(z,y). [para(4505(a,1),74(a,2,2))]. 7996 L(T(x,y),(x \ y) * z,y \ x) = z \ ((z * (y \ x)) * y). [para(4505(a,1),181(a,1,1)),rewrite([4408(3)])]. 7997 (x \ y) * (T(x,y) * z) = L(y * z,x,y). [para(4505(a,1),181(a,2,2,1)),rewrite([5444(4),4408(6)]),flip(a)]. 8002 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = R((y * (z * y)) \ x,y * (z * y),u). [para(4505(a,1),121(a,1,1,1))]. 8018 T(x,y) \ (y \ x) = y \ 1. [para(4505(a,1),1091(a,1,1))]. 8020 (x \ y) * ((z * (x \ y)) * x) = ((x \ y) * z) * T(y,x). [para(4505(a,1),189(a,1,2)),flip(a)]. 8036 T(x * (x * (y \ z)),x * (x * T(z,y))) = T(x * (x * (y \ z)),y). [para(4505(a,1),2647(a,1,2,2,2))]. 8054 a(x \ y,y,x) = 1. [para(4505(a,1),6258(a,1,1)),rewrite([4537(3)])]. 8061 T(x * ((x \ y) * z),y) = L(z,x \ y,x) * y. [para(73(a,1),4505(a,1,1)),flip(a)]. 8078 K(T(x,y),K(y \ x,y)) = 1. [para(4505(a,1),4108(a,1,1))]. 8091 x * L(y,T(z,x),z \ x) = L(x * y,z,x). [back_rewrite(5129),rewrite([7997(8)])]. 8098 L(x * ((y \ x) * z),y,x) = x * (y \ (x * z)). [back_rewrite(4261),rewrite([7997(6)])]. 8105 L(x,y,x \ y) = x. [hyper(24,a,8054,a)]. 8106 a(x,y * x,y) = 1. [para(15(a,1),8054(a,1,1))]. 8255 (x * (y / x)) * y = y * (x * (y / x)). [para(4915(a,1),63(a,1,2)),rewrite([14(5)])]. 8296 K(x,y) * (K(y,x) * z) = z. [para(4993(a,1),21(a,1,1)),rewrite([45(6),5011(7)])]. 8298 (x * K(y,z)) * K(z,y) = x. [para(4993(a,1),22(a,1,2)),rewrite([48(6),4996(7)])]. 8302 L(x \ K(y,z),x,K(z,y)) = x \ K(y,z). [para(4993(a,1),74(a,2,2)),rewrite([4407(8),6144(7),14(7)])]. 8308 L(x,K(y,z),K(z,y) * (u * K(z,y))) = L(x,u,K(z,y)). [para(4993(a,1),132(a,1,1,2,2)),rewrite([14(3),8296(7),21(6)]),flip(a)]. 8310 K(x,y) * (z * K(y,x)) = T(z,K(y,x)). [para(4993(a,1),1359(a,1,2,2,2,2)),rewrite([14(5),90(5),4993(9),14(8),23(8)])]. 8311 a(K(x,y) * (z * K(x,y)),K(y,x),u) = a(K(x,y),z,u). [para(4993(a,1),133(a,1,2,1,2,2)),rewrite([8296(5),14(6),19(7)]),flip(a)]. 8328 R(x,x \ y,y \ z) = z / ((x \ y) * (y \ z)). [para(16(a,1),81(a,2,1))]. 8331 T((x * y) / ((z \ x) * y),u) = R(T(z,u),z \ x,y). [para(81(a,1),31(a,1,1))]. 8379 R(x,x \ y,z) = z * ((z \ y) * (y \ x)). [para(81(a,2),1014(a,2)),rewrite([4407(5),4408(4),14(4),169(4)]),flip(a)]. 8393 (x * y) \ R(z,z \ x,y) = y \ (x \ z). [para(81(a,2),1829(a,1,2)),rewrite([4407(8),4408(7),14(7)])]. 8394 R(T(x,y * z),x \ y,z) = ((x \ y) * z) \ (y * z). [para(81(a,2),2643(a,1,1)),rewrite([31(4)])]. 8463 R(x,y \ 1,(x / y) \ z) = R(x,y \ 1,z). [para(1014(a,1),82(a,1,3,1)),rewrite([1014(10),3143(10),4155(9),4408(8),4180(9)])]. 8497 R(x,y,(x * y) \ T(z,y / x)) = T(z,y / x) * ((z * (y / x)) \ y). [para(3218(a,1),82(a,2,2)),rewrite([3691(3),1014(4),3691(7),1014(8),3691(9),1014(10),4155(11)])]. 8532 T(x,y) \ x = K(x \ y,x). [para(2642(a,1),4539(a,2,1)),rewrite([4408(3),7713(4)]),flip(a)]. 8534 K(x \ y,x) = K(y,y \ x). [para(4539(a,2),2711(a,2)),rewrite([159(2),4365(2),8532(2)])]. 8593 x / T(x,y) = K(x \ y,x). [back_rewrite(4365),rewrite([8532(4)])]. 8594 K(x \ y,x) = K(y,y * x). [back_rewrite(3935),rewrite([8532(4)]),flip(a)]. 8609 x * (L(y,z \ x,z) * x) = (z * ((z \ x) * y)) * x. [para(8061(a,1),90(a,1,2))]. 8679 L(x,y,z * (y * x)) = L(x,y,z). [para(17(a,1),3199(a,1,3)),flip(a)]. 8681 L(x,y,(z * y) * x) = L(x,y,R(z,y,x)). [para(22(a,1),3199(a,1,3)),flip(a)]. 8684 L(L(x,y,z),u,w / (u * x)) = L(L(x,u,w),y,z). [para(3199(a,1),34(a,1,1)),flip(a)]. 8701 L(x \ y,x,z) = ((z / y) * x) \ z. [para(3199(a,1),74(a,1)),rewrite([16(4),16(6),18(6)])]. 8972 (x \ y) * (x * x) = T(x * y,x * x). [para(3476(a,1),13(a,1)),rewrite([14(3),14(6)])]. 8992 ((x \ y) * (x * (x * z))) / T(z,T(x * y,x * (x * z))) = T(x * y,x * (x * z)). [para(3476(a,1),165(a,1,1))]. 9001 T(x,(y \ z) * (y * (y * x))) = T(x,T(y * z,y * (y * x))). [para(3476(a,1),1708(a,1,2))]. 9018 (x * y) * T(z * (z * x),y) = x * (z * (z * (x * y))). [para(2647(a,1),3476(a,1,2)),rewrite([15(7)])]. 9031 ((x \ y) * z) * (y \ x) = T(z,y \ x). [para(4137(a,1),3476(a,1,2,2,2)),rewrite([14(6),4209(5),7681(4),4408(4),4137(8),14(7)]),flip(a)]. 9037 (K(x,y) * z) * K(y,x) = T(z,K(y,x)). [para(4993(a,1),3476(a,1,2,2,2)),rewrite([14(6),4209(5),8310(4),6144(4),4993(8),14(7)]),flip(a)]. 9050 x * ((x * (y * x)) \ z) = y \ (x \ z). [para(18(a,1),3541(a,1,2,2)),rewrite([92(8)]),flip(a)]. 9085 x * a(y,z,z \ (y \ x)) = y * ((z * y) * ((y * (z * y)) \ x)). [back_rewrite(3093),rewrite([9050(4)])]. 9101 (x * (((y * z) * (z * y)) * u)) * a(x,(z * y) * (y * z),u) = (x * ((z * y) * (y * z))) * u. [para(178(a,1),312(a,1,1,2)),rewrite([3308(9),3308(14)])]. 9104 ((x * y) * (y * x)) * T(z,y * x) = (y * x) * (K(x,y) * (z * (y * x))). [para(90(a,1),178(a,1,2,2)),flip(a)]. 9114 ((x * ((y * z) * (z * y))) * u) / (((z * y) * (y * z)) * u) = R(x,(y * z) * (z * y),u). [para(178(a,1),121(a,1,2)),rewrite([3308(4),3308(14)])]. 9186 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,(y \ z) * (y * x),y). [para(179(a,1),3143(a,2)),rewrite([4407(4),4407(3)])]. 9191 x \ ((y \ z) * (((z \ y) * x) * u)) = L(u,(z \ y) * x,y \ z). [para(4137(a,1),179(a,1,1,1)),rewrite([13(2),4408(4),100(7),7715(6),4408(9),100(12),7715(11)])]. 9195 (T(x,y) * z) \ (y * (((y \ (y \ x)) * (y * z)) * u)) = L(u,x * (y * z),y). [para(4505(a,1),179(a,1,1,1)),rewrite([7513(14)])]. 9198 x \ (K(y,z) * ((K(z,y) * x) * u)) = L(u,K(z,y) * x,K(y,z)). [para(4993(a,1),179(a,1,1,1)),rewrite([13(2),6144(4),100(7),8296(6),6144(9),100(12),8296(11)])]. 9423 (x * ((x \ (y \ 1)) * ((y * z) * (y \ u)))) \ ((z / y) * u) = a(x,x / y,(y * z) * (y \ u)). [para(1014(a,1),4025(a,1,2,1)),rewrite([4408(6),45(5),3143(7),1014(14),4408(15),45(14),3143(16)])]. 9444 (x * ((x \ K(y,z)) * (K(z,y) * u))) \ u = a(x,x * K(y,z),K(z,y) * u). [para(4993(a,1),4025(a,1,1,2,2,2)),rewrite([6144(4),14(6),8298(10),6144(11),4993(14),14(13)])]. 9484 ((T(T(x,y),z) * (z * u)) * z) / (w * (w * ((T(T(x,z),y) * (z * u)) * z))) = w \ (w \ 1). [para(1907(a,1),21(a,1,2)),rewrite([3436(3),1607(17)]),flip(a)]. 9490 x \ (y * (x \ z)) = (x \ (y / x)) * z. [para(1907(a,1),129(a,1,1,2,2,2,2,2)),rewrite([9484(13),16(4),9484(15),16(6),9484(17),16(8),14(8),1014(7),3143(6),16(5),3143(4),9484(16),16(7),9484(18),16(9),9484(20),16(11),9484(22),16(13),3143(12),16(11),3143(10),3143(10),16(9),3143(8)]),flip(a)]. 9548 x * (x * (y * (x * (x * (y * (z \ ((y / z) \ (x \ (x \ (y \ 1)))))))))) = x * x. [para(14(a,1),3947(a,2,2)),rewrite([4407(6),5162(6)])]. 9553 x * (y * (y * (x * (z \ ((x * (y * (y * (x / z)))) \ u))))) = u. [para(3947(a,1),21(a,1,2)),rewrite([3436(4),15(3),15(2),1607(11)]),flip(a)]. 9559 L(x,y \ z,y) = L(x,y * z,y). [para(3947(a,1),132(a,1,1)),rewrite([5162(7),7004(9),16(6),16(5),136(6),21(6),5162(7),7004(9),16(6),16(5),2507(6)]),flip(a)]. 9575 L(x,(y * z) / x,y) = (((y * z) / x) \ y) * z. [para(3947(a,1),76(a,2,2)),rewrite([9553(10),9553(13),4501(9)])]. 9640 x * (L(y,z * x,z) * x) = (z * ((z \ x) * y)) * x. [back_rewrite(8609),rewrite([9559(2)])]. 9719 L(x,y \ 1,z * y) = L(x,y * z,y). [back_rewrite(6618),rewrite([9559(6)])]. 9729 x * (L(y,z * x,z) * (x * u)) = ((z * ((z \ x) * y)) * x) * u. [back_rewrite(6606),rewrite([9559(2)])]. 9737 K(L(x * y,x * z,x),z) = K(z * ((z * x) * y),z). [back_rewrite(5742),rewrite([9559(3)])]. 9755 x * L(y,z * x,z) = z * ((z \ x) * y). [back_rewrite(5070),rewrite([9559(2)])]. 9786 L(x * (y * z),x * y,x) = (x * y) * z. [back_rewrite(3018),rewrite([9559(4)])]. 9791 T(x,L(y * z,y * x,y)) = T(x,(x * y) * z). [back_rewrite(2700),rewrite([9559(3)])]. 9832 x \ (y * ((y \ x) * z)) = L(z,y * x,y). [back_rewrite(73),rewrite([9559(6)])]. 10000 (x / y) * ((y / x) * z) = L(z,y / x,x / y). [para(5359(a,1),21(a,1,1)),rewrite([45(6)])]. 10094 R(x,y,(x * y) \ z) * ((y * ((x * y) \ z)) / z) = 1. [para(82(a,2),5359(a,1,1))]. 10140 (x * (y / x)) * ((x * (y / x)) * z) = (x * (y * (y / x))) * z. [para(6446(a,1),178(a,1,2,1)),rewrite([5068(3),5068(6),13(7),2853(9),5068(11),189(11),18(8)])]. 10215 x / (y / z) = x * (z / y). [para(6565(a,1),1014(a,1,2)),flip(a)]. 10221 L(x,y / z,z / y) = x. [para(6565(a,1),3266(a,1,3))]. 10229 (x / y) \ z = (y / x) * z. [para(6565(a,1),3143(a,1,1)),flip(a)]. 10233 R(x,x \ y,z) \ 1 = R(x \ 1,y,z). [para(81(a,2),6565(a,1,1)),rewrite([6071(8)])]. 10235 R(x,y,(x * y) \ z) \ 1 = (y * ((x * y) \ z)) / z. [para(82(a,2),6565(a,1,1))]. 10279 ((x * y) / z) * (z / y) = R(x,y,z \ 1). [back_rewrite(1836),rewrite([10215(4)])]. 10287 (x / y) * ((y / x) * z) = z. [back_rewrite(10000),rewrite([10221(7)])]. 10295 L(x,(y * z) / x,y) = ((x / (y * z)) * y) * z. [back_rewrite(9575),rewrite([10229(6)])]. 10296 x * (x * (y * (x * (x * (y * (z \ ((z / y) * (x \ (x \ (y \ 1)))))))))) = x * x. [back_rewrite(9548),rewrite([10229(6)])]. 10305 R(x,y \ 1,(y / x) * z) = R(x,y \ 1,z). [back_rewrite(8463),rewrite([10229(4)])]. 10321 L(K(x,y),(y / x) * (x * x),y / x) = x \ T(x,y). [back_rewrite(6897),rewrite([10229(9),3169(9),4505(8),15(9)])]. 10323 L(x,y / x,z \ 1) = R(x,y \ 1,z). [back_rewrite(6707),rewrite([10229(6),169(8),4180(8)])]. 10326 K(x / y,y) / x = (y / x) / y. [back_rewrite(6575),rewrite([10229(4),1014(4)]),flip(a)]. 10347 L((x / y) * z,y / x,y) = x * (y \ z). [back_rewrite(5155),rewrite([10229(2)])]. 10366 (x / y) * (x \ y) = K(x \ 1,y). [back_rewrite(3231),rewrite([10229(3)])]. 10367 (x / y) * (y * (x \ z)) = L(z,x \ 1,y). [back_rewrite(3229),rewrite([10229(4)])]. 10393 (x / y) * (((y / x) * z) * x) = (z * (x / y)) * y. [back_rewrite(171),rewrite([10229(3)])]. 10400 (x \ y) / x = x \ (y / x). [para(92(a,1),7616(a,1,1))]. 10401 T(x \ y,z) / x = x \ T(y / x,z). [para(537(a,1),7616(a,1,1))]. 10402 T(T(T(x,y),z),u) / y = y \ T(T(x,z),u). [para(94(a,1),7616(a,1,1))]. 10408 (x / (x * y)) * y = y * (x / (x * y)). [para(2810(a,1),7616(a,1,1)),rewrite([10215(3),10229(6)]),flip(a)]. 10461 T(x,K(x / y,y)) = x. [hyper(28,a,7636,a)]. 10537 R(x,y \ z,T(y,z)) * z = (x * (y \ z)) * T(y,z). [para(2690(a,1),84(a,1,2))]. 10561 T((x * y) * z,R(x,y,z)) = (y * z) * R(x,y,z). [para(84(a,1),4209(a,1,1))]. 10562 R(x,y \ z,y) * T(z,y) = (x * (y \ z)) * y. [para(4505(a,1),84(a,1,2))]. 10592 R(T(x / y,y * z),y,z) = (y * z) \ (x * z). [para(85(a,2),92(a,1,1)),rewrite([31(4)])]. 10670 L(x,y,R(z / y,y,x)) = L(x,y,z * x). [para(85(a,2),3199(a,1,3))]. 10690 ((x / y) * z) \ x = (x * z) \ (x * y). [para(8701(a,1),21(a,2)),rewrite([16(3)]),flip(a)]. 10700 a(x / y,z,(x * z) \ (x * y)) = a(x,z,(x * z) \ (x * y)). [para(8701(a,2),57(a,1,1,2,2)),rewrite([10690(6),1105(6),10690(8)]),flip(a)]. 10702 K(x * (y / x),x / y) = K(x \ 1,y). [para(8701(a,2),67(a,1)),rewrite([10215(2),67(3),10215(4),666(5),5152(3),10215(5)]),flip(a)]. 10707 ((x * (y / z)) * z) \ x = L(y \ 1,z,x). [para(1829(a,1),8701(a,1,1)),rewrite([10215(5)]),flip(a)]. 10710 ((x \ y) * z) \ y = (y * z) \ (x * y). [para(2711(a,1),8701(a,2,1,1)),rewrite([659(3)]),flip(a)]. 10725 L(x \ (y * z),x,z) = (x \ y) * z. [para(3691(a,1),8701(a,2,1,1)),rewrite([3143(6),4408(5)])]. 10748 L(x,T(y,z) / x,y \ z) = (z * (T(y,z) / x)) \ (y * z). [back_rewrite(6696),rewrite([10710(9)])]. 10809 (x \ y) * (x * (x * z)) = T(y * x,x) * z. [para(7967(a,1),104(a,1,2,1)),rewrite([4525(5),7775(6)])]. 10810 R(T(x,y),y,y \ z) = ((y \ x) * (y * z)) / z. [para(7967(a,1),191(a,1,1,2,1)),rewrite([4525(4)]),flip(a)]. 10885 T(x,T(y * z,y * (y * x))) = T(x,T(T(z * y,y),x)). [back_rewrite(9001),rewrite([10809(4),2652(4)]),flip(a)]. 10888 T(x * y,x * (x * z)) = T(T(y * x,x),z). [back_rewrite(8992),rewrite([10809(4),10885(8),965(8)]),flip(a)]. 10900 T((x \ y) * (z * z),T(y,x)) = T(z * (z * (x \ y)),x). [back_rewrite(8036),rewrite([10888(7),101(3),4209(4),4578(3)])]. 10920 T(x * (y * y),x / z) = T(y * (y * x),z \ 1). [back_rewrite(5480),rewrite([10888(6),101(2),4209(3),4578(2)])]. 10927 T(x * (x * y),y \ z) = T(y * (x * x),z). [back_rewrite(5468),rewrite([10888(9),101(6),4209(7),4578(6)])]. 11076 L(T(x * y,x * z),L(y \ z,y,x),u) = (u * L(y \ z,y,x)) \ (u * (x * z)). [para(2705(a,1),74(a,1,1))]. 11083 (x \ y) * (z * (z * x)) = T(y * (z * z),x). [para(2254(a,1),2705(a,1,1)),rewrite([100(3),4408(4),100(6),100(8),10888(9),101(6),4209(7),4578(6)])]. 11138 (x * (y * (x \ (z / x)))) * (T(y,x \ (z / x)) \ x) = z. [para(1014(a,1),3544(a,1,1,2,2,2)),rewrite([3143(6),4408(6),45(2),1014(11),3143(10),3143(10),4155(9)])]. 11215 x * (((x \ y) / z) / T(x * y,z \ 1)) = x \ (z \ 1). [para(3640(a,1),15(a,1,2)),flip(a)]. 11218 K(x * y,x \ 1) = K(y,y \ (x \ 1)). [para(3640(a,1),20(a,1,2)),rewrite([11215(8),4505(4),8532(6),4408(3),45(2),11215(12)])]. 11219 ((x \ y) / z) / T(x * y,z \ 1) = x \ (x \ (z \ 1)). [para(3640(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 11221 x * (x / T(x * y,y \ x)) = y \ x. [para(47(a,1),3640(a,1,2,2,1)),rewrite([4408(5),14(5),989(5),1014(6),4408(8),14(8)])]. 11253 R(x,x \ (y \ 1),y * z) = z / ((x \ (y \ 1)) * (y * z)). [para(3640(a,1),82(a,1,3,1)),rewrite([11219(7),16(5),4408(6),45(5),11219(12),16(10),11219(15),16(13),16(12),4408(11),45(10)])]. 11256 (x \ (K(y \ (x \ 1),y) / x)) * z = (x \ T(x \ 1,y)) * z. [para(3640(a,1),178(a,1,1)),rewrite([11219(9),16(7),11219(13),16(11),16(10),3143(9),3143(9),9490(7),11219(14),16(12),4505(11),11219(17),16(15),16(14),1014(13),10401(11),989(9)])]. 11276 x / T(y * (y * (x * z)),z \ 1) = y \ (y \ (z \ 1)). [para(3641(a,1),21(a,1,2)),rewrite([3436(4),1607(12)]),flip(a)]. 11282 x * (x * ((y * z) / T(x * (x * (y * ((z * y) * u))),u \ (y \ 1)))) = u \ (y \ 1). [para(189(a,1),3641(a,1,2,2,2,1,2,2)),rewrite([4407(9),4407(16)])]. 11295 x * (x * (x / T(x / y,y * (x * x)))) = y * (x * x). [para(3641(a,1),3641(a,1,2,2,2,1,2)),rewrite([1014(3),11276(8),4408(7),4408(5),4408(4),45(3),4578(3),14(5),11276(14),4408(13),4408(11),4408(10),45(9),4578(9),14(11)])]. 11597 L(K(x,y) * z,K(y,x),u) = (u * K(y,x)) \ (u * z). [para(4993(a,1),180(a,1,1,2)),rewrite([6144(2),14(4),8298(10)])]. 11625 R(x,(x \ (y / x)) * (x * z),u) = ((y * z) * u) / (((x \ (y / x)) * (x * z)) * u). [para(18(a,1),183(a,1,1,1,1)),flip(a)]. 11645 (((x \ y) * z) * u) / (((y \ (x \ 1)) * (y * z)) * u) = R(y,(y \ (x \ 1)) * (y * z),u). [para(3143(a,1),183(a,1,1,1,1))]. 11726 a((x \ y) / z,x,T(y,x) \ ((x \ y) * z)) = a(x \ y,x,T(y,x) \ ((x \ y) * z)). [para(4505(a,1),10700(a,1,3,1)),rewrite([4505(10)])]. 11803 (x * ((y \ z) * z)) \ (x * ((y \ z) * ((y \ z) * u))) = L(T(y,z) \ u,(y \ z) * z,x). [para(2690(a,1),3141(a,1,2,2)),rewrite([2690(9)]),flip(a)]. 11853 L(x,(y \ z) * u,z \ y) = L(x,y \ z,u * (z \ y)). [para(4505(a,1),7679(a,1,3,2)),rewrite([90(5),4408(6)]),flip(a)]. 11861 x \ ((y \ z) * (((z \ y) * x) * u)) = L(u,z \ y,x * (y \ z)). [back_rewrite(9191),rewrite([11853(10)])]. 11862 L(T(x,y),x \ y,z * (y \ x)) = z \ ((z * (y \ x)) * y). [back_rewrite(7996),rewrite([11853(5)])]. 12076 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = (v6 * (v5 / L(L(x,y,z),u,w))) \ (v6 * v5). [para(34(a,1),6663(a,2,1,2,2))]. 12077 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = ((L(L(x,u,w),y,z) / v5) / v6) * (v6 * v5). [para(37(a,1),6663(a,2,1)),rewrite([2507(8),37(15),4501(16),1091(12),4407(12),10229(12),1014(12)])]. 12303 K(K(x,y),x) = 1. [para(15(a,1),7726(a,1,1,2))]. 12307 T(K(x,y),x) = K(x,y). [hyper(28,a,12303,a)]. 12308 K(x,y) * x = x * K(x,y). [para(12303(a,1),63(a,1,2)),rewrite([14(4)]),flip(a)]. 12309 K(x,K(x,y)) = 1. [para(12303(a,1),4993(a,1,1)),rewrite([13(4)])]. 12310 (x * K(x,y)) * ((x * K(x,y)) * z) = x * (x * (K(x,y) * (K(x,y) * z))). [para(12303(a,1),178(a,1,2,1)),rewrite([13(7),12308(8),189(11),12308(8),4578(10),37(12),100(10)])]. 12312 T(x,K(x,y)) = x. [hyper(28,a,12309,a)]. 12328 K(x,y) / x = x \ K(x,y). [para(12312(a,1),2711(a,1,2))]. 12349 K(x,y) * y = y * K(x,y). [para(12312(a,1),7616(a,1,1)),rewrite([5005(2),6144(4)]),flip(a)]. 12372 T(T(x,y),y \ 1) = x. [para(1091(a,1),7769(a,1,2)),rewrite([1708(2)])]. 12386 T(x,y / (y * x)) = x. [para(2810(a,1),7769(a,1,1)),rewrite([10229(3),10408(3),1708(4)])]. 12432 T(x,K(y,x)) = x. [para(12312(a,1),7769(a,1,1)),rewrite([6144(2),12349(2),1708(3)])]. 12473 K(x,y) / y = y \ K(x,y). [para(12432(a,1),2711(a,1,2))]. 12504 K(x,x * y) * T(y,x) = y. [para(7925(a,1),23(a,2)),rewrite([7826(5),6144(4)])]. 12506 L(T(x,K(y * L(x,z,u),y)),z,u) = L(x,z,u). [para(7925(a,1),30(a,1)),flip(a)]. 12519 T(x * y,K(x * ((z * x) * y),x * z)) = x * y. [para(189(a,1),7925(a,1,2,1))]. 12671 x \ K(x / y,y) = (y / x) / y. [para(10461(a,1),2711(a,1,2)),rewrite([10326(3)]),flip(a)]. 12698 T(T(K(x,y),z),x) = T(K(x,y),z). [para(12307(a,1),29(a,1,1)),flip(a)]. 12705 x * ((x \ (y / x)) * K(x \ (y / x),z)) = y * (x \ K(x \ (y / x),z)). [para(12307(a,1),3575(a,1,2,2)),rewrite([12308(11)]),flip(a)]. 12809 R(T(x \ 1,(x \ y) * z),y,z) = (y * z) \ ((x \ y) * z). [para(6071(a,1),2643(a,1,1)),rewrite([31(6)])]. 12830 (x \ K(y,z)) * K(z,y) = x \ 1. [para(4993(a,1),6071(a,1,2)),rewrite([48(6),4996(9)])]. 12856 L(L(T(x,K(y * L(x,z,u),y)),w,v5),z,u) = L(L(x,z,u),w,v5). [para(12506(a,1),34(a,1,1)),flip(a)]. 12884 (x * R(y,z,(y * z) \ u)) * ((z * ((y * z) \ u)) / u) = x. [para(10094(a,1),104(a,1,2,2)),rewrite([14(9),16(8)]),flip(a)]. 12928 R(x,R(y,z,(y * z) \ u),(z * ((y * z) \ u)) / u) = x. [para(10094(a,1),84(a,1,2)),rewrite([14(10),12884(17)])]. 12931 x / R(y,z,(y * z) \ u) = x * ((z * ((y * z) \ u)) / u). [para(10094(a,1),85(a,2,2)),rewrite([12928(12),48(11)])]. 13311 a(x \ y,x,T(z,y * x)) = a(x,y * x,T(z,y * x)). [para(90(a,1),3968(a,1,3,2)),rewrite([7616(2),90(6),90(7)])]. 13425 T(T(T(x,y),z),y \ 1) = T(x,z). [para(7769(a,1),4214(a,2)),rewrite([8018(7)])]. 