TSTP Solution File: GRP048-10 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP048-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:16:56 EDT 2022
% Result : Unsatisfiable 9.54s 9.83s
% Output : Refutation 9.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP048-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 07:07:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 4.22/4.50 ============================== Prover9 ===============================
% 4.22/4.50 Prover9 (32) version 2009-11A, November 2009.
% 4.22/4.50 Process 1829 was started by sandbox on n009.cluster.edu,
% 4.22/4.50 Mon Jun 13 07:07:38 2022
% 4.22/4.50 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_1664_n009.cluster.edu".
% 4.22/4.50 ============================== end of head ===========================
% 4.22/4.50
% 4.22/4.50 ============================== INPUT =================================
% 4.22/4.50
% 4.22/4.50 % Reading from file /tmp/Prover9_1664_n009.cluster.edu
% 4.22/4.50
% 4.22/4.50 set(prolog_style_variables).
% 4.22/4.50 set(auto2).
% 4.22/4.50 % set(auto2) -> set(auto).
% 4.22/4.50 % set(auto) -> set(auto_inference).
% 4.22/4.50 % set(auto) -> set(auto_setup).
% 4.22/4.50 % set(auto_setup) -> set(predicate_elim).
% 4.22/4.50 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.22/4.50 % set(auto) -> set(auto_limits).
% 4.22/4.50 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.22/4.50 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.22/4.50 % set(auto) -> set(auto_denials).
% 4.22/4.50 % set(auto) -> set(auto_process).
% 4.22/4.50 % set(auto2) -> assign(new_constants, 1).
% 4.22/4.50 % set(auto2) -> assign(fold_denial_max, 3).
% 4.22/4.50 % set(auto2) -> assign(max_weight, "200.000").
% 4.22/4.50 % set(auto2) -> assign(max_hours, 1).
% 4.22/4.50 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.22/4.50 % set(auto2) -> assign(max_seconds, 0).
% 4.22/4.50 % set(auto2) -> assign(max_minutes, 5).
% 4.22/4.50 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.22/4.50 % set(auto2) -> set(sort_initial_sos).
% 4.22/4.50 % set(auto2) -> assign(sos_limit, -1).
% 4.22/4.50 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.22/4.50 % set(auto2) -> assign(max_megs, 400).
% 4.22/4.50 % set(auto2) -> assign(stats, some).
% 4.22/4.50 % set(auto2) -> clear(echo_input).
% 4.22/4.50 % set(auto2) -> set(quiet).
% 4.22/4.50 % set(auto2) -> clear(print_initial_clauses).
% 4.22/4.50 % set(auto2) -> clear(print_given).
% 4.22/4.50 assign(lrs_ticks,-1).
% 4.22/4.50 assign(sos_limit,10000).
% 4.22/4.50 assign(order,kbo).
% 4.22/4.50 set(lex_order_vars).
% 4.22/4.50 clear(print_given).
% 4.22/4.50
% 4.22/4.50 % formulas(sos). % not echoed (10 formulas)
% 4.22/4.50
% 4.22/4.50 ============================== end of input ==========================
% 4.22/4.50
% 4.22/4.50 % From the command line: assign(max_seconds, 300).
% 4.22/4.50
% 4.22/4.50 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.22/4.50
% 4.22/4.50 % Formulas that are not ordinary clauses:
% 4.22/4.50
% 4.22/4.50 ============================== end of process non-clausal formulas ===
% 4.22/4.50
% 4.22/4.50 ============================== PROCESS INITIAL CLAUSES ===============
% 4.22/4.50
% 4.22/4.50 ============================== PREDICATE ELIMINATION =================
% 4.22/4.50
% 4.22/4.50 ============================== end predicate elimination =============
% 4.22/4.50
% 4.22/4.50 Auto_denials:
% 4.22/4.50 % copying label prove_inverse_substitution to answer in negative clause
% 4.22/4.50
% 4.22/4.50 Term ordering decisions:
% 4.22/4.50
% 4.22/4.50 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 4.22/4.50 Function symbol KB weights: true=1. identity=1. a=1. b=1. equalish=1. multiply=1. product=1. ifeq=1. inverse=0.
