============================== Prover9 =============================== Prover9 (64) version Aug-2007, Aug 2007. Process 26314 was started by veroff on titan, Sat Jan 19 14:19:06 2008 The command was "prover9 -f 4.8.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file 4.8.in clear(auto). % clear(auto) -> clear(auto_inference). % clear(auto_inference) -> clear(predicate_elim). % clear(auto_inference) -> assign(eq_defs, pass). % clear(auto) -> clear(auto_limits). % clear(auto_limits) -> assign(max_weight, 2147483647). % clear(auto_limits) -> assign(sos_limit, -1). % clear(auto) -> clear(auto_denials). % clear(auto) -> clear(auto_process). op(400,infix,[^,v,"->","=>",*]). op(200,prefix,[~,-]). lex([0,1,*,^,=>,->,v,~,-]). assign(order,kbo). set(lex_order_vars). set(paramodulation). % set(paramodulation) -> set(back_demod). set(para_units_only). % set(para_units_only) -> assign(para_lit_limit, 1). clear(back_demod). set(hyper_resolution). % set(hyper_resolution) -> set(pos_hyper_resolution). set(auto_denials). set(restrict_denials). formulas(assumptions). (x v y) v z = x v (y v z) # label("(D1)"). (x ^ y) ^ z = x ^ (y ^ z) # label("(D2)"). x v y = y v x # label("(D3)"). x ^ y = y ^ x # label("(D4)"). x v (x ^ y) = x # label("(D5)"). x ^ (x v y) = x # label("(D6)"). (x => y) => ((y => z) => (x => z)) = 1 # label("(BCK1)"). 1 => x = x # label("(BCK2)"). x => 1 = 1 # label("(BCK3)"). x => y != 1 | y => x != 1 | x = y # label("(BCK4)"). x * 1 = x # label("(M1)"). x * y = y * x # label("(M2)"). (x * y) * z = x * (y * z) # label("(M3)"). (x * y) => z = x => (y => z) # label("(P)"). x ^ 1 = x # label("(D10)"). x ^ ((x => y) => y) = x # label("(3.7)"). (x ^ y) => y = 1 # label("(3.11)"). x v 0 = x # label("(D9)"). x -> y = x => (x => y) # label("(-> def)"). ~ x = x => 0 # label("(~ def)"). -x = x => (x => 0) # label("(- def)"). x => (x => (x => y)) = x => (x => y) # label("(E_2)"). (x v y) ^ (x v z) = x v (y ^ z) # label("(D7)"). (x ^ y) v (x ^ z) = x ^ (y v z) # label("(D8)"). ~ ~ x = x # label("(DN)"). (x -> y) ^ (~ y -> ~ x) = x => y # label("(N)"). (x => y) => ((z => x) => (z => y)) = 1 # label("(BCK1')"). x => ((x => y) => y) = 1 # label("(BCK5)"). x => x = 1 # label("(3.16)"). x => (y => x) = 1 # label("(3.17)"). x => (y => z) = y => (x => z) # label("(3.18)"). (x * y) v (x * z) = x * (y v z) # label("(4.1)"). (x => y) ^ (x => z) = x => (y ^ z) # label("(4.2)"). (x * (x => y)) v y = y # label("(4.3)"). (x => y) ^ (z => y) = (x v z) => y # label("(4.4)"). ((x => y) * z) => (x => (y * z)) = 1 # label("(4.5)"). end_of_list. formulas(assumptions). (x => y) ^ y = y # label("(3.13)"). (x v y) => y = x => y # label("(4.6)"). x -> (y => z) = y => (x -> z) # label("(4.7)"). x ^ (~ x => y) = x # label("(4.8)"). x -> ((y v x) -> z) = x -> z # label("(4.9)"). x -> (~ x v y) = x -> y # label("(4.10)"). x -> x = 1 # label("(N2)"). (x -> y) ^ (x -> z) = x -> (y ^ z) # label("(N5)"). (x -> y) ^ (~ x v y) = ~ x v y # label("(N3)"). end_of_list. formulas(goals). (x ^ y) -> z = x -> (y -> z) # label("(N6)"). end_of_list. formulas(hints). x = (x ^ y) v x. (x ^ y) v x = x. x = 1 ^ x. 1 ^ x = x. (x * y) => (x => (y => z)) = (x * y) -> z. x => (y -> z) = y => (x => (y => z)). x => (y => (x => z)) = y => (x -> z). 