TSTP Solution File: GRP668-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : GRP668-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n018.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 11:20:30 EDT 2022

% Result   : Unsatisfiable 6.16s 6.38s
% Output   : Refutation 6.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : GRP668-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.11  % Command  : tptp2X_and_run_prover9 %d %s
% 0.10/0.31  % Computer : n018.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 600
% 0.10/0.31  % DateTime : Mon Jun 13 18:15:27 EDT 2022
% 0.10/0.31  % CPUTime  : 
% 6.16/6.38  ============================== Prover9 ===============================
% 6.16/6.38  Prover9 (32) version 2009-11A, November 2009.
% 6.16/6.38  Process 27991 was started by sandbox on n018.cluster.edu,
% 6.16/6.38  Mon Jun 13 18:15:28 2022
% 6.16/6.38  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27838_n018.cluster.edu".
% 6.16/6.38  ============================== end of head ===========================
% 6.16/6.38  
% 6.16/6.38  ============================== INPUT =================================
% 6.16/6.38  
% 6.16/6.38  % Reading from file /tmp/Prover9_27838_n018.cluster.edu
% 6.16/6.38  
% 6.16/6.38  set(prolog_style_variables).
% 6.16/6.38  set(auto2).
% 6.16/6.38      % set(auto2) -> set(auto).
% 6.16/6.38      % set(auto) -> set(auto_inference).
% 6.16/6.38      % set(auto) -> set(auto_setup).
% 6.16/6.38      % set(auto_setup) -> set(predicate_elim).
% 6.16/6.38      % set(auto_setup) -> assign(eq_defs, unfold).
% 6.16/6.38      % set(auto) -> set(auto_limits).
% 6.16/6.38      % set(auto_limits) -> assign(max_weight, "100.000").
% 6.16/6.38      % set(auto_limits) -> assign(sos_limit, 20000).
% 6.16/6.38      % set(auto) -> set(auto_denials).
% 6.16/6.38      % set(auto) -> set(auto_process).
% 6.16/6.38      % set(auto2) -> assign(new_constants, 1).
% 6.16/6.38      % set(auto2) -> assign(fold_denial_max, 3).
% 6.16/6.38      % set(auto2) -> assign(max_weight, "200.000").
% 6.16/6.38      % set(auto2) -> assign(max_hours, 1).
% 6.16/6.38      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 6.16/6.38      % set(auto2) -> assign(max_seconds, 0).
% 6.16/6.38      % set(auto2) -> assign(max_minutes, 5).
% 6.16/6.38      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 6.16/6.38      % set(auto2) -> set(sort_initial_sos).
% 6.16/6.38      % set(auto2) -> assign(sos_limit, -1).
% 6.16/6.38      % set(auto2) -> assign(lrs_ticks, 3000).
% 6.16/6.38      % set(auto2) -> assign(max_megs, 400).
% 6.16/6.38      % set(auto2) -> assign(stats, some).
% 6.16/6.38      % set(auto2) -> clear(echo_input).
% 6.16/6.38      % set(auto2) -> set(quiet).
% 6.16/6.38      % set(auto2) -> clear(print_initial_clauses).
% 6.16/6.38      % set(auto2) -> clear(print_given).
% 6.16/6.38  assign(lrs_ticks,-1).
% 6.16/6.38  assign(sos_limit,10000).
% 6.16/6.38  assign(order,kbo).
% 6.16/6.38  set(lex_order_vars).
% 6.16/6.38  clear(print_given).
% 6.16/6.38  
% 6.16/6.38  % formulas(sos).  % not echoed (9 formulas)
% 6.16/6.38  
% 6.16/6.38  ============================== end of input ==========================
% 6.16/6.38  
% 6.16/6.38  % From the command line: assign(max_seconds, 300).
% 6.16/6.38  
% 6.16/6.38  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 6.16/6.38  
% 6.16/6.38  % Formulas that are not ordinary clauses:
% 6.16/6.38  
% 6.16/6.38  ============================== end of process non-clausal formulas ===
% 6.16/6.38  
% 6.16/6.38  ============================== PROCESS INITIAL CLAUSES ===============
% 6.16/6.38  
% 6.16/6.38  ============================== PREDICATE ELIMINATION =================
% 6.16/6.38  
% 6.16/6.38  ============================== end predicate elimination =============
% 6.16/6.38  
% 6.16/6.38  Auto_denials:
% 6.16/6.38    % copying label goals to answer in negative clause
% 6.16/6.38  
% 6.16/6.38  Term ordering decisions:
% 6.16/6.38  Function symbol KB weights:  unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1.
