TSTP Solution File: GRP711+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : GRP711+1 : TPTP v8.1.0. Released v4.0.0.
% 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 11:20:45 EDT 2022

% Result   : Theorem 0.73s 1.07s
% 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  : GRP711+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % 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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 13 09:14:25 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.73/1.07  ============================== Prover9 ===============================
% 0.73/1.07  Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.07  Process 30657 was started by sandbox2 on n012.cluster.edu,
% 0.73/1.07  Mon Jun 13 09:14:26 2022
% 0.73/1.07  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30504_n012.cluster.edu".
% 0.73/1.07  ============================== end of head ===========================
% 0.73/1.07  
% 0.73/1.07  ============================== INPUT =================================
% 0.73/1.07  
% 0.73/1.07  % Reading from file /tmp/Prover9_30504_n012.cluster.edu
% 0.73/1.07  
% 0.73/1.07  set(prolog_style_variables).
% 0.73/1.07  set(auto2).
% 0.73/1.07      % set(auto2) -> set(auto).
% 0.73/1.07      % set(auto) -> set(auto_inference).
% 0.73/1.07      % set(auto) -> set(auto_setup).
% 0.73/1.07      % set(auto_setup) -> set(predicate_elim).
% 0.73/1.07      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.07      % set(auto) -> set(auto_limits).
% 0.73/1.07      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.07      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.07      % set(auto) -> set(auto_denials).
% 0.73/1.07      % set(auto) -> set(auto_process).
% 0.73/1.07      % set(auto2) -> assign(new_constants, 1).
% 0.73/1.07      % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.07      % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.07      % set(auto2) -> assign(max_hours, 1).
% 0.73/1.07      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.07      % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.07      % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.07      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.07      % set(auto2) -> set(sort_initial_sos).
% 0.73/1.07      % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.07      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.07      % set(auto2) -> assign(max_megs, 400).
% 0.73/1.07      % set(auto2) -> assign(stats, some).
% 0.73/1.07      % set(auto2) -> clear(echo_input).
% 0.73/1.07      % set(auto2) -> set(quiet).
% 0.73/1.07      % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.07      % set(auto2) -> clear(print_given).
% 0.73/1.07  assign(lrs_ticks,-1).
% 0.73/1.07  assign(sos_limit,10000).
% 0.73/1.07  assign(order,kbo).
% 0.73/1.07  set(lex_order_vars).
% 0.73/1.07  clear(print_given).
% 0.73/1.07  
% 0.73/1.07  % formulas(sos).  % not echoed (6 formulas)
% 0.73/1.07  
% 0.73/1.07  ============================== end of input ==========================
% 0.73/1.07  
% 0.73/1.07  % From the command line: assign(max_seconds, 300).
% 0.73/1.07  
% 0.73/1.07  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.07  
% 0.73/1.07  % Formulas that are not ordinary clauses:
% 0.73/1.07  1 (all A mult(A,unit) = A) # label(f01) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.07  2 (all A mult(unit,A) = A) # label(f02) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.07  3 (all C all B all A mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C)) # label(f03) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.07  4 (all A mult(A,i(A)) = unit) # label(f04) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.07  5 (all A mult(i(A),A) = unit) # label(f05) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.07  6 -(all X6 all X7 all X8 ((mult(X6,X7) = mult(X6,X8) -> X7 = X8) & (mult(X7,X6) = mult(X8,X6) -> X7 = X8))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.73/1.07  
% 0.73/1.07  ============================== end of process non-clausal formulas ===
% 0.73/1.07  
% 0.73/1.07  ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.07  
% 0.73/1.07  ============================== PREDICATE ELIMINATION =================
% 0.73/1.07  
% 0.73/1.07  ============================== end predicate elimination =============
% 0.73/1.07  
% 0.73/1.07  Auto_denials:  (non-Horn, no changes).
% 0.73/1.07  
% 0.73/1.07  Term ordering decisions:
% 0.73/1.07  
% 0.73/1.07  % Assigning unary symbol i kb_weight 0 and highest precedence (7).
% 0.73/1.07  Function symbol KB weights:  unit=1. c1=1. c2=1. c3=1. mult=1. i=0.
% 0.73/1.07  
% 0.73/1.07  ============================== end of process initial clauses ========
% 0.73/1.07  
% 0.73/1.07  ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.07  
% 0.73/1.07  ============================== end of clauses for search =============
% 0.73/1.07  
% 0.73/1.07  ============================== SEARCH ================================
% 0.73/1.07  
% 0.73/1.07  % Starting search at 0.01 seconds.
% 0.73/1.07  
% 0.73/1.07  ============================== PROOF =================================
% 0.73/1.07  % SZS status Theorem
% 0.73/1.07  % SZS output start Refutation
% 0.73/1.07  
% 0.73/1.07  % Proof 1 at 0.08 (+ 0.00) seconds.