% 4.22/4.50
% 4.22/4.50 ============================== end of process initial clauses ========
% 4.22/4.50
% 4.22/4.50 ============================== CLAUSES FOR SEARCH ====================
% 4.22/4.50
% 4.22/4.50 ============================== end of clauses for search =============
% 4.22/4.50
% 4.22/4.50 ============================== SEARCH ================================
% 4.22/4.50
% 4.22/4.50 % Starting search at 0.01 seconds.
% 4.22/4.50
% 4.22/4.50 Low Water (keep): wt=30.000, iters=3336
% 4.22/4.50
% 4.22/4.50 Low Water (keep): wt=26.000, iters=3365
% 4.22/4.50
% 4.22/4.50 Low Water (keep): wt=25.000, iters=3346
% 4.22/4.50
% 4.22/4.50 Low Water (keep): wt=24.000, iters=3336
% 4.22/4.50
% 4.22/4.50 Low Water (keep): wt=23.000, iters=3342
% 4.22/4.50
% 4.22/4.50 Low Water (keep): wt=22.000, iters=3333
% 4.22/4.50
% 4.22/4.50 Low Water (keep): wt=21.000, iters=3334
% 4.22/4.50
% 4.22/4.50 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 184 (0.00 of 1.10 sec).
% 4.22/4.50
% 4.22/4.50 Low Water (keep): wt=20.000, iters=3373
% 4.22/4.50
% 4.22/4.50 Low Water (displace): id=2717, wt=31.000
% 4.22/4.50
% 4.22/4.50 Low Water (displace): id=5969, wt=30.000
% 4.22/4.50
% 4.22/4.50 Low Water (displace): id=11536, wt=19.000
% 4.22/4.50
% 4.22/4.50 Low Water (displace): id=11551, wt=18.000
% 4.22/4.50
% 4.22/4.50 Low Water (displace): id=11704, wt=17.000
% 4.22/4.50
% 4.22/4.50 Low Water (displace): id=11747, wt=16.000
% 4.22/4.50
% 4.22/4.50 Low Water (displace): id=11820, wt=15.000
% 4.22/4.50
% 4.22/4.50 Low Water (displace): id=11921, wt=13.000
% 4.22/4.50
% 4.22/4.50 Low Water (displace): id=12133, wt=12.000
% 4.22/4.50
% 4.22/4.50 Low Water (keep): wt=19.000, iters=3338
% 4.22/4.50
% 4.22/4.50 Low Water (keep): wt=18.000, iters=3363
% 4.22/4.50
% 4.22/4.50 Low Water (displace): id=18656, wt=11.000
% 4.22/4.50
% 4.22/4.50 Low Water (keep): wt=17.000, iters=3345
% 4.22/4.50
% 4.22/4.50 Low Water (keep): wt=16.000, iters=3343
% 4.22/4.50
% 4.22/4.50 Low Water (keep): wt=15.000, iters=3333
% 9.54/9.83
% 9.54/9.83 Low Water (displace): id=25370, wt=10.000
% 9.54/9.83
% 9.54/9.83 Low Water (keep): wt=14.000, iters=3333
% 9.54/9.83
% 9.54/9.83 Low Water (keep): wt=13.000, iters=3568
% 9.54/9.83
% 9.54/9.83 ============================== PROOF =================================
% 9.54/9.83 % SZS status Unsatisfiable
% 9.54/9.83 % SZS output start Refutation
% 9.54/9.83
% 9.54/9.83 % Proof 1 at 8.62 (+ 0.25) seconds: prove_inverse_substitution.
% 9.54/9.83 % Length of proof is 83.
% 9.54/9.83 % Level of proof is 25.
% 9.54/9.83 % Maximum clause weight is 41.000.
% 9.54/9.83 % Given clauses 2777.
% 9.54/9.83
% 9.54/9.83 1 equalish(a,b) = true # label(a_equals_b) # label(hypothesis). [assumption].
% 9.54/9.83 2 true = equalish(a,b). [copy(1),flip(a)].
% 9.54/9.83 3 product(identity,A,A) = true # label(left_identity) # label(axiom). [assumption].
% 9.54/9.83 4 product(identity,A,A) = equalish(a,b). [copy(3),rewrite([2(3)])].
% 9.54/9.83 5 ifeq(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 9.54/9.83 6 product(inverse(A),A,identity) = true # label(left_inverse) # label(axiom). [assumption].
