TSTP Solution File: GRP610-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : GRP610-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n020.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 11:19:50 EDT 2022

% Result   : Unsatisfiable 0.75s 1.04s
% Output   : Refutation 0.75s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : GRP610-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jun 13 08:00:05 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.75/1.04  ============================== Prover9 ===============================
% 0.75/1.04  Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.04  Process 5628 was started by sandbox on n020.cluster.edu,
% 0.75/1.04  Mon Jun 13 08:00:05 2022
% 0.75/1.04  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5475_n020.cluster.edu".
% 0.75/1.04  ============================== end of head ===========================
% 0.75/1.04  
% 0.75/1.04  ============================== INPUT =================================
% 0.75/1.04  
% 0.75/1.04  % Reading from file /tmp/Prover9_5475_n020.cluster.edu
% 0.75/1.04  
% 0.75/1.04  set(prolog_style_variables).
% 0.75/1.04  set(auto2).
% 0.75/1.04      % set(auto2) -> set(auto).
% 0.75/1.04      % set(auto) -> set(auto_inference).
% 0.75/1.04      % set(auto) -> set(auto_setup).
% 0.75/1.04      % set(auto_setup) -> set(predicate_elim).
% 0.75/1.04      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.04      % set(auto) -> set(auto_limits).
% 0.75/1.04      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.04      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.04      % set(auto) -> set(auto_denials).
% 0.75/1.04      % set(auto) -> set(auto_process).
% 0.75/1.04      % set(auto2) -> assign(new_constants, 1).
% 0.75/1.04      % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.04      % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.04      % set(auto2) -> assign(max_hours, 1).
% 0.75/1.04      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.04      % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.04      % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.04      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.04      % set(auto2) -> set(sort_initial_sos).
% 0.75/1.04      % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.04      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.04      % set(auto2) -> assign(max_megs, 400).
% 0.75/1.04      % set(auto2) -> assign(stats, some).
% 0.75/1.04      % set(auto2) -> clear(echo_input).
% 0.75/1.04      % set(auto2) -> set(quiet).
% 0.75/1.04      % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.04      % set(auto2) -> clear(print_given).
% 0.75/1.04  assign(lrs_ticks,-1).
% 0.75/1.04  assign(sos_limit,10000).
% 0.75/1.04  assign(order,kbo).
% 0.75/1.04  set(lex_order_vars).
% 0.75/1.04  clear(print_given).
% 0.75/1.04  
% 0.75/1.04  % formulas(sos).  % not echoed (3 formulas)
% 0.75/1.04  
% 0.75/1.04  ============================== end of input ==========================
% 0.75/1.04  
% 0.75/1.04  % From the command line: assign(max_seconds, 300).
% 0.75/1.04  
% 0.75/1.04  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.04  
% 0.75/1.04  % Formulas that are not ordinary clauses:
% 0.75/1.04  
% 0.75/1.04  ============================== end of process non-clausal formulas ===
% 0.75/1.04  
% 0.75/1.04  ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.04  
% 0.75/1.04  ============================== PREDICATE ELIMINATION =================
% 0.75/1.04  
% 0.75/1.04  ============================== end predicate elimination =============
% 0.75/1.04  
% 0.75/1.04  Auto_denials:
% 0.75/1.04    % copying label prove_these_axioms_2 to answer in negative clause
% 0.75/1.04  
% 0.75/1.04  Term ordering decisions:
% 0.75/1.04  
% 0.75/1.04  % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.75/1.04  Function symbol KB weights:  a2=1. b2=1. double_divide=1. multiply=1. inverse=0.
% 0.75/1.04  
% 0.75/1.04  ============================== end of process initial clauses ========
% 0.75/1.04  
% 0.75/1.04  ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.04  
% 0.75/1.04  ============================== end of clauses for search =============
% 0.75/1.04  
% 0.75/1.04  ============================== SEARCH ================================
% 0.75/1.04  
% 0.75/1.04  % Starting search at 0.01 seconds.