% 0.73/1.07  % Length of proof is 47.
% 0.73/1.07  % Level of proof is 22.
% 0.73/1.07  % Maximum clause weight is 22.000.
% 0.73/1.07  % Given clauses 50.
% 0.73/1.07  
% 0.73/1.07  1 (all A mult(A,unit) = A) # label(f01) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.07  2 (all A mult(unit,A) = A) # label(f02) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.07  3 (all C all B all A mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C)) # label(f03) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.07  4 (all A mult(A,i(A)) = unit) # label(f04) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.07  5 (all A mult(i(A),A) = unit) # label(f05) # label(axiom) # label(non_clause).  [assumption].
% 0.73/1.07  6 -(all X6 all X7 all X8 ((mult(X6,X7) = mult(X6,X8) -> X7 = X8) & (mult(X7,X6) = mult(X8,X6) -> X7 = X8))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.73/1.07  7 mult(A,unit) = A # label(f01) # label(axiom).  [clausify(1)].
% 0.73/1.07  8 mult(unit,A) = A # label(f02) # label(axiom).  [clausify(2)].
% 0.73/1.07  9 mult(A,i(A)) = unit # label(f04) # label(axiom).  [clausify(4)].
% 0.73/1.07  10 mult(i(A),A) = unit # label(f05) # label(axiom).  [clausify(5)].
% 0.73/1.07  11 mult(c1,c3) = mult(c1,c2) | mult(c3,c1) = mult(c2,c1) # label(goals) # label(negated_conjecture).  [clausify(6)].
% 0.73/1.07  12 mult(mult(mult(A,B),B),C) = mult(A,mult(B,mult(B,C))) # label(f03) # label(axiom).  [clausify(3)].
% 0.73/1.07  13 c3 != c2 # label(goals) # label(negated_conjecture).  [clausify(6)].
% 0.73/1.07  15 mult(mult(A,B),B) = mult(A,mult(B,B)).  [para(12(a,1),7(a,1)),rewrite([7(2)]),flip(a)].
% 0.73/1.07  16 mult(mult(A,A),B) = mult(A,mult(A,B)).  [para(8(a,1),12(a,1,1,1)),rewrite([8(6)])].
% 0.73/1.07  17 mult(A,mult(B,mult(B,i(mult(A,mult(B,B)))))) = unit.  [para(12(a,1),9(a,1)),rewrite([15(2)])].
% 0.73/1.07  20 mult(i(A),mult(A,mult(A,B))) = mult(A,B).  [para(10(a,1),12(a,1,1,1)),rewrite([8(2)]),flip(a)].
% 0.73/1.07  30 mult(mult(A,mult(B,B)),C) = mult(A,mult(B,mult(B,C))).  [back_rewrite(12),rewrite([15(2)])].
% 0.73/1.07  36 mult(A,mult(i(A),i(A))) = i(A).  [para(9(a,1),15(a,1,1)),rewrite([8(3)]),flip(a)].
% 0.73/1.07  37 mult(i(A),mult(A,A)) = A.  [para(10(a,1),15(a,1,1)),rewrite([8(2)]),flip(a)].
% 0.73/1.07  41 mult(A,mult(A,i(mult(A,A)))) = unit.  [para(16(a,1),9(a,1))].
% 0.73/1.07  45 mult(A,mult(A,mult(i(mult(A,A)),i(mult(A,A))))) = i(mult(A,A)).  [para(16(a,1),36(a,1))].
% 0.73/1.07  53 i(i(A)) = A.  [para(37(a,1),20(a,1,2,2)),rewrite([10(4),7(4),37(5)])].
% 0.73/1.07  56 mult(A,i(mult(A,A))) = i(A).  [para(41(a,1),20(a,1,2)),rewrite([7(3)]),flip(a)].
% 0.73/1.07  58 mult(A,mult(i(mult(A,A)),i(mult(A,A)))) = mult(i(A),i(mult(A,A))).  [para(56(a,1),15(a,1,1)),flip(a)].
% 0.73/1.07  60 mult(A,mult(i(A),i(mult(A,A)))) = i(mult(A,A)).  [back_rewrite(45),rewrite([58(6)])].
% 0.73/1.07  73 i(mult(A,A)) = mult(i(A),i(A)).  [para(60(a,1),20(a,1,2,2)),rewrite([56(4),60(8)]),flip(a)].
% 0.73/1.07  101 mult(i(A),mult(A,B)) = B.  [para(10(a,1),30(a,1,1)),rewrite([8(2),73(2),16(6),20(5)]),flip(a)].
