TSTP Solution File: GRP002-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP002-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 0.68s 1.01s
% Output : Refutation 0.68s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP002-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 01:05:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.68/1.01 ============================== Prover9 ===============================
% 0.68/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.68/1.01 Process 32044 was started by sandbox on n015.cluster.edu,
% 0.68/1.01 Tue Jun 14 01:05:09 2022
% 0.68/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31860_n015.cluster.edu".
% 0.68/1.01 ============================== end of head ===========================
% 0.68/1.01
% 0.68/1.01 ============================== INPUT =================================
% 0.68/1.01
% 0.68/1.01 % Reading from file /tmp/Prover9_31860_n015.cluster.edu
% 0.68/1.01
% 0.68/1.01 set(prolog_style_variables).
% 0.68/1.01 set(auto2).
% 0.68/1.01 % set(auto2) -> set(auto).
% 0.68/1.01 % set(auto) -> set(auto_inference).
% 0.68/1.01 % set(auto) -> set(auto_setup).
% 0.68/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.68/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.68/1.01 % set(auto) -> set(auto_limits).
% 0.68/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.68/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.68/1.01 % set(auto) -> set(auto_denials).
% 0.68/1.01 % set(auto) -> set(auto_process).
% 0.68/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.68/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.68/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.68/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.68/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.68/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.68/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.68/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.68/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.68/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.68/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.68/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.68/1.01 % set(auto2) -> assign(stats, some).
% 0.68/1.01 % set(auto2) -> clear(echo_input).
% 0.68/1.01 % set(auto2) -> set(quiet).
% 0.68/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.68/1.01 % set(auto2) -> clear(print_given).
% 0.68/1.01 assign(lrs_ticks,-1).
% 0.68/1.01 assign(sos_limit,10000).
% 0.68/1.01 assign(order,kbo).
% 0.68/1.01 set(lex_order_vars).
% 0.68/1.01 clear(print_given).
% 0.68/1.01
% 0.68/1.01 % formulas(sos). % not echoed (6 formulas)
% 0.68/1.01
% 0.68/1.01 ============================== end of input ==========================
% 0.68/1.01
% 0.68/1.01 % From the command line: assign(max_seconds, 300).
% 0.68/1.01
% 0.68/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.68/1.01
% 0.68/1.01 % Formulas that are not ordinary clauses:
% 0.68/1.01
% 0.68/1.01 ============================== end of process non-clausal formulas ===
% 0.68/1.01
% 0.68/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.68/1.01
% 0.68/1.01 ============================== PREDICATE ELIMINATION =================
% 0.68/1.01
% 0.68/1.01 ============================== end predicate elimination =============
% 0.68/1.01
% 0.68/1.01 Auto_denials:
% 0.68/1.01 % copying label prove_commutator to answer in negative clause
% 0.68/1.01
% 0.68/1.01 Term ordering decisions:
% 0.68/1.01
% 0.68/1.01 % Assigning unary symbol inverse kb_weight 0 and highest precedence (7).
% 0.68/1.01 Function symbol KB weights: identity=1. a=1. b=1. multiply=1. commutator=1. inverse=0.
% 0.68/1.01
% 0.68/1.01 ============================== end of process initial clauses ========
% 0.68/1.01
% 0.68/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.68/1.01
% 0.68/1.01 ============================== end of clauses for search =============
% 0.68/1.01
% 0.68/1.01 ============================== SEARCH ================================
% 0.68/1.01
% 0.68/1.01 % Starting search at 0.01 seconds.
% 0.68/1.01
% 0.68/1.01 ============================== PROOF =================================
% 0.68/1.01 % SZS status Unsatisfiable
% 0.68/1.01 % SZS output start Refutation
% 0.68/1.01
% 0.68/1.01 % Proof 1 at 0.02 (+ 0.00) seconds: prove_commutator.
% 0.68/1.01 % Length of proof is 28.
% 0.68/1.01 % Level of proof is 10.
% 0.68/1.01 % Maximum clause weight is 27.000.
% 0.68/1.01 % Given clauses 20.
% 0.68/1.01
% 0.68/1.01 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.68/1.01 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 0.68/1.01 3 multiply(A,multiply(A,A)) = identity # label(x_cubed_is_identity) # label(hypothesis). [assumption].
% 0.68/1.01 4 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 0.68/1.01 5 commutator(A,B) = multiply(A,multiply(B,multiply(inverse(A),inverse(B)))) # label(commutator) # label(axiom). [assumption].