13457 L(x,(y \ z) * (y * u),y) = L(x,y * ((z * y) * u),y). [para(187(a,1),132(a,1,2,2)),rewrite([104(4),21(10),2507(10)]),flip(a)]. 13466 a(x,(x \ y) * (x * z),u) = a(x,x * ((y * x) * z),u). [para(187(a,1),133(a,1,1,2)),rewrite([104(9),37(10),4501(11),4498(9),2508(10)]),flip(a)]. 13523 (x \ (y \ (z \ 1))) * (y * (((y \ z) * (y * x)) * u)) = L(u,y * ((z * y) * x),y). [back_rewrite(9186),rewrite([13457(14)])]. 13639 (x * (y \ z)) * ((z \ y) * u) = (y \ z) * (((z \ y) * x) * u). [para(4137(a,1),190(a,1,2,2)),rewrite([4408(4),14(6),4408(8),5208(12)])]. 13641 T(x,y) * ((y \ z) * (y * u)) = y \ (x * ((z * y) * u)). [para(4505(a,1),190(a,1,1)),rewrite([7550(11)])]. 13663 x / T(x / y,y * (x * x)) = T(y,x * x). [para(11295(a,1),21(a,1,2)),rewrite([23(4),1607(8)]),flip(a)]. 13668 x * (x * (T(y,x * x) * z)) = y * (x * (x * z)). [para(11295(a,1),37(a,1,1)),rewrite([2040(3),13663(8)]),flip(a)]. 13687 ((x / y) * (z * (y * y))) \ (x * (y * T(z,y * y))) = a(x / y,y,y * T(z,y * y)). [para(11295(a,1),60(a,1,1,2)),rewrite([13663(9),13663(15)])]. 13702 (x * (y * (z * (z * u)))) \ ((x * (y * (z * z))) * u) = a(x,y * (z * z),u). [para(11295(a,1),139(a,1,2,1,2)),rewrite([13663(5),13668(5),13663(14),777(13)])]. 13709 L((x * (y * y)) \ z,x * (y * y),y) = (y * T(x,y * y)) \ (y \ z). [para(11295(a,1),3940(a,1,1,1)),rewrite([13663(8),777(7),13663(11)])]. 13734 x * (T(y,x * x) * x) = T(y * (x * x),x). [para(11295(a,1),4209(a,1,1)),rewrite([13663(8),101(7)]),flip(a)]. 13735 T(T(x * (y * y),y),y * T(x,y * y)) = x * (y * y). [para(11295(a,1),4209(a,2)),rewrite([13663(5),101(4),13734(4),13663(8)])]. 13845 L(x,(y * ((y \ z) * u)) * z,L(u,y * z,y)) = L(x,z,L(u,y * z,y) * (y * ((y \ z) * u))). [para(9729(a,1),132(a,1,2,2)),rewrite([9640(6),21(16),9755(12)])]. 13884 L(x,y * (z * y),y) = L(x,y,z). [para(14(a,1),13523(a,1,2,2,1,2)),rewrite([45(5),4505(5),4525(6),5885(6),14(4)]),flip(a)]. 13929 L(x,(y \ z) * u,y \ z) = L(x,z \ y,u * (y \ z)). [para(4137(a,1),13523(a,1,2,2,1,2)),rewrite([4408(5),1014(5),1829(4),4408(5),14(7),3143(8),11861(6),5208(9)]),flip(a)]. 13932 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y) * u,K(z,y)). [para(4993(a,1),13523(a,1,2,2,1,2)),rewrite([6144(5),1014(5),1829(4),6144(5),14(7),3143(8),9198(6),8298(9)])]. 14038 (x * ((x \ (y \ 1)) * ((y * z) * u))) \ ((z / y) * (y * u)) = a(x,x / y,(y * z) * u). [para(15(a,1),9423(a,1,1,2,2,2)),rewrite([15(15)])]. 14083 (x / y) * (y * (x * T(x \ (x \ 1),x * x))) = 1. [para(996(a,1),13687(a,2,3,2)),rewrite([3436(4),8972(6),16(4),87(4),14(3),3436(4),10229(9),3436(13),16(14),1072(13)])]. 14102 T(x,T(x,y) \ 1) = x. [para(541(a,1),12372(a,1,1))]. 14123 T(x,(y / x) / y) = x. [para(5067(a,1),12372(a,1,1)),rewrite([4407(4),10229(4),1014(4)])]. 14124 (x \ (x \ (y \ 1))) * z = x \ (x \ (y \ z)). [para(12372(a,1),3710(a,1,2)),rewrite([7616(7)])]. 14154 K(x,y / (y * x)) = 1. [hyper(27,a,12386,a)]. 14430 T(x,y) * K(x \ y,x) = x. [para(14102(a,1),23(a,2)),rewrite([1014(7),8593(5),4408(6),45(3)])]. 14495 T(x,(T(T(T(y,z),u),x \ 1) / x) / T(T(T(y,x \ 1),z),u)) = x. [para(3382(a,1),14123(a,1,2,1))]. 14546 K(x \ y,x / y) = 1. [para(16(a,1),14154(a,1,2,2))]. 14868 (x * x) / y = x * (x / y). [para(100(a,1),1014(a,1)),rewrite([1014(3)]),flip(a)]. 14874 L(x,y * (y * z),u) = L(x,z,u * (y * y)). [para(100(a,1),132(a,1,1,2,2)),rewrite([100(5),100(9),100(11),4501(12),1091(5),4407(5),5162(5),5610(10),100(7),2507(8)])]. 14882 a(x * (y * y),z,u) = a(x,y * (y * z),u). [para(100(a,1),133(a,1,1,2,2)),rewrite([100(6),100(9),100(11),37(12),4501(13),1091(6),4407(6),5162(6),6141(11),100(7),2508(8)]),flip(a)]. 15035 L(x,y,y * (z * z)) = x. [back_rewrite(5614),rewrite([14874(3)])]. 15045 L(x,y * (z * (z * y)),u * (z * z)) = x. [back_rewrite(2522),rewrite([14874(6)])]. 15052 x * (y * T(y \ (y \ 1),y * y)) = x / y. [para(14083(a,1),15(a,1,2)),rewrite([10229(3),14(3)]),flip(a)]. 15056 L(x * T(x \ (x \ 1),x * x),y,x) = x \ 1. [para(14083(a,1),21(a,1,2)),rewrite([18(2),3200(10)]),flip(a)]. 15079 a((x / y) * (z * (x / y)),y / x,u) = a(x / y,z,u). [para(14083(a,1),133(a,1,2,1,2,2)),rewrite([15052(9),10287(5),14(6),19(7),15052(13)]),flip(a)]. 15120 L(x,y * ((y \ z) * T(z,y)),u * ((y \ z) * (y \ z))) = x. [para(4505(a,1),15045(a,1,2,2,2))]. 15137 K(T(x * y,y),y \ 1) = K(T(x,y) \ 1,x * y). [para(165(a,1),10702(a,1,1,2)),rewrite([7775(2),6564(5)])]. 15143 K(x \ 1,T(y,x)) = K(y,y \ x). [para(2711(a,1),10702(a,1,2)),rewrite([7616(2),16(2)]),flip(a)]. 15144 K(T(x,y),y \ (x \ 1)) = K(y,x). [para(3143(a,1),10702(a,1,1)),rewrite([4155(3),45(2),23(2),6120(4),4408(9),45(7),14(7)])]. 15148 K(x \ 1,y \ x) = K(x / y,y). [para(3666(a,1),10702(a,1,1,2)),rewrite([1014(3),4155(3),16(3)]),flip(a)]. 15149 K(T(x,y),y \ 1) = K(x \ y,x). [para(3666(a,1),10702(a,1,2)),rewrite([4155(3),16(3),4505(2),4408(7),14(7)])]. 15266 (x / y) * ((y * z) / T(x * (y \ x),z)) = (y / x) * z. [para(4254(a,1),15(a,1,2)),rewrite([10229(2)]),flip(a)]. 15271 ((x / y) * (((y / x) * z) * u)) \ (z * u) = a(x / y,(y / x) * z,u). [para(4254(a,1),19(a,1,2,1)),rewrite([15266(8),15266(15)])]. 15276 (x * y) / T(z * (x \ z),y) = (x / z) * ((x / z) * y). [para(4254(a,1),21(a,1,2)),rewrite([3436(4),10229(3),10229(4),1607(12)]),flip(a)]. 15308 a(x / y,(y / x) * ((y / x) * z),u) = a(x / y,z,u). [para(4254(a,1),133(a,1,2,1,2)),rewrite([15276(8),37(8),10287(9),10287(6),19(7),15276(12),2508(12)]),flip(a)]. 15408 T(x \ y,y) * (T(x,y) * z) = T(x,y) \ ((x * y) * z). [para(4314(a,1),15(a,1,2)),flip(a)]. 15409 T(x,y) * (T(x \ y,y) * z) = (x * y) * (T(x,y) \ z). [para(16(a,1),4314(a,1,2,2))]. 15411 a(T(x,y),T(x \ y,y),T(x,y) * z) = a(x,y,z) \ 1. [para(4314(a,1),19(a,1,1)),rewrite([4304(6),4525(5),2548(5)]),flip(a)]. 15452 x \ (y * (y * z)) = ((x \ y) * y) * z. [para(7769(a,1),4314(a,1,1)),rewrite([8018(3),6134(4),7769(6),4525(6),3143(5),7617(6)])]. 15454 x * (T((y / x) / y,K(x / y,y)) * (x * z)) = (x * K(x / y,y)) * z. [para(10461(a,1),4314(a,1,1)),rewrite([12671(3),10461(8)])]. 15593 a(x \ y,z * (x \ y),T(x,y)) = a(x \ y,z,y) \ 1. [para(4344(a,1),19(a,1,1)),rewrite([128(9),2690(7),2548(7)]),flip(a)]. 15621 (((x \ y) * z) * y) \ (x \ y) = T(x,y) \ ((y \ x) / z). [para(4344(a,1),1091(a,1,1)),rewrite([4407(11),4407(10),4408(10),1014(10)])]. 15622 T(x \ y,(z * (x \ y)) * T(x,y)) = T(x \ y,((x \ y) * z) * y). [para(4344(a,1),1708(a,1,2)),flip(a)]. 15645 ((x * (y \ z)) * T(y,z)) * (y \ z) = T(((y \ z) * x) * z,y \ z). [para(4344(a,1),4209(a,1,1)),flip(a)]. 15646 T(T(((x \ y) * z) * y,x \ y),(z * (x \ y)) * T(x,y)) = ((x \ y) * z) * y. [para(4344(a,1),4209(a,2)),rewrite([15645(6)])]. 15674 (((x \ y) * z) * x) \ ((z * (y \ x)) * T(y,x)) = T(y \ x,((y \ x) * z) * x). [back_rewrite(5569),rewrite([15622(14)])]. 15862 x * ((x \ y) * (x \ y)) = y * (x \ y). [para(7769(a,1),4404(a,1,2)),rewrite([7617(7),6351(7)]),flip(a)]. 15916 x \ ((x * y) * z) = (y / x) * (x * z). [para(15(a,1),4504(a,1,2,1,1)),rewrite([1091(2),3143(5),1091(5),1014(6),4209(6)])]. 15922 L(x,x \ y,z * (y \ x)) = ((y \ x) / z) * (z * T(y,x)). [para(4504(a,1),21(a,1,2)),rewrite([7715(4),15916(5),11853(9)]),flip(a)]. 15924 T(x \ y,((y \ x) * z) * y) = T(x \ y,((x \ y) * z) * y). [para(4504(a,1),23(a,1,2)),rewrite([15674(8)]),flip(a)]. 15928 T(x,y \ z) * T(y,z) = (z \ y) * (x * z). [para(37(a,1),4504(a,1,2)),rewrite([7715(7),9031(7)]),flip(a)]. 15940 ((x * (y \ z)) * T(y,z)) / T(y \ z,((z \ y) * x) * z) = ((z \ y) * x) * z. [para(4504(a,1),165(a,1,1))]. 15943 (x \ y) * (((y \ x) / z) * y) = (z \ (x \ y)) * T(x,y). [para(1014(a,1),4504(a,1,2,1)),rewrite([3143(9)])]. 15957 x * L(y,y \ z,x * (z \ y)) = (x * (z \ y)) * T(z,y). [para(4504(a,1),72(a,2)),rewrite([7715(4),11853(4)])]. 16020 L(T(x,y),x \ y,z * (y \ x)) = ((y \ x) / z) * (z * y). [back_rewrite(11862),rewrite([15916(9)])]. 16096 a(x / (y * y),y,y * z) = a(x,y \ 1,y * z). [back_rewrite(7412),rewrite([15916(8),7628(9)])]. 16103 L(x,y * z,y) = L(x,y,z). [back_rewrite(5134),rewrite([15916(3),3276(4)]),flip(a)]. 16229 L(x,K(y,z) * u,K(z,y)) = L(x,K(z,y),u). [back_rewrite(13932),rewrite([16103(8)])]. 16231 L(x,y \ z,u * (z \ y)) = L(x,z \ y,u). [back_rewrite(13929),rewrite([16103(4)]),flip(a)]. 16256 L(x,y,z * y) = L(x,y,z). [back_rewrite(13884),rewrite([16103(3)])]. 16286 L(x,(y * ((y \ z) * u)) * z,L(u,y,z)) = L(x,z,L(u,y,z) * (y * ((y \ z) * u))). [back_rewrite(13845),rewrite([16103(6),16103(8)])]. 16343 x \ T(x,y) = K(x,y). [back_rewrite(10321),rewrite([16103(6),2254(4)]),flip(a)]. 16348 x \ (y * ((y \ x) * z)) = L(z,y,x). [back_rewrite(9832),rewrite([16103(6)])]. 16362 T(x,L(y * z,y,x)) = T(x,(x * y) * z). [back_rewrite(9791),rewrite([16103(3)])]. 16364 L(x * (y * z),x,y) = (x * y) * z. [back_rewrite(9786),rewrite([16103(4)])]. 16387 K(L(x * y,x,z),z) = K(z * ((z * x) * y),z). [back_rewrite(9737),rewrite([16103(3)])]. 16398 L(x,y \ 1,z * y) = L(x,y,z). [back_rewrite(9719),rewrite([16103(6)])]. 16465 L(x,y \ z,y) = L(x,y,z). [back_rewrite(9559),rewrite([16103(4)])]. 16470 L(x,y * z,y \ 1) = L(x,y,z). [back_rewrite(6634),rewrite([16103(6)])]. 16484 x \ (y \ (z * (y * x))) = L(T(z,y * x),y,x). [back_rewrite(5138),rewrite([16103(4)]),flip(a)]. 16485 L((x * y) \ z,x,y) = y \ (x \ z). [back_rewrite(3940),rewrite([16103(4)])]. 16487 L(L(x,y,z),z,y) = x. [back_rewrite(667),rewrite([16103(3)])]. 16505 L(T(x,y),y \ x,z) = ((y \ x) / z) * (z * y). [back_rewrite(16020),rewrite([16231(5)])]. 16508 (x * (y \ z)) * T(y,z) = x * L(z,y \ z,x). [back_rewrite(15957),rewrite([16231(4)]),flip(a)]. 16509 ((x \ y) / z) * (z * T(x,y)) = L(y,x \ y,z). [back_rewrite(15922),rewrite([16231(4)]),flip(a)]. 16517 L(x,(y \ z) * u,z \ y) = L(x,z \ y,u). [back_rewrite(11853),rewrite([16231(8)])]. 16564 K(x \ y,x) = K(y,x). [back_rewrite(4516),rewrite([16343(4)])]. 16566 T(x,y) / x = K(x,y). [back_rewrite(4366),rewrite([16343(4)])]. 16568 K(x * y,x) = K(y,x). [back_rewrite(3934),rewrite([16343(4)])]. 16569 K(x \ 1,y * x) = K(y,x). [back_rewrite(3171),rewrite([16343(6)])]. 16603 K(T(x,y),y \ 1) = K(y,x). [back_rewrite(15149),rewrite([16564(6)])]. 16623 T(x,y) * K(y,x) = x. [back_rewrite(14430),rewrite([16564(3)])]. 16660 (x \ (K(x \ 1,y) / x)) * z = (x \ T(x \ 1,y)) * z. [back_rewrite(11256),rewrite([16564(4)])]. 16686 K(x,x * y) = K(x,y). [back_rewrite(8594),rewrite([16564(2)]),flip(a)]. 16687 x / T(x,y) = K(y,x). [back_rewrite(8593),rewrite([16564(4)])]. 16710 K(x,x \ y) = K(x,y). [back_rewrite(8534),rewrite([16564(2)]),flip(a)]. 16711 T(x,y) \ x = K(y,x). [back_rewrite(8532),rewrite([16564(4)])]. 16712 K(T(x,y),K(x,y)) = 1. [back_rewrite(8078),rewrite([16564(3)])]. 16716 x * K(x,y) = T(x,y). [back_rewrite(4535),rewrite([16564(2)])]. 16717 x * (K(x,y) * (x * z)) = (x * T(x,y)) * z. [back_rewrite(4534),rewrite([16564(2)])]. 16735 K(L(x * y,x,z),z) = K((z * x) * y,z). [back_rewrite(16387),rewrite([16568(7)])]. 16813 L(L(T(x,K(L(x,y,z),u)),w,v5),y,z) = L(L(x,y,z),w,v5). [back_rewrite(12856),rewrite([16568(3)])]. 16827 K(x * y,y) = K(T(x,y),y). [back_rewrite(7876),rewrite([16568(3)])]. 16839 K(T(x,y) \ 1,x * y) = K(y,x * y). [back_rewrite(15137),rewrite([16603(5)]),flip(a)]. 16875 K(x,y) * T(y,x) = y. [back_rewrite(12504),rewrite([16686(2)])]. 16909 K(x,y * x) = K(x,T(y,x)). [back_rewrite(7875),rewrite([16686(3)])]. 16936 K(x \ 1,T(y,x)) = K(y,x). [back_rewrite(15143),rewrite([16710(6)])]. 16950 K(x * y,x \ 1) = K(y,x \ 1). [back_rewrite(11218),rewrite([16710(8)])]. 16967 K(x,y \ 1) = K(y,x / y). [back_rewrite(3163),rewrite([16710(3)]),flip(a)]. 16981 x * (y \ K(y \ (x / y),z)) = y * T(y \ (x / y),z). [back_rewrite(12705),rewrite([16716(6)]),flip(a)]. 16984 x * (x * (K(x,y) * (K(x,y) * z))) = T(x,y) * (T(x,y) * z). [back_rewrite(12310),rewrite([16716(2),16716(3)]),flip(a)]. 16985 K(x,y) * x = T(x,y). [back_rewrite(12308),rewrite([16716(4)])]. 16999 a(x,y,K(y,x)) = 1. [back_rewrite(1097),rewrite([16716(2),90(2),46(3)]),flip(a)]. 17019 K(T(x,y) \ 1,x * y) = K(y,T(x,y)). [back_rewrite(16839),rewrite([16909(7)])]. 17040 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(x \ y,y \ 1). [back_rewrite(6878),rewrite([16950(12)])]. 17093 (x \ y) * (((y \ x) * z) * ((z * (x \ y)) * u)) = z * (z * ((x \ y) * u)). [para(4137(a,1),193(a,2,1,2,1,1)),rewrite([4145(5),13639(8),13(10),37(12)])]. 17291 K(x,y \ 1) = K(x,x / y). [para(89(a,1),4809(a,1,1,1,1)),rewrite([101(3),4230(2),15452(7),1091(4),4407(4),4408(4),1014(4),10400(2),4505(3),92(2),4493(3),89(4),16686(6)])]. 17387 (x * T(y,x * x)) \ T(z,x) = ((y * (x * x)) \ z) * x. [para(23(a,1),13709(a,2,2)),rewrite([10725(7)]),flip(a)]. 17666 L(K(x,y),x,y) = K(x,y). [hyper(24,a,16999,a)]. 17730 K(x \ 1,y) = K(x,y \ 1). [para(14546(a,1),63(a,1,2)),rewrite([10366(3),14(5),4493(6)])]. 17771 K(x,T(y,x)) = K(x,y). [back_rewrite(17019),rewrite([17730(5),4407(4),15144(5)]),flip(a)]. 17772 K(x,T(y,x) \ 1) = K(y,x). [back_rewrite(16936),rewrite([17730(4)])]. 17778 (x \ (x \ K(x,y \ 1))) * z = (x \ T(x \ 1,y)) * z. [back_rewrite(16660),rewrite([17730(3),12328(4)])]. 17781 K(x,y \ 1) = K(y,x). [back_rewrite(16569),rewrite([17730(4),4407(3),16710(4)])]. 17822 K(x / y,y) = K(x,y). [back_rewrite(15148),rewrite([17730(4),4408(3),14(3),16710(2)]),flip(a)]. 17906 (x \ T(x \ 1,y)) * z = (x \ (x \ K(y,x))) * z. [back_rewrite(17778),rewrite([17781(3)]),flip(a)]. 17910 K(T(x,y),y) = K(x,y). [back_rewrite(17772),rewrite([17781(4)])]. 17913 K(x \ 1,y) = K(y,x). [back_rewrite(17730),rewrite([17781(6)])]. 17914 K(x,x / y) = K(y,x). [back_rewrite(17291),rewrite([17781(3)]),flip(a)]. 17919 ((x \ (y \ 1)) * (y * y)) \ (y / x) = K(y,x \ y). [back_rewrite(17040),rewrite([17781(11)])]. 17924 K(x,y / x) = K(x,y). [back_rewrite(16967),rewrite([17781(3)]),flip(a)]. 17974 x * (T((y / x) / y,K(x,y)) * (x * z)) = T(x,y) * z. [back_rewrite(15454),rewrite([17822(4),17822(9),16716(9)])]. 18023 (x * (y / x)) \ y = K(y,x). [back_rewrite(67),rewrite([17822(5)])]. 18043 K(x * y,y) = K(x,y). [back_rewrite(16827),rewrite([17910(4)])]. 18156 x \ (y * (x / y)) = K(y,x). [back_rewrite(66),rewrite([17924(5)])]. 18422 (T(x,y) * z) / (K(x,y) * z) = R(x,K(x,y),z). [para(16343(a,1),81(a,1,2)),rewrite([16343(6)]),flip(a)]. 18454 L(x,y,x \ 1) = x. [para(1022(a,1),16487(a,1,1))]. 18461 L(x,y,L(x,z,u)) = x. [para(16487(a,1),1689(a,1,1)),rewrite([16487(4)])]. 18472 L(x,x \ y,y) = x. [para(8105(a,1),16487(a,1,1))]. 18473 L(L(x,y,z),z / (y * x),y) = x. [para(3199(a,1),16487(a,1,1))]. 18485 L(R(x,y,z),u,x \ 1) = R(x,y,z). [para(18454(a,1),33(a,1,1)),flip(a)]. 18604 a(x,y \ x,y) = 1. [hyper(25,a,18472,a)]. 18608 L(x,T(y,x),y * x) = x. [para(23(a,1),18472(a,1,2))]. 18650 L(x,y \ 1,x / y) = x. [para(1829(a,1),18472(a,1,2))]. 18689 (x * (y * x)) \ ((x * y) * z) = L(x \ z,x,x * y). [para(101(a,1),74(a,2,1)),flip(a)]. 18690 L(x \ y,x,y * z) = ((y * z) * x) \ (y * (z * y)). [para(101(a,1),74(a,2,2))]. 18703 ((x / (y * z)) * (y * (z * y))) \ (x * y) = a(x / (y * z),y * z,y). [para(101(a,1),60(a,1,1,2))]. 18718 T(x * y,x * x) = T(y * x,x). [para(2690(a,1),101(a,2,2)),rewrite([7789(3),15928(4),8972(3),7775(5)])]. 18724 a(x * y,x,T(z,x)) = a(x,y,z * x) \ 1. [para(101(a,1),507(a,1,2,1)),rewrite([128(7),90(5),2548(7)]),flip(a)]. 18742 a(x,y,y * x) = 1. [para(101(a,1),8106(a,1,2)),rewrite([3982(4),4795(4)])]. 18750 R(x,y * z,y) * (y * (z * y)) = (x * (y * z)) * y. [para(101(a,1),84(a,1,2))]. 18752 R((x * y) / z,z,x) = (x * (y * x)) / (z * x). [para(101(a,1),85(a,2,1))]. 18763 a((x * y) / z,x,L(x \ z,x,x * y)) = a(x * y,x,L(x \ z,x,x * y)). [para(101(a,1),10700(a,1,3,1)),rewrite([18689(7),101(9),18689(12)])]. 18809 (x \ y) * (x * x) = T(y * x,x). [back_rewrite(8972),rewrite([18718(6)])]. 18848 L(x,y,z * (u * (z * (y * x)))) = L(x,y,z * (u * z)). [para(106(a,1),3199(a,1,3)),flip(a)]. 18870 (((x \ y) * z) * ((z * (y \ x)) * T(y,x))) / x = (x \ y) * (z * z). [para(4504(a,1),106(a,1,1,2)),rewrite([7715(14),4578(11)])]. 18962 x / T(x * y,y \ x) = x \ (y \ x). [para(11221(a,1),15(a,1,2)),flip(a)]. 19049 T(T(x,y) \ z,K(T(x,y) \ ((x \ y) * z),T(x \ y,y))) = T(x,y) \ z. [para(11221(a,1),12519(a,1,2,1,2,1)),rewrite([18962(4),6968(3),18962(6),6968(7),18962(10),4505(9),18962(14),6968(13)])]. 19065 x * T(x \ (x \ 1),x * x) = x \ 1. [para(15056(a,1),70(a,1)),flip(a)]. 19074 (x * y) / x = x * (y / x). [para(15056(a,1),72(a,1,2)),rewrite([1014(4),19065(8),1014(5)])]. 19167 a(x,(x / y) * ((x / y) * z),u) = a(y \ (x / y),z,u). [para(18(a,1),4636(a,2,1)),rewrite([3286(6),2508(5)]),flip(a)]. 19178 a(x * (y \ (x * x)),z,u) = a(x / y,x * (x * z),u). [para(1014(a,1),4636(a,2,1)),rewrite([3143(4)])]. 19195 a(T(x,y),(y \ x) * ((y \ x) * z),u) = a((y \ x) * (x * (y \ x)),z,u). [para(4505(a,1),4636(a,2,1)),rewrite([15862(5)]),flip(a)]. 19450 (x * ((T(y,z) * (x * x)) \ u)) \ (T(T(y,x),z) \ 1) = u \ x. [para(4713(a,1),1829(a,1,2)),rewrite([4407(11)]),flip(a)]. 19451 x / (T(T(y,z),u) * ((y \ z) * ((T(y,u) * ((y \ z) * (y \ z))) \ x))) = y \ z. [para(2642(a,1),4713(a,1,2,1,1))]. 19474 (x * (y * y)) \ z = y \ (y \ (x \ z)). [para(4713(a,1),3645(a,1,1)),rewrite([4407(12),19450(12),10927(4),2711(4),4407(13),19450(13)])]. 19479 x / (T(y,z) * ((y \ u) * (T(T(y,u),z) \ x))) = u \ y. [para(7769(a,1),4713(a,1,2,1,1)),rewrite([19474(9),4408(8),4408(9),7715(10)])]. 19486 x / (T(K(y,z),u) * (u \ (K(z,y) * x))) = u. [para(12307(a,1),4713(a,1,2,2,2,1,1)),rewrite([12698(3),19474(6),6144(4),6073(6),7550(7)])]. 19496 x / (T(y,z) * ((u / (u * y)) * ((u * (y * (y / u))) * (T(y,z) \ x)))) = u / (u * y). [para(12386(a,1),4713(a,1,2,1,1)),rewrite([19474(11),10229(10),19074(7),10229(11),19074(5),10140(11)])]. 