============================== Prover9 =============================== Prover9 (32) version 2009-02A, February 2009. Process 12007 was started by mccune on cleo, Wed Feb 25 09:58:01 2009 The command was "/home/mccune/bin/prover9 -f dist-both.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file dist-both.in assign(max_seconds,3600). assign(order,kbo). set(lex_order_vars). assign(max_weight,50). list(weights). weight(x = y) = (weight(x) + weight(y)) + depth(x = y). end_of_list. formulas(sos). f(x,x,y) = x # label(majority). f(x,y,z) = f(z,x,y) # label(2a). f(x,y,z) = f(x,z,y) # label(2b). f(f(x,w,y),w,z) = f(x,w,f(y,w,z)) # label(associativity). end_of_list. set(restrict_denials). formulas(goals). f(f(x,y,z),u,w) = f(f(x,u,w),f(y,u,w),f(z,u,w)) # label(dist_long). f(f(x,y,z),u,w) = f(x,f(y,u,w),f(z,u,w)) # label(dist_short). f(f(x,y,z),u,w) = f(f(x,u,w),f(y,u,w),f(z,u,w)) & f(f(x,y,z),u,w) = f(x,f(y,u,w),f(z,u,w)) # label(dist_both). end_of_list. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: 1 f(f(x,y,z),u,w) = f(f(x,u,w),f(y,u,w),f(z,u,w)) # label(dist_long) # label(non_clause) # label(goal). [goal]. 2 f(f(x,y,z),u,w) = f(x,f(y,u,w),f(z,u,w)) # label(dist_short) # label(non_clause) # label(goal). [goal]. 3 f(f(x,y,z),u,w) = f(f(x,u,w),f(y,u,w),f(z,u,w)) & f(f(x,y,z),u,w) = f(x,f(y,u,w),f(z,u,w)) # label(dist_both) # 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). f(x,x,y) = x # label(majority). [assumption]. f(x,y,z) = f(z,x,y) # label(2a). [assumption]. f(x,y,z) = f(x,z,y) # label(2b). [assumption]. f(f(x,y,z),y,u) = f(x,y,f(z,y,u)) # label(associativity). [assumption]. f(f(c1,c4,c5),f(c2,c4,c5),f(c3,c4,c5)) != f(f(c1,c2,c3),c4,c5) # label(dist_long). [deny(1)]. f(f(c6,c7,c8),c9,c10) != f(c6,f(c7,c9,c10),f(c8,c9,c10)) # label(dist_short). [deny(2)]. f(f(c11,c14,c15),f(c12,c14,c15),f(c13,c14,c15)) != f(f(c11,c12,c13),c14,c15) | f(f(c11,c12,c13),c14,c15) != f(c11,f(c12,c14,c15),f(c13,c14,c15)) # label(dist_both). [deny(3)]. end_of_list. formulas(demodulators). end_of_list. ============================== PREDICATE ELIMINATION ================= No predicates eliminated. ============================== end predicate elimination ============= Auto_denials: % copying label dist_long to answer in negative clause % copying label dist_short to answer in negative clause % copying label dist_both to answer in negative clause % assign(max_proofs, 3). % (Horn set with more than one neg. clause) Term ordering decisions: Function symbol KB weights: 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. f=1. Predicate symbol precedence: predicate_order([ = ]). Function symbol precedence: function_order([ c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, f ]). Skipping inverse_order, because term ordering is KBO. Unfolding symbols: (none). 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) % assign(para_lit_limit, 2). % (nonunit Horn with equality) Auto_process settings: % set(unit_deletion). % (Horn set with negative nonunits) kept: 4 f(x,x,y) = x # label(majority). [assumption]. kept: 5 f(x,y,z) = f(z,x,y) # label(2a). [assumption]. kept: 6 f(x,y,z) = f(x,z,y) # label(2b). [assumption]. 7 f(f(x,y,z),y,u) = f(x,y,f(z,y,u)) # label(associativity). [assumption]. kept: 8 f(x,y,f(x,z,u)) = f(x,z,f(x,y,u)). [copy(7),rewrite([5(2),5(2),5(3,R),6(3)]),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])]. 9 f(f(c1,c4,c5),f(c2,c4,c5),f(c3,c4,c5)) != f(f(c1,c2,c3),c4,c5) # label(dist_long) # answer(dist_long). [deny(1)]. kept: 10 f(f(c1,c4,c5),f(c2,c4,c5),f(c3,c4,c5)) != f(c4,c5,f(c1,c2,c3)) # answer(dist_long). [copy(9),rewrite([5(20),5(20)])]. 11 f(f(c6,c7,c8),c9,c10) != f(c6,f(c7,c9,c10),f(c8,c9,c10)) # label(dist_short) # answer(dist_short). [deny(2)]. kept: 12 f(c6,f(c7,c9,c10),f(c8,c9,c10)) != f(c9,c10,f(c6,c7,c8)) # answer(dist_short). [copy(11),rewrite([5(7),5(7)]),flip(a)]. 13 f(f(c11,c14,c15),f(c12,c14,c15),f(c13,c14,c15)) != f(f(c11,c12,c13),c14,c15) | f(f(c11,c12,c13),c14,c15) != f(c11,f(c12,c14,c15),f(c13,c14,c15)) # label(dist_both) # answer(dist_both). [deny(3)]. kept: 14 f(f(c11,c14,c15),f(c12,c14,c15),f(c13,c14,c15)) != f(c14,c15,f(c11,c12,c13)) | f(c11,f(c12,c14,c15),f(c13,c14,c15)) != f(c14,c15,f(c11,c12,c13)) # answer(dist_both). [copy(13),rewrite([5(20),5(20),5(28),5(28)]),flip(b)]. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). 10 f(f(c1,c4,c5),f(c2,c4,c5),f(c3,c4,c5)) != f(c4,c5,f(c1,c2,c3)) # answer(dist_long). [copy(9),rewrite([5(20),5(20)])]. 12 f(c6,f(c7,c9,c10),f(c8,c9,c10)) != f(c9,c10,f(c6,c7,c8)) # answer(dist_short). [copy(11),rewrite([5(7),5(7)]),flip(a)]. 14 f(f(c11,c14,c15),f(c12,c14,c15),f(c13,c14,c15)) != f(c14,c15,f(c11,c12,c13)) | f(c11,f(c12,c14,c15),f(c13,c14,c15)) != f(c14,c15,f(c11,c12,c13)) # answer(dist_both). [copy(13),rewrite([5(20),5(20),5(28),5(28)]),flip(b)]. end_of_list. formulas(sos). 4 f(x,x,y) = x # label(majority). [assumption]. 5 f(x,y,z) = f(z,x,y) # label(2a). [assumption]. 6 f(x,y,z) = f(x,z,y) # label(2b). [assumption]. 8 f(x,y,f(x,z,u)) = f(x,z,f(x,y,u)). [copy(7),rewrite([5(2),5(2),5(3,R),6(3)]),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])]. end_of_list. formulas(demodulators). 4 f(x,x,y) = x # label(majority). [assumption]. 5 f(x,y,z) = f(z,x,y) # label(2a). [assumption]. % (lex-dep) 6 f(x,y,z) = f(x,z,y) # label(2b). [assumption]. % (lex-dep) end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.01 seconds. given #1 (I,wt=7): 4 f(x,x,y) = x # label(majority). [assumption]. given #2 (I,wt=10): 5 f(x,y,z) = f(z,x,y) # label(2a). [assumption]. given #3 (I,wt=10): 6 f(x,y,z) = f(x,z,y) # label(2b). [assumption]. given #4 (I,wt=17): 8 f(x,y,f(x,z,u)) = f(x,z,f(x,y,u)). [copy(7),rewrite([5(2),5(2),5(3,R),6(3)]),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])]. given #5 (A,wt=7): 15 f(x,y,y) = y. [para(5(a,1),4(a,1))]. given #6 (T,wt=14): 19 f(x,y,f(x,z,y)) = f(x,z,y). [para(15(a,1),8(a,1,3)),flip(a)]. given #7 (T,wt=14): 20 f(x,y,f(x,y,z)) = f(x,y,z). [para(15(a,1),8(a,1)),rewrite([6(3),19(3)]),flip(a)]. given #8 (T,wt=17): 16 f(x,y,f(z,x,u)) = f(z,x,f(x,y,u)). [para(8(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)]),flip(a)]. given #9 (T,wt=17): 17 f(x,y,f(x,z,u)) = f(x,u,f(x,y,z)). [para(5(a,1),8(a,1,3)),rewrite([5(1,R),6(1)])]. given #10 (A,wt=24): 18 f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,y,f(x,z,w))). [para(8(a,1),8(a,1,3))]. given #11 (T,wt=17): 24 f(x,y,f(z,y,u)) = f(z,y,f(x,y,u)). [para(16(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)])]. given #12 (T,wt=17): 30 f(x,y,f(z,x,u)) = f(z,x,f(x,u,y)). [para(17(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)]),flip(a)]. given #13 (T,wt=17): 31 f(x,y,f(x,z,u)) = f(x,u,f(x,z,y)). [para(17(a,1),6(a,2)),rewrite([6(2),6(3)])]. given #14 (T,wt=21): 21 f(x,y,f(x,z,f(x,u,y))) = f(x,z,f(x,u,y)). [para(19(a,1),8(a,1,3)),flip(a)]. given #15 (A,wt=21): 22 f(x,y,f(x,z,f(x,y,u))) = f(x,z,f(x,y,u)). [para(19(a,1),8(a,2,3)),rewrite([6(1),6(4)])]. given #16 (T,wt=21): 28 f(x,y,f(y,z,f(x,y,u))) = f(x,y,f(y,z,u)). [para(16(a,2),20(a,1,3))]. given #17 (T,wt=21): 73 f(x,y,f(z,x,f(x,y,u))) = f(z,x,f(x,y,u)). [para(19(a,1),24(a,1,3)),rewrite([5(1),5(3),5(5,R),6(5)]),flip(a)]. given #18 (T,wt=21): 122 f(x,y,f(z,y,f(x,y,u))) = f(z,y,f(x,y,u)). [para(73(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])]. given #19 (T,wt=24): 25 f(x,y,f(z,u,f(x,z,w))) = f(x,z,f(x,y,f(z,u,w))). [para(16(a,2),8(a,1,3))]. given #20 (A,wt=24): 27 f(x,f(y,z,u),f(y,z,f(x,y,u))) = f(x,y,f(y,z,u)). [para(16(a,2),19(a,1,3))]. given #21 (T,wt=21): 132 f(x,y,f(z,u,f(x,z,u))) = f(x,y,f(x,z,u)). [para(15(a,1),25(a,1,3)),rewrite([6(4),95(6)]),flip(a)]. given #22 (T,wt=14): 205 f(x,y,f(z,x,y)) = f(z,x,y). [para(132(a,1),15(a,1)),rewrite([6(4),132(4),15(3)]),flip(a)]. given #23 (T,wt=21): 215 f(x,y,f(z,x,f(x,u,y))) = f(z,x,f(x,u,y)). [para(205(a,1),24(a,1,3)),rewrite([5(1),5(3),5(5,R),6(5)]),flip(a)]. given #24 (T,wt=24): 29 f(x,y,f(z,u,f(x,u,w))) = f(x,u,f(x,y,f(z,u,w))). [para(16(a,1),16(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])]. given #25 (A,wt=24): 32 f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,y,f(x,w,z))). [para(17(a,1),8(a,2,3)),flip(a)]. given #26 (T,wt=24): 33 f(x,y,f(x,z,f(x,u,w))) = f(x,w,f(x,y,f(x,z,u))). [para(17(a,2),8(a,1,3))]. given #27 (T,wt=24): 38 f(x,f(y,z,u),f(x,w,y)) = f(x,w,f(y,z,f(x,y,u))). [para(16(a,2),17(a,1,3)),flip(a)]. given #28 (T,wt=24): 40 f(x,y,f(z,x,f(x,u,w))) = f(z,x,f(x,u,f(x,y,w))). [para(18(a,1),5(a,2)),rewrite([6(3),5(5,R),6(5)]),flip(a)]. given #29 (T,wt=24): 41 f(x,y,f(y,z,f(y,u,w))) = f(y,z,f(y,u,f(x,y,w))). [para(18(a,2),5(a,2)),rewrite([6(3),5(4,R),6(4)])]. given #30 (A,wt=31): 42 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,u,f(x,y,f(x,w,f(x,z,v5)))). [para(18(a,1),8(a,1,3))]. given #31 (T,wt=21): 474 f(x,y,f(x,z,f(u,x,y))) = f(u,x,f(x,z,y)). [para(19(a,1),41(a,1,3)),flip(a)]. given #32 (T,wt=20): 628 f(x,f(y,x,z),f(x,u,z)) = f(y,x,f(x,u,z)). [para(474(a,1),17(a,1)),rewrite([6(4)]),flip(a)]. given #33 (T,wt=20): 654 f(x,f(y,x,z),f(x,z,u)) = f(y,x,f(x,z,u)). [para(628(a,1),5(a,2)),rewrite([6(2),5(3),6(4)])]. given #34 (T,wt=20): 655 f(x,f(x,y,z),f(u,x,z)) = f(u,x,f(x,y,z)). [para(628(a,1),6(a,1)),flip(a)]. given #35 (A,wt=24): 43 f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,z,f(x,y,w))). [para(18(a,1),8(a,1))]. given #36 (T,wt=20): 695 f(x,f(x,y,z),f(u,x,y)) = f(u,x,f(x,y,z)). [para(654(a,1),6(a,1)),flip(a)]. given #37 (T,wt=18): 803 f(x,y,f(x,z,f(z,y,u))) = f(x,z,y). [para(695(a,1),40(a,1,3)),rewrite([5(4,R),15(4),5(3,R),15(3),5(5),6(5),5(6,R),6(6),696(6),28(5),6(3),57(6),6(4),20(5),22(5)]),flip(a)]. given #38 (T,wt=17): 828 f(x,y,f(z,x,u)) = f(x,u,f(z,x,y)). [para(30(a,2),803(a,2)),rewrite([6(3),392(5),6(4),820(5)])]. given #39 (T,wt=17): 874 f(x,y,f(z,u,x)) = f(z,x,f(u,x,y)). [para(828(a,1),5(a,2)),rewrite([6(2),5(3)]),flip(a)]. given #40 (A,wt=31): 44 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,w,f(x,y,f(x,z,f(x,u,v5)))). [para(18(a,2),8(a,1,3))]. given #41 (T,wt=17): 897 f(x,y,f(z,u,y)) = f(z,y,f(x,u,y)). [para(874(a,1),5(a,2)),rewrite([6(2),5(3)])]. given #42 (T,wt=17): 922 f(x,f(y,z,u),f(y,z,x)) = f(y,z,x). [para(874(a,2),38(a,2)),rewrite([6(2),392(3),813(3)]),flip(a)]. given #43 (T,wt=17): 933 f(x,y,f(z,u,x)) = f(u,x,f(z,x,y)). [para(874(a,2),803(a,2)),rewrite([6(3),826(5)]),flip(a)]. given #44 (T,wt=17): 1057 f(x,f(y,z,u),f(y,x,z)) = f(y,x,z). [para(38(a,2),897(a,2)),rewrite([5(1,R),6(1),5(2,R),6(2),696(4),28(3),6(1),803(3),6(2),5(3,R),6(3),5(4),20(4)]),flip(a)]. given #45 (A,wt=24): 45 f(x,y,f(x,z,f(x,u,w))) = f(x,y,f(x,u,f(x,z,w))). [para(18(a,2),8(a,1))]. given #46 (T,wt=17): 1071 f(x,f(y,z,u),f(x,z,u)) = f(x,z,u). [para(5(a,1),922(a,1,2)),rewrite([5(2),5(4)])]. given #47 (T,wt=17): 1073 f(x,f(y,z,x),f(y,z,u)) = f(y,z,x). [para(922(a,1),6(a,1)),flip(a)]. given #48 (T,wt=17): 1074 f(x,f(x,y,z),f(y,z,u)) = f(x,y,z). [para(922(a,1),6(a,2)),rewrite([5(1),5(4)])]. given #49 (T,wt=17): 1149 f(x,y,f(z,u,y)) = f(u,y,f(x,z,y)). [para(933(a,1),5(a,2)),rewrite([6(2),5(3)])]. given #50 (A,wt=28): 50 f(x,y,f(x,z,f(x,u,f(x,w,y)))) = f(x,z,f(x,u,f(x,w,y))). [para(19(a,1),18(a,1,3,3)),flip(a)]. given #51 (T,wt=17): 1181 f(x,f(y,x,z),f(y,z,u)) = f(y,x,z). [para(1057(a,1),6(a,1)),flip(a)]. given #52 (T,wt=17): 1253 f(x,f(y,z,u),f(z,u,x)) = f(z,u,x). [para(1071(a,1),5(a,2)),rewrite([5(2),5(2),5(3),5(4),5(4)])]. given #53 (T,wt=17): 1469 f(x,y,f(z,u,y)) = f(u,y,f(z,x,y)). [para(1149(a,1),803(a,2)),rewrite([6(3),1063(5)])]. given #54 (T,wt=18): 812 f(x,y,f(y,z,f(x,z,u))) = f(x,y,z). [para(803(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(4)])]. given #55 (A,wt=28): 51 f(x,y,f(x,z,f(x,u,f(x,y,w)))) = f(x,y,f(x,z,f(x,u,w))). [para(18(a,2),20(a,1,3))]. given #56 (T,wt=18): 813 f(x,y,f(x,z,f(y,z,u))) = f(x,y,z). [para(5(a,1),803(a,1,3,3)),rewrite([5(1),6(1),6(4)])]. given #57 (T,wt=18): 827 f(x,y,f(z,u,f(x,y,z))) = f(x,y,z). [para(30(a,2),803(a,1,3)),rewrite([6(1),6(4)])]. given #58 (T,wt=18): 866 f(x,y,f(z,y,f(z,x,u))) = f(z,x,y). [back_rewrite(360),rewrite([5(2),392(3),813(3),5(2,R),6(2),5(3,R),6(3)]),flip(a)]. given #59 (T,wt=18): 868 f(x,y,f(z,y,f(x,z,u))) = f(x,z,y). [back_rewrite(239),rewrite([6(1),827(3),5(3,R),6(3)]),flip(a)]. given #60 (A,wt=31): 52 f(x,y,f(z,u,f(x,z,f(z,w,v5)))) = f(x,z,f(x,y,f(z,w,f(z,u,v5)))). [para(18(a,1),16(a,1,3)),rewrite([5(2,R),6(2),5(8,R),6(8)])]. given #61 (T,wt=18): 871 f(x,y,f(z,x,f(z,y,u))) = f(z,x,y). [back_rewrite(385),rewrite([827(4)]),flip(a)]. given #62 (T,wt=18): 910 f(x,y,f(z,u,f(x,z,y))) = f(x,z,y). [para(874(a,2),25(a,2,3)),rewrite([5(2,R),6(2),812(3),6(2)]),flip(a)]. given #63 (T,wt=18): 1030 f(x,y,f(z,u,f(x,u,y))) = f(x,u,y). [para(20(a,1),897(a,1,3)),rewrite([15(3),696(5),122(4)]),flip(a)]. given #64 (T,wt=18): 1051 f(x,y,f(z,u,f(x,y,u))) = f(x,y,u). [para(897(a,1),29(a,2,3)),rewrite([6(1),6(4),5(5,R),6(5),910(6)])]. given #65 (A,wt=31): 53 f(x,y,f(z,u,f(z,w,f(x,z,v5)))) = f(x,z,f(x,y,f(z,u,f(z,w,v5)))). [para(18(a,2),16(a,1,3)),rewrite([5(1,R),6(1),5(8,R),6(8)])]. given #66 (T,wt=18): 1072 f(x,y,f(x,z,f(y,u,z))) = f(x,y,z). [para(5(a,2),922(a,1,2)),rewrite([5(2),6(2),392(3),5(4),6(4)])]. given #67 (T,wt=18): 1634 f(x,y,f(x,z,f(u,y,z))) = f(x,y,z). [para(1071(a,1),812(a,2)),rewrite([6(5),1607(7),6(2)])]. given #68 (T,wt=18): 1669 f(x,y,f(x,z,f(z,u,y))) = f(x,z,y). [para(827(a,1),19(a,1,3)),rewrite([6(1),6(3),6(4),696(4),28(3),6(4),910(6)])]. given #69 (T,wt=18): 1713 f(x,y,f(z,u,f(z,x,y))) = f(z,x,y). [para(827(a,1),922(a,2)),rewrite([5(1),5(4),922(7),5(4)])]. given #70 (A,wt=31): 54 f(x,y,f(x,z,f(u,w,f(x,u,v5)))) = f(x,u,f(x,y,f(x,z,f(u,w,v5)))). [para(16(a,2),18(a,1,3,3))]. given #71 (T,wt=18): 1982 f(x,y,f(z,u,f(u,x,y))) = f(u,x,y). [para(1030(a,1),922(a,2)),rewrite([5(1,R),6(1),5(4,R),6(4),922(7),5(4,R),6(4)])]. given #72 (T,wt=20): 1076 f(f(x,y,z),f(x,z,u),f(x,y,z)) = f(x,y,z). [para(19(a,1),922(a,1,3)),rewrite([19(6)])]. given #73 (T,wt=20): 1077 f(f(x,y,z),f(x,y,u),f(x,y,z)) = f(x,y,z). [para(20(a,1),922(a,1,3)),rewrite([20(6)])]. given #74 (T,wt=20): 1101 f(f(x,y,z),f(y,z,u),f(x,y,z)) = f(x,y,z). [para(205(a,1),922(a,1,3)),rewrite([205(6)])]. given #75 (A,wt=31): 55 f(x,y,f(x,z,f(u,w,f(x,u,v5)))) = f(x,z,f(x,u,f(x,y,f(u,w,v5)))). [para(16(a,2),18(a,2,3,3)),flip(a)]. given #76 (T,wt=21): 914 f(x,f(y,x,z),f(z,u,f(y,x,z))) = f(y,x,z). [para(205(a,1),874(a,1,3)),rewrite([5(3,R),15(3),6(4)]),flip(a)]. given #77 (T,wt=21): 1048 f(x,f(y,x,z),f(u,z,f(y,x,z))) = f(y,x,z). [para(205(a,1),897(a,1,3)),rewrite([15(3)]),flip(a)]. given #78 (T,wt=21): 1050 f(x,y,f(x,f(x,y,z),f(u,y,z))) = f(x,y,z). [para(897(a,1),29(a,1)),rewrite([20(3),15(3)]),flip(a)]. given #79 (T,wt=21): 1079 f(x,f(y,z,f(z,u,w)),f(x,z,u)) = f(x,z,u). [para(16(a,1),922(a,1,2)),rewrite([5(3),5(5)])]. given #80 (A,wt=24): 57 f(x,f(x,y,z),f(x,u,w)) = f(x,y,f(x,u,f(x,w,z))). [para(18(a,1),17(a,1)),flip(a)]. given #81 (T,wt=21): 1088 f(x,f(y,z,f(z,u,w)),f(x,z,w)) = f(x,z,w). [para(30(a,1),922(a,1,2)),rewrite([5(3),5(5)])]. given #82 (T,wt=21): 1150 f(x,f(y,z,x),f(y,u,f(y,z,x))) = f(y,z,x). [para(19(a,1),933(a,1,3)),rewrite([5(3,R),15(3),6(4)]),flip(a)]. given #83 (T,wt=17): 3270 f(x,f(y,z,x),f(u,y,z)) = f(y,z,x). [para(1050(a,1),1150(a,1,3)),rewrite([5(2),5(2),5(5),5(5),6(6),1332(6),4(4),5(2),5(2)]),flip(a)]. given #84 (T,wt=17): 3273 f(x,f(x,y,z),f(u,y,z)) = f(x,y,z). [para(3270(a,1),19(a,1,3)),rewrite([5(2),1071(3),5(2)]),flip(a)]. given #85 (A,wt=31): 58 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,z,f(x,y,f(x,w,f(x,u,v5)))). [para(18(a,2),17(a,1,3)),rewrite([57(8)])]. given #86 (T,wt=21): 1151 f(x,f(y,x,z),f(y,u,f(y,x,z))) = f(y,x,z). [para(20(a,1),933(a,1,3)),rewrite([5(3,R),15(3),6(4)]),flip(a)]. given #87 (T,wt=21): 1159 f(x,f(y,z,x),f(z,u,f(y,z,x))) = f(y,z,x). [para(205(a,1),933(a,1,3)),rewrite([5(3,R),15(3),6(4)]),flip(a)]. given #88 (T,wt=21): 1349 f(x,f(x,y,z),f(y,u,f(y,z,w))) = f(x,y,z). [para(8(a,1),1073(a,1,3)),rewrite([5(1),5(5)])]. given #89 (T,wt=21): 1435 f(x,f(y,z,x),f(u,y,f(y,z,x))) = f(y,z,x). [para(19(a,1),1149(a,1,3)),rewrite([15(3)]),flip(a)]. given #90 (A,wt=24): 59 f(x,y,f(x,z,f(x,u,w))) = f(x,y,f(x,w,f(x,z,u))). [para(18(a,2),17(a,2)),rewrite([6(2),6(4)]),flip(a)]. given #91 (T,wt=21): 1436 f(x,f(y,x,z),f(u,y,f(y,x,z))) = f(y,x,z). [para(20(a,1),1149(a,1,3)),rewrite([15(3)]),flip(a)]. given #92 (T,wt=21): 1447 f(x,f(y,z,x),f(u,z,f(y,z,x))) = f(y,z,x). [para(205(a,1),1149(a,1,3)),rewrite([15(3)]),flip(a)]. given #93 (T,wt=21): 2830 f(x,y,f(x,f(x,y,z),f(y,u,z))) = f(x,y,z). [para(5(a,1),1050(a,1,3)),rewrite([5(1,R),6(1),5(3,R)])]. given #94 (T,wt=21): 2861 f(x,f(y,z,f(z,u,w)),f(z,u,x)) = f(z,u,x). [para(1079(a,1),5(a,2)),rewrite([5(3),5(3),5(4),5(5),5(5)])]. given #95 (A,wt=31): 60 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,u,f(x,y,f(x,v5,f(x,z,w)))). [para(17(a,1),18(a,2,3,3))]. given #96 (T,wt=21): 2884 f(x,f(y,z,f(u,y,w)),f(x,u,y)) = f(x,u,y). [para(1079(a,1),21(a,1,3)),rewrite([6(1),20(2),5(2,R),6(2),5(3,R),6(3),6(4)]),flip(a)]. given #97 (T,wt=21): 2885 f(x,f(y,z,f(u,z,w)),f(x,u,z)) = f(x,u,z). [para(1079(a,1),21(a,2)),rewrite([5(1,R),6(1),6(3),22(5),6(5)])]. given #98 (T,wt=21): 3114 f(x,f(y,z,f(z,u,w)),f(z,w,x)) = f(z,w,x). [para(1088(a,1),5(a,2)),rewrite([5(3),5(3),5(4),5(5),5(5)])]. given #99 (T,wt=21): 3475 f(x,f(y,x,z),f(y,x,f(y,z,u))) = f(y,x,z). [para(1349(a,1),122(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),15(3),5(2,R),6(2),5(3,R),6(3),57(5),6(3),20(4)]),flip(a)]. given #100 (A,wt=24): 61 f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,w,f(x,y,z))). [para(17(a,1),18(a,2,3))]. given #101 (T,wt=21): 3521 f(x,f(y,z,x),f(y,u,f(y,z,w))) = f(y,z,x). [para(1349(a,1),1253(a,2)),rewrite([5(3),5(3),5(5),5(5),1253(9),5(5),5(5)])]. given #102 (T,wt=21): 3627 f(x,f(y,z,f(y,u,w)),f(y,u,x)) = f(y,u,x). [para(2861(a,1),5(a,1)),rewrite([5(4,R),6(4),5(5,R)]),flip(a)]. given #103 (T,wt=21): 3998 f(x,y,f(y,z,f(x,u,y))) = f(x,y,f(u,y,z)). [para(474(a,1),3475(a,1,2)),rewrite([5(1),5(3),6(5),5(6,R),6(6),2997(7),6(5),1938(5),20(3),20(3),5(3),5(5,R),6(5)]),flip(a)]. given #104 (T,wt=22): 816 f(x,y,f(x,z,f(z,u,f(y,z,w)))) = f(x,y,z). [para(8(a,1),803(a,1,3,3)),rewrite([5(1,R),6(1),6(5)])]. given #105 (A,wt=31): 62 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,v5,f(x,y,f(x,z,f(x,u,w)))). [para(17(a,2),18(a,1,3,3))]. given #106 (T,wt=21): 4305 f(x,y,f(z,f(y,z,u),f(x,z,w))) = f(x,y,z). [para(30(a,2),816(a,1,3))]. given #107 (T,wt=21): 4461 f(x,y,f(z,f(x,z,u),f(z,y,w))) = f(x,z,y). [para(4305(a,1),5(a,2)),rewrite([5(2,R),6(2),6(4),5(5),5(5)])]. given #108 (T,wt=21): 4462 f(x,y,f(z,f(z,y,u),f(x,z,w))) = f(x,z,y). [para(4305(a,1),6(a,2)),rewrite([5(1,R),6(1),6(4),6(5)])]. given #109 (T,wt=21): 4463 f(x,y,f(z,f(x,z,u),f(y,z,w))) = f(x,y,z). [para(6(a,1),4305(a,1,3))]. given #110 (A,wt=38): 63 f(x,y,f(x,z,f(x,u,f(x,w,f(x,v5,v6))))) = f(x,w,f(x,y,f(x,z,f(x,v5,f(x,u,v6))))). [para(18(a,1),18(a,1,3,3))]. given #111 (T,wt=22): 819 f(x,y,f(x,z,f(y,u,f(y,z,w)))) = f(x,y,z). [para(16(a,2),803(a,1,3,3)),rewrite([5(1,R),6(1),6(5)])]. given #112 (T,wt=22): 853 f(x,y,f(z,u,f(x,z,f(y,z,w)))) = f(x,y,z). [para(40(a,2),803(a,1,3)),rewrite([5(1,R),6(1),6(5)])]. given #113 (T,wt=22): 859 f(x,y,f(y,z,f(z,u,f(x,z,w)))) = f(x,y,z). [para(41(a,1),803(a,1,3)),rewrite([5(3,R),6(3),6(5)])]. given #114 (T,wt=22): 1082 f(x,y,f(x,z,f(y,u,f(y,w,z)))) = f(x,y,z). [para(17(a,2),922(a,1,2)),rewrite([5(3),392(4),5(5)])]. given #115 (A,wt=31): 64 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,w,f(x,y,f(x,u,f(x,z,v5)))). [para(18(a,1),18(a,1,3))]. given #116 (T,wt=22): 1606 f(x,y,f(y,z,f(x,u,f(x,z,w)))) = f(x,y,z). [para(8(a,1),812(a,1,3,3))]. given #117 (T,wt=22): 1726 f(x,y,f(z,u,f(y,z,f(x,z,w)))) = f(x,y,z). [para(18(a,1),866(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5),5(5)])]. given #118 (T,wt=22): 1738 f(x,y,f(z,u,f(y,u,f(x,u,w)))) = f(x,y,u). [para(41(a,2),866(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5),5(5)])]. given #119 (T,wt=22): 1775 f(x,y,f(z,y,f(x,u,f(x,z,w)))) = f(x,z,y). [para(52(a,1),24(a,2)),rewrite([5(2,R),6(2),5(3,R),6(3),812(4),5(4,R),6(4),5(5,R),6(5)]),flip(a)]. given #120 (A,wt=38): 65 f(x,y,f(x,z,f(x,u,f(x,w,f(x,v5,v6))))) = f(x,u,f(x,y,f(x,v5,f(x,z,f(x,w,v6))))). [para(18(a,1),18(a,2,3,3))]. given #121 (T,wt=22): 1856 f(x,y,f(z,x,f(y,u,f(z,y,w)))) = f(z,x,y). [para(52(a,1),874(a,2)),rewrite([5(3),392(4),813(4),5(2,R),6(2),5(4,R),6(4)]),flip(a)]. given #122 (T,wt=21): 5467 f(x,f(y,z,f(u,y,w)),f(u,x,y)) = f(u,x,y). [para(1856(a,1),828(a,1)),flip(a)]. given #123 (T,wt=21): 5512 f(x,f(y,x,z),f(z,u,f(y,z,w))) = f(y,x,z). [para(5467(a,1),6(a,1)),flip(a)]. given #124 (T,wt=22): 1905 f(x,y,f(z,u,f(x,u,f(y,u,w)))) = f(x,y,u). [para(41(a,2),871(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5),5(5)])]. given #125 (A,wt=31): 66 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,u,f(x,w,f(x,y,f(x,z,v5)))). [para(18(a,1),18(a,2,3))]. given #126 (T,wt=22): 2013 f(x,y,f(z,y,f(x,u,f(z,x,w)))) = f(z,x,y). [para(53(a,1),24(a,1)),rewrite([813(4)]),flip(a)]. given #127 (T,wt=22): 2026 f(x,y,f(z,x,f(z,u,f(z,y,w)))) = f(z,x,y). [para(53(a,1),122(a,1,3)),rewrite([5(3,R),6(3),5(4,R),6(4),868(4),20(2),5(2,R),6(2),5(5,R),6(5)]),flip(a)]. given #128 (T,wt=21): 5800 f(x,f(y,z,f(y,u,w)),f(y,x,u)) = f(y,x,u). [para(2026(a,1),828(a,1)),flip(a)]. given #129 (T,wt=21): 5854 f(x,f(y,x,z),f(y,u,f(y,z,w))) = f(y,x,z). [para(5800(a,1),6(a,1)),flip(a)]. given #130 (A,wt=38): 67 f(x,y,f(x,z,f(x,u,f(x,w,f(x,v5,v6))))) = f(x,v5,f(x,y,f(x,z,f(x,u,f(x,w,v6))))). [para(18(a,2),18(a,1,3,3))]. given #131 (T,wt=22): 2870 f(x,y,f(x,z,f(z,u,f(z,y,w)))) = f(x,z,y). [para(1079(a,1),17(a,1)),rewrite([5(3,R),6(3),6(4)]),flip(a)]. given #132 (T,wt=22): 2966 f(x,y,f(x,z,f(u,y,f(y,z,w)))) = f(x,y,z). [para(1079(a,1),812(a,2)),rewrite([6(7),1607(9),6(3)])]. given #133 (T,wt=22): 3164 f(x,y,f(x,z,f(u,y,f(y,w,z)))) = f(x,y,z). [para(1088(a,1),812(a,2)),rewrite([6(7),1607(9),6(3)])]. given #134 (T,wt=22): 3678 f(x,y,f(z,y,f(z,u,f(z,x,w)))) = f(z,x,y). [para(2861(a,1),933(a,1)),rewrite([5(3,R),6(3)]),flip(a)]. given #135 (A,wt=38): 68 f(x,y,f(x,z,f(x,u,f(x,w,f(x,v5,v6))))) = f(x,u,f(x,y,f(x,w,f(x,v5,f(x,z,v6))))). [para(18(a,2),18(a,2,3,3))]. given #136 (T,wt=22): 3815 f(x,y,f(x,z,f(y,u,f(z,y,w)))) = f(x,z,y). [para(2884(a,1),17(a,1)),rewrite([6(4)]),flip(a)]. given #137 (T,wt=22): 3937 f(x,y,f(x,z,f(u,z,f(y,z,w)))) = f(x,y,z). [para(2885(a,1),8(a,2)),rewrite([6(3)])]. given #138 (T,wt=22): 4085 f(x,y,f(z,u,f(z,w,f(x,y,z)))) = f(x,y,z). [para(61(a,1),866(a,1,3)),rewrite([5(1),6(1),5(5),5(5)])]. given #139 (T,wt=21): 6221 f(x,y,f(z,f(x,y,z),f(z,u,w))) = f(x,y,z). [para(17(a,1),4085(a,1,3))]. given #140 (A,wt=31): 69 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,w,f(x,z,f(x,y,f(x,u,v5)))). [para(18(a,2),18(a,2,3)),flip(a)]. given #141 (T,wt=21): 6311 f(x,y,f(z,f(x,z,y),f(z,u,w))) = f(x,z,y). [para(6221(a,1),5(a,2)),rewrite([5(1),5(1),6(4),5(5),5(5)])]. given #142 (T,wt=22): 4557 f(x,y,f(z,u,f(x,z,f(z,y,w)))) = f(x,z,y). [para(2884(a,1),4305(a,2)),rewrite([5(1,R),6(1),6(3),5(4,R),6(4),6(6),5(7),6(8),6(9),4491(11),6(5)])]. given #143 (T,wt=22): 4872 f(x,y,f(z,u,f(z,y,f(x,z,w)))) = f(x,z,y). [para(853(a,1),5(a,2)),rewrite([5(2,R),6(2),6(4),5(5),5(5)])]. given #144 (T,wt=22): 4906 f(x,y,f(z,u,f(z,x,f(z,y,w)))) = f(z,x,y). [para(853(a,1),922(a,2)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5,R),6(5),5(6,R),6(6),922(9),5(5)])]. given #145 (A,wt=24): 70 f(x,y,f(z,u,f(y,z,w))) = f(y,z,f(x,y,f(z,u,w))). [para(8(a,1),24(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])]. given #146 (T,wt=20): 6720 f(x,f(y,x,z),f(y,x,u)) = f(y,x,f(x,u,z)). [para(70(a,1),17(a,1)),rewrite([5(2,R),6(2),20(3),5(4,R),6(4)]),flip(a)]. given #147 (T,wt=20): 6802 f(x,f(y,x,z),f(u,x,z)) = f(y,x,f(u,x,z)). [para(1253(a,1),70(a,2,3)),rewrite([5(3),6(3),910(5),5(4),5(5,R)]),flip(a)]. given #148 (T,wt=21): 6861 f(x,f(x,y,z),f(u,y,f(y,z,w))) = f(x,y,z). [para(1079(a,1),70(a,2,3)),rewrite([5(5),5(5),2966(6),1079(4),5(5,R)]),flip(a)]. given #149 (T,wt=21): 6870 f(x,f(x,y,z),f(u,y,f(y,w,z))) = f(x,y,z). [para(1088(a,1),70(a,2,3)),rewrite([5(5),5(5),3164(6),1088(4),5(5,R)]),flip(a)]. given #150 (A,wt=24): 71 f(x,y,f(z,u,f(z,x,w))) = f(z,x,f(x,y,f(z,u,w))). [para(8(a,1),24(a,2,3)),rewrite([5(2,R),6(2),5(6,R),6(6)]),flip(a)]. given #151 (T,wt=17): 7121 f(x,f(x,y,z),f(y,u,z)) = f(x,y,z). [para(6870(a,1),1669(a,1,3)),rewrite([392(3),1072(3)]),flip(a)]. given #152 (T,wt=17): 7301 f(x,f(y,z,x),f(y,u,z)) = f(y,z,x). [para(7121(a,1),1253(a,2)),rewrite([5(2),5(2),5(4),5(4),1253(7),5(4),5(4)])]. given #153 (T,wt=21): 7078 f(x,f(y,z,x),f(u,y,f(y,z,w))) = f(y,z,x). [para(6861(a,1),922(a,1,3)),rewrite([5(3),5(3),6(4),5(5),5(5),6(6),2954(6),5(2),5(2)]),flip(a)]. given #154 (T,wt=21): 7113 f(x,f(y,z,x),f(u,y,f(y,w,z))) = f(y,z,x). [para(6870(a,1),922(a,1,3)),rewrite([5(3),5(3),6(4),5(5),5(5),6(6),3158(6),5(2),5(2)]),flip(a)]. given #155 (A,wt=24): 72 f(x,f(y,z,u),f(y,z,f(x,z,u))) = f(x,z,f(y,z,u)). [para(24(a,1),19(a,1,3))]. given #156 (T,wt=21): 7177 f(x,y,f(y,f(x,y,z),f(u,x,z))) = f(x,y,z). [para(71(a,1),1469(a,2)),rewrite([20(3),15(3),5(3,R),6(3)]),flip(a)]. given #157 (T,wt=18): 7553 f(x,y,f(y,z,f(x,u,z))) = f(x,y,z). [para(6(a,1),7177(a,1,3)),rewrite([5(1,R),6(1),28(4),6(2)])]. given #158 (T,wt=21): 7552 f(x,y,f(y,f(x,y,z),f(x,u,z))) = f(x,y,z). [para(5(a,1),7177(a,1,3)),rewrite([5(1,R),6(1),5(3,R)])]. given #159 (T,wt=22): 5283 f(x,y,f(z,u,f(x,u,f(u,y,w)))) = f(x,u,y). [para(1738(a,1),5(a,2)),rewrite([5(1,R),6(1),6(4),5(5),5(5)])]. given #160 (A,wt=24): 74 f(x,y,f(z,u,f(y,u,w))) = f(y,u,f(x,y,f(z,u,w))). [para(16(a,1),24(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])]. given #161 (T,wt=20): 7772 f(x,f(y,z,x),f(z,x,u)) = f(y,x,f(z,x,u)). [para(922(a,1),74(a,2,3)),rewrite([5(3),6(3),122(4),19(4),5(4),5(5,R)]),flip(a)]. given #162 (T,wt=20): 7788 f(x,f(y,z,x),f(u,z,x)) = f(y,x,f(u,z,x)). [para(1253(a,1),74(a,2,3)),rewrite([5(3),6(3),1030(5),5(4),5(5,R)]),flip(a)]. given #163 (T,wt=20): 7955 f(x,f(y,x,z),f(u,y,x)) = f(u,x,f(y,x,z)). [para(7772(a,1),205(a,1,3)),rewrite([1604(5),7772(6)])]. given #164 (T,wt=22): 5284 f(x,y,f(z,u,f(u,y,f(x,u,w)))) = f(x,u,y). [para(1738(a,1),6(a,2)),rewrite([5(2,R),6(2),6(4),6(5)])]. given #165 (A,wt=24): 75 f(x,f(y,z,u),f(x,w,z)) = f(x,w,f(y,z,f(x,z,u))). [para(24(a,1),17(a,1,3)),flip(a)]. given #166 (T,wt=22): 5305 f(x,y,f(z,u,f(u,w,f(x,y,u)))) = f(x,y,u). [para(874(a,2),1738(a,1,3,3)),rewrite([5(1,R),6(1)])]. given #167 (T,wt=22): 5310 f(x,y,f(z,u,f(u,x,f(u,y,w)))) = f(u,x,y). [para(1738(a,1),922(a,2)),rewrite([5(1,R),6(1),5(2,R),6(2),5(4,R),6(4),5(5,R),6(5),5(6,R),6(6),5(8,R),6(8),922(9),5(5),6(5)])]. given #168 (T,wt=22): 5647 f(x,y,f(x,z,f(u,y,f(z,y,w)))) = f(x,z,y). [para(1905(a,1),812(a,2)),rewrite([6(7),1618(9)])]. given #169 (T,wt=21): 8713 f(x,y,f(y,z,f(u,x,y))) = f(y,z,f(u,x,y)). [para(1253(a,1),5647(a,1,3)),rewrite([5(2),5(2),5(4),5(4),5(6,R),6(6),205(6),5(5),5(5),5(7),6(7),19(7)])]. given #170 (A,wt=24): 76 f(x,y,f(z,u,f(z,x,w))) = f(z,x,f(x,y,f(z,w,u))). [para(17(a,1),24(a,2,3)),rewrite([5(2,R),6(2),5(6,R),6(6)]),flip(a)]. given #171 (T,wt=21): 8825 f(x,y,f(z,f(x,y,z),f(x,z,u))) = f(x,y,z). [para(827(a,1),76(a,2,3)),rewrite([5(2,R),6(2),5(6,R),6(6),19(6)])]. given #172 (T,wt=22): 5663 f(x,y,f(z,y,f(u,x,f(z,x,w)))) = f(z,x,y). [para(1905(a,1),1856(a,2)),rewrite([5(2,R),6(2),5(5,R),6(5),5(8,R),6(8),6(10),5(11,R),6(11),5(12,R),6(12),5453(13),5(5),5(5)])]. given #173 (T,wt=22): 5748 f(x,y,f(z,y,f(z,u,f(x,z,w)))) = f(x,z,y). [para(2013(a,1),24(a,1)),flip(a)]. given #174 (T,wt=22): 6205 f(x,y,f(x,z,f(u,z,f(z,y,w)))) = f(x,z,y). [para(3937(a,1),21(a,1,3)),rewrite([5(1,R),6(1),6(3),1079(4),5(2,R),6(2)]),flip(a)]. given #175 (A,wt=31): 77 f(x,y,f(x,z,f(u,w,f(x,w,v5)))) = f(x,w,f(x,y,f(x,z,f(u,w,v5)))). [para(24(a,1),18(a,1,3,3))]. given #176 (T,wt=22): 6213 f(x,y,f(z,u,f(z,w,f(x,z,y)))) = f(x,z,y). [para(4085(a,1),5(a,2)),rewrite([5(1),5(1),6(4),5(5),5(5)])]. given #177 (T,wt=22): 6261 f(x,y,f(z,u,f(z,w,f(z,x,y)))) = f(z,x,y). [para(4085(a,1),922(a,2)),rewrite([5(1),5(5),922(9),5(5)])]. given #178 (T,wt=22): 7757 f(x,y,f(z,u,f(z,y,f(z,x,w)))) = f(z,x,y). [para(43(a,1),74(a,2,3)),rewrite([813(4)]),flip(a)]. given #179 (T,wt=22): 7949 f(x,y,f(z,x,f(u,y,f(z,y,w)))) = f(z,x,y). [back_rewrite(5339),rewrite([7900(10)])]. given #180 (A,wt=31): 78 f(x,y,f(z,u,f(y,z,f(z,w,v5)))) = f(y,z,f(x,y,f(z,w,f(z,u,v5)))). [para(18(a,1),24(a,1,3)),rewrite([5(2,R),6(2),5(8,R),6(8)])]. given #181 (T,wt=22): 8635 f(x,y,f(z,u,f(x,u,f(u,w,y)))) = f(x,u,y). [back_rewrite(4361),rewrite([8369(11)])]. given #182 (T,wt=22): 8636 f(x,y,f(z,u,f(u,w,f(x,u,y)))) = f(x,u,y). [para(5305(a,1),5(a,2)),rewrite([5(1),5(1),6(4),5(5),5(5)])]. given #183 (T,wt=22): 8653 f(x,y,f(z,u,f(u,w,f(u,x,y)))) = f(u,x,y). [para(5305(a,1),922(a,2)),rewrite([5(1),5(5),922(9),5(5)])]. given #184 (T,wt=22): 8746 f(x,y,f(y,z,f(u,z,f(x,z,w)))) = f(x,y,z). [para(2861(a,1),8713(a,2)),rewrite([5(1,R),6(1),5(3),5(3),28(5),6(3),5(5),5(5)])]. given #185 (A,wt=31): 79 f(x,y,f(z,u,f(z,x,f(z,w,v5)))) = f(z,x,f(x,y,f(z,w,f(z,u,v5)))). [para(18(a,1),24(a,2,3)),rewrite([5(3,R),6(3),5(8,R),6(8)]),flip(a)]. given #186 (T,wt=22): 9577 f(x,y,f(z,u,f(u,x,f(u,w,y)))) = f(u,x,y). [para(8635(a,1),922(a,2)),rewrite([5(2,R),6(2),5(6,R),6(6),922(9),5(5,R),6(5)])]. given #187 (T,wt=24): 82 f(x,y,f(z,u,f(x,z,w))) = f(x,z,f(x,y,f(z,w,u))). [para(30(a,2),8(a,2,3)),flip(a)]. given #188 (T,wt=24): 83 f(x,f(y,z,u),f(y,u,f(x,y,z))) = f(x,y,f(y,z,u)). [para(30(a,2),19(a,1,3))]. given #189 (T,wt=24): 87 f(x,y,f(y,z,f(y,u,w))) = f(y,z,f(y,w,f(x,y,u))). [para(30(a,2),24(a,2,3)),rewrite([5(2,R),6(2),5(6,R),6(6)])]. given #190 (A,wt=31): 80 f(x,y,f(z,u,f(z,w,f(y,z,v5)))) = f(y,z,f(x,y,f(z,u,f(z,w,v5)))). [para(18(a,2),24(a,1,3)),rewrite([5(1,R),6(1),5(8,R),6(8)])]. given #191 (T,wt=21): 10204 f(x,f(y,z,f(u,y,w)),f(u,y,x)) = f(u,y,x). [para(80(a,1),828(a,1)),rewrite([5(3,R),6(3),813(4),5(4)]),flip(a)]. given #192 (T,wt=21): 10352 f(x,f(y,z,x),f(z,u,f(y,z,w))) = f(y,z,x). [para(10204(a,1),6(a,1)),flip(a)]. given #193 (T,wt=24): 90 f(x,y,f(x,z,f(x,u,w))) = f(x,w,f(x,y,f(x,u,z))). [para(8(a,1),31(a,2,3)),rewrite([57(3),6(1),6(4)])]. given #194 (T,wt=24): 91 f(x,y,f(x,z,f(x,u,w))) = f(x,w,f(x,u,f(x,y,z))). [para(17(a,1),31(a,2,3)),rewrite([57(3),6(1),6(4)])]. given #195 (A,wt=31): 81 f(x,y,f(z,u,f(z,w,f(z,x,v5)))) = f(z,x,f(x,y,f(z,u,f(z,w,v5)))). [para(18(a,2),24(a,2,3)),rewrite([5(3,R),6(3),5(8,R),6(8)]),flip(a)]. given #196 (T,wt=24): 92 f(x,y,f(x,z,f(x,u,w))) = f(x,y,f(x,w,f(x,u,z))). [para(31(a,1),18(a,1)),rewrite([57(3),6(1),6(4)])]. given #197 (T,wt=24): 97 f(x,y,f(z,u,f(x,z,w))) = f(x,y,f(x,z,f(z,u,w))). [para(16(a,2),21(a,2,3)),rewrite([21(5)]),flip(a)]. given #198 (T,wt=24): 105 f(x,y,f(z,u,f(x,u,w))) = f(x,y,f(x,u,f(z,u,w))). [para(24(a,1),21(a,2,3)),rewrite([21(5)]),flip(a)]. given #199 (T,wt=24): 107 f(x,y,f(z,u,f(x,z,w))) = f(x,y,f(x,z,f(z,w,u))). [para(30(a,2),21(a,2,3)),rewrite([21(5)]),flip(a)]. given #200 (A,wt=31): 85 f(x,y,f(x,z,f(u,w,f(x,u,v5)))) = f(x,z,f(x,u,f(x,y,f(u,v5,w)))). [para(30(a,2),18(a,2,3,3)),flip(a)]. given #201 (T,wt=24): 108 f(x,y,f(y,z,f(y,u,w))) = f(x,y,f(y,u,f(y,z,w))). [para(8(a,1),28(a,2,3)),rewrite([28(4)])]. given #202 (T,wt=24): 111 f(x,y,f(z,u,f(y,z,w))) = f(x,y,f(y,z,f(z,u,w))). [para(16(a,2),28(a,2,3)),rewrite([28(4)]),flip(a)]. given #203 (T,wt=24): 113 f(x,y,f(y,z,f(y,u,w))) = f(x,y,f(y,w,f(y,z,u))). [para(17(a,1),28(a,2,3)),rewrite([28(4)])]. given #204 (T,wt=24): 120 f(x,y,f(z,u,f(y,z,w))) = f(x,y,f(y,z,f(z,w,u))). [para(30(a,2),28(a,2,3)),rewrite([28(4)]),flip(a)]. given #205 (A,wt=31): 86 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,z,f(x,y,f(x,v5,f(x,u,w)))). [para(18(a,2),30(a,2,3)),rewrite([5(3,R),6(3),57(4),6(5),5(8,R),6(8)]),flip(a)]. Low Water (keep): wt=50.000, iters=6748 given #206 (T,wt=24): 125 f(x,y,f(z,u,f(z,x,w))) = f(x,y,f(z,x,f(z,u,w))). [para(8(a,1),122(a,1,3,3)),rewrite([5(3,R),6(3),103(4),5(6,R),6(6)])]. given #207 (T,wt=18): 12311 f(x,y,f(y,z,f(u,x,z))) = f(x,y,z). [para(125(a,1),1469(a,2)),rewrite([20(3),15(3),5(3,R),6(3),6720(5),6(3)]),flip(a)]. given #208 (T,wt=18): 12402 f(x,y,f(x,z,f(u,z,y))) = f(x,z,y). [para(12311(a,1),474(a,2)),rewrite([5(3,R),6(3),21(5),5(4,R),6(4)])]. given #209 (T,wt=24): 130 f(x,y,f(z,u,f(z,y,w))) = f(z,y,f(x,y,f(z,u,w))). [para(25(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5,R),6(5),5(6,R),6(6)])]. given #210 (A,wt=31): 93 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,w,f(x,u,f(x,y,f(x,z,v5)))). [para(18(a,1),31(a,2,3)),rewrite([57(4)]),flip(a)]. Low Water (keep): wt=49.000, iters=6691 given #211 (T,wt=24): 168 f(x,f(y,z,u),f(y,z,f(y,u,x))) = f(y,x,f(y,z,u)). [para(27(a,1),5(a,2)),rewrite([5(2),5(2),5(4),5(6,R),6(6)])]. given #212 (T,wt=17): 12982 f(x,f(y,z,u),f(y,u,x)) = f(y,u,x). [para(1072(a,1),168(a,1,3)),rewrite([5(2),5(2),5(3),5(3),15(4),5(3),5(3)]),flip(a)]. Low Water (keep): wt=48.000, iters=6841 given #213 (T,wt=20): 13139 f(x,f(y,z,x),f(z,u,x)) = f(y,x,f(z,u,x)). [para(12982(a,1),74(a,2,3)),rewrite([5(3),6(3),1030(5),5(4),5(5,R)]),flip(a)]. given #214 (T,wt=20): 13180 f(x,f(y,x,z),f(y,u,x)) = f(x,z,f(y,u,x)). [para(13139(a,1),922(a,2)),rewrite([5(2),5(2),6(3),5(4),5(4),12982(7),5(5,R),6(5)])]. given #215 (A,wt=31): 94 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,u,f(x,y,f(x,w,f(x,v5,z)))). [para(18(a,2),31(a,2,3)),rewrite([57(4),6(5)])]. Low Water (keep): wt=47.000, iters=6701 given #216 (T,wt=21): 13008 f(x,f(y,z,f(y,u,w)),f(y,w,x)) = f(y,w,x). [para(1082(a,1),168(a,1,3)),rewrite([5(3),5(3),5(4),5(4),15(5),5(4),5(4)]),flip(a)]. given #217 (T,wt=22): 13421 f(x,y,f(z,u,f(x,z,f(z,w,y)))) = f(x,z,y). [para(13008(a,1),1072(a,2)),rewrite([5(3),5(6),5(7,R),12402(9),12432(4),5(5)])]. given #218 (T,wt=22): 13496 f(x,y,f(z,u,f(z,x,f(z,w,y)))) = f(z,x,y). [para(13421(a,1),922(a,2)),rewrite([5(2,R),6(2),5(6,R),6(6),922(9),5(5,R),6(5)])]. given #219 (T,wt=24): 169 f(x,f(y,z,u),f(z,u,f(x,y,z))) = f(x,z,f(y,z,u)). [para(5(a,1),27(a,1,2)),rewrite([6(2),5(5)])]. given #220 (A,wt=28): 95 f(x,y,f(x,z,f(y,u,f(x,y,w)))) = f(x,z,f(y,u,f(x,y,w))). [para(21(a,1),16(a,1,3)),rewrite([5(1),5(4),5(7,R),6(7)]),flip(a)]. given #221 (T,wt=20): 13533 f(x,f(y,z,x),f(u,y,x)) = f(u,x,f(y,z,x)). [para(19(a,1),169(a,1,2)),rewrite([7298(5),19(5)])]. Low Water (keep): wt=46.000, iters=6667 given #222 (T,wt=20): 13767 f(x,f(y,z,x),f(y,x,u)) = f(x,u,f(y,z,x)). [para(13533(a,1),5(a,2)),rewrite([5(2),5(2),5(3),5(5,R),6(5)])]. given #223 (T,wt=24): 170 f(x,f(y,z,u),f(y,u,f(x,z,u))) = f(x,u,f(y,z,u)). [para(5(a,2),27(a,1,2)),rewrite([6(2),5(3,R),6(3),5(5),5(5)])]. given #224 (T,wt=24): 210 f(x,y,f(x,z,f(x,u,w))) = f(x,w,f(x,z,f(x,y,u))). [para(132(a,1),31(a,2,3)),rewrite([205(2),57(3),6(1)])]. given #225 (A,wt=31): 96 f(x,f(y,z,u),f(x,w,f(y,z,f(x,y,u)))) = f(x,w,f(x,y,f(y,z,u))). [para(16(a,2),21(a,1,3,3))]. given #226 (T,wt=22): 14180 f(x,y,f(x,z,f(z,u,f(z,w,y)))) = f(x,z,y). [para(13421(a,1),96(a,1,3)),rewrite([392(4),1082(4)]),flip(a)]. given #227 (T,wt=24): 216 f(x,y,f(z,u,f(z,y,w))) = f(x,y,f(z,y,f(z,u,w))). [para(25(a,1),205(a,1,3)),rewrite([5(1,R),6(1),5(4,R),6(4),5(5,R),6(5),176(6),5(4,R),6(4),5(6,R),6(6)]),flip(a)]. Low Water (keep): wt=45.000, iters=6763 given #228 (T,wt=24): 220 f(x,y,f(z,u,f(u,y,w))) = f(u,y,f(x,y,f(z,u,w))). [para(29(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5,R),6(5),5(6,R),6(6)])]. given #229 (T,wt=24): 262 f(x,y,f(z,u,f(u,y,w))) = f(x,y,f(u,y,f(z,u,w))). [para(29(a,1),205(a,1,3)),rewrite([5(1,R),6(1),5(4,R),6(4),5(5,R),6(5),187(6),5(4,R),6(4),5(6,R),6(6)]),flip(a)]. given #230 (A,wt=35): 98 f(x,y,f(x,z,f(x,u,f(x,w,f(x,v5,y))))) = f(x,z,f(x,u,f(x,w,f(x,v5,y)))). [para(21(a,1),18(a,1,3,3)),flip(a)]. given #231 (T,wt=24): 298 f(x,y,f(z,x,f(x,u,w))) = f(z,x,f(x,u,f(x,w,y))). [para(33(a,1),5(a,2)),rewrite([6(3),5(5,R),6(5)]),flip(a)]. given #232 (T,wt=24): 318 f(x,f(y,z,u),f(y,x,w)) = f(x,w,f(y,z,f(y,u,x))). [para(38(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4)])]. given #233 (T,wt=20): 14665 f(f(x,y,z),f(z,u,w),f(x,y,z)) = f(x,y,z). [para(1073(a,1),318(a,1,3)),rewrite([9279(10)])]. given #234 (T,wt=20): 14673 f(f(x,y,z),f(y,u,w),f(x,y,z)) = f(x,y,z). [para(1181(a,1),318(a,1,3)),rewrite([9281(10)])]. given #235 (A,wt=35): 99 f(x,y,f(x,z,f(x,u,f(x,w,f(x,y,v5))))) = f(x,z,f(x,w,f(x,y,f(x,u,v5)))). [para(18(a,1),21(a,1,3,3)),rewrite([57(7),6(5),57(5),6(3),21(3),20(4)])]. given #236 (T,wt=20): 14825 f(f(x,y,z),f(x,u,w),f(x,y,z)) = f(x,y,z). [para(318(a,1),216(a,2)),rewrite([6(4),4(6),19(5),20(5)]),flip(a)]. given #237 (T,wt=24): 319 f(x,f(y,z,u),f(w,y,x)) = f(w,x,f(y,z,f(y,x,u))). [para(38(a,2),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5),5(5)]),flip(a)]. given #238 (T,wt=17): 15212 f(x,f(y,x,z),f(u,y,z)) = f(y,x,z). [para(319(a,2),8713(a,1,3)),rewrite([5(2,R),6(2),5(4),5(4),20(4),7293(5),5(6,R),6(6),5(7,R),6(7),3946(7),1982(6)])]. given #239 (T,wt=17): 15213 f(x,f(y,z,u),f(z,x,u)) = f(z,x,u). [para(319(a,2),8713(a,2)),rewrite([5(4,R),6(4),5(5,R),6(5),3946(5),1982(4),15(3),5(2,R),6(2),5(4),5(4),20(4)]),flip(a)]. given #240 (A,wt=31): 100 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,y,f(x,w,f(x,z,f(x,u,v5)))). [para(18(a,1),21(a,2,3)),rewrite([21(7)])]. given #241 (T,wt=18): 15289 f(x,y,f(z,x,f(z,u,y))) = f(z,x,y). [back_rewrite(5760),rewrite([15189(9)])]. given #242 (T,wt=20): 15161 f(f(x,y,z),f(u,w,v5),f(x,y,z)) = f(x,y,z). [para(319(a,1),54(a,2,3)),rewrite([5(5),5(5),19(5),20(5),5(5,R),15(5),6(9),4(11),5(7,R),15(7)])]. given #243 (T,wt=22): 15288 f(x,y,f(z,u,f(z,y,f(z,w,x)))) = f(z,x,y). [back_rewrite(13417),rewrite([15153(9),6(2)])]. given #244 (T,wt=17): 15771 f(x,f(y,z,u),f(x,z,u)) = f(x,z,u). [para(15288(a,1),922(a,1,2)),rewrite([5(2),5(4)])]. given #245 (A,wt=31): 101 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,y,f(x,v5,f(x,z,f(x,u,w)))). [para(18(a,2),21(a,1,3,3)),rewrite([6(3),57(7),6(5),57(5),6(3),22(3),22(4),22(5)])]. given #246 (T,wt=17): 15796 f(x,f(y,z,u),f(x,y,u)) = f(x,y,u). [para(15288(a,1),2885(a,1,2))]. given #247 (T,wt=17): 15821 f(x,f(y,z,u),f(x,y,z)) = f(x,y,z). [para(15288(a,1),5467(a,1,2)),rewrite([5(2,R),6(2),5(4,R),6(4)])]. given #248 (T,wt=21): 15794 f(x,f(y,z,f(z,u,w)),f(x,z,w)) = f(x,z,w). [para(15288(a,1),2861(a,1,2,3)),rewrite([5(1,R),6(1),5(3),5(5)])]. given #249 (T,wt=21): 15800 f(x,f(y,z,f(y,u,w)),f(x,y,w)) = f(x,y,w). [para(15288(a,1),3627(a,1,2,3)),rewrite([5(1,R),6(1),5(3),5(5)])]. given #250 (A,wt=28): 102 f(x,y,f(z,x,f(y,u,f(x,y,w)))) = f(z,x,f(y,u,f(x,y,w))). [para(21(a,1),24(a,1,3)),rewrite([5(1),5(4),5(7,R),6(7)]),flip(a)]. given #251 (T,wt=21): 15929 f(x,f(y,z,f(z,u,w)),f(x,z,u)) = f(x,z,u). [para(2861(a,1),15771(a,2)),rewrite([5(3),5(7),15771(9),5(5)])]. given #252 (T,wt=21): 15935 f(x,f(y,z,f(y,u,w)),f(x,y,u)) = f(x,y,u). [para(3627(a,1),15771(a,2)),rewrite([5(3),5(7),15771(9),5(5)])]. given #253 (T,wt=24): 321 f(x,f(y,z,u),f(x,u,w)) = f(x,w,f(y,u,f(x,z,u))). [para(5(a,2),38(a,1,2)),rewrite([6(2),6(4),5(5,R),6(5)])]. given #254 (T,wt=17): 16490 f(x,f(y,z,u),f(y,x,u)) = f(y,x,u). [para(321(a,2),30(a,2)),rewrite([5(2,R),6(2),15796(3),5(3)]),flip(a)]. given #255 (A,wt=28): 103 f(x,y,f(y,z,f(x,u,f(x,y,w)))) = f(y,z,f(x,u,f(x,y,w))). [para(21(a,1),24(a,2,3)),rewrite([6(1),5(3,R),6(3),6(5),5(7,R),6(7)])]. given #256 (T,wt=21): 16471 f(x,y,f(z,y,f(x,u,y))) = f(x,y,f(z,u,y)). [para(15(a,1),321(a,1,3)),rewrite([6(2)]),flip(a)]. given #257 (T,wt=24): 436 f(x,y,f(z,y,f(y,u,w))) = f(z,y,f(y,u,f(x,y,w))). [para(40(a,1),5(a,2)),rewrite([6(3),5(4,R),6(4)])]. given #258 (T,wt=24): 471 f(x,y,f(y,z,f(y,u,w))) = f(y,u,f(y,z,f(x,y,w))). [para(41(a,2),8(a,1))]. given #259 (T,wt=24): 478 f(x,f(y,x,z),f(x,u,w)) = f(y,x,f(x,u,f(x,w,z))). [para(41(a,2),17(a,1)),flip(a)]. given #260 (A,wt=31): 104 f(x,f(y,z,u),f(x,w,f(y,z,f(x,z,u)))) = f(x,w,f(x,z,f(y,z,u))). [para(24(a,1),21(a,1,3,3))]. given #261 (T,wt=22): 17596 f(x,y,f(x,z,f(u,z,f(z,w,y)))) = f(x,z,y). [para(8635(a,1),104(a,1,3)),rewrite([15794(4)]),flip(a)]. given #262 (T,wt=24): 479 f(x,y,f(y,z,f(y,u,w))) = f(y,u,f(y,w,f(x,y,z))). [para(17(a,1),41(a,1,3))]. given #263 (T,wt=24): 482 f(x,y,f(y,z,f(y,u,w))) = f(y,w,f(y,z,f(x,y,u))). [para(17(a,2),41(a,1,3))]. given #264 (T,wt=24): 495 f(x,y,f(y,z,f(y,u,w))) = f(y,w,f(y,u,f(x,y,z))). [para(31(a,1),41(a,1,3))]. given #265 (A,wt=31): 106 f(x,f(y,z,u),f(x,w,f(y,u,f(x,y,z)))) = f(x,w,f(x,y,f(y,z,u))). [para(30(a,2),21(a,1,3,3))]. given #266 (T,wt=24): 630 f(x,y,f(z,u,f(z,x,w))) = f(x,y,f(z,w,f(z,x,u))). [para(474(a,1),24(a,2,3)),rewrite([5(1),5(1),5(3,R),6(3),103(4),6(4),5(5,R),6(5),5(6,R),6(6)])]. given #267 (T,wt=22): 18363 f(x,y,f(z,u,f(y,u,f(x,z,u)))) = f(x,y,u). [para(630(a,1),9577(a,1,3)),rewrite([5(1),6(1),5(2,R),6(2),5(5),5(5)])]. Low Water (keep): wt=44.000, iters=6709 given #268 (T,wt=18): 18457 f(x,y,f(z,y,f(x,u,z))) = f(x,z,y). [para(18363(a,1),6(a,2)),rewrite([5(2,R),6(2),8713(3),6(3),6(4)])]. given #269 (T,wt=18): 18491 f(x,y,f(z,y,f(z,u,x))) = f(z,x,y). [para(18363(a,1),4461(a,2)),rewrite([5(2,R),6(2),8713(3),5(5,R),6(5),8713(6),6(6),4572(8),6(4)])]. given #270 (A,wt=28): 110 f(x,y,f(y,z,f(y,u,f(x,y,w)))) = f(x,y,f(y,z,f(y,u,w))). [para(16(a,2),28(a,1,3,3))]. given #271 (T,wt=24): 738 f(x,y,f(z,u,f(x,z,w))) = f(x,y,f(z,w,f(x,z,u))). [para(474(a,1),655(a,1,3)),rewrite([5(1),6(1),5(4),5(5,R),6(5),6(6),653(6),5(4),6(4),5(7,R),6(7),95(7)])]. given #272 (T,wt=24): 847 f(x,f(y,z,u),f(x,w,f(x,y,z))) = f(x,w,f(x,y,z)). [para(803(a,1),33(a,1,3)),rewrite([6(4)]),flip(a)]. given #273 (T,wt=24): 854 f(x,y,f(z,x,f(x,u,w))) = f(x,u,f(z,x,f(x,y,w))). [para(40(a,2),803(a,2)),rewrite([6(5),392(7),6(6),820(7)])]. given #274 (T,wt=24): 860 f(x,y,f(z,x,f(x,u,w))) = f(x,y,f(x,u,f(z,x,w))). [para(41(a,1),803(a,2)),rewrite([6(5),392(7),6(6),820(7)])]. given #275 (A,wt=35): 114 f(x,y,f(x,z,f(x,u,f(y,w,f(x,y,v5))))) = f(x,z,f(x,u,f(x,y,f(y,w,v5)))). [para(28(a,1),18(a,1,3,3)),flip(a)]. given #276 (T,wt=24): 872 f(x,y,f(x,f(z,y,u),f(x,w,z))) = f(x,w,f(x,z,y)). [back_rewrite(411),rewrite([866(3)]),flip(a)]. given #277 (T,wt=21): 19048 f(x,f(y,z,f(u,w,y)),f(x,u,y)) = f(x,u,y). [para(1072(a,1),872(a,2)),rewrite([6(3),2175(6)])]. Low Water (keep): wt=43.000, iters=6673 given #278 (T,wt=21): 19051 f(x,f(y,z,f(u,w,y)),f(x,w,y)) = f(x,w,y). [para(1634(a,1),872(a,2)),rewrite([6(3),1254(6)])]. given #279 (T,wt=21): 19249 f(x,f(y,z,f(u,w,z)),f(x,w,z)) = f(x,w,z). [para(5(a,2),19051(a,1,2)),rewrite([6(2)])]. given #280 (A,wt=31): 115 f(x,y,f(x,z,f(u,w,f(x,u,v5)))) = f(x,z,f(x,y,f(x,u,f(u,w,v5)))). [para(28(a,1),18(a,2,3,3)),rewrite([95(4)])]. given #281 (T,wt=24): 905 f(x,y,f(z,u,f(x,w,z))) = f(x,y,f(x,z,f(w,z,u))). [para(874(a,2),21(a,2,3)),rewrite([21(5)]),flip(a)]. given #282 (T,wt=24): 929 f(x,y,f(z,u,f(x,w,z))) = f(x,z,f(x,y,f(w,z,u))). [para(874(a,2),474(a,2,3)),rewrite([5(3,R),6(3),21(5),5(6,R),6(6)]),flip(a)]. given #283 (T,wt=24): 1037 f(x,y,f(z,u,f(x,w,u))) = f(x,y,f(x,u,f(z,w,u))). [para(897(a,1),21(a,2,3)),rewrite([21(5)]),flip(a)]. given #284 (T,wt=24): 1062 f(x,y,f(z,u,f(x,w,u))) = f(x,u,f(x,y,f(z,w,u))). [para(897(a,1),474(a,2,3)),rewrite([5(3,R),6(3),21(5),5(6,R),6(6)]),flip(a)]. given #285 (A,wt=31): 116 f(x,y,f(y,z,f(y,u,f(y,w,v5)))) = f(x,y,f(y,w,f(y,z,f(y,u,v5)))). [para(18(a,1),28(a,2,3)),rewrite([28(5)])]. given #286 (T,wt=24): 1105 f(x,y,f(z,u,f(u,x,w))) = f(u,x,f(x,y,f(z,u,w))). [para(29(a,1),922(a,2)),rewrite([5(1,R),6(1),5(4,R),6(4),922(7),5(6,R),6(6)])]. given #287 (T,wt=24): 1119 f(x,f(y,z,u),f(y,x,w)) = f(x,w,f(y,z,f(y,x,u))). [para(38(a,2),922(a,2)),rewrite([5(1,R),6(1),5(4,R),6(4),922(7),5(5)]),flip(a)]. given #288 (T,wt=24): 1136 f(x,f(y,z,u),f(x,w,f(y,z,w))) = f(x,w,f(y,z,u)). [para(922(a,1),803(a,1,3,3))]. given #289 (T,wt=24): 1138 f(f(x,y,z),f(x,y,f(y,z,u)),f(x,z,w)) = f(x,y,z). [para(803(a,1),922(a,1,3)),rewrite([5(5),803(8)])]. given #290 (A,wt=35): 117 f(x,y,f(y,z,f(x,u,f(x,w,f(x,y,v5))))) = f(x,y,f(y,z,f(x,u,f(x,w,v5)))). [para(18(a,2),28(a,1,3,3))]. given #291 (T,wt=24): 1142 f(x,f(y,z,x),f(u,f(y,z,w),f(y,z,x))) = f(y,z,x). [para(922(a,1),874(a,1,3)),rewrite([5(3,R),15(3),5(5)]),flip(a)]. given #292 (T,wt=24): 1148 f(x,f(y,z,u),f(x,u,f(y,z,w))) = f(x,u,f(y,z,w)). [para(922(a,1),922(a,1,2)),rewrite([5(3),5(6)])]. given #293 (T,wt=24): 1176 f(x,f(y,z,u),f(x,u,w)) = f(x,w,f(z,u,f(x,y,u))). [para(933(a,1),828(a,2,3)),rewrite([5(2,R),6(2),5(4)])]. given #294 (T,wt=24): 1179 f(f(x,y,z),f(x,y,u),f(u,w,f(x,y,u))) = f(x,y,u). [para(922(a,1),933(a,1,3)),rewrite([5(3,R),15(3),6(5)]),flip(a)]. given #295 (A,wt=28): 118 f(x,y,f(z,x,f(x,u,f(x,y,w)))) = f(z,x,f(x,y,f(x,u,w))). [para(28(a,1),24(a,1,3)),rewrite([5(2,R),6(2),5(4,R),6(4),5(7,R),6(7)]),flip(a)]. Low Water (keep): wt=42.000, iters=6821 given #296 (T,wt=24): 1197 f(x,f(y,z,u),f(w,x,y)) = f(w,x,f(y,z,f(x,y,u))). [para(38(a,2),1057(a,2)),rewrite([6(3),5(6,R),6(6),392(7),1072(7),5(5,R),6(5)]),flip(a)]. given #297 (T,wt=24): 1208 f(x,f(y,x,z),f(u,f(y,z,w),f(y,x,z))) = f(y,x,z). [para(1057(a,1),874(a,1,3)),rewrite([5(3,R),15(3),5(5)]),flip(a)]. given #298 (T,wt=24): 1212 f(f(x,y,z),f(x,u,y),f(u,w,f(x,u,y))) = f(x,u,y). [para(1057(a,1),933(a,1,3)),rewrite([5(3,R),15(3),6(5)]),flip(a)]. given #299 (T,wt=24): 1254 f(x,f(y,z,u),f(x,w,f(x,z,u))) = f(x,w,f(x,z,u)). [para(1071(a,1),8(a,2,3))]. given #300 (A,wt=28): 123 f(x,y,f(x,z,f(u,y,f(x,y,w)))) = f(x,z,f(u,y,f(x,y,w))). [para(73(a,1),16(a,1,3)),rewrite([5(1,R),6(1),5(4,R),6(4),5(7,R),6(7)]),flip(a)]. given #301 (T,wt=24): 1286 f(x,f(y,z,u),f(x,u,f(x,z,w))) = f(x,w,f(x,z,u)). [para(1071(a,1),32(a,2,3)),rewrite([6(2)])]. Low Water (keep): wt=41.000, iters=6700 given #302 (T,wt=24): 1301 f(x,y,f(x,f(z,x,u),f(y,u,w))) = f(z,x,f(x,y,u)). [para(1071(a,1),41(a,1,3)),rewrite([5(3),5(3),392(6)]),flip(a)]. given #303 (T,wt=24): 1323 f(x,y,f(x,f(y,z,u),f(x,w,z))) = f(x,w,f(x,y,z)). [para(1071(a,1),43(a,1,3)),rewrite([5(3),5(3)]),flip(a)]. given #304 (T,wt=24): 1329 f(x,f(y,z,u),f(x,w,f(z,u,w))) = f(x,w,f(y,z,u)). [para(1071(a,1),803(a,1,3,3)),rewrite([5(2),5(2)])]. given #305 (A,wt=28): 124 f(x,y,f(z,x,f(u,y,f(x,y,w)))) = f(z,x,f(u,y,f(x,y,w))). [para(73(a,1),24(a,1,3)),rewrite([5(1,R),6(1),5(4,R),6(4),5(7,R),6(7)]),flip(a)]. given #306 (T,wt=24): 1341 f(x,y,f(x,f(z,u,w),f(y,z,u))) = f(x,y,f(z,u,w)). [para(1071(a,1),922(a,1,2)),rewrite([5(2),5(2),5(3),392(4),5(5),5(5),5(6)])]. given #307 (T,wt=21): 21542 f(x,y,f(z,f(x,y,z),f(u,w,v5))) = f(x,y,z). [para(1341(a,1),6221(a,1,3))]. given #308 (T,wt=21): 21599 f(x,y,f(z,f(x,z,y),f(u,w,v5))) = f(x,z,y). [para(21542(a,1),5(a,2)),rewrite([5(1),5(1),6(4),5(5),5(5)])]. given #309 (T,wt=24): 1342 f(f(x,y,z),f(u,x,y),f(u,w,f(u,x,y))) = f(u,x,y). [para(1071(a,1),933(a,1,3)),rewrite([5(3,R),15(3),5(2),5(2),6(5)]),flip(a)]. given #310 (A,wt=35): 127 f(x,y,f(x,z,f(x,u,f(w,y,f(x,y,v5))))) = f(x,z,f(x,u,f(w,y,f(x,y,v5)))). [para(122(a,1),18(a,1,3,3)),flip(a)]. given #311 (T,wt=24): 1344 f(f(x,y,z),f(y,z,u),f(u,w,f(y,z,u))) = f(y,z,u). [para(1071(a,1),1057(a,1,3)),rewrite([5(2),5(2),6(3),5(4),5(4),6(5),5(7),5(7),1253(8)])]. given #312 (T,wt=24): 1355 f(x,f(y,z,x),f(u,f(y,z,x),f(y,z,w))) = f(y,z,x). [para(1073(a,1),24(a,1,3)),rewrite([15(3)]),flip(a)]. given #313 (T,wt=24): 1393 f(f(x,y,z),f(x,z,u),f(x,y,f(y,z,w))) = f(x,y,z). [para(803(a,1),1073(a,1,2)),rewrite([5(5,R),803(8)])]. Low Water (keep): wt=40.000, iters=6694 given #314 (T,wt=24): 1394 f(f(x,y,z),f(x,y,u),f(z,w,f(x,y,z))) = f(x,y,z). [para(1073(a,1),828(a,1,3)),rewrite([5(3,R),15(3),6(5)]),flip(a)]. given #315 (A,wt=31): 128 f(x,y,f(z,u,f(z,x,f(z,w,v5)))) = f(x,y,f(z,x,f(z,w,f(z,u,v5)))). [para(18(a,1),122(a,1,3,3)),rewrite([5(4,R),6(4),103(5),5(8,R),6(8)])]. given #316 (T,wt=24): 1404 f(x,y,f(x,f(z,u,w),f(y,u,w))) = f(x,y,f(z,u,w)). [para(1071(a,1),1073(a,1,3)),rewrite([5(2),6(4),392(4),5(6)])]. given #317 (T,wt=24): 1430 f(f(x,y,z),f(y,z,u),f(x,w,f(x,y,z))) = f(x,y,z). [para(1074(a,1),828(a,1,3)),rewrite([5(3,R),15(3),6(5)]),flip(a)]. given #318 (T,wt=24): 1440 f(x,y,f(z,u,f(x,w,u))) = f(x,y,f(x,u,f(w,z,u))). [para(1149(a,1),21(a,2,3)),rewrite([21(5)]),flip(a)]. given #319 (T,wt=24): 1463 f(x,y,f(z,u,f(x,w,u))) = f(x,u,f(x,y,f(w,z,u))). [para(1149(a,1),474(a,2,3)),rewrite([5(3,R),6(3),21(5),5(6,R),6(6)]),flip(a)]. given #320 (A,wt=31): 131 f(x,y,f(z,u,f(x,w,f(x,z,v5)))) = f(x,z,f(x,y,f(z,u,f(x,w,v5)))). [para(8(a,1),25(a,1,3,3))]. given #321 (T,wt=24): 1474 f(f(x,y,z),f(x,y,u),f(w,u,f(x,y,u))) = f(x,y,u). [para(922(a,1),1149(a,1,3)),rewrite([15(3)]),flip(a)]. given #322 (T,wt=24): 1475 f(f(x,y,z),f(x,u,y),f(w,u,f(x,u,y))) = f(x,u,y). [para(1057(a,1),1149(a,1,3)),rewrite([15(3)]),flip(a)]. given #323 (T,wt=24): 1478 f(f(x,y,z),f(u,x,y),f(w,u,f(u,x,y))) = f(u,x,y). [para(1071(a,1),1149(a,1,3)),rewrite([15(3),5(2),5(2)]),flip(a)]. given #324 (T,wt=24): 1541 f(x,f(y,x,z),f(u,f(y,x,z),f(y,z,w))) = f(y,x,z). [para(1181(a,1),24(a,1,3)),rewrite([15(3)]),flip(a)]. given #325 (A,wt=31): 133 f(x,y,f(z,u,f(x,z,f(u,w,v5)))) = f(x,z,f(x,y,f(u,w,f(z,u,v5)))). [para(25(a,1),16(a,1,3)),rewrite([5(2,R),6(2),5(8,R),6(8)])]. given #326 (T,wt=24): 1557 f(f(x,y,z),f(x,z,u),f(y,w,f(x,y,z))) = f(x,y,z). [para(1181(a,1),828(a,1,3)),rewrite([5(3,R),15(3),6(5)]),flip(a)]. given #327 (T,wt=24): 1630 f(x,y,f(y,f(z,u,w),f(x,z,u))) = f(x,y,f(z,u,w)). [para(922(a,1),812(a,1,3,3)),rewrite([5(2)])]. given #328 (T,wt=24): 1633 f(x,y,f(y,f(z,u,w),f(x,u,w))) = f(x,y,f(z,u,w)). [para(1071(a,1),812(a,1,3,3))]. given #329 (T,wt=24): 1661 f(x,y,f(x,z,f(x,u,w))) = f(x,w,f(x,z,f(x,u,y))). [para(33(a,1),813(a,2)),rewrite([6(5),696(6),57(6),6(4),1200(7)])]. given #330 (A,wt=31): 135 f(x,y,f(z,u,f(x,z,f(z,w,v5)))) = f(x,z,f(x,y,f(z,v5,f(z,u,w)))). [para(17(a,1),25(a,2,3,3))]. Low Water (keep): wt=39.000, iters=6707 given #331 (T,wt=24): 1671 f(x,f(y,z,f(x,u,y)),f(x,w,u)) = f(x,w,f(x,u,y)). [para(827(a,1),17(a,1,3)),flip(a)]. given #332 (T,wt=24): 1724 f(f(x,y,z),f(x,u,f(x,y,z)),f(y,z,w)) = f(x,y,z). [back_rewrite(1712),rewrite([1713(8)])]. given #333 (T,wt=24): 1750 f(f(x,y,z),f(x,y,f(x,z,u)),f(y,z,w)) = f(x,y,z). [para(866(a,1),922(a,1,3)),rewrite([5(3,R),6(3),6(4),5(5),866(8),6(6)])]. Low Water (keep): wt=38.000, iters=6668 given #334 (T,wt=24): 1757 f(f(x,y,z),f(y,z,u),f(x,y,f(x,z,w))) = f(x,y,z). [para(866(a,1),1073(a,1,2)),rewrite([6(3),5(4,R),6(4),5(5,R),866(8),6(6)])]. given #335 (A,wt=38): 136 f(x,y,f(x,z,f(x,u,f(w,v5,f(x,w,v6))))) = f(x,z,f(x,u,f(x,w,f(x,y,f(w,v5,v6))))). [para(25(a,1),18(a,1,3,3)),flip(a)]. given #336 (T,wt=24): 1766 f(x,y,f(y,f(x,z,u),f(z,u,w))) = f(x,y,f(z,u,w)). [para(922(a,1),868(a,1,3,3)),rewrite([5(2),5(3,R),6(6)])]. given #337 (T,wt=21): 23355 f(x,y,f(z,f(y,z,u),f(x,w,z))) = f(x,y,z). [para(1738(a,1),1766(a,1,3)),rewrite([6(2),7553(3),5(4,R),8713(5)]),flip(a)]. given #338 (T,wt=24): 1769 f(x,y,f(y,f(x,z,u),f(w,z,u))) = f(x,y,f(w,z,u)). [para(1071(a,1),868(a,1,3,3)),rewrite([5(3,R),6(6)])]. given #339 (T,wt=24): 1906 f(x,f(y,z,u),f(y,z,f(z,u,x))) = f(z,x,f(y,z,u)). [para(628(a,1),871(a,1,3)),rewrite([6(2),5(4,R),6(4),6(6)])]. given #340 (A,wt=38): 137 f(x,y,f(x,z,f(x,u,f(w,v5,f(x,w,v6))))) = f(x,u,f(x,y,f(x,w,f(x,z,f(w,v5,v6))))). [para(25(a,1),18(a,2,3,3))]. given #341 (T,wt=24): 1987 f(f(x,y,z),f(y,z,u),f(w,x,f(x,y,z))) = f(x,y,z). [para(1030(a,1),1073(a,1,2)),rewrite([5(1,R),6(1),5(3,R),6(3),5(5,R),5(6,R),6(6),1982(8)])]. given #342 (T,wt=24): 1998 f(f(x,y,z),f(u,x,f(x,y,z)),f(y,z,w)) = f(x,y,z). [para(1051(a,1),922(a,1,3)),rewrite([5(1),5(4),5(5),5(6),1982(8)])]. given #343 (T,wt=24): 2175 f(x,f(y,z,u),f(x,w,f(x,y,u))) = f(x,w,f(x,y,u)). [para(1072(a,1),50(a,1,3,3)),rewrite([1072(7)])]. given #344 (T,wt=24): 2206 f(f(x,y,z),f(x,y,f(y,u,z)),f(x,z,w)) = f(x,y,z). [para(1634(a,1),922(a,1,3)),rewrite([5(1),6(4),5(5),5(6),1669(8)])]. given #345 (A,wt=38): 138 f(x,y,f(x,z,f(x,u,f(w,v5,f(x,w,v6))))) = f(x,w,f(x,y,f(x,z,f(x,u,f(w,v5,v6))))). [para(25(a,2),18(a,1,3,3))]. given #346 (T,wt=24): 2209 f(f(x,y,z),f(x,z,u),f(x,y,f(y,w,z))) = f(x,y,z). [para(1634(a,1),1073(a,1,2)),rewrite([5(1),6(3),5(5,R),5(6),1669(8)])]. given #347 (T,wt=24): 3301 f(f(x,y,z),f(y,z,u),f(w,u,f(y,z,u))) = f(y,z,u). [para(3270(a,1),1253(a,1,3)),rewrite([6(5),3270(8)])]. given #348 (T,wt=24): 4003 f(x,y,f(x,f(y,z,u),f(z,u,w))) = f(x,y,f(z,u,w)). [para(922(a,1),3475(a,1,3,3)),rewrite([5(2,R),6(2),5(3),5(4,R),6(4),57(5),20(5),5(6,R),6(6)])]. given #349 (T,wt=21): 23662 f(x,y,f(z,f(x,z,u),f(y,w,z))) = f(x,y,z). [para(1738(a,1),4003(a,1,3)),rewrite([6(2),1072(3),5(4,R),8713(5)]),flip(a)]. given #350 (A,wt=38): 139 f(x,y,f(x,z,f(x,u,f(w,v5,f(x,w,v6))))) = f(x,z,f(x,w,f(x,y,f(x,u,f(w,v5,v6))))). [para(25(a,2),18(a,2,3,3)),flip(a)]. given #351 (T,wt=24): 4005 f(x,y,f(x,f(y,z,u),f(w,z,u))) = f(x,y,f(w,z,u)). [para(1071(a,1),3475(a,1,3,3)),rewrite([5(2,R),6(2),5(4,R),6(4),57(5),20(5),5(6,R),6(6)])]. given #352 (T,wt=24): 4278 f(x,y,f(z,u,f(y,w,u))) = f(x,y,f(y,u,f(w,z,u))). [para(933(a,1),3998(a,2,3)),rewrite([6(2),28(4),6(2),5(4)]),flip(a)]. given #353 (T,wt=24): 5019 f(x,y,f(x,f(z,u,w),f(y,z,w))) = f(x,y,f(z,u,w)). [para(1072(a,1),1082(a,1,3,3))]. given #354 (T,wt=24): 5247 f(x,y,f(z,x,f(x,u,w))) = f(x,u,f(x,y,f(z,x,w))). [para(41(a,1),1726(a,2)),rewrite([6(7),696(8),57(8),6(6),5(9,R),6(9),5244(10)])]. given #355 (A,wt=31): 140 f(x,y,f(x,z,f(u,w,f(x,u,v5)))) = f(x,u,f(x,z,f(x,y,f(u,w,v5)))). [para(25(a,2),18(a,2,3)),flip(a)]. given #356 (T,wt=24): 5454 f(x,y,f(z,x,f(x,u,w))) = f(x,y,f(x,w,f(z,x,u))). [para(32(a,2),1856(a,2)),rewrite([6(7),5(8,R),6(8),5(9,R),6(9),392(10),6(9),4302(10),5(4,R),6(4)])]. given #357 (T,wt=24): 5455 f(x,y,f(z,x,f(x,u,w))) = f(x,w,f(z,x,f(x,y,u))). [para(33(a,1),1856(a,2)),rewrite([6(7),5(8,R),6(8),5(9,R),6(9),392(10),6(9),4302(10),5(5,R),6(5)])]. given #358 (T,wt=24): 5459 f(x,y,f(z,y,f(y,u,w))) = f(x,y,f(y,u,f(z,y,w))). [para(40(a,1),1856(a,2)),rewrite([6(7),5(8,R),6(8),5(9,R),6(9),5448(10),5(4,R),6(4)])]. given #359 (T,wt=24): 5496 f(x,y,f(z,x,f(x,u,w))) = f(z,x,f(x,w,f(x,y,u))). [para(59(a,1),1856(a,2)),rewrite([6(7),5(8,R),6(8),5(9,R),6(9),392(10),6(9),4302(10),5(6,R),6(6)])]. given #360 (A,wt=38): 141 f(x,y,f(z,u,f(x,w,f(x,z,f(x,v5,v6))))) = f(x,z,f(x,y,f(z,u,f(x,v5,f(x,w,v6))))). [para(18(a,1),25(a,1,3,3))]. given #361 (T,wt=24): 5502 f(x,y,f(z,x,f(x,u,w))) = f(x,u,f(x,w,f(z,x,y))). [para(61(a,1),1856(a,2)),rewrite([6(7),5(8,R),6(8),5(9,R),6(9),392(10),6(9),4302(10),5(4,R),6(4)])]. given #362 (T,wt=21): 23961 f(x,y,f(z,x,f(u,x,y))) = f(z,x,f(u,x,y)). [para(5502(a,2),1469(a,2)),rewrite([4(3),6(2),5(4),122(5)]),flip(a)]. given #363 (T,wt=24): 6071 f(x,y,f(z,x,f(x,u,w))) = f(x,w,f(z,x,f(x,u,y))). [para(33(a,1),3678(a,2)),rewrite([5(5,R),6(5),57(7),6065(8),5(5,R),6(5)])]. given #364 (T,wt=24): 6107 f(x,y,f(z,x,f(x,u,w))) = f(z,x,f(x,w,f(x,u,y))). [para(59(a,1),3678(a,2)),rewrite([5(5,R),6(5),57(7),6065(8),5(6,R),6(6)])]. given #365 (A,wt=38): 142 f(x,y,f(z,u,f(x,z,f(z,w,f(z,v5,v6))))) = f(x,z,f(x,y,f(z,v5,f(z,u,f(z,w,v6))))). [para(18(a,1),25(a,2,3,3))]. given #366 (T,wt=24): 6694 f(x,f(y,z,f(x,u,y)),f(w,x,u)) = f(x,y,f(w,x,u)). [para(1071(a,1),4906(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. given #367 (T,wt=24): 6719 f(x,y,f(z,u,f(y,z,w))) = f(y,z,f(x,y,f(z,w,u))). [para(5(a,1),70(a,1,3)),rewrite([5(2),5(2),6(4)])]. given #368 (T,wt=24): 7307 f(x,f(y,z,u),f(x,w,f(y,u,w))) = f(x,w,f(y,z,u)). [para(7121(a,1),1669(a,1,3,3)),rewrite([5(2),5(2)])]. given #369 (T,wt=24): 7334 f(f(x,y,z),f(x,z,u),f(u,w,f(x,z,u))) = f(x,z,u). [back_rewrite(7294),rewrite([7301(8)])]. given #370 (A,wt=38): 143 f(x,y,f(z,u,f(x,w,f(x,v5,f(x,z,v6))))) = f(x,z,f(x,y,f(z,u,f(x,w,f(x,v5,v6))))). [para(18(a,2),25(a,1,3,3))]. given #371 (T,wt=24): 7335 f(f(x,y,z),f(x,z,u),f(w,u,f(x,z,u))) = f(x,z,u). [para(7301(a,1),1253(a,1,3)),rewrite([6(5),7301(8)])]. given #372 (T,wt=24): 7338 f(x,y,f(z,u,f(z,y,w))) = f(x,y,f(z,y,f(z,w,u))). [para(17(a,1),72(a,2,3)),rewrite([72(6)]),flip(a)]. given #373 (T,wt=24): 7343 f(x,y,f(z,y,f(y,u,w))) = f(x,y,f(y,w,f(z,y,u))). [para(30(a,2),72(a,2,3)),rewrite([72(6)])]. given #374 (T,wt=24): 7405 f(x,f(y,z,u),f(y,z,f(z,x,u))) = f(z,x,f(y,z,u)). [para(72(a,1),922(a,1,3)),rewrite([5(1,R),6(1),6(4),5(6,R),6(6),2455(7),5(4,R),6(4)]),flip(a)]. given #375 (A,wt=38): 144 f(x,y,f(z,u,f(x,z,f(z,w,f(z,v5,v6))))) = f(x,z,f(x,y,f(z,w,f(z,v5,f(z,u,v6))))). [para(18(a,2),25(a,2,3,3))]. given #376 (T,wt=24): 7671 f(x,y,f(y,f(z,u,w),f(x,z,w))) = f(x,y,f(z,u,w)). [para(7121(a,1),7553(a,1,3,3))]. given #377 (T,wt=24): 7681 f(x,y,f(y,f(x,z,u),f(z,w,u))) = f(x,y,f(z,w,u)). [para(7121(a,1),7552(a,1,3,3)),rewrite([6(4),28(5)])]. given #378 (T,wt=24): 7761 f(x,f(y,z,u),f(w,x,z)) = f(w,x,f(y,z,f(x,z,u))). [para(74(a,2),828(a,1)),flip(a)]. given #379 (T,wt=24): 8102 f(x,f(y,z,u),f(z,x,w)) = f(x,w,f(y,z,f(z,u,x))). [para(75(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4)])]. given #380 (A,wt=31): 145 f(x,y,f(z,u,f(y,z,f(u,w,v5)))) = f(y,z,f(x,y,f(u,w,f(z,u,v5)))). [para(25(a,1),24(a,1,3)),rewrite([5(2,R),6(2),5(8,R),6(8)])]. given #381 (T,wt=24): 8103 f(x,f(y,z,u),f(w,z,x)) = f(w,x,f(y,z,f(z,x,u))). [para(75(a,2),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5),5(5)]),flip(a)]. given #382 (T,wt=24): 8219 f(x,f(y,z,u),f(z,x,w)) = f(x,w,f(y,z,f(z,x,u))). [para(75(a,2),922(a,2)),rewrite([5(1,R),6(1),5(4,R),6(4),922(7),5(5)]),flip(a)]. given #383 (T,wt=24): 8330 f(x,y,f(x,f(z,u,w),f(z,y,u))) = f(x,y,f(z,u,w)). [para(75(a,2),1088(a,1,2)),rewrite([392(3),813(3),8150(4)])]. given #384 (T,wt=24): 8849 f(x,y,f(z,u,f(z,x,w))) = f(x,y,f(z,x,f(z,w,u))). [para(76(a,2),1076(a,2)),rewrite([6(6),2446(10)]),flip(a)]. given #385 (A,wt=31): 147 f(x,y,f(z,u,f(z,x,f(u,w,v5)))) = f(z,x,f(x,y,f(u,w,f(z,u,v5)))). [para(25(a,1),24(a,2,3)),rewrite([5(3,R),6(3),5(8,R),6(8)]),flip(a)]. given #386 (T,wt=24): 9417 f(x,y,f(z,u,f(y,z,w))) = f(x,y,f(z,w,f(y,z,u))). [para(874(a,1),78(a,1,3,3)),rewrite([5(1),5(1),5(2,R),6(2),20(2),5(4),102(7)])]. given #387 (T,wt=24): 9821 f(x,f(y,z,u),f(y,u,f(y,z,x))) = f(y,x,f(y,z,u)). [para(83(a,1),5(a,2)),rewrite([5(2),5(2),5(4),5(6,R),6(6)])]. given #388 (T,wt=24): 9937 f(x,f(y,x,z),f(x,u,w)) = f(y,x,f(x,u,f(x,z,w))). [para(87(a,2),17(a,1)),flip(a)]. given #389 (T,wt=24): 9988 f(x,y,f(x,f(z,y,u),f(w,x,z))) = f(w,x,f(x,z,y)). [para(803(a,1),87(a,1,3)),flip(a)]. given #390 (A,wt=31): 149 f(x,y,f(z,u,f(y,w,f(y,z,v5)))) = f(y,z,f(x,y,f(z,u,f(y,w,v5)))). [para(25(a,2),24(a,1,3)),rewrite([5(1,R),6(1),5(8,R),6(8)])]. given #391 (T,wt=24): 10010 f(x,y,f(x,f(y,z,u),f(w,x,z))) = f(w,x,f(x,y,z)). [para(813(a,1),87(a,1,3)),flip(a)]. given #392 (T,wt=24): 10494 f(x,y,f(x,z,f(x,u,w))) = f(x,w,f(x,u,f(x,z,y))). [para(91(a,1),6(a,2)),rewrite([6(3),6(4)])]. given #393 (T,wt=24): 10617 f(x,y,f(z,x,f(x,u,w))) = f(x,w,f(x,u,f(z,x,y))). [para(91(a,1),1856(a,2)),rewrite([6(7),5(8,R),6(8),5(9,R),6(9),392(10),6(9),4302(10),5(4,R),6(4)])]. given #394 (T,wt=24): 10630 f(x,y,f(z,x,f(x,u,w))) = f(x,w,f(x,y,f(z,x,u))). [para(91(a,1),3678(a,2)),rewrite([5(5,R),6(5),57(7),6065(8),5(4,R),6(4)])]. given #395 (A,wt=31): 150 f(x,y,f(z,u,f(x,w,f(z,x,v5)))) = f(z,x,f(x,y,f(z,u,f(x,w,v5)))). [para(25(a,2),24(a,2,3)),rewrite([5(3,R),6(3),5(8,R),6(8)]),flip(a)]. given #396 (T,wt=24): 11098 f(x,y,f(z,u,f(x,w,z))) = f(x,y,f(w,z,f(x,z,u))). [para(874(a,2),105(a,2,3)),flip(a)]. given #397 (T,wt=22): 24834 f(x,y,f(z,x,f(y,u,f(z,w,y)))) = f(z,x,y). [para(11098(a,2),74(a,2,3)),rewrite([1738(4)]),flip(a)]. given #398 (T,wt=24): 11105 f(x,y,f(z,u,f(u,x,w))) = f(x,y,f(u,x,f(z,u,w))). [para(105(a,1),922(a,2)),rewrite([5(1,R),6(1),5(4,R),6(4),922(7),5(5,R),6(5)])]. given #399 (T,wt=24): 12966 f(x,f(y,z,x),f(x,u,f(y,z,w))) = f(x,u,f(y,z,x)). [para(922(a,1),168(a,1,3,3)),rewrite([922(6)]),flip(a)]. given #400 (A,wt=31): 151 f(x,y,f(z,u,f(x,z,f(u,w,v5)))) = f(x,z,f(x,y,f(u,v5,f(z,u,w)))). [para(30(a,2),25(a,2,3,3))]. given #401 (T,wt=24): 12971 f(x,f(y,z,u),f(x,w,f(y,z,x))) = f(x,w,f(y,z,x)). [para(1073(a,1),168(a,1,3,3)),rewrite([15(6)]),flip(a)]. given #402 (T,wt=24): 12992 f(x,f(y,z,u),f(x,w,f(z,u,x))) = f(x,w,f(z,u,x)). [para(3270(a,1),168(a,1,3,3)),rewrite([15(6)]),flip(a)]. given #403 (T,wt=24): 13034 f(x,f(y,z,u),f(x,w,f(y,u,x))) = f(x,w,f(y,u,x)). [para(7301(a,1),168(a,1,3,3)),rewrite([15(6)]),flip(a)]. given #404 (T,wt=24): 13531 f(x,f(y,z,u),f(z,u,f(y,z,x))) = f(z,x,f(y,z,u)). [para(169(a,1),5(a,2)),rewrite([5(2),5(2),5(4),5(6,R),6(6)])]. given #405 (A,wt=35): 155 f(x,y,f(x,z,f(y,u,f(x,w,f(x,y,v5))))) = f(x,z,f(y,u,f(x,w,f(x,y,v5)))). [para(21(a,1),25(a,1,3,3)),rewrite([6(1),6(5)]),flip(a)]. given #406 (T,wt=24): 14376 f(x,y,f(z,u,f(y,w,z))) = f(x,y,f(w,z,f(y,z,u))). [para(828(a,1),262(a,2,3)),rewrite([5(1,R),6(1),5(4)]),flip(a)]. given #407 (T,wt=22): 24970 f(x,y,f(x,z,f(y,u,f(z,w,y)))) = f(x,z,y). [para(14376(a,2),29(a,2,3)),rewrite([1905(4)]),flip(a)]. given #408 (T,wt=24): 14600 f(x,f(y,z,u),f(w,y,x)) = f(w,x,f(y,z,f(y,u,x))). [para(318(a,2),5(a,2)),rewrite([6(3),5(5)]),flip(a)]. given #409 (T,wt=24): 15095 f(x,f(y,z,u),f(y,w,x)) = f(w,x,f(y,z,f(y,u,x))). [para(319(a,1),5(a,2)),rewrite([5(2,R),6(2),5(3),6(4)])]. given #410 (A,wt=31): 156 f(x,y,f(x,z,f(z,u,f(z,w,v5)))) = f(x,z,f(x,y,f(z,w,f(z,u,v5)))). [para(21(a,1),25(a,2,3,3)),rewrite([6(1),118(4),6(5)])]. given #411 (T,wt=24): 15096 f(x,f(y,x,z),f(z,u,w)) = f(y,x,f(z,u,f(x,z,w))). [para(319(a,1),6(a,1)),rewrite([5(1,R),6(1),6(4)]),flip(a)]. given #412 (T,wt=24): 15338 f(f(x,y,z),f(x,y,f(x,u,z)),f(y,z,w)) = f(x,y,z). [para(15289(a,1),922(a,1,3)),rewrite([5(5),15289(8)])]. given #413 (T,wt=24): 15340 f(f(x,y,z),f(y,z,u),f(x,y,f(x,w,z))) = f(x,y,z). [para(15289(a,1),1073(a,1,2)),rewrite([5(5,R),15289(8)])]. given #414 (T,wt=24): 15403 f(x,f(x,y,z),f(u,w,v5)) = f(x,y,f(x,z,f(u,w,v5))). [para(15161(a,1),111(a,2)),rewrite([5(3,R),5(6),5(6),5(8),5(8),15402(8),5(6,R)]),flip(a)]. given #415 (A,wt=35): 158 f(x,y,f(y,z,f(x,u,f(y,w,f(x,y,v5))))) = f(x,y,f(y,z,f(x,u,f(y,w,v5)))). [para(25(a,2),28(a,1,3,3))]. given #416 (T,wt=24): 15408 f(x,f(y,z,u),f(x,w,v5)) = f(x,w,f(x,v5,f(y,z,u))). [para(15161(a,1),130(a,2,3)),rewrite([6(4),15379(6),15403(3)]),flip(a)]. given #417 (T,wt=24): 15410 f(x,f(y,x,z),f(u,w,v5)) = f(y,x,f(x,z,f(u,w,v5))). [para(15161(a,1),220(a,1)),rewrite([6(2),6(6),5(10),6(10),15383(10),19(8)]),flip(a)]. given #418 (T,wt=22): 25878 f(x,y,f(z,u,f(x,z,f(y,w,z)))) = f(x,y,z). [back_rewrite(22775),rewrite([5(2,R),6(2),25793(3),5(4),5(4),25472(6),921(5),15403(4),25146(4),6(1),5(2,R),6(2),23712(5),5(5),5(5)])]. given #419 (T,wt=21): 26005 f(x,f(y,z,f(y,u,w)),f(x,y,u)) = f(x,y,u). [para(25878(a,1),38(a,2)),rewrite([5(1),6(3),6(5)])]. given #420 (A,wt=35): 159 f(x,y,f(x,z,f(y,u,f(y,w,f(x,y,v5))))) = f(x,z,f(y,u,f(x,y,f(y,w,v5)))). [para(28(a,1),25(a,1,3,3)),flip(a)]. given #421 (T,wt=21): 26017 f(x,f(y,z,f(y,u,w)),f(x,y,w)) = f(x,y,w). [para(5(a,1),26005(a,1,2,3)),rewrite([5(1,R),6(1)])]. given #422 (T,wt=24): 15738 f(x,f(y,z,u),f(x,y,w)) = f(x,w,f(y,z,f(x,y,u))). [back_rewrite(15561),rewrite([15714(7)])]. given #423 (T,wt=24): 15766 f(x,f(y,z,f(u,x,y)),f(u,x,w)) = f(x,y,f(u,x,w)). [para(803(a,1),15288(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. given #424 (T,wt=24): 15783 f(x,f(y,z,f(u,x,y)),f(u,w,x)) = f(x,y,f(u,w,x)). [para(1669(a,1),15288(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. given #425 (A,wt=31): 160 f(x,y,f(x,z,f(u,w,f(z,u,v5)))) = f(x,z,f(x,y,f(z,u,f(u,w,v5)))). [para(28(a,1),25(a,2,3,3)),rewrite([102(4)])]. given #426 (T,wt=24): 15824 f(x,f(y,z,f(y,u,x)),f(y,u,f(u,x,w))) = f(y,u,x). [para(1905(a,1),15288(a,1,3,3)),rewrite([5(1,R),6(1),6(3),5(5,R),5(6,R),6(6),6(8),803(8)])]. given #427 (T,wt=22): 26506 f(x,y,f(z,u,f(x,z,f(w,z,y)))) = f(x,z,y). [para(3301(a,1),15824(a,1,3)),rewrite([5(3),5(4),15771(4),5(3,R),5(4),6(5),15403(5),25475(5),5(3,R),6(3),5(6),5(7),15771(7)])]. given #428 (T,wt=24): 15844 f(x,f(y,z,f(u,y,x)),f(u,w,f(u,y,x))) = f(u,y,x). [para(5305(a,1),15288(a,1,3,3)),rewrite([5(1),5(3),5(5,R),5(6),6(8),1713(8)])]. given #429 (T,wt=24): 15845 f(x,f(y,z,f(u,y,x)),f(u,y,f(u,x,w))) = f(u,y,x). [para(5310(a,1),15288(a,1,3,3)),rewrite([5(5,R),6(8),871(8)])]. given #430 (A,wt=31): 161 f(x,y,f(z,u,f(z,x,f(u,w,v5)))) = f(x,y,f(z,x,f(u,w,f(z,u,v5)))). [para(25(a,1),122(a,1,3,3)),rewrite([5(4,R),6(4),103(5),5(8,R),6(8)])]. given #431 (T,wt=24): 15853 f(x,f(y,z,f(y,u,x)),f(y,u,f(u,w,x))) = f(y,u,x). [para(8635(a,1),15288(a,1,3,3)),rewrite([5(5,R),6(8),1669(8)])]. given #432 (T,wt=24): 15854 f(x,f(y,z,f(u,y,x)),f(u,y,f(u,w,x))) = f(u,y,x). [para(9577(a,1),15288(a,1,3,3)),rewrite([5(5,R),6(8),15289(8)])]. given #433 (T,wt=24): 15868 f(x,f(y,z,f(u,x,y)),f(w,u,x)) = f(x,y,f(w,u,x)). [para(12402(a,1),15288(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. given #434 (T,wt=24): 15903 f(x,f(y,z,u),f(x,y,f(w,x,z))) = f(w,x,f(x,y,z)). [para(15771(a,1),41(a,1,3)),rewrite([5(3),5(3)]),flip(a)]. given #435 (A,wt=31): 163 f(x,y,f(z,u,f(z,w,f(x,z,v5)))) = f(x,y,f(z,u,f(x,z,f(z,w,v5)))). [para(122(a,1),25(a,1,3,3)),rewrite([5(2,R),6(2),5(6,R),6(6),159(9)])]. given #436 (T,wt=24): 15909 f(x,f(y,z,u),f(x,y,f(z,u,w))) = f(x,y,f(z,u,w)). [para(15771(a,1),922(a,1,2)),rewrite([5(2),5(2),5(3),5(5),5(5),5(6)])]. given #437 (T,wt=24): 15913 f(x,f(y,z,u),f(x,y,f(w,z,u))) = f(x,y,f(w,z,u)). [para(15771(a,1),1073(a,1,3)),rewrite([5(2),6(4),5(6)])]. given #438 (T,wt=24): 15921 f(x,y,f(x,f(z,u,y),f(w,z,u))) = f(x,y,f(w,z,u)). [para(15771(a,1),866(a,1,3,3)),rewrite([5(2),5(2),5(3,R),6(3),5(4,R),15403(4),5(6)])]. given #439 (T,wt=24): 15966 f(x,f(y,z,u),f(x,z,w)) = f(x,w,f(y,z,f(x,z,u))). [para(75(a,1),15771(a,2)),rewrite([6(2),6(5),15771(7)])]. given #440 (A,wt=38): 164 f(x,y,f(z,u,f(x,w,f(x,z,f(w,v5,v6))))) = f(x,z,f(x,y,f(z,u,f(w,v5,f(x,w,v6))))). [para(25(a,1),25(a,1,3,3))]. given #441 (T,wt=24): 15968 f(x,f(y,z,f(x,u,z)),f(w,x,u)) = f(x,z,f(w,x,u)). [para(15771(a,1),5310(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. given #442 (T,wt=24): 15972 f(x,f(y,z,f(u,x,z)),f(w,u,x)) = f(x,z,f(w,u,x)). [para(15771(a,1),9577(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. given #443 (T,wt=24): 15973 f(x,f(y,z,u),f(x,z,f(w,x,y))) = f(w,x,f(x,y,z)). [para(15771(a,1),87(a,1,3)),rewrite([5(3),5(3)]),flip(a)]. given #444 (T,wt=24): 16054 f(x,f(y,z,u),f(x,u,f(x,y,w))) = f(x,w,f(x,y,u)). [para(15796(a,1),32(a,2,3)),rewrite([6(2)])]. given #445 (A,wt=38): 165 f(x,y,f(z,u,f(x,z,f(w,v5,f(z,w,v6))))) = f(x,z,f(x,y,f(z,w,f(z,u,f(w,v5,v6))))). [para(25(a,1),25(a,2,3,3))]. given #446 (T,wt=24): 16066 f(x,f(y,z,u),f(x,y,f(z,w,u))) = f(x,y,f(z,w,u)). [para(15796(a,1),1073(a,1,3)),rewrite([5(2),6(4),5(6)])]. given #447 (T,wt=24): 16068 f(x,f(y,z,u),f(x,z,f(y,u,w))) = f(x,z,f(y,u,w)). [para(1181(a,1),15796(a,1,2))]. given #448 (T,wt=24): 16071 f(x,y,f(x,f(z,u,y),f(z,w,u))) = f(x,y,f(z,w,u)). [para(15796(a,1),866(a,1,3,3)),rewrite([5(2),5(2),5(3,R),6(3),5(4,R),15403(4),5(6)])]. given #449 (T,wt=24): 16124 f(x,f(y,z,f(u,x,z)),f(u,w,x)) = f(x,z,f(u,w,x)). [para(15796(a,1),9577(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. given #450 (A,wt=38): 166 f(x,y,f(z,u,f(x,w,f(z,v5,f(x,z,v6))))) = f(x,z,f(x,y,f(z,u,f(x,w,f(z,v5,v6))))). [para(25(a,2),25(a,1,3,3))]. given #451 (T,wt=24): 16158 f(x,y,f(x,f(z,u,y),f(z,u,w))) = f(x,y,f(z,u,w)). [para(15821(a,1),866(a,1,3,3)),rewrite([5(2),5(2),5(3,R),6(3),5(4,R),15403(4),5(6)])]. given #452 (T,wt=24): 16173 f(x,f(y,z,f(u,x,z)),f(u,x,w)) = f(x,z,f(u,x,w)). [para(15821(a,1),9577(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. given #453 (T,wt=24): 16467 f(x,f(y,z,u),f(u,x,w)) = f(x,w,f(y,u,f(z,u,x))). [para(321(a,1),5(a,2)),rewrite([5(2,R),6(2),5(3),5(4),5(4)])]. given #454 (T,wt=24): 16468 f(x,f(y,z,u),f(x,z,w)) = f(x,w,f(z,u,f(x,y,z))). [para(5(a,2),321(a,1,2)),rewrite([5(5,R),6(5)])]. given #455 (A,wt=38): 167 f(x,y,f(z,u,f(x,z,f(z,w,f(u,v5,v6))))) = f(x,z,f(x,y,f(z,w,f(u,v5,f(z,u,v6))))). [para(25(a,2),25(a,2,3,3))]. given #456 (T,wt=21): 27497 f(x,f(y,z,f(u,z,w)),f(x,z,w)) = f(x,z,w). [para(16468(a,2),2861(a,1,2)),rewrite([15(2),6(2),5(3),5(5)])]. given #457 (T,wt=24): 16473 f(x,f(y,z,u),f(x,w,u)) = f(x,w,f(y,u,f(x,z,u))). [para(321(a,2),20(a,1,3)),rewrite([6(2),22(4)])]. given #458 (T,wt=24): 16497 f(x,y,f(z,u,f(z,w,v5))) = f(x,y,f(z,w,f(z,u,v5))). [para(22(a,1),321(a,1,2)),rewrite([6(5),19(6),15403(9),15403(8),243(8),15297(8)])]. given #459 (T,wt=24): 16629 f(x,f(y,z,u),f(x,z,f(y,w,u))) = f(x,z,f(y,w,u)). [para(321(a,2),3114(a,1,2)),rewrite([6(2),15796(3),5(3),5(6)])]. given #460 (A,wt=34): 172 f(x,f(y,z,f(x,u,w)),f(y,z,f(x,u,f(x,y,w)))) = f(x,y,f(y,z,f(x,u,w))). [para(8(a,1),27(a,1,3,3))]. given #461 (T,wt=21): 27742 f(x,f(y,z,f(y,u,w)),f(x,y,u)) = f(x,y,u). [para(2861(a,1),16629(a,1,3)),rewrite([5(2,R),6(2),5(3),5(4),6(5),15403(5),2870(4),20(2),5(3,R),6(3),5(4)]),flip(a)]. given #462 (T,wt=21): 27778 f(x,f(y,z,f(y,u,w)),f(y,x,w)) = f(y,x,w). [para(3114(a,1),172(a,2,3)),rewrite([5(2,R),6(2),6(3),5(6,R),6(6),15(7),6(7),15(9),6(5),20(6)])]. given #463 (T,wt=22): 27795 f(x,y,f(y,z,f(x,u,f(x,w,z)))) = f(x,y,z). [para(27778(a,1),103(a,2)),rewrite([20(5),6(5),25793(5),51(4),28(5),20(6)])]. given #464 (T,wt=24): 16711 f(x,y,f(z,u,f(y,w,u))) = f(y,u,f(x,y,f(z,w,u))). [para(321(a,2),74(a,1,3)),rewrite([15(2),6(2),19(5)])]. given #465 (A,wt=34): 176 f(x,f(y,z,f(y,u,w)),f(y,u,f(x,u,f(y,z,w)))) = f(x,u,f(y,u,f(y,z,w))). [para(16(a,2),27(a,1,2)),rewrite([5(1,R),6(1),5(5,R),6(5),5(8,R),6(8)])]. given #466 (T,wt=21): 27876 f(x,f(y,z,f(u,z,w)),f(u,x,z)) = f(u,x,z). [para(8746(a,1),16711(a,2,3)),rewrite([19(6),8746(4)]),flip(a)]. given #467 (T,wt=24): 16726 f(x,y,f(x,f(y,z,u),f(x,w,u))) = f(x,w,f(x,y,u)). [para(321(a,2),76(a,2,3)),rewrite([5(2,R),6(2),16490(3),6(4),5(6,R),6(6)]),flip(a)]. given #468 (T,wt=24): 17086 f(x,y,f(y,f(x,z,u),f(y,z,w))) = f(y,w,f(x,y,z)). [para(1057(a,1),471(a,2,3)),rewrite([6(2)])]. given #469 (T,wt=24): 17223 f(x,y,f(y,f(x,z,u),f(y,u,w))) = f(y,w,f(x,y,u)). [para(15213(a,1),471(a,2,3)),rewrite([5(1,R),6(1),6(2)])]. given #470 (A,wt=34): 179 f(x,f(y,z,f(x,u,w)),f(y,z,f(x,w,f(x,y,u)))) = f(x,y,f(y,z,f(x,u,w))). [para(17(a,1),27(a,1,3,3))]. given #471 (T,wt=21): 28139 f(x,f(y,z,f(u,w,y)),f(u,x,y)) = f(u,x,y). [para(813(a,1),17223(a,1,3)),rewrite([6(2),7553(3),5(3),5(3)]),flip(a)]. given #472 (T,wt=22): 28146 f(x,y,f(z,u,f(y,z,f(x,w,z)))) = f(x,y,z). [para(1738(a,1),17223(a,1,3)),rewrite([6(2),7553(3),5(4,R),25793(4),6(6),25793(6),102(6)]),flip(a)]. given #473 (T,wt=22): 28147 f(x,y,f(y,z,f(z,u,f(x,w,z)))) = f(x,y,z). [para(1905(a,1),17223(a,1,3)),rewrite([6(2),7553(3),5(3),5(3),6(6),25793(6),73(6)]),flip(a)]. given #474 (T,wt=24): 17732 f(x,y,f(x,z,f(u,x,w))) = f(x,w,f(x,y,f(u,x,z))). [para(479(a,1),812(a,2)),rewrite([6(5),15403(6),15403(5),16989(7)]),flip(a)]. given #475 (A,wt=38): 181 f(x,f(y,z,u),f(x,w,f(x,v5,f(y,z,f(x,y,u))))) = f(x,w,f(x,v5,f(x,y,f(y,z,u)))). [para(27(a,1),18(a,1,3,3)),flip(a)]. given #476 (T,wt=24): 17987 f(x,f(y,z,u),f(w,x,f(x,y,z))) = f(w,x,f(x,y,z)). [para(7078(a,1),482(a,1,3)),rewrite([5(1),5(4),15403(6),474(6),6(4)]),flip(a)]. given #477 (T,wt=24): 18078 f(x,y,f(x,z,f(u,x,w))) = f(x,w,f(x,z,f(u,x,y))). [para(495(a,1),812(a,2)),rewrite([6(5),15403(6),15403(5),16989(7)])]. given #478 (T,wt=24): 18230 f(x,y,f(z,u,f(z,w,y))) = f(x,y,f(z,w,f(z,y,u))). [para(630(a,1),5(a,2)),rewrite([6(3),6(4),5(6,R),6(6)]),flip(a)]. given #479 (T,wt=24): 18271 f(x,y,f(z,u,f(z,w,x))) = f(x,y,f(z,w,f(z,x,u))). [para(630(a,1),922(a,2)),rewrite([922(7),6(4)]),flip(a)]. given #480 (A,wt=44): 183 f(x,f(y,z,f(x,u,f(x,w,v5))),f(y,z,f(x,w,f(x,y,f(x,u,v5))))) = f(x,y,f(y,z,f(x,u,f(x,w,v5)))). [para(18(a,1),27(a,1,3,3))]. given #481 (T,wt=24): 18322 f(x,y,f(z,u,f(z,w,y))) = f(z,y,f(x,y,f(z,w,u))). [para(630(a,1),1856(a,2)),rewrite([6(7),5(8,R),6(8),5(9,R),6(9),5450(10),6(4),5(6,R),6(6)]),flip(a)]. given #482 (T,wt=24): 18414 f(x,y,f(z,u,f(y,w,z))) = f(y,z,f(x,y,f(w,z,u))). [para(630(a,1),220(a,1,3)),rewrite([5(1),6(1),8713(3),5(4,R),6(4),20(5),5(6,R),6(6)])]. given #483 (T,wt=24): 18461 f(x,y,f(y,f(x,z,u),f(y,w,u))) = f(y,w,f(x,y,u)). [para(18363(a,1),24(a,2,3)),rewrite([5(4,R),6(4),8145(4),6(2),5(6,R),6(6)])]. given #484 (T,wt=24): 18481 f(x,f(y,z,f(x,u,y)),f(z,w,f(x,y,z))) = f(x,y,z). [para(18363(a,1),910(a,1,3,3)),rewrite([5(2,R),6(2),8713(3),6(3),5(7,R),6(7),8713(8),18457(8)])]. given #485 (A,wt=44): 185 f(x,f(y,z,f(x,u,f(x,w,v5))),f(y,z,f(x,u,f(x,w,f(x,y,v5))))) = f(x,y,f(y,z,f(x,u,f(x,w,v5)))). [para(18(a,2),27(a,1,3,3))]. given #486 (T,wt=24): 18704 f(x,f(y,z,u),f(x,y,w)) = f(x,w,f(y,u,f(x,y,z))). [para(738(a,1),38(a,2)),rewrite([6(2)])]. given #487 (T,wt=24): 18837 f(x,f(y,z,u),f(w,x,f(w,y,z))) = f(w,x,f(y,z,u)). [para(847(a,1),220(a,2,3)),rewrite([1630(5),19(4)]),flip(a)]. given #488 (T,wt=23): 28531 f(f(x,y,z),f(u,x,y),f(u,x,z)) = f(x,z,f(u,x,y)). [para(1906(a,1),18837(a,2)),rewrite([5(5),5(5),922(6),6(5),28513(5)])]. given #489 (T,wt=23): 28559 f(f(x,y,z),f(u,x,y),f(u,y,z)) = f(y,z,f(u,x,y)). [back_rewrite(23483),rewrite([28512(5)])]. given #490 (A,wt=34): 187 f(x,f(y,z,f(z,u,w)),f(z,u,f(x,u,f(y,z,w)))) = f(x,u,f(z,u,f(y,z,w))). [para(24(a,1),27(a,1,2)),rewrite([5(1,R),6(1),5(5,R),6(5),5(8,R),6(8)])]. given #491 (T,wt=18): 28837 f(x,y,f(z,x,f(u,z,y))) = f(z,x,y). [para(7338(a,1),28559(a,2)),rewrite([6(2),5(4,R),6(4),6(6),20(6),5(6),19832(6),15403(4),1030(3),20(2),5(3),5(5,R),6(5),25793(5),20(4)]),flip(a)]. given #492 (T,wt=22): 28862 f(x,y,f(z,y,f(u,z,f(x,z,w)))) = f(x,z,y). [para(29(a,1),187(a,1,3,3)),rewrite([871(7),6(5),15403(5),5284(4),20(2)]),flip(a)]. given #493 (T,wt=23): 28565 f(f(x,y,z),f(x,y,u),f(x,z,u)) = f(x,y,f(x,z,u)). [para(28531(a,1),5(a,1)),rewrite([5(1,R),6(1),5(3),5(3),6(4),5(5,R),6(5)]),flip(a)]. given #494 (T,wt=23): 28566 f(f(x,y,z),f(x,y,u),f(y,z,u)) = f(y,u,f(x,y,z)). [para(28531(a,1),5(a,2))]. given #495 (A,wt=44): 200 f(x,f(y,z,f(u,w,f(x,u,v5))),f(y,z,f(x,u,f(x,y,f(u,w,v5))))) = f(x,y,f(y,z,f(u,w,f(x,u,v5)))). [para(25(a,1),27(a,1,3,3))]. given #496 (T,wt=23): 28567 f(f(x,y,z),f(y,z,u),f(x,y,u)) = f(x,y,f(y,z,u)). [para(5(a,1),28531(a,1,1)),rewrite([5(2),5(2),5(3),6(3),5(5),5(5),5(6,R),6(6)])]. given #497 (T,wt=23): 28568 f(f(x,y,z),f(x,z,u),f(y,z,u)) = f(y,z,f(x,z,u)). [para(5(a,2),28531(a,1,1)),rewrite([5(2),6(2),5(3),6(3),5(5),6(5),5(6,R),6(6)])]. given #498 (T,wt=23): 28569 f(f(x,y,z),f(x,y,u),f(x,u,z)) = f(x,y,f(x,u,z)). [para(28531(a,1),6(a,1)),rewrite([5(1,R),6(1),6(3),5(4),5(4),5(5,R),6(5)]),flip(a)]. given #499 (T,wt=23): 28570 f(f(x,y,z),f(x,z,u),f(x,y,u)) = f(x,z,f(x,y,u)). [para(28531(a,1),6(a,2)),rewrite([5(2),5(2),5(3),5(3),5(5),5(5)])]. given #500 (A,wt=44): 202 f(x,f(y,z,f(x,u,f(y,w,v5))),f(y,z,f(x,u,f(y,w,f(x,y,v5))))) = f(x,y,f(y,z,f(x,u,f(y,w,v5)))). [para(25(a,2),27(a,1,3,3))]. given #501 (T,wt=23): 28610 f(f(x,y,z),f(u,x,z),f(u,x,y)) = f(x,y,f(u,x,z)). [para(28531(a,1),922(a,2)),rewrite([6(2),5(4),6(5),1253(9)])]. given #502 (T,wt=23): 28747 f(f(x,y,z),f(y,z,u),f(x,z,u)) = f(x,z,f(y,z,u)). [para(5(a,1),28559(a,1,1)),rewrite([5(2),5(2),5(3),6(3),5(5),5(5),5(6,R),6(6)])]. given #503 (T,wt=23): 28817 f(f(x,y,z),f(x,u,z),f(x,y,u)) = f(x,y,f(x,u,z)). [para(28559(a,1),15161(a,1,1)),rewrite([5(1),5(4),5(4),5(5),5(6),5(6),28715(8),15356(6),5(3),5(3),5(4),5(5),5(5)]),flip(a)]. given #504 (T,wt=23): 28915 f(f(x,y,z),f(x,u,y),f(x,u,z)) = f(x,u,f(x,y,z)). [para(28565(a,1),5(a,1)),flip(a)]. given #505 (A,wt=41): 208 f(x,y,f(z,f(x,u,f(x,w,v5)),f(x,u,f(x,w,f(x,z,v5))))) = f(x,y,f(x,z,f(x,u,f(x,w,v5)))). [para(18(a,2),132(a,1,3,3))]. given #506 (T,wt=23): 28979 f(f(x,y,z),f(x,u,z),f(x,u,y)) = f(x,u,f(x,y,z)). [para(28566(a,1),6(a,1)),rewrite([5(1,R),6(1),5(3,R),6(3),6(4),5(5),5(5)]),flip(a)]. given #507 (T,wt=23): 28988 f(f(x,y,z),f(x,y,u),f(y,u,z)) = f(y,z,f(x,y,u)). [para(28566(a,1),205(a,1,3)),rewrite([6(2),25263(5),205(2),19(2),6(5)]),flip(a)]. given #508 (T,wt=23): 29122 f(f(x,y,z),f(y,u,z),f(x,y,u)) = f(x,y,f(y,u,z)). [para(28567(a,1),922(a,2)),rewrite([6(3),5(4),6(6),1253(9),6(5)])]. given #509 (T,wt=23): 29200 f(f(x,y,z),f(x,u,y),f(u,y,z)) = f(u,y,f(x,y,z)). [para(28568(a,1),19(a,1,3)),rewrite([28511(5),28568(8)])]. given #510 (A,wt=31): 221 f(x,y,f(x,z,f(u,w,f(x,w,v5)))) = f(x,z,f(x,w,f(x,y,f(u,w,v5)))). [para(29(a,1),8(a,2,3))]. given #511 (T,wt=24): 18854 f(x,y,f(z,y,f(y,u,w))) = f(y,u,f(z,y,f(x,y,w))). [para(854(a,1),5(a,2)),rewrite([6(3),5(4,R),6(4)])]. given #512 (T,wt=24): 19030 f(x,y,f(z,u,f(x,w,u))) = f(x,y,f(w,u,f(x,z,u))). [para(1149(a,1),872(a,2,3)),rewrite([6(3),6(4),19021(6)])]. given #513 (T,wt=24): 19176 f(x,f(y,z,f(y,x,u)),f(x,u,w)) = f(y,x,f(x,u,w)). [para(872(a,1),220(a,2,3)),rewrite([5(1,R),6(1),5(2,R),6(2),6(3),5(4,R),1072(6),5(3,R),6(3),6(4),5(6,R)]),flip(a)]. given #514 (T,wt=24): 19273 f(x,y,f(z,u,f(w,z,v5))) = f(x,y,f(w,z,f(z,u,v5))). [para(80(a,1),19051(a,1,2)),rewrite([5(5,R),14692(5),1072(5),20(3),16501(6)]),flip(a)]. given #515 (A,wt=31): 222 