0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s 0.14/0.36 % Computer : n004.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 1440 0.14/0.36 % WCLimit : 180 0.14/0.36 % DateTime : Mon Jul 3 05:16:15 EDT 2023 0.14/0.36 % CPUTime : 0.49/1.05 ============================== Prover9 =============================== 0.49/1.05 Prover9 (32) version 2009-11A, November 2009. 0.49/1.05 Process 9502 was started by sandbox2 on n004.cluster.edu, 0.49/1.05 Mon Jul 3 05:16:16 2023 0.49/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1440 -f /tmp/Prover9_9348_n004.cluster.edu". 0.49/1.05 ============================== end of head =========================== 0.49/1.05 0.49/1.05 ============================== INPUT ================================= 0.49/1.05 0.49/1.05 % Reading from file /tmp/Prover9_9348_n004.cluster.edu 0.49/1.05 0.49/1.05 set(prolog_style_variables). 0.49/1.05 set(auto2). 0.49/1.05 % set(auto2) -> set(auto). 0.49/1.05 % set(auto) -> set(auto_inference). 0.49/1.05 % set(auto) -> set(auto_setup). 0.49/1.05 % set(auto_setup) -> set(predicate_elim). 0.49/1.05 % set(auto_setup) -> assign(eq_defs, unfold). 0.49/1.05 % set(auto) -> set(auto_limits). 0.49/1.05 % set(auto_limits) -> assign(max_weight, "100.000"). 0.49/1.05 % set(auto_limits) -> assign(sos_limit, 20000). 0.49/1.05 % set(auto) -> set(auto_denials). 0.49/1.05 % set(auto) -> set(auto_process). 0.49/1.05 % set(auto2) -> assign(new_constants, 1). 0.49/1.05 % set(auto2) -> assign(fold_denial_max, 3). 0.49/1.05 % set(auto2) -> assign(max_weight, "200.000"). 0.49/1.05 % set(auto2) -> assign(max_hours, 1). 0.49/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.49/1.05 % set(auto2) -> assign(max_seconds, 0). 0.49/1.05 % set(auto2) -> assign(max_minutes, 5). 0.49/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.49/1.05 % set(auto2) -> set(sort_initial_sos). 0.49/1.05 % set(auto2) -> assign(sos_limit, -1). 0.49/1.05 % set(auto2) -> assign(lrs_ticks, 3000). 0.49/1.05 % set(auto2) -> assign(max_megs, 400). 0.49/1.05 % set(auto2) -> assign(stats, some). 0.49/1.05 % set(auto2) -> clear(echo_input). 0.49/1.05 % set(auto2) -> set(quiet). 0.49/1.05 % set(auto2) -> clear(print_initial_clauses). 0.49/1.05 % set(auto2) -> clear(print_given). 0.49/1.05 assign(lrs_ticks,-1). 0.49/1.05 assign(sos_limit,10000). 0.49/1.05 assign(order,kbo). 0.49/1.05 set(lex_order_vars). 0.49/1.05 clear(print_given). 0.49/1.05 0.49/1.05 % formulas(sos). % not echoed (19 formulas) 0.49/1.05 0.49/1.05 ============================== end of input ========================== 0.49/1.05 0.49/1.05 % From the command line: assign(max_seconds, 1440). 0.49/1.05 0.49/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.49/1.05 0.49/1.05 % Formulas that are not ordinary clauses: 0.49/1.05 1 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 2 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 3 (all A zero = multiplication(A,zero)) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 4 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 5 (all C all B all A addition(addition(A,B),C) = addition(A,addition(B,C))) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 6 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 7 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 8 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 9 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 10 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 11 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 12 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 13 (all X0 ((exists X1 complement(X1,X0)) <-> test(X0))) # label(test_1) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 14 (all X0 (-test(X0) -> zero = c(X0))) # label(test_4) # label(axiom) # label(non_clause). [assumption]. 