19499 x / (T(y,z) * (T(y,u) \ ((T(y,z) * (T(y,u) \ (T(y,u) \ 1))) \ x))) = T(y,u) \ 1. [para(14102(a,1),4713(a,1,2,1,1)),rewrite([1014(12),10400(10),989(9),3143(13)])]. 19502 x / (T(y,z) * (((u / y) / u) * ((u * (y * (y / u))) * (T(y,z) \ x)))) = (u / y) / u. [para(14123(a,1),4713(a,1,2,1,1)),rewrite([19474(11),10229(10),10215(7),10229(11),10215(5),10140(11)])]. 19536 x / (T(T(y,z),u) * ((z \ y) * (T(y,u) \ x))) = y \ z. [back_rewrite(19451),rewrite([19474(9),4408(8),4408(9),7715(10)])]. 19567 K(x,y \ x) = K(y,x). [back_rewrite(17919),rewrite([19474(7),4408(5),4408(3),45(2),3032(3),19074(2),15(4),18156(3)]),flip(a)]. 19570 (x * T(y,x * x)) \ T(z,x) = T(x \ (y \ z),x). [back_rewrite(17387),rewrite([19474(8),4505(9)])]. 19639 (x * (y * (z * x))) \ (x * (z * (x * T(y,z * x)))) = a(x * z,x,T(y,z * x)). [para(90(a,1),196(a,1,1,2))]. 19647 (x * ((y \ x) * z)) \ (x * (y \ (x * z))) = a(x / y,x,z). [para(1014(a,1),196(a,2,1)),rewrite([3143(3),3143(7)])]. 19659 a(x / y,x,z) = a(x,y \ x,z). [para(2690(a,1),196(a,2,1)),rewrite([7789(4),4525(5),7997(9),8098(7),19647(7)])]. 19660 (x * (y * (x * z))) \ (x * (y * (x * L(z,x,y)))) = a(x * y,x,L(z,x,y)). [para(72(a,1),196(a,1,1,2))]. 19674 a((x \ y) * z,x \ y,x) = a(x \ y,z,T(y,x)) \ 1. [para(4505(a,1),196(a,1,2,2,2)),rewrite([8020(5),2548(9)]),flip(a)]. 19707 R(x * y,y * x,(y * x) \ (K(y,x) * z)) = R(x * y,K(y,x),z). [para(16(a,1),202(a,2,1,2)),rewrite([6144(5),6144(11),2858(12)])]. 19771 T(x * (x / y),y) = y \ (x * x). [para(87(a,1),10900(a,1,2)),rewrite([3143(4),88(4),1014(5)]),flip(a)]. 19991 (x * (y * x)) / z = x * (y * (x / z)). [para(13(a,1),1851(a,1,1,2,2,2,2)),rewrite([14(4),13(4),13(4),989(8),1014(9),13(8),13(8),13(8)])]. 20016 R((x * y) / z,z,x) = x * (y / z). [back_rewrite(18752),rewrite([19991(7),3691(5),1014(6)])]. 20095 L(a(x / y,y,z),(x / y) * (y * z),u) * ((u * (x * z)) \ (u * ((x / y) * (y * z)))) = 1. [para(1961(a,2),4137(a,1,1))]. 20341 a(x * y,y,x) = 1. [para(15(a,1),18604(a,1,2))]. 20387 a(x,y / x,y) = 1. [para(18(a,1),18742(a,1,3))]. 20390 (x * y) * (y * x) = x * (y * (y * x)). [para(18742(a,1),209(a,1,1)),rewrite([45(5),18742(8),88(8)])]. 20397 a(T(x,y),y,x * y) = 1. [para(90(a,1),18742(a,1,3))]. 20504 ((x * (y * (z * (z * y)))) * u) / (z * (y * (y * (z * u)))) = R(x,y * (z * (z * y)),u). [back_rewrite(9114),rewrite([20390(3),20390(8),2213(9),20390(13)])]. 20509 (x * y) * (K(y,x) * (z * (x * y))) = y * (x * (x * (y * T(z,x * y)))). [back_rewrite(9104),rewrite([20390(3),2213(6)]),flip(a)]. 20510 (x * (y * (z * (z * (y * u))))) * a(x,z * (y * (y * z)),u) = (x * (z * (y * (y * z)))) * u. [back_rewrite(9101),rewrite([20390(3),2213(4),20390(8),20390(13)])]. 20551 a(x,y,x \ y) = 1. [para(2690(a,1),20341(a,1,1)),rewrite([4582(3)])]. 20620 (x * (y * (x / y))) / (y * (x * (y \ x))) = 1. [para(20387(a,1),265(a,1,2,2)),rewrite([8255(3),4230(5),88(8),20387(9)])]. 20692 a(x * (y * z),(x * y) * z,a(x,y,z)) = 1. [para(19(a,1),20551(a,1,3))]. 20939 T(T(x,y),z) / T(x,z) = K(T(x,z),y). [para(29(a,1),16566(a,1,1))]. 20967 ((x * K(y,z)) * y) / T(y,z) = R(x,K(y,z),y). [para(16566(a,1),86(a,1,1,1,2)),rewrite([16566(7)])]. 20994 K((x * y) * z,R(x,y,z)) = K(y * z,R(x,y,z)). [para(84(a,1),16568(a,1,1))]. 21045 L(K(x,y) * z,K(y,x),T(x,y)) = x \ (T(x,y) * z). [para(16623(a,1),74(a,2,1)),rewrite([6144(2)])]. 21062 T(x,y) * (x * z) = x * (T(x,y) * z). [para(16623(a,1),189(a,1,1)),rewrite([16875(7)]),flip(a)]. 21063 K(x,y) * (y * z) = y * (K(x,y) * z). [para(16623(a,1),189(a,2,2,1)),rewrite([16875(3)]),flip(a)]. 21070 x * L(y,K(z,x),T(x,z)) = T(x,z) * (K(z,x) * y). [para(16623(a,1),72(a,1,1))]. 21095 R(x / T(y,z),T(y,z),K(z,y)) = (x * K(z,y)) / y. [para(16623(a,1),85(a,2,2))]. 21316 T((x / y) * (z * (x / y)),y) = (y \ x) * (y \ (z * x)). [para(18(a,1),122(a,1,2,2,2)),rewrite([6135(4)]),flip(a)]. 21447 x * (y \ ((y / x) * z)) = L(z,y / x,y). [para(16(a,1),10347(a,1,1)),rewrite([10229(4)]),flip(a)]. 21463 T(x,y) * ((x * y) \ z) = L(y \ z,y,x). [para(165(a,1),10347(a,1,2)),rewrite([6564(3),3143(3),16256(3)]),flip(a)]. 21472 L((x \ y) * z,y \ x,x) = T(y,x) * (x \ z). [para(2711(a,1),10347(a,1,2)),rewrite([7616(2)])]. 21500 L(x * (y \ z),y,y / x) = (x / y) * z. [para(10347(a,1),16487(a,1,1))]. 21504 L(K(x,y) * z,K(y,x),x) = T(x,y) * (x \ z). [para(16566(a,1),10347(a,1,1,1)),rewrite([16687(4)])]. 21505 L(K(x,y) * z,K(y,x),T(y,x)) = y * (T(y,x) \ z). [para(16566(a,1),10347(a,1,2)),rewrite([16687(2)])]. 21507 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z / y,z))))) = x * x. [back_rewrite(10296),rewrite([21447(8)])]. 21510 R(x,y,(x * y) \ T(z,y / x)) = L(x,y / x,z). [back_rewrite(8497),rewrite([21463(11),10229(7),18(7)])]. 21676 T(a(x,x * y,z),x * (x * ((y * z) / (x * ((x * y) * z))))) = a(x,x * y,z). [para(37(a,1),4950(a,1,2,1)),rewrite([1839(9)])]. 21704 R(x,y * (y * z),z \ ((y \ (y \ z)) * u)) = R(x,z,u). [para(15(a,1),5194(a,2,3)),rewrite([6073(5)])]. 21705 R(x,y * z,(z \ y) * (y \ (y \ u))) = R(x,y \ z,(z \ y) * u). [para(16(a,1),5194(a,1,2,2)),rewrite([4408(5),4408(9)])]. 21708 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * (u * w))) = R(x,z * u,L(w,u,z)). [para(21(a,1),5194(a,2,3)),rewrite([6073(8)])]. 21713 (x * (y * (y * z))) * (z \ (y \ (y \ u))) = z * ((z \ x) * u). [para(5194(a,1),341(a,1,1)),rewrite([16(6),16(5),16(4),200(3)]),flip(a)]. 21715 R(x,y * (y * (z * u)),(z * u) \ ((y \ (y \ z)) * w)) = R(x,z * u,L(u \ w,u,z)). [para(74(a,2),5194(a,2,3)),rewrite([6073(7)])]. 21721 R(x,(y \ (y \ z)) * u,((y \ (y \ z)) * u) \ z) = R(x,z * u,u \ 1). [para(1091(a,1),5194(a,1,3)),rewrite([7550(4),16(3)]),flip(a)]. 21722 R(x,y * (z * (z * y)),K(y,z) * ((y * z) \ ((y * z) \ u))) = R(x,K(z,y),K(y,z) * u). [para(63(a,1),5194(a,1,2,2)),rewrite([20390(3),6144(9),6144(13)])]. 21734 (x * ((x \ ((y \ z) * z)) * (z \ (z \ u)))) / u = R(y \ 1,x,x \ u). [para(5194(a,1),6071(a,2)),rewrite([15452(3),169(7),37(13),16(11),16(10),16(9)])]. 22110 R(T(x,y),y \ x,(x \ y) * z) = ((y \ x) * (y * z)) / z. [para(18454(a,1),203(a,2,1,2,1)),rewrite([3143(4),23(2),3143(4),3143(5),4408(4),3143(8)])]. 22202 ((x \ y) * z) * ((z * (y \ x)) * u) = (x \ y) * (z * (z * ((y \ x) * u))). [para(17093(a,1),15(a,1,2)),rewrite([15452(6),4408(2),4578(3),2040(6)]),flip(a)]. 22239 (x * y) * (T(x,y) \ (y * (x * z))) = y * ((y * x) * z). [para(17093(a,1),190(a,2,2)),rewrite([16(5),6968(6),136(10)])]. 22250 x \ (y * (z * z)) = (x \ y) * (z * z). [back_rewrite(18870),rewrite([22202(7),2690(4),11083(4),7616(4)])]. 22270 x * T(y,x * x) = T(y * x,x). [back_rewrite(1323),rewrite([22250(3),18809(3)]),flip(a)]. 22283 T(x * y,y) \ T(z,y) = T(y \ (x \ z),y). [back_rewrite(19570),rewrite([22270(3)])]. 22354 T(T(x * (y * y),y),T(x * y,y)) = x * (y * y). [back_rewrite(13735),rewrite([22270(6)])]. 22386 L(x,y / x,z) \ (z * y) = T(z * (y / x),z * y). [para(6694(a,1),23(a,2)),rewrite([72(7),18(4)])]. 22398 x \ (y * y) = (x \ y) * y. [para(6257(a,1),6694(a,1,2)),rewrite([19771(3),18718(6),4230(4),4209(5)])]. 22429 a(x * ((y \ x) * x),z,u) = a(x / y,x * (x * z),u). [back_rewrite(19178),rewrite([22398(2)])]. 22608 L(x,y * (z * y),z) = L(x,y,z * (y * z)). [para(13(a,1),16286(a,1,2,1)),rewrite([45(2),101(2),70(4),70(5),45(6),13(6)])]. 22726 T(x,y) / T(T(x,z),y) = K(z,T(x,y)). [para(29(a,1),16687(a,1,2))]. 22862 T(x,y) * K(x,y) = K(x,y) * T(x,y). [para(16712(a,1),63(a,1,2)),rewrite([14(5)]),flip(a)]. 22892 ((x * y) * K(y,z)) / T(y,z) = R(x,y,K(y,z)). [para(16716(a,1),22(a,1,2))]. 22893 x * (x * (K(x,y) * z)) = (x * T(x,y)) * z. [para(16716(a,1),37(a,1,1,2)),flip(a)]. 22906 L(K(x,y) * z,K(y,x),y) = T(y,x) \ (y * z). [para(16716(a,1),74(a,2,1)),rewrite([6144(2)])]. 22923 (x * (y * T(x,z))) \ (x * (y * (x * (K(x,z) * u)))) = L(u,K(x,z),x * (y * x)). [para(16716(a,1),132(a,1,1,2,2))]. 22925 x * ((y * x) * K(x,z)) = (x * y) * T(x,z). [para(16716(a,1),189(a,1,2)),flip(a)]. 22926 T(x,y) * (K(x,y) * z) = K(x,y) * (T(x,y) * z). [para(16716(a,1),189(a,2,2,1)),rewrite([16985(2)])]. 22931 T(x,y) * L(z,K(x,y),x) = x * (K(x,y) * z). [para(16716(a,1),72(a,1,1))]. 22947 R(x,K(x,y),T(x,y) \ z) = z / (K(x,y) * (T(x,y) \ z)). [para(16716(a,1),82(a,1,3,1)),rewrite([16716(7)])]. 22976 a(T(x,y),x * (x * z),u) = a(T(x,y),z,u). [para(16716(a,1),4636(a,2,1)),rewrite([16717(4),101(3),547(2),2508(4)]),flip(a)]. 22979 a(x * y,x,K(x,z)) = a(x,y,T(x,z)) \ 1. [para(16716(a,1),196(a,1,2,2,2)),rewrite([22925(4),2548(7)]),flip(a)]. 23000 (x * T(x,y)) * (K(x,y) * z) = T(x,y) * (T(x,y) * z). [back_rewrite(16984),rewrite([22893(6)])]. 23022 x \ (K(y,x) * (T(x,y) * z)) = L(z,T(x,y),K(y,x)). [para(16875(a,1),21(a,1,1))]. 23033 L(T(x,y) \ z,T(x,y),K(y,x)) = x \ (K(y,x) * z). [para(16875(a,1),74(a,2,1))]. 23108 T(x,y) \ (K(x,y) * (x * z)) = L(z,x,K(x,y)). [para(16985(a,1),21(a,1,1))]. 23144 (x * (y * (y * T(z,u)))) \ ((x * (y * (y * K(z,u)))) * z) = a(x,y * (y * K(z,u)),z). [para(16985(a,1),139(a,1,1,2,2,2))]. 23173 R(x,K(y,z),y) * T(y,z) = (x * K(y,z)) * y. [para(16985(a,1),84(a,1,2))]. 23380 T(x,T(y,x)) = T(x,y). [para(17771(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 23443 T(x,y * x) = T(x,y). [back_rewrite(2652),rewrite([23380(4)])]. 23494 a(x * y,x,z) = a(x,y * x,z). [para(128(a,1),19(a,1,2)),rewrite([196(7)])]. 23575 K(x,y) * (T(y,x) * (K(x,y) * z)) = (y * K(x,y)) * z. [para(16623(a,1),128(a,1,1,2)),rewrite([12349(2)]),flip(a)]. 23584 K(x,y) * (x * (K(x,y) * z)) = (K(x,y) * T(x,y)) * z. [para(16716(a,1),128(a,1,1,2)),flip(a)]. 23589 a(x,y * x,K(x,z)) = a(x,y,T(x,z)) \ 1. [back_rewrite(22979),rewrite([23494(3)])]. 23629 a(x \ y,z * (x \ y),x) = a(x \ y,z,T(y,x)) \ 1. [back_rewrite(19674),rewrite([23494(4)])]. 23643 (x * (y * (x * z))) \ (x * (y * (x * L(z,x,y)))) = a(x,y * x,L(z,x,y)). [back_rewrite(19660),rewrite([23494(11)])]. 23655 (x * (y * (z * x))) \ (x * (z * (x * T(y,z * x)))) = a(x,z * x,T(y,z * x)). [back_rewrite(19639),rewrite([23494(13)])]. 23662 a((x * y) / z,x,L(x \ z,x,x * y)) = a(x,y * x,L(x \ z,x,x * y)). [back_rewrite(18763),rewrite([23494(11)])]. 23663 a(x,y * x,T(z,x)) = a(x,y,z * x) \ 1. [back_rewrite(18724),rewrite([23494(3)])]. 23697 (x / y) * (y * z) = y * ((y \ x) * z). [para(136(a,1),15(a,1,2)),rewrite([15916(3)])]. 23711 (x * y) * (y * ((y \ z) * u)) = y * ((y \ x) * ((y * z) * u)). [para(136(a,1),104(a,1,2,2)),flip(a)]. 23717 ((x \ y) * z) \ (x \ u) = ((x * y) * z) \ (x * u). [para(136(a,1),74(a,2,1)),rewrite([16103(8),16485(7)])]. 23718 (x * y) \ ((x * z) * u) = (y \ x) * ((x \ z) * u). [para(136(a,1),74(a,2,2)),rewrite([4480(5)]),flip(a)]. 23735 x * ((x \ y) * ((x * y) * z)) = y * (x * (y * z)). [para(1091(a,1),136(a,1,2,2,1)),rewrite([3143(5),169(4),23711(5),101(7),128(8)])]. 23736 T(x,(x \ y) * z) = T(x,(x * y) * z). [para(136(a,1),1708(a,1,2)),rewrite([1708(7)]),flip(a)]. 23766 x * (((x \ y) * z) * x) = T((x * y) * z,x). [para(136(a,1),4209(a,1,1)),rewrite([101(7)]),flip(a)]. 23819 K((x \ y) * z,x) = K((x * y) * z,x). [para(136(a,1),16568(a,1,1)),rewrite([16568(7)]),flip(a)]. 23885 L(a(x / y,y,z),y * ((y \ x) * z),u) * ((u * (x * z)) \ (u * (y * ((y \ x) * z)))) = 1. [back_rewrite(20095),rewrite([23697(5),23697(11)])]. 23926 x * ((x \ (y \ z)) * T(y,z)) = L(z,y \ z,x). [back_rewrite(16509),rewrite([23697(5)])]. 23927 L(T(x,y),y \ x,z) = z * ((z \ (y \ x)) * y). [back_rewrite(16505),rewrite([23697(7)])]. 24002 x \ ((x * y) * z) = x * ((x \ y) * z). [back_rewrite(15916),rewrite([23697(6)])]. 24009 (x * ((x \ (y \ 1)) * ((y * z) * u))) \ (y * ((y \ z) * u)) = a(x,x / y,(y * z) * u). [back_rewrite(14038),rewrite([23697(10)])]. 24016 L(L(L(x,y,z),u,w),v5 / L(L(x,u,w),y,z),v6) = L(L(R(x,v5 \ 1,v6),u,w),y,z). [back_rewrite(12077),rewrite([23697(12),4180(12),33(11),33(10)])]. 24021 x * ((x \ y) * (y \ z)) = L(z,y \ 1,x). [back_rewrite(10367),rewrite([23697(4)])]. 24030 a(x,y \ 1,y * z) = a(x,y,y \ z). [back_rewrite(7628),rewrite([23697(4),192(5)]),flip(a)]. 24034 T(x * ((x \ y) * z),y * z) = a(y / x,x,z) \ (y * z). [back_rewrite(4206),rewrite([23697(3)])]. 24035 x * ((x \ y) * ((y / x) * z)) = y * (y * (x \ z)). [back_rewrite(3286),rewrite([23697(5)])]. 24043 R(x,y \ 1,y * z) = R(x,y,y \ z). [back_rewrite(2760),rewrite([23697(3),191(4)]),flip(a)]. 24057 a(x / y,y,z) = a(y,y * x,z). [back_rewrite(60),rewrite([23697(3),4032(5)]),flip(a)]. 24066 (x * y) * ((x * y) * z) = x * (y * (x * (y * z))). [back_rewrite(5783),rewrite([23711(5),23735(5)]),flip(a)]. 24075 (T(x,y) \ (z \ (z \ u))) * ((((u \ z) * z) * K(x,y)) * x) = a(u,z * (z * K(x,y)),x). [back_rewrite(23144),rewrite([23718(10),5162(4),15452(8)])]. 24100 L(x \ y,x,x * z) = T(z,x) \ ((x \ z) * y). [back_rewrite(18689),rewrite([23718(5),6955(5)]),flip(a)]. 24114 a(x \ 1,y,z * (z * u)) = a(x,y * (z * z),u). [back_rewrite(13702),rewrite([23718(9),22250(7),2040(8),6068(9)])]. 24163 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,y * (y * (x / u)),u). [back_rewrite(3753),rewrite([23718(9),5162(3),15452(7)])]. 24164 (x \ (y \ (y \ z))) * (u * ((u \ ((z \ y) * y)) * x)) = a(z,y * (y * u),u \ x). [back_rewrite(3752),rewrite([23718(9),5162(3),15452(6),169(8)])]. 24189 a(x \ 1,y,z) = a(x,y,z). [back_rewrite(19),rewrite([23718(5),6068(5)])]. 24229 (x * (a(y \ x,z,z \ T(y,x)) * u)) / u = L(x,y \ x,z). [back_rewrite(5841),rewrite([23926(5),33(4),480(2)]),flip(a)]. 24261 (x * (y / L(L(z,u,w),v5,v6))) \ (x * y) = L(L(R(z,y \ 1,x),v5,v6),u,w). [back_rewrite(12076),rewrite([24016(6)]),flip(a)]. 24264 R(x,x \ y,z) = L(x,y \ 1,z). [back_rewrite(8379),rewrite([24021(6)])]. 24267 (x * (a(y,z,z \ (y \ x)) * u)) / u = L(x,y \ 1,z). [back_rewrite(5816),rewrite([24021(4),33(5),480(2)]),flip(a)]. 24268 R(x,y,y \ ((x \ y) * z)) = L(x,y \ 1,z). [back_rewrite(4470),rewrite([24021(8)])]. 24279 a(x / (y * y),y,y * z) = a(x,y,y \ z). [back_rewrite(16096),rewrite([24030(8)])]. 24285 a(x,x * y,z) \ 1 = a(y,x,x \ z). [back_rewrite(7607),rewrite([24057(2),24030(8)])]. 24305 T(x * ((x \ y) * z),y * z) = a(x,x * y,z) \ (y * z). [back_rewrite(24034),rewrite([24057(7)])]. 24350 L(a(x,x * y,z),x * ((x \ y) * z),u) * ((u * (y * z)) \ (u * (x * ((x \ y) * z)))) = 1. [back_rewrite(23885),rewrite([24057(2)])]. 24428 ((x / (y * z)) * (y * (z * y))) \ (x * y) = a(y * z,(y * z) * x,y). [back_rewrite(18703),rewrite([24057(11)])]. 24477 ((x / y) * (z * y)) \ (x * T(z,y)) = a(y,y * x,T(z,y)). [back_rewrite(1958),rewrite([24057(9)])]. 24479 ((x / (y * (y * z))) * (y * (y * (z * u)))) \ (x * u) = a(z,y * (y * (z * x)),u). [back_rewrite(1952),rewrite([24057(15),37(14),2508(15)])]. 24531 (x * (y * (y / x))) * z = x * (y * (y * (x \ z))). [back_rewrite(10140),rewrite([24066(6),23697(5),24035(5)]),flip(a)]. 24558 (x * (y * (x * y))) * z = x * (y * (x * (y * z))). [back_rewrite(426),rewrite([24066(8)])]. 24566 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(z,y,T(x,y)). [back_rewrite(6149),rewrite([24189(10)])]. 24596 a(x,y * (z * z),u) = a(x,y,z * (z * u)). [back_rewrite(24114),rewrite([24189(5)]),flip(a)]. 24624 ((x * y) \ z) * ((z \ x) * y) = a(z,x,y). [back_rewrite(6068),rewrite([24189(8)])]. 24638 (x * y) / ((z \ x) * y) = L(z,x \ 1,y). [back_rewrite(5665),rewrite([24268(4)]),flip(a)]. 24644 x / (T(y,z) * (u * (y * (u \ (T(y,z) \ x))))) = (u / y) / u. [back_rewrite(19502),rewrite([24531(9),23697(10),1829(3),10809(9),13(3),89(2)])]. 24645 (x / y) / x = x / (x * y). [back_rewrite(19496),rewrite([24531(9),3169(10),1091(3),10809(9),13(3),89(2),24644(8)])]. 24749 R(T(x,y),x \ z,u) = L(T(x,y),z \ 1,u). [back_rewrite(8331),rewrite([24638(4),30(4)]),flip(a)]. 24764 x * (T(y / (y * x),K(x,y)) * (x * z)) = T(x,y) * z. [back_rewrite(17974),rewrite([24645(2)])]. 24890 ((K(x,y) * z) \ u) / T(K(y,x),u) = z \ u. [para(19486(a,1),1829(a,1,2)),rewrite([4407(9),4408(9),1014(9)]),flip(a)]. 24897 x * ((T(K(y,z),u) * (u \ (K(z,y) * x))) \ T(w,x * u)) = x \ (w * (x * u)). [para(19486(a,1),3218(a,1,2,2,2,2)),rewrite([19486(17)])]. 24915 x / (K(y,z) * (y \ (K(z,y) * x))) = y. [para(12307(a,1),19486(a,1,2,1))]. 25093 (x \ y) / T(z * (z / x),y) = z \ (z \ y). [para(12372(a,1),5364(a,1,2,2)),rewrite([1014(4),7616(2),1014(4),12372(9)])]. 25357 a(x,y * (x * y),z) = 1. [para(14(a,1),5524(a,1,2,1)),rewrite([45(3),70(3),4578(2),1708(4),14882(4),90(2)])]. 25410 a(x * (y * x),y,z) = 1. [back_rewrite(3735),rewrite([25357(6)])]. 25524 (x * ((x * y) * z)) * ((x * (y * z)) \ T(y,x)) = y * x. [para(22239(a,1),17(a,1,1)),rewrite([4155(8)])]. 26340 (x * (y / x)) * K(y,x) = y. [para(17822(a,1),63(a,1,2)),rewrite([18(6)])]. 26495 K(x,y) * T(x,y) = T(T(x,y),y). [para(17910(a,1),16716(a,1,2)),rewrite([22862(3)])]. 26526 K(x,y) * (x * (K(x,y) * z)) = T(T(x,y),y) * z. [back_rewrite(23584),rewrite([26495(8)])]. 26628 K((x \ y) * z,R(x \ 1,y,z)) = K(y * z,(x \ y) * z). [para(6071(a,1),17914(a,1,2))]. 26642 x * K(y,x) = T(x,x / y). [para(17914(a,1),16716(a,1,2))]. 26699 K(x,y) * (T(y,x) * (K(x,y) * z)) = T(y,y / x) * z. [back_rewrite(23575),rewrite([26642(8)])]. 26745 K(x,y) * y = T(y,y / x). [back_rewrite(12349),rewrite([26642(4)])]. 26753 K(x * y,R(z \ 1,x,y)) = K(x * y,(z \ x) * y). [para(6071(a,1),17924(a,1,2))]. 26764 T(x,y / x) = T(x,y). [para(17924(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 26839 T(x,L(x,y,z)) = x. [para(160(a,1),16487(a,1,1)),rewrite([16487(2)]),flip(a)]. 26897 x / T(y * (y * (x / z)),z) = y \ (y \ z). [para(1925(a,1),21(a,1,2)),rewrite([3436(2),1607(8)]),flip(a)]. 