1 ^ (x => y) = x => (x ^ y). x => (x ^ y) = 1 ^ (x => y). x -> (y -> z) = y => (x -> (y => z)). x => (y -> (x => z)) = y -> (x -> z). x -> ((x v y) -> z) = x -> z. x v (y => x) = y => x. x => (x ^ y) = x => y. x -> ((y => x) -> z) = x -> z. x => (x => (y -> z)) = y -> (x -> z). x -> (y -> z) = y -> (x -> z). (x v y) -> (y -> z) = y -> z. (x v y) -> (x -> z) = x -> z. x -> ((x ^ y) -> z) = (x ^ y) -> z. x -> ((y * (y => x)) -> z) = (y * (y => x)) -> z. (x * y) -> z = x => (y => (x => (y => z))). x => (y => (x => (y => z))) = (x * y) -> z. x => (x => (y -> z)) = (x * y) -> z. (x * y) -> z = x -> (y -> z). x -> (y -> ((y => x) -> z)) = (y * (y => x)) -> z. (x * (x => y)) -> z = x -> (y -> ((x => y) -> z)). x -> (y -> ((x => y) -> z)) = (x * (x => y)) -> z. x -> (y -> z) = (x * (x => y)) -> z. (x * (x => y)) -> z = x -> (y -> z). x -> (y -> z) = x -> ((x => y) -> z). x -> ((x => y) -> z) = x -> (y -> z). x -> ((x => y) -> z) = x -> ((x ^ y) -> z). x -> ((x ^ y) -> z) = x -> (y -> z). x -> (y -> z) = (x ^ y) -> z. end_of_list. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: 1 (x ^ y) -> z = x -> (y -> z) # label("(N6)") # 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). (x v y) v z = x v (y v z) # label("(D1)"). [assumption]. (x ^ y) ^ z = x ^ (y ^ z) # label("(D2)"). [assumption]. x v y = y v x # label("(D3)"). [assumption]. x ^ y = y ^ x # label("(D4)"). [assumption]. x v (x ^ y) = x # label("(D5)"). [assumption]. x ^ (x v y) = x # label("(D6)"). [assumption]. (x => y) => ((y => z) => (x => z)) = 1 # label("(BCK1)"). [assumption]. 1 => x = x # label("(BCK2)"). [assumption]. x => 1 = 1 # label("(BCK3)"). [assumption]. x => y != 1 | y => x != 1 | x = y # label("(BCK4)"). [assumption]. x * 1 = x # label("(M1)"). [assumption]. x * y = y * x # label("(M2)"). [assumption]. (x * y) * z = x * (y * z) # label("(M3)"). [assumption]. (x * y) => z = x => (y => z) # label("(P)"). [assumption]. x ^ 1 = x # label("(D10)"). [assumption]. x ^ ((x => y) => y) = x # label("(3.7)"). [assumption]. (x ^ y) => y = 1 # label("(3.11)"). [assumption]. x v 0 = x # label("(D9)"). [assumption]. x -> y = x => (x => y) # label("(-> def)"). [assumption]. ~ x = x => 0 # label("(~ def)"). [assumption]. -x = x => (x => 0) # label("(- def)"). [assumption]. x => (x => (x => y)) = x => (x => y) # label("(E_2)"). [assumption]. (x v y) ^ (x v z) = x v (y ^ z) # label("(D7)"). [assumption]. (x ^ y) v (x ^ z) = x ^ (y v z) # label("(D8)"). [assumption]. ~ ~ x = x # label("(DN)"). [assumption]. (x -> y) ^ (~ y -> ~ x) = x => y # label("(N)"). [assumption]. (x => y) => ((z => x) => (z => y)) = 1 # label("(BCK1')"). [assumption]. x => ((x => y) => y) = 1 # label("(BCK5)"). [assumption]. x => x = 1 # label("(3.16)"). [assumption]. x => (y => x) = 1 # label("(3.17)"). [assumption]. x => (y => z) = y => (x => z) # label("(3.18)"). [assumption]. (x * y) v (x * z) = x * (y v z) # label("(4.1)"). [assumption]. (x => y) ^ (x => z) = x => (y ^ z) # label("(4.2)"). [assumption]. (x * (x => y)) v y = y # label("(4.3)"). [assumption]. (x => y) ^ (z => y) = (x v z) => y # label("(4.4)"). [assumption]. ((x => y) * z) => (x => (y * z)) = 1 # label("(4.5)"). [assumption]. (x => y) ^ y = y # label("(3.13)"). [assumption]. (x v y) => y = x => y # label("(4.6)"). [assumption]. x -> (y => z) = y => (x -> z) # label("(4.7)"). [assumption]. x ^ (~ x => y) = x # label("(4.8)"). [assumption]. x -> ((y v x) -> z) = x -> z # label("(4.9)"). [assumption]. x -> (~ x v y) = x -> y # label("(4.10)"). [assumption]. x -> x = 1 # label("(N2)"). [assumption]. (x -> y) ^ (x -> z) = x -> (y ^ z) # label("(N5)"). [assumption]. (x -> y) ^ (~ x v y) = ~ x v y # label("(N3)"). [assumption]. (c1 ^ c2) -> c3 != c1 -> (c2 -> c3) # label("(N6)"). [deny(1)]. end_of_list. formulas(demodulators). end_of_list. % 35 hints input. Auto_denials: % copying label "(N6)" to answer in negative clause Term ordering decisions: Function symbol KB weights: 0=1. 1=1. c1=1. c2=1. c3=1. *=1. ^=1. =>=1. ->=1. v=1. ~=1. -=1. Predicate symbol precedence: predicate_order([ = ]). Function symbol precedence: function_order([ 0, 1, c1, c2, c3, *, ^, =>, ->, v, ~, - ]). Skipping inverse_order, because there is a function_order (lex) command. % Operation v is commutative; C redundancy checks enabled. % Operation ^ is commutative; C redundancy checks enabled. % Operation * is commutative; C redundancy checks enabled. restricted denial: (wt=11): 50 (c1 ^ c2) -> c3 != c1 -> (c2 -> c3) # label("(N6)") # answer("(N6)"). [deny(1)]. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). 50 (c1 ^ c2) -> c3 != c1 -> (c2 -> c3) # label("(N6)") # answer("(N6)"). [deny(1)]. end_of_list. formulas(sos). 2 (x v y) v z = x v (y v z) # label("(D1)"). [assumption]. 3 (x ^ y) ^ z = x ^ (y ^ z) # label("(D2)"). [assumption]. 4 x v y = y v x # label("(D3)"). [assumption]. 5 x ^ y = y ^ x # label("(D4)"). [assumption]. 6 x v (x ^ y) = x # label("(D5)"). [assumption]. 7 x ^ (x v y) = x # label("(D6)"). [assumption]. 8 (x => y) => ((y => z) => (x => z)) = 1 # label("(BCK1)"). [assumption]. 9 1 => x = x # label("(BCK2)"). [assumption]. 10 x => 1 = 1 # label("(BCK3)"). [assumption]. 11 x => y != 1 | y => x != 1 | x = y # label("(BCK4)"). [assumption]. 12 x * 1 = x # label("(M1)"). [assumption]. 13 x * y = y * x # label("(M2)"). [assumption]. 14 (x * y) * z = x * (y * z) # label("(M3)"). [assumption]. 