TSTP Solution File: GRP409-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : GRP409-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n008.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 11:18:58 EDT 2022

% Result   : Unsatisfiable 1.11s 1.43s
% Output   : Refutation 1.11s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP409-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 13 13:44:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.11/1.43  ============================== Prover9 ===============================
% 1.11/1.43  Prover9 (32) version 2009-11A, November 2009.
% 1.11/1.43  Process 22702 was started by sandbox on n008.cluster.edu,
% 1.11/1.43  Mon Jun 13 13:44:23 2022
% 1.11/1.43  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22548_n008.cluster.edu".
% 1.11/1.43  ============================== end of head ===========================
% 1.11/1.43  
% 1.11/1.43  ============================== INPUT =================================
% 1.11/1.43  
% 1.11/1.43  % Reading from file /tmp/Prover9_22548_n008.cluster.edu
% 1.11/1.43  
% 1.11/1.43  set(prolog_style_variables).
% 1.11/1.43  set(auto2).
% 1.11/1.43      % set(auto2) -> set(auto).
% 1.11/1.43      % set(auto) -> set(auto_inference).
% 1.11/1.43      % set(auto) -> set(auto_setup).
% 1.11/1.43      % set(auto_setup) -> set(predicate_elim).
% 1.11/1.43      % set(auto_setup) -> assign(eq_defs, unfold).
% 1.11/1.43      % set(auto) -> set(auto_limits).
% 1.11/1.43      % set(auto_limits) -> assign(max_weight, "100.000").
% 1.11/1.43      % set(auto_limits) -> assign(sos_limit, 20000).
% 1.11/1.43      % set(auto) -> set(auto_denials).
% 1.11/1.43      % set(auto) -> set(auto_process).
% 1.11/1.43      % set(auto2) -> assign(new_constants, 1).
% 1.11/1.43      % set(auto2) -> assign(fold_denial_max, 3).
% 1.11/1.43      % set(auto2) -> assign(max_weight, "200.000").
% 1.11/1.43      % set(auto2) -> assign(max_hours, 1).
% 1.11/1.43      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.11/1.43      % set(auto2) -> assign(max_seconds, 0).
% 1.11/1.43      % set(auto2) -> assign(max_minutes, 5).
% 1.11/1.43      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.11/1.43      % set(auto2) -> set(sort_initial_sos).
% 1.11/1.43      % set(auto2) -> assign(sos_limit, -1).
% 1.11/1.43      % set(auto2) -> assign(lrs_ticks, 3000).
% 1.11/1.43      % set(auto2) -> assign(max_megs, 400).
% 1.11/1.43      % set(auto2) -> assign(stats, some).
% 1.11/1.43      % set(auto2) -> clear(echo_input).
% 1.11/1.43      % set(auto2) -> set(quiet).
% 1.11/1.43      % set(auto2) -> clear(print_initial_clauses).
% 1.11/1.43      % set(auto2) -> clear(print_given).
% 1.11/1.43  assign(lrs_ticks,-1).
% 1.11/1.43  assign(sos_limit,10000).
% 1.11/1.43  assign(order,kbo).
% 1.11/1.43  set(lex_order_vars).
% 1.11/1.43  clear(print_given).
% 1.11/1.43  
% 1.11/1.43  % formulas(sos).  % not echoed (2 formulas)
% 1.11/1.43  
% 1.11/1.43  ============================== end of input ==========================
% 1.11/1.43  
% 1.11/1.43  % From the command line: assign(max_seconds, 300).
% 1.11/1.43  
% 1.11/1.43  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.11/1.43  
% 1.11/1.43  % Formulas that are not ordinary clauses:
% 1.11/1.43  
% 1.11/1.43  ============================== end of process non-clausal formulas ===
% 1.11/1.43  
% 1.11/1.43  ============================== PROCESS INITIAL CLAUSES ===============
% 1.11/1.43  
% 1.11/1.43  ============================== PREDICATE ELIMINATION =================
% 1.11/1.43  
% 1.11/1.43  ============================== end predicate elimination =============
% 1.11/1.43  
% 1.11/1.43  Auto_denials:
% 1.11/1.43    % copying label prove_these_axioms_1 to answer in negative clause
% 1.11/1.43  
% 1.11/1.43  Term ordering decisions:
% 1.11/1.43  
% 1.11/1.43  % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 1.11/1.43  Function symbol KB weights:  a1=1. b1=1. multiply=1. inverse=0.
% 1.11/1.43  
% 1.11/1.43  ============================== end of process initial clauses ========
% 1.11/1.43  
% 1.11/1.43  ============================== CLAUSES FOR SEARCH ====================
% 1.11/1.43  
% 1.11/1.43  ============================== end of clauses for search =============
% 1.11/1.43  
% 1.11/1.43  ============================== SEARCH ================================
% 1.11/1.43  
% 1.11/1.43  % Starting search at 0.01 seconds.
% 1.11/1.43  
% 1.11/1.43  ============================== PROOF =================================
% 1.11/1.43  % SZS status Unsatisfiable
% 1.11/1.43  % SZS output start Refutation
% 1.11/1.43  
% 1.11/1.43  % Proof 1 at 0.45 (+ 0.01) seconds: prove_these_axioms_1.
% 1.11/1.43  % Length of proof is 24.
% 1.11/1.43  % Level of proof is 13.
% 1.11/1.43  % Maximum clause weight is 56.000.
% 1.11/1.43  % Given clauses 34.
% 1.11/1.43  
% 1.11/1.43  1 multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))) = B # label(single_axiom) # label(axiom).  [assumption].
