TSTP Solution File: GRP002-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP002-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.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 11:16:38 EDT 2022
% Result : Unsatisfiable 0.45s 1.01s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP002-4 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n022.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 16:27:18 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.45/1.01 ============================== Prover9 ===============================
% 0.45/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.01 Process 23633 was started by sandbox on n022.cluster.edu,
% 0.45/1.01 Mon Jun 13 16:27:19 2022
% 0.45/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23480_n022.cluster.edu".
% 0.45/1.01 ============================== end of head ===========================
% 0.45/1.01
% 0.45/1.01 ============================== INPUT =================================
% 0.45/1.01
% 0.45/1.01 % Reading from file /tmp/Prover9_23480_n022.cluster.edu
% 0.45/1.01
% 0.45/1.01 set(prolog_style_variables).
% 0.45/1.01 set(auto2).
% 0.45/1.01 % set(auto2) -> set(auto).
% 0.45/1.01 % set(auto) -> set(auto_inference).
% 0.45/1.01 % set(auto) -> set(auto_setup).
% 0.45/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.01 % set(auto) -> set(auto_limits).
% 0.45/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.01 % set(auto) -> set(auto_denials).
% 0.45/1.01 % set(auto) -> set(auto_process).
% 0.45/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.01 % set(auto2) -> assign(stats, some).
% 0.45/1.01 % set(auto2) -> clear(echo_input).
% 0.45/1.01 % set(auto2) -> set(quiet).
% 0.45/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.01 % set(auto2) -> clear(print_given).
% 0.45/1.01 assign(lrs_ticks,-1).
% 0.45/1.01 assign(sos_limit,10000).
% 0.45/1.01 assign(order,kbo).
% 0.45/1.01 set(lex_order_vars).
% 0.45/1.01 clear(print_given).
% 0.45/1.01
% 0.45/1.01 % formulas(sos). % not echoed (8 formulas)
% 0.45/1.01
% 0.45/1.01 ============================== end of input ==========================
% 0.45/1.01
% 0.45/1.01 % From the command line: assign(max_seconds, 300).
% 0.45/1.01
% 0.45/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.01
% 0.45/1.01 % Formulas that are not ordinary clauses:
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% 0.45/1.01 ============================== end of process non-clausal formulas ===
% 0.45/1.01
% 0.45/1.01 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.45/1.01 ============================== PREDICATE ELIMINATION =================
% 0.45/1.01
% 0.45/1.01 ============================== end predicate elimination =============
% 0.45/1.01
% 0.45/1.01 Auto_denials:
% 0.45/1.01 % copying label prove_commutator to answer in negative clause
% 0.45/1.01
% 0.45/1.01 Term ordering decisions:
% 0.45/1.01
% 0.45/1.01 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.45/1.01 Function symbol KB weights: identity=1. a=1. b=1. multiply=1. commutator=1. inverse=0.
% 0.45/1.01
% 0.45/1.01 ============================== end of process initial clauses ========
% 0.45/1.01
% 0.45/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.45/1.01
% 0.45/1.01 ============================== end of clauses for search =============
% 0.45/1.01
% 0.45/1.01 ============================== SEARCH ================================
% 0.45/1.01
% 0.45/1.01 % Starting search at 0.01 seconds.
% 0.45/1.01
% 0.45/1.01 ============================== PROOF =================================
% 0.45/1.01 % SZS status Unsatisfiable
% 0.45/1.01 % SZS output start Refutation
% 0.45/1.01
% 0.45/1.01 % Proof 1 at 0.01 (+ 0.00) seconds: prove_commutator.
% 0.45/1.01 % Length of proof is 24.
% 0.45/1.01 % Level of proof is 6.
% 0.45/1.01 % Maximum clause weight is 27.000.
% 0.45/1.01 % Given clauses 20.
% 0.45/1.01
% 0.45/1.01 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.45/1.01 2 multiply(A,identity) = A # label(right_identity) # label(axiom). [assumption].
% 0.45/1.01 3 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 0.45/1.01 4 multiply(A,inverse(A)) = identity # label(right_inverse) # label(axiom). [assumption].
% 0.45/1.01 5 multiply(A,multiply(A,A)) = identity # label(x_cubed_is_identity) # label(hypothesis). [assumption].