f(x,y,f(z,u,f(x,w,f(x,u,v5)))) = f(x,u,f(x,y,f(z,u,f(x,w,v5)))). [para(8(a,1),29(a,1,3,3))]. given #516 (T,wt=24): 19494 f(x,y,f(z,u,f(w,u,v5))) = f(x,y,f(w,u,f(z,u,v5))). [para(72(a,1),1037(a,2,3,3)),rewrite([16954(7),4249(6),5(3,R),6(3),1634(5),6(8),16957(8)])]. given #517 (T,wt=24): 19503 f(x,y,f(x,f(z,y,u),f(x,w,u))) = f(x,w,f(x,y,u)). [para(19(a,1),1062(a,1,3,3)),rewrite([15(3),15403(7),16472(6),6(4)]),flip(a)]. given #518 (T,wt=21): 29727 f(x,f(y,z,f(u,y,w)),f(x,u,y)) = f(x,u,y). [para(19503(a,1),847(a,1)),rewrite([6(2),813(3),5(3)]),flip(a)]. given #519 (T,wt=24): 19546 f(x,y,f(x,f(z,u,y),f(x,w,u))) = f(x,w,f(x,u,y)). [para(75(a,2),1062(a,2,3)),rewrite([20(3),15(3),15403(7),50(7)]),flip(a)]. given #520 (A,wt=31): 223 f(x,y,f(z,u,f(x,u,f(z,w,v5)))) = f(x,u,f(x,y,f(z,w,f(z,u,v5)))). [para(8(a,1),29(a,2,3,3))]. given #521 (T,wt=24): 19702 f(x,f(y,z,u),f(x,w,f(w,y,z))) = f(x,w,f(y,z,u)). [para(1136(a,1),5(a,1)),rewrite([5(3),5(6,R)]),flip(a)]. given #522 (T,wt=24): 19710 f(x,y,f(z,u,f(z,w,v5))) = f(x,y,f(z,v5,f(z,u,w))). [para(17(a,1),1136(a,2,3)),rewrite([1136(5)])]. given #523 (T,wt=24): 19716 f(x,y,f(z,u,f(w,z,v5))) = f(x,y,f(w,z,f(z,v5,u))). [para(30(a,1),1136(a,1,2)),rewrite([3153(5)]),flip(a)]. given #524 (T,wt=24): 19743 f(x,y,f(z,u,f(z,w,v5))) = f(x,y,f(z,v5,f(z,w,u))). [para(474(a,1),1136(a,2,3)),rewrite([5(1),5(1),22(3),3529(5),6(4),5(5,R),6(5)])]. given #525 (A,wt=31): 225 f(x,y,f(z,u,f(u,w,f(x,u,v5)))) = f(x,u,f(x,y,f(z,u,f(u,w,v5)))). [para(16(a,2),29(a,1,3,3))]. given #526 (T,wt=24): 19755 f(x,f(y,z,u),f(y,w,f(x,z,w))) = f(x,w,f(y,z,u)). [para(897(a,1),1136(a,1,3))]. given #527 (T,wt=24): 19762 f(x,f(y,z,u),f(z,w,f(x,y,w))) = f(x,w,f(y,z,u)). [para(1149(a,1),1136(a,1,3))]. given #528 (T,wt=24): 19809 f(x,y,f(x,f(z,u,w),f(z,u,y))) = f(x,y,f(z,u,w)). [para(1136(a,1),859(a,2)),rewrite([6(9),5(10,R),6(10),4944(12)])]. given #529 (T,wt=24): 19891 f(x,f(y,z,u),f(u,x,f(y,z,w))) = f(u,x,f(y,z,w)). [para(1136(a,1),168(a,1,3)),rewrite([5(3),5(5,R),6(5),15(6),5(5)]),flip(a)]. given #530 (A,wt=31): 226 f(x,y,f(z,u,f(x,u,f(u,w,v5)))) = f(x,u,f(x,y,f(u,w,f(z,u,v5)))). [para(16(a,2),29(a,2,3,3))]. given #531 (T,wt=21): 30148 f(x,f(y,z,x),f(y,u,f(y,w,z))) = f(y,z,x). [para(19051(a,1),19891(a,1,3)),rewrite([5(1),5(3,R),15(3),5(3),6(3),5(4,R),5(5),5(7),6(7),13008(8)])]. given #532 (T,wt=24): 19961 f(f(x,y,z),f(x,u,y),f(x,u,f(u,y,w))) = f(x,u,y). [para(1138(a,1),5(a,1)),flip(a)]. given #533 (T,wt=24): 19962 f(f(x,y,z),f(y,z,f(x,z,u)),f(x,y,w)) = f(x,y,z). [para(5(a,1),1138(a,1,1)),rewrite([5(2,R),6(2),5(4,R),6(4),5(6)])]. given #534 (T,wt=24): 19963 f(f(x,y,z),f(x,z,f(x,y,u)),f(y,z,w)) = f(x,y,z). [para(5(a,2),1138(a,1,1)),rewrite([5(3,R),6(3),5(4,R),6(4),5(6),5(6)])]. given #535 (A,wt=31): 227 f(x,y,f(x,z,f(u,w,f(x,w,v5)))) = f(x,z,f(x,y,f(x,w,f(u,w,v5)))). [para(29(a,2),17(a,1,3)),rewrite([57(8)])]. given #536 (T,wt=24): 19964 f(f(x,y,z),f(x,z,f(y,z,u)),f(x,y,w)) = f(x,y,z). [para(6(a,1),1138(a,1,1)),rewrite([5(2,R),6(2),6(6)])]. given #537 (T,wt=24): 19971 f(f(x,y,z),f(y,z,f(x,y,u)),f(x,z,w)) = f(x,y,z). [para(16(a,2),1138(a,1,2))]. given #538 (T,wt=24): 20313 f(x,f(y,z,u),f(w,y,f(x,w,z))) = f(x,w,f(y,z,u)). [para(1148(a,1),4461(a,2)),rewrite([5(3),5(4),6(5),5(6),5(9),15403(11),15438(11)])]. given #539 (T,wt=24): 20324 f(x,f(y,z,u),f(y,w,f(z,w,x))) = f(w,x,f(y,z,u)). [para(1148(a,1),2013(a,2)),rewrite([5(3,R),6(3),5(5,R),6(5),6(8),5(9,R),6(9),16672(11),5(6,R),6(6)])]. given #540 (A,wt=31): 228 f(x,y,f(z,u,f(x,u,f(z,w,v5)))) = f(x,u,f(x,y,f(z,v5,f(z,u,w)))). [para(17(a,1),29(a,2,3,3))]. given #541 (T,wt=24): 20338 f(x,f(y,z,x),f(u,x,f(y,z,w))) = f(u,x,f(y,z,x)). [para(1148(a,1),74(a,2,3)),rewrite([5(4,R),922(4),19(4),5(6,R),6(6)]),flip(a)]. given #542 (T,wt=24): 20390 f(x,f(y,z,u),f(u,x,w)) = f(x,w,f(z,u,f(y,u,x))). [para(1176(a,1),5(a,2)),rewrite([5(2,R),6(2),5(3),5(4),5(4)])]. given #543 (T,wt=24): 20392 f(x,f(y,z,u),f(x,w,u)) = f(x,w,f(z,u,f(x,y,u))). [para(1176(a,2),20(a,1,3)),rewrite([6(2),22(4)])]. given #544 (T,wt=24): 20581 f(x,f(y,z,u),f(x,w,y)) = f(x,w,f(y,u,f(x,y,z))). [para(1176(a,1),872(a,2)),rewrite([5(1,R),6(1),5(2),6(3),19603(5),822(5),6(4),5(5,R),6(5)])]. given #545 (A,wt=38): 229 f(x,y,f(x,z,f(x,u,f(w,v5,f(x,v5,v6))))) = f(x,u,f(x,y,f(x,v5,f(x,z,f(w,v5,v6))))). [para(29(a,1),18(a,2,3,3))]. given #546 (T,wt=24): 20595 f(f(x,y,z),f(z,u,f(x,y,z)),f(x,y,w)) = f(x,y,z). [para(1179(a,1),5(a,1)),rewrite([5(6)]),flip(a)]. given #547 (T,wt=24): 20617 f(f(x,y,z),f(x,y,u),f(x,u,f(y,u,w))) = f(x,y,u). [para(874(a,1),1179(a,1,3))]. given #548 (T,wt=24): 20621 f(f(x,y,z),f(x,y,u),f(y,u,f(x,u,w))) = f(x,y,u). [para(933(a,1),1179(a,1,3))]. given #549 (T,wt=24): 20959 f(x,f(y,z,u),f(w,x,f(x,z,u))) = f(w,x,f(x,z,u)). [para(1254(a,1),74(a,1,3)),rewrite([15771(3),15771(6)]),flip(a)]. given #550 (A,wt=38): 230 f(x,y,f(x,z,f(x,u,f(w,v5,f(x,v5,v6))))) = f(x,v5,f(x,y,f(x,z,f(x,u,f(w,v5,v6))))). [para(29(a,2),18(a,1,3,3))]. given #551 (T,wt=18): 30898 f(x,y,f(z,y,f(u,x,z))) = f(x,z,y). [para(20959(a,1),71(a,2)),rewrite([5(3),5(4,R),6(4),5(5,R),6(5),23961(5),5(5),5(5),5(6,R),3270(6)])]. given #552 (T,wt=24): 20973 f(x,f(y,z,u),f(w,x,f(w,z,u))) = f(w,x,f(y,z,u)). [para(1254(a,1),220(a,2,3)),rewrite([1633(5),19(4)]),flip(a)]. given #553 (T,wt=24): 20990 f(x,f(y,z,u),f(u,x,f(z,x,w))) = f(x,w,f(z,u,x)). [para(1286(a,1),5(a,2)),rewrite([5(2,R),6(2),5(3,R),6(3),5(4),5(5),5(5)])]. given #554 (T,wt=24): 21079 f(x,f(y,z,f(y,u,x)),f(w,u,x)) = f(y,x,f(w,u,x)). [para(1286(a,1),74(a,2,3)),rewrite([5(4,R),1669(6),5(6,R)]),flip(a)]. given #555 (A,wt=38): 231 f(x,y,f(z,u,f(x,w,f(x,u,f(x,v5,v6))))) = f(x,u,f(x,y,f(z,u,f(x,v5,f(x,w,v6))))). [para(18(a,1),29(a,1,3,3))]. given #556 (T,wt=24): 21113 f(x,f(y,z,x),f(u,w,f(u,z,x))) = f(u,x,f(y,z,x)). [para(1286(a,1),220(a,2,3)),rewrite([803(6)]),flip(a)]. given #557 (T,wt=22): 31406 f(x,y,f(z,x,f(z,u,f(z,w,y)))) = f(z,x,y). [para(19176(a,1),21113(a,2)),rewrite([1713(5),1713(6),30976(6),5(4,R),15403(4),51(4),1713(7),20(6)])]. given #558 (T,wt=24): 21349 f(x,f(y,z,u),f(x,w,f(w,z,u))) = f(x,w,f(y,z,u)). [para(1329(a,1),5(a,1)),rewrite([5(3),5(6,R)]),flip(a)]. given #559 (T,wt=24): 21385 f(x,f(y,z,u),f(z,w,f(x,u,w))) = f(x,w,f(y,z,u)). [para(897(a,1),1329(a,1,3))]. given #560 (A,wt=38): 232 f(x,y,f(z,u,f(x,u,f(z,w,f(z,v5,v6))))) = f(x,u,f(x,y,f(z,v5,f(z,u,f(z,w,v6))))). [para(18(a,1),29(a,2,3,3))]. given #561 (T,wt=24): 21387 f(x,f(y,z,u),f(u,w,f(x,z,w))) = f(x,w,f(y,z,u)). [para(1149(a,1),1329(a,1,3))]. given #562 (T,wt=18): 31556 f(x,y,f(z,y,f(u,z,x))) = f(z,x,y). [para(21387(a,1),24(a,1)),rewrite([15(3),19(6),31065(5),5(3,R),6(3)]),flip(a)]. given #563 (T,wt=24): 21451 f(x,y,f(x,f(z,u,w),f(u,w,y))) = f(x,y,f(z,u,w)). [para(1329(a,1),130(a,2,3)),rewrite([22(6),19(8)])]. given #564 (T,wt=24): 21477 f(x,f(y,z,u),f(x,u,f(w,y,z))) = f(x,u,f(w,y,z)). [para(1329(a,1),1062(a,2,3)),rewrite([19(5),1329(4)]),flip(a)]. given #565 (A,wt=38): 233 f(x,y,f(z,u,f(x,w,f(x,v5,f(x,u,v6))))) = f(x,u,f(x,y,f(z,u,f(x,w,f(x,v5,v6))))). [para(18(a,2),29(a,1,3,3))]. given #566 (T,wt=24): 21540 f(x,f(y,z,u),f(w,z,f(w,x,y))) = f(w,x,f(y,z,u)). [para(1341(a,1),2013(a,2)),rewrite([5(7,R),6(7),15403(9),19428(10),5(6,R),6(6)])]. given #567 (T,wt=24): 21563 f(x,f(y,z,u),f(y,x,f(z,u,w))) = f(y,x,f(z,u,w)). [para(1341(a,1),168(a,1,3)),rewrite([5(3,R),6(3),5(5,R),6(5),15(6),5(5,R),6(5)]),flip(a)]. given #568 (T,wt=24): 21854 f(f(x,y,z),f(y,z,u),f(y,u,f(z,u,w))) = f(y,z,u). [para(874(a,1),1344(a,1,3))]. given #569 (T,wt=24): 21855 f(f(x,y,z),f(y,z,u),f(z,u,f(y,u,w))) = f(y,z,u). [para(933(a,1),1344(a,1,3))]. Low Water (keep): wt=37.000, iters=6684 given #570 (A,wt=38): 234 f(x,y,f(z,u,f(x,u,f(z,w,f(z,v5,v6))))) = f(x,u,f(x,y,f(z,w,f(z,v5,f(z,u,v6))))). [para(18(a,2),29(a,2,3,3))]. given #571 (T,wt=24): 21883 f(x,f(y,z,x),f(u,f(w,y,z),f(y,z,x))) = f(y,z,x). [para(1344(a,1),16471(a,2)),rewrite([5(6,R),10036(8)])]. given #572 (T,wt=21): 31966 f(x,y,f(z,y,f(u,x,y))) = f(z,y,f(u,x,y)). [para(1051(a,1),21883(a,1,3)),rewrite([6(2),6(4),6(7),5(8),4(8),6(4)]),flip(a)]. given #573 (T,wt=22): 31961 f(x,y,f(z,u,f(x,u,f(w,u,y)))) = f(x,u,y). [para(21883(a,1),6(a,2)),rewrite([5(2),5(4),6(5),15403(5),25146(5),5(3,R),6(3),5(5)])]. given #574 (T,wt=24): 22000 f(f(x,y,z),f(x,y,u),f(y,z,f(x,z,w))) = f(x,y,z). [para(5(a,1),1393(a,1,1)),rewrite([5(2,R),6(2),5(3,R),6(3),5(6)])]. given #575 (A,wt=31): 235 f(x,y,f(z,u,f(z,x,f(w,u,v5)))) = f(z,x,f(x,y,f(w,u,f(z,u,v5)))). [para(29(a,1),24(a,2,3)),rewrite([5(3,R),6(3),5(8,R),6(8)]),flip(a)]. given #576 (T,wt=24): 22001 f(f(x,y,z),f(y,z,u),f(x,z,f(x,y,w))) = f(x,y,z). [para(5(a,2),1393(a,1,1)),rewrite([5(2,R),6(2),5(4,R),6(4),5(6),5(6)])]. given #577 (T,wt=24): 22002 f(f(x,y,z),f(x,y,u),f(x,z,f(y,z,w))) = f(x,y,z). [para(6(a,1),1393(a,1,1)),rewrite([5(3,R),6(3),6(6)])]. given #578 (T,wt=24): 22008 f(f(x,y,z),f(x,z,u),f(y,z,f(x,y,w))) = f(x,y,z). [para(16(a,2),1393(a,1,3))]. given #579 (T,wt=24): 22158 f(f(x,y,z),f(x,y,u),f(w,z,f(x,y,z))) = f(x,y,z). [para(1394(a,1),8713(a,1,3)),rewrite([15(3),5(5,R),6(5)]),flip(a)]. given #580 (A,wt=31): 238 f(x,y,f(z,u,f(x,u,f(u,w,v5)))) = f(x,u,f(x,y,f(u,v5,f(z,u,w)))). [para(30(a,2),29(a,2,3,3))]. given #581 (T,wt=24): 22259 f(x,f(y,z,u),f(w,z,f(x,w,u))) = f(x,w,f(y,z,u)). [para(1404(a,1),54(a,2,3)),rewrite([95(5),20(7)])]. given #582 (T,wt=24): 22275 f(x,f(y,z,u),f(w,u,f(w,x,z))) = f(w,x,f(y,z,u)). [para(1404(a,1),2013(a,2)),rewrite([5(7,R),6(7),15403(9),19428(10),5(6,R),6(6)])]. given #583 (T,wt=24): 22656 f(f(x,y,z),f(x,z,u),f(w,y,f(x,y,z))) = f(x,y,z). [para(1557(a,1),8713(a,1,3)),rewrite([15(3),5(5,R),6(5)]),flip(a)]. given #584 (T,wt=24): 22714 f(x,f(y,z,u),f(w,x,y)) = f(w,x,f(y,u,f(x,y,z))). [para(75(a,2),1630(a,1,3)),rewrite([6(3),6(4),28(4),6(2),17086(5),6(5)])]. given #585 (A,wt=35): 243 f(x,y,f(x,z,f(u,y,f(x,w,f(x,y,v5))))) = f(x,z,f(u,y,f(x,w,f(x,y,v5)))). [para(21(a,1),29(a,1,3,3)),rewrite([6(1),6(5)]),flip(a)]. given #586 (T,wt=24): 22726 f(x,f(y,z,u),f(w,x,z)) = f(w,x,f(z,u,f(x,y,z))). [para(321(a,2),1630(a,1,3)),rewrite([6(3),3998(4),17223(5),6(5)])]. given #587 (T,wt=24): 22744 f(x,f(y,z,u),f(w,y,f(w,x,z))) = f(w,x,f(y,z,u)). [para(1630(a,1),131(a,2,3)),rewrite([103(5),20(7)])]. given #588 (T,wt=24): 22825 f(x,f(y,z,u),f(w,z,f(w,x,u))) = f(w,x,f(y,z,u)). [para(1633(a,1),131(a,2,3)),rewrite([103(5),20(7)])]. given #589 (T,wt=24): 23372 f(x,f(y,z,u),f(w,x,u)) = f(w,x,f(y,u,f(x,z,u))). [para(321(a,2),1766(a,1,3)),rewrite([13514(5)])]. given #590 (A,wt=35): 246 f(x,y,f(x,z,f(u,y,f(y,w,f(x,y,v5))))) = f(x,z,f(u,y,f(x,y,f(y,w,v5)))). [para(28(a,1),29(a,1,3,3)),flip(a)]. given #591 (T,wt=20): 32432 f(x,f(y,z,x),f(y,u,x)) = f(y,x,f(u,z,x)). [para(23372(a,2),828(a,1)),rewrite([5(2,R),15(2),6(2),5(4)]),flip(a)]. given #592 (T,wt=24): 23382 f(x,f(y,z,u),f(w,x,u)) = f(w,x,f(z,u,f(x,y,u))). [para(1176(a,2),1766(a,1,3)),rewrite([13514(5)])]. given #593 (T,wt=24): 23417 f(x,y,f(z,u,f(w,v5,z))) = f(x,y,f(w,z,f(v5,z,u))). [para(828(a,1),1769(a,2,3)),rewrite([5(4,R),6(4),7681(6),5(4)]),flip(a)]. given #594 (T,wt=24): 23419 f(x,y,f(z,u,f(w,v5,u))) = f(x,y,f(w,u,f(z,v5,u))). [para(874(a,1),1769(a,2,3)),rewrite([5(4,R),6(4),7681(6),5(4)])]. given #595 (A,wt=31): 250 f(x,y,f(x,z,f(u,y,f(y,w,v5)))) = f(x,y,f(x,z,f(y,w,f(u,y,v5)))). [para(122(a,1),29(a,2,3,3)),rewrite([5(2,R),6(2),247(5),5(6,R),6(6)])]. given #596 (T,wt=24): 23421 f(x,y,f(z,u,f(w,v5,u))) = f(x,y,f(v5,u,f(z,w,u))). [para(933(a,1),1769(a,2,3)),rewrite([5(4,R),6(4),7681(6),5(4)])]. given #597 (T,wt=24): 23477 f(x,f(y,z,u),f(w,x,f(y,z,x))) = f(w,x,f(y,z,x)). [para(1073(a,1),1906(a,1,3,3)),rewrite([15(6)]),flip(a)]. given #598 (T,wt=24): 23480 f(x,f(y,z,u),f(w,x,f(z,u,x))) = f(w,x,f(z,u,x)). [para(3270(a,1),1906(a,1,3,3)),rewrite([15(6)]),flip(a)]. given #599 (T,wt=24): 23484 f(x,f(y,z,u),f(w,x,f(y,u,x))) = f(w,x,f(y,u,x)). [para(7301(a,1),1906(a,1,3,3)),rewrite([15(6)]),flip(a)]. given #600 (A,wt=38): 251 f(x,y,f(z,u,f(x,z,f(w,v5,f(z,v5,v6))))) = f(x,z,f(x,y,f(z,v5,f(z,u,f(w,v5,v6))))). [para(29(a,1),25(a,2,3,3))]. given #601 (T,wt=24): 23494 f(x,f(y,z,u),f(w,x,f(y,z,w))) = f(w,x,f(y,z,u)). [para(1766(a,1),1906(a,1,3)),rewrite([5(2),5(2),922(6),5(4),5(4)]),flip(a)]. given #602 (T,wt=24): 23495 f(x,f(y,z,u),f(w,x,f(z,u,w))) = f(w,x,f(y,z,u)). [para(1769(a,1),1906(a,1,3)),rewrite([5(2),5(2),922(6),5(4),5(4)]),flip(a)]. given #603 (T,wt=24): 23502 f(f(x,y,z),f(z,u,f(x,y,z)),f(w,x,y)) = f(x,y,z). [para(1329(a,1),1987(a,1,3)),rewrite([5(3,R),3270(3),6(3),5(6,R),15(6),5(8,R),3270(8)])]. given #604 (T,wt=24): 23511 f(f(x,y,z),f(u,x,y),f(z,w,f(x,y,z))) = f(x,y,z). [para(1329(a,1),1998(a,1,2)),rewrite([5(3,R),3270(3),5(4,R),15(4),6(4),5(8,R),3270(8)])]. given #605 (A,wt=38): 253 f(x,y,f(z,u,f(x,w,f(x,u,f(w,v5,v6))))) = f(x,u,f(x,y,f(z,u,f(w,v5,f(x,w,v6))))). [para(25(a,1),29(a,1,3,3))]. given #606 (T,wt=24): 23543 f(x,f(y,z,u),f(w,x,f(x,y,u))) = f(w,x,f(x,y,u)). [para(2175(a,1),74(a,1,3)),rewrite([15796(3),15796(6)]),flip(a)]. given #607 (T,wt=24): 23553 f(x,f(y,z,u),f(w,x,f(w,y,u))) = f(w,x,f(y,z,u)). [para(2175(a,1),220(a,2,3)),rewrite([7671(5),19(4)]),flip(a)]. given #608 (T,wt=24): 23721 f(x,y,f(x,z,f(u,w,y))) = f(x,z,f(x,y,f(z,u,w))). [para(4005(a,1),54(a,2,3)),rewrite([6(2),5(3,R),6(3),21385(4),5(4),5(4)]),flip(a)]. given #609 (T,wt=23): 32772 f(x,f(y,z,u),f(x,w,y)) = f(x,f(w,z,u),f(x,w,y)). [para(23721(a,1),1286(a,1,3)),rewrite([26704(5),5(4)]),flip(a)]. Low Water (displace): id=11683, wt=50.000 Low Water (displace): id=33116, wt=35.000 Low Water (displace): id=33173, wt=34.000 given #610 (A,wt=38): 255 f(x,y,f(z,u,f(x,u,f(w,v5,f(z,w,v6))))) = f(x,u,f(x,y,f(z,w,f(z,u,f(w,v5,v6))))). [para(25(a,1),29(a,2,3,3))]. given #611 (T,wt=23): 32849 f(x,f(y,z,u),f(x,w,u)) = f(x,f(w,y,z),f(x,w,u)). [para(32772(a,1),5(a,1)),rewrite([5(5),5(5),5(6,R)]),flip(a)]. Low Water (displace): id=33251, wt=32.000 Low Water (displace): id=33271, wt=31.000 Low Water (displace): id=33277, wt=30.000 Low Water (displace): id=33282, wt=27.000 given #612 (T,wt=23): 32850 f(x,f(y,z,u),f(w,x,u)) = f(x,f(w,y,z),f(w,x,u)). [para(32772(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4),5(5)]),flip(a)]. given #613 (T,wt=23): 32851 f(x,f(y,z,u),f(x,w,u)) = f(x,f(y,w,z),f(x,w,u)). [para(5(a,1),32772(a,1,2)),rewrite([6(2),5(4),6(4),6(5)]),flip(a)]. given #614 (T,wt=23): 32852 f(x,f(y,z,u),f(x,w,u)) = f(x,f(y,z,w),f(x,w,u)). [para(5(a,2),32772(a,1,2)),rewrite([6(2),5(4),5(4),6(5)]),flip(a)]. given #615 (A,wt=38): 257 f(x,y,f(z,u,f(x,w,f(u,v5,f(x,u,v6))))) = f(x,u,f(x,y,f(z,u,f(x,w,f(u,v5,v6))))). [para(25(a,2),29(a,1,3,3))]. given #616 (T,wt=23): 33227 f(x,f(y,z,u),f(w,x,u)) = f(x,f(y,z,w),f(w,x,u)). [para(32849(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4),5(5)]),flip(a)]. given #617 (T,wt=23): 33425 f(x,f(y,z,u),f(w,u,x)) = f(x,f(y,z,w),f(w,u,x)). [para(32850(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4),5(5)]),flip(a)]. given #618 (T,wt=23): 33445 f(x,f(y,z,u),f(w,x,y)) = f(x,f(w,z,u),f(w,x,y)). [para(32850(a,1),922(a,2)),rewrite([5(2),6(3),5(4),12982(7)])]. given #619 (T,wt=23): 33581 f(x,f(y,z,u),f(w,x,u)) = f(x,f(y,w,z),f(w,x,u)). [para(32851(a,2),5(a,2)),rewrite([5(2,R),6(2),5(3),5(5,R),6(5)]),flip(a)]. given #620 (A,wt=38): 258 f(x,y,f(z,u,f(x,u,f(z,w,f(u,v5,v6))))) = f(x,u,f(x,y,f(z,w,f(u,v5,f(z,u,v6))))). [para(25(a,2),29(a,2,3,3))]. given #621 (T,wt=23): 33593 f(x,f(y,z,u),f(x,w,z)) = f(x,f(w,y,u),f(x,w,z)). [para(32851(a,1),21(a,1,3)),rewrite([6(2),22(4),5(4),6(5)])]. given #622 (T,wt=23): 33783 f(x,f(y,z,u),f(w,y,x)) = f(x,f(w,z,u),f(w,y,x)). [para(33425(a,1),922(a,2)),rewrite([5(2),6(3),5(4),12982(7),5(4)])]. given #623 (T,wt=23): 33823 f(x,f(y,z,u),f(w,u,x)) = f(x,f(w,y,z),f(w,u,x)). [para(33445(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4),5(5)]),flip(a)]. given #624 (T,wt=23): 33941 f(x,f(y,z,u),f(x,w,z)) = f(x,f(y,w,u),f(x,w,z)). [para(803(a,1),33593(a,1,3)),rewrite([6(3),6(5),15403(5),27688(5),6(1),5(4,R),6(4),803(7)]),flip(a)]. given #625 (A,wt=44): 259 f(x,f(y,z,f(u,w,f(x,w,v5))),f(y,z,f(x,w,f(x,y,f(u,w,v5))))) = f(x,y,f(y,z,f(u,w,f(x,w,v5)))). [para(29(a,1),27(a,1,3,3))]. given #626 (T,wt=24): 23787 f(x,y,f(x,z,f(y,u,w))) = f(x,z,f(x,y,f(z,u,w))). [back_rewrite(7713),rewrite([23762(4),23762(7)])]. given #627 (T,wt=24): 23789 f(x,y,f(x,f(z,u,w),f(z,w,y))) = f(x,y,f(z,u,w)). [para(5019(a,1),6(a,2)),rewrite([5(2),5(2),6(4)])]. given #628 (T,wt=24): 23790 f(x,f(y,z,u),f(x,w,f(w,y,u))) = f(x,w,f(y,z,u)). [para(5019(a,1),8(a,1)),flip(a)]. given #629 (T,wt=24): 23798 f(x,f(y,z,u),f(y,w,f(x,u,w))) = f(x,w,f(y,z,u)). [para(5019(a,1),25(a,2)),rewrite([6(2),5(3,R),6(3)])]. given #630 (A,wt=38): 265 f(x,y,f(z,u,f(x,u,f(w,v5,f(z,v5,v6))))) = f(x,u,f(x,y,f(z,v5,f(z,u,f(w,v5,v6))))). [para(29(a,1),29(a,2,3,3))]. given #631 (T,wt=24): 23815 f(x,f(y,z,u),f(x,u,f(y,w,z))) = f(x,u,f(y,w,z)). [para(5019(a,1),910(a,1,3,3)),rewrite([5(2),5(2),15403(7),1700(7),5(6),5(6),23789(8)])]. given #632 (T,wt=24): 23818 f(x,f(y,z,u),f(w,y,f(x,w,u))) = f(x,w,f(y,z,u)). [para(5019(a,1),54(a,2,3)),rewrite([95(5),20(7)])]. given #633 (T,wt=24): 23830 f(x,f(y,z,u),f(w,u,f(w,x,y))) = f(w,x,f(y,z,u)). [para(5019(a,1),2013(a,2)),rewrite([5(7,R),6(7),15403(9),19428(10),5(6,R),6(6)])]. given #634 (T,wt=21): 34370 f(x,f(y,z,f(u,z,w)),f(u,z,x)) = f(u,z,x). [para(23830(a,1),18854(a,1,3)),rewrite([5(4,R),15(4),15(3),5(6),6(6),25130(7),28598(7),15(3),5(6,R),6(6),13767(6)]),flip(a)]. given #635 (A,wt=31): 266 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,w,f(x,y,f(x,z,f(x,v5,u)))). [para(32(a,2),8(a,2,3)),flip(a)]. given #636 (T,wt=24): 23841 f(x,f(y,z,u),f(u,w,f(x,y,w))) = f(x,w,f(y,z,u)). [para(5019(a,1),82(a,2)),rewrite([6(2),5(3,R),6(3)])]. given #637 (T,wt=24): 23868 f(x,y,f(x,f(y,z,u),f(z,w,u))) = f(x,y,f(z,w,u)). [para(5019(a,1),1105(a,2,3)),rewrite([5(4,R),19(5),5(8,R),6(8),19(8)])]. given #638 (T,wt=24): 23878 f(x,f(y,z,x),f(u,f(y,w,z),f(y,z,x))) = f(y,z,x). [para(5019(a,1),1478(a,1,3)),rewrite([5(2),5(2),5(3),5(5),5(5),12982(6),4(6),5(5),6(5),5(7),5(7),12982(8)])]. given #639 (T,wt=24): 23883 f(x,y,f(z,y,f(y,u,w))) = f(y,u,f(x,y,f(z,y,w))). [para(5247(a,1),5(a,2)),rewrite([6(3),5(5,R),6(5)])]. given #640 (A,wt=31): 268 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,v5,f(x,y,f(x,u,f(x,z,w)))). [para(32(a,1),17(a,1,3)),rewrite([57(8)])]. given #641 (T,wt=22): 34487 f(x,y,f(z,y,f(u,x,f(x,z,w)))) = f(x,z,y). [para(22275(a,1),23883(a,1,3)),rewrite([5(4,R),15(4),15(3),5(6),6(6),205(7),30976(6),5(6,R),6(6),7772(6)]),flip(a)]. given #642 (T,wt=24): 23912 f(x,y,f(z,y,f(y,u,w))) = f(y,w,f(z,y,f(x,y,u))). [para(5455(a,1),5(a,2)),rewrite([6(3),5(4,R),6(4)])]. given #643 (T,wt=24): 23924 f(x,y,f(y,z,f(u,y,w))) = f(u,y,f(y,z,f(x,y,w))). [para(5459(a,1),169(a,2)),rewrite([15403(5),17039(6)])]. given #644 (T,wt=24): 23927 f(x,y,f(z,y,f(y,u,w))) = f(z,y,f(y,w,f(x,y,u))). [para(5496(a,1),5(a,2)),rewrite([6(3),5(4,R),6(4)])]. given #645 (A,wt=38): 269 f(x,y,f(x,z,f(x,u,f(x,w,f(x,v5,v6))))) = f(x,w,f(x,y,f(x,z,f(x,v6,f(x,u,v5))))). [para(32(a,1),18(a,1,3,3))]. given #646 (T,wt=24): 23953 f(x,y,f(z,y,f(y,u,w))) = f(y,u,f(y,w,f(x,z,y))). [para(5502(a,1),5(a,2)),rewrite([6(3),5(4)])]. given #647 (T,wt=24): 23983 f(x,y,f(x,f(z,u,y),f(x,w,z))) = f(x,w,f(x,z,y)). [para(321(a,2),5502(a,1,3)),rewrite([5(2),16490(3),5(4),5(4)]),flip(a)]. given #648 (T,wt=24): 24038 f(x,y,f(z,u,f(z,y,w))) = f(z,y,f(x,y,f(z,w,u))). [para(6719(a,2),5(a,2)),rewrite([6(3),5(4,R),6(4)]),flip(a)]. given #649 (T,wt=24): 24145 f(f(x,y,z),f(z,u,f(x,y,z)),f(x,w,y)) = f(x,y,z). [para(7307(a,1),1987(a,1,3)),rewrite([5(3,R),7301(3),6(3),5(6,R),15(6),5(8,R),7301(8)])]. given #650 (A,wt=38): 270 f(x,y,f(x,z,f(x,u,f(x,w,f(x,v5,v6))))) = f(x,u,f(x,y,f(x,w,f(x,v6,f(x,z,v5))))). [para(32(a,2),18(a,2,3,3))]. given #651 (T,wt=24): 24146 f(f(x,y,z),f(x,u,y),f(z,w,f(x,y,z))) = f(x,y,z). [para(7307(a,1),1998(a,1,2)),rewrite([5(3,R),7301(3),5(4,R),15(4),6(4),5(8,R),7301(8)])]. given #652 (T,wt=24): 24160 f(f(x,y,z),f(x,z,u),f(x,u,f(z,u,w))) = f(x,z,u). [para(874(a,1),7334(a,1,3))]. given #653 (T,wt=24): 24161 f(f(x,y,z),f(x,z,u),f(z,u,f(x,u,w))) = f(x,z,u). [para(933(a,1),7334(a,1,3))]. given #654 (T,wt=24): 24243 f(x,y,f(y,z,f(u,y,w))) = f(u,y,f(y,w,f(x,y,z))). [para(7343(a,1),169(a,2)),rewrite([15403(5),17039(6)])]. given #655 (A,wt=31): 271 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,w,f(x,z,f(x,y,f(x,v5,u)))). [para(32(a,2),18(a,2,3)),flip(a)]. given #656 (T,wt=24): 24333 f(x,f(y,z,u),f(w,y,f(w,x,u))) = f(w,x,f(y,z,u)). [para(7671(a,1),131(a,2,3)),rewrite([103(5),20(7)])]. given #657 (T,wt=24): 24339 f(x,f(y,z,u),f(w,x,f(y,u,w))) = f(w,x,f(y,z,u)). [para(7671(a,1),7405(a,1,3)),rewrite([5(2),5(2),922(6),5(4),5(4)]),flip(a)]. given #658 (T,wt=24): 24368 f(x,f(y,z,u),f(z,w,x)) = f(w,x,f(y,z,f(z,u,x))). [para(7761(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4)])]. given #659 (T,wt=24): 24429 f(x,f(y,z,u),f(w,z,x)) = f(w,x,f(y,z,f(z,u,x))). [para(8102(a,2),5(a,2)),rewrite([6(3),5(5)]),flip(a)]. given #660 (A,wt=38): 272 f(x,y,f(x,z,f(x,u,f(x,w,f(x,v5,v6))))) = f(x,u,f(x,y,f(x,v5,f(x,w,f(x,z,v6))))). [para(18(a,1),32(a,2,3,3)),rewrite([57(4)])]. given #661 (T,wt=24): 24437 f(x,y,f(z,u,f(u,w,y))) = f(x,y,f(u,y,f(z,u,w))). [para(8102(a,2),205(a,1,3)),rewrite([5(4),9850(6),5(6,R),6(6)]),flip(a)]. given #662 (T,wt=24): 24576 f(x,f(y,z,u),f(z,x,f(y,u,w))) = f(z,x,f(y,u,w)). [para(8330(a,1),168(a,1,3)),rewrite([5(3,R),6(3),5(5,R),6(5),15(6),5(5,R),6(5)]),flip(a)]. given #663 (T,wt=24): 24614 f(x,y,f(z,u,f(z,w,x))) = f(z,x,f(x,y,f(z,w,u))). [para(9417(a,1),2861(a,2)),rewrite([5(1,R),6(1),5(3,R),6(3),5(5,R),6(5),5(7,R),6(7),6889(8),5(4),5(4),5(6,R),6(6)]),flip(a)]. given #664 (T,wt=24): 24716 f(x,f(y,z,f(z,x,u)),f(y,w,f(y,z,x))) = f(y,z,x). [para(6694(a,1),9988(a,2)),rewrite([5(1),5(3),5(6),5(8),4(8),5(6),19176(6),5(5,R),5(6),5(8),5(8),1713(8),5(7,R),6(7),20(7)])]. given #665 (A,wt=38): 273 f(x,y,f(x,z,f(x,u,f(x,w,f(x,v5,v6))))) = f(x,u,f(x,y,f(x,z,f(x,v5,f(x,v6,w))))). [para(18(a,2),32(a,2,3,3)),rewrite([57(4),6(6)])]. given #666 (T,wt=24): 24756 f(x,y,f(z,y,f(y,u,w))) = f(y,w,f(y,u,f(x,z,y))). [para(10617(a,1),5(a,2)),rewrite([6(3),5(4)])]. given #667 (T,wt=24): 24764 f(x,f(y,z,u),f(x,u,f(x,w,y))) = f(x,w,f(x,y,u)). [para(321(a,2),10617(a,1,3)),rewrite([5(2),16490(3),5(4),5(4)]),flip(a)]. given #668 (T,wt=24): 24769 f(x,y,f(z,y,f(y,u,w))) = f(y,w,f(x,y,f(z,y,u))). [para(10630(a,1),5(a,2)),rewrite([6(3),5(5,R),6(5)])]. given #669 (T,wt=24): 24847 f(x,f(y,z,u),f(x,w,z)) = f(x,w,f(z,u,f(x,y,z))). [para(11098(a,2),1404(a,2)),rewrite([19633(5),20(5),822(5)])]. given #670 (A,wt=31): 274 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,w,f(x,u,f(x,y,f(x,v5,z)))). [para(18(a,2),32(a,2,3)),rewrite([57(3),6(1)]),flip(a)]. given #671 (T,wt=24): 24938 f(x,f(y,z,u),f(y,x,f(x,z,w))) = f(x,w,f(y,x,z)). [para(866(a,1),13531(a,1,3,3)),rewrite([5(3,R),6(3),6(4),24803(6),5(5,R),6(5),24673(6)]),flip(a)]. given #672 (T,wt=24): 24956 f(x,y,f(z,x,f(u,x,w))) = f(u,x,f(x,y,f(z,x,w))). [para(5247(a,1),13531(a,2)),rewrite([5(4),15403(5),17039(6),5(5,R),6(5)]),flip(a)]. given #673 (T,wt=24): 24957 f(x,y,f(z,x,f(u,x,w))) = f(z,x,f(x,w,f(u,x,y))). [para(5455(a,1),13531(a,2)),rewrite([5(4),15403(5),17039(6),5(4,R),6(4)]),flip(a)]. given #674 (T,wt=24): 24959 f(x,y,f(y,z,f(u,y,w))) = f(y,z,f(y,w,f(u,x,y))). [para(5502(a,1),13531(a,2)),rewrite([5(4),15403(5),17039(6),5(4)])]. given #675 (A,wt=31): 275 f(x,y,f(z,u,f(y,z,f(z,w,v5)))) = f(y,z,f(x,y,f(z,v5,f(z,u,w)))). [para(32(a,1),24(a,1,3)),rewrite([5(2,R),6(2),5(8,R),6(8)])]. given #676 (T,wt=24): 24961 f(x,y,f(y,z,f(u,y,w))) = f(y,w,f(y,z,f(u,x,y))). [para(10617(a,1),13531(a,2)),rewrite([5(4),15403(5),17039(6),5(4)])]. given #677 (T,wt=24): 24962 f(x,y,f(z,x,f(u,x,w))) = f(u,x,f(x,w,f(z,x,y))). [para(10630(a,1),13531(a,2)),rewrite([5(4),15403(5),17039(6),5(5,R),6(5)]),flip(a)]. given #678 (T,wt=24): 24963 f(x,y,f(z,u,f(y,w,u))) = f(x,y,f(w,u,f(y,z,u))). [para(5(a,2),14376(a,1,3)),rewrite([6(2),6(4)])]. given #679 (T,wt=24): 24976 f(x,y,f(z,u,f(w,z,x))) = f(z,x,f(x,y,f(w,z,u))). [para(14376(a,2),2861(a,2)),rewrite([5(1,R),6(1),5(3,R),6(3),5(5,R),6(5),5(7,R),6(7),7856(8),5(4),5(4),5(6,R),6(6)]),flip(a)]. given #680 (A,wt=31): 276 f(x,y,f(z,u,f(z,w,f(z,x,v5)))) = f(z,x,f(x,y,f(z,u,f(z,v5,w)))). [para(32(a,2),24(a,2,3)),rewrite([5(3,R),6(3),5(8,R),6(8)]),flip(a)]. given #681 (T,wt=24): 25009 f(x,f(y,z,u),f(y,w,x)) = f(w,x,f(y,z,f(y,x,u))). [para(15095(a,1),922(a,2)),rewrite([6(3),12982(7),6(4)])]. given #682 (T,wt=24): 25033 f(x,f(y,z,x),f(z,u,w)) = f(y,x,f(z,u,f(z,x,w))). [para(15096(a,2),6(a,2)),rewrite([5(1,R),6(1),6(3),6(4)]),flip(a)]. given #683 (T,wt=24): 25098 f(x,f(y,z,x),f(z,u,w)) = f(z,x,f(y,x,f(z,u,w))). [para(15096(a,2),1329(a,2)),rewrite([5(1,R),6(1),5(3,R),6(3),6(4),19602(6),21430(6),6(4)]),flip(a)]. given #684 (T,wt=24): 25109 f(x,f(y,z,x),f(z,u,w)) = f(y,x,f(z,x,f(z,u,w))). [para(15096(a,2),7307(a,2)),rewrite([5(1,R),6(1),5(3,R),6(3),6(4),20(4),19602(5),14230(5),6(4)]),flip(a)]. given #685 (A,wt=31): 278 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,z,f(x,y,f(x,v5,f(x,w,u)))). [para(32(a,2),30(a,2,3)),rewrite([5(3,R),6(3),57(4),6(5),5(8,R),6(8)])]. given #686 (T,wt=24): 25345 f(x,f(y,z,x),f(x,u,f(w,y,z))) = f(x,u,f(y,z,x)). [back_rewrite(20920),rewrite([25157(9),18491(6),6(3)])]. given #687 (T,wt=24): 25346 f(x,f(y,z,u),f(y,x,w)) = f(x,w,f(y,u,f(y,x,z))). [back_rewrite(19428),rewrite([25157(8),1775(5)])]. given #688 (T,wt=24): 25373 f(x,f(y,z,u),f(y,x,f(x,u,w))) = f(x,w,f(y,x,u)). [back_rewrite(24701),rewrite([25262(6),15289(3),19(2)]),flip(a)]. given #689 (T,wt=24): 25388 