% 6.16/6.38  
% 6.16/6.38  ============================== end of process initial clauses ========
% 6.16/6.38  
% 6.16/6.38  ============================== CLAUSES FOR SEARCH ====================
% 6.16/6.38  
% 6.16/6.38  ============================== end of clauses for search =============
% 6.16/6.38  
% 6.16/6.38  ============================== SEARCH ================================
% 6.16/6.38  
% 6.16/6.38  % Starting search at 0.01 seconds.
% 6.16/6.38  
% 6.16/6.38  Low Water (keep): wt=71.000, iters=3356
% 6.16/6.38  
% 6.16/6.38  Low Water (keep): wt=63.000, iters=3381
% 6.16/6.38  
% 6.16/6.38  Low Water (keep): wt=59.000, iters=3340
% 6.16/6.38  
% 6.16/6.38  Low Water (keep): wt=55.000, iters=3375
% 6.16/6.38  
% 6.16/6.38  Low Water (keep): wt=51.000, iters=3385
% 6.16/6.38  
% 6.16/6.38  Low Water (keep): wt=47.000, iters=3366
% 6.16/6.38  
% 6.16/6.38  Low Water (keep): wt=43.000, iters=3340
% 6.16/6.38  
% 6.16/6.38  Low Water (keep): wt=39.000, iters=3344
% 6.16/6.38  
% 6.16/6.38  Low Water (keep): wt=35.000, iters=3336
% 6.16/6.38  
% 6.16/6.38  ============================== PROOF =================================
% 6.16/6.38  % SZS status Unsatisfiable
% 6.16/6.38  % SZS output start Refutation
% 6.16/6.38  
% 6.16/6.38  % Proof 1 at 5.44 (+ 0.07) seconds: goals.
% 6.16/6.38  % Length of proof is 39.
% 6.16/6.38  % Level of proof is 15.
% 6.16/6.38  % Maximum clause weight is 19.000.
% 6.16/6.38  % Given clauses 274.
% 6.16/6.38  
% 6.16/6.38  1 mult(A,unit) = A # label(c05) # label(axiom).  [assumption].
% 6.16/6.38  2 mult(unit,A) = A # label(c06) # label(axiom).  [assumption].
% 6.16/6.38  3 mult(A,ld(A,B)) = B # label(c01) # label(axiom).  [assumption].
% 6.16/6.38  4 ld(A,mult(A,B)) = B # label(c02) # label(axiom).  [assumption].
% 6.16/6.38  5 mult(rd(A,B),B) = A # label(c03) # label(axiom).  [assumption].
% 6.16/6.38  6 rd(mult(A,B),B) = A # label(c04) # label(axiom).  [assumption].
% 6.16/6.38  7 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(c08) # label(axiom).  [assumption].
% 6.16/6.38  8 mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) # label(c07) # label(axiom).  [assumption].
% 6.16/6.38  9 mult(mult(mult(A,B),B),C) = mult(A,mult(B,mult(B,C))).  [copy(8),flip(a)].
% 6.16/6.38  10 mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),c) # label(goals) # label(negated_conjecture) # answer(goals).  [assumption].
% 6.16/6.38  11 mult(mult(a,mult(b,mult(c,b))),c) != mult(mult(a,b),mult(c,mult(b,c))) # answer(goals).  [copy(10),rewrite([7(8),7(15)]),flip(a)].
% 6.16/6.38  13 ld(A,A) = unit.  [para(1(a,1),4(a,1,2))].
% 6.16/6.38  18 mult(A,mult(ld(A,B),A)) = mult(B,A).  [para(3(a,1),7(a,1,1)),flip(a)].
% 6.16/6.38  23 mult(mult(A,B),B) = mult(A,mult(B,B)).  [para(9(a,1),1(a,1)),rewrite([1(2)]),flip(a)].
% 6.16/6.38  25 mult(A,mult(B,mult(B,ld(mult(A,mult(B,B)),C)))) = C.  [para(9(a,1),3(a,1)),rewrite([23(2)])].
% 6.16/6.38  29 mult(rd(A,B),mult(B,mult(B,C))) = mult(mult(A,B),C).  [para(5(a,1),9(a,1,1,1)),flip(a)].
% 6.16/6.38  32 rd(mult(A,mult(B,mult(B,C))),C) = mult(A,mult(B,B)).  [para(9(a,1),6(a,1,1)),rewrite([23(6)])].
% 6.16/6.38  51 ld(A,mult(B,A)) = mult(ld(A,B),A).  [para(18(a,1),4(a,1,2))].
% 6.16/6.38  84 mult(ld(A,unit),A) = unit.  [para(2(a,1),51(a,1,2)),rewrite([13(1)]),flip(a)].