0.49/1.05 15 (all X0 all X1 (zero = multiplication(X0,X1) & one = addition(X0,X1) & multiplication(X1,X0) = zero <-> complement(X1,X0))) # label(test_2) # label(axiom) # label(non_clause). [assumption]. 0.92/1.18 16 (all X0 all X1 (test(X0) -> (complement(X0,X1) <-> c(X0) = X1))) # label(test_3) # label(axiom) # label(non_clause). [assumption]. 0.92/1.18 17 (all X0 all X1 (test(X0) & test(X1) -> multiplication(c(X0),c(X1)) = c(addition(X0,X1)))) # label(test_deMorgan1) # label(axiom) # label(non_clause). [assumption]. 0.92/1.18 18 (all X0 all X1 (test(X1) & test(X0) -> c(multiplication(X0,X1)) = addition(c(X0),c(X1)))) # label(test_deMorgan2) # label(axiom) # label(non_clause). [assumption]. 0.92/1.18 19 -(all X0 all X1 (test(X0) & test(X1) -> leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 0.92/1.18 0.92/1.18 ============================== end of process non-clausal formulas === 0.92/1.18 0.92/1.18 ============================== PROCESS INITIAL CLAUSES =============== 0.92/1.18 0.92/1.18 ============================== PREDICATE ELIMINATION ================= 0.92/1.18 20 complement(f1(A),A) | -test(A) # label(test_1) # label(axiom). [clausify(13)]. 0.92/1.18 21 -complement(A,B) | test(B) # label(test_1) # label(axiom). [clausify(13)]. 0.92/1.18 22 multiplication(A,B) = zero | -complement(B,A) # label(test_2) # label(axiom). [clausify(15)]. 0.92/1.18 Derived: multiplication(A,f1(A)) = zero | -test(A). [resolve(22,b,20,a)]. 0.92/1.18 23 addition(A,B) = one | -complement(B,A) # label(test_2) # label(axiom). [clausify(15)]. 0.92/1.18 Derived: addition(A,f1(A)) = one | -test(A). [resolve(23,b,20,a)]. 0.92/1.18 24 multiplication(A,B) = zero | -complement(A,B) # label(test_2) # label(axiom). [clausify(15)]. 0.92/1.18 Derived: multiplication(f1(A),A) = zero | -test(A). [resolve(24,b,20,a)]. 0.92/1.18 25 -test(A) | -complement(A,B) | c(A) = B # label(test_3) # label(axiom). [clausify(16)]. 0.92/1.18 Derived: -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(25,b,20,a)]. 0.92/1.18 26 -test(A) | complement(A,B) | c(A) != B # label(test_3) # label(axiom). [clausify(16)]. 0.92/1.18 Derived: -test(A) | c(A) != B | test(B). [resolve(26,b,21,a)]. 0.92/1.18 Derived: -test(A) | c(A) != B | multiplication(B,A) = zero. [resolve(26,b,22,b)]. 0.92/1.18 Derived: -test(A) | c(A) != B | addition(B,A) = one. [resolve(26,b,23,b)]. 0.92/1.18 Derived: -test(A) | c(A) != B | multiplication(A,B) = zero. [resolve(26,b,24,b)]. 0.92/1.18 27 multiplication(A,B) != zero | addition(A,B) != one | multiplication(B,A) != zero | complement(B,A) # label(test_2) # label(axiom). [clausify(15)]. 0.92/1.18 Derived: multiplication(A,B) != zero | addition(A,B) != one | multiplication(B,A) != zero | test(A). [resolve(27,d,21,a)]. 0.92/1.18 Derived: multiplication(A,B) != zero | addition(A,B) != one | multiplication(B,A) != zero | -test(B) | c(B) = A. [resolve(27,d,25,b)]. 0.92/1.18 0.92/1.18 ============================== end predicate elimination ============= 0.92/1.18 0.92/1.18 Auto_denials: (non-Horn, no changes). 0.92/1.18 0.92/1.18 Term ordering decisions: 0.92/1.18 Function symbol KB weights: zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1. 0.92/1.18 0.92/1.18 ============================== end of process initial clauses ======== 0.92/1.18 0.92/1.18 ============================== CLAUSES FOR SEARCH ==================== 0.92/1.18 0.92/1.18 ============================== end of clauses for search ============= 0.92/1.18 0.92/1.18 ============================== SEARCH ================================ 0.92/1.18 0.92/1.18 % Starting search at 0.02 seconds. 