26903 L(x,y,y \ z) = L(x,z,y). [para(1925(a,1),132(a,1,1,2)),rewrite([26897(6),7550(5),16(4),21(4),26897(6),2507(6),16465(4)]),flip(a)]. 26952 T(x,y) \ ((y \ x) * z) = L(y \ z,x,y). [back_rewrite(7981),rewrite([26903(3)]),flip(a)]. 26963 L(x \ y,x,x * z) = L(x \ y,z,x). [back_rewrite(24100),rewrite([26952(7)])]. 26968 a((x \ y) / z,x,L(x \ z,y,x)) = a(x \ y,x,L(x \ z,y,x)). [back_rewrite(11726),rewrite([26952(6),26952(10)])]. 26973 a((x * y) / z,x,L(x \ z,y,x)) = a(x,y * x,L(x \ z,y,x)). [back_rewrite(23662),rewrite([26963(5),26963(9)])]. 27047 x * ((x \ y) * T(z,x)) = (y / x) * (z * x). [para(165(a,1),10393(a,1,2,1,1)),rewrite([6564(3),3143(6),24002(4),6564(7),1014(7)])]. 27119 L(x,y * T(y,z),u * ((z \ y) * (z \ y))) = x. [back_rewrite(15120),rewrite([27047(4),3169(3),4505(2)])]. 27447 ((x * (y * (x \ y))) / (x * (y / x))) * K(x,y) = x * (y / x). [para(20620(a,1),5560(a,1,2)),rewrite([18023(3),4407(10),6144(9),14(9),10229(8),20620(17),88(12)])]. 27454 (x * (y * (y * (y * x)))) \ y = y \ ((y * x) \ (x \ 1)). [para(5600(a,1),17(a,1,1)),rewrite([989(5),4407(5),6567(5)]),flip(a)]. 27459 L(x,y,z * (y * z)) = x. [para(5600(a,1),21(a,1,1)),rewrite([27454(6),24558(10),6600(11),45(5),27454(11),3050(12)])]. 27549 L(x,y * (z * y),z) = x. [back_rewrite(22608),rewrite([27459(6)])]. 27556 (x * (y * (x * y))) \ (x * z) = (y * (x * y)) \ z. [back_rewrite(3118),rewrite([27459(6)]),flip(a)]. 27573 x * (y * (x * (z / (z * (x * (y * (x * z))))))) = z \ 1. [para(5674(a,1),15(a,1,2)),flip(a)]. 27619 (((x * y) * z) * x) * (((z * x) \ ((x * y) \ z)) / z) = 1. [para(5674(a,1),193(a,2)),rewrite([27573(23),4407(9),193(12),169(11),4458(7),1014(10)])]. 27689 (x * (a(x / (y * z),y,z) * u)) / u = R(x,z \ (y \ 1),y). [para(15(a,1),5817(a,1,1,2,1,3)),rewrite([4407(9)])]. 27706 R(x,T(y,x) \ 1,z) = L(x,y \ x,z). [para(2711(a,1),5817(a,1,1,2,1,1)),rewrite([24229(7)]),flip(a)]. 27732 R(((x / (y * z)) * y) * z,x,x \ u) = R(x,z \ (y \ 1),y). [back_rewrite(437),rewrite([27689(12)])]. 27871 L(x,L(x,y,z),u) = x. [para(16487(a,1),6024(a,1,1)),rewrite([16487(4)])]. 28029 L(x,((y * z) \ (y * u)) / x,y * z) = ((y * z) * (L(z \ u,z,y) / x)) \ (y * u). [para(74(a,1),6697(a,1,2,1)),rewrite([16(13)])]. 28379 L(x,(y \ K(z,u)) / x,K(u,z) * y) = (x * (K(u,z) * y)) * (y \ K(z,u)). [para(4993(a,1),28029(a,1,2,1,2)),rewrite([4407(4),6144(3),14(3),8302(12),4993(15),4407(14),4407(13),6144(12),14(12),10229(12),4155(9),6144(8)])]. 28464 T(T(x,y),L(x,z,u)) = T(x,y). [para(26839(a,1),29(a,1,1)),flip(a)]. 28473 L(x,y,z) * x = x * L(x,y,z). [para(26839(a,1),90(a,1,2))]. 28505 x / L(x,y,z) = L(x,y,z) \ x. [para(26839(a,1),7616(a,1,1))]. 28511 T(x,L(x,y,z) \ x) = x. [para(26839(a,1),7769(a,1,1))]. 28851 T(L(x,y,z) * (u / x),L(x,y,z) * u) = T(L(x,y,z) * (u / x),x). [para(18461(a,1),6694(a,1,2)),flip(a)]. 28965 T(x,x / y) = T(x,y \ x). [para(19567(a,1),16716(a,1,2)),rewrite([26642(2)])]. 28991 K(x,y) * y = T(y,x \ y). [back_rewrite(26745),rewrite([28965(4)])]. 29035 K(x,y) * (T(y,x) * (K(x,y) * z)) = T(y,x \ y) * z. [back_rewrite(26699),rewrite([28965(8)])]. 29216 T(x \ y,y) * T(x,y) = T(y,x). [para(23380(a,1),4505(a,2)),rewrite([4278(2)])]. 29325 (x \ y) * (y / x) = y * (x \ (x \ y)). [para(23443(a,1),3218(a,1,2,2)),rewrite([2643(2),3169(7),15(8)]),flip(a)]. 29339 T(x,y) / (y * x) = (y * x) \ x. [para(23443(a,1),7616(a,1,1))]. 29418 (x / y) * (y \ x) = x * (y \ (y \ x)). [back_rewrite(2903),rewrite([29325(6)])]. 29466 T(x,y * ((y \ z) * x)) = T(x,R(z,y,y \ x)). [para(191(a,1),26764(a,1,2)),flip(a)]. 29584 (T(x,y) * z) / a(y \ x,y,z) = (y \ x) * (y * z). [para(4505(a,1),162(a,1,1,1))]. 30202 ((T(x,y) * z) \ T(T(x,y),y)) * (x * z) = T(T(x,z),y). [para(16875(a,1),6152(a,1,2,1)),rewrite([6144(5),26495(5),16875(11),2644(10)])]. 30410 (x \ (T(y,x) \ 1)) * T(z,y \ x) = (x \ (x \ z)) * (y \ x). [para(2711(a,1),6185(a,1,2,2)),rewrite([2711(11)])]. 30432 (x \ (x \ y)) / z = x \ (x \ (y / z)). [para(3691(a,1),6185(a,1,2,2)),rewrite([4407(3),14124(8),6095(4),3691(7),1014(8)]),flip(a)]. 30455 x \ (y * (x / z)) = T(y,x) / z. [para(6185(a,1),3683(a,1,2)),rewrite([1840(5),4505(2)]),flip(a)]. 30508 x * (T(y,x) / z) = y * (x / z). [para(6185(a,1),136(a,1,2,2)),rewrite([1840(5),4505(2),1014(6),90(7)])]. 30512 (x \ (x \ y)) * T(z,y) = (x \ (x \ z)) * y. [para(19486(a,1),6185(a,1,2,2)),rewrite([4407(8),4408(8),1014(8),24890(6),19486(13)])]. 30627 x * ((y * x) \ T(z,x / y)) = T(z,x) / y. [back_rewrite(7622),rewrite([30455(8)])]. 30654 L(x,T(y,z) / x,y \ z) = (y * (z / x)) \ (y * z). [back_rewrite(10748),rewrite([30508(7)])]. 30703 T(T(x,y),y) = T(x,y * y). [para(6188(a,1),45(a,1)),rewrite([48(4),18809(4),4505(2),48(4)])]. 30840 (T(K(x,y),z) * (z \ (K(y,x) * u))) \ T(w,u * z) = (u \ (u \ w)) * (u * z). [para(19486(a,1),6188(a,1,2,2,2)),rewrite([19486(18)])]. 30881 ((T(x,y) * z) \ T(x,y * y)) * (x * z) = T(T(x,z),y). [back_rewrite(30202),rewrite([30703(4)])]. 30944 K(x,y) * (x * (K(x,y) * z)) = T(x,y * y) * z. [back_rewrite(26526),rewrite([30703(7)])]. 30953 K(x,y) * T(x,y) = T(x,y * y). [back_rewrite(26495),rewrite([30703(5)])]. 32180 (x * L(y,z,u)) * y = x * (y * L(y,z,u)). [para(27871(a,1),72(a,1,2)),rewrite([28473(5)])]. 32743 R(x * y,y * x,z) = x * y. [para(4209(a,1),493(a,1,1)),rewrite([4209(5)])]. 32749 (x * T(x,y)) * z = x * (T(x,y) * z). [para(493(a,1),84(a,1,1)),rewrite([21062(3),547(5)]),flip(a)]. 32816 R(x * y,K(y,x),z) = x * y. [back_rewrite(19707),rewrite([32743(7)]),flip(a)]. 32894 x * (K(x,y) * (T(x,y) * z)) = T(x,y) * (T(x,y) * z). [back_rewrite(23000),rewrite([32749(5),22926(4)])]. 33039 L(T(x \ 1,y),x,z) = T(x \ 1,y). [para(1077(a,1),30(a,1,1)),flip(a)]. 33049 a(x,y,T(x,z)) = 1. [hyper(25,a,1685,a)]. 33075 L(x,y,T(x,z)) = x. [para(7769(a,1),1685(a,1,1)),rewrite([7769(5)])]. 33091 a(x,y * x,K(x,z)) = 1. [back_rewrite(23589),rewrite([33049(5),46(6)])]. 33119 a(x / y,z,y \ x) = 1. [para(92(a,1),33049(a,1,3))]. 33180 (T(x,y) * z) * x = T(x,y) * (z * x). [para(33075(a,1),72(a,1,2))]. 33181 (T(x,y) * (z * x)) \ (x * (T(x,y) * z)) = K(x,T(x,y) * z). [para(33075(a,1),2934(a,1,2,1)),rewrite([33075(9)])]. 33249 R(x,y * z,a(x,y,z)) \ ((x * y) * z) = (y * z) * a(x,y,z). [para(54(a,1),166(a,1,2))]. 33258 (x * y) \ ((y * x) * z) = K(y,x) * z. [para(63(a,1),166(a,1,2,1)),rewrite([32816(3)])]. 33300 R(x,K(x,y),z) \ (T(x,y) * z) = K(x,y) * z. [para(16716(a,1),166(a,1,2,1))]. 33324 T(x,y) \ (x * (T(x,y) * z)) = x * z. [para(493(a,1),166(a,1,1)),rewrite([547(3),32749(4)])]. 33334 L(x,K(y,z),z * y) = x. [back_rewrite(2857),rewrite([33258(6),8296(4)]),flip(a)]. 33346 (x * y) * (K(y,x) * z) = (y * x) * z. [back_rewrite(5116),rewrite([33334(4)]),flip(a)]. 33415 x * (y * (y * (x * T(z,y * x)))) = (x * y) * (z * (y * x)). [back_rewrite(20509),rewrite([33346(6)]),flip(a)]. 33450 (x \ (y / x)) * (x * z) = x \ (y * z). [para(18(a,1),168(a,1,2,1)),flip(a)]. 33472 (x \ (y \ 1)) * (x * z) = x \ ((y \ x) * z). [para(3143(a,1),168(a,1,2,1)),flip(a)]. 33476 (x \ (x \ y)) * (x * z) = x \ (T(y,x) * z). [para(4505(a,1),168(a,1,2,1)),flip(a)]. 33497 K(x,y) * (x * z) = T(x,y) * z. [para(16343(a,1),168(a,2,1)),rewrite([547(2),32749(3),15(4)]),flip(a)]. 33507 K(x,y) * (T(y,x) * z) = y * z. [para(16711(a,1),168(a,2,1)),rewrite([32749(4),33324(5)]),flip(a)]. 33511 (x \ K(x,y)) * (x * z) = x \ (T(x,y) * z). [para(16985(a,1),168(a,1,2,1)),flip(a)]. 33545 R(x,x \ (y * z),u) = L(x,z \ (y \ 1),u). [back_rewrite(11625),rewrite([33450(4),33450(9),24638(9),4407(6)])]. 33575 R(x,x \ ((y \ x) * z),u) = L(x,z \ (x \ y),u). [back_rewrite(11645),rewrite([33472(8),24638(8),4407(4),4408(3),14(3),33472(8)]),flip(a)]. 33590 (T(K(x,y),z) * (z \ (K(y,x) * u))) \ T(w,u * z) = u \ (T(w,u) * z). [back_rewrite(30840),rewrite([33476(13)])]. 33664 L(x,y * (z * u),z) = L(x,z,T(y,z) * u). [back_rewrite(9195),rewrite([33476(6),16348(8)]),flip(a)]. 33705 K(x,y) * (T(x,y) * z) = T(x,y * y) * z. [back_rewrite(30944),rewrite([33497(5),22926(4)])]. 33734 L(x,y,K(y,z)) = x. [back_rewrite(23108),rewrite([33497(4),15(4)]),flip(a)]. 33781 T(x,y \ x) * z = x * (K(y,x) * z). [back_rewrite(29035),rewrite([33507(6)]),flip(a)]. 33796 L(x,T(y,z),K(z,y)) = x. [back_rewrite(23022),rewrite([33507(4),15(2)]),flip(a)]. 33957 x \ (y * (x * z)) = T(y,x) * z. [back_rewrite(24897),rewrite([33590(9),16(4)]),flip(a)]. 33969 L(x,y,z * T(z,y)) = x. [back_rewrite(27549),rewrite([33664(3),547(2)])]. 33981 L(a(x,y,z),y,T(x,y) * z) = a(y,x,y * z). [back_rewrite(2971),rewrite([33664(4)])]. 33992 T(x,y) * (T(x,y) * z) = x * (T(x,y * y) * z). [back_rewrite(32894),rewrite([33705(4)]),flip(a)]. 34091 x \ (K(y,x) * z) = T(x,y) \ z. [back_rewrite(23033),rewrite([33796(5)]),flip(a)]. 34275 L(T(x,y * z),y,z) = T(T(x,y),z). [back_rewrite(16484),rewrite([33957(3),23(3)]),flip(a)]. 34415 x / (K(y,z) * (T(y,z) \ x)) = y. [back_rewrite(24915),rewrite([34091(4)])]. 34554 R(x,K(x,y),T(x,y) \ z) = x. [back_rewrite(22947),rewrite([34415(9)])]. 34768 (x * y) \ T(z,y / x) = y \ (T(z,y) / x). [para(30627(a,1),15(a,1,2)),flip(a)]. 34798 x * (T(y * x,x) \ T(z,y \ x)) = T(z,x) / T(y,x). [para(2711(a,1),30627(a,1,2,2,2)),rewrite([7775(2)])]. 34823 (x * y) \ y = y \ (x \ y). [para(12386(a,1),30627(a,1,2,2)),rewrite([101(2),9050(4),29339(5)]),flip(a)]. 34860 R(x,y,y \ (T(z,y) / x)) = L(x,y / x,z). [back_rewrite(21510),rewrite([34768(4)])]. 35223 K(x,y) * (T(x,y) \ z) = x \ z. [para(16(a,1),33300(a,1,2)),rewrite([34554(4)]),flip(a)]. 35247 (K(x,y) * z) * R(x,K(x,y),z) = T(T(x,y) * z,R(x,K(x,y),z)). [para(33300(a,1),4505(a,1,1))]. 35274 K(R(x,K(x,y),z),T(x,y) * z) = K(R(x,K(x,y),z),K(x,y) * z). [para(33300(a,1),16710(a,1,2)),flip(a)]. 35287 K(R(x,K(x,y),z),K(x,y) * z) = K(T(x,y) * z,K(x,y) * z). [para(33300(a,1),19567(a,1,2)),rewrite([35274(10)]),flip(a)]. 35301 K(R(x,K(x,y),z),T(x,y) * z) = K(T(x,y) * z,K(x,y) * z). [back_rewrite(35274),rewrite([35287(10)])]. 35536 L(a(x,y,T(z,y)),x * (z * y),(x * y) * T(z,y)) = a(x,y,T(z,y)). [hyper(24,a,6438,a)]. 35645 (x \ (y \ 1)) * z = (y * x) \ z. [para(13(a,1),6953(a,1,1,2,1)),rewrite([46(3),45(8),45(7)])]. 35648 (x \ (y \ (z \ 1))) * u = ((z * y) * x) \ u. [para(16(a,1),6953(a,1,1,2,1)),rewrite([23717(10),16(9)])]. 35675 (x * ((y * z) \ (y \ 1))) * u = (x / z) * (y \ (y \ u)). [para(1014(a,1),6953(a,2,1)),rewrite([4408(7),45(2),10229(10)])]. 35683 x * (T(y,x) \ (x \ z)) = y \ z. [para(1091(a,1),6953(a,1,1)),rewrite([3143(3),35645(6),5162(4),16(5),4408(6),4408(3),169(6),6968(5)]),flip(a)]. 35698 (x \ ((y \ z) * z)) * u = (((y * x) \ z) * z) * u. [para(3143(a,1),6953(a,1,1,2,1)),rewrite([4408(5),45(3),14(3),4408(2),4408(10),45(9),4408(9),45(7),15452(8)])]. 35803 (x * y) \ (y * z) = y \ ((x \ y) * z). [back_rewrite(33472),rewrite([35645(5)])]. 35829 T(x * y,y) \ T(z,x \ y) = (y \ (y \ z)) * (x \ y). [back_rewrite(30410),rewrite([35645(7),7775(2)])]. 35865 a(x,x / y,(y * z) * u) = a(x,x * y,(y \ z) * u). [back_rewrite(24009),rewrite([35645(6),23718(4),4032(9)]),flip(a)]. 35905 R(x,x \ (y \ 1),y * z) = z * ((y * z) \ (y * x)). [back_rewrite(11253),rewrite([35645(10),4155(9)])]. 35922 R(x,x \ (y \ 1),z) = L(x,y,z \ 1). [back_rewrite(3646),rewrite([35645(9),4155(8),6070(8)])]. 35944 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,y * (y * u),u \ x). [back_rewrite(24164),rewrite([35698(7)])]. 35945 (x * ((y * x) \ z)) / z = R(y \ 1,x,x \ z). [back_rewrite(21734),rewrite([35698(6),169(6),6968(5),35683(5)])]. 35978 T(x,y) / T(z,y) = y \ (x * (z \ y)). [back_rewrite(34798),rewrite([35829(5),7550(5)]),flip(a)]. 36021 x * ((y * x) \ (y * z)) = L(z,y,x \ (y \ 1)). [back_rewrite(35905),rewrite([35922(5),4407(3)]),flip(a)]. 36043 x / R(y,z,(y * z) \ u) = x * R(y \ 1,z,z \ u). [back_rewrite(12931),rewrite([35945(8)])]. 36066 R(x,y,(x * y) \ z) \ 1 = R(x \ 1,y,y \ z). [back_rewrite(10235),rewrite([35945(9)])]. 36081 x \ (y * (T(y,z) \ x)) = K(z,T(y,x)). [back_rewrite(22726),rewrite([35978(4)])]. 36084 x \ (T(y,z) * (y \ x)) = K(T(y,x),z). [back_rewrite(20939),rewrite([35978(4)])]. 36652 (x * y) * T(x * y,y) = x * (x * (y * y)). [para(100(a,1),3184(a,1,2,2)),rewrite([18809(3),540(4),14(2),18809(6),547(7)]),flip(a)]. 37107 L(x,K(y,z),y) = x. [para(33734(a,1),16487(a,1,1))]. 37125 x * (K(x,y) * z) = T(x,y) * z. [back_rewrite(22931),rewrite([37107(3)]),flip(a)]. 37126 T(x,y) \ (x * z) = K(y,x) * z. [back_rewrite(22906),rewrite([37107(4)]),flip(a)]. 37146 L(L(x,T(y,z),u),u * T(y,z),y) = L(x,K(y,z),y * (u * y)). [back_rewrite(22923),rewrite([37125(6),638(8)])]. 37216 L(x,K(y,z),z) = x. [para(17781(a,1),37107(a,1,2))]. 37218 L(x,K(y,z),T(y,z)) = x. [para(17910(a,1),37107(a,1,2))]. 37224 T(x,y) * (x \ z) = K(x,y) * z. [back_rewrite(21504),rewrite([37216(4)]),flip(a)]. 37229 x * (T(x,y) \ z) = K(y,x) * z. [back_rewrite(21505),rewrite([37218(5)]),flip(a)]. 37231 T(K(x,y),z) = K(T(x,z),y). [back_rewrite(36084),rewrite([37224(3),23(3)])]. 37242 K(T(x,y),z) = K(x,T(z,y)). [back_rewrite(36081),rewrite([37229(3),23(3),37231(2)])]. 37402 ((K(x,y) * z) \ u) * K(x,T(y,u)) = z \ u. [back_rewrite(24890),rewrite([37231(5),37242(5),5005(6),37242(5)])]. 37429 T(K(x,y),z) = K(x,T(y,z)). [back_rewrite(37231),rewrite([37242(4)])]. 38196 L(x,K(y,z),T(z,y)) = x. [para(17771(a,1),37216(a,1,2))]. 38207 T(x,y) * (K(y,x) * z) = x * z. [back_rewrite(21070),rewrite([38196(3)]),flip(a)]. 38208 x \ (T(x,y) * z) = K(x,y) * z. [back_rewrite(21045),rewrite([38196(5)]),flip(a)]. 38223 (x \ K(x,y)) * (x * z) = K(x,y) * z. [back_rewrite(33511),rewrite([38208(7)])]. 38305 x * ((x \ (y / x)) * z) = y * (x \ z). [para(18(a,1),169(a,1,1)),flip(a)]. 38314 x * (x * (y * ((y \ (x \ (x \ z))) * u))) = y * ((y \ z) * u). [para(37(a,1),169(a,2)),rewrite([5162(6),21713(7),5162(6)]),flip(a)]. 38342 (x \ y) * (y \ z) = y * ((x * y) \ z). [para(3143(a,1),169(a,1,1)),rewrite([35645(7)])]. 38356 T(x,y) * (y \ z) = y \ (x * z). [para(4505(a,1),169(a,1,1)),rewrite([7550(7)])]. 38365 (x * y) * T(y \ z,y) = (x / y) * (z * y). [para(7967(a,1),169(a,1,2)),rewrite([27047(8)])]. 38393 K(x,y) * (T(y,x * x) * z) = T(y,x) * z. [para(16623(a,1),169(a,1,1)),rewrite([6144(2),37125(3),6144(6),30953(6)]),flip(a)]. 38402 x * (y * (x * ((y * x) \ z))) = (y * x) * (T(y,x) \ z). [para(169(a,1),128(a,1)),rewrite([34823(3),6968(4)]),flip(a)]. 38445 (x * (y * (y * z))) * (z \ u) = z * ((z \ x) * (y * (y * u))). [back_rewrite(5200),rewrite([38314(9)]),flip(a)]. 38475 x * (y * ((x * y) \ z)) = L(z,y \ 1,x). [back_rewrite(24021),rewrite([38342(3)])]. 38476 R(x,y * z,y * ((z * y) \ (y \ u))) = R(x,y \ z,(z \ y) * u). [back_rewrite(21705),rewrite([38342(5)])]. 38485 R(x,x \ y,y \ z) = z / (y * ((x * y) \ z)). [back_rewrite(8328),rewrite([38342(6)])]. 38488 L(x,y,z \ (y \ 1)) = L(x,y,z \ 1). [back_rewrite(6070),rewrite([38342(4),36021(4)])]. 38503 L((x \ y) * z,y \ x,x) = x \ (y * z). [back_rewrite(21472),rewrite([38356(7)])]. 38534 R(x,y * (y * z),z \ u) = R(x,z,((z \ y) * y) * u). [back_rewrite(340),rewrite([38445(5),191(8),15452(3)]),flip(a)]. 38535 (x * y) * (T(x,y) \ z) = y * L(z,y \ 1,x). [back_rewrite(38402),rewrite([38475(4)]),flip(a)]. 38568 x * a(y,z,z \ (y \ x)) = L(x,y,z \ 1). [back_rewrite(9085),rewrite([38475(10),4407(7),16465(8)])]. 38590 x * ((y * x) \ (y * z)) = L(z,y,x \ 1). [back_rewrite(36021),rewrite([38488(8)])]. 38623 L(L(R(x,y,z),u,w),v5,x \ 1) = L(R(x,y,z),u,w). [back_rewrite(6793),rewrite([38488(6)])]. 38642 R(x,y * z,L(z \ u,z,y)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(21715),rewrite([38534(9)]),flip(a)]. 38643 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,z,y)). [back_rewrite(21708),rewrite([38534(10)])]. 38644 R(x,y,((y \ z) * z) * ((z \ (z \ y)) * u)) = R(x,y,u). [back_rewrite(21704),rewrite([38534(7)])]. 38658 T(x,y) * (T(x \ y,y) * z) = y * L(z,y \ 1,x). [back_rewrite(15409),rewrite([38535(9)])]. 38713 R(x,K(x,y),z) = x. [para(16985(a,1),170(a,1,1,1)),rewrite([38223(6),18422(5)])]. 38747 K(T(x,y) * z,K(x,y) * z) = K(x,T(x,y) * z). [back_rewrite(35301),rewrite([38713(2)]),flip(a)]. 38752 K(x,T(x,y) * z) = K(x,K(x,y) * z). [back_rewrite(35287),rewrite([38713(2),38747(8)]),flip(a)]. 38770 (K(x,y) * z) * x = T(T(x,y) * z,x). [back_rewrite(35247),rewrite([38713(4),38713(7)])]. 38815 (T(x,y) * (z * x)) \ (x * (T(x,y) * z)) = K(x,K(x,y) * z). [back_rewrite(33181),rewrite([38752(10)])]. 39396 a(x / y,y * (y * z),u) = a(x * y,z,u). [para(33450(a,1),4636(a,1,1,2)),rewrite([23(2),90(2),16(5)]),flip(a)]. 39505 (x * y) \ (x \ 1) = y \ (x \ (x \ 1)). [para(1607(a,1),6591(a,1,1)),flip(a)]. 39506 (x * y) \ (y \ 1) = y \ (x \ (y \ 1)). [para(1667(a,1),6591(a,1,1)),flip(a)]. 39650 (x * (y \ (z \ (z \ 1)))) * u = (x / y) * (z \ (z \ u)). [back_rewrite(35675),rewrite([39505(4)])]. 39699 x / (y * (y * (z * x))) = z \ (y \ (y \ 1)). [back_rewrite(4420),rewrite([39505(8)])]. 39792 x / (y * (z * (y * x))) = y \ (z \ (y \ 1)). [back_rewrite(4421),rewrite([39506(8)])]. 40866 (((x \ y) * z) \ (y * z)) * R(x \ 1,y,z) = K(y * z,(x \ y) * z). [para(26628(a,1),16711(a,2)),rewrite([31(6),12809(6),4408(8)])]. 41620 T(x \ 1,y) * z = T(x,y) \ z. [para(104(a,1),11803(a,1,1)),rewrite([101(2),128(3),15(5),15(5),27556(7),15452(5),1091(3),4407(3),4505(4),1708(6),15(8),33664(9),547(8),33969(9)])]. 41919 x \ ((y \ z) * z) = ((y * x) \ z) * z. [para(2748(a,1),6591(a,1,1)),rewrite([4408(5),4408(3),45(2),14(3),22398(2),4408(9),4408(7),45(6),14(7),22398(6)])]. 42192 (x * (y * z)) \ (x * (u * ((u \ y) * z))) = L(a(y,u,u \ z),y * z,x). [para(192(a,1),74(a,1,1)),flip(a)]. 