% 0.75/1.04  
% 0.75/1.04  ============================== PROOF =================================
% 0.75/1.04  % SZS status Unsatisfiable
% 0.75/1.04  % SZS output start Refutation
% 0.75/1.04  
% 0.75/1.04  % Proof 1 at 0.02 (+ 0.00) seconds: prove_these_axioms_2.
% 0.75/1.04  % Length of proof is 48.
% 0.75/1.04  % Level of proof is 18.
% 0.75/1.04  % Maximum clause weight is 30.000.
% 0.75/1.04  % Given clauses 14.
% 0.75/1.04  
% 0.75/1.04  1 multiply(A,B) = inverse(double_divide(B,A)) # label(multiply) # label(axiom).  [assumption].
% 0.75/1.04  2 inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B # label(single_axiom) # label(axiom).  [assumption].
% 0.75/1.04  3 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2).  [assumption].
% 0.75/1.04  4 inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 # answer(prove_these_axioms_2).  [copy(3),rewrite([1(4),1(7)])].
% 0.75/1.04  5 inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(inverse(double_divide(C,A)),D)),B))) = double_divide(C,D).  [para(2(a,1),2(a,1,1,1,1,1))].
% 0.75/1.04  6 inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),double_divide(B,C)))) = C.  [para(2(a,1),2(a,1,1,1))].
% 0.75/1.04  7 inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(inverse(double_divide(D,E)),C))) = double_divide(inverse(double_divide(inverse(double_divide(A,D)),B)),E).  [para(5(a,1),2(a,1,1,1,1,1))].
% 0.75/1.04  8 inverse(double_divide(double_divide(A,B),double_divide(C,double_divide(inverse(double_divide(inverse(double_divide(A,C)),B)),D)))) = D.  [para(5(a,1),2(a,1,1,1))].
% 0.75/1.04  16 double_divide(A,inverse(double_divide(B,double_divide(inverse(double_divide(A,B)),C)))) = C.  [para(6(a,1),5(a,1)),flip(a)].
% 0.75/1.04  20 inverse(double_divide(inverse(A),double_divide(B,inverse(double_divide(C,double_divide(inverse(double_divide(inverse(double_divide(B,D)),C)),A)))))) = D.  [para(16(a,1),2(a,1,1,1,1))].
% 0.75/1.04  25 inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(C),B))) = double_divide(D,inverse(double_divide(E,double_divide(inverse(double_divide(inverse(double_divide(D,A)),E)),C)))).  [para(16(a,1),5(a,1,1,2,1,1))].
% 0.75/1.04  28 double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(double_divide(B,C)))) = C.  [para(5(a,1),16(a,1,2))].
% 0.75/1.04  33 inverse(double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(B,C)),A)),D))) = double_divide(B,inverse(double_divide(C,D))).  [para(16(a,1),16(a,1,2,1,2)),flip(a)].
% 0.75/1.04  35 inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(C),B))) = double_divide(D,double_divide(D,inverse(double_divide(A,C)))).  [back_rewrite(25),rewrite([33(13)])].
% 0.75/1.04  36 inverse(double_divide(inverse(A),double_divide(B,double_divide(B,inverse(double_divide(C,A)))))) = C.  [back_rewrite(20),rewrite([33(8)])].
% 0.75/1.04  37 inverse(double_divide(inverse(double_divide(inverse(A),B)),double_divide(inverse(double_divide(C,D)),B))) = double_divide(C,inverse(double_divide(D,A))).  [para(28(a,1),2(a,1,1,1,1,1,1))].
% 0.75/1.04  50 inverse(double_divide(A,double_divide(inverse(double_divide(B,A)),C))) = double_divide(inverse(double_divide(D,B)),double_divide(D,inverse(C))).  [para(16(a,1),28(a,1,2,2,1)),flip(a)].
% 0.75/1.04  58 inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,B))) = double_divide(D,double_divide(E,double_divide(E,inverse(double_divide(C,double_divide(D,A)))))).  [para(36(a,1),5(a,1,1,2,1))].