0.92/1.18 0.92/1.18 ============================== PROOF ================================= 0.92/1.18 % SZS status Theorem 0.92/1.18 % SZS output start Refutation 0.92/1.18 0.92/1.18 % Proof 1 at 0.13 (+ 0.01) seconds. 0.92/1.18 % Length of proof is 80. 0.92/1.18 % Level of proof is 12. 0.92/1.18 % Maximum clause weight is 46.000. 0.92/1.18 % Given clauses 185. 0.92/1.18 0.92/1.18 1 (all A all B (leq(A,B) <-> addition(A,B) = B)) # label(order) # label(axiom) # label(non_clause). [assumption]. 0.92/1.18 2 (all A all B addition(A,B) = addition(B,A)) # label(additive_commutativity) # label(axiom) # label(non_clause). [assumption]. 0.92/1.18 3 (all A zero = multiplication(A,zero)) # label(right_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 4 (all A all B all C multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C))) # label(left_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 5 (all C all B all A addition(addition(A,B),C) = addition(A,addition(B,C))) # label(additive_associativity) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 6 (all A addition(A,A) = A) # label(additive_idempotence) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 7 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 8 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 9 (all A multiplication(zero,A) = zero) # label(left_annihilation) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 11 (all A all B all C multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C))) # label(right_distributivity) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 12 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 13 (all X0 ((exists X1 complement(X1,X0)) <-> test(X0))) # label(test_1) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 15 (all X0 all X1 (zero = multiplication(X0,X1) & one = addition(X0,X1) & multiplication(X1,X0) = zero <-> complement(X1,X0))) # label(test_2) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 16 (all X0 all X1 (test(X0) -> (complement(X0,X1) <-> c(X0) = X1))) # label(test_3) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 17 (all X0 all X1 (test(X0) & test(X1) -> multiplication(c(X0),c(X1)) = c(addition(X0,X1)))) # label(test_deMorgan1) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 18 (all X0 all X1 (test(X1) & test(X0) -> c(multiplication(X0,X1)) = addition(c(X0),c(X1)))) # label(test_deMorgan2) # label(axiom) # label(non_clause). [assumption]. 0.92/1.19 19 -(all X0 all X1 (test(X0) & test(X1) -> leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption]. 0.92/1.19 20 complement(f1(A),A) | -test(A) # label(test_1) # label(axiom). [clausify(13)]. 0.92/1.19 21 -complement(A,B) | test(B) # label(test_1) # label(axiom). [clausify(13)]. 0.92/1.19 23 addition(A,B) = one | -complement(B,A) # label(test_2) # label(axiom). [clausify(15)]. 0.92/1.19 24 multiplication(A,B) = zero | -complement(A,B) # label(test_2) # label(axiom). [clausify(15)]. 0.92/1.19 25 -test(A) | -complement(A,B) | c(A) = B # label(test_3) # label(axiom). [clausify(16)]. 0.92/1.19 26 -test(A) | complement(A,B) | c(A) != B # label(test_3) # label(axiom). [clausify(16)]. 0.92/1.19 27 multiplication(A,B) != zero | addition(A,B) != one | multiplication(B,A) != zero | complement(B,A) # label(test_2) # label(axiom). [clausify(15)]. 0.92/1.19 28 test(c1) # label(goals) # label(negated_conjecture). [clausify(19)]. 