42198 a(x,x * y,(x * y) \ z) = a(x,y,y \ z). [para(1091(a,1),192(a,1,2,2,1)),rewrite([3143(5),169(4),192(5)]),flip(a)]. 42212 a(x,x * y,z) \ (y * z) = a(y,x,x \ z) * (y * z). [para(192(a,1),4505(a,1,1)),rewrite([24305(9)]),flip(a)]. 42284 L(a(x,x * y,z),x * ((x \ y) * z),u) * L(a(y,x,x \ z),y * z,u) = 1. [back_rewrite(24350),rewrite([42192(13)])]. 42295 T(x * ((x \ y) * z),a(x,x * y,z)) = a(y,x,x \ z) * (y * z). [back_rewrite(4031),rewrite([42212(10)])]. 42314 R(x * y,x,x \ T(z,y)) = (x * (z * y)) / T(z,y). [para(90(a,1),198(a,2,1,2))]. 42356 R(x * (y \ z),x,x \ y) = (x * T(z,y)) / y. [para(4505(a,1),198(a,2,1,2))]. 42387 R(x * (y * z),x,x \ y) = (x * (y * (z * y))) / y. [para(101(a,1),198(a,2,1,2))]. 42416 K(R(x * y,x,x \ z),z) = K(x * (y * z),z). [para(198(a,2),17822(a,1,1))]. 42429 T(x,R(y * z,y,y \ x)) = T(x,y * (z * x)). [para(198(a,2),26764(a,1,2))]. 42662 ((x * y) * R(z,x,y)) / ((z * x) * y) = K(x * y,R(z,x,y)). [para(20994(a,1),16566(a,2)),rewrite([10561(4)])]. 42829 R(x,y,z) * (x * u) = x * (R(x,y,z) * u). [para(16(a,1),7353(a,1,2,2)),rewrite([16(6)])]. 42834 T(R(x,y,z) \ x,x) * (R(x,y,z) * u) = L(x * u,x,R(x,y,z)). [para(7353(a,1),21(a,1,2)),rewrite([42829(5),15452(7),34823(3),4505(4)])]. 42930 a(x \ (y / x),x,z) = a(x,y,z). [para(15(a,1),7682(a,1,2)),rewrite([1091(2),1091(4),1014(5),3143(4),1091(5),24189(6)])]. 42940 a(x * (y \ z),z \ y,u) = a(y \ z,(z \ y) * x,u). [para(4505(a,1),7682(a,1,1,2)),rewrite([90(4),4408(7)])]. 42971 a(x \ y,(y \ x) * z,T(y,x)) = ((z * (x \ y)) * x) \ (z * T(y,x)). [back_rewrite(4335),rewrite([42940(5)])]. 43418 ((x * (y \ z)) * y) * a(y \ z,(z \ y) * x,T(z,y)) = x * T(z,y). [para(7969(a,1),54(a,1,1)),rewrite([7715(13)])]. 44128 a(x,y,y \ z) \ 1 = a(y,y * x,z). [para(18(a,1),4007(a,1,1,2)),rewrite([92(4),169(4),18(7),42295(7),3691(6),18(7)])]. 44649 L(L(x,y / x,z),z * (y / x),z * y) = (z * (y / x)) \ (z * y). [para(76(a,2),6368(a,1,1))]. 44671 L(L(L(x,y,z),u,w),v5 \ 1,v5 \ x) = L(L(x,y,z),u,w). [para(6416(a,1),97(a,2,1,1))]. 44709 L(L(L(L(x,y,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(L(x,u,w),y,z),v5,v6). [para(6416(a,1),229(a,1,1,1)),flip(a)]. 45267 (x * ((x \ y) * z)) / R(T(y,z),x,x \ z) = z. [para(200(a,1),165(a,1,1)),rewrite([31(6)])]. 45271 x * (a(x / (y * z),y,z) * u) = R(x,z \ (y \ 1),y) * u. [para(59(a,1),200(a,2,2,1)),rewrite([27732(6)]),flip(a)]. 45295 R(x,y,T(y \ z,y)) * T(z,y) = (x / y) * (z * y). [para(7967(a,1),200(a,1,1,3)),rewrite([27047(9)])]. 45359 (((x / (y * z)) * y) * z) \ (R(x,z \ (y \ 1),y) * u) = L(u,a(x / (y * z),y,z),x). [back_rewrite(6623),rewrite([45271(9)])]. 45676 (x * y) \ L(y \ z,y,x) = (y * (x * y)) \ z. [para(74(a,2),25093(a,2,2)),rewrite([25093(9),6073(5),1091(3),39506(4),35648(5),101(2)]),flip(a)]. 46495 (R(x / y,y,z) * (y * (z * y))) \ ((x * z) * y) = a(y * z,(y * z) * (x * z),y). [para(85(a,2),24428(a,1,1,1))]. 46497 (R(x \ 1,y,z) * (y * (z * y))) \ (((x \ y) * z) * y) = a(y * z,(y * z) * ((x \ y) * z),y). [para(6071(a,1),24428(a,1,1,1))]. 46810 a(x * y,x * (y * x),z) = a(y,y * x,z). [para(14(a,1),4021(a,1,2,1)),rewrite([1077(4),3143(4),169(3),4032(5),14(6)]),flip(a)]. 46815 a(x,y * (y * (x * (y * z))),u) = a(x,x * (y \ z),u). [para(37(a,1),4021(a,1,1)),rewrite([16103(4),16485(3),23718(9),1091(6),4407(6),23717(6),14(5),4498(7),101(7),128(8),2508(10)]),flip(a)]. 47034 L(L(L(R(x,y \ 1,z),u,w),v5,v6),v7 \ 1,v7 \ L(x,u,w)) = L(L(R(x,y \ 1,z),v5,v6),u,w). [para(76(a,1),44709(a,1,1)),rewrite([24261(6),24016(16)])]. 47036 L(L(x,y,z),u \ 1,u \ L(x,w,v5)) = L(x,y,z). [para(16487(a,1),44709(a,1,1,1)),rewrite([16487(8)])]. 47734 L(x,y * z,y * (z * (y * y))) = x. [para(189(a,1),15035(a,1,3)),rewrite([4578(3)])]. 47883 L(K(x,T(y,z)),x,y) = K(x,T(y,z)). [para(17666(a,1),30(a,1,1)),rewrite([37429(2),37429(4)]),flip(a)]. 48247 T(x,R(x,y,z) \ 1) = x. [para(89(a,1),960(a,1,2,1)),rewrite([19074(4),2771(4,R)])]. 48405 T(x,y) \ (y \ z) = y \ (x \ z). [para(3143(a,1),38503(a,2,2)),rewrite([35645(4),4408(5),45(4),2975(4),5147(4)])]. 48721 L(x,y * K(z,u),K(u,z)) = L(x,K(z,u),K(u,z) * y). [para(18(a,1),8308(a,1,3,2)),rewrite([5005(6)]),flip(a)]. 48733 L(x,K(y,z),u * K(z,y)) = L(x,K(z,y),u). [para(4505(a,1),8308(a,1,3,2)),rewrite([90(5),6144(6),16229(8)])]. 48767 a(x * K(y,z),K(z,y),u) = a(K(y,z),K(z,y) * x,u). [para(4505(a,1),8311(a,1,1,2)),rewrite([90(4),6144(7)])]. 48772 a(K(x,y),K(y,x) * z,u) = a(K(x,y),K(x,y) * z,u). [para(101(a,1),8311(a,1,1,2)),rewrite([2508(8),48767(4)])]. 49860 L(x,T(y,z),y) = x. [para(18604(a,1),439(a,1,2,2,1)),rewrite([4247(3),23(2),4505(4),4505(6),480(8),4505(4),13(6),32749(5),21(6)])]. 50186 L(L(R(x,y \ 1,z),u,w),v5,v6) = L(L(L(x,y,z \ 1),u,w),v5,v6). [para(82(a,1),47034(a,2,1,1)),rewrite([1014(5),10229(4),10305(5),47034(10),1014(10),10229(9),3143(10),4155(9),10690(8),38590(9)])]. 50188 L(R(x,y \ 1,z),u \ 1,u \ L(x,w,v5)) = R(x,y \ 1,z). [para(16487(a,1),47034(a,1,1)),rewrite([16487(13)])]. 50190 L(R(x,y \ 1,z),u,w) = L(L(x,y,z \ 1),u,w). [para(18454(a,1),47034(a,1,3,2)),rewrite([18485(6),50186(8),44671(8),38623(11)]),flip(a)]. 50224 R(x,y \ 1,z) = L(x,y,z \ 1). [back_rewrite(50188),rewrite([50190(8),47036(8)]),flip(a)]. 50298 L(x,T(y,x),z \ 1) = L(x,y \ x,z). [back_rewrite(27706),rewrite([50224(4)])]. 50308 R(x,y,y \ z) = L(x,y,z \ 1). [back_rewrite(24043),rewrite([50224(4),4407(3),38488(4)]),flip(a)]. 50323 L(x,y / x,z \ 1) = L(x,y,z \ 1). [back_rewrite(10323),rewrite([50224(7)])]. 50345 ((x / y) * (z * y)) / T(z,y) = L(x,z \ 1,y). [back_rewrite(2802),rewrite([50224(9),4407(8),26903(9)])]. 50347 a(x,T(x,y),z) = 1. [hyper(25,a,49860,a)]. 50359 L(x,y * z,z * y) = x. [para(4209(a,1),49860(a,1,2))]. 50365 L(x,y,T(y,z)) = x. [para(7769(a,1),49860(a,1,2))]. 50404 K(x,y) * ((x * y) \ z) = (y * x) \ z. [back_rewrite(6238),rewrite([50359(5)]),flip(a)]. 50423 R(x,y * (z * (z * y)),(z * y) \ ((y * z) \ u)) = R(x,K(z,y),K(y,z) * u). [back_rewrite(21722),rewrite([50404(9)])]. 50785 L(L(x,y / x,z),z * y,z * (y / x)) = L(x,y / x,z). [para(6694(a,1),18608(a,1,2)),rewrite([72(11),18(8),4581(8)])]. 50886 x * (y \ (y \ 1)) = (x / y) / y. [para(18650(a,1),164(a,1,2)),rewrite([3143(4),29418(3),19074(4),30432(3),47(1),1014(8)])]. 51015 x / (T(y,z) * (T(y,u) * (T(y,z) \ x))) = T(y,u) \ 1. [back_rewrite(19499),rewrite([50886(9),10229(8),10215(7),3228(8),33992(8),37126(9),38393(8)])]. 51318 T(x,y) * (y * (x * y)) = x * (x * (y * y)). [para(20397(a,1),209(a,1,1)),rewrite([7775(3),547(5),36652(5),15452(5),45(2),100(3),20397(10),88(9)]),flip(a)]. 51385 T(x,y) * (y * (x * (y * z))) = x * (x * (y * (y * z))). [back_rewrite(7257),rewrite([51318(4),37(4),100(2)]),flip(a)]. 51470 R(x / (y * ((z * y) \ x)),z,u) = R(z,y,(z * y) \ x). [para(82(a,1),495(a,1,1))]. 51780 (x / (y * (z * x))) * y = L(z \ 1,x \ 1,y). [para(1014(a,1),10707(a,1,1)),rewrite([4155(3),45(2),10229(4)])]. 52573 L(x,y \ 1,z) = L(x,y,z \ 1). [para(14(a,1),24267(a,1,1,2)),rewrite([38568(4),48(5)]),flip(a)]. 52576 x * (a(y,z,z \ (y \ x)) * u) = L(x,y,z \ 1) * u. [para(24267(a,1),18(a,1,1)),rewrite([52573(3)]),flip(a)]. 52596 L(x,y,z \ 1) = L(x,y,z). [para(7679(a,1),24267(a,2)),rewrite([45(2),45(2),45(4),45(4),42198(7),52576(7),4407(3),26903(4),52573(3),17(5),45(5)])]. 52619 T(x,y) \ 1 = T(x \ 1,y). [para(6020(a,1),24267(a,2)),rewrite([52576(11),52596(6),33039(4),41620(4),3666(3)])]. 52627 L(x,y,T(y \ 1,z)) = x. [para(50347(a,1),24267(a,1,1,2,1)),rewrite([13(2),17(2),52573(4),52619(3)]),flip(a)]. 52635 (x / (y * (z * x))) * y = L(z \ 1,x,y). [back_rewrite(51780),rewrite([52573(9),52596(9)])]. 52653 ((x / y) * (z * y)) / T(z,y) = L(x,z,y). [back_rewrite(50345),rewrite([52573(8),52596(8)])]. 52724 T(x,y) * (T(x \ y,y) * z) = y * L(z,y,x). [back_rewrite(38658),rewrite([52573(8),52596(8)])]. 52760 (x * y) * (T(x,y) \ z) = y * L(z,y,x). [back_rewrite(38535),rewrite([52573(7),52596(7)])]. 52764 x * (y * ((x * y) \ z)) = L(z,y,x). [back_rewrite(38475),rewrite([52573(7),52596(7)])]. 52794 R(T(x,y),x \ z,u) = L(T(x,y),z,u). [back_rewrite(24749),rewrite([52573(7),52596(7)])]. 52843 R(x,x \ y,z) = L(x,y,z). [back_rewrite(24264),rewrite([52573(5),52596(5)])]. 52858 L(x,y,z) = L(x,z,y). [back_rewrite(16398),rewrite([52573(4),4407(3),26903(4),52573(3),52596(3)])]. 52942 L(x,y,z / x) = L(x,z,y). [back_rewrite(50323),rewrite([52596(4),52858(2),52596(5)])]. 52953 R(x,y,y \ z) = L(x,y,z). [back_rewrite(50308),rewrite([52596(5)])]. 52963 L(x,y,z \ x) = L(x,y,T(z,x)). [back_rewrite(50298),rewrite([52596(4),52858(2),52858(4)]),flip(a)]. 53065 x * ((y * x) \ (y * z)) = L(z,x,y). [back_rewrite(38590),rewrite([52596(7),52858(5)])]. 53163 L(x,y,y * z) = L(x,y,z). [back_rewrite(16470),rewrite([52596(4),52858(2)])]. 53170 (x \ y) * L(z,x,y) = x \ (y * z). [back_rewrite(6145),rewrite([52596(4),52858(2)])]. 53195 x / (T(y,z) * (T(y,u) * (T(y,z) \ x))) = T(y \ 1,u). [back_rewrite(51015),rewrite([52619(10)])]. 53431 ((x \ y) * z) \ (y * z) = T(T(x,y),z). [back_rewrite(8394),rewrite([52794(4),34275(3)]),flip(a)]. 53473 x / (y * ((z * y) \ x)) = L(z,y,x). [back_rewrite(38485),rewrite([52843(3),26903(2),52858(1)]),flip(a)]. 53483 L(x,y,z \ (x \ u)) = L(x,y,(u \ x) * z). [back_rewrite(33575),rewrite([52843(4),52858(3),52858(6)]),flip(a)]. 53484 L(x,y,z \ (u \ 1)) = L(x,y,u * z). [back_rewrite(33545),rewrite([52843(3),52858(2),52858(6)]),flip(a)]. 53550 L(x,y,z) \ 1 = R(x \ 1,y,z). [back_rewrite(10233),rewrite([52843(2)])]. 53564 (x * y) \ L(z,x,y) = y \ (x \ z). [back_rewrite(8393),rewrite([52843(3)])]. 53598 x * (y * ((x * y) \ z)) = L(z,x,y). [back_rewrite(52764),rewrite([52858(5)])]. 53600 (x * y) * (T(x,y) \ z) = y * L(z,x,y). [back_rewrite(52760),rewrite([52858(5)])]. 53617 T(x,y) * (T(x \ y,y) * z) = y * L(z,x,y). [back_rewrite(52724),rewrite([52858(6)])]. 53634 ((x / y) * (z * y)) / T(z,y) = L(x,y,z). [back_rewrite(52653),rewrite([52858(6)])]. 53804 L(L(x,y,z),z * y,z * (y / x)) = L(x,y,z). [back_rewrite(50785),rewrite([52858(2),52942(2),52858(7),52942(7)])]. 53894 L(x,K(y,z),u * K(z,y)) = L(x,u,K(z,y)). [back_rewrite(48733),rewrite([52858(6)])]. 53895 L(x,K(y,z),K(z,y) * u) = L(x,u,K(y,z)). [back_rewrite(48721),rewrite([52858(4),53894(4)]),flip(a)]. 54309 (x * (y * x)) \ z = x \ (y \ (x \ z)). [back_rewrite(45676),rewrite([52858(3),53564(4)]),flip(a)]. 54321 (((x / (y * z)) * y) * z) \ (R(x,z \ (y \ 1),y) * u) = L(u,x,a(x / (y * z),y,z)). [back_rewrite(45359),rewrite([52858(14)])]. 54371 (x * (y / z)) \ (x * y) = L(z,y,x). [back_rewrite(44649),rewrite([52858(2),52942(2),52858(5),53804(5)]),flip(a)]. 54493 L(a(x,x * y,z),u,x * ((x \ y) * z)) * L(a(y,x,x \ z),u,y * z) = 1. [back_rewrite(42284),rewrite([52858(6),52858(10)])]. 54757 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * (z * w))) = R(x,y * z,L(w,y,z)). [back_rewrite(38643),rewrite([52858(12)])]. 54758 R(x,y * z,L(z \ u,y,z)) = R(x,y * z,(((y * z) \ w) * w) * ((w \ (w \ y)) * u)). [back_rewrite(38642),rewrite([52858(3)])]. 54785 L(L(x,y,T(z,u)),z,y * T(z,u)) = L(x,K(z,u),z * (y * z)). [back_rewrite(37146),rewrite([52858(2),52858(5)])]. 54855 L(x,y,T(z,y)) = L(x,y,z). [back_rewrite(34860),rewrite([52953(4),52942(3),52858(2),52858(4),52942(4)])]. 54918 L(x,y,T(z,y) * u) = L(x,y,z * (y * u)). [back_rewrite(33664),rewrite([52858(3)]),flip(a)]. 54976 L(x,T(y,z),y \ z) = L(x,y,z). [back_rewrite(30654),rewrite([52858(4),52942(4),54371(7),52858(4)])]. 55103 (x * (K(y,z) * u)) * (u \ K(z,y)) = L(x,K(y,z) * u,u \ K(z,y)). [back_rewrite(28379),rewrite([52858(6),52942(6),52858(5)]),flip(a)]. 55235 a((x * y) / z,x,L(x \ z,x,y)) = a(x,y * x,L(x \ z,x,y)). [back_rewrite(26973),rewrite([52858(4),52858(8)])]. 55237 a((x \ y) / z,x,L(x \ z,x,y)) = a(x \ y,x,L(x \ z,x,y)). [back_rewrite(26968),rewrite([52858(4),52858(8)])]. 55249 L(x,y,y \ z) = L(x,y,z). [back_rewrite(26903),rewrite([52858(3)])]. 55404 L(T(x,y),z,y \ x) = z * ((z \ (y \ x)) * y). [back_rewrite(23927),rewrite([52858(3)])]. 55494 T(x * (y / z),x * y) = L(z,y,x) \ (x * y). [back_rewrite(22386),rewrite([52858(2),52942(2)]),flip(a)]. 55548 x * (x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y))))) = x * x. [back_rewrite(21507),rewrite([52858(6)])]. 55568 x * (y \ ((y / x) * z)) = L(z,y,y / x). [back_rewrite(21447),rewrite([52858(6)])]. 55660 L(L(x,y,z),y,z) = x. [back_rewrite(18473),rewrite([52858(4),8684(4)])]. 55725 L(x,y \ z,(z \ y) * u) = L(x,u,y \ z). [back_rewrite(16517),rewrite([52858(4),52858(6)])]. 55731 (x * (y \ z)) * T(y,z) = x * L(z,x,T(y,z)). [back_rewrite(16508),rewrite([52858(6),52963(6)])]. 55771 T(x,L(y * z,x,y)) = T(x,(x * y) * z). [back_rewrite(16362),rewrite([52858(2)])]. 55776 x \ (y * ((y \ x) * z)) = L(z,x,y). [back_rewrite(16348),rewrite([52858(5)])]. 55819 L(x,y,z * (u * u)) = L(x,y,z). [back_rewrite(14874),rewrite([52858(3),2507(3),52858(1)]),flip(a)]. 55915 L(K(x,y) * z,u,K(y,x)) = (u * K(y,x)) \ (u * z). [back_rewrite(11597),rewrite([52858(4)])]. 55954 L(T(x * y,x * z),u,L(y \ z,x,y)) = (u * L(y \ z,x,y)) \ (u * (x * z)). [back_rewrite(11076),rewrite([52858(5),52858(6),52858(8)])]. 56000 ((x / (y * z)) * y) * z = L(x,y,z). [back_rewrite(10295),rewrite([52858(3),52942(3),52858(2),53163(2)]),flip(a)]. 56040 x * L(y,x,z) = L(x * y,x,z). [back_rewrite(8091),rewrite([54976(3),52858(1),52858(4)])]. 56084 L(x,y,x * z) = (y * (z \ (x \ 1))) \ (y / z). [back_rewrite(6676),rewrite([52858(4),53483(4),45(2)])]. 56136 (x * (y * (z * u))) \ (x * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),x,y * (z * u)). [back_rewrite(5337),rewrite([52858(13)])]. 56176 (x * (y * z)) \ (x * y) = R(z \ 1,x,y). [back_rewrite(4138),rewrite([52858(5),53550(7)])]. 56215 a(x,y,L(z,x,y)) = a(x,y,z) \ 1. [back_rewrite(1098),rewrite([52858(1),3204(3),2548(5),52858(4)]),flip(a)]. 56223 R(x,y * z,L(z \ u,y,z)) = L(x,y * z,y * u). [back_rewrite(648),rewrite([52858(3),52953(9)])]. 56231 (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),x,y * (z * u)). [back_rewrite(589),rewrite([52858(11)])]. 56240 (x * y) * L(z,x,y) = x * (y * z). [back_rewrite(72),rewrite([52858(2)])]. 56531 (x * ((x \ y) * z)) / L(T(y,z),x,z) = z. [back_rewrite(45267),rewrite([52953(6)])]. 56576 T(x,(x * y) * z) = T(x,y * (z * x)). [back_rewrite(42429),rewrite([52953(3),52858(2),55771(3)])]. 56588 K((x * y) * z,x) = K(y * (z * x),x). [back_rewrite(42416),rewrite([52953(3),16735(3)])]. 56609 (x * (y * (z * y))) / y = (x * y) * z. [back_rewrite(42387),rewrite([52953(4),16364(3)]),flip(a)]. 56632 L(x * (y \ z),x,y) = (x * T(z,y)) / y. [back_rewrite(42356),rewrite([52953(4)])]. 56659 L(x * y,x,T(z,y)) = (x * (z * y)) / T(z,y). [back_rewrite(42314),rewrite([52953(4)])]. 56731 R(x,y,(x * y) \ z) \ 1 = L(x \ 1,y,z). [back_rewrite(36066),rewrite([52953(9)])]. 56746 x / R(y,z,(y * z) \ u) = x * L(y \ 1,z,u). [back_rewrite(36043),rewrite([52953(8)])]. 56831 T(x,y * ((y \ z) * x)) = T(x,L(z,x,y)). [back_rewrite(29466),rewrite([52953(6),52858(5)])]. 56835 R(x,y \ (z \ 1),z) = L(x,z,y). [back_rewrite(27732),rewrite([56000(4),52953(3),6022(2)]),flip(a)]. 56903 R(x,y * z,z \ 1) = L(x,y,(u \ (u \ y)) * z). [back_rewrite(21721),rewrite([52953(8),52858(4)]),flip(a)]. 56973 ((x \ y) * (x * z)) / z = L(T(y,x),x,z). [back_rewrite(10810),rewrite([52953(3)]),flip(a)]. 57033 L(x * y,y,z) = (x * (y * z)) / z. [back_rewrite(4583),rewrite([52953(3)])]. 57044 L(x,y,x * z) = L(x,z,y). [back_rewrite(3213),rewrite([52953(4),52858(2),52953(4)])]. 57089 x \ (y * ((y \ z) * x)) = L(T(z,x),x,y). [back_rewrite(538),rewrite([52953(7),52858(6)])]. 57097 (x * ((x \ y) * z)) / z = L(y,x,z). [back_rewrite(191),rewrite([52953(6)])]. 57173 ((L(x,y,z) * (y * (z * y))) \ (y * ((z * y) * x))) * K(L(x,y,z),y * (z * y)) = 1. [back_rewrite(7701),rewrite([53163(2),53163(10)])]. 57197 T(T(x,y),z) * R(x \ 1,y,z) = K(y * z,(x \ y) * z). [back_rewrite(40866),rewrite([53431(4)])]. 57210 R(x,y,(x * y) \ z) = L(x,z,y). [back_rewrite(51470),rewrite([53473(4),52858(1),33(2),480(1)]),flip(a)]. 57428 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = R(y \ (z \ (y \ x)),y * (z * y),u). [back_rewrite(8002),rewrite([54309(11)])]. 57506 L(a(x,y,z),y,x * (y * z)) = a(y,x,y * z). [back_rewrite(33981),rewrite([54918(4)])]. 57568 T(L(x,y,z) * (u / x),x) = x \ (L(x,y,z) * u). [back_rewrite(28851),rewrite([55494(6),18461(2)]),flip(a)]. 57670 L(x,y,z * T(z,u)) = x. [back_rewrite(27119),rewrite([55819(7),52858(3)])]. 57764 L(x,y,a(y / (z * u),z,u)) = x. [back_rewrite(54321),rewrite([56000(4),56835(5),15(4)]),flip(a)]. 57831 x * a(x / (y * z),y,z) = L(x,y,z). [back_rewrite(582),rewrite([56000(8)])]. 57837 L(x * y,x,T(z,y)) = (x * (z \ y)) * T(z,y). [back_rewrite(55731),rewrite([56040(7)]),flip(a)]. 57867 a(x,y * x,L(z,x,y)) = a(x,y,x * z). [back_rewrite(23643),rewrite([56040(5),3204(7),189(6),56231(7),57506(4)]),flip(a)]. 57908 R(x,y * z,(((y * z) \ u) * u) * ((u \ (u \ y)) * w)) = L(x,y * z,y * w). [back_rewrite(54758),rewrite([56223(4)]),flip(a)]. 57969 T(x,(x \ y) * z) = T(x,y * (z * x)). [back_rewrite(23736),rewrite([56576(6)])]. 57975 T(x \ y,((y \ x) * z) * y) = T(x \ y,z * (y * (x \ y))). [back_rewrite(15924),rewrite([56576(10)])]. 57979 T(x \ y,(z * (x \ y)) * T(x,y)) = T(x \ y,z * (y * (x \ y))). [back_rewrite(15622),rewrite([56576(11)])]. 58035 K((x \ y) * z,x) = K(y * (z * x),x). [back_rewrite(23819),rewrite([56588(6)])]. 58065 R(T(x,y),y \ x,(x \ y) * z) = L(T(x,y),y,z). [back_rewrite(22110),rewrite([56973(9)])]. 58091 (x * (y \ (z \ 1))) \ (x / y) = L(z,x,y). [back_rewrite(56084),rewrite([57044(2),52858(1)]),flip(a)]. 