% 0.75/1.04  63 double_divide(inverse(double_divide(A,inverse(B))),inverse(double_divide(C,B))) = double_divide(A,C).  [para(36(a,1),16(a,1,2)),flip(a)].
% 0.75/1.04  71 double_divide(inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)),D) = double_divide(B,D).  [para(7(a,1),5(a,1))].
% 0.75/1.04  79 inverse(double_divide(inverse(double_divide(double_divide(A,B),C)),double_divide(inverse(D),C))) = double_divide(inverse(double_divide(inverse(double_divide(A,E)),B)),inverse(double_divide(F,double_divide(inverse(double_divide(E,F)),D)))).  [para(16(a,1),7(a,1,1,2,1,1))].
% 0.75/1.04  87 double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C)))) = inverse(double_divide(C,B)).  [para(63(a,1),2(a,1,1,1,1,1,1)),rewrite([37(10)])].
% 0.75/1.04  90 double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),D) = double_divide(A,inverse(double_divide(inverse(double_divide(B,D)),C))).  [para(2(a,1),63(a,1,2))].
% 0.75/1.04  92 double_divide(inverse(double_divide(A,B)),inverse(double_divide(C,double_divide(B,D)))) = double_divide(inverse(double_divide(A,inverse(D))),C).  [para(63(a,1),5(a,1,1,2,1,1,1,1)),rewrite([37(11)])].
% 0.75/1.04  103 inverse(double_divide(inverse(inverse(double_divide(A,B))),double_divide(C,double_divide(C,inverse(double_divide(D,A)))))) = inverse(double_divide(D,inverse(B))).  [para(63(a,1),36(a,1,1,2,2,2,1))].
% 0.75/1.04  115 double_divide(inverse(inverse(double_divide(A,double_divide(B,A)))),C) = double_divide(B,C).  [back_rewrite(71),rewrite([90(6),87(6)])].
% 0.75/1.04  133 double_divide(inverse(inverse(A)),B) = double_divide(A,B).  [para(28(a,1),115(a,1,1,1,1))].
% 0.75/1.04  135 inverse(inverse(double_divide(A,double_divide(B,A)))) = B.  [para(115(a,1),36(a,1,1,2,2,2,1)),rewrite([36(7)]),flip(a)].
% 0.75/1.04  140 inverse(double_divide(double_divide(A,B),double_divide(C,double_divide(C,inverse(double_divide(D,A)))))) = inverse(double_divide(D,inverse(B))).  [back_rewrite(103),rewrite([133(8)])].
% 0.75/1.04  149 inverse(inverse(A)) = A.  [para(133(a,1),36(a,1,1,2,2,2,1)),rewrite([36(7)]),flip(a)].
% 0.75/1.04  153 double_divide(A,double_divide(B,A)) = B.  [back_rewrite(135),rewrite([149(4)])].
% 0.75/1.04  159 double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(inverse(double_divide(C,A)),D)),B)) = inverse(double_divide(C,D)).  [para(5(a,1),149(a,1,1)),flip(a)].
% 0.75/1.04  167 inverse(double_divide(double_divide(A,B),double_divide(C,D))) = double_divide(inverse(double_divide(A,C)),inverse(double_divide(B,D))).  [para(16(a,1),8(a,1,1,2,2)),rewrite([33(13)])].
% 0.75/1.04  171 double_divide(inverse(double_divide(A,B)),inverse(double_divide(C,double_divide(double_divide(D,E),double_divide(F,double_divide(inverse(double_divide(inverse(double_divide(D,F)),E)),B)))))) = double_divide(A,C).  [para(8(a,1),63(a,1,1,1,2))].
% 0.75/1.04  172 double_divide(double_divide(A,B),double_divide(C,double_divide(inverse(double_divide(inverse(double_divide(A,C)),B)),D))) = inverse(D).  [para(8(a,1),149(a,1,1)),flip(a)].