15 (x * y) => z = x => (y => z) # label("(P)"). [assumption]. 16 x ^ 1 = x # label("(D10)"). [assumption]. 17 x ^ ((x => y) => y) = x # label("(3.7)"). [assumption]. 18 (x ^ y) => y = 1 # label("(3.11)"). [assumption]. 19 x v 0 = x # label("(D9)"). [assumption]. 21 x => (x => y) = x -> y. [copy(20),flip(a)]. 23 x => 0 = ~ x. [copy(22),flip(a)]. 25 x => (x => 0) = -x. [copy(24),flip(a)]. 26 x => (x => (x => y)) = x => (x => y) # label("(E_2)"). [assumption]. 27 (x v y) ^ (x v z) = x v (y ^ z) # label("(D7)"). [assumption]. 28 (x ^ y) v (x ^ z) = x ^ (y v z) # label("(D8)"). [assumption]. 29 ~ ~ x = x # label("(DN)"). [assumption]. 30 (x -> y) ^ (~ y -> ~ x) = x => y # label("(N)"). [assumption]. 31 (x => y) => ((z => x) => (z => y)) = 1 # label("(BCK1')"). [assumption]. 32 x => ((x => y) => y) = 1 # label("(BCK5)"). [assumption]. 33 x => x = 1 # label("(3.16)"). [assumption]. 34 x => (y => x) = 1 # label("(3.17)"). [assumption]. 35 x => (y => z) = y => (x => z) # label("(3.18)"). [assumption]. 36 (x * y) v (x * z) = x * (y v z) # label("(4.1)"). [assumption]. 37 (x => y) ^ (x => z) = x => (y ^ z) # label("(4.2)"). [assumption]. 38 (x * (x => y)) v y = y # label("(4.3)"). [assumption]. 39 (x => y) ^ (z => y) = (x v z) => y # label("(4.4)"). [assumption]. 40 ((x => y) * z) => (x => (y * z)) = 1 # label("(4.5)"). [assumption]. 41 (x => y) ^ y = y # label("(3.13)"). [assumption]. 42 (x v y) => y = x => y # label("(4.6)"). [assumption]. 43 x -> (y => z) = y => (x -> z) # label("(4.7)"). [assumption]. 44 x ^ (~ x => y) = x # label("(4.8)"). [assumption]. 45 x -> ((y v x) -> z) = x -> z # label("(4.9)"). [assumption]. 46 x -> (~ x v y) = x -> y # label("(4.10)"). [assumption]. 47 x -> x = 1 # label("(N2)"). [assumption]. 48 (x -> y) ^ (x -> z) = x -> (y ^ z) # label("(N5)"). [assumption]. 49 (x -> y) ^ (~ x v y) = ~ x v y # label("(N3)"). [assumption]. end_of_list. formulas(demodulators). end_of_list. % 35 hints processed (9 are redundant). ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.00 seconds. given #1 (I,wt=11): 2 (x v y) v z = x v (y v z) # label("(D1)"). [assumption]. given #2 (I,wt=11): 3 (x ^ y) ^ z = x ^ (y ^ z) # label("(D2)"). [assumption]. given #3 (I,wt=7): 4 x v y = y v x # label("(D3)"). [assumption]. given #4 (I,wt=7): 5 x ^ y = y ^ x # label("(D4)"). [assumption]. given #5 (I,wt=7): 6 x v (x ^ y) = x # label("(D5)"). [assumption]. given #6 (I,wt=7): 7 x ^ (x v y) = x # label("(D6)"). [assumption]. given #7 (I,wt=13): 8 (x => y) => ((y => z) => (x => z)) = 1 # label("(BCK1)"). [assumption]. given #8 (I,wt=5): 9 1 => x = x # label("(BCK2)"). [assumption]. given #9 (I,wt=5): 10 x => 1 = 1 # label("(BCK3)"). [assumption]. given #10 (I,wt=13): 11 x => y != 1 | y => x != 1 | x = y # label("(BCK4)"). [assumption]. given #11 (I,wt=5): 12 x * 1 = x # label("(M1)"). [assumption]. given #12 (I,wt=7): 13 x * y = y * x # label("(M2)"). [assumption]. given #13 (I,wt=11): 14 (x * y) * z = x * (y * z) # label("(M3)"). [assumption]. given #14 (I,wt=11): 15 (x * y) => z = x => (y => z) # label("(P)"). [assumption]. given #15 (I,wt=5): 16 x ^ 1 = x # label("(D10)"). [assumption]. given #16 (I,wt=9): 17 x ^ ((x => y) => y) = x # label("(3.7)"). [assumption]. given #17 (I,wt=7): 18 (x ^ y) => y = 1 # label("(3.11)"). [assumption]. given #18 (I,wt=5): 19 x v 0 = x # label("(D9)"). [assumption]. given #19 (I,wt=9): 21 x => (x => y) = x -> y. [copy(20),flip(a)]. given #20 (I,wt=6): 23 x => 0 = ~ x. [copy(22),flip(a)]. given #21 (I,wt=8): 25 x => (x => 0) = -x. [copy(24),flip(a)]. given #22 (I,wt=13): 26 x => (x => (x => y)) = x => (x => y) # label("(E_2)"). [assumption]. given #23 (I,wt=13): 27 (x v y) ^ (x v z) = x v (y ^ z) # label("(D7)"). [assumption]. given #24 (I,wt=13): 28 (x ^ y) v (x ^ z) = x ^ (y v z) # label("(D8)"). [assumption]. given #25 (I,wt=5): 29 ~ ~ x = x # label("(DN)"). [assumption]. given #26 (I,wt=13): 30 (x -> y) ^ (~ y -> ~ x) = x => y # label("(N)"). [assumption]. given #27 (I,wt=13): 31 (x => y) => ((z => x) => (z => y)) = 1 # label("(BCK1')"). [assumption]. given #28 (I,wt=9): 32 x => ((x => y) => y) = 1 # label("(BCK5)"). [assumption]. given #29 (I,wt=5): 33 x => x = 1 # label("(3.16)"). [assumption]. given #30 (I,wt=7): 34 x => (y => x) = 1 # label("(3.17)"). [assumption]. given #31 (I,wt=11): 35 x => (y => z) = y => (x => z) # label("(3.18)"). [assumption]. given #32 (I,wt=13): 36 (x * y) v (x * z) = x * (y v z) # label("(4.1)"). [assumption]. given #33 (I,wt=13): 37 (x => y) ^ (x => z) = x => (y ^ z) # label("(4.2)"). [assumption]. given #34 (I,wt=9): 38 (x * (x => y)) v y = y # label("(4.3)"). [assumption]. given #35 (I,wt=13): 39 (x => y) ^ (z => y) = (x v z) => y # label("(4.4)"). [assumption]. given #36 (I,wt=13): 40 ((x => y) * z) => (x => (y * z)) = 1 # label("(4.5)"). [assumption]. given #37 (I,wt=7): 41 (x => y) ^ y = y # label("(3.13)"). [assumption]. given #38 (I,wt=9): 42 (x v y) => y = x => y # label("(4.6)"). [assumption]. given #39 (I,wt=11): 43 x -> (y => z) = y => (x -> z) # label("(4.7)"). [assumption]. given #40 (I,wt=8): 44 x ^ (~ x => y) = x # label("(4.8)"). [assumption]. given #41 (I,wt=11): 45 x -> ((y v x) -> z) = x -> z # label("(4.9)"). [assumption]. given #42 (I,wt=10): 46 x -> (~ x v y) = x -> y # label("(4.10)"). [assumption]. given #43 (I,wt=5): 47 x -> x = 1 # label("(N2)"). [assumption]. given #44 (I,wt=13): 48 (x -> y) ^ (x -> z) = x -> (y ^ z) # label("(N5)"). [assumption]. given #45 (I,wt=13): 49 (x -> y) ^ (~ x v y) = ~ x v y # label("(N3)"). [assumption]. given #46 (H,wt=5): 114 1 ^ x = x. [para(16(a,1),5(a,1)),flip(a)]. given #47 (H,wt=7): 69 (x ^ y) v x = x. [para(6(a,1),4(a,1)),flip(a)]. given #48 (H,wt=9): 787 x v (y => x) = y => x. [para(41(a,1),69(a,1,1))]. given #49 (H,wt=11): 