TSTP Solution File: ALG240-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : ALG240-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n021.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 : Thu Jul 14 17:54:13 EDT 2022

% Result   : Unsatisfiable 0.83s 1.09s
% Output   : Refutation 0.83s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ALG240-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.33  % Computer : n021.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 : Thu Jun  9 04:18:53 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.83/1.09  ============================== Prover9 ===============================
% 0.83/1.09  Prover9 (32) version 2009-11A, November 2009.
% 0.83/1.09  Process 14652 was started by sandbox2 on n021.cluster.edu,
% 0.83/1.09  Thu Jun  9 04:18:53 2022
% 0.83/1.09  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_14498_n021.cluster.edu".
% 0.83/1.09  ============================== end of head ===========================
% 0.83/1.09  
% 0.83/1.09  ============================== INPUT =================================
% 0.83/1.09  
% 0.83/1.09  % Reading from file /tmp/Prover9_14498_n021.cluster.edu
% 0.83/1.09  
% 0.83/1.09  set(prolog_style_variables).
% 0.83/1.09  set(auto2).
% 0.83/1.09      % set(auto2) -> set(auto).
% 0.83/1.09      % set(auto) -> set(auto_inference).
% 0.83/1.09      % set(auto) -> set(auto_setup).
% 0.83/1.09      % set(auto_setup) -> set(predicate_elim).
% 0.83/1.09      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.83/1.09      % set(auto) -> set(auto_limits).
% 0.83/1.09      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.83/1.09      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.83/1.09      % set(auto) -> set(auto_denials).
% 0.83/1.09      % set(auto) -> set(auto_process).
% 0.83/1.09      % set(auto2) -> assign(new_constants, 1).
% 0.83/1.09      % set(auto2) -> assign(fold_denial_max, 3).
% 0.83/1.09      % set(auto2) -> assign(max_weight, "200.000").
% 0.83/1.09      % set(auto2) -> assign(max_hours, 1).
% 0.83/1.09      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.83/1.09      % set(auto2) -> assign(max_seconds, 0).
% 0.83/1.09      % set(auto2) -> assign(max_minutes, 5).
% 0.83/1.09      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.83/1.09      % set(auto2) -> set(sort_initial_sos).
% 0.83/1.09      % set(auto2) -> assign(sos_limit, -1).
% 0.83/1.09      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.83/1.09      % set(auto2) -> assign(max_megs, 400).
% 0.83/1.09      % set(auto2) -> assign(stats, some).
% 0.83/1.09      % set(auto2) -> clear(echo_input).
% 0.83/1.09      % set(auto2) -> set(quiet).
% 0.83/1.09      % set(auto2) -> clear(print_initial_clauses).
% 0.83/1.09      % set(auto2) -> clear(print_given).
% 0.83/1.09  assign(lrs_ticks,-1).
% 0.83/1.09  assign(sos_limit,10000).
% 0.83/1.09  assign(order,kbo).
% 0.83/1.09  set(lex_order_vars).
% 0.83/1.09  clear(print_given).
% 0.83/1.09  
% 0.83/1.09  % formulas(sos).  % not echoed (5 formulas)
% 0.83/1.09  
% 0.83/1.09  ============================== end of input ==========================
% 0.83/1.09  
% 0.83/1.09  % From the command line: assign(max_seconds, 300).
% 0.83/1.09  
% 0.83/1.09  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.83/1.09  
% 0.83/1.09  % Formulas that are not ordinary clauses:
% 0.83/1.09  
% 0.83/1.09  ============================== end of process non-clausal formulas ===
% 0.83/1.09  
% 0.83/1.09  ============================== PROCESS INITIAL CLAUSES ===============
% 0.83/1.09  
% 0.83/1.09  ============================== PREDICATE ELIMINATION =================
% 0.83/1.09  
% 0.83/1.09  ============================== end predicate elimination =============
% 0.83/1.09  
% 0.83/1.09  Auto_denials:
% 0.83/1.09    % copying label goals to answer in negative clause
% 0.83/1.09  
% 0.83/1.09  Term ordering decisions:
% 0.83/1.09  Function symbol KB weights:  a=1. b=1. c=1. d=1. mult=1.