% 0.75/1.04  174 inverse(double_divide(A,inverse(B))) = double_divide(inverse(A),B).  [back_rewrite(140),rewrite([167(7),92(8),149(3),153(2)]),flip(a)].
% 0.75/1.04  179 double_divide(inverse(double_divide(A,B)),double_divide(inverse(C),B)) = double_divide(A,C).  [back_rewrite(171),rewrite([172(10),174(5)])].
% 0.75/1.04  191 double_divide(double_divide(inverse(A),double_divide(B,C)),D) = double_divide(A,inverse(double_divide(inverse(double_divide(B,D)),C))).  [back_rewrite(90),rewrite([174(4)])].
% 0.75/1.04  196 inverse(double_divide(a2,double_divide(inverse(b2),b2))) != a2 # answer(prove_these_axioms_2).  [back_rewrite(4),rewrite([174(6)])].
% 0.75/1.04  198 double_divide(A,double_divide(inverse(double_divide(B,A)),C)) = inverse(double_divide(B,C)).  [back_rewrite(159),rewrite([179(8)])].
% 0.75/1.04  202 double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(B,D)) = inverse(double_divide(double_divide(A,C),D)).  [back_rewrite(79),rewrite([179(6),198(11),149(10)]),flip(a)].
% 0.75/1.04  204 double_divide(A,double_divide(A,inverse(double_divide(B,C)))) = inverse(double_divide(B,C)).  [back_rewrite(35),rewrite([179(5)]),flip(a)].
% 0.75/1.04  223 double_divide(inverse(double_divide(A,B)),double_divide(A,inverse(C))) = double_divide(B,C).  [back_rewrite(50),rewrite([198(4),149(3)]),flip(a)].
% 0.75/1.04  226 double_divide(inverse(double_divide(A,B)),C) = double_divide(A,inverse(double_divide(B,C))).  [back_rewrite(33),rewrite([198(6),149(5)])].
% 0.75/1.04  240 double_divide(A,inverse(double_divide(B,double_divide(A,C)))) = double_divide(inverse(C),B).  [back_rewrite(58),rewrite([226(4),153(2),174(3),204(7)]),flip(a)].
% 0.75/1.04  251 double_divide(A,B) = double_divide(B,A).  [back_rewrite(223),rewrite([226(5),240(5),149(2)])].
% 0.75/1.04  256 inverse(double_divide(A,double_divide(B,C))) = double_divide(C,double_divide(A,inverse(B))).  [back_rewrite(202),rewrite([251(3),174(4),191(5),251(4),240(4),251(2),174(3),251(2),251(5)]),flip(a)].
% 0.75/1.04  294 $F # answer(prove_these_axioms_2).  [back_rewrite(196),rewrite([251(5),256(7),153(7)]),xx(a)].
% 0.75/1.04  
% 0.75/1.04  % SZS output end Refutation
% 0.75/1.04  ============================== end of proof ==========================
% 0.75/1.04  
% 0.75/1.04  ============================== STATISTICS ============================
% 0.75/1.04  
% 0.75/1.04  Given=14. Generated=549. Kept=292. proofs=1.
% 0.75/1.04  Usable=2. Sos=10. Demods=44. Limbo=43, Disabled=240. Hints=0.
% 0.75/1.04  Megabytes=0.32.
% 0.75/1.04  User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.75/1.04  
% 0.75/1.04  ============================== end of statistics =====================
% 0.75/1.04  
% 0.75/1.04  ============================== end of search =========================
% 0.75/1.04  
% 0.75/1.04  THEOREM PROVED
% 0.75/1.04  % SZS status Unsatisfiable
% 0.75/1.04  
% 0.75/1.04  Exiting with 1 proof.
% 0.75/1.04  
% 0.75/1.04  Process 5628 exit (max_proofs) Mon Jun 13 08:00:05 2022
% 0.75/1.04  Prover9 interrupted
%------------------------------------------------------------------------------