% 9.54/9.83 7 product(inverse(A),A,identity) = equalish(a,b). [copy(6),rewrite([2(4)])].
% 9.54/9.83 8 product(A,B,multiply(A,B)) = true # label(total_function1) # label(axiom). [assumption].
% 9.54/9.83 9 product(A,B,multiply(A,B)) = equalish(a,b). [copy(8),rewrite([2(3)])].
% 9.54/9.83 10 ifeq(product(A,B,C),true,ifeq(product(A,B,D),true,equalish(D,C),true),true) = true # label(total_function2) # label(axiom). [assumption].
% 9.54/9.83 11 ifeq(product(A,B,C),equalish(a,b),ifeq(product(A,B,D),equalish(a,b),equalish(D,C),equalish(a,b)),equalish(a,b)) = equalish(a,b). [copy(10),rewrite([2(2),2(6),2(10),2(14),2(18)])].
% 9.54/9.83 12 ifeq(equalish(A,B),true,ifeq(product(C,D,A),true,product(C,D,B),true),true) = true # label(product_substitution3) # label(axiom). [assumption].
% 9.54/9.83 13 ifeq(equalish(A,B),equalish(a,b),ifeq(product(C,D,A),equalish(a,b),product(C,D,B),equalish(a,b)),equalish(a,b)) = equalish(a,b). [copy(12),rewrite([2(2),2(6),2(10),2(14),2(18)])].
% 9.54/9.83 14 ifeq(product(A,B,C),true,ifeq(product(D,B,E),true,ifeq(product(F,D,A),true,product(F,E,C),true),true),true) = true # label(associativity1) # label(axiom). [assumption].
% 9.54/9.83 15 ifeq(product(A,B,C),equalish(a,b),ifeq(product(D,B,E),equalish(a,b),ifeq(product(F,D,A),equalish(a,b),product(F,E,C),equalish(a,b)),equalish(a,b)),equalish(a,b)) = equalish(a,b). [copy(14),rewrite([2(2),2(6),2(10),2(14),2(18),2(22),2(26)])].
% 9.54/9.83 16 ifeq(product(A,B,C),true,ifeq(product(D,C,E),true,ifeq(product(D,A,F),true,product(F,B,E),true),true),true) = true # label(associativity2) # label(axiom). [assumption].
% 9.54/9.83 17 ifeq(product(A,B,C),equalish(a,b),ifeq(product(D,C,E),equalish(a,b),ifeq(product(D,A,F),equalish(a,b),product(F,B,E),equalish(a,b)),equalish(a,b)),equalish(a,b)) = equalish(a,b). [copy(16),rewrite([2(2),2(6),2(10),2(14),2(18),2(22),2(26)])].
% 9.54/9.83 18 equalish(inverse(a),inverse(b)) != true # label(prove_inverse_substitution) # label(negated_conjecture) # answer(prove_inverse_substitution). [assumption].
% 9.54/9.83 19 equalish(inverse(a),inverse(b)) != equalish(a,b) # answer(prove_inverse_substitution). [copy(18),rewrite([2(6)])].
% 9.54/9.83 20 ifeq(product(identity,A,B),equalish(a,b),equalish(B,A),equalish(a,b)) = equalish(a,b). [para(4(a,1),11(a,1,1)),rewrite([5(20)])].
% 9.54/9.83 23 ifeq(product(inverse(A),A,B),equalish(a,b),equalish(identity,B),equalish(a,b)) = equalish(a,b). [para(7(a,1),11(a,1,3,1)),rewrite([5(17)])].
% 9.54/9.83 26 ifeq(equalish(A,B),equalish(a,b),product(identity,A,B),equalish(a,b)) = equalish(a,b). [para(4(a,1),13(a,1,3,1)),rewrite([5(16)])].
% 9.54/9.83 31 ifeq(equalish(multiply(A,B),C),equalish(a,b),product(A,B,C),equalish(a,b)) = equalish(a,b). [para(9(a,1),13(a,1,3,1)),rewrite([5(16)])].
% 9.54/9.83 43 ifeq(product(multiply(A,B),C,D),equalish(a,b),ifeq(product(B,C,E),equalish(a,b),product(A,E,D),equalish(a,b)),equalish(a,b)) = equalish(a,b). [para(9(a,1),15(a,1,3,3,1)),rewrite([5(20)])].
