TSTP Solution File: GRP401-1 by Prover9---1109a

View Problem - 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
%------------------------------------------------------------------------------
%----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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