58133 x * L(y \ 1,z,u) = x / L(y,z,u). [back_rewrite(56746),rewrite([57210(3),52858(1)]),flip(a)]. 58139 R(x \ 1,y,z) = L(x \ 1,y,z). [back_rewrite(56731),rewrite([57210(3),52858(1),53550(3)])]. 58268 a((x * y) / z,x,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(55235),rewrite([57867(9),16(7)])]. 58275 L(x,y * z,y * (z * u)) = R(x,y * z,L(u,y,z)). [back_rewrite(54757),rewrite([57908(10)])]. 58306 ((x * (y \ z)) * T(y,z)) / T(y \ z,x * (z * (y \ z))) = ((z \ y) * x) * z. [back_rewrite(15940),rewrite([57975(9)])]. 58399 T(T(x,y),z) / L(x,y,z) = K(y * z,(x \ y) * z). [back_rewrite(57197),rewrite([58139(5),58133(6)])]. 58412 (x * (y * z)) \ (x * y) = L(z \ 1,x,y). [back_rewrite(56176),rewrite([58139(7)])]. 58434 L(x,y,z) \ 1 = L(x \ 1,y,z). [back_rewrite(53550),rewrite([58139(6)])]. 58458 (L(x \ 1,y,z) * (y * (z * y))) \ (((x \ y) * z) * y) = a(y * z,(y * z) * ((x \ y) * z),y). [back_rewrite(46497),rewrite([58139(3)])]. 58518 K(x * y,L(z \ 1,x,y)) = K(x * y,(z \ x) * y). [back_rewrite(26753),rewrite([58139(4)])]. 58601 R(x,y * z,L(y * y,y,z)) = x. [back_rewrite(47734),rewrite([58275(5)])]. 58647 R(T(x,(y * z) * a(x,y,z)),y * z,a(x,y,z)) = R(T(x,y * (z * x)),y * z,a(x,y,z)). [para(33249(a,1),2642(a,1,2)),rewrite([31(7),31(13),56576(10)])]. 62320 R(x,y,T(y \ z,y)) = L(x,y,z). [para(4505(a,1),516(a,1,2)),rewrite([38365(4),53634(5)]),flip(a)]. 62433 L(x,y,z) * T(z,y) = (x / y) * (z * y). [back_rewrite(45295),rewrite([62320(3)])]. 62444 (x * y) * T(T(z,u),y) = (x * y) * T(T(z,y),u). [para(517(a,1),104(a,1,2,2)),rewrite([522(5)])]. 63757 (x * (y \ L(y,z,y \ (x / y)))) * a(y,z * (y \ (x / y)),T(z,y \ (x / y)) \ y) = x. [para(11138(a,1),54(a,2)),rewrite([53600(8),38305(7)])]. 64162 L(x * x,x,y) = x * x. [para(1077(a,1),55954(a,1,3)),rewrite([14(3),4209(2),52596(4),52858(2),1607(5),1014(5),14(5),10229(5),23697(5),6351(5)])]. 64186 R(x,y * z,y * y) = x. [back_rewrite(58601),rewrite([64162(3)])]. 64241 K(T(x,y) \ z,K(T(x,y) \ ((x \ y) * z),T(x \ y,y))) = 1. [hyper(27,a,19049,a)]. 64397 T(x,(T(T(T(T(T(y,z),x \ 1),u),w),v5) / x) / T(T(T(T(T(y,w),u),x \ 1),z),v5)) = x. [para(4097(a,2),14495(a,1,2,1))]. 65408 x * (y * (T(y,x) * z)) = y * (x * (y * z)). [para(25410(a,1),262(a,1,1)),rewrite([33957(4),547(3),32749(4),45(6),128(7),25410(11),88(9)])]. 65748 L(x \ 1,y,z) * x = L(x,y,z) \ x. [para(996(a,1),518(a,1,2,1)),rewrite([58133(4),28505(2)]),flip(a)]. 65880 x * K(y,T(z,x)) = K(y,z) * x. [para(17666(a,1),518(a,2,1)),rewrite([37429(2),47883(3)])]. 65951 R(x,y,z) * x = x * R(x,y,z). [para(89(a,1),519(a,1,2,1)),flip(a)]. 67485 a(x \ (y \ (x \ 1)),x * (y * (x * z)),u) = a(T(y,x),T(y,x) * z,u). [para(106(a,1),15271(a,1,1,2,1,1)),rewrite([39792(4),128(7),35648(9),101(2),23718(7),34823(2),33957(5),6968(6),24002(5),4032(7),39792(8),106(12),128(11)]),flip(a)]. 68727 ((x * y) * T(z,y)) / T(y,x * (z * (y * y))) = (y \ x) * (z * y). [para(522(a,1),165(a,1,1)),rewrite([57969(7),4578(5)])]. 68754 x * ((y * x) \ (z * x)) = (y \ x) * T(z,x). [para(3143(a,1),522(a,2,1)),rewrite([35645(5)])]. 68763 ((x \ y) * (z * x)) * x = T((y * x) * T(z,x),x). [para(522(a,1),4209(a,1,1)),flip(a)]. 68786 K((x * y) * T(z,y),y) = K(x * (z * (y * y)),y). [para(522(a,1),16568(a,1,1)),rewrite([58035(8),4578(6)])]. 68796 x * (y * (x * T(z,y * x))) = x * L(z * (y * x),y,x). [para(128(a,1),522(a,2)),rewrite([34823(3),6968(6),53600(6)]),flip(a)]. 68958 (x * (y * (z * x))) \ L(x * (y * (z * x)),x,z) = a(x,z * x,T(y,z * x)). [back_rewrite(23655),rewrite([68796(8),52858(6),56040(7)])]. 68979 R(T(x,y * (z * x)),y * z,a(x,y,z)) = ((y * z) * a(x,y,z)) \ ((x * y) * z). [para(54(a,1),536(a,1,2)),rewrite([58647(13)]),flip(a)]. 69080 R(T(x,(y * z) * a(x,y,z)),y * z,a(x,y,z)) = ((y * z) * a(x,y,z)) \ ((x * y) * z). [back_rewrite(58647),rewrite([68979(13)])]. 70643 ((x * y) * z) / (x * (x * (y * z))) = L(x \ 1,y,z). [para(3691(a,1),342(a,1,1)),rewrite([58139(5),52858(5),2507(5),52858(3)]),flip(a)]. 70649 R(x * K(y,z),K(z,y),u) = (x * u) / (K(z,y) * u). [para(4993(a,1),342(a,1,1,2,2)),rewrite([14(3),5005(2),4993(6),14(5),8296(10)])]. 70674 R(x / (y * T(y,z)),y * T(y,z),u) = (x * u) / (y * (T(y,z) * u)). [para(16623(a,1),342(a,1,1,2,2)),rewrite([547(2),16623(7),547(5),38207(12),21062(10)])]. 70731 x * (L(x,y,z) \ x) = R(x,x * (x * y),z). [back_rewrite(1932),rewrite([70643(6),58133(4),28505(2)])]. 70983 (x * (y * (z * (y * x)))) \ (x * (y * (z * ((y * x) * (u * (x * y)))))) = x * (y * T(u,x * y)). [para(33415(a,1),2214(a,1,2,2,2,2))]. 72562 K(L(x,y,z),T(x,u)) = 1. [para(28464(a,1),16687(a,1,2)),rewrite([47(3)]),flip(a)]. 72844 a(T(x \ y,y),T(x,y),T(z,x * y)) = a(T(x,y),x * y,T(z,x * y)). [para(90(a,1),13311(a,1,3,2)),rewrite([4278(2),90(9),90(10)])]. 72886 a(x,(x \ y) * z,u) = a(x,(x * y) * z,u). [para(16(a,1),13466(a,1,2,2)),rewrite([169(6),136(7)])]. 72954 x \ (y * (z * x)) = T(y,x) * T(z,x). [para(14(a,1),13641(a,1,2,2)),rewrite([4505(3),14(6)]),flip(a)]. 73156 T(x,y) * T(x \ z,y) = L(T(z,y),y,x). [back_rewrite(57089),rewrite([72954(4)])]. 73876 ((x * (y * z)) * (y * ((z * y) \ u))) / (y * u) = R(x,y * z,y * ((z * y) \ u)). [para(16(a,1),346(a,1,2,2))]. 74086 (x * (y * (x \ y))) / (x * (y / x)) = y. [para(27447(a,1),17(a,1,1)),rewrite([5005(4),26340(4)]),flip(a)]. 74176 a(x * (y / x),y * (y * z),u) = a(T(y,x \ y),z,u). [para(27447(a,1),4636(a,2,1)),rewrite([74086(6),74086(7),74086(7),21063(3),28991(2),2508(5),74086(11),74086(11)]),flip(a)]. 74728 K((x * (y \ z)) * T(y,z),T(x * z,a(x,y \ z,T(y,z)))) = K(a(x,y \ z,T(y,z)),x * z). [para(4315(a,1),17822(a,1,1)),rewrite([17771(9)]),flip(a)]. 75476 a(x,y,K(x,z)) = 1. [para(18(a,1),33091(a,1,2))]. 75493 (x * y) * K(y,z) = x * T(y,z). [para(33091(a,1),33249(a,1,1,3)),rewrite([80(5),128(4),16716(2),15(4),75476(8),14(7)]),flip(a)]. 75570 R(x,y,K(y,z)) = x. [back_rewrite(22892),rewrite([75493(3),17(4)]),flip(a)]. 75628 R(x,y,K(z,y)) = x. [para(17781(a,1),75570(a,1,3))]. 75689 R(x,T(y,z),K(z,y)) = x. [para(17771(a,1),75628(a,1,3))]. 75750 (x * K(y,z)) / z = x / T(z,y). [back_rewrite(21095),rewrite([75689(5)]),flip(a)]. 75804 a(x,y,z \ (x \ z)) = 1. [para(3666(a,1),33119(a,1,1)),rewrite([24189(5)])]. 76377 T(x * (x * y),z \ 1) * (z / y) = z * (x * x). [para(10920(a,1),7616(a,1,1)),rewrite([10215(7),22250(11),10229(9),18(9)])]. 77305 a(x \ ((y \ ((x \ (z / x)) / y)) / x),x * (y * x),u) = a(x \ (y \ (x \ 1)),z,u). [para(106(a,1),15079(a,1,2)),rewrite([39792(4),39792(8),35648(10),101(2),54309(8),9490(6),9490(7),1014(7),39792(13)])]. 77469 ((x / y) * (z * u)) * a(y / x,z,u) = ((x / y) * z) * u. [para(15308(a,1),54(a,1,2)),rewrite([37(6),10287(7),10287(12)])]. 77479 a(x,x * (y \ (y \ (x \ z))),u) = a(x,y * (y * z),u). [para(3645(a,1),15308(a,1,2,1)),rewrite([10215(7),76377(7),3645(13),35648(11),4578(8),19474(9),35648(10),4578(4),19474(8),14882(9),16(7),16(6),3954(5),10215(12),76377(12),14882(8)])]. 77481 a(T(x,y),y * (y * z),u) = a(y \ (x \ (y \ 1)),z,u). [para(106(a,1),15308(a,1,2,1)),rewrite([39792(4),106(10),128(9),189(10),4578(6),189(9),100(6),189(8),101(6),128(7),67485(11),51385(6),22976(6),39792(8)])]. 78102 x * (((T(y,x) * (x * z)) / u) / T(x * (y * (x * (x * z))),u \ 1)) = x \ (u \ 1). [para(4640(a,1),15(a,1,2)),flip(a)]. 78147 a((x \ y) * y,z,u) = a(x,y * (y * z),u). [para(4640(a,1),4636(a,2,1)),rewrite([78102(13),18809(5),3143(3),90(3),24189(8)])]. 79623 L(x,y,R(z \ (y \ 1),y,x)) = L(x,y,T(z,x)). [para(3143(a,1),10670(a,2,3)),rewrite([6120(3),52963(7)])]. 79632 L(x,y,z * x) = L(x,y,z). [para(101(a,1),10670(a,2,3)),rewrite([20016(3),57044(3),52858(2),3200(2),57044(4),52858(3)]),flip(a)]. 79704 L(x,y,R(z,y,x)) = L(x,y,z). [back_rewrite(8681),rewrite([79632(3),16256(2)]),flip(a)]. 79714 L(x,y,T(z,x)) = L(x,y,z). [back_rewrite(79623),rewrite([79704(5),53484(4),53163(2)]),flip(a)]. 79784 L(x,y,z \ x) = L(x,y,z). [back_rewrite(52963),rewrite([79714(4)])]. 79922 (x * (y * z)) / T(y,z) = L(x * z,z,y). [para(90(a,1),57033(a,2,1,2)),rewrite([54855(3)]),flip(a)]. 79940 L(x * (y \ z),y,z) = (x * z) / T(y,z). [para(2690(a,1),57033(a,2,1,2)),rewrite([52858(5),54976(5)])]. 79946 (x * T(y,z)) / z = (x * y) / T(z,y). [para(4505(a,1),57033(a,2,1,2)),rewrite([52858(4),55249(4),79940(3)]),flip(a)]. 79974 R(x,y \ z,T(y,z)) = L(x,y,z). [para(4504(a,1),57033(a,2,1)),rewrite([7715(4),52858(3),79632(3),55249(2),52858(1),2708(6)]),flip(a)]. 79977 L(x * (y * z),y,z) = (x * y) * z. [para(101(a,1),57033(a,2,1,2)),rewrite([52858(4),53163(4),56609(7)])]. 79991 (x * y) / T(y,z) = x * K(z,y). [para(16875(a,1),57033(a,2,1,2)),rewrite([38196(5)]),flip(a)]. 80004 K(L(x * y,y,z),z) = K(x * (y * z),z). [para(57033(a,2),17822(a,1,1))]. 80058 R(x,y \ z,y) = L(x,y,z). [para(7969(a,1),57033(a,2,1)),rewrite([7715(4),52858(4),79632(4),54976(3),52858(1),7966(6)]),flip(a)]. 80171 L(x * y,x,T(z,y)) = L(x * y,y,z). [back_rewrite(56659),rewrite([79922(7)])]. 80225 (x * (y \ z)) * T(y,z) = L(x,y,z) * z. [back_rewrite(10537),rewrite([79974(3)]),flip(a)]. 80273 x * (y * (x * T(z,y * x))) = L(x * (z * (y * x)),x,y). [back_rewrite(68796),rewrite([52858(8),56040(9)])]. 80289 R(x,K(y,z),y) = x. [back_rewrite(20967),rewrite([79991(5),8298(4)]),flip(a)]. 80501 (x * (y \ z)) * y = (x / y) * (z * y). [back_rewrite(10562),rewrite([80058(2),62433(3)]),flip(a)]. 80509 L(x,y,z) * y = L(x * y,y,z). [back_rewrite(57837),rewrite([80171(3),80225(6),52858(3)]),flip(a)]. 80568 K(L(x,y,z) * z,T(x * z,a(x,y \ z,T(y,z)))) = K(a(x,y \ z,T(y,z)),x * z). [back_rewrite(74728),rewrite([80225(4)])]. 80615 (L(x,y,z) * z) / T(y \ z,x * (z * (y \ z))) = ((z \ y) * x) * z. [back_rewrite(58306),rewrite([80225(4)])]. 80627 T(x \ y,z * (y * (x \ y))) = T(x \ y,L(z,x,y) * y). [back_rewrite(57979),rewrite([80225(5)]),flip(a)]. 80744 T(T(((x \ y) * z) * y,x \ y),L(z,x,y) * y) = ((x \ y) * z) * y. [back_rewrite(15646),rewrite([80225(9)])]. 80745 T(((x \ y) * z) * y,x \ y) = (L(z,x,y) * y) * (x \ y). [back_rewrite(15645),rewrite([80225(4)]),flip(a)]. 80766 (x * y) * a(x,z \ y,T(z,y)) = L(x * y,y,z). [back_rewrite(4308),rewrite([80225(9),52858(6),80509(7)])]. 80776 (x * K(y,z)) * y = x * T(y,z). [back_rewrite(23173),rewrite([80289(2)]),flip(a)]. 81010 ((x / y) * (z * y)) * a(y \ z,(z \ y) * x,T(z,y)) = x * T(z,y). [back_rewrite(43418),rewrite([80501(3)])]. 81016 a(x \ y,(y \ x) * z,T(y,x)) = a(x,x * z,T(y,x)). [back_rewrite(42971),rewrite([80501(8),24477(11)])]. 81056 (x \ y) * ((z / x) * (y * x)) = ((x \ y) * z) * T(y,x). [back_rewrite(8020),rewrite([80501(4)])]. 81224 (x \ y) * (L(z,y,x) * x) = ((x \ y) * z) * x. [back_rewrite(80615),rewrite([80627(7),2711(7),4408(4)])]. 81235 (x \ y) * (L(z,x,y) * y) = ((x \ y) * z) * y. [back_rewrite(80744),rewrite([80745(5),4209(7)])]. 81262 a(x,y * (y * K(z,u)),z) = 1. [back_rewrite(24075),rewrite([80776(9),5410(9)]),flip(a)]. 81309 ((x / y) * (z * y)) * a(y,y * x,T(z,y)) = x * T(z,y). [back_rewrite(81010),rewrite([81016(8)])]. 81564 (T(x,y) * z) / a(T(y \ x,x),T(y,x),z) = T(y,x) \ ((y * x) * z). [para(15408(a,1),162(a,2)),rewrite([29216(4)])]. 81596 T(x,y) \ ((x * y) * (y * L(z,x,y))) = (T(x \ y,y) * z) * T(T(x * y,y),z). [para(15408(a,1),9018(a,2)),rewrite([73156(8),89(5),6018(5),7775(5),53617(14)]),flip(a)]. 81698 a(x \ y,(y \ x) * x,(x \ y) * z) = a(y,x,x \ z). [para(92(a,1),15411(a,1,1)),rewrite([10229(3),4230(3),4209(4),92(5),24057(8),24285(10)])]. 82112 a(x \ y,z * (y \ x),y) \ 1 = a(x \ y,z,T(x,y)). [para(18(a,1),15593(a,1,2)),rewrite([4155(6)]),flip(a)]. 82121 a(x,y / x,x * z) = a(x,y,z) \ 1. [para(1091(a,1),15593(a,1,1)),rewrite([1091(4),1014(5),4209(5),24189(5),1091(5),24189(6)])]. 82123 a(x,y / x,T(z,x \ z)) = a(x,y,z / x) \ 1. [para(1829(a,1),15593(a,1,1)),rewrite([1829(4),1014(5),28965(5),24189(6),1829(6),24189(8)])]. 82129 a(x,y,x \ z) \ 1 = a(x,y / x,z). [para(7769(a,1),15593(a,1,3)),rewrite([48405(3),46(1),48405(5),46(3),1014(5),24189(4),48405(5),46(3),24189(6)]),flip(a)]. 82165 ((x * y) * z) \ x = (x * z) \ (x / y). [para(15(a,1),15621(a,2,2,1)),rewrite([1091(2),3143(3),1091(4),23717(5),14(4),4209(5)])]. 82190 x * ((y * x) \ (z \ 1)) = (x * y) \ (x / z). [para(1829(a,1),15621(a,2,2,1)),rewrite([10229(2),18(2),10229(4),18(4),82165(3),2643(5),6120(7),4408(8),38342(8)]),flip(a)]. 82774 x * (y * (x * (x * L(x \ (x \ (y \ 1)),z,z / y)))) = x. [para(55548(a,1),15(a,1,2)),rewrite([15(2)]),flip(a)]. 82800 R(x / y,y,x) = x / y. [para(55548(a,1),85(a,2,1)),rewrite([82774(11),82774(13),14868(5),3691(4),1014(5)])]. 82841 x * (y \ (z \ (z \ 1))) = x / (z * (z * y)). [para(55548(a,1),342(a,2,1)),rewrite([82774(15),82800(6),82774(14),14868(8),39699(7)]),flip(a)]. 82892 (x / (y * (y * z))) * u = (x / z) * (y \ (y \ u)). [back_rewrite(39650),rewrite([82841(5)])]. 82924 a(x,y * (y * (x * z)),u) = a(x,x * z,u). [back_rewrite(24479),rewrite([82892(7),15(5),15(4),23697(3),4032(5)]),flip(a)]. 82939 a(x,x * (y \ z),u) = a(x,x * (y * z),u). [back_rewrite(46815),rewrite([82924(5)]),flip(a)]. 82951 a(x,y * (y * z),u) = a(x,z,u). [back_rewrite(77479),rewrite([82939(5),16(3),16(2)]),flip(a)]. 82978 a(x,K(y,z),y) = 1. [back_rewrite(81262),rewrite([82951(4)])]. 83003 a((x \ y) * y,z,u) = a(x,z,u). [back_rewrite(78147),rewrite([82951(6)])]. 83005 a(x \ (y \ (x \ 1)),z,u) = a(T(y,x),z,u). [back_rewrite(77481),rewrite([82951(4)]),flip(a)]. 83038 a(T(x,y \ x),z,u) = a(y * (x / y),z,u). [back_rewrite(74176),rewrite([82951(5)]),flip(a)]. 83180 a(x / y,z,u) = a(x * y,z,u). [back_rewrite(39396),rewrite([82951(4)])]. 83185 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,u,u \ x). [back_rewrite(35944),rewrite([82951(13)])]. 83213 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,x / u,u). [back_rewrite(24163),rewrite([82951(13)])]. 83221 a(x * ((y \ x) * x),z,u) = a(x * y,z,u). [back_rewrite(22429),rewrite([82951(8),83180(6)])]. 83245 a((x \ y) * (y * (x \ y)),z,u) = a(T(y,x),z,u). [back_rewrite(19195),rewrite([82951(6)]),flip(a)]. 83255 a(x \ (y / x),z,u) = a(y,z,u). [back_rewrite(19167),rewrite([82951(5)]),flip(a)]. 83266 a(x * (y * y),z,u) = a(x,z,u). [back_rewrite(14882),rewrite([82951(6)])]. 83285 a(x,y * (z * (z * y)),u) = 1. [back_rewrite(2486),rewrite([82951(6)])]. 83292 a(x,y * (z * y),u) = a(T(z,y),x,u). [back_rewrite(77305),rewrite([83255(9),83255(7),83255(5),83005(8)])]. 83423 ((x / y) * (z * u)) * a(y * x,z,u) = ((x / y) * z) * u. [back_rewrite(77469),rewrite([83180(5)])]. 83804 a((x * y) * z,x,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(58268),rewrite([83180(5)])]. 83819 x * a(x * (y * z),y,z) = L(x,y,z). [back_rewrite(57831),rewrite([83180(3)])]. 83854 L(x,y,a(y * (z * u),z,u)) = x. [back_rewrite(57764),rewrite([83180(3)])]. 83865 a((x \ y) * z,x,L(x \ z,x,y)) = a(x \ y,x,L(x \ z,x,y)). [back_rewrite(55237),rewrite([83180(5)])]. 84069 a(x,y,y \ z) = a(x,y,y * z). [back_rewrite(24279),rewrite([83180(4),83266(4)]),flip(a)]. 84082 a(x,y \ x,z) = a(x,y * x,z). [back_rewrite(19659),rewrite([83180(2),23494(2)]),flip(a)]. 84171 a(x,y,z) = a(y,x,z). [back_rewrite(42930),rewrite([83255(3)])]. 84200 (x * (y * (z * (z * y)))) * u = x * (z * (y * (y * (z * u)))). [back_rewrite(20510),rewrite([83285(9),14(7)]),flip(a)]. 84267 a(T(x,y),y * x,z) = a(x,x * y,z). [back_rewrite(46810),rewrite([83292(4)])]. 84365 (x \ (y \ (y \ z))) * (u * ((((z * u) \ y) * y) * x)) = a(z,u,u * x). [back_rewrite(83185),rewrite([84069(11)])]. 84378 a(x \ y,(y \ x) * x,(x \ y) * z) = a(x,y,x \ z). [back_rewrite(81698),rewrite([84171(8)])]. 84525 L(a(x,x * y,z),u,x * ((x \ y) * z)) * L(a(x,y,x \ z),u,y * z) = 1. [back_rewrite(54493),rewrite([84171(8)])]. 84641 a(x,y * x,z) = a(x,x * y,z). [back_rewrite(44128),rewrite([84069(2),7836(4),84171(2)])]. 84738 a(x,x * y,z) \ 1 = a(x,y,x \ z). [back_rewrite(24285),rewrite([84171(6)])]. 84799 a(x,y * x,z) \ 1 = a(y,x,x * z). [back_rewrite(4795),rewrite([84171(2)])]. 84975 a(x,(x * y) * z,L(x \ z,x,y)) = a(x,x * y,L(x \ z,x,y)). [back_rewrite(83865),rewrite([84171(5),72886(5),84171(9),3954(9)])]. 84982 L(x,y,a(z,y * (z * u),u)) = x. [back_rewrite(83854),rewrite([84171(3)])]. 85014 x * a(y,x * (y * z),z) = L(x,y,z). [back_rewrite(83819),rewrite([84171(3)])]. 85028 a(x,x * y,L(x \ z,x,y)) = a(x,y,z). [back_rewrite(83804),rewrite([84171(5),84975(5)])]. 85167 ((x / y) * (z * u)) * a(z,y * x,u) = ((x / y) * z) * u. [back_rewrite(83423),rewrite([84171(5)])]. 85230 a(x,y * (z * y),u) = a(x,T(z,y),u). [back_rewrite(83292),rewrite([84171(5)])]. 85233 a(x,y,z * (z * u)) = a(x,y,u). [back_rewrite(83266),rewrite([84171(3),24596(3),84171(3)])]. 85235 a(x,y \ (z / y),u) = a(z,x,u). [back_rewrite(83255),rewrite([84171(3)])]. 85241 a(x,T(y,z \ y),u) = a(x,T(y,z),u). [back_rewrite(83245),rewrite([84171(5),85230(5),84171(5)])]. 85251 a(x,T(y \ z,z),u) = a(x,z * y,u). [back_rewrite(83221),rewrite([84171(4),85230(4),84171(5)])]. 85263 a(x,y / z,u) = a(x,y * z,u). [back_rewrite(83180),rewrite([84171(2),84171(4)])]. 85290 a(x,y * (z / y),u) = a(x,T(z,y),u). [back_rewrite(83038),rewrite([84171(3),85241(3),84171(5)]),flip(a)]. 85298 a(x,(y \ z) * z,u) = a(y,x,u). [back_rewrite(83003),rewrite([84171(3)])]. 85357 a(x \ y,z * (y \ x),y) \ 1 = a(z,x \ y,T(x,y)). [back_rewrite(82112),rewrite([84171(9)])]. 85392 (T(x,y) * z) / a(y,y * x,z) = T(y,x) \ ((y * x) * z). [back_rewrite(81564),rewrite([84171(6),85251(6),84267(5)])]. 85865 a(T(x,y),x * y,T(z,x * y)) = a(x,x * y,T(z,x * y)). [back_rewrite(72844),rewrite([84171(6),85251(6),84267(5)]),flip(a)]. 