TSTP Solution File: GRP401-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP401-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 0.73s 1.02s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP401-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n012.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
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 600
% 0.19/0.34 % DateTime : Tue Jun 14 13:05:10 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.73/1.02 ============================== Prover9 ===============================
% 0.73/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.02 Process 26130 was started by sandbox2 on n012.cluster.edu,
% 0.73/1.02 Tue Jun 14 13:05:10 2022
% 0.73/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25977_n012.cluster.edu".
% 0.73/1.02 ============================== end of head ===========================
% 0.73/1.02
% 0.73/1.02 ============================== INPUT =================================
% 0.73/1.02
% 0.73/1.02 % Reading from file /tmp/Prover9_25977_n012.cluster.edu
% 0.73/1.02
% 0.73/1.02 set(prolog_style_variables).
% 0.73/1.02 set(auto2).
% 0.73/1.02 % set(auto2) -> set(auto).
% 0.73/1.02 % set(auto) -> set(auto_inference).
% 0.73/1.02 % set(auto) -> set(auto_setup).
% 0.73/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.02 % set(auto) -> set(auto_limits).
% 0.73/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.02 % set(auto) -> set(auto_denials).
% 0.73/1.02 % set(auto) -> set(auto_process).
% 0.73/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.02 % set(auto2) -> assign(stats, some).
% 0.73/1.02 % set(auto2) -> clear(echo_input).
% 0.73/1.02 % set(auto2) -> set(quiet).
% 0.73/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.02 % set(auto2) -> clear(print_given).
% 0.73/1.02 assign(lrs_ticks,-1).
% 0.73/1.02 assign(sos_limit,10000).
% 0.73/1.02 assign(order,kbo).
% 0.73/1.02 set(lex_order_vars).
% 0.73/1.02 clear(print_given).
% 0.73/1.02
% 0.73/1.02 % formulas(sos). % not echoed (6 formulas)
% 0.73/1.02
% 0.73/1.02 ============================== end of input ==========================
% 0.73/1.02
% 0.73/1.02 % From the command line: assign(max_seconds, 300).
% 0.73/1.02
% 0.73/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.02
% 0.73/1.02 % Formulas that are not ordinary clauses:
% 0.73/1.02
% 0.73/1.02 ============================== end of process non-clausal formulas ===
% 0.73/1.02
% 0.73/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.02
% 0.73/1.02 ============================== PREDICATE ELIMINATION =================
% 0.73/1.02
% 0.73/1.02 ============================== end predicate elimination =============
% 0.73/1.02
% 0.73/1.02 Auto_denials:
% 0.73/1.02 % copying label prove_nilpotency to answer in negative clause
% 0.73/1.02
% 0.73/1.02 Term ordering decisions:
% 0.73/1.02 Function symbol KB weights: a=1. b=1. c=1. multiply=1. commutator=1.
% 0.73/1.02
% 0.73/1.02 ============================== end of process initial clauses ========
% 0.73/1.02
% 0.73/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.02
% 0.73/1.02 ============================== end of clauses for search =============
% 0.73/1.02
% 0.73/1.02 ============================== SEARCH ================================
% 0.73/1.02
% 0.73/1.02 % Starting search at 0.01 seconds.
% 0.73/1.02
% 0.73/1.02 ============================== PROOF =================================
% 0.73/1.02 % SZS status Unsatisfiable
% 0.73/1.02 % SZS output start Refutation
% 0.73/1.02
% 0.73/1.02 % Proof 1 at 0.05 (+ 0.00) seconds: prove_nilpotency.
% 0.73/1.02 % Length of proof is 15.
% 0.73/1.02 % Level of proof is 5.
% 0.73/1.02 % Maximum clause weight is 19.000.
% 0.73/1.02 % Given clauses 37.
% 0.73/1.02
% 0.73/1.02 1 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity_of_multiply) # label(axiom). [assumption].