0.92/1.19 29 test(c2) # label(goals) # label(negated_conjecture). [clausify(19)]. 0.92/1.19 30 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom). [clausify(3)]. 0.92/1.19 31 addition(A,A) = A # label(additive_idempotence) # label(axiom). [clausify(6)]. 0.92/1.19 32 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom). [clausify(7)]. 0.92/1.19 33 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom). [clausify(8)]. 0.92/1.19 34 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom). [clausify(9)]. 0.92/1.19 35 addition(A,zero) = A # label(additive_identity) # label(axiom). [clausify(12)]. 0.92/1.19 37 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom). [clausify(2)]. 0.92/1.19 38 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom). [clausify(5)]. 0.92/1.19 39 addition(A,addition(B,C)) = addition(C,addition(A,B)). [copy(38),rewrite([37(2)]),flip(a)]. 0.92/1.19 41 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom). [clausify(4)]. 0.92/1.19 42 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B). [copy(41),flip(a)]. 0.92/1.19 43 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom). [clausify(11)]. 0.92/1.19 44 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)). [copy(43),flip(a)]. 0.92/1.19 45 -leq(one,addition(addition(addition(addition(multiplication(c2,c1),multiplication(c(c2),c1)),multiplication(c1,c2)),multiplication(c(c1),c2)),multiplication(c(c1),c(c2)))) | -leq(addition(addition(addition(addition(multiplication(c2,c1),multiplication(c(c2),c1)),multiplication(c1,c2)),multiplication(c(c1),c2)),multiplication(c(c1),c(c2))),one) # label(goals) # label(negated_conjecture). [clausify(19)]. 0.92/1.19 46 -leq(one,addition(multiplication(c1,c2),addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(addition(c2,c(c2)),c1))))) | -leq(addition(multiplication(c1,c2),addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(addition(c2,c(c2)),c1)))),one). [copy(45),rewrite([42(9),37(11),37(16),39(16,R),37(15),37(22),39(22,R),37(21),39(21,R),37(20),42(31),37(33),37(38),39(38,R),37(37),37(44),39(44,R),37(43),39(43,R),37(42)])]. 0.92/1.19 48 leq(A,B) | addition(A,B) != B # label(order) # label(axiom). [clausify(1)]. 0.92/1.19 49 -test(A) | -test(B) | c(addition(A,B)) = multiplication(c(A),c(B)) # label(test_deMorgan1) # label(axiom). [clausify(17)]. 0.92/1.19 50 -test(A) | -test(B) | multiplication(c(A),c(B)) = c(addition(A,B)). [copy(49),flip(c)]. 0.92/1.19 51 -test(A) | -test(B) | c(multiplication(B,A)) = addition(c(B),c(A)) # label(test_deMorgan2) # label(axiom). [clausify(18)]. 0.92/1.19 52 -test(A) | -test(B) | addition(c(A),c(B)) = c(multiplication(B,A)). [copy(51),rewrite([37(7)]),flip(c)]. 0.92/1.19 54 addition(A,f1(A)) = one | -test(A). [resolve(23,b,20,a)]. 0.92/1.19 55 multiplication(f1(A),A) = zero | -test(A). [resolve(24,b,20,a)]. 0.92/1.19 56 -test(f1(A)) | c(f1(A)) = A | -test(A). [resolve(25,b,20,a)]. 0.92/1.19 59 -test(A) | c(A) != B | addition(B,A) = one. [resolve(26,b,23,b)]. 0.92/1.19 60 -test(A) | c(A) != B | addition(A,B) = one. [copy(59),rewrite([37(4)])]. 0.92/1.19 62 multiplication(A,B) != zero | addition(A,B) != one | multiplication(B,A) != zero | test(A). [resolve(27,d,21,a)]. 0.92/1.19 64 -test(A) | multiplication(c(A),c(A)) = c(A). [factor(50,a,b),rewrite([31(5)])]. 0.92/1.19 68 addition(A,addition(A,B)) = addition(A,B). [para(39(a,1),31(a,1)),rewrite([37(1),37(2),39(2,R),31(1),37(3)])]. 0.92/1.19 73 multiplication(A,addition(B,one)) = addition(A,multiplication(A,B)). [para(32(a,1),44(a,1,1)),rewrite([37(4)]),flip(a)]. 