TSTP Solution File: GRP402-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP402-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 11:18:56 EDT 2022
% Result : Unsatisfiable 0.77s 1.14s
% Output : Refutation 0.77s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP402-1 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.37 % Computer : n021.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Mon Jun 13 11:52:57 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.77/1.14 ============================== Prover9 ===============================
% 0.77/1.14 Prover9 (32) version 2009-11A, November 2009.
% 0.77/1.14 Process 4009 was started by sandbox2 on n021.cluster.edu,
% 0.77/1.14 Mon Jun 13 11:52:57 2022
% 0.77/1.14 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3855_n021.cluster.edu".
% 0.77/1.14 ============================== end of head ===========================
% 0.77/1.14
% 0.77/1.14 ============================== INPUT =================================
% 0.77/1.14
% 0.77/1.14 % Reading from file /tmp/Prover9_3855_n021.cluster.edu
% 0.77/1.14
% 0.77/1.14 set(prolog_style_variables).
% 0.77/1.14 set(auto2).
% 0.77/1.14 % set(auto2) -> set(auto).
% 0.77/1.14 % set(auto) -> set(auto_inference).
% 0.77/1.14 % set(auto) -> set(auto_setup).
% 0.77/1.14 % set(auto_setup) -> set(predicate_elim).
% 0.77/1.14 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.77/1.14 % set(auto) -> set(auto_limits).
% 0.77/1.14 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.77/1.14 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.77/1.14 % set(auto) -> set(auto_denials).
% 0.77/1.14 % set(auto) -> set(auto_process).
% 0.77/1.14 % set(auto2) -> assign(new_constants, 1).
% 0.77/1.14 % set(auto2) -> assign(fold_denial_max, 3).
% 0.77/1.14 % set(auto2) -> assign(max_weight, "200.000").
% 0.77/1.14 % set(auto2) -> assign(max_hours, 1).
% 0.77/1.14 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.77/1.14 % set(auto2) -> assign(max_seconds, 0).
% 0.77/1.14 % set(auto2) -> assign(max_minutes, 5).
% 0.77/1.14 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.77/1.14 % set(auto2) -> set(sort_initial_sos).
% 0.77/1.14 % set(auto2) -> assign(sos_limit, -1).
% 0.77/1.14 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.77/1.14 % set(auto2) -> assign(max_megs, 400).
% 0.77/1.14 % set(auto2) -> assign(stats, some).
% 0.77/1.14 % set(auto2) -> clear(echo_input).
% 0.77/1.14 % set(auto2) -> set(quiet).
% 0.77/1.14 % set(auto2) -> clear(print_initial_clauses).
% 0.77/1.14 % set(auto2) -> clear(print_given).
% 0.77/1.14 assign(lrs_ticks,-1).
% 0.77/1.14 assign(sos_limit,10000).
% 0.77/1.14 assign(order,kbo).
% 0.77/1.14 set(lex_order_vars).
% 0.77/1.14 clear(print_given).
% 0.77/1.14
% 0.77/1.14 % formulas(sos). % not echoed (6 formulas)
% 0.77/1.14
% 0.77/1.14 ============================== end of input ==========================
% 0.77/1.14
% 0.77/1.14 % From the command line: assign(max_seconds, 300).
% 0.77/1.14
% 0.77/1.14 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.77/1.14
% 0.77/1.14 % Formulas that are not ordinary clauses:
% 0.77/1.14
% 0.77/1.14 ============================== end of process non-clausal formulas ===
% 0.77/1.14
% 0.77/1.14 ============================== PROCESS INITIAL CLAUSES ===============
% 0.77/1.14
% 0.77/1.14 ============================== PREDICATE ELIMINATION =================
% 0.77/1.14
% 0.77/1.14 ============================== end predicate elimination =============
% 0.77/1.14
% 0.77/1.14 Auto_denials:
% 0.77/1.14 % copying label prove_commutator_is_associative to answer in negative clause
% 0.77/1.14
% 0.77/1.14 Term ordering decisions:
% 0.77/1.14 Function symbol KB weights: a=1. b=1. c=1. multiply=1. commutator=1.
% 0.77/1.14
% 0.77/1.14 ============================== end of process initial clauses ========
% 0.77/1.14
% 0.77/1.14 ============================== CLAUSES FOR SEARCH ====================
% 0.77/1.14
% 0.77/1.14 ============================== end of clauses for search =============
% 0.77/1.14
% 0.77/1.14 ============================== SEARCH ================================
% 0.77/1.14
% 0.77/1.14 % Starting search at 0.01 seconds.
% 0.77/1.14
% 0.77/1.14 ============================== PROOF =================================
% 0.77/1.14 % SZS status Unsatisfiable
% 0.77/1.14 % SZS output start Refutation
% 0.77/1.14
% 0.77/1.14 % Proof 1 at 0.10 (+ 0.00) seconds: prove_commutator_is_associative.
% 0.77/1.14 % Length of proof is 27.
% 0.77/1.14 % Level of proof is 10.
% 0.77/1.14 % Maximum clause weight is 39.000.
% 0.77/1.14 % Given clauses 59.
% 0.77/1.14
% 0.77/1.14 1 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity_of_multiply) # label(axiom). [assumption].
% 0.77/1.14 2 multiply(A,B) = multiply(B,multiply(A,commutator(A,B))) # label(commutator) # label(axiom). [assumption].