449 x => (x ^ y) = 1 ^ (x => y). [para(33(a,1),37(a,1,1)),flip(a)]. given #50 (H,wt=9): 897 x => (x ^ y) = x => y. [para(449(a,2),114(a,1))]. given #51 (H,wt=11): 678 x -> ((x v y) -> z) = x -> z. [para(4(a,1),45(a,1,2,1))]. given #52 (H,wt=11): 983 x -> ((y => x) -> z) = x -> z. [para(787(a,1),678(a,1,2,1))]. given #53 (H,wt=13): 370 x => (y => (x => z)) = y => (x -> z). [para(21(a,1),35(a,1,2)),flip(a)]. given #54 (H,wt=13): 647 x => (y -> (x => z)) = y -> (x -> z). [para(21(a,1),43(a,1,2)),flip(a)]. given #55 (H,wt=13): 1138 x => (x => (y -> z)) = y -> (x -> z). [para(43(a,1),647(a,1,2))]. given #56 (H,wt=11): 1172 x -> (y -> z) = y -> (x -> z). [para(1138(a,1),21(a,1))]. given #57 (H,wt=11): 1225 (x v y) -> (y -> z) = y -> z. [para(1172(a,1),45(a,1))]. given #58 (H,wt=11): 1235 (x v y) -> (x -> z) = x -> z. [para(1172(a,1),678(a,1))]. given #59 (H,wt=13): 1247 x -> ((x ^ y) -> z) = (x ^ y) -> z. [para(6(a,1),1225(a,1,1))]. given #60 (H,wt=15): 144 (x * y) => (x => (y => z)) = (x * y) -> z. [para(15(a,1),21(a,1,2))]. given #61 (H,wt=15): 1402 x => (y => (x => (y => z))) = (x * y) -> z. [para(144(a,1),15(a,1)),flip(a)]. given #62 (H,wt=13): 1560 x => (x => (y -> z)) = (x * y) -> z. [para(370(a,1),1402(a,1,2))]. given #63 (H,wt=11): 1587 (x * y) -> z = x -> (y -> z). [para(1560(a,1),21(a,1))]. given #64 (H,wt=17): 1286 x -> ((y * (y => x)) -> z) = (y * (y => x)) -> z. [para(38(a,1),1235(a,1,1))]. given #65 (H,wt=17): 1794 x -> (y -> ((y => x) -> z)) = (y * (y => x)) -> z. [para(1587(a,1),1286(a,1,2))]. given #66 (H,wt=17): 1878 x -> (y -> ((x => y) -> z)) = (x * (x => y)) -> z. [para(1794(a,1),1172(a,1)),flip(a)]. given #67 (H,wt=13): 1971 (x * (x => y)) -> z = x -> (y -> z). [para(983(a,1),1878(a,1,2)),flip(a)]. given #68 (H,wt=13): 2100 x -> ((x => y) -> z) = x -> (y -> z). [para(1971(a,1),1587(a,1)),flip(a)]. given #69 (H,wt=15): 2153 x -> ((x => y) -> z) = x -> ((x ^ y) -> z). [para(897(a,1),2100(a,1,2,1))]. given #70 (H,wt=13): 2337 x -> ((x ^ y) -> z) = x -> (y -> z). [para(2153(a,1),2100(a,1))]. -------- Proof 1 -------- "(N6)". ============================== PROOF ================================= % Proof 1 at 0.09 (+ 0.00) seconds: "(N6)". % Length of proof is 43. % Level of proof is 14. % Maximum clause weight is 17. % Given clauses 70. 1 (x ^ y) -> z = x -> (y -> z) # label("(N6)") # label(non_clause) # label(goal). [goal]. 4 x v y = y v x # label("(D3)"). [assumption]. 5 x ^ y = y ^ x # label("(D4)"). [assumption]. 6 x v (x ^ y) = x # label("(D5)"). [assumption]. 15 (x * y) => z = x => (y => z) # label("(P)"). [assumption]. 16 x ^ 1 = x # label("(D10)"). [assumption]. 20 x -> y = x => (x => y) # label("(-> def)"). [assumption]. 21 x => (x => y) = x -> y. [copy(20),flip(a)]. 33 x => x = 1 # label("(3.16)"). [assumption]. 35 x => (y => z) = y => (x => z) # label("(3.18)"). [assumption]. 