f(x,f(y,z,f(z,x,u)),f(x,u,w)) = f(x,w,f(z,x,u)). [back_rewrite(12981),rewrite([25262(6),1982(3),19(2)]),flip(a)]. given #690 (A,wt=31): 280 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,u,f(x,y,f(x,v5,f(x,w,z)))). [para(32(a,2),31(a,2,3)),rewrite([57(4),6(5)])]. given #691 (T,wt=22): 35259 f(x,y,f(z,u,f(w,z,f(z,x,y)))) = f(z,x,y). [para(25388(a,1),21079(a,2)),rewrite([1982(5),1982(7),5(6),30962(6),73(3),6(8),25793(8),73(7),1982(7)])]. given #692 (T,wt=22): 35273 f(x,y,f(z,u,f(w,z,f(x,y,z)))) = f(x,y,z). [para(5(a,1),35259(a,1,3)),rewrite([5(1),5(1),5(3),5(3),5(5),5(5)])]. given #693 (T,wt=22): 35274 f(x,y,f(z,u,f(w,u,f(x,y,u)))) = f(x,y,u). [para(5(a,2),35259(a,1,3)),rewrite([5(1),5(1),6(3),5(5),5(5)])]. given #694 (T,wt=22): 35282 f(x,y,f(z,u,f(w,u,f(x,u,y)))) = f(x,u,y). [para(35259(a,1),21477(a,1,3)),rewrite([5(1,R),6(1),6(3),5(4,R),6(4),6(5),15403(5),32978(5),5(1,R),15(1),19(2),5(2,R),6(2),5(4,R),6(4)]),flip(a)]. given #695 (A,wt=31): 283 f(x,y,f(z,u,f(z,x,f(z,w,v5)))) = f(z,x,f(x,y,f(z,v5,f(z,u,w)))). [para(32(a,1),28(a,1,3,3)),rewrite([103(5)])]. given #696 (T,wt=24): 25631 f(x,y,f(y,f(x,z,u),f(y,w,z))) = f(x,y,f(y,w,z)). [para(75(a,2),158(a,2,3)),rewrite([868(3),28(3)]),flip(a)]. given #697 (T,wt=24): 25659 f(x,y,f(x,f(y,z,u),f(x,z,w))) = f(x,w,f(x,y,z)). [para(803(a,1),15408(a,2,3)),rewrite([6(3),15403(4)])]. given #698 (T,wt=24): 25663 f(x,y,f(x,f(z,y,u),f(x,z,w))) = f(x,w,f(x,z,y)). [para(812(a,1),15408(a,2,3)),rewrite([6(3),25476(4)])]. given #699 (T,wt=24): 25664 f(x,y,f(x,f(y,z,u),f(x,u,w))) = f(x,w,f(x,y,u)). [para(827(a,1),15408(a,2,3)),rewrite([6(1),6(3),25472(4),6(5)])]. given #700 (A,wt=31): 285 f(x,y,f(z,u,f(z,x,f(z,w,v5)))) = f(x,y,f(z,x,f(z,v5,f(z,u,w)))). [para(32(a,1),122(a,1,3,3)),rewrite([5(4,R),6(4),103(5),5(8,R),6(8)])]. given #701 (T,wt=24): 25665 f(x,y,f(x,f(z,y,u),f(x,u,w))) = f(x,w,f(x,y,u)). [para(1030(a,1),15408(a,2,3)),rewrite([6(3),25476(4)])]. given #702 (T,wt=24): 25716 f(x,f(y,z,u),f(x,y,f(x,z,w))) = f(x,w,f(x,y,z)). [para(15408(a,2),1301(a,1)),rewrite([5(2),5(2),5(6,R),6(6)])]. given #703 (T,wt=24): 25793 f(x,f(y,x,z),f(u,w,v5)) = f(x,z,f(y,x,f(u,w,v5))). [para(15410(a,2),853(a,2)),rewrite([6(7),25130(8),5(7,R),6(7),25150(8)]),flip(a)]. given #704 (T,wt=24): 26198 f(x,f(y,z,u),f(y,x,w)) = f(x,w,f(y,u,f(y,z,x))). [para(15738(a,1),319(a,2)),rewrite([5(2,R),6(2),4(4),5(3),6(5),5(6),5(6),15403(8),25157(7),5(5,R),6(5),205(5)])]. given #705 (A,wt=38): 286 f(x,y,f(z,u,f(x,w,f(x,z,f(x,v5,v6))))) = f(x,z,f(x,y,f(z,u,f(x,v6,f(x,w,v5))))). [para(32(a,1),25(a,1,3,3))]. given #706 (T,wt=24): 26290 f(x,f(y,z,f(y,u,x)),f(u,x,w)) = f(y,x,f(u,x,w)). [para(15766(a,1),5(a,2)),rewrite([5(1),5(4),5(6,R),6(6)])]. given #707 (T,wt=24): 26291 f(x,f(y,z,u),f(x,y,f(x,u,w))) = f(x,w,f(x,y,u)). [para(15766(a,1),20(a,1,3)),rewrite([5(1),5(1),5(3,R),6(3),25472(5),22(5),5(5),5(5),5(7,R),6(7),25472(8),25664(8)])]. given #708 (T,wt=24): 26332 f(x,f(y,z,f(y,u,x)),f(u,w,f(y,u,x))) = f(y,u,x). [para(15766(a,1),70(a,1)),rewrite([5(1),5(1),5(3),5(3),5(4,R),6(4),4009(5),5(2),5(2),5(4),5(4),5(6,R),6(6),25472(7),6(4),25659(7),5(6,R)]),flip(a)]. given #709 (T,wt=24): 26334 f(x,f(y,z,f(y,x,u)),f(z,w,f(y,z,x))) = f(y,z,x). [para(15766(a,1),70(a,2,3)),rewrite([5(1),5(1),5(3),5(3),5(5),5(5),5(6,R),6(6),1669(7),910(3),5(2),5(2),5(4,R),6(4),5(6,R)]),flip(a)]. given #710 (A,wt=38): 287 f(x,y,f(z,u,f(x,z,f(z,w,f(z,v5,v6))))) = f(x,z,f(x,y,f(z,w,f(z,v6,f(z,u,v5))))). [para(32(a,2),25(a,2,3,3))]. given #711 (T,wt=24): 26705 f(x,f(y,z,u),f(y,x,f(z,x,w))) = f(x,w,f(y,z,x)). [para(15903(a,1),5(a,2)),rewrite([5(2),6(2),5(3,R),6(3),5(4),5(5),5(5),5(6,R),6(6)])]. given #712 (T,wt=24): 26706 f(x,f(y,z,u),f(x,y,f(x,w,z))) = f(x,w,f(x,y,z)). [para(15903(a,1),19(a,1,3)),rewrite([5(1,R),6(1),5(4,R),6(4),15403(5),15403(4),21(3),20(3),22(3),5(4,R),6(4)]),flip(a)]. given #713 (T,wt=24): 26824 f(x,f(y,z,u),f(w,y,f(w,z,x))) = f(w,x,f(y,z,u)). [para(15909(a,1),866(a,2)),rewrite([5(3,R),6(3),5(5,R),6(5),6(7),25793(8),26153(9),5(6,R),6(6)])]. given #714 (T,wt=24): 26833 f(x,f(y,z,u),f(w,z,f(x,w,y))) = f(x,w,f(y,z,u)). [para(15909(a,1),1606(a,2)),rewrite([6(7),25148(9),15403(6),25238(8),1775(5)])]. given #715 (A,wt=31): 289 f(x,y,f(x,f(y,z,u),f(x,w,v5))) = f(x,w,f(x,v5,f(y,z,f(x,y,u)))). [para(25(a,2),32(a,2,3))]. given #716 (T,wt=24): 26961 f(x,y,f(x,z,f(u,w,y))) = f(x,z,f(x,y,f(u,w,z))). [para(15921(a,1),140(a,2,3)),rewrite([6(2),5(3,R),6(3),21531(5),5(4),5(4)])]. given #717 (T,wt=24): 27091 f(x,f(y,z,f(z,u,x)),f(u,x,w)) = f(z,x,f(u,x,w)). [para(15972(a,1),5(a,2)),rewrite([5(1),5(3),5(3),5(4),5(5),5(5),5(6,R),6(6)])]. given #718 (T,wt=24): 27114 f(x,f(y,z,f(y,x,u)),f(w,z,f(y,z,x))) = f(y,z,x). [para(15972(a,1),74(a,2,3)),rewrite([5(1),5(1),5(3),5(3),5(5),6(5),1030(5),5(4,R),6(4),25476(5),1667(5),15771(3),5(2),5(2),5(4),6(4),5(6,R)]),flip(a)]. given #719 (T,wt=22): 35721 f(x,y,f(z,u,f(x,z,f(w,y,z)))) = f(x,y,z). [para(27114(a,1),19(a,1,3)),rewrite([5(1),6(1),5(3),6(3),6(4),15403(4),1030(3),20(2),5(2,R),6(2),5(3,R),6(3),5(4),6(4),35685(6),25793(4)]),flip(a)]. given #720 (A,wt=44): 291 f(x,f(y,z,f(x,u,f(x,w,v5))),f(y,z,f(x,u,f(x,v5,f(x,y,w))))) = f(x,y,f(y,z,f(x,u,f(x,w,v5)))). [para(32(a,2),27(a,1,3,3))]. given #721 (T,wt=22): 35729 f(x,y,f(x,z,f(y,u,f(w,z,y)))) = f(x,z,y). [para(27114(a,1),7307(a,2)),rewrite([5(1),6(1),5(3,R),6(3),5(4,R),6(4),5(5),6(5),5(6,R),6(6),5(7,R),6(7),1098(9),29939(7),35685(4),5(5),6(5)])]. given #722 (T,wt=24): 27116 f(x,f(y,z,f(u,z,x)),f(u,z,f(u,x,w))) = f(u,z,x). [para(15972(a,1),220(a,2,3)),rewrite([5(1),5(1),5(3),5(3),5(5),1030(5),5(4,R),6(4),25476(5),1667(5),15771(3),5(2),5(2),5(4),6(4)]),flip(a)]. given #723 (T,wt=22): 35783 f(x,y,f(z,u,f(w,z,f(x,z,y)))) = f(x,z,y). [para(27116(a,1),15821(a,1,3)),rewrite([5(1),6(1),5(3,R),6(3),5(4,R),6(4),5(5),5(6),6(6),6(7),15403(7),34219(7),6(3),122(3),5(3,R),6(3),5(5),6(5),5(7,R),6(7),5(8,R),6(8),25476(9),818(9),15771(7)])]. given #724 (T,wt=22): 35792 f(x,y,f(z,y,f(x,u,f(x,w,z)))) = f(x,z,y). [para(15972(a,1),27116(a,1,3)),rewrite([6(1),6(3),5(5),1030(5),6(4),31065(4),5(1,R),6(1),5(2,R),6(2),5(4,R),15(4),5(4,R),15(4),6(4),6(5),5(7),1030(7)])]. given #725 (A,wt=38): 292 f(x,y,f(z,u,f(x,w,f(x,u,f(x,v5,v6))))) = f(x,u,f(x,y,f(z,u,f(x,v6,f(x,w,v5))))). [para(32(a,1),29(a,1,3,3))]. given #726 (T,wt=22): 35797 f(x,y,f(z,u,f(u,y,f(u,x,w)))) = f(u,x,y). [para(19755(a,1),27116(a,1,2)),rewrite([5(1,R),6(1),5(3,R),6(3),5(4,R),6(4),15(5),5(4,R),6(4),5(5,R),6(5),6(7),25793(8),7855(7),27050(7),30919(6),25793(4),15403(4),501(4),5(5,R),6(5),5(6,R),6(6),25793(8),73(7),1982(7)])]. given #727 (T,wt=24): 27123 f(x,f(y,z,u),f(z,x,f(y,x,w))) = f(x,w,f(y,z,x)). [para(15973(a,1),5(a,2)),rewrite([5(2),6(2),5(3,R),6(3),5(4),5(5),5(5),5(6,R),6(6)])]. given #728 (T,wt=24): 27185 f(x,f(y,z,u),f(u,x,f(y,x,w))) = f(x,w,f(y,u,x)). [para(16054(a,1),5(a,2)),rewrite([5(2,R),6(2),5(3,R),6(3),5(4),5(5),5(5)])]. given #729 (T,wt=24): 27214 f(x,f(y,z,f(y,u,x)),f(u,w,x)) = f(y,x,f(u,w,x)). [para(16054(a,1),74(a,2,3)),rewrite([5(4,R),1669(6),5(6,R)]),flip(a)]. given #730 (A,wt=38): 293 f(x,y,f(z,u,f(x,u,f(z,w,f(z,v5,v6))))) = f(x,u,f(x,y,f(z,w,f(z,v6,f(z,u,v5))))). [para(32(a,2),29(a,2,3,3))]. given #731 (T,wt=24): 27221 f(x,y,f(x,f(z,u,y),f(x,z,w))) = f(x,w,f(x,z,y)). [para(16054(a,1),130(a,2,3)),rewrite([22(6),2175(8)])]. given #732 (T,wt=24): 27223 f(x,f(y,z,x),f(u,w,f(u,y,x))) = f(u,x,f(y,z,x)). [para(16054(a,1),220(a,2,3)),rewrite([803(6)]),flip(a)]. given #733 (T,wt=24): 27288 f(x,f(y,z,u),f(x,w,f(y,w,z))) = f(x,w,f(y,z,u)). [para(16068(a,1),812(a,2)),rewrite([6(7),25130(8),5(5,R),25793(5),1700(7)])]. given #734 (T,wt=24): 27308 f(x,y,f(x,f(z,y,u),f(z,u,w))) = f(x,y,f(z,u,w)). [para(16068(a,1),130(a,2,3)),rewrite([22(6),16068(8)])]. given #735 (A,wt=38): 295 f(x,y,f(x,z,f(x,u,f(w,v5,f(x,v5,v6))))) = f(x,z,f(x,u,f(x,v5,f(x,y,f(w,v5,v6))))). [para(29(a,2),32(a,2,3,3)),rewrite([6(3),57(4)]),flip(a)]. given #736 (T,wt=24): 27400 f(x,f(y,z,f(z,u,x)),f(z,u,f(u,x,w))) = f(z,u,x). [para(16173(a,1),102(a,1,3)),rewrite([5(1),5(3),5(5),5(5),27050(6),5(5,R),6(5),803(5),5(4),5(4),25793(4),73(3),1982(3),5(2),5(4),5(6),5(6),27050(7)]),flip(a)]. given #737 (T,wt=24): 27439 f(x,f(y,z,u),f(x,y,f(x,w,u))) = f(x,w,f(x,y,u)). [para(16467(a,2),5455(a,1,3)),rewrite([5(2),6(2),16490(3),5(3),5(5,R),6(5)]),flip(a)]. given #738 (T,wt=24): 27446 f(x,f(y,z,u),f(z,x,w)) = f(x,w,f(z,u,f(y,z,x))). [para(16468(a,1),5(a,2)),rewrite([5(2,R),6(2),5(3),5(4),5(4)])]. given #739 (T,wt=24): 27751 f(x,y,f(x,z,f(u,w,y))) = f(x,z,f(x,y,f(u,z,w))). [para(16629(a,1),77(a,2,3)),rewrite([6(2),23819(5),6(4)]),flip(a)]. given #740 (A,wt=38): 296 f(x,y,f(x,z,f(x,u,f(x,w,f(x,v5,v6))))) = f(x,u,f(x,y,f(x,z,f(x,v6,f(x,v5,w))))). [para(32(a,2),32(a,2,3,3)),rewrite([57(4),6(6)])]. given #741 (T,wt=24): 27772 f(x,f(y,z,u),f(w,u,f(x,w,y))) = f(x,w,f(y,z,u)). [para(16629(a,1),16468(a,1)),rewrite([6(4)]),flip(a)]. given #742 (T,wt=24): 27787 f(x,y,f(x,f(y,z,u),f(w,x,u))) = f(w,x,f(x,y,u)). [para(6694(a,1),172(a,2,3)),rewrite([6(1),25472(4),6(5),20(8),25472(8),15(9),28(7)])]. given #743 (T,wt=24): 27789 f(x,y,f(x,f(z,y,u),f(w,x,u))) = f(w,x,f(x,y,u)). [para(15968(a,1),172(a,2,3)),rewrite([6(1),25476(4),6(5),20(8),25476(8),15(9),28(7)])]. given #744 (T,wt=24): 27824 f(x,f(y,z,u),f(y,x,f(w,z,u))) = f(y,x,f(w,z,u)). [para(1633(a,1),27795(a,2)),rewrite([15403(9),25511(9),5(6,R),6(6),825(8)])]. given #745 (A,wt=31): 297 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,w,f(x,v5,f(x,y,f(x,u,z)))). [para(32(a,2),32(a,2,3)),rewrite([57(3),6(1)]),flip(a)]. given #746 (T,wt=24): 27828 f(x,f(y,z,u),f(y,x,f(z,w,u))) = f(y,x,f(z,w,u)). [para(7671(a,1),27795(a,2)),rewrite([15403(9),25511(9),5(6,R),6(6),825(8)])]. given #747 (T,wt=24): 27872 f(x,y,f(z,u,f(w,z,v5))) = f(x,y,f(z,v5,f(w,z,u))). [para(8713(a,1),16711(a,2,3,3)),rewrite([5(1),5(1),5(3),5(3),25133(6),5(2),25793(4),1051(3),5(4),5(4),5(6),5(6),205(9)])]. given #748 (T,wt=24): 27998 f(x,f(y,z,f(y,x,u)),f(x,w,u)) = f(x,u,f(y,x,w)). [para(16726(a,1),220(a,2,3)),rewrite([6(3),5(4,R),25130(5),825(5),5(6,R)]),flip(a)]. given #749 (T,wt=24): 28033 f(x,y,f(x,f(z,y,u),f(w,x,z))) = f(x,y,f(w,x,z)). [para(803(a,1),17086(a,1,3,3)),rewrite([6(2),17086(4),5(3,R),6(3),15403(6)]),flip(a)]. given #750 (A,wt=31): 299 f(x,f(y,z,u),f(x,w,f(x,v5,y))) = f(x,w,f(x,v5,f(y,z,f(x,y,u)))). [para(16(a,2),33(a,1,3,3)),flip(a)]. given #751 (T,wt=24): 28039 f(x,f(y,z,u),f(x,z,f(y,x,w))) = f(x,w,f(y,x,z)). [para(17086(a,1),812(a,2)),rewrite([6(7),15403(8),15403(7),16989(9)])]. given #752 (T,wt=24): 28063 f(x,f(y,z,u),f(x,w,f(y,x,z))) = f(x,w,f(y,x,z)). [para(17086(a,1),74(a,2,3)),rewrite([20(5),17086(4)]),flip(a)]. given #753 (T,wt=24): 28137 f(x,f(y,z,u),f(x,u,f(y,x,w))) = f(x,w,f(y,x,u)). [para(17223(a,1),812(a,2)),rewrite([6(7),15403(8),15403(7),16989(9)])]. given #754 (T,wt=24): 28148 f(x,f(y,z,u),f(x,w,f(y,x,u))) = f(x,w,f(y,x,u)). [para(17223(a,1),74(a,2,3)),rewrite([20(5),17223(4)]),flip(a)]. given #755 (A,wt=38): 300 f(x,y,f(x,z,f(x,u,f(x,w,f(x,v5,v6))))) = f(x,u,f(x,y,f(x,v6,f(x,z,f(x,w,v5))))). [para(33(a,1),18(a,2,3,3))]. given #756 (T,wt=24): 28286 f(x,y,f(z,u,f(z,w,y))) = f(z,y,f(x,y,f(z,u,w))). [para(18322(a,1),6(a,2)),rewrite([6(3),6(4)])]. given #757 (T,wt=24): 28301 f(x,y,f(z,u,f(z,w,x))) = f(z,x,f(x,y,f(z,u,w))). [para(18322(a,1),922(a,2)),rewrite([5(3,R),6(3),5(6,R),6(6),922(7),6(4),5(5,R),6(5)])]. given #758 (T,wt=24): 28684 f(f(x,y,z),f(x,y,u),f(x,u,f(y,z,u))) = f(x,y,u). [para(28531(a,1),70(a,2,3)),rewrite([5(2),5(2),5(3),5(3),5(4),6(4),5(5,R),6(5),16471(5),5(3,R),6(3),5(6),5(6),5(7),5(7),5(9,R),6(9),3521(9)])]. given #759 (T,wt=24): 28783 f(x,y,f(x,f(z,y,u),f(z,x,w))) = f(x,w,f(z,x,y)). [para(813(a,1),28559(a,1,1)),rewrite([5(2),5(2),5(5,R),6(5),28640(6),5(5),5(5),25476(6)]),flip(a)]. given #760 (A,wt=31): 301 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,u,f(x,v5,f(x,y,f(x,z,w)))). [para(33(a,1),18(a,2,3))]. given #761 (T,wt=24): 28887 f(x,f(y,z,f(x,u,z)),f(u,z,f(x,w,u))) = f(x,u,z). [para(15972(a,1),187(a,1,3,3)),rewrite([5(1,R),6(1),5(3),1051(3),5(3,R),6(3),5(5),16382(7),18491(5),6(4),15403(4),1030(3),20(2),5(2,R),6(2),5(4,R),6(4),5(6),16124(7)]),flip(a)]. given #762 (T,wt=24): 28934 f(x,f(y,z,f(y,x,u)),f(x,z,w)) = f(x,w,f(y,x,z)). [para(866(a,1),28565(a,1,1)),rewrite([6(5),28633(6),6(7),24777(8)])]. given #763 (T,wt=24): 28962 f(x,y,f(x,f(z,u,y),f(x,u,w))) = f(x,w,f(x,u,y)). [para(1286(a,1),28565(a,2)),rewrite([6(2),6(8),28565(8)])]. given #764 (T,wt=24): 28999 f(x,f(y,z,f(z,x,u)),f(y,x,w)) = f(x,w,f(y,z,x)). [para(803(a,1),28566(a,1,1)),rewrite([6(5),28770(6),803(7)])]. given #765 (A,wt=38): 302 f(x,y,f(x,z,f(x,u,f(x,w,f(x,v5,v6))))) = f(x,v6,f(x,y,f(x,z,f(x,u,f(x,w,v5))))). [para(33(a,2),18(a,1,3,3))]. given #766 (T,wt=24): 29009 f(x,f(y,z,f(y,x,u)),f(z,x,w)) = f(x,w,f(y,z,x)). [para(871(a,1),28566(a,1,1)),rewrite([6(5),28788(6),871(7)])]. given #767 (T,wt=24): 29010 f(x,f(y,z,f(u,y,x)),f(u,x,w)) = f(x,w,f(u,y,x)). [para(910(a,1),28566(a,1,1)),rewrite([6(5),28791(6),910(7)])]. given #768 (T,wt=24): 29132 f(x,f(y,z,u),f(x,u,f(w,x,y))) = f(w,x,f(x,y,u)). [para(1030(a,1),28567(a,2,3)),rewrite([6(2),1051(4),6(3),29011(6),6(5)])]. given #769 (T,wt=24): 29321 f(f(x,y,z),f(x,z,u),f(x,u,f(y,z,u))) = f(x,z,u). [para(28570(a,1),16711(a,2,3)),rewrite([5(4),5(4),16471(5),5(9,R),6(9),1073(9)])]. given #770 (A,wt=31): 303 f(x,y,f(z,u,f(z,x,f(z,w,v5)))) = f(z,x,f(x,y,f(z,w,f(z,v5,u)))). [para(33(a,1),24(a,2,3)),rewrite([5(3,R),6(3),5(8,R),6(8)]),flip(a)]. given #771 (T,wt=24): 29410 f(x,y,f(y,z,f(u,y,w))) = f(y,z,f(y,w,f(x,u,y))). [para(145(a,1),28747(a,2)),rewrite([5(3,R),6(3),20(4),5(5,R),6(5),1604(7),25793(4),205(3),15403(3),5(7,R),6(7),7347(7)]),flip(a)]. given #772 (T,wt=24): 29643 f(x,f(y,z,f(y,x,u)),f(u,w,f(y,x,u))) = f(y,x,u). [para(19176(a,1),4278(a,1)),rewrite([5(3),6(3),26370(4),813(3),5(6),5(6),5(7,R),25793(7),1713(6)]),flip(a)]. given #773 (T,wt=24): 29908 f(x,f(y,z,u),f(y,w,f(x,w,z))) = f(x,w,f(y,z,u)). [para(19755(a,1),19(a,1,3)),rewrite([6(1),25476(5),16068(4),20(3),6(4)]),flip(a)]. given #774 (T,wt=24): 29928 f(x,f(y,z,u),f(y,w,f(w,x,z))) = f(w,x,f(y,z,u)). [para(19755(a,1),922(a,2)),rewrite([5(1),6(4),5(6),12982(9),5(6,R),6(6)])]. given #775 (A,wt=31): 304 f(x,f(y,z,u),f(x,w,f(x,v5,z))) = f(x,w,f(x,v5,f(y,z,f(x,z,u)))). [para(24(a,1),33(a,1,3,3)),flip(a)]. given #776 (T,wt=24): 29932 f(x,f(y,z,u),f(y,w,f(z,x,w))) = f(x,w,f(y,z,u)). [para(19755(a,1),1057(a,2)),rewrite([5(2,R),6(2),6(4),5(6,R),6(6),16490(9)])]. given #777 (T,wt=24): 29945 f(x,f(y,z,f(x,u,z)),f(y,u,w)) = f(x,z,f(y,u,w)). [para(19755(a,1),1072(a,2)),rewrite([5(7,R),12402(9)])]. given #778 (T,wt=24): 30034 f(x,f(y,z,u),f(z,w,f(y,w,x))) = f(w,x,f(y,z,u)). [para(19762(a,1),5(a,2)),rewrite([5(2),5(2),5(4),5(6,R),6(6)])]. given #779 (T,wt=24): 30046 f(x,f(y,z,u),f(z,w,f(y,x,w))) = f(x,w,f(y,z,u)). [para(19762(a,1),1057(a,2)),rewrite([5(2,R),6(2),6(4),5(6,R),6(6),16490(9)])]. given #780 (A,wt=31): 305 f(x,y,f(x,z,f(x,u,f(x,w,v5)))) = f(x,w,f(x,y,f(x,u,f(x,v5,z)))). [para(33(a,1),30(a,2,3)),rewrite([5(3,R),6(3),57(4),5(8,R),6(8)]),flip(a)]. given #781 (T,wt=24): 30055 f(x,f(y,z,f(x,u,z)),f(u,y,w)) = f(x,z,f(u,y,w)). [para(19762(a,1),1072(a,2)),rewrite([5(7,R),12402(9)])]. given #782 (T,wt=24): 30098 f(f(x,y,z),f(u,x,y),f(w,z,f(x,y,z))) = f(x,y,z). [para(3301(a,1),19762(a,2)),rewrite([5(7,R),20512(9)])]. given #783 (T,wt=24): 30100 f(f(x,y,z),f(x,u,y),f(w,z,f(x,y,z))) = f(x,y,z). [para(7335(a,1),19762(a,2)),rewrite([5(7,R),20512(9)])]. given #784 (T,wt=24): 30122 f(x,f(y,z,u),f(y,u,f(x,z,w))) = f(y,u,f(x,z,w)). [back_rewrite(29568),rewrite([5(2,R),6(2),19762(4),5(3,R),6(3)]),flip(a)]. given #785 (A,wt=38): 309 f(x,y,f(z,u,f(x,z,f(z,w,f(z,v5,v6))))) = f(x,z,f(x,y,f(z,v6,f(z,u,f(z,w,v5))))). [para(33(a,1),25(a,2,3,3))]. given #786 (T,wt=23): 36738 f(f(x,y,z),f(u,x,w),f(u,w,y)) = f(u,w,f(x,y,z)). [para(30122(a,1),18837(a,2)),rewrite([5(2,R),6(2),5(5),5(5),12982(6),6(5),28512(5),5(5,R),6(5)])]. Low Water (keep): wt=36.000, iters=6700 given #787 (T,wt=20): 36780 f(x,f(y,z,u),f(y,z,w)) = f(y,z,f(w,u,x)). [para(36738(a,1),5(a,1)),rewrite([6(5),35717(6)]),flip(a)]. given #788 (T,wt=20): 36856 f(x,f(y,z,u),f(y,w,z)) = f(y,z,f(w,u,x)). [para(36738(a,1),18491(a,2)),rewrite([5(7,R),30898(9),33573(4)])]. given #789 (T,wt=20): 36895 f(x,f(y,z,u),f(y,u,w)) = f(y,u,f(z,w,x)). [para(36738(a,1),22275(a,2)),rewrite([5(6),5(7,R),6(7),25793(7),30959(7),5(5,R),6(5),474(5),6(3),33570(6)])]. given #790 (A,wt=38): 315 f(x,y,f(z,u,f(x,u,f(z,w,f(z,v5,v6))))) = f(x,u,f(x,y,f(z,v6,f(z,u,f(z,w,v5))))). [para(33(a,1),29(a,2,3,3))]. given #791 (T,wt=20): 37170 f(x,f(y,z,u),f(z,u,w)) = f(z,u,f(x,y,w)). [back_rewrite(36790),rewrite([6(2),6(4),5(5,R),6(5),36880(6)])]. ============================== PROOF ================================= % Proof 1 at 657.96 (+ 1.04) seconds: dist_both. % Length of proof is 235. % Level of proof is 31. % Maximum clause weight is 46. % Given clauses 791. 3 f(f(x,y,z),u,w) = f(f(x,u,w),f(y,u,w),f(z,u,w)) & f(f(x,y,z),u,w) = f(x,f(y,u,w),f(z,u,w)) # label(dist_both) # label(non_clause) # label(goal). [goal]. 4 f(x,x,y) = x # label(majority). [assumption]. 5 f(x,y,z) = f(z,x,y) # label(2a). [assumption]. 6 f(x,y,z) = f(x,z,y) # label(2b). [assumption]. 7 f(f(x,y,z),y,u) = f(x,y,f(z,y,u)) # label(associativity). [assumption]. 8 f(x,y,f(x,z,u)) = f(x,z,f(x,y,u)). [copy(7),rewrite([5(2),5(2),5(3,R),6(3)]),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])]. 13 f(f(c11,c14,c15),f(c12,c14,c15),f(c13,c14,c15)) != f(f(c11,c12,c13),c14,c15) | f(f(c11,c12,c13),c14,c15) != f(c11,f(c12,c14,c15),f(c13,c14,c15)) # label(dist_both) # answer(dist_both). [deny(3)]. 14 f(f(c11,c14,c15),f(c12,c14,c15),f(c13,c14,c15)) != f(c14,c15,f(c11,c12,c13)) | f(c11,f(c12,c14,c15),f(c13,c14,c15)) != f(c14,c15,f(c11,c12,c13)) # answer(dist_both). [copy(13),rewrite([5(20),5(20),5(28),5(28)]),flip(b)]. 15 f(x,y,y) = y. [para(5(a,1),4(a,1))]. 16 f(x,y,f(z,x,u)) = f(z,x,f(x,y,u)). [para(8(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)]),flip(a)]. 17 f(x,y,f(x,z,u)) = f(x,u,f(x,y,z)). [para(5(a,1),8(a,1,3)),rewrite([5(1,R),6(1)])]. 18 f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,y,f(x,z,w))). [para(8(a,1),8(a,1,3))]. 19 f(x,y,f(x,z,y)) = f(x,z,y). [para(15(a,1),8(a,1,3)),flip(a)]. 20 f(x,y,f(x,y,z)) = f(x,y,z). [para(15(a,1),8(a,1)),rewrite([6(3),19(3)]),flip(a)]. 21 f(x,y,f(x,z,f(x,u,y))) = f(x,z,f(x,u,y)). [para(19(a,1),8(a,1,3)),flip(a)]. 22 f(x,y,f(x,z,f(x,y,u))) = f(x,z,f(x,y,u)). [para(19(a,1),8(a,2,3)),rewrite([6(1),6(4)])]. 24 f(x,y,f(z,y,u)) = f(z,y,f(x,y,u)). [para(16(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)])]. 25 f(x,y,f(z,u,f(x,z,w))) = f(x,z,f(x,y,f(z,u,w))). [para(16(a,2),8(a,1,3))]. 27 f(x,f(y,z,u),f(y,z,f(x,y,u))) = f(x,y,f(y,z,u)). [para(16(a,2),19(a,1,3))]. 28 f(x,y,f(y,z,f(x,y,u))) = f(x,y,f(y,z,u)). [para(16(a,2),20(a,1,3))]. 29 f(x,y,f(z,u,f(x,u,w))) = f(x,u,f(x,y,f(z,u,w))). [para(16(a,1),16(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])]. 30 f(x,y,f(z,x,u)) = f(z,x,f(x,u,y)). [para(17(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)]),flip(a)]. 32 f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,y,f(x,w,z))). [para(17(a,1),8(a,2,3)),flip(a)]. 33 f(x,y,f(x,z,f(x,u,w))) = f(x,w,f(x,y,f(x,z,u))). [para(17(a,2),8(a,1,3))]. 38 f(x,f(y,z,u),f(x,w,y)) = f(x,w,f(y,z,f(x,y,u))). [para(16(a,2),17(a,1,3)),flip(a)]. 40 f(x,y,f(z,x,f(x,u,w))) = f(z,x,f(x,u,f(x,y,w))). [para(18(a,1),5(a,2)),rewrite([6(3),5(5,R),6(5)]),flip(a)]. 41 f(x,y,f(y,z,f(y,u,w))) = f(y,z,f(y,u,f(x,y,w))). [para(18(a,2),5(a,2)),rewrite([6(3),5(4,R),6(4)])]. 52 f(x,y,f(z,u,f(x,z,f(z,w,v5)))) = f(x,z,f(x,y,f(z,w,f(z,u,v5)))). [para(18(a,1),16(a,1,3)),rewrite([5(2,R),6(2),5(8,R),6(8)])]. 54 f(x,y,f(x,z,f(u,w,f(x,u,v5)))) = f(x,u,f(x,y,f(x,z,f(u,w,v5)))). [para(16(a,2),18(a,1,3,3))]. 57 f(x,f(x,y,z),f(x,u,w)) = f(x,y,f(x,u,f(x,w,z))). [para(18(a,1),17(a,1)),flip(a)]. 61 f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,w,f(x,y,z))). [para(17(a,1),18(a,2,3))]. 70 f(x,y,f(z,u,f(y,z,w))) = f(y,z,f(x,y,f(z,u,w))). [para(8(a,1),24(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])]. 71 f(x,y,f(z,u,f(z,x,w))) = f(z,x,f(x,y,f(z,u,w))). [para(8(a,1),24(a,2,3)),rewrite([5(2,R),6(2),5(6,R),6(6)]),flip(a)]. 73 f(x,y,f(z,x,f(x,y,u))) = f(z,x,f(x,y,u)). [para(19(a,1),24(a,1,3)),rewrite([5(1),5(3),5(5,R),6(5)]),flip(a)]. 74 f(x,y,f(z,u,f(y,u,w))) = f(y,u,f(x,y,f(z,u,w))). [para(16(a,1),24(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])]. 75 f(x,f(y,z,u),f(x,w,z)) = f(x,w,f(y,z,f(x,z,u))). [para(24(a,1),17(a,1,3)),flip(a)]. 87 f(x,y,f(y,z,f(y,u,w))) = f(y,z,f(y,w,f(x,y,u))). [para(30(a,2),24(a,2,3)),rewrite([5(2,R),6(2),5(6,R),6(6)])]. 95 f(x,y,f(x,z,f(y,u,f(x,y,w)))) = f(x,z,f(y,u,f(x,y,w))). [para(21(a,1),16(a,1,3)),rewrite([5(1),5(4),5(7,R),6(7)]),flip(a)]. 103 f(x,y,f(y,z,f(x,u,f(x,y,w)))) = f(y,z,f(x,u,f(x,y,w))). [para(21(a,1),24(a,2,3)),rewrite([6(1),5(3,R),6(3),6(5),5(7,R),6(7)])]. 105 f(x,y,f(z,u,f(x,u,w))) = f(x,y,f(x,u,f(z,u,w))). [para(24(a,1),21(a,2,3)),rewrite([21(5)]),flip(a)]. 111 f(x,y,f(z,u,f(y,z,w))) = f(x,y,f(y,z,f(z,u,w))). [para(16(a,2),28(a,2,3)),rewrite([28(4)]),flip(a)]. 113 f(x,y,f(y,z,f(y,u,w))) = f(x,y,f(y,w,f(y,z,u))). [para(17(a,1),28(a,2,3)),rewrite([28(4)])]. 122 f(x,y,f(z,y,f(x,y,u))) = f(z,y,f(x,y,u)). [para(73(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])]. 125 f(x,y,f(z,u,f(z,x,w))) = f(x,y,f(z,x,f(z,u,w))). [para(8(a,1),122(a,1,3,3)),rewrite([5(3,R),6(3),103(4),5(6,R),6(6)])]. 132 f(x,y,f(z,u,f(x,z,u))) = f(x,y,f(x,z,u)). [para(15(a,1),25(a,1,3)),rewrite([6(4),95(6)]),flip(a)]. 168 f(x,f(y,z,u),f(y,z,f(y,u,x))) = f(y,x,f(y,z,u)). [para(27(a,1),5(a,2)),rewrite([5(2),5(2),5(4),5(6,R),6(6)])]. 187 f(x,f(y,z,f(z,u,w)),f(z,u,f(x,u,f(y,z,w)))) = f(x,u,f(z,u,f(y,z,w))). [para(24(a,1),27(a,1,2)),rewrite([5(1,R),6(1),5(5,R),6(5),5(8,R),6(8)])]. 200 f(x,f(y,z,f(u,w,f(x,u,v5))),f(y,z,f(x,u,f(x,y,f(u,w,v5))))) = f(x,y,f(y,z,f(u,w,f(x,u,v5)))). [para(25(a,1),27(a,1,3,3))]. 205 f(x,y,f(z,x,y)) = f(z,x,y). [para(132(a,1),15(a,1)),rewrite([6(4),132(4),15(3)]),flip(a)]. 220 f(x,y,f(z,u,f(u,y,w))) = f(u,y,f(x,y,f(z,u,w))). [para(29(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5,R),6(5),5(6,R),6(6)])]. 262 f(x,y,f(z,u,f(u,y,w))) = f(x,y,f(u,y,f(z,u,w))). [para(29(a,1),205(a,1,3)),rewrite([5(1,R),6(1),5(4,R),6(4),5(5,R),6(5),187(6),5(4,R),6(4),5(6,R),6(6)]),flip(a)]. 318 f(x,f(y,z,u),f(y,x,w)) = f(x,w,f(y,z,f(y,u,x))). [para(38(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4)])]. 319 f(x,f(y,z,u),f(w,y,x)) = f(w,x,f(y,z,f(y,x,u))). [para(38(a,2),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5),5(5)]),flip(a)]. 321 f(x,f(y,z,u),f(x,u,w)) = f(x,w,f(y,u,f(x,z,u))). [para(5(a,2),38(a,1,2)),rewrite([6(2),6(4),5(5,R),6(5)])]. 331 f(x,y,f(z,f(x,y,u),f(x,w,f(x,y,u)))) = f(x,f(x,y,u),f(z,w,f(x,y,u))). [para(20(a,1),38(a,1,3)),rewrite([5(2),5(2),6(4),6(7),5(8,R),6(8)]),flip(a)]. 360 f(x,f(y,z,u),f(y,z,x)) = f(y,z,f(z,x,f(y,x,u))). [para(38(a,2),24(a,2)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5),6(5)]),flip(a)]. 385 f(x,y,f(z,f(x,y,u),f(x,y,z))) = f(y,z,f(x,y,f(x,z,u))). [para(38(a,2),122(a,1,3)),rewrite([5(2),6(2),5(5,R),6(5),5(7,R),6(7)])]. 392 f(x,f(y,z,u),f(x,y,w)) = f(x,y,f(x,w,f(y,z,u))). [para(38(a,2),25(a,1)),rewrite([6(2)])]. 474 f(x,y,f(x,z,f(u,x,y))) = f(u,x,f(x,z,y)). [para(19(a,1),41(a,1,3)),flip(a)]. 628 f(x,f(y,x,z),f(x,u,z)) = f(y,x,f(x,u,z)). [para(474(a,1),17(a,1)),rewrite([6(4)]),flip(a)]. 630 f(x,y,f(z,u,f(z,x,w))) = f(x,y,f(z,w,f(z,x,u))). [para(474(a,1),24(a,2,3)),rewrite([5(1),5(1),5(3,R),6(3),103(4),6(4),5(5,R),6(5),5(6,R),6(6)])]. 654 f(x,f(y,x,z),f(x,z,u)) = f(y,x,f(x,z,u)). [para(628(a,1),5(a,2)),rewrite([6(2),5(3),6(4)])]. 695 f(x,f(x,y,z),f(u,x,y)) = f(u,x,f(x,y,z)). [para(654(a,1),6(a,1)),flip(a)]. 696 f(x,f(x,y,z),f(u,w,f(x,y,z))) = f(x,z,f(x,y,f(u,w,f(x,y,z)))). [para(654(a,1),25(a,2)),rewrite([5(1),5(1),5(2),5(2),6(3),5(4,R),6(4),331(5),5(5),5(5),5(6),5(6),5(8,R),6(8)])]. 803 f(x,y,f(x,z,f(z,y,u))) = f(x,z,y). [para(695(a,1),40(a,1,3)),rewrite([5(4,R),15(4),5(3,R),15(3),5(5),6(5),5(6,R),6(6),696(6),28(5),6(3),57(6),6(4),20(5),22(5)]),flip(a)]. 812 f(x,y,f(y,z,f(x,z,u))) = f(x,y,z). [para(803(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(4)])]. 813 f(x,y,f(x,z,f(y,z,u))) = f(x,y,z). [para(5(a,1),803(a,1,3,3)),rewrite([5(1),6(1),6(4)])]. 814 f(x,y,f(x,z,f(x,u,f(u,y,w)))) = f(x,z,f(x,u,y)). [para(803(a,1),8(a,1,3)),flip(a)]. 816 f(x,y,f(x,z,f(z,u,f(y,z,w)))) = f(x,y,z). [para(8(a,1),803(a,1,3,3)),rewrite([5(1,R),6(1),6(5)])]. 820 f(x,y,f(x,f(y,z,u),f(y,w,f(y,z,u)))) = f(y,z,f(x,y,u)). [para(16(a,2),803(a,2)),rewrite([6(3),392(5),6(4)])]. 826 f(x,f(y,z,u),f(x,z,f(z,w,f(y,z,u)))) = f(y,z,f(x,z,u)). [para(24(a,1),803(a,2)),rewrite([6(3)])]. 827 f(x,y,f(z,u,f(x,y,z))) = f(x,y,z). [para(30(a,2),803(a,1,3)),rewrite([6(1),6(4)])]. 828 f(x,y,f(z,x,u)) = f(x,u,f(z,x,y)). [para(30(a,2),803(a,2)),rewrite([6(3),392(5),6(4),820(5)])]. 847 f(x,f(y,z,u),f(x,w,f(x,y,z))) = f(x,w,f(x,y,z)). [para(803(a,1),33(a,1,3)),rewrite([6(4)]),flip(a)]. 866 f(x,y,f(z,y,f(z,x,u))) = f(z,x,y). [back_rewrite(360),rewrite([5(2),392(3),813(3),5(2,R),6(2),5(3,R),6(3)]),flip(a)]. 871 f(x,y,f(z,x,f(z,y,u))) = f(z,x,y). [back_rewrite(385),rewrite([827(4)]),flip(a)]. 874 f(x,y,f(z,u,x)) = f(z,x,f(u,x,y)). [para(828(a,1),5(a,2)),rewrite([6(2),5(3)]),flip(a)]. 897 f(x,y,f(z,u,y)) = f(z,y,f(x,u,y)). [para(874(a,1),5(a,2)),rewrite([6(2),5(3)])]. 922 f(x,f(y,z,u),f(y,z,x)) = f(y,z,x). [para(874(a,2),38(a,2)),rewrite([6(2),392(3),813(3)]),flip(a)]. 