% 6.16/6.38  94 mult(ld(A,unit),mult(A,A)) = A.  [para(84(a,1),23(a,1,1)),rewrite([2(2)]),flip(a)].
% 6.16/6.38  124 mult(ld(A,unit),mult(A,B)) = B.  [para(94(a,1),25(a,1,2,2,2,1)),rewrite([3(4)])].
% 6.16/6.38  125 mult(ld(A,unit),B) = ld(A,B).  [para(3(a,1),124(a,1,2))].
% 6.16/6.38  127 rd(A,mult(B,A)) = ld(B,unit).  [para(124(a,1),6(a,1,1))].
% 6.16/6.38  137 ld(A,mult(B,B)) = mult(ld(A,B),B).  [para(125(a,1),23(a,1,1)),rewrite([125(6)]),flip(a)].
% 6.16/6.38  145 ld(rd(A,B),unit) = rd(B,A).  [para(5(a,1),127(a,1,2)),flip(a)].
% 6.16/6.38  166 mult(rd(A,B),rd(B,A)) = unit.  [para(145(a,1),3(a,1,2))].
% 6.16/6.38  234 mult(mult(A,rd(B,C)),rd(C,B)) = A.  [para(166(a,1),29(a,1,2,2)),rewrite([1(5),5(4)]),flip(a)].
% 6.16/6.38  305 mult(A,mult(ld(A,B),B)) = mult(B,B).  [para(137(a,1),3(a,1,2))].
% 6.16/6.38  360 mult(mult(A,B),ld(B,unit)) = A.  [para(6(a,1),234(a,1,1,2)),rewrite([127(3)])].
% 6.16/6.38  384 mult(A,ld(B,unit)) = rd(A,B).  [para(5(a,1),360(a,1,1))].
% 6.16/6.38  385 rd(A,ld(B,unit)) = mult(A,B).  [para(360(a,1),6(a,1,1))].
% 6.16/6.38  392 mult(mult(A,mult(B,mult(C,B))),C) = mult(A,mult(mult(B,C),mult(B,C))).  [para(360(a,1),32(a,1,1,2,2)),rewrite([7(2),385(6)])].
% 6.16/6.38  410 mult(mult(a,b),mult(c,mult(b,c))) != mult(a,mult(mult(b,c),mult(b,c))) # answer(goals).  [back_rewrite(11),rewrite([392(9)]),flip(a)].
% 6.16/6.38  477 mult(mult(A,mult(B,rd(B,C))),C) = mult(A,mult(B,B)).  [para(384(a,1),32(a,1,1,2,2)),rewrite([385(6)])].
% 6.16/6.38  590 mult(mult(A,B),mult(A,B)) = mult(A,mult(B,mult(A,B))).  [para(4(a,1),305(a,1,2,1)),flip(a)].
% 6.16/6.38  610 mult(mult(a,b),mult(c,mult(b,c))) != mult(a,mult(b,mult(c,mult(b,c)))) # answer(goals).  [back_rewrite(410),rewrite([590(17)])].
% 6.16/6.38  4841 mult(mult(A,rd(B,C)),mult(C,B)) = mult(A,mult(B,B)).  [para(127(a,1),477(a,1,1,2,2)),rewrite([384(3)])].
% 6.16/6.38  16005 mult(mult(A,B),mult(C,mult(B,C))) = mult(A,mult(B,mult(C,mult(B,C)))).  [para(6(a,1),4841(a,1,1,2)),rewrite([590(7)])].
% 6.16/6.38  16006 $F # answer(goals).  [resolve(16005,a,610,a)].
% 6.16/6.38  
% 6.16/6.38  % SZS output end Refutation
% 6.16/6.38  ============================== end of proof ==========================
% 6.16/6.38  
% 6.16/6.38  ============================== STATISTICS ============================
% 6.16/6.38  
% 6.16/6.38  Given=274. Generated=64468. Kept=16003. proofs=1.
% 6.16/6.38  Usable=171. Sos=6939. Demods=7074. Limbo=0, Disabled=8901. Hints=0.
% 6.16/6.38  Megabytes=19.68.
% 6.16/6.38  User_CPU=5.44, System_CPU=0.07, Wall_clock=6.
% 6.16/6.38  
% 6.16/6.38  ============================== end of statistics =====================
% 6.16/6.38  
% 6.16/6.38  ============================== end of search =========================
% 6.16/6.38  
% 6.16/6.38  THEOREM PROVED
% 6.16/6.38  % SZS status Unsatisfiable
% 6.16/6.38  
% 6.16/6.38  Exiting with 1 proof.
% 6.16/6.38  
% 6.16/6.38  Process 27991 exit (max_proofs) Mon Jun 13 18:15:34 2022
% 6.16/6.38  Prover9 interrupted
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