% 1.11/1.43  2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) # label(prove_these_axioms_1) # label(negated_conjecture) # answer(prove_these_axioms_1).  [assumption].
% 1.11/1.43  3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) # answer(prove_these_axioms_1).  [copy(2),flip(a)].
% 1.11/1.43  4 multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))).  [para(1(a,1),1(a,1,1,1,1,2,1)),flip(a)].
% 1.11/1.43  5 multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(C))),inverse(multiply(inverse(C),C))) = inverse(C).  [para(1(a,1),1(a,1,1,1,1))].
% 1.11/1.43  8 multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(C),C))) = B.  [para(4(a,1),1(a,1,1))].
% 1.11/1.43  10 multiply(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C)))),multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))) = inverse(inverse(multiply(inverse(C),C))).  [para(4(a,2),1(a,1,1,1,1))].
% 1.11/1.43  12 multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),C)))),multiply(A,inverse(C))) = B.  [para(4(a,2),1(a,1))].
% 1.11/1.43  22 multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(multiply(B,C)))),multiply(D,inverse(C))).  [para(4(a,2),4(a,2))].
% 1.11/1.43  23 multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))),inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,inverse(D))))) = inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(D),D))),D)))).  [para(12(a,1),1(a,1,1,1,1,2,1))].
% 1.11/1.43  24 multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(multiply(D,inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C)))),multiply(inverse(C),C))))),B) = D.  [para(1(a,1),12(a,1,2))].
% 1.11/1.43  35 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))) = multiply(inverse(multiply(E,inverse(B))),multiply(E,inverse(multiply(C,inverse(D))))).  [para(12(a,1),22(a,1,1,1,2,1)),rewrite([12(19)])].
% 1.11/1.43  57 inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(C))),inverse(multiply(inverse(C),C))),C)))) = B.  [para(35(a,1),1(a,1,1)),rewrite([23(19)])].
% 1.11/1.43  60 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C))).  [para(1(a,1),35(a,1,2,2,1)),rewrite([1(20)])].
% 1.11/1.43  138 multiply(inverse(multiply(A,B)),multiply(A,inverse(C))) = multiply(inverse(multiply(D,B)),multiply(D,inverse(C))).  [para(57(a,1),60(a,1,1,1,2)),rewrite([57(16)])].
% 1.11/1.43  152 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)).  [para(57(a,1),138(a,1,2,2)),rewrite([57(17)])].
% 1.11/1.43  808 inverse(inverse(multiply(inverse(multiply(A,B)),multiply(A,B)))) = inverse(inverse(multiply(inverse(multiply(C,B)),multiply(C,B)))).  [para(152(a,1),10(a,2,1,1)),rewrite([10(43)])].
% 1.11/1.43  896 inverse(inverse(multiply(inverse(multiply(A,multiply(B,inverse(C)))),multiply(A,multiply(B,inverse(C)))))) = inverse(inverse(multiply(inverse(D),D))).  [para(12(a,1),808(a,1,1,1,1,1)),rewrite([12(12)]),flip(a)].
% 1.11/1.43  975 inverse(multiply(inverse(multiply(A,multiply(B,inverse(C)))),multiply(A,multiply(B,inverse(C))))) = inverse(multiply(inverse(D),D)).  [para(896(a,1),8(a,1,1,1,1,1,2)),rewrite([8(26)]),flip(a)].
% 1.11/1.43  1557 inverse(multiply(inverse(A),A)) = inverse(multiply(inverse(B),B)).  [para(12(a,1),975(a,1,1,1,1)),rewrite([12(12)])].
% 1.11/1.43  1647 multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C))))),B) = multiply(inverse(D),multiply(multiply(inverse(multiply(E,inverse(multiply(D,multiply(inverse(C),C))))),multiply(E,inverse(multiply(inverse(C),C)))),inverse(multiply(inverse(C),C)))).  [para(5(a,1),24(a,1,1,1,2,1,1))].
% 1.11/1.43  1730 multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(D),D))) = B.  [para(1557(a,1),1(a,1,2))].
% 1.11/1.43  1774 multiply(inverse(A),A) = multiply(inverse(B),B).  [back_rewrite(1647),rewrite([1730(15),1730(18)])].
% 1.11/1.43  1775 $F # answer(prove_these_axioms_1).  [resolve(1774,a,3,a)].
% 1.11/1.43  
% 1.11/1.43  % SZS output end Refutation
% 1.11/1.43  ============================== end of proof ==========================
% 1.11/1.43  
% 1.11/1.43  ============================== STATISTICS ============================
% 1.11/1.43  
% 1.11/1.43  Given=34. Generated=3638. Kept=1773. proofs=1.
% 1.11/1.43  Usable=18. Sos=988. Demods=434. Limbo=44, Disabled=724. Hints=0.
% 1.11/1.43  Megabytes=5.07.
% 1.11/1.43  User_CPU=0.45, System_CPU=0.01, Wall_clock=0.
% 1.11/1.43  
% 1.11/1.43  ============================== end of statistics =====================
% 1.11/1.43  
% 1.11/1.43  ============================== end of search =========================
% 1.11/1.43  
% 1.11/1.43  THEOREM PROVED
% 1.11/1.43  % SZS status Unsatisfiable
% 1.11/1.43  
% 1.11/1.43  Exiting with 1 proof.
% 1.11/1.43  
% 1.11/1.43  Process 22702 exit (max_proofs) Mon Jun 13 13:44:23 2022
% 1.11/1.43  Prover9 interrupted
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