% 0.73/1.07  120 mult(c1,c3) = mult(c1,c2) | mult(i(c3),mult(c2,c1)) = c1.  [para(11(b,1),101(a,1,2))].
% 0.73/1.07  122 mult(i(mult(A,B)),mult(A,mult(B,B))) = B.  [para(15(a,1),101(a,1,2))].
% 0.73/1.07  123 mult(A,mult(A,i(mult(B,mult(A,A))))) = i(B).  [para(17(a,1),101(a,1,2)),rewrite([7(3)]),flip(a)].
% 0.73/1.07  124 mult(A,mult(i(A),B)) = B.  [para(53(a,1),101(a,1,1))].
% 0.73/1.07  172 mult(A,i(mult(B,mult(A,A)))) = mult(i(A),i(B)).  [para(123(a,1),101(a,1,2)),flip(a)].
% 0.73/1.07  176 mult(A,i(mult(B,mult(A,mult(A,mult(A,A)))))) = mult(i(A),i(mult(B,mult(A,A)))).  [para(15(a,1),172(a,1,2,1)),rewrite([16(3)])].
% 0.73/1.07  177 i(mult(A,mult(B,B))) = mult(i(B),mult(i(B),i(A))).  [para(172(a,1),16(a,1)),rewrite([73(2),16(5),16(8),176(11),124(11)]),flip(a)].
% 0.73/1.07  266 i(mult(i(A),mult(i(A),i(B)))) = mult(B,mult(A,A)).  [para(177(a,1),53(a,1,1))].
% 0.73/1.07  318 i(mult(A,mult(A,i(B)))) = mult(B,mult(i(A),i(A))).  [para(53(a,1),266(a,1,1,1)),rewrite([53(2)])].
% 0.73/1.07  324 i(mult(A,mult(A,B))) = mult(i(B),mult(i(A),i(A))).  [para(53(a,1),318(a,1,1,2,2))].
% 0.73/1.07  338 mult(i(mult(A,B)),mult(A,A)) = i(mult(i(A),B)).  [para(101(a,1),324(a,1,1,2)),rewrite([53(7),53(7)]),flip(a)].
% 0.73/1.07  356 mult(i(mult(i(mult(A,B)),A)),i(mult(i(A),B))) = A.  [para(338(a,1),122(a,1,2))].
% 0.73/1.07  532 mult(i(mult(i(A),i(B))),i(A)) = B.  [para(101(a,1),356(a,1,2,1)),rewrite([324(3),30(6),10(4),7(4)])].
% 0.73/1.07  539 mult(c1,c3) = mult(c1,c2) | mult(i(mult(i(mult(c3,mult(c2,c1))),c3)),i(c1)) = c3.  [para(120(b,1),356(a,1,2,1))].
% 0.73/1.07  614 i(mult(A,i(B))) = mult(B,i(A)).  [para(532(a,1),15(a,1,1)),rewrite([338(10),53(4)]),flip(a)].
% 0.73/1.07  621 mult(i(mult(A,B)),A) = i(B).  [para(532(a,1),101(a,1,2)),rewrite([614(4),53(2)])].
% 0.73/1.07  639 mult(mult(A,B),i(B)) = A.  [back_rewrite(532),rewrite([614(4),53(2)])].
% 0.73/1.07  647 mult(c1,c3) = mult(c1,c2).  [back_rewrite(539),rewrite([621(15),53(12),639(13)]),flip(b),unit_del(b,13)].
% 0.73/1.07  651 $F.  [para(647(a,1),101(a,1,2)),rewrite([101(6)]),flip(a),unit_del(a,13)].
% 0.73/1.07  
% 0.73/1.07  % SZS output end Refutation
% 0.73/1.07  ============================== end of proof ==========================
% 0.73/1.07  
% 0.73/1.07  ============================== STATISTICS ============================
% 0.73/1.07  
% 0.73/1.07  Given=50. Generated=2258. Kept=644. proofs=1.
% 0.73/1.07  Usable=27. Sos=233. Demods=260. Limbo=1, Disabled=390. Hints=0.
% 0.73/1.07  Megabytes=1.04.
% 0.73/1.07  User_CPU=0.08, System_CPU=0.00, Wall_clock=0.
% 0.73/1.07  
% 0.73/1.07  ============================== end of statistics =====================
% 0.73/1.07  
% 0.73/1.07  ============================== end of search =========================
% 0.73/1.07  
% 0.73/1.07  THEOREM PROVED
% 0.73/1.07  % SZS status Theorem
% 0.73/1.07  
% 0.73/1.07  Exiting with 1 proof.
% 0.73/1.07  
% 0.73/1.07  Process 30657 exit (max_proofs) Mon Jun 13 09:14:26 2022
% 0.73/1.07  Prover9 interrupted
%------------------------------------------------------------------------------