933 f(x,y,f(z,u,x)) = f(u,x,f(z,x,y)). [para(874(a,2),803(a,2)),rewrite([6(3),826(5)]),flip(a)]. 1030 f(x,y,f(z,u,f(x,u,y))) = f(x,u,y). [para(20(a,1),897(a,1,3)),rewrite([15(3),696(5),122(4)]),flip(a)]. 1036 f(x,f(y,z,u),f(y,w,f(y,z,u))) = f(w,f(y,z,u),f(y,u,f(x,y,z))). [para(30(a,2),897(a,2,3)),rewrite([5(3,R),6(3)])]. 1050 f(x,y,f(x,f(x,y,z),f(u,y,z))) = f(x,y,z). [para(897(a,1),29(a,1)),rewrite([20(3),15(3)]),flip(a)]. 1057 f(x,f(y,z,u),f(y,x,z)) = f(y,x,z). [para(38(a,2),897(a,2)),rewrite([5(1,R),6(1),5(2,R),6(2),696(4),28(3),6(1),803(3),6(2),5(3,R),6(3),5(4),20(4)]),flip(a)]. 1063 f(x,f(y,z,u),f(x,u,f(u,w,f(y,z,u)))) = f(y,u,f(x,z,u)). [para(897(a,1),803(a,2)),rewrite([6(3)])]. 1071 f(x,f(y,z,u),f(x,z,u)) = f(x,z,u). [para(5(a,1),922(a,1,2)),rewrite([5(2),5(4)])]. 1072 f(x,y,f(x,z,f(y,u,z))) = f(x,y,z). [para(5(a,2),922(a,1,2)),rewrite([5(2),6(2),392(3),5(4),6(4)])]. 1073 f(x,f(y,z,x),f(y,z,u)) = f(y,z,x). [para(922(a,1),6(a,1)),flip(a)]. 1079 f(x,f(y,z,f(z,u,w)),f(x,z,u)) = f(x,z,u). [para(16(a,1),922(a,1,2)),rewrite([5(3),5(5)])]. 1082 f(x,y,f(x,z,f(y,u,f(y,w,z)))) = f(x,y,z). [para(17(a,2),922(a,1,2)),rewrite([5(3),392(4),5(5)])]. 1088 f(x,f(y,z,f(z,u,w)),f(x,z,w)) = f(x,z,w). [para(30(a,1),922(a,1,2)),rewrite([5(3),5(5)])]. 1101 f(f(x,y,z),f(y,z,u),f(x,y,z)) = f(x,y,z). [para(205(a,1),922(a,1,3)),rewrite([205(6)])]. 1136 f(x,f(y,z,u),f(x,w,f(y,z,w))) = f(x,w,f(y,z,u)). [para(922(a,1),803(a,1,3,3))]. 1140 f(f(x,y,z),f(x,y,u),f(u,w,f(x,y,z))) = f(w,f(x,y,u),f(x,y,z)). [para(922(a,1),828(a,2,3)),rewrite([6(4),5(8,R)])]. 1142 f(x,f(y,z,x),f(u,f(y,z,w),f(y,z,x))) = f(y,z,x). [para(922(a,1),874(a,1,3)),rewrite([5(3,R),15(3),5(5)]),flip(a)]. 1148 f(x,f(y,z,u),f(x,u,f(y,z,w))) = f(x,u,f(y,z,w)). [para(922(a,1),922(a,1,2)),rewrite([5(3),5(6)])]. 1149 f(x,y,f(z,u,y)) = f(u,y,f(x,z,y)). [para(933(a,1),5(a,2)),rewrite([6(2),5(3)])]. 1150 f(x,f(y,z,x),f(y,u,f(y,z,x))) = f(y,z,x). [para(19(a,1),933(a,1,3)),rewrite([5(3,R),15(3),6(4)]),flip(a)]. 1176 f(x,f(y,z,u),f(x,u,w)) = f(x,w,f(z,u,f(x,y,u))). [para(933(a,1),828(a,2,3)),rewrite([5(2,R),6(2),5(4)])]. 1181 f(x,f(y,x,z),f(y,z,u)) = f(y,x,z). [para(1057(a,1),6(a,1)),flip(a)]. 1197 f(x,f(y,z,u),f(w,x,y)) = f(w,x,f(y,z,f(x,y,u))). [para(38(a,2),1057(a,2)),rewrite([6(3),5(6,R),6(6),392(7),1072(7),5(5,R),6(5)]),flip(a)]. 1253 f(x,f(y,z,u),f(z,u,x)) = f(z,u,x). [para(1071(a,1),5(a,2)),rewrite([5(2),5(2),5(3),5(4),5(4)])]. 1254 f(x,f(y,z,u),f(x,w,f(x,z,u))) = f(x,w,f(x,z,u)). [para(1071(a,1),8(a,2,3))]. 1286 f(x,f(y,z,u),f(x,u,f(x,z,w))) = f(x,w,f(x,z,u)). [para(1071(a,1),32(a,2,3)),rewrite([6(2)])]. 1321 f(x,f(y,z,f(z,u,w)),f(x,f(y,z,u),f(z,u,w))) = f(x,f(y,z,u),f(z,u,w)). [para(654(a,1),1071(a,1,2))]. 1329 f(x,f(y,z,u),f(x,w,f(z,u,w))) = f(x,w,f(y,z,u)). [para(1071(a,1),803(a,1,3,3)),rewrite([5(2),5(2)])]. 1332 f(f(x,y,z),f(y,z,u),f(u,w,f(x,y,z))) = f(w,f(y,z,u),f(x,y,z)). [para(1071(a,1),828(a,2,3)),rewrite([5(2),5(2),6(4),5(7),5(7),5(8,R)])]. 1341 f(x,y,f(x,f(z,u,w),f(y,z,u))) = f(x,y,f(z,u,w)). [para(1071(a,1),922(a,1,2)),rewrite([5(2),5(2),5(3),392(4),5(5),5(5),5(6)])]. 1344 f(f(x,y,z),f(y,z,u),f(u,w,f(y,z,u))) = f(y,z,u). [para(1071(a,1),1057(a,1,3)),rewrite([5(2),5(2),6(3),5(4),5(4),6(5),5(7),5(7),1253(8)])]. 1349 f(x,f(x,y,z),f(y,u,f(y,z,w))) = f(x,y,z). [para(8(a,1),1073(a,1,3)),rewrite([5(1),5(5)])]. 1404 f(x,y,f(x,f(z,u,w),f(y,u,w))) = f(x,y,f(z,u,w)). [para(1071(a,1),1073(a,1,3)),rewrite([5(2),6(4),392(4),5(6)])]. 1469 f(x,y,f(z,u,y)) = f(u,y,f(z,x,y)). [para(1149(a,1),803(a,2)),rewrite([6(3),1063(5)])]. 1605 f(f(x,y,z),f(x,z,u),f(y,w,f(x,z,u))) = f(w,f(x,z,u),f(x,y,z)). [para(1181(a,1),1469(a,2,3))]. 1618 f(x,y,f(y,f(z,u,f(x,u,w)),f(x,v5,f(z,u,f(x,u,w))))) = f(x,u,f(x,y,f(z,u,w))). [para(29(a,1),812(a,2)),rewrite([6(5)])]. 1630 f(x,y,f(y,f(z,u,w),f(x,z,u))) = f(x,y,f(z,u,w)). [para(922(a,1),812(a,1,3,3)),rewrite([5(2)])]. 1856 f(x,y,f(z,x,f(y,u,f(z,y,w)))) = f(z,x,y). [para(52(a,1),874(a,2)),rewrite([5(3),392(4),813(4),5(2,R),6(2),5(4,R),6(4)]),flip(a)]. 1905 f(x,y,f(z,u,f(x,u,f(y,u,w)))) = f(x,y,u). [para(41(a,2),871(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5),5(5)])]. 1906 f(x,f(y,z,u),f(y,z,f(z,u,x))) = f(z,x,f(y,z,u)). [para(628(a,1),871(a,1,3)),rewrite([6(2),5(4,R),6(4),6(6)])]. 1982 f(x,y,f(z,u,f(u,x,y))) = f(u,x,y). [para(1030(a,1),922(a,2)),rewrite([5(1,R),6(1),5(4,R),6(4),922(7),5(4,R),6(4)])]. 2276 f(x,f(y,z,f(x,y,u)),f(x,w,v5)) = f(x,y,f(x,w,f(x,v5,f(y,z,u)))). [para(54(a,1),17(a,1)),flip(a)]. 2885 f(x,f(y,z,f(u,z,w)),f(x,u,z)) = f(x,u,z). [para(1079(a,1),21(a,2)),rewrite([5(1,R),6(1),6(3),22(5),6(5)])]. 2997 f(x,f(y,z,f(x,z,u)),f(x,w,v5)) = f(x,z,f(x,w,f(x,v5,f(y,z,u)))). [para(24(a,1),57(a,1,2))]. 3270 f(x,f(y,z,x),f(u,y,z)) = f(y,z,x). [para(1050(a,1),1150(a,1,3)),rewrite([5(2),5(2),5(5),5(5),6(6),1332(6),4(4),5(2),5(2)]),flip(a)]. 3475 f(x,f(y,x,z),f(y,x,f(y,z,u))) = f(y,x,z). [para(1349(a,1),122(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),15(3),5(2,R),6(2),5(3,R),6(3),57(5),6(3),20(4)]),flip(a)]. 3946 f(x,f(y,x,z),f(u,y,f(y,x,w))) = f(x,z,f(u,y,f(y,x,w))). [para(2885(a,1),871(a,1,3)),rewrite([5(1,R),6(1),5(3),6(3),5(4,R),5(5,R),6(5),5(7)])]. 4005 f(x,y,f(x,f(y,z,u),f(w,z,u))) = f(x,y,f(w,z,u)). [para(1071(a,1),3475(a,1,3,3)),rewrite([5(2,R),6(2),5(4,R),6(4),57(5),20(5),5(6,R),6(6)])]. 4085 f(x,y,f(z,u,f(z,w,f(x,y,z)))) = f(x,y,z). [para(61(a,1),866(a,1,3)),rewrite([5(1),6(1),5(5),5(5)])]. 4302 f(x,y,f(x,f(y,z,u),f(w,f(y,z,u),f(y,v5,f(y,z,u))))) = f(y,z,f(x,y,u)). [para(16(a,2),816(a,2)),rewrite([6(4),5(5,R),6(5)])]. 4305 f(x,y,f(z,f(y,z,u),f(x,z,w))) = f(x,y,z). [para(30(a,2),816(a,1,3))]. 4361 f(x,f(y,z,f(z,u,w)),f(x,f(x,z,w),f(v5,f(x,z,w),f(v6,f(y,z,f(z,u,w)),f(x,z,w))))) = f(x,z,w). [para(1088(a,1),816(a,2)),rewrite([5(8),5(9,R),6(9)])]. 4461 f(x,y,f(z,f(x,z,u),f(z,y,w))) = f(x,z,y). [para(4305(a,1),5(a,2)),rewrite([5(2,R),6(2),6(4),5(5),5(5)])]. 4572 f(x,f(y,z,u),f(z,f(x,z,w),f(z,v5,f(y,z,u)))) = f(y,z,f(x,z,u)). [para(24(a,1),4461(a,2)),rewrite([6(4)])]. 5467 f(x,f(y,z,f(u,y,w)),f(u,x,y)) = f(u,x,y). [para(1856(a,1),828(a,1)),flip(a)]. 5502 f(x,y,f(z,x,f(x,u,w))) = f(x,u,f(x,w,f(z,x,y))). [para(61(a,1),1856(a,2)),rewrite([6(7),5(8,R),6(8),5(9,R),6(9),392(10),6(9),4302(10),5(4,R),6(4)])]. 5647 f(x,y,f(x,z,f(u,y,f(z,y,w)))) = f(x,z,y). [para(1905(a,1),812(a,2)),rewrite([6(7),1618(9)])]. 6261 f(x,y,f(z,u,f(z,w,f(z,x,y)))) = f(z,x,y). [para(4085(a,1),922(a,2)),rewrite([5(1),5(5),922(9),5(5)])]. 6720 f(x,f(y,x,z),f(y,x,u)) = f(y,x,f(x,u,z)). [para(70(a,1),17(a,1)),rewrite([5(2,R),6(2),20(3),5(4,R),6(4)]),flip(a)]. 7772 f(x,f(y,z,x),f(z,x,u)) = f(y,x,f(z,x,u)). [para(922(a,1),74(a,2,3)),rewrite([5(3),6(3),122(4),19(4),5(4),5(5,R)]),flip(a)]. 7788 f(x,f(y,z,x),f(u,z,x)) = f(y,x,f(u,z,x)). [para(1253(a,1),74(a,2,3)),rewrite([5(3),6(3),1030(5),5(4),5(5,R)]),flip(a)]. 8028 f(f(x,y,z),f(x,u,f(x,y,z)),f(x,z,f(x,y,w))) = f(u,f(x,y,z),f(x,w,f(x,y,z))). [para(30(a,2),7788(a,1,3)),rewrite([5(3,R),6(3),5(4),5(4),5(9,R),6(9)])]. 8369 f(x,f(y,z,u),f(x,f(x,z,w),f(v5,f(x,z,w),f(v6,f(y,z,u),f(x,z,w))))) = f(x,w,f(y,z,f(x,z,u))). [para(75(a,1),816(a,2)),rewrite([6(2),6(3),6(5),5(6),5(7,R),6(7)])]. 8635 f(x,y,f(z,u,f(x,u,f(u,w,y)))) = f(x,u,y). [back_rewrite(4361),rewrite([8369(11)])]. 8713 f(x,y,f(y,z,f(u,x,y))) = f(y,z,f(u,x,y)). [para(1253(a,1),5647(a,1,3)),rewrite([5(2),5(2),5(4),5(4),5(6,R),6(6),205(6),5(5),5(5),5(7),6(7),19(7)])]. 9281 f(f(x,y,z),f(x,z,u),f(y,w,f(y,v5,f(x,y,z)))) = f(x,y,z). [para(1181(a,1),6261(a,1,3,3,3)),rewrite([1181(9)])]. 9577 f(x,y,f(z,u,f(u,x,f(u,w,y)))) = f(u,x,y). [para(8635(a,1),922(a,2)),rewrite([5(2,R),6(2),5(6,R),6(6),922(9),5(5,R),6(5)])]. 10036 f(f(x,y,z),f(y,z,u),f(w,f(y,z,u),f(v5,f(y,z,u),f(x,y,z)))) = f(w,f(y,z,u),f(v5,f(x,y,z),f(y,z,u))). [para(1101(a,1),87(a,2,3,3)),rewrite([5(6),5(7,R),6(7),5(12,R),5(13,R),6(13)])]. 11098 f(x,y,f(z,u,f(x,w,z))) = f(x,y,f(w,z,f(x,z,u))). [para(874(a,2),105(a,2,3)),flip(a)]. 12311 f(x,y,f(y,z,f(u,x,z))) = f(x,y,z). [para(125(a,1),1469(a,2)),rewrite([20(3),15(3),5(3,R),6(3),6720(5),6(3)]),flip(a)]. 12402 f(x,y,f(x,z,f(u,z,y))) = f(x,z,y). [para(12311(a,1),474(a,2)),rewrite([5(3,R),6(3),21(5),5(4,R),6(4)])]. 12982 f(x,f(y,z,u),f(y,u,x)) = f(y,u,x). [para(1072(a,1),168(a,1,3)),rewrite([5(2),5(2),5(3),5(3),15(4),5(3),5(3)]),flip(a)]. 12992 f(x,f(y,z,u),f(x,w,f(z,u,x))) = f(x,w,f(z,u,x)). [para(3270(a,1),168(a,1,3,3)),rewrite([15(6)]),flip(a)]. 13008 f(x,f(y,z,f(y,u,w)),f(y,w,x)) = f(y,w,x). [para(1082(a,1),168(a,1,3)),rewrite([5(3),5(3),5(4),5(4),15(5),5(4),5(4)]),flip(a)]. 13139 f(x,f(y,z,x),f(z,u,x)) = f(y,x,f(z,u,x)). [para(12982(a,1),74(a,2,3)),rewrite([5(3),6(3),1030(5),5(4),5(5,R)]),flip(a)]. 13180 f(x,f(y,x,z),f(y,u,x)) = f(x,z,f(y,u,x)). [para(13139(a,1),922(a,2)),rewrite([5(2),5(2),6(3),5(4),5(4),12982(7),5(5,R),6(5)])]. 13417 f(f(x,y,f(x,z,u)),f(x,u,w),f(w,f(x,u,w),f(w,v5,f(x,y,f(x,z,u))))) = f(x,u,w). [para(13008(a,1),866(a,2)),rewrite([6(7)])]. 14376 f(x,y,f(z,u,f(y,w,z))) = f(x,y,f(w,z,f(y,z,u))). [para(828(a,1),262(a,2,3)),rewrite([5(1,R),6(1),5(4)]),flip(a)]. 14673 f(f(x,y,z),f(y,u,w),f(x,y,z)) = f(x,y,z). [para(1181(a,1),318(a,1,3)),rewrite([9281(10)])]. 14946 f(x,f(y,z,u),f(y,u,f(y,z,f(w,x,f(y,z,u))))) = f(w,f(y,z,u),f(y,x,f(y,z,u))). [para(14673(a,1),40(a,1,3)),rewrite([5(3),5(3),5(4,R),6(4),5(6),5(6),5(10),5(10),5(11,R),6(11),696(11),5(12,R),6(12),8028(12),6(9),696(9)]),flip(a)]. 14966 f(x,f(y,z,u),f(y,u,f(y,z,f(x,w,f(y,z,u))))) = f(y,u,f(y,z,f(x,w,f(y,z,u)))). [para(14673(a,1),816(a,1,3)),rewrite([6(3),5(4,R),6(4),696(4),6(7),5(8,R),6(8),696(8),5(9,R),15(9),6(7),5(8,R),6(8),696(8),5(10),5(10)]),flip(a)]. 15096 f(x,f(y,x,z),f(z,u,w)) = f(y,x,f(z,u,f(x,z,w))). [para(319(a,1),6(a,1)),rewrite([5(1,R),6(1),6(4)]),flip(a)]. 15120 f(f(x,y,z),f(u,w,f(x,y,z)),f(x,y,f(x,z,f(u,w,f(x,y,z))))) = f(x,z,f(x,y,f(u,w,f(x,y,z)))). [para(319(a,1),40(a,2)),rewrite([5(3),5(3),5(6),5(6),5(7,R),7788(7),696(5),5(6,R),6(6),14966(6),5(7),5(7),5(9),5(9),6(10)]),flip(a)]. 15153 f(f(x,y,z),f(x,u,w),f(w,f(x,u,w),f(w,v5,f(x,y,z)))) = f(u,w,f(x,y,f(x,z,w))). [para(319(a,1),866(a,2)),rewrite([5(2,R),6(2),5(3,R),6(3),6(5),6(8)])]. 15161 f(f(x,y,z),f(u,w,v5),f(x,y,z)) = f(x,y,z). [para(319(a,1),54(a,2,3)),rewrite([5(5),5(5),19(5),20(5),5(5,R),15(5),6(9),4(11),5(7,R),15(7)])]. 15213 f(x,f(y,z,u),f(z,x,u)) = f(z,x,u). [para(319(a,2),8713(a,2)),rewrite([5(4,R),6(4),5(5,R),6(5),3946(5),1982(4),15(3),5(2,R),6(2),5(4),5(4),20(4)]),flip(a)]. 15245 f(x,f(y,z,u),f(w,f(y,z,u),f(y,x,f(y,z,u)))) = f(y,u,f(y,z,f(x,w,f(y,z,u)))). [para(319(a,1),113(a,1)),rewrite([5(3),5(3),5(5),5(5),6(6),15120(8),5(6),5(6),5(10),5(10),5(11,R),6(11),5(12,R),6(12),7772(12)]),flip(a)]. 15288 f(x,y,f(z,u,f(z,y,f(z,w,x)))) = f(z,x,y). [back_rewrite(13417),rewrite([15153(9),6(2)])]. 15375 f(x,f(y,z,u),f(w,f(y,z,u),f(x,v5,f(y,z,u)))) = f(w,f(y,z,u),f(x,v5,f(y,z,u))). [para(15161(a,1),816(a,1,3)),rewrite([6(3),5(4,R),6(4),6(7),5(8,R),6(8),5(9,R),15(9),6(7),5(8,R),6(8),5(10),5(10)]),flip(a)]. 15402 f(f(x,y,z),f(u,w,f(u,v5,f(x,y,z))),f(u,f(u,w,v5),f(x,y,z))) = f(u,w,f(u,v5,f(x,y,z))). [para(15161(a,1),111(a,1)),rewrite([5(2),5(2),5(5),5(5),5(10,R),5(11,R),6(11)]),flip(a)]. 15403 f(x,f(x,y,z),f(u,w,v5)) = f(x,y,f(x,z,f(u,w,v5))). [para(15161(a,1),111(a,2)),rewrite([5(3,R),5(6),5(6),5(8),5(8),15402(8),5(6,R)]),flip(a)]. 15417 f(x,f(y,z,u),f(w,y,f(y,z,u))) = f(y,u,f(y,z,f(w,x,f(y,z,u)))). [back_rewrite(15245),rewrite([5(4,R),6(4),15375(6)])]. 15771 f(x,f(y,z,u),f(x,z,u)) = f(x,z,u). [para(15288(a,1),922(a,1,2)),rewrite([5(2),5(4)])]. 15796 f(x,f(y,z,u),f(x,y,u)) = f(x,y,u). [para(15288(a,1),2885(a,1,2))]. 15821 f(x,f(y,z,u),f(x,y,z)) = f(x,y,z). [para(15288(a,1),5467(a,1,2)),rewrite([5(2,R),6(2),5(4,R),6(4)])]. 15868 f(x,f(y,z,f(u,x,y)),f(w,u,x)) = f(x,y,f(w,u,x)). [para(12402(a,1),15288(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. 15909 f(x,f(y,z,u),f(x,y,f(z,u,w))) = f(x,y,f(z,u,w)). [para(15771(a,1),922(a,1,2)),rewrite([5(2),5(2),5(3),5(5),5(5),5(6)])]. 15921 f(x,y,f(x,f(z,u,y),f(w,z,u))) = f(x,y,f(w,z,u)). [para(15771(a,1),866(a,1,3,3)),rewrite([5(2),5(2),5(3,R),6(3),5(4,R),15403(4),5(6)])]. 15972 f(x,f(y,z,f(u,x,z)),f(w,u,x)) = f(x,z,f(w,u,x)). [para(15771(a,1),9577(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. 16471 f(x,y,f(z,y,f(x,u,y))) = f(x,y,f(z,u,y)). [para(15(a,1),321(a,1,3)),rewrite([6(2)]),flip(a)]. 16711 f(x,y,f(z,u,f(y,w,u))) = f(y,u,f(x,y,f(z,w,u))). [para(321(a,2),74(a,1,3)),rewrite([15(2),6(2),19(5)])]. 18363 f(x,y,f(z,u,f(y,u,f(x,z,u)))) = f(x,y,u). [para(630(a,1),9577(a,1,3)),rewrite([5(1),6(1),5(2,R),6(2),5(5),5(5)])]. 18491 f(x,y,f(z,y,f(z,u,x))) = f(z,x,y). [para(18363(a,1),4461(a,2)),rewrite([5(2,R),6(2),8713(3),5(5,R),6(5),8713(6),6(6),4572(8),6(4)])]. 18837 f(x,f(y,z,u),f(w,x,f(w,y,z))) = f(w,x,f(y,z,u)). [para(847(a,1),220(a,2,3)),rewrite([1630(5),19(4)]),flip(a)]. 19724 f(x,y,f(x,z,f(x,f(y,u,w),f(u,w,v5)))) = f(x,z,f(x,y,f(u,w,v5))). [para(1136(a,1),32(a,1,3)),rewrite([5(4)]),flip(a)]. 19762 f(x,f(y,z,u),f(z,w,f(x,y,w))) = f(x,w,f(y,z,u)). [para(1149(a,1),1136(a,1,3))]. 20436 f(x,y,f(f(z,u,w),f(u,w,v5),f(x,u,f(u,w,v5)))) = f(x,f(z,u,f(u,w,v5)),f(x,y,f(u,w,v5))). [para(654(a,1),1176(a,1,2)),rewrite([6(4)]),flip(a)]. 20765 f(x,f(y,z,u),f(x,y,f(x,w,v5))) = f(x,y,f(x,w,f(x,v5,f(y,z,u)))). [para(1197(a,2),13180(a,1,2)),rewrite([5(2),5(2),5(4),15403(5),15403(4),20(3),5(7),2276(8)])]. 20959 f(x,f(y,z,u),f(w,x,f(x,z,u))) = f(w,x,f(x,z,u)). [para(1254(a,1),74(a,1,3)),rewrite([15771(3),15771(6)]),flip(a)]. 21385 f(x,f(y,z,u),f(z,w,f(x,u,w))) = f(x,w,f(y,z,u)). [para(897(a,1),1329(a,1,3))]. 21496 f(x,y,f(x,f(y,z,u),f(z,w,f(x,y,u)))) = f(x,y,f(z,w,f(x,y,u))). [para(25(a,1),1341(a,1,3)),rewrite([6(2),6(4),20(6),6(7)])]. 21883 f(x,f(y,z,x),f(u,f(w,y,z),f(y,z,x))) = f(y,z,x). [para(1344(a,1),16471(a,2)),rewrite([5(6,R),10036(8)])]. 22316 f(x,f(y,z,u),f(z,u,f(x,w,f(y,z,u)))) = f(z,u,f(x,w,f(y,z,u))). [para(1404(a,1),1142(a,1,3)),rewrite([6(2),5(3),5(3),6(6),5(7),5(7),6(10),6(12),19(12),5(11),21883(11),6(6),5(7),5(7)]),flip(a)]. 23721 f(x,y,f(x,z,f(u,w,y))) = f(x,z,f(x,y,f(z,u,w))). [para(4005(a,1),54(a,2,3)),rewrite([6(2),5(3,R),6(3),21385(4),5(4),5(4)]),flip(a)]. 23961 f(x,y,f(z,x,f(u,x,y))) = f(z,x,f(u,x,y)). [para(5502(a,2),1469(a,2)),rewrite([4(3),6(2),5(4),122(5)]),flip(a)]. 24846 f(x,f(y,z,f(x,u,y)),f(x,w,v5)) = f(x,y,f(x,w,f(x,v5,f(u,y,z)))). [para(11098(a,1),1286(a,1,3,3)),rewrite([1286(6),2997(4)]),flip(a)]. 25097 f(x,y,f(x,z,f(u,w,f(x,z,y)))) = f(x,y,f(z,u,f(x,z,w))). [para(15096(a,1),1329(a,2)),rewrite([5(2),5(2),5(3),5(3),15403(5),20765(6),6(4),19724(6),5(7,R),6(7)])]. 25130 f(x,f(y,z,u),f(y,w,f(y,z,u))) = f(y,u,f(x,z,f(y,z,w))). [back_rewrite(15417),rewrite([5(3,R),6(3),5(6,R),6(6),25097(8),5(6,R),6(6)])]. 25132 f(x,f(y,z,u),f(y,u,f(x,z,f(y,z,w)))) = f(y,u,f(x,z,f(y,z,w))). [back_rewrite(14966),rewrite([25097(5),5(3,R),6(3),25097(9),5(7,R),6(7)])]. 25133 f(x,f(y,z,u),f(w,y,f(y,z,u))) = f(y,u,f(w,z,f(y,z,x))). [back_rewrite(14946),rewrite([5(3,R),6(3),25097(5),5(3,R),6(3),25132(5),5(6,R),6(6)]),flip(a)]. 25262 f(x,f(y,z,u),f(y,u,f(w,y,z))) = f(y,u,f(w,z,f(y,z,x))). [back_rewrite(1036),rewrite([25130(4)]),flip(a)]. 25278 f(x,f(y,z,f(z,u,w)),f(x,v5,f(z,u,w))) = f(x,v5,f(z,w,f(x,u,f(y,z,u)))). [back_rewrite(20436),rewrite([25133(5),205(2)]),flip(a)]. 25399 f(x,f(y,z,u),f(z,w,f(x,u,f(y,z,u)))) = f(x,f(y,z,u),f(z,u,w)). [back_rewrite(1321),rewrite([25278(6)])]. 26704 f(x,f(y,z,u),f(x,z,f(x,u,w))) = f(x,w,f(x,z,u)). [para(15868(a,1),12992(a,2)),rewrite([5(2,R),6(2),5(4),24846(5),814(5),5(5)])]. 27091 f(x,f(y,z,f(z,u,x)),f(u,x,w)) = f(z,x,f(u,x,w)). [para(15972(a,1),5(a,2)),rewrite([5(1),5(3),5(3),5(4),5(5),5(5),5(6,R),6(6)])]. 27912 f(f(x,y,z),f(y,z,u),f(w,x,f(y,z,u))) = f(w,f(y,z,u),f(x,y,z)). [para(15909(a,1),16711(a,2,3)),rewrite([5(5,R),15821(5),19(5)]),flip(a)]. 28511 f(f(x,y,z),f(y,z,u),f(y,z,w)) = f(w,f(x,y,z),f(y,z,u)). [para(15771(a,1),18837(a,1,3)),rewrite([5(3),5(3)])]. 28512 f(f(x,y,z),f(x,z,u),f(x,z,w)) = f(w,f(x,y,z),f(x,z,u)). [para(15796(a,1),18837(a,1,3)),rewrite([5(3),5(3)])]. 28513 f(f(x,y,z),f(x,y,u),f(x,y,w)) = f(w,f(x,y,z),f(x,y,u)). [para(15821(a,1),18837(a,1,3)),rewrite([5(3),5(3)])]. 28531 f(f(x,y,z),f(u,x,y),f(u,x,z)) = f(x,z,f(u,x,y)). [para(1906(a,1),18837(a,2)),rewrite([5(5),5(5),922(6),6(5),28513(5)])]. 28539 f(x,f(y,z,f(x,u,w)),f(x,w,f(y,u,w))) = f(x,w,f(y,z,f(x,u,w))). [para(14376(a,1),18837(a,1,3)),rewrite([6(2),6(3),5(5,R),6(5),16471(5),5(3,R),6(3),6(7),5(8,R),6(8)])]. 28566 f(f(x,y,z),f(x,y,u),f(y,z,u)) = f(y,u,f(x,y,z)). [para(28531(a,1),5(a,2))]. 28568 f(f(x,y,z),f(x,z,u),f(y,z,u)) = f(y,z,f(x,z,u)). [para(5(a,2),28531(a,1,1)),rewrite([5(2),6(2),5(3),6(3),5(5),6(5),5(6,R),6(6)])]. 29055 f(f(x,y,z),f(u,x,z),f(u,w,f(x,y,z))) = f(w,f(u,x,z),f(x,y,z)). [para(12982(a,1),28566(a,1,2)),rewrite([6(2),5(3),5(5),5(6,R),5(7,R),6(7),15213(7),5(5),6(7)]),flip(a)]. 29200 f(f(x,y,z),f(x,u,y),f(u,y,z)) = f(u,y,f(x,y,z)). [para(28568(a,1),19(a,1,3)),rewrite([28511(5),28568(8)])]. 29568 f(x,f(y,z,u),f(z,w,f(y,x,w))) = f(y,f(z,x,w),f(x,w,f(y,z,u))). [para(29200(a,1),200(a,1,2)),rewrite([5(2,R),6(2),5(5,R),6(5),5(6),5(6),5(8,R),6(8),6(10),21496(11),5(10,R),6(10),27912(10),6(7),25278(8),25399(6),5(6,R),6(6),5(8,R),6(8),5(9),5(9),5(12,R),28566(12),25262(10),5(6)]),flip(a)]. 30122 f(x,f(y,z,u),f(y,u,f(x,z,w))) = f(y,u,f(x,z,w)). [back_rewrite(29568),rewrite([5(2,R),6(2),19762(4),5(3,R),6(3)]),flip(a)]. 30898 f(x,y,f(z,y,f(u,x,z))) = f(x,z,y). [para(20959(a,1),71(a,2)),rewrite([5(3),5(4,R),6(4),5(5,R),6(5),23961(5),5(5),5(5),5(6,R),3270(6)])]. 32772 f(x,f(y,z,u),f(x,w,y)) = f(x,f(w,z,u),f(x,w,y)). [para(23721(a,1),1286(a,1,3)),rewrite([26704(5),5(4)]),flip(a)]. 32850 f(x,f(y,z,u),f(w,x,u)) = f(x,f(w,y,z),f(w,x,u)). [para(32772(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4),5(5)]),flip(a)]. 33448 f(f(x,y,z),f(x,y,u),f(w,v5,f(x,y,u))) = f(f(x,y,z),f(w,v5,u),f(x,y,u)). [para(922(a,1),32850(a,1,3)),rewrite([6(5),5(7),5(7),922(10)])]. 33505 f(f(x,y,z),f(x,z,u),f(w,v5,f(x,z,u))) = f(f(x,y,z),f(w,v5,u),f(x,z,u)). [para(12982(a,1),32850(a,1,3)),rewrite([6(5),5(7),5(7),12982(10)])]. 33573 f(f(x,y,z),f(y,u,w),f(x,z,u)) = f(w,f(x,z,u),f(x,y,z)). [back_rewrite(1605),rewrite([33505(5),6(2)])]. 35717 f(f(x,y,z),f(u,z,w),f(x,y,u)) = f(w,f(x,y,z),f(x,y,u)). [para(1148(a,1),27091(a,1,2)),rewrite([5(4,R),922(4),6(4),1140(5),6(7),33448(8),5(5)]),flip(a)]. 36738 f(f(x,y,z),f(u,x,w),f(u,w,y)) = f(u,w,f(x,y,z)). [para(30122(a,1),18837(a,2)),rewrite([5(2,R),6(2),5(5),5(5),12982(6),6(5),28512(5),5(5,R),6(5)])]. 36780 f(x,f(y,z,u),f(y,z,w)) = f(y,z,f(w,u,x)). [para(36738(a,1),5(a,1)),rewrite([6(5),35717(6)]),flip(a)]. 36790 f(x,f(y,z,u),f(z,w,u)) = f(z,u,f(y,x,f(z,w,u))). [para(19(a,1),36738(a,1,3)),rewrite([6(2),5(3,R),6(3),5(5),6(5),29055(5),6(5)])]. 36856 f(x,f(y,z,u),f(y,w,z)) = f(y,z,f(w,u,x)). [para(36738(a,1),18491(a,2)),rewrite([5(7,R),30898(9),33573(4)])]. 36866 f(x,y,f(z,u,f(x,w,y))) = f(x,y,f(z,u,w)). [para(1341(a,1),36738(a,2)),rewrite([5(2),5(2),36780(3),5(1),6(1),4(3),5(5),5(5),15403(5),36780(4),5(2),6(2),20(2)])]. 36880 f(x,y,f(z,u,f(x,y,w))) = f(x,y,f(z,u,w)). [para(15921(a,1),36738(a,2)),rewrite([5(2),5(2),36780(3),5(1),6(1),4(3),5(5,R),15403(5),36780(4),5(2),6(2),20(2),5(4),5(4)])]. 37170 f(x,f(y,z,u),f(z,u,w)) = f(z,u,f(x,y,w)). [back_rewrite(36790),rewrite([6(2),6(4),5(5,R),6(5),36880(6)])]. 37187 f(x,f(y,z,f(x,u,w)),f(x,w,f(y,u,w))) = f(x,w,f(y,z,u)). [back_rewrite(28539),rewrite([36866(8)])]. 37194 f(x,y,f(z,u,f(w,x,y))) = f(x,y,f(z,w,u)). [back_rewrite(22316),rewrite([36866(5),37170(3)]),flip(a)]. 38298 f(x,f(y,z,f(u,w,v5)),f(u,v5,f(y,w,v5))) = f(y,f(u,w,v5),f(x,v5,z)). [para(897(a,1),36856(a,1,3)),rewrite([6(2),5(7)])]. 38353 f(x,f(y,z,u),f(y,w,u)) = f(y,u,f(x,w,z)). [back_rewrite(37187),rewrite([38298(5),6(2)])]. 38852 f(x,f(y,z,u),f(w,z,u)) = f(z,u,f(w,x,y)). [para(37170(a,1),36780(a,2)),rewrite([6(2),6(4),38353(5),5(4)])]. 38910 $F # answer(dist_both). [back_rewrite(14),rewrite([38852(13),5(9),37194(10),5(6,R),6(6),38852(25),5(21),5(21)]),xx(a),xx(b)]. ============================== end of proof ========================== ============================== PROOF ================================= % Proof 2 at 657.97 (+ 1.04) seconds: dist_short. % Length of proof is 226. % Level of proof is 31. % Maximum clause weight is 45. % Given clauses 791. 2 f(f(x,y,z),u,w) = f(x,f(y,u,w),f(z,u,w)) # label(dist_short) # label(non_clause) # label(goal). [goal]. 4 f(x,x,y) = x # label(majority). [assumption]. 5 f(x,y,z) = f(z,x,y) # label(2a). [assumption]. 6 f(x,y,z) = f(x,z,y) # label(2b). [assumption]. 7 f(f(x,y,z),y,u) = f(x,y,f(z,y,u)) # label(associativity). [assumption]. 8 f(x,y,f(x,z,u)) = f(x,z,f(x,y,u)). [copy(7),rewrite([5(2),5(2),5(3,R),6(3)]),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])]. 11 f(f(c6,c7,c8),c9,c10) != f(c6,f(c7,c9,c10),f(c8,c9,c10)) # label(dist_short) # answer(dist_short). [deny(2)]. 12 f(c6,f(c7,c9,c10),f(c8,c9,c10)) != f(c9,c10,f(c6,c7,c8)) # answer(dist_short). [copy(11),rewrite([5(7),5(7)]),flip(a)]. 15 f(x,y,y) = y. [para(5(a,1),4(a,1))]. 16 f(x,y,f(z,x,u)) = f(z,x,f(x,y,u)). [para(8(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)]),flip(a)]. 17 f(x,y,f(x,z,u)) = f(x,u,f(x,y,z)). [para(5(a,1),8(a,1,3)),rewrite([5(1,R),6(1)])]. 18 f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,y,f(x,z,w))). [para(8(a,1),8(a,1,3))]. 19 f(x,y,f(x,z,y)) = f(x,z,y). [para(15(a,1),8(a,1,3)),flip(a)]. 20 f(x,y,f(x,y,z)) = f(x,y,z). [para(15(a,1),8(a,1)),rewrite([6(3),19(3)]),flip(a)]. 21 f(x,y,f(x,z,f(x,u,y))) = f(x,z,f(x,u,y)). [para(19(a,1),8(a,1,3)),flip(a)]. 22 f(x,y,f(x,z,f(x,y,u))) = f(x,z,f(x,y,u)). [para(19(a,1),8(a,2,3)),rewrite([6(1),6(4)])]. 24 f(x,y,f(z,y,u)) = f(z,y,f(x,y,u)). [para(16(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)])]. 25 f(x,y,f(z,u,f(x,z,w))) = f(x,z,f(x,y,f(z,u,w))). [para(16(a,2),8(a,1,3))]. 27 f(x,f(y,z,u),f(y,z,f(x,y,u))) = f(x,y,f(y,z,u)). [para(16(a,2),19(a,1,3))]. 28 f(x,y,f(y,z,f(x,y,u))) = f(x,y,f(y,z,u)). [para(16(a,2),20(a,1,3))]. 29 f(x,y,f(z,u,f(x,u,w))) = f(x,u,f(x,y,f(z,u,w))). [para(16(a,1),16(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])]. 30 f(x,y,f(z,x,u)) = f(z,x,f(x,u,y)). [para(17(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)]),flip(a)]. 32 f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,y,f(x,w,z))). [para(17(a,1),8(a,2,3)),flip(a)]. 33 f(x,y,f(x,z,f(x,u,w))) = f(x,w,f(x,y,f(x,z,u))). [para(17(a,2),8(a,1,3))]. 38 f(x,f(y,z,u),f(x,w,y)) = f(x,w,f(y,z,f(x,y,u))). [para(16(a,2),17(a,1,3)),flip(a)]. 40 f(x,y,f(z,x,f(x,u,w))) = f(z,x,f(x,u,f(x,y,w))). [para(18(a,1),5(a,2)),rewrite([6(3),5(5,R),6(5)]),flip(a)]. 41 f(x,y,f(y,z,f(y,u,w))) = f(y,z,f(y,u,f(x,y,w))). [para(18(a,2),5(a,2)),rewrite([6(3),5(4,R),6(4)])]. 52 f(x,y,f(z,u,f(x,z,f(z,w,v5)))) = f(x,z,f(x,y,f(z,w,f(z,u,v5)))). [para(18(a,1),16(a,1,3)),rewrite([5(2,R),6(2),5(8,R),6(8)])]. 54 f(x,y,f(x,z,f(u,w,f(x,u,v5)))) = f(x,u,f(x,y,f(x,z,f(u,w,v5)))). [para(16(a,2),18(a,1,3,3))]. 57 f(x,f(x,y,z),f(x,u,w)) = f(x,y,f(x,u,f(x,w,z))). [para(18(a,1),17(a,1)),flip(a)]. 61 f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,w,f(x,y,z))). [para(17(a,1),18(a,2,3))]. 70 f(x,y,f(z,u,f(y,z,w))) = f(y,z,f(x,y,f(z,u,w))). [para(8(a,1),24(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])]. 71 f(x,y,f(z,u,f(z,x,w))) = f(z,x,f(x,y,f(z,u,w))). [para(8(a,1),24(a,2,3)),rewrite([5(2,R),6(2),5(6,R),6(6)]),flip(a)]. 73 f(x,y,f(z,x,f(x,y,u))) = f(z,x,f(x,y,u)). [para(19(a,1),24(a,1,3)),rewrite([5(1),5(3),5(5,R),6(5)]),flip(a)]. 74 f(x,y,f(z,u,f(y,u,w))) = f(y,u,f(x,y,f(z,u,w))). [para(16(a,1),24(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])]. 75 f(x,f(y,z,u),f(x,w,z)) = f(x,w,f(y,z,f(x,z,u))). [para(24(a,1),17(a,1,3)),flip(a)]. 95 f(x,y,f(x,z,f(y,u,f(x,y,w)))) = f(x,z,f(y,u,f(x,y,w))). [para(21(a,1),16(a,1,3)),rewrite([5(1),5(4),5(7,R),6(7)]),flip(a)]. 103 f(x,y,f(y,z,f(x,u,f(x,y,w)))) = f(y,z,f(x,u,f(x,y,w))). [para(21(a,1),24(a,2,3)),rewrite([6(1),5(3,R),6(3),6(5),5(7,R),6(7)])]. 105 f(x,y,f(z,u,f(x,u,w))) = f(x,y,f(x,u,f(z,u,w))). [para(24(a,1),21(a,2,3)),rewrite([21(5)]),flip(a)]. 111 f(x,y,f(z,u,f(y,z,w))) = f(x,y,f(y,z,f(z,u,w))). [para(16(a,2),28(a,2,3)),rewrite([28(4)]),flip(a)]. 113 f(x,y,f(y,z,f(y,u,w))) = f(x,y,f(y,w,f(y,z,u))). [para(17(a,1),28(a,2,3)),rewrite([28(4)])]. 122 f(x,y,f(z,y,f(x,y,u))) = f(z,y,f(x,y,u)). [para(73(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])]. 125 f(x,y,f(z,u,f(z,x,w))) = f(x,y,f(z,x,f(z,u,w))). [para(8(a,1),122(a,1,3,3)),rewrite([5(3,R),6(3),103(4),5(6,R),6(6)])]. 132 f(x,y,f(z,u,f(x,z,u))) = f(x,y,f(x,z,u)). [para(15(a,1),25(a,1,3)),rewrite([6(4),95(6)]),flip(a)]. 168 f(x,f(y,z,u),f(y,z,f(y,u,x))) = f(y,x,f(y,z,u)). [para(27(a,1),5(a,2)),rewrite([5(2),5(2),5(4),5(6,R),6(6)])]. 187 f(x,f(y,z,f(z,u,w)),f(z,u,f(x,u,f(y,z,w)))) = f(x,u,f(z,u,f(y,z,w))). [para(24(a,1),27(a,1,2)),rewrite([5(1,R),6(1),5(5,R),6(5),5(8,R),6(8)])]. 200 f(x,f(y,z,f(u,w,f(x,u,v5))),f(y,z,f(x,u,f(x,y,f(u,w,v5))))) = f(x,y,f(y,z,f(u,w,f(x,u,v5)))). [para(25(a,1),27(a,1,3,3))]. 205 f(x,y,f(z,x,y)) = f(z,x,y). [para(132(a,1),15(a,1)),rewrite([6(4),132(4),15(3)]),flip(a)]. 220 f(x,y,f(z,u,f(u,y,w))) = f(u,y,f(x,y,f(z,u,w))). [para(29(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5,R),6(5),5(6,R),6(6)])]. 262 f(x,y,f(z,u,f(u,y,w))) = f(x,y,f(u,y,f(z,u,w))). [para(29(a,1),205(a,1,3)),rewrite([5(1,R),6(1),5(4,R),6(4),5(5,R),6(5),187(6),5(4,R),6(4),5(6,R),6(6)]),flip(a)]. 318 f(x,f(y,z,u),f(y,x,w)) = f(x,w,f(y,z,f(y,u,x))). [para(38(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4)])]. 