% 0.77/1.14 3 multiply(A,multiply(B,commutator(B,A))) = multiply(B,A). [copy(2),flip(a)].
% 0.77/1.14 4 multiply(commutator(A,B),C) = multiply(C,commutator(A,B)) # label(nilpotency) # label(axiom). [assumption].
% 0.77/1.14 5 commutator(commutator(a,b),c) != commutator(a,commutator(b,c)) # label(prove_commutator_is_associative) # label(negated_conjecture) # answer(prove_commutator_is_associative). [assumption].
% 0.77/1.14 6 multiply(A,B) != multiply(C,B) | A = C # label(right_cancellation) # label(axiom). [assumption].
% 0.77/1.14 7 multiply(A,B) != multiply(A,C) | B = C # label(left_cancellation) # label(axiom). [assumption].
% 0.77/1.14 8 multiply(A,multiply(B,multiply(C,commutator(B,A)))) = multiply(B,multiply(A,C)). [para(3(a,1),1(a,1,1)),rewrite([1(2),1(5),4(4)]),flip(a)].
% 0.77/1.14 12 multiply(A,commutator(commutator(a,b),c)) != multiply(A,commutator(a,commutator(b,c))) # answer(prove_commutator_is_associative). [ur(6,b,5,a),rewrite([4(6),4(12)])].
% 0.77/1.14 14 multiply(A,multiply(B,commutator(B,C))) != multiply(B,C) | C = A. [para(3(a,1),6(a,1)),flip(a)].
% 0.77/1.14 17 multiply(A,commutator(A,A)) = A. [hyper(7,a,3,a)].
% 0.77/1.14 20 multiply(A,multiply(B,commutator(A,A))) = multiply(A,B). [hyper(7,a,8,a)].
% 0.77/1.14 30 multiply(A,multiply(B,commutator(commutator(a,b),c))) != multiply(A,multiply(B,commutator(a,commutator(b,c)))) # answer(prove_commutator_is_associative). [ur(7,b,12,a)].
% 0.77/1.14 47 multiply(A,B) != A | commutator(A,A) = B. [para(17(a,1),7(a,1)),flip(a)].
% 0.77/1.14 60 multiply(A,multiply(B,C)) != multiply(A,B) | commutator(multiply(A,B),multiply(A,B)) = C. [para(1(a,1),47(a,1))].
% 0.77/1.14 95 multiply(A,commutator(B,B)) = A. [hyper(7,a,20,a)].
% 0.77/1.14 99 commutator(A,A) = commutator(B,B). [hyper(47,a,95,a)].
% 0.77/1.14 103 commutator(A,A) = c_0. [new_symbol(99)].
% 0.77/1.14 109 multiply(A,c_0) = A. [back_rewrite(95),rewrite([103(1)])].
% 0.77/1.14 115 multiply(A,multiply(B,C)) != multiply(A,B) | c_0 = C. [back_rewrite(60),rewrite([103(7)])].
% 0.77/1.14 116 multiply(c_0,A) = A. [para(103(a,1),4(a,1,1)),rewrite([103(3),109(4)])].
% 0.77/1.14 305 multiply(A,B) != multiply(B,A) | commutator(A,B) = c_0. [para(3(a,1),115(a,1)),flip(b)].
% 0.77/1.14 365 multiply(A,B) != multiply(B,B) | B = A. [para(103(a,1),14(a,1,2,2)),rewrite([109(2)])].
% 0.77/1.14 426 multiply(A,multiply(B,multiply(commutator(commutator(a,b),c),multiply(A,multiply(B,commutator(a,commutator(b,c))))))) != multiply(A,multiply(B,multiply(commutator(a,commutator(b,c)),multiply(A,multiply(B,commutator(a,commutator(b,c))))))) # answer(prove_commutator_is_associative). [ur(365,b,30,a(flip)),rewrite([1(15),1(14),1(30),1(29)])].
% 0.77/1.14 439 commutator(commutator(A,B),C) = c_0. [hyper(305,a,4,a)].
% 0.77/1.14 441 commutator(A,commutator(B,C)) = c_0. [hyper(305,a,4,a(flip))].
% 0.77/1.14 455 $F # answer(prove_commutator_is_associative). [back_rewrite(426),rewrite([439(5),441(6),109(3),116(3),441(8),441(9),109(6),116(6)]),xx(a)].
% 0.77/1.14
% 0.77/1.14 % SZS output end Refutation
% 0.77/1.14 ============================== end of proof ==========================
% 0.77/1.14
% 0.77/1.14 ============================== STATISTICS ============================
% 0.77/1.14
% 0.77/1.14 Given=59. Generated=1447. Kept=453. proofs=1.
% 0.77/1.14 Usable=48. Sos=308. Demods=48. Limbo=16, Disabled=87. Hints=0.
% 0.77/1.14 Megabytes=0.65.
% 0.77/1.14 User_CPU=0.10, System_CPU=0.00, Wall_clock=0.
% 0.77/1.14
% 0.77/1.14 ============================== end of statistics =====================
% 0.77/1.14
% 0.77/1.14 ============================== end of search =========================
% 0.77/1.14
% 0.77/1.14 THEOREM PROVED
% 0.77/1.14 % SZS status Unsatisfiable
% 0.77/1.14
% 0.77/1.14 Exiting with 1 proof.
% 0.77/1.14
% 0.77/1.14 Process 4009 exit (max_proofs) Mon Jun 13 11:52:57 2022
% 0.77/1.14 Prover9 interrupted
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