0.92/1.19 74 -leq(one,addition(multiplication(c1,c2),addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(addition(c2,c(c2)),c1))))) | -leq(addition(multiplication(c1,c2),addition(multiplication(addition(c2,c(c2)),c1),multiplication(c(c1),addition(c2,c(c2))))),one). [para(39(a,1),46(b,1,2)),rewrite([44(42)])]. 0.92/1.19 77 leq(A,A). [resolve(48,b,31,a)]. 0.92/1.19 88 -test(A) | addition(c(A),c(c2)) = c(multiplication(A,c2)). [resolve(52,a,29,a),rewrite([37(5)])]. 0.92/1.19 89 -test(A) | addition(c(A),c(c1)) = c(multiplication(A,c1)). [resolve(52,a,28,a),rewrite([37(5)])]. 0.92/1.19 97 addition(c2,f1(c2)) = one. [resolve(54,b,29,a)]. 0.92/1.19 111 c(c2) != A | addition(A,c2) = one. [resolve(60,a,29,a),rewrite([37(5)])]. 0.92/1.19 112 c(c1) != A | addition(A,c1) = one. [resolve(60,a,28,a),rewrite([37(5)])]. 0.92/1.19 116 test(one). [resolve(62,b,35,a),rewrite([30(3),32(6)]),xx(a),xx(b)]. 0.92/1.19 129 multiplication(c(c2),c(c2)) = c(c2). [resolve(64,a,29,a)]. 0.92/1.19 130 multiplication(c(c1),c(c1)) = c(c1). [resolve(64,a,28,a)]. 0.92/1.19 136 -leq(one,addition(multiplication(c1,c2),addition(multiplication(addition(c2,c(c2)),c1),multiplication(c(c1),addition(c2,c(c2)))))) | -leq(addition(multiplication(c1,c2),addition(multiplication(addition(c2,c(c2)),c1),multiplication(c(c1),addition(c2,c(c2))))),one). [para(39(a,1),74(a,2,2)),rewrite([44(20)])]. 0.92/1.19 146 f1(one) = zero. [resolve(116,a,55,b),rewrite([32(4)])]. 0.92/1.19 147 addition(zero,one) = one. [resolve(116,a,54,b),rewrite([146(3),37(3)])]. 0.92/1.19 151 -test(zero) | c(zero) = one. [para(146(a,1),56(a,1)),rewrite([146(4)]),unit_del(c,116)]. 0.92/1.19 169 test(zero). [resolve(147,a,62,b),rewrite([32(3),30(6)]),xx(a),xx(b)]. 0.92/1.19 171 c(zero) = one. [back_unit_del(151),unit_del(a,169)]. 0.92/1.19 200 addition(one,c2) = one. [para(97(a,1),68(a,1,2)),rewrite([37(3),97(7)])]. 0.92/1.19 548 addition(one,c(c2)) = one. [resolve(88,a,169,a),rewrite([171(2),34(7),171(6)])]. 0.92/1.19 552 addition(A,multiplication(A,c(c2))) = A. [para(548(a,1),44(a,2,2)),rewrite([32(2),32(6)])]. 0.92/1.19 570 addition(one,c(c1)) = one. [resolve(89,a,169,a),rewrite([171(2),34(7),171(6)])]. 0.92/1.19 574 addition(A,multiplication(A,c(c1))) = A. [para(570(a,1),44(a,2,2)),rewrite([32(2),32(6)])]. 0.92/1.19 1028 addition(c2,c(c2)) = one. [resolve(111,a,552,a(flip)),rewrite([129(7),31(5),37(4)])]. 0.92/1.19 1044 -leq(one,addition(c1,c(c1))) | -leq(addition(c1,c(c1)),one). [back_rewrite(136),rewrite([1028(8),33(7),1028(11),32(9),39(9),37(8),73(8,R),37(7),200(7),32(6),37(5),1028(13),33(12),1028(16),32(14),39(14),37(13),73(13,R),37(12),200(12),32(11),37(10)])]. 0.92/1.19 1045 addition(c1,c(c1)) = one. [resolve(112,a,574,a(flip)),rewrite([130(7),31(5),37(4)])]. 0.92/1.19 1047 $F. [back_rewrite(1044),rewrite([1045(5),1045(7)]),merge(b),unit_del(a,77)]. 0.92/1.19 0.92/1.19 % SZS output end Refutation 0.92/1.19 ============================== end of proof ========================== 0.92/1.19 0.92/1.19 ============================== STATISTICS ============================ 0.92/1.19 0.92/1.19 Given=185. Generated=2935. Kept=1012. proofs=1. 0.92/1.19 Usable=162. Sos=694. Demods=351. Limbo=2, Disabled=191. Hints=0. 0.92/1.19 Megabytes=1.05. 0.92/1.19 User_CPU=0.14, System_CPU=0.01, Wall_clock=0. 0.92/1.19 0.92/1.19 ============================== end of statistics ===================== 0.92/1.19 0.92/1.19 ============================== end of search ========================= 0.92/1.19 0.92/1.19 THEOREM PROVED 0.92/1.19 % SZS status Theorem 0.92/1.19 0.92/1.19 Exiting with 1 proof. 0.92/1.19 0.92/1.19 Process 9502 exit (max_proofs) Mon Jul 3 05:16:16 2023 0.92/1.19 Prover9 interrupted 0.92/1.19 EOF