% 0.73/1.02 2 multiply(A,B) = multiply(B,multiply(A,commutator(A,B))) # label(commutator) # label(axiom). [assumption].
% 0.73/1.02 3 multiply(A,multiply(B,commutator(B,A))) = multiply(B,A). [copy(2),flip(a)].
% 0.73/1.02 4 commutator(multiply(A,B),C) = multiply(commutator(A,C),commutator(B,C)) # label(commutator_distributes_over_product) # label(axiom). [assumption].
% 0.73/1.02 5 multiply(commutator(A,B),commutator(C,B)) = commutator(multiply(A,C),B). [copy(4),flip(a)].
% 0.73/1.02 6 multiply(commutator(a,b),c) != multiply(c,commutator(a,b)) # label(prove_nilpotency) # label(negated_conjecture) # answer(prove_nilpotency). [assumption].
% 0.73/1.02 7 multiply(A,B) != multiply(C,B) | A = C # label(right_cancellation) # label(axiom). [assumption].
% 0.73/1.02 8 multiply(A,B) != multiply(A,C) | B = C # label(left_cancellation) # label(axiom). [assumption].
% 0.73/1.02 9 multiply(A,multiply(B,multiply(commutator(B,A),C))) = multiply(B,multiply(A,C)). [para(3(a,1),1(a,1,1)),rewrite([1(2),1(5)]),flip(a)].
% 0.73/1.02 11 multiply(A,multiply(B,multiply(C,commutator(multiply(B,C),A)))) = multiply(B,multiply(C,A)). [para(1(a,1),3(a,1,2)),rewrite([1(7)])].
% 0.73/1.02 20 multiply(A,multiply(commutator(a,b),c)) != multiply(A,multiply(c,commutator(a,b))) # answer(prove_nilpotency). [ur(8,b,6,a)].
% 0.73/1.02 45 multiply(A,multiply(B,multiply(commutator(a,b),c))) != multiply(A,multiply(B,multiply(c,commutator(a,b)))) # answer(prove_nilpotency). [ur(8,b,20,a)].
% 0.73/1.02 187 multiply(b,multiply(a,multiply(c,commutator(a,b)))) != multiply(a,multiply(b,c)) # answer(prove_nilpotency). [para(9(a,1),45(a,1)),flip(a)].
% 0.73/1.02 191 multiply(b,multiply(a,multiply(c,multiply(commutator(a,b),A)))) != multiply(a,multiply(b,multiply(c,A))) # answer(prove_nilpotency). [ur(7,b,187,a),rewrite([1(10),1(9),1(8),1(16),1(15)])].
% 0.73/1.02 280 $F # answer(prove_nilpotency). [para(3(a,1),191(a,2,2)),rewrite([5(10),11(11)]),xx(a)].
% 0.73/1.02
% 0.73/1.02 % SZS output end Refutation
% 0.73/1.02 ============================== end of proof ==========================
% 0.73/1.02
% 0.73/1.02 ============================== STATISTICS ============================
% 0.73/1.02
% 0.73/1.02 Given=37. Generated=827. Kept=277. proofs=1.
% 0.73/1.02 Usable=24. Sos=125. Demods=52. Limbo=3, Disabled=131. Hints=0.
% 0.73/1.02 Megabytes=0.37.
% 0.73/1.02 User_CPU=0.05, System_CPU=0.00, Wall_clock=1.
% 0.73/1.02
% 0.73/1.02 ============================== end of statistics =====================
% 0.73/1.02
% 0.73/1.02 ============================== end of search =========================
% 0.73/1.02
% 0.73/1.02 THEOREM PROVED
% 0.73/1.02 % SZS status Unsatisfiable
% 0.73/1.02
% 0.73/1.02 Exiting with 1 proof.
% 0.73/1.02
% 0.73/1.02 Process 26130 exit (max_proofs) Tue Jun 14 13:05:11 2022
% 0.73/1.02 Prover9 interrupted
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