319 f(x,f(y,z,u),f(w,y,x)) = f(w,x,f(y,z,f(y,x,u))). [para(38(a,2),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5),5(5)]),flip(a)]. 321 f(x,f(y,z,u),f(x,u,w)) = f(x,w,f(y,u,f(x,z,u))). [para(5(a,2),38(a,1,2)),rewrite([6(2),6(4),5(5,R),6(5)])]. 331 f(x,y,f(z,f(x,y,u),f(x,w,f(x,y,u)))) = f(x,f(x,y,u),f(z,w,f(x,y,u))). [para(20(a,1),38(a,1,3)),rewrite([5(2),5(2),6(4),6(7),5(8,R),6(8)]),flip(a)]. 360 f(x,f(y,z,u),f(y,z,x)) = f(y,z,f(z,x,f(y,x,u))). [para(38(a,2),24(a,2)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5),6(5)]),flip(a)]. 385 f(x,y,f(z,f(x,y,u),f(x,y,z))) = f(y,z,f(x,y,f(x,z,u))). [para(38(a,2),122(a,1,3)),rewrite([5(2),6(2),5(5,R),6(5),5(7,R),6(7)])]. 392 f(x,f(y,z,u),f(x,y,w)) = f(x,y,f(x,w,f(y,z,u))). [para(38(a,2),25(a,1)),rewrite([6(2)])]. 474 f(x,y,f(x,z,f(u,x,y))) = f(u,x,f(x,z,y)). [para(19(a,1),41(a,1,3)),flip(a)]. 628 f(x,f(y,x,z),f(x,u,z)) = f(y,x,f(x,u,z)). [para(474(a,1),17(a,1)),rewrite([6(4)]),flip(a)]. 630 f(x,y,f(z,u,f(z,x,w))) = f(x,y,f(z,w,f(z,x,u))). [para(474(a,1),24(a,2,3)),rewrite([5(1),5(1),5(3,R),6(3),103(4),6(4),5(5,R),6(5),5(6,R),6(6)])]. 654 f(x,f(y,x,z),f(x,z,u)) = f(y,x,f(x,z,u)). [para(628(a,1),5(a,2)),rewrite([6(2),5(3),6(4)])]. 695 f(x,f(x,y,z),f(u,x,y)) = f(u,x,f(x,y,z)). [para(654(a,1),6(a,1)),flip(a)]. 696 f(x,f(x,y,z),f(u,w,f(x,y,z))) = f(x,z,f(x,y,f(u,w,f(x,y,z)))). [para(654(a,1),25(a,2)),rewrite([5(1),5(1),5(2),5(2),6(3),5(4,R),6(4),331(5),5(5),5(5),5(6),5(6),5(8,R),6(8)])]. 803 f(x,y,f(x,z,f(z,y,u))) = f(x,z,y). [para(695(a,1),40(a,1,3)),rewrite([5(4,R),15(4),5(3,R),15(3),5(5),6(5),5(6,R),6(6),696(6),28(5),6(3),57(6),6(4),20(5),22(5)]),flip(a)]. 812 f(x,y,f(y,z,f(x,z,u))) = f(x,y,z). [para(803(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(4)])]. 813 f(x,y,f(x,z,f(y,z,u))) = f(x,y,z). [para(5(a,1),803(a,1,3,3)),rewrite([5(1),6(1),6(4)])]. 814 f(x,y,f(x,z,f(x,u,f(u,y,w)))) = f(x,z,f(x,u,y)). [para(803(a,1),8(a,1,3)),flip(a)]. 816 f(x,y,f(x,z,f(z,u,f(y,z,w)))) = f(x,y,z). [para(8(a,1),803(a,1,3,3)),rewrite([5(1,R),6(1),6(5)])]. 820 f(x,y,f(x,f(y,z,u),f(y,w,f(y,z,u)))) = f(y,z,f(x,y,u)). [para(16(a,2),803(a,2)),rewrite([6(3),392(5),6(4)])]. 826 f(x,f(y,z,u),f(x,z,f(z,w,f(y,z,u)))) = f(y,z,f(x,z,u)). [para(24(a,1),803(a,2)),rewrite([6(3)])]. 827 f(x,y,f(z,u,f(x,y,z))) = f(x,y,z). [para(30(a,2),803(a,1,3)),rewrite([6(1),6(4)])]. 828 f(x,y,f(z,x,u)) = f(x,u,f(z,x,y)). [para(30(a,2),803(a,2)),rewrite([6(3),392(5),6(4),820(5)])]. 847 f(x,f(y,z,u),f(x,w,f(x,y,z))) = f(x,w,f(x,y,z)). [para(803(a,1),33(a,1,3)),rewrite([6(4)]),flip(a)]. 866 f(x,y,f(z,y,f(z,x,u))) = f(z,x,y). [back_rewrite(360),rewrite([5(2),392(3),813(3),5(2,R),6(2),5(3,R),6(3)]),flip(a)]. 871 f(x,y,f(z,x,f(z,y,u))) = f(z,x,y). [back_rewrite(385),rewrite([827(4)]),flip(a)]. 874 f(x,y,f(z,u,x)) = f(z,x,f(u,x,y)). [para(828(a,1),5(a,2)),rewrite([6(2),5(3)]),flip(a)]. 897 f(x,y,f(z,u,y)) = f(z,y,f(x,u,y)). [para(874(a,1),5(a,2)),rewrite([6(2),5(3)])]. 922 f(x,f(y,z,u),f(y,z,x)) = f(y,z,x). [para(874(a,2),38(a,2)),rewrite([6(2),392(3),813(3)]),flip(a)]. 933 f(x,y,f(z,u,x)) = f(u,x,f(z,x,y)). [para(874(a,2),803(a,2)),rewrite([6(3),826(5)]),flip(a)]. 1030 f(x,y,f(z,u,f(x,u,y))) = f(x,u,y). [para(20(a,1),897(a,1,3)),rewrite([15(3),696(5),122(4)]),flip(a)]. 1036 f(x,f(y,z,u),f(y,w,f(y,z,u))) = f(w,f(y,z,u),f(y,u,f(x,y,z))). [para(30(a,2),897(a,2,3)),rewrite([5(3,R),6(3)])]. 1050 f(x,y,f(x,f(x,y,z),f(u,y,z))) = f(x,y,z). [para(897(a,1),29(a,1)),rewrite([20(3),15(3)]),flip(a)]. 1057 f(x,f(y,z,u),f(y,x,z)) = f(y,x,z). [para(38(a,2),897(a,2)),rewrite([5(1,R),6(1),5(2,R),6(2),696(4),28(3),6(1),803(3),6(2),5(3,R),6(3),5(4),20(4)]),flip(a)]. 1063 f(x,f(y,z,u),f(x,u,f(u,w,f(y,z,u)))) = f(y,u,f(x,z,u)). [para(897(a,1),803(a,2)),rewrite([6(3)])]. 1071 f(x,f(y,z,u),f(x,z,u)) = f(x,z,u). [para(5(a,1),922(a,1,2)),rewrite([5(2),5(4)])]. 1072 f(x,y,f(x,z,f(y,u,z))) = f(x,y,z). [para(5(a,2),922(a,1,2)),rewrite([5(2),6(2),392(3),5(4),6(4)])]. 1073 f(x,f(y,z,x),f(y,z,u)) = f(y,z,x). [para(922(a,1),6(a,1)),flip(a)]. 1079 f(x,f(y,z,f(z,u,w)),f(x,z,u)) = f(x,z,u). [para(16(a,1),922(a,1,2)),rewrite([5(3),5(5)])]. 1082 f(x,y,f(x,z,f(y,u,f(y,w,z)))) = f(x,y,z). [para(17(a,2),922(a,1,2)),rewrite([5(3),392(4),5(5)])]. 1088 f(x,f(y,z,f(z,u,w)),f(x,z,w)) = f(x,z,w). [para(30(a,1),922(a,1,2)),rewrite([5(3),5(5)])]. 1136 f(x,f(y,z,u),f(x,w,f(y,z,w))) = f(x,w,f(y,z,u)). [para(922(a,1),803(a,1,3,3))]. 1140 f(f(x,y,z),f(x,y,u),f(u,w,f(x,y,z))) = f(w,f(x,y,u),f(x,y,z)). [para(922(a,1),828(a,2,3)),rewrite([6(4),5(8,R)])]. 1148 f(x,f(y,z,u),f(x,u,f(y,z,w))) = f(x,u,f(y,z,w)). [para(922(a,1),922(a,1,2)),rewrite([5(3),5(6)])]. 1149 f(x,y,f(z,u,y)) = f(u,y,f(x,z,y)). [para(933(a,1),5(a,2)),rewrite([6(2),5(3)])]. 1150 f(x,f(y,z,x),f(y,u,f(y,z,x))) = f(y,z,x). [para(19(a,1),933(a,1,3)),rewrite([5(3,R),15(3),6(4)]),flip(a)]. 1176 f(x,f(y,z,u),f(x,u,w)) = f(x,w,f(z,u,f(x,y,u))). [para(933(a,1),828(a,2,3)),rewrite([5(2,R),6(2),5(4)])]. 1181 f(x,f(y,x,z),f(y,z,u)) = f(y,x,z). [para(1057(a,1),6(a,1)),flip(a)]. 1197 f(x,f(y,z,u),f(w,x,y)) = f(w,x,f(y,z,f(x,y,u))). [para(38(a,2),1057(a,2)),rewrite([6(3),5(6,R),6(6),392(7),1072(7),5(5,R),6(5)]),flip(a)]. 1253 f(x,f(y,z,u),f(z,u,x)) = f(z,u,x). [para(1071(a,1),5(a,2)),rewrite([5(2),5(2),5(3),5(4),5(4)])]. 1254 f(x,f(y,z,u),f(x,w,f(x,z,u))) = f(x,w,f(x,z,u)). [para(1071(a,1),8(a,2,3))]. 1286 f(x,f(y,z,u),f(x,u,f(x,z,w))) = f(x,w,f(x,z,u)). [para(1071(a,1),32(a,2,3)),rewrite([6(2)])]. 1321 f(x,f(y,z,f(z,u,w)),f(x,f(y,z,u),f(z,u,w))) = f(x,f(y,z,u),f(z,u,w)). [para(654(a,1),1071(a,1,2))]. 1329 f(x,f(y,z,u),f(x,w,f(z,u,w))) = f(x,w,f(y,z,u)). [para(1071(a,1),803(a,1,3,3)),rewrite([5(2),5(2)])]. 1332 f(f(x,y,z),f(y,z,u),f(u,w,f(x,y,z))) = f(w,f(y,z,u),f(x,y,z)). [para(1071(a,1),828(a,2,3)),rewrite([5(2),5(2),6(4),5(7),5(7),5(8,R)])]. 1341 f(x,y,f(x,f(z,u,w),f(y,z,u))) = f(x,y,f(z,u,w)). [para(1071(a,1),922(a,1,2)),rewrite([5(2),5(2),5(3),392(4),5(5),5(5),5(6)])]. 1349 f(x,f(x,y,z),f(y,u,f(y,z,w))) = f(x,y,z). [para(8(a,1),1073(a,1,3)),rewrite([5(1),5(5)])]. 1469 f(x,y,f(z,u,y)) = f(u,y,f(z,x,y)). [para(1149(a,1),803(a,2)),rewrite([6(3),1063(5)])]. 1605 f(f(x,y,z),f(x,z,u),f(y,w,f(x,z,u))) = f(w,f(x,z,u),f(x,y,z)). [para(1181(a,1),1469(a,2,3))]. 1618 f(x,y,f(y,f(z,u,f(x,u,w)),f(x,v5,f(z,u,f(x,u,w))))) = f(x,u,f(x,y,f(z,u,w))). [para(29(a,1),812(a,2)),rewrite([6(5)])]. 1630 f(x,y,f(y,f(z,u,w),f(x,z,u))) = f(x,y,f(z,u,w)). [para(922(a,1),812(a,1,3,3)),rewrite([5(2)])]. 1856 f(x,y,f(z,x,f(y,u,f(z,y,w)))) = f(z,x,y). [para(52(a,1),874(a,2)),rewrite([5(3),392(4),813(4),5(2,R),6(2),5(4,R),6(4)]),flip(a)]. 1905 f(x,y,f(z,u,f(x,u,f(y,u,w)))) = f(x,y,u). [para(41(a,2),871(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5),5(5)])]. 1906 f(x,f(y,z,u),f(y,z,f(z,u,x))) = f(z,x,f(y,z,u)). [para(628(a,1),871(a,1,3)),rewrite([6(2),5(4,R),6(4),6(6)])]. 1982 f(x,y,f(z,u,f(u,x,y))) = f(u,x,y). [para(1030(a,1),922(a,2)),rewrite([5(1,R),6(1),5(4,R),6(4),922(7),5(4,R),6(4)])]. 2276 f(x,f(y,z,f(x,y,u)),f(x,w,v5)) = f(x,y,f(x,w,f(x,v5,f(y,z,u)))). [para(54(a,1),17(a,1)),flip(a)]. 2885 f(x,f(y,z,f(u,z,w)),f(x,u,z)) = f(x,u,z). [para(1079(a,1),21(a,2)),rewrite([5(1,R),6(1),6(3),22(5),6(5)])]. 2997 f(x,f(y,z,f(x,z,u)),f(x,w,v5)) = f(x,z,f(x,w,f(x,v5,f(y,z,u)))). [para(24(a,1),57(a,1,2))]. 3270 f(x,f(y,z,x),f(u,y,z)) = f(y,z,x). [para(1050(a,1),1150(a,1,3)),rewrite([5(2),5(2),5(5),5(5),6(6),1332(6),4(4),5(2),5(2)]),flip(a)]. 3475 f(x,f(y,x,z),f(y,x,f(y,z,u))) = f(y,x,z). [para(1349(a,1),122(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),15(3),5(2,R),6(2),5(3,R),6(3),57(5),6(3),20(4)]),flip(a)]. 3946 f(x,f(y,x,z),f(u,y,f(y,x,w))) = f(x,z,f(u,y,f(y,x,w))). [para(2885(a,1),871(a,1,3)),rewrite([5(1,R),6(1),5(3),6(3),5(4,R),5(5,R),6(5),5(7)])]. 4005 f(x,y,f(x,f(y,z,u),f(w,z,u))) = f(x,y,f(w,z,u)). [para(1071(a,1),3475(a,1,3,3)),rewrite([5(2,R),6(2),5(4,R),6(4),57(5),20(5),5(6,R),6(6)])]. 4085 f(x,y,f(z,u,f(z,w,f(x,y,z)))) = f(x,y,z). [para(61(a,1),866(a,1,3)),rewrite([5(1),6(1),5(5),5(5)])]. 4302 f(x,y,f(x,f(y,z,u),f(w,f(y,z,u),f(y,v5,f(y,z,u))))) = f(y,z,f(x,y,u)). [para(16(a,2),816(a,2)),rewrite([6(4),5(5,R),6(5)])]. 4305 f(x,y,f(z,f(y,z,u),f(x,z,w))) = f(x,y,z). [para(30(a,2),816(a,1,3))]. 4361 f(x,f(y,z,f(z,u,w)),f(x,f(x,z,w),f(v5,f(x,z,w),f(v6,f(y,z,f(z,u,w)),f(x,z,w))))) = f(x,z,w). [para(1088(a,1),816(a,2)),rewrite([5(8),5(9,R),6(9)])]. 4461 f(x,y,f(z,f(x,z,u),f(z,y,w))) = f(x,z,y). [para(4305(a,1),5(a,2)),rewrite([5(2,R),6(2),6(4),5(5),5(5)])]. 4572 f(x,f(y,z,u),f(z,f(x,z,w),f(z,v5,f(y,z,u)))) = f(y,z,f(x,z,u)). [para(24(a,1),4461(a,2)),rewrite([6(4)])]. 5467 f(x,f(y,z,f(u,y,w)),f(u,x,y)) = f(u,x,y). [para(1856(a,1),828(a,1)),flip(a)]. 5502 f(x,y,f(z,x,f(x,u,w))) = f(x,u,f(x,w,f(z,x,y))). [para(61(a,1),1856(a,2)),rewrite([6(7),5(8,R),6(8),5(9,R),6(9),392(10),6(9),4302(10),5(4,R),6(4)])]. 5647 f(x,y,f(x,z,f(u,y,f(z,y,w)))) = f(x,z,y). [para(1905(a,1),812(a,2)),rewrite([6(7),1618(9)])]. 6261 f(x,y,f(z,u,f(z,w,f(z,x,y)))) = f(z,x,y). [para(4085(a,1),922(a,2)),rewrite([5(1),5(5),922(9),5(5)])]. 6720 f(x,f(y,x,z),f(y,x,u)) = f(y,x,f(x,u,z)). [para(70(a,1),17(a,1)),rewrite([5(2,R),6(2),20(3),5(4,R),6(4)]),flip(a)]. 7772 f(x,f(y,z,x),f(z,x,u)) = f(y,x,f(z,x,u)). [para(922(a,1),74(a,2,3)),rewrite([5(3),6(3),122(4),19(4),5(4),5(5,R)]),flip(a)]. 7788 f(x,f(y,z,x),f(u,z,x)) = f(y,x,f(u,z,x)). [para(1253(a,1),74(a,2,3)),rewrite([5(3),6(3),1030(5),5(4),5(5,R)]),flip(a)]. 8028 f(f(x,y,z),f(x,u,f(x,y,z)),f(x,z,f(x,y,w))) = f(u,f(x,y,z),f(x,w,f(x,y,z))). [para(30(a,2),7788(a,1,3)),rewrite([5(3,R),6(3),5(4),5(4),5(9,R),6(9)])]. 8369 f(x,f(y,z,u),f(x,f(x,z,w),f(v5,f(x,z,w),f(v6,f(y,z,u),f(x,z,w))))) = f(x,w,f(y,z,f(x,z,u))). [para(75(a,1),816(a,2)),rewrite([6(2),6(3),6(5),5(6),5(7,R),6(7)])]. 8635 f(x,y,f(z,u,f(x,u,f(u,w,y)))) = f(x,u,y). [back_rewrite(4361),rewrite([8369(11)])]. 8713 f(x,y,f(y,z,f(u,x,y))) = f(y,z,f(u,x,y)). [para(1253(a,1),5647(a,1,3)),rewrite([5(2),5(2),5(4),5(4),5(6,R),6(6),205(6),5(5),5(5),5(7),6(7),19(7)])]. 9281 f(f(x,y,z),f(x,z,u),f(y,w,f(y,v5,f(x,y,z)))) = f(x,y,z). [para(1181(a,1),6261(a,1,3,3,3)),rewrite([1181(9)])]. 9577 f(x,y,f(z,u,f(u,x,f(u,w,y)))) = f(u,x,y). [para(8635(a,1),922(a,2)),rewrite([5(2,R),6(2),5(6,R),6(6),922(9),5(5,R),6(5)])]. 11098 f(x,y,f(z,u,f(x,w,z))) = f(x,y,f(w,z,f(x,z,u))). [para(874(a,2),105(a,2,3)),flip(a)]. 12311 f(x,y,f(y,z,f(u,x,z))) = f(x,y,z). [para(125(a,1),1469(a,2)),rewrite([20(3),15(3),5(3,R),6(3),6720(5),6(3)]),flip(a)]. 12402 f(x,y,f(x,z,f(u,z,y))) = f(x,z,y). [para(12311(a,1),474(a,2)),rewrite([5(3,R),6(3),21(5),5(4,R),6(4)])]. 12982 f(x,f(y,z,u),f(y,u,x)) = f(y,u,x). [para(1072(a,1),168(a,1,3)),rewrite([5(2),5(2),5(3),5(3),15(4),5(3),5(3)]),flip(a)]. 12992 f(x,f(y,z,u),f(x,w,f(z,u,x))) = f(x,w,f(z,u,x)). [para(3270(a,1),168(a,1,3,3)),rewrite([15(6)]),flip(a)]. 13008 f(x,f(y,z,f(y,u,w)),f(y,w,x)) = f(y,w,x). [para(1082(a,1),168(a,1,3)),rewrite([5(3),5(3),5(4),5(4),15(5),5(4),5(4)]),flip(a)]. 13139 f(x,f(y,z,x),f(z,u,x)) = f(y,x,f(z,u,x)). [para(12982(a,1),74(a,2,3)),rewrite([5(3),6(3),1030(5),5(4),5(5,R)]),flip(a)]. 13180 f(x,f(y,x,z),f(y,u,x)) = f(x,z,f(y,u,x)). [para(13139(a,1),922(a,2)),rewrite([5(2),5(2),6(3),5(4),5(4),12982(7),5(5,R),6(5)])]. 13417 f(f(x,y,f(x,z,u)),f(x,u,w),f(w,f(x,u,w),f(w,v5,f(x,y,f(x,z,u))))) = f(x,u,w). [para(13008(a,1),866(a,2)),rewrite([6(7)])]. 14376 f(x,y,f(z,u,f(y,w,z))) = f(x,y,f(w,z,f(y,z,u))). [para(828(a,1),262(a,2,3)),rewrite([5(1,R),6(1),5(4)]),flip(a)]. 14673 f(f(x,y,z),f(y,u,w),f(x,y,z)) = f(x,y,z). [para(1181(a,1),318(a,1,3)),rewrite([9281(10)])]. 14946 f(x,f(y,z,u),f(y,u,f(y,z,f(w,x,f(y,z,u))))) = f(w,f(y,z,u),f(y,x,f(y,z,u))). [para(14673(a,1),40(a,1,3)),rewrite([5(3),5(3),5(4,R),6(4),5(6),5(6),5(10),5(10),5(11,R),6(11),696(11),5(12,R),6(12),8028(12),6(9),696(9)]),flip(a)]. 14966 f(x,f(y,z,u),f(y,u,f(y,z,f(x,w,f(y,z,u))))) = f(y,u,f(y,z,f(x,w,f(y,z,u)))). [para(14673(a,1),816(a,1,3)),rewrite([6(3),5(4,R),6(4),696(4),6(7),5(8,R),6(8),696(8),5(9,R),15(9),6(7),5(8,R),6(8),696(8),5(10),5(10)]),flip(a)]. 15096 f(x,f(y,x,z),f(z,u,w)) = f(y,x,f(z,u,f(x,z,w))). [para(319(a,1),6(a,1)),rewrite([5(1,R),6(1),6(4)]),flip(a)]. 15120 f(f(x,y,z),f(u,w,f(x,y,z)),f(x,y,f(x,z,f(u,w,f(x,y,z))))) = f(x,z,f(x,y,f(u,w,f(x,y,z)))). [para(319(a,1),40(a,2)),rewrite([5(3),5(3),5(6),5(6),5(7,R),7788(7),696(5),5(6,R),6(6),14966(6),5(7),5(7),5(9),5(9),6(10)]),flip(a)]. 15153 f(f(x,y,z),f(x,u,w),f(w,f(x,u,w),f(w,v5,f(x,y,z)))) = f(u,w,f(x,y,f(x,z,w))). [para(319(a,1),866(a,2)),rewrite([5(2,R),6(2),5(3,R),6(3),6(5),6(8)])]. 15161 f(f(x,y,z),f(u,w,v5),f(x,y,z)) = f(x,y,z). [para(319(a,1),54(a,2,3)),rewrite([5(5),5(5),19(5),20(5),5(5,R),15(5),6(9),4(11),5(7,R),15(7)])]. 15213 f(x,f(y,z,u),f(z,x,u)) = f(z,x,u). [para(319(a,2),8713(a,2)),rewrite([5(4,R),6(4),5(5,R),6(5),3946(5),1982(4),15(3),5(2,R),6(2),5(4),5(4),20(4)]),flip(a)]. 15245 f(x,f(y,z,u),f(w,f(y,z,u),f(y,x,f(y,z,u)))) = f(y,u,f(y,z,f(x,w,f(y,z,u)))). [para(319(a,1),113(a,1)),rewrite([5(3),5(3),5(5),5(5),6(6),15120(8),5(6),5(6),5(10),5(10),5(11,R),6(11),5(12,R),6(12),7772(12)]),flip(a)]. 15288 f(x,y,f(z,u,f(z,y,f(z,w,x)))) = f(z,x,y). [back_rewrite(13417),rewrite([15153(9),6(2)])]. 15375 f(x,f(y,z,u),f(w,f(y,z,u),f(x,v5,f(y,z,u)))) = f(w,f(y,z,u),f(x,v5,f(y,z,u))). [para(15161(a,1),816(a,1,3)),rewrite([6(3),5(4,R),6(4),6(7),5(8,R),6(8),5(9,R),15(9),6(7),5(8,R),6(8),5(10),5(10)]),flip(a)]. 15402 f(f(x,y,z),f(u,w,f(u,v5,f(x,y,z))),f(u,f(u,w,v5),f(x,y,z))) = f(u,w,f(u,v5,f(x,y,z))). [para(15161(a,1),111(a,1)),rewrite([5(2),5(2),5(5),5(5),5(10,R),5(11,R),6(11)]),flip(a)]. 15403 f(x,f(x,y,z),f(u,w,v5)) = f(x,y,f(x,z,f(u,w,v5))). [para(15161(a,1),111(a,2)),rewrite([5(3,R),5(6),5(6),5(8),5(8),15402(8),5(6,R)]),flip(a)]. 15417 f(x,f(y,z,u),f(w,y,f(y,z,u))) = f(y,u,f(y,z,f(w,x,f(y,z,u)))). [back_rewrite(15245),rewrite([5(4,R),6(4),15375(6)])]. 15771 f(x,f(y,z,u),f(x,z,u)) = f(x,z,u). [para(15288(a,1),922(a,1,2)),rewrite([5(2),5(4)])]. 15796 f(x,f(y,z,u),f(x,y,u)) = f(x,y,u). [para(15288(a,1),2885(a,1,2))]. 15821 f(x,f(y,z,u),f(x,y,z)) = f(x,y,z). [para(15288(a,1),5467(a,1,2)),rewrite([5(2,R),6(2),5(4,R),6(4)])]. 15868 f(x,f(y,z,f(u,x,y)),f(w,u,x)) = f(x,y,f(w,u,x)). [para(12402(a,1),15288(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. 15909 f(x,f(y,z,u),f(x,y,f(z,u,w))) = f(x,y,f(z,u,w)). [para(15771(a,1),922(a,1,2)),rewrite([5(2),5(2),5(3),5(5),5(5),5(6)])]. 15921 f(x,y,f(x,f(z,u,y),f(w,z,u))) = f(x,y,f(w,z,u)). [para(15771(a,1),866(a,1,3,3)),rewrite([5(2),5(2),5(3,R),6(3),5(4,R),15403(4),5(6)])]. 15972 f(x,f(y,z,f(u,x,z)),f(w,u,x)) = f(x,z,f(w,u,x)). [para(15771(a,1),9577(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. 16471 f(x,y,f(z,y,f(x,u,y))) = f(x,y,f(z,u,y)). [para(15(a,1),321(a,1,3)),rewrite([6(2)]),flip(a)]. 16711 f(x,y,f(z,u,f(y,w,u))) = f(y,u,f(x,y,f(z,w,u))). [para(321(a,2),74(a,1,3)),rewrite([15(2),6(2),19(5)])]. 18363 f(x,y,f(z,u,f(y,u,f(x,z,u)))) = f(x,y,u). [para(630(a,1),9577(a,1,3)),rewrite([5(1),6(1),5(2,R),6(2),5(5),5(5)])]. 18491 f(x,y,f(z,y,f(z,u,x))) = f(z,x,y). [para(18363(a,1),4461(a,2)),rewrite([5(2,R),6(2),8713(3),5(5,R),6(5),8713(6),6(6),4572(8),6(4)])]. 18837 f(x,f(y,z,u),f(w,x,f(w,y,z))) = f(w,x,f(y,z,u)). [para(847(a,1),220(a,2,3)),rewrite([1630(5),19(4)]),flip(a)]. 19724 f(x,y,f(x,z,f(x,f(y,u,w),f(u,w,v5)))) = f(x,z,f(x,y,f(u,w,v5))). [para(1136(a,1),32(a,1,3)),rewrite([5(4)]),flip(a)]. 19762 f(x,f(y,z,u),f(z,w,f(x,y,w))) = f(x,w,f(y,z,u)). [para(1149(a,1),1136(a,1,3))]. 20436 f(x,y,f(f(z,u,w),f(u,w,v5),f(x,u,f(u,w,v5)))) = f(x,f(z,u,f(u,w,v5)),f(x,y,f(u,w,v5))). [para(654(a,1),1176(a,1,2)),rewrite([6(4)]),flip(a)]. 20765 f(x,f(y,z,u),f(x,y,f(x,w,v5))) = f(x,y,f(x,w,f(x,v5,f(y,z,u)))). [para(1197(a,2),13180(a,1,2)),rewrite([5(2),5(2),5(4),15403(5),15403(4),20(3),5(7),2276(8)])]. 20959 f(x,f(y,z,u),f(w,x,f(x,z,u))) = f(w,x,f(x,z,u)). [para(1254(a,1),74(a,1,3)),rewrite([15771(3),15771(6)]),flip(a)]. 21385 f(x,f(y,z,u),f(z,w,f(x,u,w))) = f(x,w,f(y,z,u)). [para(897(a,1),1329(a,1,3))]. 21496 f(x,y,f(x,f(y,z,u),f(z,w,f(x,y,u)))) = f(x,y,f(z,w,f(x,y,u))). [para(25(a,1),1341(a,1,3)),rewrite([6(2),6(4),20(6),6(7)])]. 23721 f(x,y,f(x,z,f(u,w,y))) = f(x,z,f(x,y,f(z,u,w))). [para(4005(a,1),54(a,2,3)),rewrite([6(2),5(3,R),6(3),21385(4),5(4),5(4)]),flip(a)]. 23961 f(x,y,f(z,x,f(u,x,y))) = f(z,x,f(u,x,y)). [para(5502(a,2),1469(a,2)),rewrite([4(3),6(2),5(4),122(5)]),flip(a)]. 24846 f(x,f(y,z,f(x,u,y)),f(x,w,v5)) = f(x,y,f(x,w,f(x,v5,f(u,y,z)))). [para(11098(a,1),1286(a,1,3,3)),rewrite([1286(6),2997(4)]),flip(a)]. 25097 f(x,y,f(x,z,f(u,w,f(x,z,y)))) = f(x,y,f(z,u,f(x,z,w))). [para(15096(a,1),1329(a,2)),rewrite([5(2),5(2),5(3),5(3),15403(5),20765(6),6(4),19724(6),5(7,R),6(7)])]. 25130 f(x,f(y,z,u),f(y,w,f(y,z,u))) = f(y,u,f(x,z,f(y,z,w))). [back_rewrite(15417),rewrite([5(3,R),6(3),5(6,R),6(6),25097(8),5(6,R),6(6)])]. 25132 f(x,f(y,z,u),f(y,u,f(x,z,f(y,z,w)))) = f(y,u,f(x,z,f(y,z,w))). [back_rewrite(14966),rewrite([25097(5),5(3,R),6(3),25097(9),5(7,R),6(7)])]. 25133 f(x,f(y,z,u),f(w,y,f(y,z,u))) = f(y,u,f(w,z,f(y,z,x))). [back_rewrite(14946),rewrite([5(3,R),6(3),25097(5),5(3,R),6(3),25132(5),5(6,R),6(6)]),flip(a)]. 25262 f(x,f(y,z,u),f(y,u,f(w,y,z))) = f(y,u,f(w,z,f(y,z,x))). [back_rewrite(1036),rewrite([25130(4)]),flip(a)]. 25278 f(x,f(y,z,f(z,u,w)),f(x,v5,f(z,u,w))) = f(x,v5,f(z,w,f(x,u,f(y,z,u)))). [back_rewrite(20436),rewrite([25133(5),205(2)]),flip(a)]. 25399 f(x,f(y,z,u),f(z,w,f(x,u,f(y,z,u)))) = f(x,f(y,z,u),f(z,u,w)). [back_rewrite(1321),rewrite([25278(6)])]. 26704 f(x,f(y,z,u),f(x,z,f(x,u,w))) = f(x,w,f(x,z,u)). [para(15868(a,1),12992(a,2)),rewrite([5(2,R),6(2),5(4),24846(5),814(5),5(5)])]. 27091 f(x,f(y,z,f(z,u,x)),f(u,x,w)) = f(z,x,f(u,x,w)). [para(15972(a,1),5(a,2)),rewrite([5(1),5(3),5(3),5(4),5(5),5(5),5(6,R),6(6)])]. 27912 f(f(x,y,z),f(y,z,u),f(w,x,f(y,z,u))) = f(w,f(y,z,u),f(x,y,z)). [para(15909(a,1),16711(a,2,3)),rewrite([5(5,R),15821(5),19(5)]),flip(a)]. 28511 f(f(x,y,z),f(y,z,u),f(y,z,w)) = f(w,f(x,y,z),f(y,z,u)). [para(15771(a,1),18837(a,1,3)),rewrite([5(3),5(3)])]. 28512 f(f(x,y,z),f(x,z,u),f(x,z,w)) = f(w,f(x,y,z),f(x,z,u)). [para(15796(a,1),18837(a,1,3)),rewrite([5(3),5(3)])]. 28513 f(f(x,y,z),f(x,y,u),f(x,y,w)) = f(w,f(x,y,z),f(x,y,u)). [para(15821(a,1),18837(a,1,3)),rewrite([5(3),5(3)])]. 28531 f(f(x,y,z),f(u,x,y),f(u,x,z)) = f(x,z,f(u,x,y)). [para(1906(a,1),18837(a,2)),rewrite([5(5),5(5),922(6),6(5),28513(5)])]. 28539 f(x,f(y,z,f(x,u,w)),f(x,w,f(y,u,w))) = f(x,w,f(y,z,f(x,u,w))). [para(14376(a,1),18837(a,1,3)),rewrite([6(2),6(3),5(5,R),6(5),16471(5),5(3,R),6(3),6(7),5(8,R),6(8)])]. 28566 f(f(x,y,z),f(x,y,u),f(y,z,u)) = f(y,u,f(x,y,z)). [para(28531(a,1),5(a,2))]. 28568 f(f(x,y,z),f(x,z,u),f(y,z,u)) = f(y,z,f(x,z,u)). [para(5(a,2),28531(a,1,1)),rewrite([5(2),6(2),5(3),6(3),5(5),6(5),5(6,R),6(6)])]. 29055 f(f(x,y,z),f(u,x,z),f(u,w,f(x,y,z))) = f(w,f(u,x,z),f(x,y,z)). [para(12982(a,1),28566(a,1,2)),rewrite([6(2),5(3),5(5),5(6,R),5(7,R),6(7),15213(7),5(5),6(7)]),flip(a)]. 29200 f(f(x,y,z),f(x,u,y),f(u,y,z)) = f(u,y,f(x,y,z)). [para(28568(a,1),19(a,1,3)),rewrite([28511(5),28568(8)])]. 29568 f(x,f(y,z,u),f(z,w,f(y,x,w))) = f(y,f(z,x,w),f(x,w,f(y,z,u))). [para(29200(a,1),200(a,1,2)),rewrite([5(2,R),6(2),5(5,R),6(5),5(6),5(6),5(8,R),6(8),6(10),21496(11),5(10,R),6(10),27912(10),6(7),25278(8),25399(6),5(6,R),6(6),5(8,R),6(8),5(9),5(9),5(12,R),28566(12),25262(10),5(6)]),flip(a)]. 30122 f(x,f(y,z,u),f(y,u,f(x,z,w))) = f(y,u,f(x,z,w)). [back_rewrite(29568),rewrite([5(2,R),6(2),19762(4),5(3,R),6(3)]),flip(a)]. 30898 f(x,y,f(z,y,f(u,x,z))) = f(x,z,y). [para(20959(a,1),71(a,2)),rewrite([5(3),5(4,R),6(4),5(5,R),6(5),23961(5),5(5),5(5),5(6,R),3270(6)])]. 32772 f(x,f(y,z,u),f(x,w,y)) = f(x,f(w,z,u),f(x,w,y)). [para(23721(a,1),1286(a,1,3)),rewrite([26704(5),5(4)]),flip(a)]. 32850 f(x,f(y,z,u),f(w,x,u)) = f(x,f(w,y,z),f(w,x,u)). [para(32772(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4),5(5)]),flip(a)]. 33448 f(f(x,y,z),f(x,y,u),f(w,v5,f(x,y,u))) = f(f(x,y,z),f(w,v5,u),f(x,y,u)). [para(922(a,1),32850(a,1,3)),rewrite([6(5),5(7),5(7),922(10)])]. 33505 f(f(x,y,z),f(x,z,u),f(w,v5,f(x,z,u))) = f(f(x,y,z),f(w,v5,u),f(x,z,u)). [para(12982(a,1),32850(a,1,3)),rewrite([6(5),5(7),5(7),12982(10)])]. 33573 f(f(x,y,z),f(y,u,w),f(x,z,u)) = f(w,f(x,z,u),f(x,y,z)). [back_rewrite(1605),rewrite([33505(5),6(2)])]. 35717 f(f(x,y,z),f(u,z,w),f(x,y,u)) = f(w,f(x,y,z),f(x,y,u)). [para(1148(a,1),27091(a,1,2)),rewrite([5(4,R),922(4),6(4),1140(5),6(7),33448(8),5(5)]),flip(a)]. 36738 f(f(x,y,z),f(u,x,w),f(u,w,y)) = f(u,w,f(x,y,z)). [para(30122(a,1),18837(a,2)),rewrite([5(2,R),6(2),5(5),5(5),12982(6),6(5),28512(5),5(5,R),6(5)])]. 36780 f(x,f(y,z,u),f(y,z,w)) = f(y,z,f(w,u,x)). [para(36738(a,1),5(a,1)),rewrite([6(5),35717(6)]),flip(a)]. 36790 f(x,f(y,z,u),f(z,w,u)) = f(z,u,f(y,x,f(z,w,u))). [para(19(a,1),36738(a,1,3)),rewrite([6(2),5(3,R),6(3),5(5),6(5),29055(5),6(5)])]. 36856 f(x,f(y,z,u),f(y,w,z)) = f(y,z,f(w,u,x)). [para(36738(a,1),18491(a,2)),rewrite([5(7,R),30898(9),33573(4)])]. 36866 f(x,y,f(z,u,f(x,w,y))) = f(x,y,f(z,u,w)). [para(1341(a,1),36738(a,2)),rewrite([5(2),5(2),36780(3),5(1),6(1),4(3),5(5),5(5),15403(5),36780(4),5(2),6(2),20(2)])]. 36880 f(x,y,f(z,u,f(x,y,w))) = f(x,y,f(z,u,w)). [para(15921(a,1),36738(a,2)),rewrite([5(2),5(2),36780(3),5(1),6(1),4(3),5(5,R),15403(5),36780(4),5(2),6(2),20(2),5(4),5(4)])]. 37170 f(x,f(y,z,u),f(z,u,w)) = f(z,u,f(x,y,w)). [back_rewrite(36790),rewrite([6(2),6(4),5(5,R),6(5),36880(6)])]. 37187 f(x,f(y,z,f(x,u,w)),f(x,w,f(y,u,w))) = f(x,w,f(y,z,u)). [back_rewrite(28539),rewrite([36866(8)])]. 38298 f(x,f(y,z,f(u,w,v5)),f(u,v5,f(y,w,v5))) = f(y,f(u,w,v5),f(x,v5,z)). [para(897(a,1),36856(a,1,3)),rewrite([6(2),5(7)])]. 38353 f(x,f(y,z,u),f(y,w,u)) = f(y,u,f(x,w,z)). [back_rewrite(37187),rewrite([38298(5),6(2)])]. 38852 f(x,f(y,z,u),f(w,z,u)) = f(z,u,f(w,x,y)). [para(37170(a,1),36780(a,2)),rewrite([6(2),6(4),38353(5),5(4)])]. 38911 $F # answer(dist_short). [back_rewrite(12),rewrite([38852(10),5(6),5(6)]),xx(a)]. ============================== end of proof ========================== ============================== PROOF ================================= % Proof 3 at 657.97 (+ 1.04) seconds: dist_long. % Length of proof is 235. % Level of proof is 31. % Maximum clause weight is 46. % Given clauses 791. 1 f(f(x,y,z),u,w) = f(f(x,u,w),f(y,u,w),f(z,u,w)) # label(dist_long) # label(non_clause) # label(goal). [goal]. 4 f(x,x,y) = x # label(majority). [assumption]. 5 f(x,y,z) = f(z,x,y) # label(2a). [assumption]. 6 f(x,y,z) = f(x,z,y) # label(2b). [assumption]. 7 f(f(x,y,z),y,u) = f(x,y,f(z,y,u)) # label(associativity). [assumption]. 8 f(x,y,f(x,z,u)) = f(x,z,f(x,y,u)). [copy(7),rewrite([5(2),5(2),5(3,R),6(3)]),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])]. 9 f(f(c1,c4,c5),f(c2,c4,c5),f(c3,c4,c5)) != f(f(c1,c2,c3),c4,c5) # label(dist_long) # answer(dist_long). [deny(1)]. 10 f(f(c1,c4,c5),f(c2,c4,c5),f(c3,c4,c5)) != f(c4,c5,f(c1,c2,c3)) # answer(dist_long). [copy(9),rewrite([5(20),5(20)])]. 15 f(x,y,y) = y. [para(5(a,1),4(a,1))]. 16 f(x,y,f(z,x,u)) = f(z,x,f(x,y,u)). [para(8(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)]),flip(a)]. 17 f(x,y,f(x,z,u)) = f(x,u,f(x,y,z)). [para(5(a,1),8(a,1,3)),rewrite([5(1,R),6(1)])]. 18 f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,y,f(x,z,w))). [para(8(a,1),8(a,1,3))]. 19 f(x,y,f(x,z,y)) = f(x,z,y). [para(15(a,1),8(a,1,3)),flip(a)]. 20 f(x,y,f(x,y,z)) = f(x,y,z). [para(15(a,1),8(a,1)),rewrite([6(3),19(3)]),flip(a)]. 21 f(x,y,f(x,z,f(x,u,y))) = f(x,z,f(x,u,y)). [para(19(a,1),8(a,1,3)),flip(a)]. 22 f(x,y,f(x,z,f(x,y,u))) = f(x,z,f(x,y,u)). [para(19(a,1),8(a,2,3)),rewrite([6(1),6(4)])]. 24 f(x,y,f(z,y,u)) = f(z,y,f(x,y,u)). [para(16(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)])]. 25 f(x,y,f(z,u,f(x,z,w))) = f(x,z,f(x,y,f(z,u,w))). [para(16(a,2),8(a,1,3))]. 27 f(x,f(y,z,u),f(y,z,f(x,y,u))) = f(x,y,f(y,z,u)). [para(16(a,2),19(a,1,3))]. 28 f(x,y,f(y,z,f(x,y,u))) = f(x,y,f(y,z,u)). [para(16(a,2),20(a,1,3))]. 29 f(x,y,f(z,u,f(x,u,w))) = f(x,u,f(x,y,f(z,u,w))). [para(16(a,1),16(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])]. 30 f(x,y,f(z,x,u)) = f(z,x,f(x,u,y)). [para(17(a,1),5(a,2)),rewrite([6(2),5(3,R),6(3)]),flip(a)]. 32 f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,y,f(x,w,z))). [para(17(a,1),8(a,2,3)),flip(a)]. 33 f(x,y,f(x,z,f(x,u,w))) = f(x,w,f(x,y,f(x,z,u))). [para(17(a,2),8(a,1,3))]. 38 f(x,f(y,z,u),f(x,w,y)) = f(x,w,f(y,z,f(x,y,u))). [para(16(a,2),17(a,1,3)),flip(a)]. 40 f(x,y,f(z,x,f(x,u,w))) = f(z,x,f(x,u,f(x,y,w))). [para(18(a,1),5(a,2)),rewrite([6(3),5(5,R),6(5)]),flip(a)]. 41 f(x,y,f(y,z,f(y,u,w))) = f(y,z,f(y,u,f(x,y,w))). [para(18(a,2),5(a,2)),rewrite([6(3),5(4,R),6(4)])]. 52 f(x,y,f(z,u,f(x,z,f(z,w,v5)))) = f(x,z,f(x,y,f(z,w,f(z,u,v5)))). [para(18(a,1),16(a,1,3)),rewrite([5(2,R),6(2),5(8,R),6(8)])]. 54 f(x,y,f(x,z,f(u,w,f(x,u,v5)))) = f(x,u,f(x,y,f(x,z,f(u,w,v5)))). [para(16(a,2),18(a,1,3,3))]. 57 f(x,f(x,y,z),f(x,u,w)) = f(x,y,f(x,u,f(x,w,z))). [para(18(a,1),17(a,1)),flip(a)]. 61 f(x,y,f(x,z,f(x,u,w))) = f(x,u,f(x,w,f(x,y,z))). [para(17(a,1),18(a,2,3))]. 70 f(x,y,f(z,u,f(y,z,w))) = f(y,z,f(x,y,f(z,u,w))). [para(8(a,1),24(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])]. 71 f(x,y,f(z,u,f(z,x,w))) = f(z,x,f(x,y,f(z,u,w))). [para(8(a,1),24(a,2,3)),rewrite([5(2,R),6(2),5(6,R),6(6)]),flip(a)]. 73 f(x,y,f(z,x,f(x,y,u))) = f(z,x,f(x,y,u)). [para(19(a,1),24(a,1,3)),rewrite([5(1),5(3),5(5,R),6(5)]),flip(a)]. 74 f(x,y,f(z,u,f(y,u,w))) = f(y,u,f(x,y,f(z,u,w))). [para(16(a,1),24(a,1,3)),rewrite([5(1,R),6(1),5(6,R),6(6)])]. 75 f(x,f(y,z,u),f(x,w,z)) = f(x,w,f(y,z,f(x,z,u))). [para(24(a,1),17(a,1,3)),flip(a)]. 