% 0.83/1.09  
% 0.83/1.09  ============================== end of process initial clauses ========
% 0.83/1.09  
% 0.83/1.09  ============================== CLAUSES FOR SEARCH ====================
% 0.83/1.09  
% 0.83/1.09  ============================== end of clauses for search =============
% 0.83/1.09  
% 0.83/1.09  ============================== SEARCH ================================
% 0.83/1.09  
% 0.83/1.09  % Starting search at 0.01 seconds.
% 0.83/1.09  
% 0.83/1.09  ============================== PROOF =================================
% 0.83/1.09  % SZS status Unsatisfiable
% 0.83/1.09  % SZS output start Refutation
% 0.83/1.09  
% 0.83/1.09  % Proof 1 at 0.10 (+ 0.00) seconds: goals.
% 0.83/1.09  % Length of proof is 25.
% 0.83/1.09  % Level of proof is 10.
% 0.83/1.09  % Maximum clause weight is 51.000.
% 0.83/1.09  % Given clauses 18.
% 0.83/1.09  
% 0.83/1.09  1 mult(A,mult(B,C)) = mult(mult(A,B),mult(A,C)) # label(c01) # label(axiom).  [assumption].
% 0.83/1.09  2 mult(mult(A,B),mult(A,C)) = mult(A,mult(B,C)).  [copy(1),flip(a)].
% 0.83/1.09  3 mult(mult(A,B),C) = mult(mult(A,C),mult(B,C)) # label(c02) # label(axiom).  [assumption].
% 0.83/1.09  4 mult(mult(A,B),mult(C,B)) = mult(mult(A,C),B).  [copy(3),flip(a)].
% 0.83/1.09  5 mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D)))) = mult(mult(A,C),mult(B,D)) # label(c03) # label(axiom).  [assumption].
% 0.83/1.09  6 mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),mult(mult(A,C),mult(B,D))) = mult(mult(A,B),mult(C,D)) # label(c04) # label(axiom).  [assumption].
% 0.83/1.09  7 mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) != mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))) # label(goals) # label(negated_conjecture) # answer(goals).  [assumption].
% 0.83/1.09  8 mult(mult(mult(a,c),mult(b,d)),mult(mult(a,b),mult(c,d))) != mult(mult(mult(a,b),mult(c,d)),mult(mult(a,c),mult(b,d))) # answer(goals).  [copy(7),flip(a)].
% 0.83/1.09  13 mult(mult(A,A),B) = mult(A,mult(B,B)).  [para(4(a,1),2(a,1))].
% 0.83/1.09  23 mult(mult(A,mult(A,mult(A,A))),mult(B,C)) = mult(mult(A,A),mult(B,C)).  [para(2(a,1),5(a,1,1)),rewrite([2(5),4(8),4(7)])].
% 0.83/1.09  26 mult(mult(A,A),mult(B,C)) = mult(A,mult(B,C)).  [para(2(a,1),5(a,1,2,2)),rewrite([4(9),13(5),4(8),2(4),23(5),2(6)])].
% 0.83/1.09  30 mult(mult(A,mult(mult(mult(B,C),mult(D,E)),mult(mult(B,D),mult(C,E)))),mult(mult(B,D),mult(C,E))) = mult(mult(A,mult(mult(B,C),mult(D,E))),mult(mult(mult(B,C),mult(D,E)),mult(mult(B,D),mult(C,E)))).  [para(5(a,1),4(a,1,2))].
% 0.83/1.09  45 mult(mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),E),mult(mult(A,B),mult(C,D))) = mult(mult(mult(mult(A,B),mult(C,D)),E),mult(mult(A,C),mult(B,D))).  [para(6(a,1),2(a,1,2)),rewrite([4(24)])].