86937 T(x,y) \ ((x * y) * z) = (x \ y) * (x * z). [back_rewrite(29584),rewrite([84171(4),3954(4),85392(5)])]. 86984 ((x * y) \ z) * ((z \ x) * y) = a(x,z,y). [back_rewrite(24624),rewrite([84171(6)])]. 86989 ((x * y) \ z) * ((z \ y) * T(x,y)) = a(y,z,T(x,y)). [back_rewrite(24566),rewrite([84171(8)])]. 86999 a(x,y \ 1,z) = a(y,x,z). [back_rewrite(24189),rewrite([84171(3)])]. 87019 a(x \ y,z * (x \ y),x) = a(z,x \ y,T(y,x)) \ 1. [back_rewrite(23629),rewrite([84171(7)])]. 87102 a(x \ y,z * (x \ y),T(x,y)) = a(z,x \ y,y) \ 1. [back_rewrite(15593),rewrite([84171(7)])]. 87185 a(x,T(y,x),z) = a(x,y,z). [back_rewrite(4582),rewrite([84171(3)])]. 87186 a(T(x,y),y \ x,z) = a(x,y * x,z). [back_rewrite(4537),rewrite([84171(5),84082(5)])]. 87206 R(x,y * (z * (z * y)),u) = x. [back_rewrite(20504),rewrite([84200(5),17(10)]),flip(a)]. 87367 (x \ (y \ (y \ z))) * ((((z \ y) * y) * (x / u)) * u) = a(z,x * u,u). [back_rewrite(83213),rewrite([85263(11)])]. 87375 a(x,y,x \ z) \ 1 = a(x,y * x,z). [back_rewrite(82129),rewrite([85263(6)])]. 87376 a(x,y * x,T(z,x \ z)) = a(x,y,z / x) \ 1. [back_rewrite(82123),rewrite([85263(4)])]. 87377 a(x,y * x,x * z) = a(x,y,z) \ 1. [back_rewrite(82121),rewrite([85263(3)])]. 87830 a(x,x * y,(y \ z) * u) = a(x,x * y,(y * z) * u). [back_rewrite(35865),rewrite([85263(4)]),flip(a)]. 87988 a(x,y * x,(y \ x) * z) = a(y,x,y \ z). [back_rewrite(84378),rewrite([85298(6),84082(4)])]. 88057 (T(x \ y,y) * z) * T(T(x * y,y),z) = (x \ y) * ((x * y) * z). [back_rewrite(81596),rewrite([86937(6),3204(4)]),flip(a)]. 88170 R(x,K(y,z),K(z,y) * u) = x. [back_rewrite(50423),rewrite([87206(8)]),flip(a)]. 88394 x * (((T(T(y,x),z) * (x * u)) * w) / T(x * (T(y,z) * (x * (x * u))),w)) = x \ w. [para(4714(a,1),15(a,1,2)),flip(a)]. 88400 R(x,y,((y \ z) * z) * u) = L(x,y,u). [para(4714(a,1),148(a,1,2,2,2)),rewrite([88394(16),38445(5),57097(8),2507(3),88394(16),38534(5)]),flip(a)]. 88449 L(x,y,(z \ (z \ y)) * u) = R(x,y,u). [back_rewrite(38644),rewrite([88400(7)])]. 88465 R(x,y * z,z \ 1) = R(x,y,z). [back_rewrite(56903),rewrite([88449(8)])]. 89358 a(x,K(y,z),z \ 1) = 1. [para(17913(a,1),82978(a,1,2))]. 90470 (x * y) \ (x * z) = x \ ((x / y) * z). [para(15(a,1),15943(a,1,2,1,1)),rewrite([1091(2),3143(5),1091(5),4209(8),35645(8)]),flip(a)]. 90726 x * (y * T(z,x * y)) = (z * x) * y. [back_rewrite(70983),rewrite([90470(12),39792(4),35648(11),101(2),90470(9),3691(2),3143(8),15(6),24002(5),55776(6),79977(3)]),flip(a)]. 90841 x \ ((x / (y * z)) * y) = L(z \ 1,x,y). [back_rewrite(58412),rewrite([90470(4)])]. 90887 x \ ((x / (y * (z * u))) * ((y * z) * u)) = L(a(y,z,u),x,y * (z * u)). [back_rewrite(56231),rewrite([90470(7)])]. 90904 x \ ((x / (y * (z * u))) * ((y * u) * T(z,u))) = L(a(y,u,T(z,u)),x,y * (z * u)). [back_rewrite(56136),rewrite([90470(8)])]. 90948 L(K(x,y) * z,u,K(y,x)) = u * ((u \ K(x,y)) * z). [back_rewrite(55915),rewrite([90470(8),5005(6),24002(8)])]. 91095 L(x,y,y / z) = L(x,z,y). [back_rewrite(53065),rewrite([90470(3),55568(4)])]. 91332 L(x * (y * (z * x)),x,z) = x * ((y * z) * x). [back_rewrite(80273),rewrite([90726(4)]),flip(a)]. 91469 (x * T(y,z)) / z = (x / z) * y. [back_rewrite(21500),rewrite([91095(4),56632(3)])]. 91534 ((x * (y * z)) \ z) * T(x * y,z) = a(z,y * z,T(x,y * z)). [back_rewrite(68958),rewrite([91332(7),90470(7),72954(7),2643(4)])]. 91628 (x * y) / T(z,y) = (x / z) * y. [back_rewrite(79946),rewrite([91469(3)]),flip(a)]. 92765 (x * (y * z)) * (y * ((z * y) \ u)) = (y * z) * (((y * z) \ x) * (y * u)). [para(16(a,1),418(a,1,2,2,2)),flip(a)]. 92871 R(x,y * z,y * ((z * y) \ u)) = L(x,y * z,y * u). [back_rewrite(73876),rewrite([92765(6),57097(8)]),flip(a)]. 92882 R(x,y \ z,(z \ y) * u) = L(x,u,y * z). [back_rewrite(38476),rewrite([92871(6),16(3),52858(2)]),flip(a)]. 92926 L(T(x,y),z,y * x) = L(T(x,y),y,z). [back_rewrite(58065),rewrite([92882(5)])]. 92946 K(a(x,x * y,z),x * (x * ((y * z) / (x * ((x * y) * z))))) = 1. [hyper(27,a,21676,a)]. 92952 T(T(a(x,x * y,z),u),x * (x * ((y * z) / (x * ((x * y) * z))))) = T(a(x,x * y,z),u). [para(21676(a,1),29(a,1,1)),flip(a)]. 92963 a(x,x * y,z) \ u = a(x,y,x \ z) * u. [para(21676(a,1),5226(a,1,1,1)),rewrite([21676(12),92952(17),30512(10),46(7),84738(4),21676(13)]),flip(a)]. 92967 ((a(x,y,x \ z) / u) * a(x,x * y,z)) * u = K(a(x,x * y,z),u). [para(21676(a,1),38815(a,1,1,1)),rewrite([21676(18),15452(13),1091(9),4407(5),92963(5),1014(5),92946(19),13(11)])]. 93030 (T(x,K(y,z)) * K(z,y)) * (x \ K(y,z)) = 1. [para(4993(a,1),27619(a,1,2,1,1)),rewrite([9037(4),45(10),5005(10),12830(10),4407(8),6144(7),14(7)])]. 93714 L(x,y * (z * u),(y * z) * u) = R(x,y * (z * u),a(y,z,u)). [para(597(a,1),57033(a,2,1)),rewrite([16(6),52858(6),79784(6),52858(5),592(13)])]. 94677 T(x,R(x,y,z)) = x. [para(48247(a,1),7769(a,1,1)),rewrite([4408(4),45(3),65951(2),1708(3)])]. 94843 T(R(x,y,z) \ x,x) = R(x,y,z) \ x. [para(94677(a,1),7967(a,1,2)),rewrite([4231(6,R)]),flip(a)]. 94910 ((x * R(y,z,u)) * y) / (y * R(y,z,u)) = R(x,R(y,z,u),y). [para(94677(a,1),516(a,1,1,2)),rewrite([94677(9)])]. 94948 (R(x,y,z) \ x) * (R(x,y,z) * u) = L(x * u,x,R(x,y,z)). [back_rewrite(42834),rewrite([94843(3)])]. 95623 T(x,K(y,z)) * K(z,y) = K(z,y) * x. [para(93030(a,1),17(a,1,1)),rewrite([4155(4),6144(3),13(4)]),flip(a)]. 95624 R(K(x,y) * z,z \ K(y,x),u) = K(x,y) * z. [para(93030(a,1),22(a,1,1,1)),rewrite([13(2),3691(4),4408(4),6144(2),14(4),95623(6)]),flip(a)]. 95626 R(x,K(y,z) * u,u \ K(z,y)) = L(x,K(y,z) * u,u \ K(z,y)). [para(93030(a,1),22(a,1,2)),rewrite([95623(4),55103(6),48(7),95623(9)]),flip(a)]. 95631 L(x,K(y,z) * u,u \ K(z,y)) = x. [para(93030(a,1),104(a,1,2,2)),rewrite([95623(4),95623(6),14(7),16(6),95623(4),55103(6)]),flip(a)]. 95652 x / (K(y,z) * u) = x * (u \ K(z,y)). [para(93030(a,1),85(a,2,2)),rewrite([95623(4),95623(7),95626(8),95631(8),48(8)])]. 95681 (K(x,y) * z) \ u = (z \ K(y,x)) * u. [para(93030(a,1),166(a,1,2,1)),rewrite([95623(4),95624(5),13(4)])]. 95687 (x \ K(y,z)) * (K(z,y) * (x * (K(z,y) * (x * u)))) = (K(z,y) * x) * u. [para(93030(a,1),169(a,1,1)),rewrite([4408(4),6144(3),13(5),95623(11),4408(10),6144(7),189(10),101(9),24558(11)]),flip(a)]. 95798 R(x * K(y,z),K(z,y),u) = u * ((u \ x) * K(y,z)). [back_rewrite(70649),rewrite([95652(8),169(8)])]. 95979 ((x \ K(y,z)) * u) * K(z,T(y,u)) = x \ u. [back_rewrite(37402),rewrite([95681(3)])]. 98284 (x * (y * z)) * (a(x,y,z) * ((x * y) * z)) = (x * y) * (z * ((x * y) * z)). [para(601(a,1),209(a,1,2)),rewrite([84171(6),20692(6),45(9),54(13),189(12),101(11),84171(18),20692(18),88(14)])]. 98289 (x \ T(x \ 1,y * z)) * (((y * z) \ x) * (y * (z * x))) = a(y,z,x) \ 1. [para(601(a,1),1091(a,1,1)),rewrite([98284(7),23718(11),54309(5),6072(4,R)])]. 98840 (x * y) \ T(x,z) = y \ K(x,z). [para(52627(a,1),6591(a,1,1)),rewrite([52619(5),4408(4),45(2),14(2),16343(2),52619(8),4408(7),45(5),14(5)]),flip(a)]. 99352 L(x,y,z) * z = L(x * z,y,z). [para(2642(a,1),602(a,1,2,3)),rewrite([16(2),80766(5),52858(2),2642(6),80225(6)]),flip(a)]. 99651 x \ (y * (z * y)) = ((x \ y) * z) * y. [back_rewrite(81235),rewrite([99352(3),53170(4)])]. 99656 ((x \ y) * z) * x = T(y,x) * T(z,x). [back_rewrite(81224),rewrite([52858(2),80509(3),53170(4),72954(3)]),flip(a)]. 99742 K(a(x,y \ z,T(y,z)),x * z) = 1. [back_rewrite(80568),rewrite([99352(2),72562(8)]),flip(a)]. 100197 L(x \ y,x,y * z) = (((y * x) \ (y / z)) * z) * y. [back_rewrite(18690),rewrite([99651(8),82165(6)])]. 100284 T(x,y) * T(z * y,y) = T((x * y) * T(z,y),y). [back_rewrite(68763),rewrite([99656(4)])]. 100316 T((x * y) * z,x) = y * (z * x). [back_rewrite(23766),rewrite([99656(3),4525(4),90(2)]),flip(a)]. 101793 x * T(y \ 1,z) = x / T(y,z). [para(19049(a,1),16981(a,2,2)),rewrite([64241(15),52619(3),16(10)])]. 103664 x * (y \ (z \ 1)) = x / (z * y). [para(64186(a,1),85(a,1)),rewrite([189(7),4578(6),4613(8),39792(6),16(7)]),flip(a)]. 103756 x / (y * (z * x)) = (x * z) \ (x / y). [back_rewrite(82190),rewrite([103664(5)])]. 103820 R(x,y,z \ 1) = L(x,z,y). [back_rewrite(58091),rewrite([103664(4),10229(4),10279(4)])]. 103993 ((x * y) \ (x / z)) * z = L(y \ 1,x,z). [back_rewrite(52635),rewrite([103756(3)])]. 104117 R(x,y,z) = L(x,y,z). [back_rewrite(88465),rewrite([103820(4),16256(2),52858(1)]),flip(a)]. 104458 L(x \ y,x,y * z) = L(x \ y,y,z). [back_rewrite(100197),rewrite([103993(7),80509(7),3143(6)])]. 105327 L(x * K(y,z),u,K(z,y)) = u * ((u \ x) * K(y,z)). [back_rewrite(95798),rewrite([104117(4),52858(4)])]. 105371 (L(x,y,z) \ x) * (L(x,y,z) * u) = L(x * u,x,L(x,y,z)). [back_rewrite(94948),rewrite([104117(1),104117(3),104117(7)])]. 105379 L(x,y,L(y,z,u)) = x. [back_rewrite(94910),rewrite([104117(1),32180(3),104117(4),17(6),104117(1),104117(2),52858(2)]),flip(a)]. 105551 L(x,y * (z * u),(y * z) * u) = L(x,a(y,z,u),y * (z * u)). [back_rewrite(93714),rewrite([104117(9),52858(9)])]. 105587 L(x,y,z \ u) = L(x,y,z * u). [back_rewrite(92882),rewrite([104117(4),55725(4)])]. 105864 L(x,y,K(z,u)) = x. [back_rewrite(88170),rewrite([104117(4),53895(4)])]. 106927 x * (L(x,y,z) \ x) = L(x,y,z). [back_rewrite(70731),rewrite([104117(6),52858(6),57044(6),52858(5),57044(5)])]. 106960 (x * y) / (z * (T(z,u) * y)) = x / (z * T(z,u)). [back_rewrite(70674),rewrite([104117(6),52858(6),57670(6)]),flip(a)]. 107041 ((x * y) * a(z,x,y)) \ ((z * x) * y) = T(T(z,x * y),a(z,x,y)). [back_rewrite(69080),rewrite([104117(7),34275(7)]),flip(a)]. 107091 L(T(x,y * (z * x)),y * z,a(x,y,z)) = T(T(x,y * z),a(x,y,z)). [back_rewrite(68979),rewrite([104117(6),107041(12)])]. 107917 (T(x,y * (z * y)) * u) / (y * (z * (y * u))) = L(y \ (z \ (y \ x)),u,y * (z * y)). [back_rewrite(57428),rewrite([104117(14),52858(14)])]. 108469 (L(x / y,y,z) * (y * (z * y))) \ ((x * z) * y) = a(y * z,(y * z) * (x * z),y). [back_rewrite(46495),rewrite([104117(2)])]. 108634 (x * (y * z)) / ((z * x) * y) = K(x * y,L(z,x,y)). [back_rewrite(42662),rewrite([104117(2),56240(3),104117(7)])]. 109339 L(x,y,z) * (y * (z * y)) = (x * (y * z)) * y. [back_rewrite(18750),rewrite([104117(2),52858(2),53163(2)])]. 109537 (x * y) \ (z * y) = T(x \ z,y). [back_rewrite(10592),rewrite([104117(4),34275(4),92(2)]),flip(a)]. 109828 (L(x,y,z) \ x) * (L(x,y,z) * u) = x * u. [back_rewrite(105371),rewrite([105379(8)])]. 110184 (x * (y \ L(y,x,z))) * a(y,z * (y \ (x / y)),T(z,y \ (x / y)) \ y) = x. [back_rewrite(63757),rewrite([105587(3),57044(3),52858(2),52942(2)])]. 110241 x * ((x \ (y \ z)) * y) = L(T(z,y),y,x). [back_rewrite(55404),rewrite([105587(3),92926(3)]),flip(a)]. 110290 L(x,y,z / u) = L(x,y,u * z). [back_rewrite(53484),rewrite([105587(4),1014(3)])]. 110366 ((x \ y) * z) \ T(y,x) = L(z \ x,x,y). [back_rewrite(7982),rewrite([105587(3),104458(3)]),flip(a)]. 110378 x * ((x \ y) * K(z,u)) = y * K(z,u). [back_rewrite(105327),rewrite([105864(4)]),flip(a)]. 110402 x * ((x \ K(y,z)) * u) = K(y,z) * u. [back_rewrite(90948),rewrite([105864(4)]),flip(a)]. 110793 a(x * y,(x * y) * (z * y),x) = a(z,y,x). [back_rewrite(108469),rewrite([109339(5),23697(3),101(4),99656(3),4525(4),90(2),23718(5),86984(5),84171(1)]),flip(a)]. 110800 T(a(x,y,z),y) = a(z,x \ y,y). [back_rewrite(58458),rewrite([109339(6),3143(4),109537(7),4408(5),86984(5),84171(1),110793(8),84171(4)])]. 110804 (x \ (((y * (x * z)) \ x) * ((z * x) * y))) * K(L(y,x,z),x * (z * x)) = 1. [back_rewrite(57173),rewrite([109339(4),35803(7)])]. 110982 (x \ y) * T(z,y) = (x \ z) * y. [back_rewrite(68754),rewrite([109537(3),90(3)]),flip(a)]. 111960 a(x,x * K(y,z),K(z,y) * u) = 1. [back_rewrite(9444),rewrite([110402(6),8296(4),46(1)]),flip(a)]. 112152 a(x,y * x,T(z,y * x)) = L(x,z,y) \ x. [back_rewrite(91534),rewrite([110982(6),90470(4),90841(4),65748(4)]),flip(a)]. 112164 a(x,y,T(z,x)) = a(z,y,x). [back_rewrite(86989),rewrite([110982(5),86984(5)]),flip(a)]. 112420 ((x / y) * z) * y = x * T(z,y). [back_rewrite(81309),rewrite([112164(6),85167(6)])]. 112421 a(x \ y,(y \ x) * z,T(y,x)) = a(y,x * z,x). [back_rewrite(81016),rewrite([112164(8)])]. 112508 a(x,y,z * x) \ 1 = a(z,y * x,x). [back_rewrite(23663),rewrite([112164(3)]),flip(a)]. 112766 a(x,y,x \ z) * T(a(x,x * y,z),u) = K(a(x,x * y,z),u). [back_rewrite(92967),rewrite([112420(7)])]. 112951 (x * (y / z)) * z = z * ((z \ x) * y). [back_rewrite(10393),rewrite([112420(4),23697(4),110982(3)]),flip(a)]. 113434 a(x,y * z,z) = a(x,z,z * y). [back_rewrite(87367),rewrite([112951(8),41919(6),84365(9)]),flip(a)]. 113707 a(x,y,z * x) \ 1 = a(x,z,x * y). [back_rewrite(112508),rewrite([113434(6),84171(6)])]. 113933 (x * y) \ K(z,u) = y \ (x \ K(z,u)). [para(105864(a,1),6591(a,1,1)),rewrite([6144(3),14(3),6144(7),14(7)]),flip(a)]. 114859 (x * y) * T(T(z,y),u) = (x * T(z,u)) * y. [para(62444(a,1),136(a,2)),rewrite([110982(4),136(5)]),flip(a)]. 114936 (x * y) * T(z,y) = (x * z) * y. [para(64397(a,1),62444(a,1,2,1)),rewrite([114859(23),64397(20)])]. 115135 (x \ y) * ((x * y) * z) = y * (T(y,x) * z). [back_rewrite(88057),rewrite([114936(7),100284(5),114936(4),4505(2),547(2),4209(3),547(2),32749(3)]),flip(a)]. 115350 L(a(x,y,T(z,y)),u,x * (z * y)) = L(a(x,z,y),u,x * (z * y)). [back_rewrite(90904),rewrite([114936(6),90887(7)]),flip(a)]. 115440 K(x * (y * (z * z)),z) = K(x * y,z). [back_rewrite(68786),rewrite([114936(3),18043(3)]),flip(a)]. 115458 (x \ y) * (z * x) = T(y * z,x). [back_rewrite(68727),rewrite([114936(3),79991(7),115440(5),16716(4)]),flip(a)]. 115485 a(x,y,T(z,y)) = a(x,z,y). [back_rewrite(35536),rewrite([114936(7),105551(7),115350(6),6018(5)]),flip(a)]. 116274 L(x,y,z) \ x = a(x,z,y * x). [back_rewrite(112152),rewrite([115485(4),52858(3)]),flip(a)]. 116288 a(x,T(y,z),y * z) = a(y,x,y * z). [back_rewrite(85865),rewrite([115485(5),84171(3),115485(7)])]. 116749 a(x,y,z * x) * (L(x,z,y) * u) = x * u. [back_rewrite(109828),rewrite([116274(2)])]. 116751 x * a(x,y,z * x) = L(x,z,y). [back_rewrite(106927),rewrite([116274(2)])]. 116872 T(x,a(x,y,z * x)) = x. [back_rewrite(28511),rewrite([116274(2)])]. 118635 L(x,K(y,z),y * (u * y)) = x. [para(52858(a,1),54785(a,2)),rewrite([54785(5),105864(8)])]. 118636 L(x,y,z * T(y,u)) = L(x,z,T(y,u)). [para(54785(a,1),55660(a,1,1)),rewrite([118635(4)])]. 118653 L(x,K(y,z),T(y \ u,w)) = x. [para(625(a,1),54785(a,2,3,2)),rewrite([118636(9),55660(8),2507(6)]),flip(a)]. 118966 (x * T(x,y)) \ z = T(x,y) \ (x \ z). [para(16875(a,1),107917(a,1,1,1,2,2)),rewrite([547(2),33507(9),21062(7),106960(8),7616(6),6144(8),35223(8),16875(10),547(8),57670(9)])]. 118967 (x \ (x \ K(y,x))) * z = T(x,y) \ (x \ z). [para(16985(a,1),107917(a,1,1,1,2,2)),rewrite([33497(7),106960(8),7616(6),118966(3),6144(6),9490(7),12473(5),16985(9),57670(10)]),flip(a)]. 119011 (x \ T(x \ 1,y)) * z = T(x,y) \ (x \ z). [back_rewrite(17906),rewrite([118967(9)])]. 119022 T(x,y * z) \ (x \ (((y * z) \ x) * (y * (z * x)))) = a(y,z,x) \ 1. [back_rewrite(98289),rewrite([119011(11)])]. 119325 a(x,y,x \ K(z,x)) = 1. [para(23(a,1),75804(a,1,3,2)),rewrite([98840(3)])]. 121557 x \ (L(x,y,z) * (a(y,z,(y * z) \ x) * u)) = L(u,L(x,y,z),a(y,z,(y * z) \ x)). [para(16(a,1),588(a,1,1)),rewrite([53598(4),53598(14),52858(12)])]. 122955 x * (y \ K(z,y)) = x / T(y,z). [para(89358(a,1),209(a,1,1)),rewrite([1014(6),75750(4),45(4),1014(6),12473(4),89358(9),88(7)]),flip(a)]. 123069 T(x,y) \ (x \ z) = x \ (T(x,y) \ z). [para(634(a,1),50365(a,1)),rewrite([547(2),118966(3)])]. 123095 x \ (K(y,z) * u) = (x \ K(y,z)) * u. [para(634(a,1),105864(a,1)),rewrite([95681(3),6144(5)]),flip(a)]. 123146 a(x,y,z) \ 1 = z \ L(z,x,y). [back_rewrite(119022),rewrite([123069(9),26952(8),90470(4),23697(3),55776(4),6022(3)]),flip(a)]. 128856 x / (T(y,z) * ((y \ L(y,u,w)) * (T(y,z) \ x))) = a(y,w,u * y). [para(26839(a,1),19479(a,1,2,2,2,1,1)),rewrite([116274(10)])]. 129028 x / (T(y,z) * (a(y,u,w * y) * (T(y,z) \ x))) = y \ L(y,w,u). [para(26839(a,1),19536(a,1,2,1,1)),rewrite([116274(3)])]. 131120 T(x,a(x,y,z)) = x. [para(18(a,1),116872(a,1,2,3))]. 131121 a(x,y,z * x) \ L(x,y,z) = x. [para(116872(a,1),23(a,2)),rewrite([116751(5),52858(3)])]. 131133 T(x,a(y,z,x)) = x. [para(4505(a,1),116872(a,1,2,3)),rewrite([112164(2),84171(1)])]. 131212 T(a(x,y,z),x) = a(x,y,z). [hyper(26,a,131120,a)]. 131213 T(T(x,y),a(x,z,u)) = T(x,y). [para(131120(a,1),29(a,1,1)),flip(a)]. 131234 T(x,a(x,y,z) \ x) = x. [para(131120(a,1),7769(a,1,1))]. 131246 K(a(x,y,z),x) = 1. [para(131120(a,1),16687(a,1,2)),rewrite([47(1)]),flip(a)]. 131352 L(T(x,y * (z * x)),y * z,a(x,y,z)) = T(x,y * z). [back_rewrite(107091),rewrite([131213(10)])]. 133057 L(a(x,x * y,z),u,x * ((x \ y) * z)) = L(a(x,y * x,z),u,y * z). [para(84525(a,1),17(a,1,1)),rewrite([989(6),58434(6),87375(4)]),flip(a)]. 133073 a(x,y * x,z) * a(x,y,x \ z) = 1. [para(1607(a,1),84525(a,1,2)),rewrite([133057(7),1607(5)])]. 133580 x / a(y,z,x) = a(y,z,x) \ x. [para(131133(a,1),7616(a,1,1))]. 133716 K(a(x,y,z),y) = 1. [para(84171(a,1),131246(a,1,1))]. 133728 a(x,y \ z,z) = a(y,z,x). [hyper(28,a,133716,a),rewrite([110800(2)])]. 133748 a(x \ y,z * (x \ y),T(x,y)) = a(x,y,z) \ 1. [back_rewrite(87102),rewrite([133728(7)])]. 134004 (x * y) / T(x,z) = x * (y / T(x,z)). [para(119325(a,1),209(a,1,1)),rewrite([122955(5),45(5),122955(6),119325(9),88(8)])]. 134179 ((x \ y) * z) * L(z \ x,x,y) = T(y,x). [para(4505(a,1),1251(a,1,2,2)),rewrite([80501(4),81056(5),134004(9),2711(8),110366(6),4505(7)])]. 135160 T(x * (y / z),z) = (z \ x) * y. [para(4505(a,1),21316(a,1,1,2)),rewrite([90(4),10229(6),112420(7),15(7),110982(6)])]. 135282 x \ (L(x,y,z) * u) = (x \ L(x,y,z)) * u. [back_rewrite(57568),rewrite([135160(4)]),flip(a)]. 