% 9.54/9.83 46 ifeq(product(A,B,C),equalish(a,b),ifeq(product(identity,A,D),equalish(a,b),product(D,B,C),equalish(a,b)),equalish(a,b)) = equalish(a,b). [para(4(a,1),17(a,1,3,1)),rewrite([5(24)])].
% 9.54/9.83 51 ifeq(product(A,B,C),equalish(a,b),ifeq(product(inverse(A),C,D),equalish(a,b),product(identity,B,D),equalish(a,b)),equalish(a,b)) = equalish(a,b). [para(7(a,1),17(a,1,3,3,1)),rewrite([5(21)])].
% 9.54/9.83 53 ifeq(product(A,multiply(B,C),D),equalish(a,b),ifeq(product(A,B,E),equalish(a,b),product(E,C,D),equalish(a,b)),equalish(a,b)) = equalish(a,b). [para(9(a,1),17(a,1,1)),rewrite([5(28)])].
% 9.54/9.83 54 ifeq(product(A,B,C),equalish(a,b),ifeq(product(D,A,E),equalish(a,b),product(E,B,multiply(D,C)),equalish(a,b)),equalish(a,b)) = equalish(a,b). [para(9(a,1),17(a,1,3,1)),rewrite([5(24)])].
% 9.54/9.83 57 equalish(a,b) = equalish(A,A). [para(4(a,1),20(a,1,1)),rewrite([5(11)]),flip(a)].
% 9.54/9.83 58 equalish(multiply(identity,A),A) = equalish(a,b). [para(9(a,1),20(a,1,1)),rewrite([5(13)])].
% 9.54/9.83 66 ifeq(equalish(A,B),equalish(C,C),ifeq(product(D,E,A),equalish(a,b),product(D,E,B),equalish(a,b)),equalish(a,b)) = equalish(a,b). [para(57(a,1),13(a,1,2))].
% 9.54/9.83 83 equalish(inverse(a),inverse(b)) != equalish(A,A) # answer(prove_inverse_substitution). [para(57(a,1),19(a,2))].
% 9.54/9.83 84 ifeq(product(identity,A,B),equalish(C,C),equalish(B,A),equalish(a,b)) = equalish(a,b). [para(57(a,1),20(a,1,2))].
% 9.54/9.83 87 equalish(A,A) = equalish(B,B). [para(57(a,1),57(a,1))].
% 9.54/9.83 88 equalish(A,A) = c_0. [new_symbol(87)].
% 9.54/9.83 91 ifeq(product(identity,A,B),c_0,equalish(B,A),equalish(a,b)) = equalish(a,b). [back_rewrite(84),rewrite([88(3)])].
% 9.54/9.83 92 equalish(inverse(a),inverse(b)) != c_0 # answer(prove_inverse_substitution). [back_rewrite(83),rewrite([88(6)])].
% 9.54/9.83 108 ifeq(equalish(A,B),c_0,ifeq(product(C,D,A),equalish(a,b),product(C,D,B),equalish(a,b)),equalish(a,b)) = equalish(a,b). [back_rewrite(66),rewrite([88(2)])].
% 9.54/9.83 115 equalish(a,b) = c_0. [back_rewrite(57),rewrite([88(4)])].
% 9.54/9.83 118 ifeq(equalish(A,B),c_0,ifeq(product(C,D,A),c_0,product(C,D,B),c_0),c_0) = c_0. [back_rewrite(108),rewrite([115(6),115(8),115(10),115(12)])].
% 9.54/9.83 121 ifeq(product(identity,A,B),c_0,equalish(B,A),c_0) = c_0. [back_rewrite(91),rewrite([115(7),115(9)])].
% 9.54/9.83 125 equalish(multiply(identity,A),A) = c_0. [back_rewrite(58),rewrite([115(6)])].
% 9.54/9.83 128 ifeq(product(A,B,C),c_0,ifeq(product(D,A,E),c_0,product(E,B,multiply(D,C)),c_0),c_0) = c_0. [back_rewrite(54),rewrite([115(4),115(6),115(9),115(11),115(13)])].
% 9.54/9.83 129 ifeq(product(A,multiply(B,C),D),c_0,ifeq(product(A,B,E),c_0,product(E,C,D),c_0),c_0) = c_0. [back_rewrite(53),rewrite([115(5),115(7),115(9),115(11),115(13)])].