37 (x => y) ^ (x => z) = x => (y ^ z) # label("(4.2)"). [assumption]. 38 (x * (x => y)) v y = y # label("(4.3)"). [assumption]. 41 (x => y) ^ y = y # label("(3.13)"). [assumption]. 43 x -> (y => z) = y => (x -> z) # label("(4.7)"). [assumption]. 45 x -> ((y v x) -> z) = x -> z # label("(4.9)"). [assumption]. 50 (c1 ^ c2) -> c3 != c1 -> (c2 -> c3) # label("(N6)") # answer("(N6)"). [deny(1)]. 69 (x ^ y) v x = x. [para(6(a,1),4(a,1)),flip(a)]. 114 1 ^ x = x. [para(16(a,1),5(a,1)),flip(a)]. 144 (x * y) => (x => (y => z)) = (x * y) -> z. [para(15(a,1),21(a,1,2))]. 370 x => (y => (x => z)) = y => (x -> z). [para(21(a,1),35(a,1,2)),flip(a)]. 449 x => (x ^ y) = 1 ^ (x => y). [para(33(a,1),37(a,1,1)),flip(a)]. 647 x => (y -> (x => z)) = y -> (x -> z). [para(21(a,1),43(a,1,2)),flip(a)]. 678 x -> ((x v y) -> z) = x -> z. [para(4(a,1),45(a,1,2,1))]. 787 x v (y => x) = y => x. [para(41(a,1),69(a,1,1))]. 897 x => (x ^ y) = x => y. [para(449(a,2),114(a,1))]. 983 x -> ((y => x) -> z) = x -> z. [para(787(a,1),678(a,1,2,1))]. 1138 x => (x => (y -> z)) = y -> (x -> z). [para(43(a,1),647(a,1,2))]. 1172 x -> (y -> z) = y -> (x -> z). [para(1138(a,1),21(a,1))]. 1225 (x v y) -> (y -> z) = y -> z. [para(1172(a,1),45(a,1))]. 1235 (x v y) -> (x -> z) = x -> z. [para(1172(a,1),678(a,1))]. 1247 x -> ((x ^ y) -> z) = (x ^ y) -> z. [para(6(a,1),1225(a,1,1))]. 1286 x -> ((y * (y => x)) -> z) = (y * (y => x)) -> z. [para(38(a,1),1235(a,1,1))]. 1402 x => (y => (x => (y => z))) = (x * y) -> z. [para(144(a,1),15(a,1)),flip(a)]. 1560 x => (x => (y -> z)) = (x * y) -> z. [para(370(a,1),1402(a,1,2))]. 1587 (x * y) -> z = x -> (y -> z). [para(1560(a,1),21(a,1))]. 1794 x -> (y -> ((y => x) -> z)) = (y * (y => x)) -> z. [para(1587(a,1),1286(a,1,2))]. 1878 x -> (y -> ((x => y) -> z)) = (x * (x => y)) -> z. [para(1794(a,1),1172(a,1)),flip(a)]. 1971 (x * (x => y)) -> z = x -> (y -> z). [para(983(a,1),1878(a,1,2)),flip(a)]. 2100 x -> ((x => y) -> z) = x -> (y -> z). [para(1971(a,1),1587(a,1)),flip(a)]. 2153 x -> ((x => y) -> z) = x -> ((x ^ y) -> z). [para(897(a,1),2100(a,1,2,1))]. 2337 x -> ((x ^ y) -> z) = x -> (y -> z). [para(2153(a,1),2100(a,1))]. 2403 (x ^ y) -> z = x -> (y -> z). [para(2337(a,1),1247(a,1)),flip(a)]. 2404 $F # answer("(N6)"). [resolve(2403,a,50,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=70. Generated=2956. Kept=2399. proofs=1. Usable=71. Sos=2235. Demods=0. Limbo=59, Disabled=79. Hints=35. Weight_deleted=0. Literals_deleted=0. Forward_subsumed=557. Back_subsumed=33. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. Demod_attempts=0. Demod_rewrites=0. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=1. Megabytes=3.19. User_CPU=0.09, System_CPU=0.00, Wall_clock=0. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED THEOREM PROVED Exiting with 1 proof. ------ process 26314 exit (max_proofs) ------  Process 26314 exit (max_proofs) Sat Jan 19 14:19:06 2008