% 0.45/1.01 6 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 0.45/1.01 7 commutator(A,B) = multiply(A,multiply(B,multiply(inverse(A),inverse(B)))) # label(commutator) # label(axiom). [assumption].
% 0.45/1.01 8 commutator(commutator(a,b),b) != identity # label(prove_commutator) # label(negated_conjecture) # answer(prove_commutator). [assumption].
% 0.45/1.01 9 multiply(a,multiply(b,multiply(inverse(a),multiply(inverse(b),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b))))))) != identity # answer(prove_commutator). [copy(8),rewrite([7(3),7(11),6(25),6(24),6(23)])].
% 0.45/1.01 11 multiply(inverse(A),multiply(A,B)) = B. [para(3(a,1),6(a,1,1)),rewrite([1(2)]),flip(a)].
% 0.45/1.01 12 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(6(a,1),4(a,1))].
% 0.45/1.01 13 multiply(A,multiply(inverse(A),B)) = B. [para(4(a,1),6(a,1,1)),rewrite([1(2)]),flip(a)].
% 0.45/1.01 16 multiply(a,multiply(b,multiply(inverse(a),multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b))))) != identity # answer(prove_commutator). [back_rewrite(9),rewrite([11(22)])].
% 0.45/1.01 17 inverse(inverse(A)) = A. [para(3(a,1),11(a,1,2)),rewrite([2(4)])].
% 0.45/1.01 18 multiply(A,A) = inverse(A). [para(5(a,1),11(a,1,2)),rewrite([2(3)]),flip(a)].
% 0.45/1.01 20 multiply(A,multiply(A,B)) = multiply(inverse(A),B). [para(18(a,1),6(a,1,1)),flip(a)].
% 0.45/1.01 21 multiply(A,multiply(B,multiply(A,B))) = inverse(multiply(A,B)). [para(18(a,1),6(a,1)),flip(a)].
% 0.45/1.01 24 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(12(a,1),11(a,1,2)),rewrite([2(3)]),flip(a)].
% 0.45/1.01 28 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(24(a,1),11(a,1,2)),flip(a)].
% 0.45/1.01 29 multiply(A,multiply(B,multiply(A,B))) = multiply(inverse(B),inverse(A)). [back_rewrite(21),rewrite([28(5)])].
% 0.45/1.01 30 multiply(a,multiply(b,multiply(inverse(a),multiply(b,multiply(a,multiply(inverse(b),multiply(inverse(a),inverse(b)))))))) != identity # answer(prove_commutator). [back_rewrite(16),rewrite([28(14),28(12),28(10),17(7),17(8),6(10),6(13),6(12),6(16),6(15),6(14)])].
% 0.45/1.01 31 multiply(A,multiply(B,multiply(A,multiply(B,C)))) = multiply(inverse(B),multiply(inverse(A),C)). [para(20(a,1),6(a,1)),rewrite([28(2),6(4),6(6)]),flip(a)].
% 0.45/1.01 34 multiply(A,multiply(inverse(B),A)) = multiply(B,multiply(inverse(A),B)). [para(29(a,1),13(a,1,2)),rewrite([17(3)])].
% 0.45/1.01 42 $F # answer(prove_commutator). [para(34(a,1),30(a,1,2,2,2,2,2)),rewrite([17(10),20(12),31(13),17(7),18(7),13(8),4(4)]),xx(a)].
% 0.45/1.01
% 0.45/1.01 % SZS output end Refutation
% 0.45/1.01 ============================== end of proof ==========================
% 0.45/1.01
% 0.45/1.01 ============================== STATISTICS ============================
% 0.45/1.01
% 0.45/1.01 Given=20. Generated=306. Kept=40. proofs=1.
% 0.45/1.01 Usable=16. Sos=4. Demods=19. Limbo=6, Disabled=22. Hints=0.
% 0.45/1.01 Megabytes=0.06.
% 0.45/1.01 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.45/1.01
% 0.45/1.01 ============================== end of statistics =====================
% 0.45/1.01
% 0.45/1.01 ============================== end of search =========================
% 0.45/1.01
% 0.45/1.01 THEOREM PROVED
% 0.45/1.01 % SZS status Unsatisfiable
% 0.45/1.01
% 0.45/1.01 Exiting with 1 proof.
% 0.45/1.01
% 0.45/1.01 Process 23633 exit (max_proofs) Mon Jun 13 16:27:19 2022
% 0.45/1.01 Prover9 interrupted
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