87 f(x,y,f(y,z,f(y,u,w))) = f(y,z,f(y,w,f(x,y,u))). [para(30(a,2),24(a,2,3)),rewrite([5(2,R),6(2),5(6,R),6(6)])]. 95 f(x,y,f(x,z,f(y,u,f(x,y,w)))) = f(x,z,f(y,u,f(x,y,w))). [para(21(a,1),16(a,1,3)),rewrite([5(1),5(4),5(7,R),6(7)]),flip(a)]. 103 f(x,y,f(y,z,f(x,u,f(x,y,w)))) = f(y,z,f(x,u,f(x,y,w))). [para(21(a,1),24(a,2,3)),rewrite([6(1),5(3,R),6(3),6(5),5(7,R),6(7)])]. 105 f(x,y,f(z,u,f(x,u,w))) = f(x,y,f(x,u,f(z,u,w))). [para(24(a,1),21(a,2,3)),rewrite([21(5)]),flip(a)]. 111 f(x,y,f(z,u,f(y,z,w))) = f(x,y,f(y,z,f(z,u,w))). [para(16(a,2),28(a,2,3)),rewrite([28(4)]),flip(a)]. 113 f(x,y,f(y,z,f(y,u,w))) = f(x,y,f(y,w,f(y,z,u))). [para(17(a,1),28(a,2,3)),rewrite([28(4)])]. 122 f(x,y,f(z,y,f(x,y,u))) = f(z,y,f(x,y,u)). [para(73(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(4,R),6(4)])]. 125 f(x,y,f(z,u,f(z,x,w))) = f(x,y,f(z,x,f(z,u,w))). [para(8(a,1),122(a,1,3,3)),rewrite([5(3,R),6(3),103(4),5(6,R),6(6)])]. 132 f(x,y,f(z,u,f(x,z,u))) = f(x,y,f(x,z,u)). [para(15(a,1),25(a,1,3)),rewrite([6(4),95(6)]),flip(a)]. 168 f(x,f(y,z,u),f(y,z,f(y,u,x))) = f(y,x,f(y,z,u)). [para(27(a,1),5(a,2)),rewrite([5(2),5(2),5(4),5(6,R),6(6)])]. 187 f(x,f(y,z,f(z,u,w)),f(z,u,f(x,u,f(y,z,w)))) = f(x,u,f(z,u,f(y,z,w))). [para(24(a,1),27(a,1,2)),rewrite([5(1,R),6(1),5(5,R),6(5),5(8,R),6(8)])]. 200 f(x,f(y,z,f(u,w,f(x,u,v5))),f(y,z,f(x,u,f(x,y,f(u,w,v5))))) = f(x,y,f(y,z,f(u,w,f(x,u,v5)))). [para(25(a,1),27(a,1,3,3))]. 205 f(x,y,f(z,x,y)) = f(z,x,y). [para(132(a,1),15(a,1)),rewrite([6(4),132(4),15(3)]),flip(a)]. 220 f(x,y,f(z,u,f(u,y,w))) = f(u,y,f(x,y,f(z,u,w))). [para(29(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5,R),6(5),5(6,R),6(6)])]. 262 f(x,y,f(z,u,f(u,y,w))) = f(x,y,f(u,y,f(z,u,w))). [para(29(a,1),205(a,1,3)),rewrite([5(1,R),6(1),5(4,R),6(4),5(5,R),6(5),187(6),5(4,R),6(4),5(6,R),6(6)]),flip(a)]. 318 f(x,f(y,z,u),f(y,x,w)) = f(x,w,f(y,z,f(y,u,x))). [para(38(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4)])]. 319 f(x,f(y,z,u),f(w,y,x)) = f(w,x,f(y,z,f(y,x,u))). [para(38(a,2),5(a,2)),rewrite([5(1,R),6(1),6(3),5(5),5(5)]),flip(a)]. 321 f(x,f(y,z,u),f(x,u,w)) = f(x,w,f(y,u,f(x,z,u))). [para(5(a,2),38(a,1,2)),rewrite([6(2),6(4),5(5,R),6(5)])]. 331 f(x,y,f(z,f(x,y,u),f(x,w,f(x,y,u)))) = f(x,f(x,y,u),f(z,w,f(x,y,u))). [para(20(a,1),38(a,1,3)),rewrite([5(2),5(2),6(4),6(7),5(8,R),6(8)]),flip(a)]. 360 f(x,f(y,z,u),f(y,z,x)) = f(y,z,f(z,x,f(y,x,u))). [para(38(a,2),24(a,2)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5),6(5)]),flip(a)]. 385 f(x,y,f(z,f(x,y,u),f(x,y,z))) = f(y,z,f(x,y,f(x,z,u))). [para(38(a,2),122(a,1,3)),rewrite([5(2),6(2),5(5,R),6(5),5(7,R),6(7)])]. 392 f(x,f(y,z,u),f(x,y,w)) = f(x,y,f(x,w,f(y,z,u))). [para(38(a,2),25(a,1)),rewrite([6(2)])]. 474 f(x,y,f(x,z,f(u,x,y))) = f(u,x,f(x,z,y)). [para(19(a,1),41(a,1,3)),flip(a)]. 628 f(x,f(y,x,z),f(x,u,z)) = f(y,x,f(x,u,z)). [para(474(a,1),17(a,1)),rewrite([6(4)]),flip(a)]. 630 f(x,y,f(z,u,f(z,x,w))) = f(x,y,f(z,w,f(z,x,u))). [para(474(a,1),24(a,2,3)),rewrite([5(1),5(1),5(3,R),6(3),103(4),6(4),5(5,R),6(5),5(6,R),6(6)])]. 654 f(x,f(y,x,z),f(x,z,u)) = f(y,x,f(x,z,u)). [para(628(a,1),5(a,2)),rewrite([6(2),5(3),6(4)])]. 695 f(x,f(x,y,z),f(u,x,y)) = f(u,x,f(x,y,z)). [para(654(a,1),6(a,1)),flip(a)]. 696 f(x,f(x,y,z),f(u,w,f(x,y,z))) = f(x,z,f(x,y,f(u,w,f(x,y,z)))). [para(654(a,1),25(a,2)),rewrite([5(1),5(1),5(2),5(2),6(3),5(4,R),6(4),331(5),5(5),5(5),5(6),5(6),5(8,R),6(8)])]. 803 f(x,y,f(x,z,f(z,y,u))) = f(x,z,y). [para(695(a,1),40(a,1,3)),rewrite([5(4,R),15(4),5(3,R),15(3),5(5),6(5),5(6,R),6(6),696(6),28(5),6(3),57(6),6(4),20(5),22(5)]),flip(a)]. 812 f(x,y,f(y,z,f(x,z,u))) = f(x,y,z). [para(803(a,1),5(a,2)),rewrite([5(1,R),6(1),6(3),5(4)])]. 813 f(x,y,f(x,z,f(y,z,u))) = f(x,y,z). [para(5(a,1),803(a,1,3,3)),rewrite([5(1),6(1),6(4)])]. 814 f(x,y,f(x,z,f(x,u,f(u,y,w)))) = f(x,z,f(x,u,y)). [para(803(a,1),8(a,1,3)),flip(a)]. 816 f(x,y,f(x,z,f(z,u,f(y,z,w)))) = f(x,y,z). [para(8(a,1),803(a,1,3,3)),rewrite([5(1,R),6(1),6(5)])]. 820 f(x,y,f(x,f(y,z,u),f(y,w,f(y,z,u)))) = f(y,z,f(x,y,u)). [para(16(a,2),803(a,2)),rewrite([6(3),392(5),6(4)])]. 826 f(x,f(y,z,u),f(x,z,f(z,w,f(y,z,u)))) = f(y,z,f(x,z,u)). [para(24(a,1),803(a,2)),rewrite([6(3)])]. 827 f(x,y,f(z,u,f(x,y,z))) = f(x,y,z). [para(30(a,2),803(a,1,3)),rewrite([6(1),6(4)])]. 828 f(x,y,f(z,x,u)) = f(x,u,f(z,x,y)). [para(30(a,2),803(a,2)),rewrite([6(3),392(5),6(4),820(5)])]. 847 f(x,f(y,z,u),f(x,w,f(x,y,z))) = f(x,w,f(x,y,z)). [para(803(a,1),33(a,1,3)),rewrite([6(4)]),flip(a)]. 866 f(x,y,f(z,y,f(z,x,u))) = f(z,x,y). [back_rewrite(360),rewrite([5(2),392(3),813(3),5(2,R),6(2),5(3,R),6(3)]),flip(a)]. 871 f(x,y,f(z,x,f(z,y,u))) = f(z,x,y). [back_rewrite(385),rewrite([827(4)]),flip(a)]. 874 f(x,y,f(z,u,x)) = f(z,x,f(u,x,y)). [para(828(a,1),5(a,2)),rewrite([6(2),5(3)]),flip(a)]. 897 f(x,y,f(z,u,y)) = f(z,y,f(x,u,y)). [para(874(a,1),5(a,2)),rewrite([6(2),5(3)])]. 922 f(x,f(y,z,u),f(y,z,x)) = f(y,z,x). [para(874(a,2),38(a,2)),rewrite([6(2),392(3),813(3)]),flip(a)]. 933 f(x,y,f(z,u,x)) = f(u,x,f(z,x,y)). [para(874(a,2),803(a,2)),rewrite([6(3),826(5)]),flip(a)]. 1030 f(x,y,f(z,u,f(x,u,y))) = f(x,u,y). [para(20(a,1),897(a,1,3)),rewrite([15(3),696(5),122(4)]),flip(a)]. 1036 f(x,f(y,z,u),f(y,w,f(y,z,u))) = f(w,f(y,z,u),f(y,u,f(x,y,z))). [para(30(a,2),897(a,2,3)),rewrite([5(3,R),6(3)])]. 1050 f(x,y,f(x,f(x,y,z),f(u,y,z))) = f(x,y,z). [para(897(a,1),29(a,1)),rewrite([20(3),15(3)]),flip(a)]. 1057 f(x,f(y,z,u),f(y,x,z)) = f(y,x,z). [para(38(a,2),897(a,2)),rewrite([5(1,R),6(1),5(2,R),6(2),696(4),28(3),6(1),803(3),6(2),5(3,R),6(3),5(4),20(4)]),flip(a)]. 1063 f(x,f(y,z,u),f(x,u,f(u,w,f(y,z,u)))) = f(y,u,f(x,z,u)). [para(897(a,1),803(a,2)),rewrite([6(3)])]. 1071 f(x,f(y,z,u),f(x,z,u)) = f(x,z,u). [para(5(a,1),922(a,1,2)),rewrite([5(2),5(4)])]. 1072 f(x,y,f(x,z,f(y,u,z))) = f(x,y,z). [para(5(a,2),922(a,1,2)),rewrite([5(2),6(2),392(3),5(4),6(4)])]. 1073 f(x,f(y,z,x),f(y,z,u)) = f(y,z,x). [para(922(a,1),6(a,1)),flip(a)]. 1079 f(x,f(y,z,f(z,u,w)),f(x,z,u)) = f(x,z,u). [para(16(a,1),922(a,1,2)),rewrite([5(3),5(5)])]. 1082 f(x,y,f(x,z,f(y,u,f(y,w,z)))) = f(x,y,z). [para(17(a,2),922(a,1,2)),rewrite([5(3),392(4),5(5)])]. 1088 f(x,f(y,z,f(z,u,w)),f(x,z,w)) = f(x,z,w). [para(30(a,1),922(a,1,2)),rewrite([5(3),5(5)])]. 1101 f(f(x,y,z),f(y,z,u),f(x,y,z)) = f(x,y,z). [para(205(a,1),922(a,1,3)),rewrite([205(6)])]. 1136 f(x,f(y,z,u),f(x,w,f(y,z,w))) = f(x,w,f(y,z,u)). [para(922(a,1),803(a,1,3,3))]. 1140 f(f(x,y,z),f(x,y,u),f(u,w,f(x,y,z))) = f(w,f(x,y,u),f(x,y,z)). [para(922(a,1),828(a,2,3)),rewrite([6(4),5(8,R)])]. 1142 f(x,f(y,z,x),f(u,f(y,z,w),f(y,z,x))) = f(y,z,x). [para(922(a,1),874(a,1,3)),rewrite([5(3,R),15(3),5(5)]),flip(a)]. 1148 f(x,f(y,z,u),f(x,u,f(y,z,w))) = f(x,u,f(y,z,w)). [para(922(a,1),922(a,1,2)),rewrite([5(3),5(6)])]. 1149 f(x,y,f(z,u,y)) = f(u,y,f(x,z,y)). [para(933(a,1),5(a,2)),rewrite([6(2),5(3)])]. 1150 f(x,f(y,z,x),f(y,u,f(y,z,x))) = f(y,z,x). [para(19(a,1),933(a,1,3)),rewrite([5(3,R),15(3),6(4)]),flip(a)]. 1176 f(x,f(y,z,u),f(x,u,w)) = f(x,w,f(z,u,f(x,y,u))). [para(933(a,1),828(a,2,3)),rewrite([5(2,R),6(2),5(4)])]. 1181 f(x,f(y,x,z),f(y,z,u)) = f(y,x,z). [para(1057(a,1),6(a,1)),flip(a)]. 1197 f(x,f(y,z,u),f(w,x,y)) = f(w,x,f(y,z,f(x,y,u))). [para(38(a,2),1057(a,2)),rewrite([6(3),5(6,R),6(6),392(7),1072(7),5(5,R),6(5)]),flip(a)]. 1253 f(x,f(y,z,u),f(z,u,x)) = f(z,u,x). [para(1071(a,1),5(a,2)),rewrite([5(2),5(2),5(3),5(4),5(4)])]. 1254 f(x,f(y,z,u),f(x,w,f(x,z,u))) = f(x,w,f(x,z,u)). [para(1071(a,1),8(a,2,3))]. 1286 f(x,f(y,z,u),f(x,u,f(x,z,w))) = f(x,w,f(x,z,u)). [para(1071(a,1),32(a,2,3)),rewrite([6(2)])]. 1321 f(x,f(y,z,f(z,u,w)),f(x,f(y,z,u),f(z,u,w))) = f(x,f(y,z,u),f(z,u,w)). [para(654(a,1),1071(a,1,2))]. 1329 f(x,f(y,z,u),f(x,w,f(z,u,w))) = f(x,w,f(y,z,u)). [para(1071(a,1),803(a,1,3,3)),rewrite([5(2),5(2)])]. 1332 f(f(x,y,z),f(y,z,u),f(u,w,f(x,y,z))) = f(w,f(y,z,u),f(x,y,z)). [para(1071(a,1),828(a,2,3)),rewrite([5(2),5(2),6(4),5(7),5(7),5(8,R)])]. 1341 f(x,y,f(x,f(z,u,w),f(y,z,u))) = f(x,y,f(z,u,w)). [para(1071(a,1),922(a,1,2)),rewrite([5(2),5(2),5(3),392(4),5(5),5(5),5(6)])]. 1344 f(f(x,y,z),f(y,z,u),f(u,w,f(y,z,u))) = f(y,z,u). [para(1071(a,1),1057(a,1,3)),rewrite([5(2),5(2),6(3),5(4),5(4),6(5),5(7),5(7),1253(8)])]. 1349 f(x,f(x,y,z),f(y,u,f(y,z,w))) = f(x,y,z). [para(8(a,1),1073(a,1,3)),rewrite([5(1),5(5)])]. 1404 f(x,y,f(x,f(z,u,w),f(y,u,w))) = f(x,y,f(z,u,w)). [para(1071(a,1),1073(a,1,3)),rewrite([5(2),6(4),392(4),5(6)])]. 1469 f(x,y,f(z,u,y)) = f(u,y,f(z,x,y)). [para(1149(a,1),803(a,2)),rewrite([6(3),1063(5)])]. 1605 f(f(x,y,z),f(x,z,u),f(y,w,f(x,z,u))) = f(w,f(x,z,u),f(x,y,z)). [para(1181(a,1),1469(a,2,3))]. 1618 f(x,y,f(y,f(z,u,f(x,u,w)),f(x,v5,f(z,u,f(x,u,w))))) = f(x,u,f(x,y,f(z,u,w))). [para(29(a,1),812(a,2)),rewrite([6(5)])]. 1630 f(x,y,f(y,f(z,u,w),f(x,z,u))) = f(x,y,f(z,u,w)). [para(922(a,1),812(a,1,3,3)),rewrite([5(2)])]. 1856 f(x,y,f(z,x,f(y,u,f(z,y,w)))) = f(z,x,y). [para(52(a,1),874(a,2)),rewrite([5(3),392(4),813(4),5(2,R),6(2),5(4,R),6(4)]),flip(a)]. 1905 f(x,y,f(z,u,f(x,u,f(y,u,w)))) = f(x,y,u). [para(41(a,2),871(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),5(5),5(5)])]. 1906 f(x,f(y,z,u),f(y,z,f(z,u,x))) = f(z,x,f(y,z,u)). [para(628(a,1),871(a,1,3)),rewrite([6(2),5(4,R),6(4),6(6)])]. 1982 f(x,y,f(z,u,f(u,x,y))) = f(u,x,y). [para(1030(a,1),922(a,2)),rewrite([5(1,R),6(1),5(4,R),6(4),922(7),5(4,R),6(4)])]. 2276 f(x,f(y,z,f(x,y,u)),f(x,w,v5)) = f(x,y,f(x,w,f(x,v5,f(y,z,u)))). [para(54(a,1),17(a,1)),flip(a)]. 2885 f(x,f(y,z,f(u,z,w)),f(x,u,z)) = f(x,u,z). [para(1079(a,1),21(a,2)),rewrite([5(1,R),6(1),6(3),22(5),6(5)])]. 2997 f(x,f(y,z,f(x,z,u)),f(x,w,v5)) = f(x,z,f(x,w,f(x,v5,f(y,z,u)))). [para(24(a,1),57(a,1,2))]. 3270 f(x,f(y,z,x),f(u,y,z)) = f(y,z,x). [para(1050(a,1),1150(a,1,3)),rewrite([5(2),5(2),5(5),5(5),6(6),1332(6),4(4),5(2),5(2)]),flip(a)]. 3475 f(x,f(y,x,z),f(y,x,f(y,z,u))) = f(y,x,z). [para(1349(a,1),122(a,1,3)),rewrite([5(1,R),6(1),5(2,R),6(2),15(3),5(2,R),6(2),5(3,R),6(3),57(5),6(3),20(4)]),flip(a)]. 3946 f(x,f(y,x,z),f(u,y,f(y,x,w))) = f(x,z,f(u,y,f(y,x,w))). [para(2885(a,1),871(a,1,3)),rewrite([5(1,R),6(1),5(3),6(3),5(4,R),5(5,R),6(5),5(7)])]. 4005 f(x,y,f(x,f(y,z,u),f(w,z,u))) = f(x,y,f(w,z,u)). [para(1071(a,1),3475(a,1,3,3)),rewrite([5(2,R),6(2),5(4,R),6(4),57(5),20(5),5(6,R),6(6)])]. 4085 f(x,y,f(z,u,f(z,w,f(x,y,z)))) = f(x,y,z). [para(61(a,1),866(a,1,3)),rewrite([5(1),6(1),5(5),5(5)])]. 4302 f(x,y,f(x,f(y,z,u),f(w,f(y,z,u),f(y,v5,f(y,z,u))))) = f(y,z,f(x,y,u)). [para(16(a,2),816(a,2)),rewrite([6(4),5(5,R),6(5)])]. 4305 f(x,y,f(z,f(y,z,u),f(x,z,w))) = f(x,y,z). [para(30(a,2),816(a,1,3))]. 4361 f(x,f(y,z,f(z,u,w)),f(x,f(x,z,w),f(v5,f(x,z,w),f(v6,f(y,z,f(z,u,w)),f(x,z,w))))) = f(x,z,w). [para(1088(a,1),816(a,2)),rewrite([5(8),5(9,R),6(9)])]. 4461 f(x,y,f(z,f(x,z,u),f(z,y,w))) = f(x,z,y). [para(4305(a,1),5(a,2)),rewrite([5(2,R),6(2),6(4),5(5),5(5)])]. 4572 f(x,f(y,z,u),f(z,f(x,z,w),f(z,v5,f(y,z,u)))) = f(y,z,f(x,z,u)). [para(24(a,1),4461(a,2)),rewrite([6(4)])]. 5467 f(x,f(y,z,f(u,y,w)),f(u,x,y)) = f(u,x,y). [para(1856(a,1),828(a,1)),flip(a)]. 5502 f(x,y,f(z,x,f(x,u,w))) = f(x,u,f(x,w,f(z,x,y))). [para(61(a,1),1856(a,2)),rewrite([6(7),5(8,R),6(8),5(9,R),6(9),392(10),6(9),4302(10),5(4,R),6(4)])]. 5647 f(x,y,f(x,z,f(u,y,f(z,y,w)))) = f(x,z,y). [para(1905(a,1),812(a,2)),rewrite([6(7),1618(9)])]. 6261 f(x,y,f(z,u,f(z,w,f(z,x,y)))) = f(z,x,y). [para(4085(a,1),922(a,2)),rewrite([5(1),5(5),922(9),5(5)])]. 6720 f(x,f(y,x,z),f(y,x,u)) = f(y,x,f(x,u,z)). [para(70(a,1),17(a,1)),rewrite([5(2,R),6(2),20(3),5(4,R),6(4)]),flip(a)]. 7772 f(x,f(y,z,x),f(z,x,u)) = f(y,x,f(z,x,u)). [para(922(a,1),74(a,2,3)),rewrite([5(3),6(3),122(4),19(4),5(4),5(5,R)]),flip(a)]. 7788 f(x,f(y,z,x),f(u,z,x)) = f(y,x,f(u,z,x)). [para(1253(a,1),74(a,2,3)),rewrite([5(3),6(3),1030(5),5(4),5(5,R)]),flip(a)]. 8028 f(f(x,y,z),f(x,u,f(x,y,z)),f(x,z,f(x,y,w))) = f(u,f(x,y,z),f(x,w,f(x,y,z))). [para(30(a,2),7788(a,1,3)),rewrite([5(3,R),6(3),5(4),5(4),5(9,R),6(9)])]. 8369 f(x,f(y,z,u),f(x,f(x,z,w),f(v5,f(x,z,w),f(v6,f(y,z,u),f(x,z,w))))) = f(x,w,f(y,z,f(x,z,u))). [para(75(a,1),816(a,2)),rewrite([6(2),6(3),6(5),5(6),5(7,R),6(7)])]. 8635 f(x,y,f(z,u,f(x,u,f(u,w,y)))) = f(x,u,y). [back_rewrite(4361),rewrite([8369(11)])]. 8713 f(x,y,f(y,z,f(u,x,y))) = f(y,z,f(u,x,y)). [para(1253(a,1),5647(a,1,3)),rewrite([5(2),5(2),5(4),5(4),5(6,R),6(6),205(6),5(5),5(5),5(7),6(7),19(7)])]. 9281 f(f(x,y,z),f(x,z,u),f(y,w,f(y,v5,f(x,y,z)))) = f(x,y,z). [para(1181(a,1),6261(a,1,3,3,3)),rewrite([1181(9)])]. 9577 f(x,y,f(z,u,f(u,x,f(u,w,y)))) = f(u,x,y). [para(8635(a,1),922(a,2)),rewrite([5(2,R),6(2),5(6,R),6(6),922(9),5(5,R),6(5)])]. 10036 f(f(x,y,z),f(y,z,u),f(w,f(y,z,u),f(v5,f(y,z,u),f(x,y,z)))) = f(w,f(y,z,u),f(v5,f(x,y,z),f(y,z,u))). [para(1101(a,1),87(a,2,3,3)),rewrite([5(6),5(7,R),6(7),5(12,R),5(13,R),6(13)])]. 11098 f(x,y,f(z,u,f(x,w,z))) = f(x,y,f(w,z,f(x,z,u))). [para(874(a,2),105(a,2,3)),flip(a)]. 12311 f(x,y,f(y,z,f(u,x,z))) = f(x,y,z). [para(125(a,1),1469(a,2)),rewrite([20(3),15(3),5(3,R),6(3),6720(5),6(3)]),flip(a)]. 12402 f(x,y,f(x,z,f(u,z,y))) = f(x,z,y). [para(12311(a,1),474(a,2)),rewrite([5(3,R),6(3),21(5),5(4,R),6(4)])]. 12982 f(x,f(y,z,u),f(y,u,x)) = f(y,u,x). [para(1072(a,1),168(a,1,3)),rewrite([5(2),5(2),5(3),5(3),15(4),5(3),5(3)]),flip(a)]. 12992 f(x,f(y,z,u),f(x,w,f(z,u,x))) = f(x,w,f(z,u,x)). [para(3270(a,1),168(a,1,3,3)),rewrite([15(6)]),flip(a)]. 13008 f(x,f(y,z,f(y,u,w)),f(y,w,x)) = f(y,w,x). [para(1082(a,1),168(a,1,3)),rewrite([5(3),5(3),5(4),5(4),15(5),5(4),5(4)]),flip(a)]. 13139 f(x,f(y,z,x),f(z,u,x)) = f(y,x,f(z,u,x)). [para(12982(a,1),74(a,2,3)),rewrite([5(3),6(3),1030(5),5(4),5(5,R)]),flip(a)]. 13180 f(x,f(y,x,z),f(y,u,x)) = f(x,z,f(y,u,x)). [para(13139(a,1),922(a,2)),rewrite([5(2),5(2),6(3),5(4),5(4),12982(7),5(5,R),6(5)])]. 13417 f(f(x,y,f(x,z,u)),f(x,u,w),f(w,f(x,u,w),f(w,v5,f(x,y,f(x,z,u))))) = f(x,u,w). [para(13008(a,1),866(a,2)),rewrite([6(7)])]. 14376 f(x,y,f(z,u,f(y,w,z))) = f(x,y,f(w,z,f(y,z,u))). [para(828(a,1),262(a,2,3)),rewrite([5(1,R),6(1),5(4)]),flip(a)]. 14673 f(f(x,y,z),f(y,u,w),f(x,y,z)) = f(x,y,z). [para(1181(a,1),318(a,1,3)),rewrite([9281(10)])]. 14946 f(x,f(y,z,u),f(y,u,f(y,z,f(w,x,f(y,z,u))))) = f(w,f(y,z,u),f(y,x,f(y,z,u))). [para(14673(a,1),40(a,1,3)),rewrite([5(3),5(3),5(4,R),6(4),5(6),5(6),5(10),5(10),5(11,R),6(11),696(11),5(12,R),6(12),8028(12),6(9),696(9)]),flip(a)]. 14966 f(x,f(y,z,u),f(y,u,f(y,z,f(x,w,f(y,z,u))))) = f(y,u,f(y,z,f(x,w,f(y,z,u)))). [para(14673(a,1),816(a,1,3)),rewrite([6(3),5(4,R),6(4),696(4),6(7),5(8,R),6(8),696(8),5(9,R),15(9),6(7),5(8,R),6(8),696(8),5(10),5(10)]),flip(a)]. 15096 f(x,f(y,x,z),f(z,u,w)) = f(y,x,f(z,u,f(x,z,w))). [para(319(a,1),6(a,1)),rewrite([5(1,R),6(1),6(4)]),flip(a)]. 15120 f(f(x,y,z),f(u,w,f(x,y,z)),f(x,y,f(x,z,f(u,w,f(x,y,z))))) = f(x,z,f(x,y,f(u,w,f(x,y,z)))). [para(319(a,1),40(a,2)),rewrite([5(3),5(3),5(6),5(6),5(7,R),7788(7),696(5),5(6,R),6(6),14966(6),5(7),5(7),5(9),5(9),6(10)]),flip(a)]. 15153 f(f(x,y,z),f(x,u,w),f(w,f(x,u,w),f(w,v5,f(x,y,z)))) = f(u,w,f(x,y,f(x,z,w))). [para(319(a,1),866(a,2)),rewrite([5(2,R),6(2),5(3,R),6(3),6(5),6(8)])]. 15161 f(f(x,y,z),f(u,w,v5),f(x,y,z)) = f(x,y,z). [para(319(a,1),54(a,2,3)),rewrite([5(5),5(5),19(5),20(5),5(5,R),15(5),6(9),4(11),5(7,R),15(7)])]. 15213 f(x,f(y,z,u),f(z,x,u)) = f(z,x,u). [para(319(a,2),8713(a,2)),rewrite([5(4,R),6(4),5(5,R),6(5),3946(5),1982(4),15(3),5(2,R),6(2),5(4),5(4),20(4)]),flip(a)]. 15245 f(x,f(y,z,u),f(w,f(y,z,u),f(y,x,f(y,z,u)))) = f(y,u,f(y,z,f(x,w,f(y,z,u)))). [para(319(a,1),113(a,1)),rewrite([5(3),5(3),5(5),5(5),6(6),15120(8),5(6),5(6),5(10),5(10),5(11,R),6(11),5(12,R),6(12),7772(12)]),flip(a)]. 15288 f(x,y,f(z,u,f(z,y,f(z,w,x)))) = f(z,x,y). [back_rewrite(13417),rewrite([15153(9),6(2)])]. 15375 f(x,f(y,z,u),f(w,f(y,z,u),f(x,v5,f(y,z,u)))) = f(w,f(y,z,u),f(x,v5,f(y,z,u))). [para(15161(a,1),816(a,1,3)),rewrite([6(3),5(4,R),6(4),6(7),5(8,R),6(8),5(9,R),15(9),6(7),5(8,R),6(8),5(10),5(10)]),flip(a)]. 15402 f(f(x,y,z),f(u,w,f(u,v5,f(x,y,z))),f(u,f(u,w,v5),f(x,y,z))) = f(u,w,f(u,v5,f(x,y,z))). [para(15161(a,1),111(a,1)),rewrite([5(2),5(2),5(5),5(5),5(10,R),5(11,R),6(11)]),flip(a)]. 15403 f(x,f(x,y,z),f(u,w,v5)) = f(x,y,f(x,z,f(u,w,v5))). [para(15161(a,1),111(a,2)),rewrite([5(3,R),5(6),5(6),5(8),5(8),15402(8),5(6,R)]),flip(a)]. 15417 f(x,f(y,z,u),f(w,y,f(y,z,u))) = f(y,u,f(y,z,f(w,x,f(y,z,u)))). [back_rewrite(15245),rewrite([5(4,R),6(4),15375(6)])]. 15771 f(x,f(y,z,u),f(x,z,u)) = f(x,z,u). [para(15288(a,1),922(a,1,2)),rewrite([5(2),5(4)])]. 15796 f(x,f(y,z,u),f(x,y,u)) = f(x,y,u). [para(15288(a,1),2885(a,1,2))]. 15821 f(x,f(y,z,u),f(x,y,z)) = f(x,y,z). [para(15288(a,1),5467(a,1,2)),rewrite([5(2,R),6(2),5(4,R),6(4)])]. 15868 f(x,f(y,z,f(u,x,y)),f(w,u,x)) = f(x,y,f(w,u,x)). [para(12402(a,1),15288(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. 15909 f(x,f(y,z,u),f(x,y,f(z,u,w))) = f(x,y,f(z,u,w)). [para(15771(a,1),922(a,1,2)),rewrite([5(2),5(2),5(3),5(5),5(5),5(6)])]. 15921 f(x,y,f(x,f(z,u,y),f(w,z,u))) = f(x,y,f(w,z,u)). [para(15771(a,1),866(a,1,3,3)),rewrite([5(2),5(2),5(3,R),6(3),5(4,R),15403(4),5(6)])]. 15972 f(x,f(y,z,f(u,x,z)),f(w,u,x)) = f(x,z,f(w,u,x)). [para(15771(a,1),9577(a,1,3,3)),rewrite([5(2),5(2),5(4,R),5(6)])]. 16471 f(x,y,f(z,y,f(x,u,y))) = f(x,y,f(z,u,y)). [para(15(a,1),321(a,1,3)),rewrite([6(2)]),flip(a)]. 16711 f(x,y,f(z,u,f(y,w,u))) = f(y,u,f(x,y,f(z,w,u))). [para(321(a,2),74(a,1,3)),rewrite([15(2),6(2),19(5)])]. 18363 f(x,y,f(z,u,f(y,u,f(x,z,u)))) = f(x,y,u). [para(630(a,1),9577(a,1,3)),rewrite([5(1),6(1),5(2,R),6(2),5(5),5(5)])]. 18491 f(x,y,f(z,y,f(z,u,x))) = f(z,x,y). [para(18363(a,1),4461(a,2)),rewrite([5(2,R),6(2),8713(3),5(5,R),6(5),8713(6),6(6),4572(8),6(4)])]. 18837 f(x,f(y,z,u),f(w,x,f(w,y,z))) = f(w,x,f(y,z,u)). [para(847(a,1),220(a,2,3)),rewrite([1630(5),19(4)]),flip(a)]. 19724 f(x,y,f(x,z,f(x,f(y,u,w),f(u,w,v5)))) = f(x,z,f(x,y,f(u,w,v5))). [para(1136(a,1),32(a,1,3)),rewrite([5(4)]),flip(a)]. 19762 f(x,f(y,z,u),f(z,w,f(x,y,w))) = f(x,w,f(y,z,u)). [para(1149(a,1),1136(a,1,3))]. 20436 f(x,y,f(f(z,u,w),f(u,w,v5),f(x,u,f(u,w,v5)))) = f(x,f(z,u,f(u,w,v5)),f(x,y,f(u,w,v5))). [para(654(a,1),1176(a,1,2)),rewrite([6(4)]),flip(a)]. 20765 f(x,f(y,z,u),f(x,y,f(x,w,v5))) = f(x,y,f(x,w,f(x,v5,f(y,z,u)))). [para(1197(a,2),13180(a,1,2)),rewrite([5(2),5(2),5(4),15403(5),15403(4),20(3),5(7),2276(8)])]. 20959 f(x,f(y,z,u),f(w,x,f(x,z,u))) = f(w,x,f(x,z,u)). [para(1254(a,1),74(a,1,3)),rewrite([15771(3),15771(6)]),flip(a)]. 21385 f(x,f(y,z,u),f(z,w,f(x,u,w))) = f(x,w,f(y,z,u)). [para(897(a,1),1329(a,1,3))]. 21496 f(x,y,f(x,f(y,z,u),f(z,w,f(x,y,u)))) = f(x,y,f(z,w,f(x,y,u))). [para(25(a,1),1341(a,1,3)),rewrite([6(2),6(4),20(6),6(7)])]. 21883 f(x,f(y,z,x),f(u,f(w,y,z),f(y,z,x))) = f(y,z,x). [para(1344(a,1),16471(a,2)),rewrite([5(6,R),10036(8)])]. 22316 f(x,f(y,z,u),f(z,u,f(x,w,f(y,z,u)))) = f(z,u,f(x,w,f(y,z,u))). [para(1404(a,1),1142(a,1,3)),rewrite([6(2),5(3),5(3),6(6),5(7),5(7),6(10),6(12),19(12),5(11),21883(11),6(6),5(7),5(7)]),flip(a)]. 23721 f(x,y,f(x,z,f(u,w,y))) = f(x,z,f(x,y,f(z,u,w))). [para(4005(a,1),54(a,2,3)),rewrite([6(2),5(3,R),6(3),21385(4),5(4),5(4)]),flip(a)]. 23961 f(x,y,f(z,x,f(u,x,y))) = f(z,x,f(u,x,y)). [para(5502(a,2),1469(a,2)),rewrite([4(3),6(2),5(4),122(5)]),flip(a)]. 24846 f(x,f(y,z,f(x,u,y)),f(x,w,v5)) = f(x,y,f(x,w,f(x,v5,f(u,y,z)))). [para(11098(a,1),1286(a,1,3,3)),rewrite([1286(6),2997(4)]),flip(a)]. 25097 f(x,y,f(x,z,f(u,w,f(x,z,y)))) = f(x,y,f(z,u,f(x,z,w))). [para(15096(a,1),1329(a,2)),rewrite([5(2),5(2),5(3),5(3),15403(5),20765(6),6(4),19724(6),5(7,R),6(7)])]. 25130 f(x,f(y,z,u),f(y,w,f(y,z,u))) = f(y,u,f(x,z,f(y,z,w))). [back_rewrite(15417),rewrite([5(3,R),6(3),5(6,R),6(6),25097(8),5(6,R),6(6)])]. 25132 f(x,f(y,z,u),f(y,u,f(x,z,f(y,z,w)))) = f(y,u,f(x,z,f(y,z,w))). [back_rewrite(14966),rewrite([25097(5),5(3,R),6(3),25097(9),5(7,R),6(7)])]. 25133 f(x,f(y,z,u),f(w,y,f(y,z,u))) = f(y,u,f(w,z,f(y,z,x))). [back_rewrite(14946),rewrite([5(3,R),6(3),25097(5),5(3,R),6(3),25132(5),5(6,R),6(6)]),flip(a)]. 25262 f(x,f(y,z,u),f(y,u,f(w,y,z))) = f(y,u,f(w,z,f(y,z,x))). [back_rewrite(1036),rewrite([25130(4)]),flip(a)]. 25278 f(x,f(y,z,f(z,u,w)),f(x,v5,f(z,u,w))) = f(x,v5,f(z,w,f(x,u,f(y,z,u)))). [back_rewrite(20436),rewrite([25133(5),205(2)]),flip(a)]. 25399 f(x,f(y,z,u),f(z,w,f(x,u,f(y,z,u)))) = f(x,f(y,z,u),f(z,u,w)). [back_rewrite(1321),rewrite([25278(6)])]. 26704 f(x,f(y,z,u),f(x,z,f(x,u,w))) = f(x,w,f(x,z,u)). [para(15868(a,1),12992(a,2)),rewrite([5(2,R),6(2),5(4),24846(5),814(5),5(5)])]. 27091 f(x,f(y,z,f(z,u,x)),f(u,x,w)) = f(z,x,f(u,x,w)). [para(15972(a,1),5(a,2)),rewrite([5(1),5(3),5(3),5(4),5(5),5(5),5(6,R),6(6)])]. 27912 f(f(x,y,z),f(y,z,u),f(w,x,f(y,z,u))) = f(w,f(y,z,u),f(x,y,z)). [para(15909(a,1),16711(a,2,3)),rewrite([5(5,R),15821(5),19(5)]),flip(a)]. 28511 f(f(x,y,z),f(y,z,u),f(y,z,w)) = f(w,f(x,y,z),f(y,z,u)). [para(15771(a,1),18837(a,1,3)),rewrite([5(3),5(3)])]. 28512 f(f(x,y,z),f(x,z,u),f(x,z,w)) = f(w,f(x,y,z),f(x,z,u)). [para(15796(a,1),18837(a,1,3)),rewrite([5(3),5(3)])]. 28513 f(f(x,y,z),f(x,y,u),f(x,y,w)) = f(w,f(x,y,z),f(x,y,u)). [para(15821(a,1),18837(a,1,3)),rewrite([5(3),5(3)])]. 28531 f(f(x,y,z),f(u,x,y),f(u,x,z)) = f(x,z,f(u,x,y)). [para(1906(a,1),18837(a,2)),rewrite([5(5),5(5),922(6),6(5),28513(5)])]. 28539 f(x,f(y,z,f(x,u,w)),f(x,w,f(y,u,w))) = f(x,w,f(y,z,f(x,u,w))). [para(14376(a,1),18837(a,1,3)),rewrite([6(2),6(3),5(5,R),6(5),16471(5),5(3,R),6(3),6(7),5(8,R),6(8)])]. 28566 f(f(x,y,z),f(x,y,u),f(y,z,u)) = f(y,u,f(x,y,z)). [para(28531(a,1),5(a,2))]. 28568 f(f(x,y,z),f(x,z,u),f(y,z,u)) = f(y,z,f(x,z,u)). [para(5(a,2),28531(a,1,1)),rewrite([5(2),6(2),5(3),6(3),5(5),6(5),5(6,R),6(6)])]. 29055 f(f(x,y,z),f(u,x,z),f(u,w,f(x,y,z))) = f(w,f(u,x,z),f(x,y,z)). [para(12982(a,1),28566(a,1,2)),rewrite([6(2),5(3),5(5),5(6,R),5(7,R),6(7),15213(7),5(5),6(7)]),flip(a)]. 29200 f(f(x,y,z),f(x,u,y),f(u,y,z)) = f(u,y,f(x,y,z)). [para(28568(a,1),19(a,1,3)),rewrite([28511(5),28568(8)])]. 29568 f(x,f(y,z,u),f(z,w,f(y,x,w))) = f(y,f(z,x,w),f(x,w,f(y,z,u))). [para(29200(a,1),200(a,1,2)),rewrite([5(2,R),6(2),5(5,R),6(5),5(6),5(6),5(8,R),6(8),6(10),21496(11),5(10,R),6(10),27912(10),6(7),25278(8),25399(6),5(6,R),6(6),5(8,R),6(8),5(9),5(9),5(12,R),28566(12),25262(10),5(6)]),flip(a)]. 30122 f(x,f(y,z,u),f(y,u,f(x,z,w))) = f(y,u,f(x,z,w)). [back_rewrite(29568),rewrite([5(2,R),6(2),19762(4),5(3,R),6(3)]),flip(a)]. 30898 f(x,y,f(z,y,f(u,x,z))) = f(x,z,y). [para(20959(a,1),71(a,2)),rewrite([5(3),5(4,R),6(4),5(5,R),6(5),23961(5),5(5),5(5),5(6,R),3270(6)])]. 32772 f(x,f(y,z,u),f(x,w,y)) = f(x,f(w,z,u),f(x,w,y)). [para(23721(a,1),1286(a,1,3)),rewrite([26704(5),5(4)]),flip(a)]. 32850 f(x,f(y,z,u),f(w,x,u)) = f(x,f(w,y,z),f(w,x,u)). [para(32772(a,1),5(a,2)),rewrite([5(2),5(3),5(4),5(4),5(5)]),flip(a)]. 33448 f(f(x,y,z),f(x,y,u),f(w,v5,f(x,y,u))) = f(f(x,y,z),f(w,v5,u),f(x,y,u)). [para(922(a,1),32850(a,1,3)),rewrite([6(5),5(7),5(7),922(10)])]. 33505 f(f(x,y,z),f(x,z,u),f(w,v5,f(x,z,u))) = f(f(x,y,z),f(w,v5,u),f(x,z,u)). [para(12982(a,1),32850(a,1,3)),rewrite([6(5),5(7),5(7),12982(10)])]. 33573 f(f(x,y,z),f(y,u,w),f(x,z,u)) = f(w,f(x,z,u),f(x,y,z)). [back_rewrite(1605),rewrite([33505(5),6(2)])]. 35717 f(f(x,y,z),f(u,z,w),f(x,y,u)) = f(w,f(x,y,z),f(x,y,u)). [para(1148(a,1),27091(a,1,2)),rewrite([5(4,R),922(4),6(4),1140(5),6(7),33448(8),5(5)]),flip(a)]. 36738 f(f(x,y,z),f(u,x,w),f(u,w,y)) = f(u,w,f(x,y,z)). [para(30122(a,1),18837(a,2)),rewrite([5(2,R),6(2),5(5),5(5),12982(6),6(5),28512(5),5(5,R),6(5)])]. 36780 f(x,f(y,z,u),f(y,z,w)) = f(y,z,f(w,u,x)). [para(36738(a,1),5(a,1)),rewrite([6(5),35717(6)]),flip(a)]. 36790 f(x,f(y,z,u),f(z,w,u)) = f(z,u,f(y,x,f(z,w,u))). [para(19(a,1),36738(a,1,3)),rewrite([6(2),5(3,R),6(3),5(5),6(5),29055(5),6(5)])]. 36856 f(x,f(y,z,u),f(y,w,z)) = f(y,z,f(w,u,x)). [para(36738(a,1),18491(a,2)),rewrite([5(7,R),30898(9),33573(4)])]. 36866 f(x,y,f(z,u,f(x,w,y))) = f(x,y,f(z,u,w)). [para(1341(a,1),36738(a,2)),rewrite([5(2),5(2),36780(3),5(1),6(1),4(3),5(5),5(5),15403(5),36780(4),5(2),6(2),20(2)])]. 36880 f(x,y,f(z,u,f(x,y,w))) = f(x,y,f(z,u,w)). [para(15921(a,1),36738(a,2)),rewrite([5(2),5(2),36780(3),5(1),6(1),4(3),5(5,R),15403(5),36780(4),5(2),6(2),20(2),5(4),5(4)])]. 37170 f(x,f(y,z,u),f(z,u,w)) = f(z,u,f(x,y,w)). [back_rewrite(36790),rewrite([6(2),6(4),5(5,R),6(5),36880(6)])]. 37187 f(x,f(y,z,f(x,u,w)),f(x,w,f(y,u,w))) = f(x,w,f(y,z,u)). [back_rewrite(28539),rewrite([36866(8)])]. 37194 f(x,y,f(z,u,f(w,x,y))) = f(x,y,f(z,w,u)). [back_rewrite(22316),rewrite([36866(5),37170(3)]),flip(a)]. 38298 f(x,f(y,z,f(u,w,v5)),f(u,v5,f(y,w,v5))) = f(y,f(u,w,v5),f(x,v5,z)). [para(897(a,1),36856(a,1,3)),rewrite([6(2),5(7)])]. 38353 f(x,f(y,z,u),f(y,w,u)) = f(y,u,f(x,w,z)). [back_rewrite(37187),rewrite([38298(5),6(2)])]. 38852 f(x,f(y,z,u),f(w,z,u)) = f(z,u,f(w,x,y)). [para(37170(a,1),36780(a,2)),rewrite([6(2),6(4),38353(5),5(4)])]. 38912 $F # answer(dist_long). [back_rewrite(10),rewrite([38852(13),5(9),37194(10),5(6,R),6(6)]),xx(a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=791. Generated=3335027. Kept=38902. proofs=3. Usable=434. Sos=15970. Demods=9648. Limbo=58, Disabled=22447. Hints=0. Kept_by_rule=0, Deleted_by_rule=368323. Forward_subsumed=2215058. Back_subsumed=2521. Sos_limit_deleted=712741. Sos_displaced=2509. Sos_removed=0. New_demodulators=28058 (2 lex), Back_demodulated=17410. Back_unit_deleted=0. Demod_attempts=67977586. Demod_rewrites=25488863. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=1. Megabytes=32.77. User_CPU=657.98, System_CPU=1.04, Wall_clock=660. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED Exiting with 3 proofs. Process 12007 exit (max_proofs) Wed Feb 25 10:09:01 2009