% 0.68/1.01 6 commutator(commutator(a,b),b) != identity # label(prove_commutator) # label(negated_conjecture) # answer(prove_commutator). [assumption].
% 0.68/1.01 7 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(6),rewrite([5(3),5(11),4(25),4(24),4(23)])].
% 0.68/1.01 8 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),4(a,1,1)),rewrite([1(2)]),flip(a)].
% 0.68/1.01 10 multiply(A,multiply(A,multiply(A,B))) = B. [para(3(a,1),4(a,1,1)),rewrite([1(2),4(2)]),flip(a)].
% 0.68/1.01 11 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(7),rewrite([8(22)])].
% 0.68/1.01 13 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),8(a,1,2))].
% 0.68/1.01 14 multiply(inverse(A),identity) = multiply(A,A). [para(3(a,1),8(a,1,2))].
% 0.68/1.01 15 multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C. [para(4(a,1),8(a,1,2))].
% 0.68/1.01 16 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(8(a,1),8(a,1,2))].
% 0.68/1.01 17 multiply(A,identity) = A. [back_rewrite(13),rewrite([16(4)])].
% 0.68/1.01 18 multiply(A,A) = inverse(A). [back_rewrite(14),rewrite([17(3)]),flip(a)].
% 0.68/1.01 19 multiply(A,inverse(A)) = identity. [back_rewrite(3),rewrite([18(1)])].
% 0.68/1.01 21 multiply(A,multiply(A,B)) = multiply(inverse(A),B). [para(18(a,1),4(a,1,1)),flip(a)].
% 0.68/1.01 22 multiply(A,multiply(B,multiply(A,B))) = inverse(multiply(A,B)). [para(18(a,1),4(a,1)),flip(a)].
% 0.68/1.01 23 inverse(inverse(A)) = A. [para(18(a,1),8(a,1,2)),rewrite([18(3)])].
% 0.68/1.01 24 multiply(A,multiply(inverse(A),B)) = B. [back_rewrite(10),rewrite([21(2)])].
% 0.68/1.01 32 multiply(inverse(multiply(A,B)),A) = inverse(B). [para(19(a,1),15(a,1,2,2)),rewrite([17(4)])].
% 0.68/1.01 35 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(8(a,1),32(a,1,1,1)),flip(a)].
% 0.68/1.01 36 multiply(A,multiply(B,multiply(A,B))) = multiply(inverse(B),inverse(A)). [back_rewrite(22),rewrite([35(5)])].
% 0.68/1.01 37 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(11),rewrite([35(14),35(12),35(10),23(7),23(8),4(10),4(13),4(12),4(16),4(15),4(14)])].
% 0.68/1.01 38 multiply(A,multiply(B,multiply(A,multiply(B,C)))) = multiply(inverse(B),multiply(inverse(A),C)). [para(21(a,1),4(a,1)),rewrite([35(2),4(4),4(6)]),flip(a)].
% 0.68/1.01 41 multiply(A,multiply(inverse(B),A)) = multiply(B,multiply(inverse(A),B)). [para(36(a,1),24(a,1,2)),rewrite([23(3)])].
% 0.68/1.01 48 $F # answer(prove_commutator). [para(41(a,1),37(a,1,2,2,2,2,2)),rewrite([23(10),21(12),38(13),23(7),18(7),24(8),19(4)]),xx(a)].
% 0.68/1.01
% 0.68/1.01 % SZS output end Refutation
% 0.68/1.01 ============================== end of proof ==========================
% 0.68/1.01
% 0.68/1.01 ============================== STATISTICS ============================
% 0.68/1.01
% 0.68/1.01 Given=20. Generated=318. Kept=46. proofs=1.
% 0.68/1.01 Usable=16. Sos=4. Demods=18. Limbo=5, Disabled=27. Hints=0.
% 0.68/1.01 Megabytes=0.06.
% 0.68/1.01 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.68/1.01
% 0.68/1.01 ============================== end of statistics =====================
% 0.68/1.01
% 0.68/1.01 ============================== end of search =========================
% 0.68/1.01
% 0.68/1.01 THEOREM PROVED
% 0.68/1.01 % SZS status Unsatisfiable
% 0.68/1.01
% 0.68/1.01 Exiting with 1 proof.
% 0.68/1.01
% 0.68/1.01 Process 32044 exit (max_proofs) Tue Jun 14 01:05:09 2022
% 0.68/1.01 Prover9 interrupted
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