135292 (x \ L(x,y,z)) * (a(y,z,(y * z) \ x) * u) = L(u,L(x,y,z),a(y,z,(y * z) \ x)). [back_rewrite(121557),rewrite([135282(7)])]. 136169 a(x,y,x * z) \ 1 = a(x,y * x,z). [para(15(a,1),87019(a,1,1)),rewrite([15(2),15(4),4209(4),84171(4)]),flip(a)]. 136171 a(x \ y,z * (y \ x),T(y,x)) \ 1 = a(z,x \ y,x). [para(18(a,1),87019(a,1,2)),rewrite([84171(2),4155(4),84171(7)]),flip(a)]. 136177 a(x \ (y / x),z * (x \ (y / x)),x) = a(y,z,x \ y) \ 1. [para(92(a,1),87019(a,2,1,3)),rewrite([85235(10)])]. 136185 a(x \ 1,y * x,z * x) = a(y,z,x) \ 1. [para(1091(a,1),87019(a,1,1)),rewrite([1091(4),1014(5),85263(5),1091(7),1708(9),86999(9),112164(7),84171(6)])]. 136188 a(x \ 1,y * x,z) = a(x,y * x,z). [para(1829(a,1),87019(a,1,1)),rewrite([1829(4),1014(5),85263(4),1829(6),2643(8),86999(8),87375(8)])]. 136196 a(x,y * z,y) \ 1 = a(z,y \ x,y). [para(4505(a,1),87019(a,1,2)),rewrite([87185(4),84171(2),4408(4),84171(7),112421(7)]),flip(a)]. 136206 a(x * y,z * (x * y),y \ 1) = a(y,x \ z,x). [para(12372(a,1),87019(a,2,1,3)),rewrite([4408(4),45(2),90(2),4408(5),45(3),90(3),4408(10),45(8),90(8),136196(10)])]. 136217 a(T(x \ y,y),z * T(x \ y,y),T(x,y)) = a(z,y * x,T(y,x)) \ 1. [para(23380(a,1),87019(a,2,1,3)),rewrite([4278(2),4278(4),4278(9),85251(11)])]. 136223 a(x \ y,x * ((x \ z) * y),x) = a(z * x,x \ y,T(y,x)) \ 1. [para(169(a,1),87019(a,1,2))]. 136232 a(x,y,z * (x * x)) \ 1 = a(z,x,y) \ 1. [para(22354(a,1),87019(a,2,1,3)),rewrite([22283(6),15(3),15(2),89(1),22283(6),15(3),15(2),89(1),112164(4),113434(3),84171(3),87377(3),84171(1),22283(9),15(6),15(5),89(4),84171(6)]),flip(a)]. 136306 a(x,y * x,z * x) = a(y,z,x) \ 1. [back_rewrite(136185),rewrite([136188(5)])]. 138261 (T(T(x,y),z) * u) * y = T(T(x,z) * (y * u),y). [para(1466(a,1),4209(a,2)),rewrite([4525(4)]),flip(a)]. 138368 (T(x,y) * z) * y = T(x * (y * z),y). [para(64397(a,1),1466(a,1,1,1,1)),rewrite([138261(23),64397(20)])]. 139543 a(x,y,x \ z) = a(x,y,x * z). [para(133073(a,1),15(a,1,2)),rewrite([84799(4),84171(2)]),flip(a)]. 139565 T(a(x,y,x * z),a(x,y * x,z)) = a(x,y,x * z). [para(133073(a,1),12386(a,1,2,2)),rewrite([139543(2),48(6),139543(7)])]. 139577 a(a(x,y,x * z),a(x,y * x,z),u) \ u = a(x,y * x,z) * (a(x,y,x * z) * u). [para(133073(a,1),162(a,1,1,1)),rewrite([13(2),139543(4),84171(5),133580(6),139543(10)])]. 139595 T(a(x,y,x * z),(a(x,y * x,z) \ a(x,y,x * z)) * u) = T(a(x,y,x * z),u). [para(133073(a,1),6973(a,1,1,2)),rewrite([139543(2),4407(5),136169(4),139543(7),115458(10),16(8),139543(5),139543(9)]),flip(a)]. 139610 L(x,a(y,z,y * u),a(y,z * y,u)) = x. [para(133073(a,1),27459(a,1,3,2)),rewrite([139543(4),14(6),52858(5)])]. 139615 x / a(y,z,y * u) = x * a(y,z * y,u). [para(133073(a,1),57033(a,2,1,2)),rewrite([139543(7),52858(8),139610(8),14(5),139543(5)]),flip(a)]. 139762 a(x,y,x * z) * T(a(x,x * y,z),u) = K(a(x,x * y,z),u). [back_rewrite(112766),rewrite([139543(2)])]. 139811 a(x,y * x,(y \ x) * z) = a(x,y,y * z). [back_rewrite(87988),rewrite([84171(6),84069(6)])]. 141555 T(x,y) * ((z / (x * T(x,y))) * (x * (T(x,y) * u))) = x * ((K(x,y) * z) * u). [para(7416(a,1),15(a,1,2)),rewrite([24002(5),38208(3)]),flip(a)]. 141573 x * (((K(x,y) * z) * u) * x) = (T(x,y) * z) * (u * x). [para(7416(a,1),4209(a,1,1)),rewrite([100316(5),141555(13),101(9)]),flip(a)]. 146366 a(x,y,x * z) \ ((a(x,y * x,z) \ a(x,y,x * z)) * u) = a(x,y,x * z) * u. [para(139595(a,1),2711(a,1,2)),rewrite([91628(10),139615(8),4505(8),139565(5)]),flip(a)]. 147584 T(T(x,y),z) / L(x,u,w) = L(x,u,w) \ T(T(x,y),z). [para(26839(a,1),10402(a,1,1,1,1))]. 147739 L(x,y,z) \ T(T(x,y),z) = K(y * z,(x \ y) * z). [back_rewrite(58399),rewrite([147584(4)])]. 151591 x \ (a(x,y,z) \ x) = a(x,y,z) \ 1. [para(131234(a,1),2711(a,1,2)),rewrite([3666(3)]),flip(a)]. 151649 x / (T(y,z) * (a(y,u,w) * (T(y,z) \ x))) = a(y,u,w) \ 1. [para(131234(a,1),19536(a,1,2,1,1)),rewrite([4408(4),4505(4),131212(3),151591(10)])]. 151677 x \ L(x,y,z) = a(x,z,x * y). [back_rewrite(129028),rewrite([151649(8),113707(4),52858(3)]),flip(a)]. 151689 a(x,y,x * z) * (a(z,y,(z * y) \ x) * u) = L(u,L(x,z,y),a(z,y,(z * y) \ x)). [back_rewrite(135292),rewrite([151677(2)])]. 151698 a(x,y * x,z) = a(x,y,z * x). [back_rewrite(128856),rewrite([151677(3),151649(8),136169(4)])]. 151701 a(x,y,y * z) = a(z,x,y) \ 1. [back_rewrite(123146),rewrite([151677(5),84171(5)]),flip(a)]. 151723 (x * a(y,z,y * x)) * a(y,z * (y \ (x / y)),T(z,y \ (x / y)) \ y) = x. [back_rewrite(110184),rewrite([151677(2)])]. 151813 a(x,y,x * z) \ ((a(x,y,z * x) \ a(x,y,x * z)) * u) = a(x,y,x * z) * u. [back_rewrite(146366),rewrite([151698(4)])]. 151860 a(x,y,((y \ x) * z) * x) = a(x,y,y * z). [back_rewrite(139811),rewrite([151698(4)])]. 151925 a(a(x,y,x * z),a(x,y,z * x),u) \ u = a(x,y,z * x) * (a(x,y,x * z) * u). [back_rewrite(139577),rewrite([151698(4),151698(8)])]. 151954 a(x,y,z * (x * x)) = a(y,z,x) \ 1. [back_rewrite(136306),rewrite([151698(3),4578(2)])]. 152016 a(x,y * z,T(y,z)) \ 1 = a(x,y * z,y). [back_rewrite(136217),rewrite([151698(7),73156(6),89(3),6018(3),84171(3),85251(3)]),flip(a)]. 152025 a(x,y * z,T(y,z)) = a(z,y \ x,y). [back_rewrite(136206),rewrite([151698(6),115458(5),13(3),84171(3)])]. 152039 a(x,y,z * x) = a(y,z,x \ y) \ 1. [back_rewrite(136177),rewrite([151698(6),16(5),84171(4),133728(4),85263(2),151698(2)])]. 152050 a(x,y,z \ x) = a(z,x,y) \ 1. [back_rewrite(133748),rewrite([151698(5),37224(4),28991(3),84171(4),115485(4),84171(2)])]. 152277 a(x,y,z / x) \ 1 = a(x,y,x * z). [back_rewrite(87376),rewrite([151698(4),33781(3),16985(2),90(2)]),flip(a)]. 152280 a(T(x,y),y \ x,z) = a(x,y,z * x). [back_rewrite(87186),rewrite([151698(5)])]. 152337 a(x,x * y,z) = a(x,y,z * x). [back_rewrite(84641),rewrite([151698(2)]),flip(a)]. 152342 a(x,y \ x,z) = a(x,y,z * x). [back_rewrite(84082),rewrite([151698(4)])]. 152407 a(x,y,z) \ 1 = a(z,y,x). [back_rewrite(136232),rewrite([151954(3),4408(5),45(3),14(3),84171(2)]),flip(a)]. 152415 a(x,y * z,y) = a(x,y,z * y). [back_rewrite(152016),rewrite([152025(3),152407(4),3954(2),152337(2),84171(2)]),flip(a)]. 152485 a(x,y * (x * z),z) = a(z,x,(y * z) * x). [back_rewrite(136223),rewrite([152415(5),99656(4),84171(5),3954(5),152337(5),138368(4),90(2),112164(4),84171(3),152407(9),152280(7),84171(6)])]. 152683 a(x,y,x * z) * T(a(x,y,z * x),u) = K(a(x,y,z * x),u). [back_rewrite(139762),rewrite([152337(4),152337(8)])]. 153027 a(x,K(y,z),(K(z,y) * u) * x) = 1. [back_rewrite(111960),rewrite([152337(5)])]. 153030 a(x,y,y * (z * y)) = a(y,z,x). [back_rewrite(110793),rewrite([152337(5),85233(5),113434(3),84171(3),151698(3),101(2),84171(3),84171(4)])]. 153147 a(x,y,((y \ z) * u) * x) = a(x,y,((y * z) * u) * x). [back_rewrite(87830),rewrite([152337(4),152337(8)])]. 153242 a(x,y,z) = a(x,z,y). [back_rewrite(85028),rewrite([152337(4),80509(3),4505(2),56215(3),112164(2),84171(1),152407(3)])]. 153314 a(x,y,x * (z \ u)) = a(x,y,x * (z * u)). [back_rewrite(82939),rewrite([153242(3),153242(6)])]. 153371 a(x,K(y,z),K(z,y) * u) = a(x,K(y,z),K(y,z) * u). [back_rewrite(48772),rewrite([153242(4),84171(4),153242(8),84171(8)])]. 153473 a(x,y,z / x) = a(x,y,x * z). [back_rewrite(152277),rewrite([152407(4),84171(2),153242(2),84171(2)])]. 153478 a(x,y,z \ x) = a(x,y,z). [back_rewrite(152050),rewrite([84171(3),153242(3),152407(5),84171(3),153242(3),84171(3)])]. 153484 a(x,y,z * x) = a(x,y,z). [back_rewrite(152039),rewrite([153478(4),153242(3),84171(3),152407(5),84171(3),153242(3),84171(3)])]. 153502 a(x,y,y * z) = a(x,y,z). [back_rewrite(151701),rewrite([84171(3),153242(3),152407(5),84171(3),153242(3),84171(3)])]. 153528 a(x,y,x * z) = a(z,x,y). [back_rewrite(136196),rewrite([153242(2),153502(2),152407(3),84171(1),153242(1),84171(1),153242(3),84171(3),139543(3)]),flip(a)]. 153530 a(x,y,(z / y) * (x * y)) = a(x,y,z). [back_rewrite(136171),rewrite([153242(5),84171(5),152280(5),80501(3),84171(4),152407(6),84171(4),153242(4),84171(4),153242(6),84171(6),139543(6),153528(6),84171(5)])]. 153607 a(x,T(y,z),y \ z) = a(y,z,x). [back_rewrite(85357),rewrite([153242(4),84171(4),152342(4),80501(3),84171(4),153530(4),152407(3),84171(1),153242(1),84171(1),153242(4)]),flip(a)]. 153757 a(x,y,z) * (a(x,y,z) * u) = u. [back_rewrite(151925),rewrite([153528(2),84171(1),153242(1),153484(3),1300(3),45(2),153484(2),153528(3),84171(2),153242(2)]),flip(a)]. 153764 a(x,y,z) \ u = a(x,y,z) * u. [back_rewrite(151813),rewrite([153528(2),84171(1),153242(1),153484(3),153528(4),84171(3),153242(3),46(4),13(3),153528(4),84171(3),153242(3)])]. 153769 a(x,y,z) * L(x,y,z) = x. [back_rewrite(131121),rewrite([153484(2),153764(3)])]. 153777 a(x,y,(y \ x) * z) = a(x,y,z). [back_rewrite(151860),rewrite([153484(4),153502(5)])]. 153815 a(x,y,z * y) = a(x,y,z). [back_rewrite(153030),rewrite([153502(3),153242(3),84171(3)])]. 153874 a(x,y,z * (x * y)) = a(x,z,y). [back_rewrite(152485),rewrite([153242(3),84171(6),153484(6),153815(5),153242(4)])]. 156427 K(a(x,y,z),x * z) = 1. [back_rewrite(99742),rewrite([153242(3),153607(3),153242(1),84171(1)])]. 157152 a(x,y,z * (u / z)) = a(x,y,T(u,z)). [back_rewrite(85290),rewrite([153242(3),153242(5)])]. 157169 a(x,y,z \ (u / z)) = a(x,u,y). [back_rewrite(85235),rewrite([153242(3),84171(4)])]. 157230 x * a(x,y,z) = L(x,y,z). [back_rewrite(85014),rewrite([153242(3),153874(3),84171(1)])]. 157238 L(x,y,a(y,z,u)) = x. [back_rewrite(84982),rewrite([153242(3),153874(3),84171(1)])]. 157958 L(x,y,z) * a(x,y,z) = x. [back_rewrite(151723),rewrite([153528(2),157230(2),153478(9),153242(8),116288(8),84171(5),153502(5),139543(4),153528(4),84171(3),153242(3),153473(3),153528(3)])]. 158059 a(x,y,(y \ z) * u) = a(x,y,(y * z) * u). [back_rewrite(153147),rewrite([153484(4),153484(7)])]. 158117 a(x,K(y,z),K(z,y) * u) = 1. [back_rewrite(153027),rewrite([153484(5)])]. 158223 a(x,y,z) * T(a(x,y,z),u) = K(a(x,y,z),u). [back_rewrite(152683),rewrite([153528(2),84171(1),153242(1),153484(3),153484(6)])]. 158546 a(x,y,z) * (L(x,y,z) * u) = x * u. [back_rewrite(116749),rewrite([153484(2),52858(2)])]. 158552 L(x,y,z) \ x = a(x,y,z). [back_rewrite(116274),rewrite([153484(4),153242(3)])]. 158590 a(x,y,K(z,u)) = 1. [back_rewrite(153371),rewrite([158117(4),153502(5),153242(3)]),flip(a)]. 158938 a(x,y,z \ u) = a(x,y,z * u). [back_rewrite(153314),rewrite([153528(3),84171(2),153242(2),153528(5),84171(4),153242(4)])]. 158992 a(x,y,z) * (a(y,z,(z * y) * x) * u) = L(u,L(x,y,z),a(y,z,(z * y) * x)). [back_rewrite(151689),rewrite([153528(2),84171(1),153242(1),84171(4),158938(4),52858(7),84171(10),158938(10)])]. 160232 a(x,y,(y * x) * z) = a(x,y,z). [back_rewrite(153777),rewrite([158059(3)])]. 160751 a(x,y,T(z,u)) = a(x,y,z). [back_rewrite(157169),rewrite([158938(3),157152(3),153242(3)])]. 161700 L(x,a(y,z,u),L(y,z,u)) = x. [back_rewrite(158992),rewrite([160232(4),153242(2),84171(2),153757(4),160232(4),153242(2),84171(2),52858(3)]),flip(a)]. 163437 (x * y) * K(z,u) = x * (y * K(z,u)). [para(158590(a,1),54(a,1,2)),rewrite([14(5)]),flip(a)]. 163614 (x \ K(y,z)) * (K(z,y) * u) = x \ u. [back_rewrite(95979),rewrite([163437(6),65880(5)])]. 163693 (K(x,y) * z) * u = K(x,y) * (z * u). [back_rewrite(95687),rewrite([163614(9),15(5)]),flip(a)]. 163798 (T(x,y) * z) * (u * x) = T(x,y) * ((z * u) * x). [back_rewrite(141573),rewrite([163693(3),38770(4),90(5),33180(4)]),flip(a)]. 165291 a(x,y,z) * (u * L(x,y,z)) = x * T(u,L(x,y,z)). [para(90(a,1),158546(a,1,2))]. 167247 a(x,y,z) * (((u * x) \ a(x,y,z)) * (x * T(u,L(x,y,z)))) = 1. [para(158546(a,1),110804(a,1,2,2)),rewrite([153769(4),157958(7),153764(7),161700(10),157230(9),163437(10),163437(9),163437(8),16716(7)])]. 168431 K(a(x,y,z),T(y,x)) = 1. [para(4505(a,1),156427(a,1,2)),rewrite([84171(2),153242(2),84171(2),158938(2),153528(2),84171(1)])]. 170607 T(x / (x * y),K(y,x)) * (y * z) = K(y,x) * z. [para(24764(a,1),15(a,1,2)),rewrite([38208(3)]),flip(a)]. 170861 a(x,y,z) * (L(T(x,u),y,z) * w) = x * (K(L(x,y,z),u) * w). [para(24764(a,1),158546(a,1,2)),rewrite([30(3),170607(14)])]. 173117 K(a(x,y,z),T(y,u)) = 1. [para(13425(a,1),168431(a,1,2)),rewrite([153242(5),84171(5),160751(5),160751(4),153242(3),84171(3),158938(3),14(2),153242(1),84171(1)])]. 177098 K(x,T(a(x,y,z),u)) = 1. [para(173117(a,1),4993(a,1,1)),rewrite([84171(3),37242(4),13(5)])]. 181313 T(x,T(a(x,y,z),u)) = x. [hyper(28,a,177098,a)]. 181315 T(T(a(x,y,z),u),x) = T(a(x,y,z),u). [para(177098(a,1),16623(a,1,2)),rewrite([14(5)])]. 183896 K(x * (y * z),z) = K(x * y,L(z,x,y)). [para(136(a,1),2925(a,1,2)),rewrite([101(4),99656(3),4525(4),90(2),108634(5),16568(7),58035(6)]),flip(a)]. 184265 L(x,y,z * (u * z)) = L(x,y,T(u,z)). [para(90(a,1),2507(a,1,3,2))]. 184282 L(x,y,z * (u * (z * w))) = L(x,y,u * w). [para(169(a,1),2507(a,1,3,2)),rewrite([23711(5),115135(4),65408(4),105587(6)])]. 184298 L(x,y,T(z,u)) = L(x,y,z). [para(18848(a,1),2507(a,2)),rewrite([2507(7),184282(5),8679(3),184265(4)]),flip(a)]. 186144 L(x,K(y,z),y * u) = x. [back_rewrite(118653),rewrite([184298(4),105587(3)])]. 187171 T(T(x,y),z) / (x * y) = y \ K(x,z). [para(2644(a,1),7616(a,1,1)),rewrite([98840(7)])]. 193371 T(x,L(x,y,z) * u) = T(x,u). [para(2645(a,1),55660(a,1,1)),rewrite([55660(3)]),flip(a)]. 193392 x * (K(L(x,y,z),u) * w) = T(x,u) * w. [para(2645(a,1),158546(a,1,2,1)),rewrite([193371(3),84171(2),153242(2),160751(2),153242(1),84171(1),170861(5),193371(7)])]. 194121 L(x,y,a(x,z,u)) = x. [para(181313(a,1),134179(a,2)),rewrite([52858(10),184298(10),157238(9),169(8),110241(8),181313(3),52858(3),184298(3)])]. 196290 L(x,K(y,z),u * w) = x. [para(11282(a,1),186144(a,1,3)),rewrite([105587(5),1014(4),110290(3)])]. 196788 L(T(x,y),z,a(x,u,w)) = T(x,y). [para(194121(a,1),30(a,1,1)),flip(a)]. 196821 (x * y) \ a(y,z,u) = y \ (x \ a(y,z,u)). [para(194121(a,1),6591(a,1,1)),rewrite([153764(3),14(3),153764(7),14(7)]),flip(a)]. 196855 T(x,y * (z * x)) = T(x,y * z). [back_rewrite(131352),rewrite([196788(6)])]. 196856 a(x,y,z) * ((x \ (u \ a(x,y,z))) * (x * T(u,L(x,y,z)))) = 1. [back_rewrite(167247),rewrite([196821(4)])]. 196936 T(x,L(y,x,z)) = T(x,y). [back_rewrite(56831),rewrite([196855(4),16(2)]),flip(a)]. 197293 K(L(x,y,z),y) = K(x,y). [para(196936(a,1),16687(a,1,2)),rewrite([16687(2)]),flip(a)]. 198001 K(L(x,y,z),z) = K(x,z). [para(52858(a,1),197293(a,1,1))]. 198088 K(x * (y * z),z) = K(x * y,z). [back_rewrite(80004),rewrite([198001(3)]),flip(a)]. 198118 K(x * y,L(z,x,y)) = K(x * y,z). [back_rewrite(183896),rewrite([198088(3)]),flip(a)]. 198251 K(x * y,(z \ x) * y) = K(z,x * y). [back_rewrite(58518),rewrite([198118(5),17781(4)]),flip(a)]. 198284 L(x,y,z) \ T(T(x,y),z) = K(x,y * z). [back_rewrite(147739),rewrite([198251(8)])]. 204095 (x * K(y,z)) * u = x * (K(y,z) * u). [para(6144(a,1),104(a,1,2,1)),rewrite([163693(6),8296(7)]),flip(a)]. 208399 T(T(x,K(y,z)),u) = T(x,K(y,z) * u). [para(8296(a,1),2705(a,2,1)),rewrite([95681(3),52858(7),196290(7),123095(6),113933(5),4408(4),6144(2),163437(4),8310(4),4505(4)])]. 208429 T(T(x,y),K(z,u)) = T(x,K(z,u) * y). [para(517(a,1),8296(a,1,2)),rewrite([8310(5),208399(6)])]. 228215 (T(x,y) * z) \ T(x,y * y) = z \ K(x,y). [para(30881(a,1),17(a,1,1)),rewrite([187171(4)]),flip(a)]. 228407 T(x,T(y,L(x,z,u))) = T(x,y). [para(131120(a,1),30881(a,2,1)),rewrite([228215(6),153764(3),157230(5),204095(5),165291(5),37429(3),16716(4)])]. 230608 T(x,K(L(x,y,z),u)) = x. [para(16813(a,1),55660(a,1)),rewrite([55660(2)]),flip(a)]. 231489 K(L(x,y,z),u) * x = x * K(L(x,y,z),u). [para(230608(a,1),90(a,1,2))]. 231501 K(x,L(y,z,u)) * y = y * K(x,L(y,z,u)). [para(230608(a,1),7616(a,1,1)),rewrite([5005(3),6144(6)]),flip(a)]. 231502 T(x,K(y,L(x,z,u))) = x. [para(230608(a,1),7769(a,1,1)),rewrite([6144(3),231501(3),1708(4)])]. 231568 x * K(L(x,y,z),u) = T(x,u). [para(230608(a,1),25524(a,1,2,2)),rewrite([231489(5),204095(6),193392(6),95681(10),113933(9),163693(11),163798(10),16(8),4505(7),37429(6),30(5),89(4),8310(7),208429(4),16985(3),228407(3)]),flip(a)]. 231594 K(L(x,y,z),u) * x = T(x,u). [back_rewrite(231489),rewrite([231568(6)])]. 231954 K(x,L(y,z,u)) / y = y \ K(x,L(y,z,u)). [para(231502(a,1),2711(a,1,2))]. 231983 x \ K(y,L(x,z,u)) = T(x \ 1,y). [para(231502(a,1),19536(a,1,2,1,1)),rewrite([6144(4),231594(4),53195(7)]),flip(a)]. 232004 K(x,L(y,z,u)) = K(x,y). [para(231502(a,1),56531(a,1,2,1)),rewrite([110378(5),105864(6),19074(4),231954(3),231983(3),101793(4),16687(2)]),flip(a)]. 235046 T(x,L(y,z,u)) = T(x,y). [para(232004(a,1),16716(a,1,2)),rewrite([16716(2)]),flip(a)]. 235228 K(a(x,y,z),u) = 1. [back_rewrite(196856),rewrite([235046(6),90(6),115458(6),4505(4),181315(4),158223(4)])]. 258700 T(a(x,y,z),u) = a(x,y,z). [hyper(28,a,235228,a)]. 301066 a(x,y,a(z,u,w)) = 1. [para(235228(a,1),198284(a,2)),rewrite([258700(4),258700(4),158552(4),84171(2),153242(2)])]. 301069 $F # answer("aa3"). [resolve(301066,a,44,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=2809. Generated=1939939. Kept=301041. proofs=7. Usable=612. Sos=71470. Demods=60219. Limbo=183, Disabled=228806. Hints=0. Kept_by_rule=0, Deleted_by_rule=777445. Forward_subsumed=861447. Back_subsumed=371. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=273035 (43 lex), Back_demodulated=228400. Back_unit_deleted=0. Demod_attempts=55566859. Demod_rewrites=6295432. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=14. Megabytes=461.07. User_CPU=186.52, System_CPU=0.65, Wall_clock=187. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED THEOREM PROVED Exiting with 7 proofs. ------ process 3230 exit (max_proofs) ------  Process 3230 exit (max_proofs) Mon Feb 20 11:49:02 2012