% 9.54/9.83 131 ifeq(product(A,B,C),c_0,ifeq(product(inverse(A),C,D),c_0,product(identity,B,D),c_0),c_0) = c_0. [back_rewrite(51),rewrite([115(4),115(7),115(10),115(12),115(14)])].
% 9.54/9.83 136 ifeq(product(A,B,C),c_0,ifeq(product(identity,A,D),c_0,product(D,B,C),c_0),c_0) = c_0. [back_rewrite(46),rewrite([115(4),115(7),115(9),115(11),115(13)])].
% 9.54/9.83 139 ifeq(product(multiply(A,B),C,D),c_0,ifeq(product(B,C,E),c_0,product(A,E,D),c_0),c_0) = c_0. [back_rewrite(43),rewrite([115(5),115(7),115(9),115(11),115(13)])].
% 9.54/9.83 151 ifeq(equalish(multiply(A,B),C),c_0,product(A,B,C),c_0) = c_0. [back_rewrite(31),rewrite([115(5),115(7),115(9)])].
% 9.54/9.83 156 ifeq(equalish(A,B),c_0,product(identity,A,B),c_0) = c_0. [back_rewrite(26),rewrite([115(4),115(7),115(9)])].
% 9.54/9.83 159 ifeq(product(inverse(A),A,B),c_0,equalish(identity,B),c_0) = c_0. [back_rewrite(23),rewrite([115(5),115(8),115(10)])].
% 9.54/9.83 162 product(A,B,multiply(A,B)) = c_0. [back_rewrite(9),rewrite([115(5)])].
% 9.54/9.83 163 product(inverse(A),A,identity) = c_0. [back_rewrite(7),rewrite([115(6)])].
% 9.54/9.83 164 product(identity,A,A) = c_0. [back_rewrite(4),rewrite([115(5)])].
% 9.54/9.83 167 product(identity,a,b) = c_0. [para(115(a,1),156(a,1,1)),rewrite([5(8)])].
% 9.54/9.83 168 product(identity,multiply(identity,A),A) = c_0. [para(125(a,1),156(a,1,1)),rewrite([5(8)])].
% 9.54/9.83 300 equalish(identity,multiply(inverse(A),A)) = c_0. [para(162(a,1),159(a,1,1)),rewrite([5(8)])].
% 9.54/9.83 331 product(identity,identity,multiply(inverse(A),A)) = c_0. [para(300(a,1),156(a,1,1)),rewrite([5(9)])].
% 9.54/9.83 336 equalish(multiply(inverse(A),A),identity) = c_0. [para(331(a,1),121(a,1,1)),rewrite([5(8)])].
% 9.54/9.83 352 ifeq(product(A,B,multiply(inverse(C),C)),c_0,product(A,B,identity),c_0) = c_0. [para(336(a,1),118(a,1,1)),rewrite([5(12)])].
% 9.54/9.83 414 ifeq(product(A,identity,B),c_0,product(B,C,multiply(A,C)),c_0) = c_0. [para(164(a,1),128(a,1,1)),rewrite([5(11)])].
% 9.54/9.83 416 ifeq(product(A,inverse(B),C),c_0,product(C,B,multiply(A,identity)),c_0) = c_0. [para(163(a,1),128(a,1,1)),rewrite([5(12)])].
% 9.54/9.83 417 ifeq(product(A,B,C),c_0,product(identity,B,multiply(inverse(A),C)),c_0) = c_0. [para(163(a,1),128(a,1,3,1)),rewrite([5(10)])].
% 9.54/9.83 499 ifeq(product(identity,identity,A),c_0,product(A,B,B),c_0) = c_0. [para(168(a,1),129(a,1,1)),rewrite([5(11)])].
% 9.54/9.83 602 ifeq(product(inverse(inverse(A)),identity,B),c_0,product(identity,A,B),c_0) = c_0. [para(163(a,1),131(a,1,1)),rewrite([5(13)])].
% 9.54/9.83 1011 ifeq(product(a,A,B),c_0,product(b,A,B),c_0) = c_0. [para(167(a,1),136(a,1,3,1)),rewrite([5(9)])].
% 9.54/9.83 1551 product(multiply(inverse(A),A),B,B) = c_0. [para(331(a,1),499(a,1,1)),rewrite([5(7)])].
% 9.54/9.83 1781 ifeq(product(A,B,C),c_0,product(inverse(A),C,B),c_0) = c_0. [para(1551(a,1),139(a,1,1)),rewrite([5(10)])].
% 9.54/9.83 20740 product(identity,A,multiply(inverse(inverse(A)),identity)) = c_0. [para(163(a,1),416(a,1,1)),rewrite([5(10)])].
% 9.54/9.83 20818 equalish(multiply(inverse(inverse(A)),identity),A) = c_0. [para(20740(a,1),121(a,1,1)),rewrite([5(9)])].
% 9.54/9.83 20869 product(inverse(inverse(A)),identity,A) = c_0. [para(20818(a,1),151(a,1,1)),rewrite([5(8)])].
% 9.54/9.83 20940 product(A,B,multiply(inverse(inverse(A)),B)) = c_0. [para(20869(a,1),414(a,1,1)),rewrite([5(8)])].
% 9.54/9.83 22104 product(A,inverse(A),identity) = c_0. [para(20940(a,1),352(a,1,1)),rewrite([5(7)])].
% 9.54/9.83 22165 product(b,inverse(a),identity) = c_0. [para(22104(a,1),1011(a,1,1)),rewrite([5(9)])].
% 9.54/9.83 22223 product(identity,inverse(a),multiply(inverse(b),identity)) = c_0. [para(22165(a,1),417(a,1,1)),rewrite([5(12)])].
% 9.54/9.83 26532 equalish(multiply(inverse(b),identity),inverse(a)) = c_0. [para(22223(a,1),121(a,1,1)),rewrite([5(11)])].
% 9.54/9.83 26550 product(inverse(b),identity,inverse(a)) = c_0. [para(26532(a,1),151(a,1,1)),rewrite([5(10)])].
% 9.54/9.83 26569 product(identity,identity,multiply(inverse(inverse(b)),inverse(a))) = c_0. [para(26550(a,1),417(a,1,1)),rewrite([5(13)])].
% 9.54/9.83 39421 equalish(multiply(inverse(inverse(b)),inverse(a)),identity) = c_0. [para(26569(a,1),121(a,1,1)),rewrite([5(12)])].
% 9.54/9.83 39444 product(inverse(inverse(b)),inverse(a),identity) = c_0. [para(39421(a,1),151(a,1,1)),rewrite([5(11)])].
% 9.54/9.83 40606 product(inverse(inverse(inverse(b))),identity,inverse(a)) = c_0. [para(39444(a,1),1781(a,1,1)),rewrite([5(12)])].
% 9.54/9.83 41401 product(identity,inverse(b),inverse(a)) = c_0. [para(40606(a,1),602(a,1,1)),rewrite([5(10)])].
% 9.54/9.83 41422 equalish(inverse(a),inverse(b)) = c_0. [para(41401(a,1),121(a,1,1)),rewrite([5(9)])].
% 9.54/9.83 41423 $F # answer(prove_inverse_substitution). [resolve(41422,a,92,a)].
% 9.54/9.83
% 9.54/9.83 % SZS output end Refutation
% 9.54/9.83 ============================== end of proof ==========================
% 9.54/9.83
% 9.54/9.83 ============================== STATISTICS ============================
% 9.54/9.83
% 9.54/9.83 Given=2777. Generated=384775. Kept=41413. proofs=1.
% 9.54/9.83 Usable=2349. Sos=9999. Demods=12347. Limbo=0, Disabled=29074. Hints=0.
% 9.54/9.83 Megabytes=26.21.
% 9.54/9.83 User_CPU=8.62, System_CPU=0.25, Wall_clock=9.
% 9.54/9.83
% 9.54/9.83 ============================== end of statistics =====================
% 9.54/9.83
% 9.54/9.83 ============================== end of search =========================
% 9.54/9.83
% 9.54/9.83 THEOREM PROVED
% 9.54/9.83 % SZS status Unsatisfiable
% 9.54/9.83
% 9.54/9.83 Exiting with 1 proof.
% 9.54/9.83
% 9.54/9.83 Process 1829 exit (max_proofs) Mon Jun 13 07:07:47 2022
% 9.54/9.83 Prover9 interrupted
%------------------------------------------------------------------------------