% 0.83/1.09  50 mult(mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))),E),mult(mult(A,C),mult(B,D))) = mult(mult(mult(A,B),mult(C,D)),mult(E,mult(mult(A,C),mult(B,D)))).  [para(6(a,1),4(a,1,1)),flip(a)].
% 0.83/1.09  51 mult(mult(A,mult(mult(B,C),mult(D,E))),mult(mult(mult(B,C),mult(D,E)),mult(mult(B,D),mult(C,E)))) = mult(mult(A,mult(mult(B,D),mult(C,E))),mult(mult(B,C),mult(D,E))).  [para(6(a,1),4(a,1,2)),rewrite([30(20)]),flip(a)].
% 0.83/1.09  75 mult(mult(A,mult(mult(mult(B,C),mult(D,E)),mult(mult(B,D),mult(C,E)))),mult(mult(B,D),mult(C,E))) = mult(mult(A,mult(mult(B,D),mult(C,E))),mult(mult(B,C),mult(D,E))).  [back_rewrite(30),rewrite([51(24)])].
% 0.83/1.09  112 mult(A,mult(B,mult(C,C))) = mult(A,mult(B,C)).  [para(13(a,1),2(a,2)),rewrite([2(5),26(3),2(5)]),flip(a)].
% 0.83/1.09  120 mult(mult(A,B),A) = mult(A,mult(B,A)).  [para(13(a,1),4(a,1)),rewrite([2(3),112(3)]),flip(a)].
% 0.83/1.09  127 mult(mult(A,mult(B,A)),mult(C,A)) = mult(mult(mult(A,B),C),A).  [para(120(a,1),4(a,1,1))].
% 0.83/1.09  128 mult(mult(A,B),mult(B,mult(C,B))) = mult(mult(A,mult(B,C)),B).  [para(120(a,1),4(a,1,2))].
% 0.83/1.09  141 mult(mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,C),mult(B,D)),mult(mult(A,B),mult(C,D)))),mult(mult(A,C),mult(B,D))) = mult(mult(A,C),mult(B,D)).  [para(6(a,1),120(a,1,1)),rewrite([5(11),128(22)]),flip(a)].
% 0.83/1.09  233 mult(mult(mult(mult(A,B),mult(C,D)),mult(E,mult(mult(A,B),mult(C,D)))),mult(mult(A,C),mult(B,D))) = mult(mult(mult(A,B),mult(C,D)),mult(mult(E,mult(mult(A,C),mult(B,D))),mult(mult(A,B),mult(C,D)))).  [para(5(a,1),127(a,1,2)),rewrite([50(20),75(15),45(24),4(28),120(20)]),flip(a)].
% 0.83/1.09  263 mult(mult(mult(A,B),mult(C,D)),mult(mult(mult(A,C),mult(B,D)),mult(mult(A,B),mult(C,D)))) = mult(mult(A,C),mult(B,D)).  [back_rewrite(141),rewrite([233(15),2(10),2(7),112(7)])].
% 0.83/1.09  277 mult(mult(mult(A,B),mult(C,D)),mult(mult(A,C),mult(B,D))) = mult(mult(mult(A,C),mult(B,D)),mult(mult(A,B),mult(C,D))).  [para(5(a,1),128(a,2,1)),rewrite([2(7),2(4),112(4),263(14)])].
% 0.83/1.09  278 $F # answer(goals).  [resolve(277,a,8,a)].
% 0.83/1.09  
% 0.83/1.09  % SZS output end Refutation
% 0.83/1.09  ============================== end of proof ==========================
% 0.83/1.09  
% 0.83/1.09  ============================== STATISTICS ============================
% 0.83/1.09  
% 0.83/1.09  Given=18. Generated=1773. Kept=274. proofs=1.
% 0.83/1.09  Usable=18. Sos=213. Demods=229. Limbo=12, Disabled=35. Hints=0.
% 0.83/1.09  Megabytes=0.62.
% 0.83/1.09  User_CPU=0.10, System_CPU=0.00, Wall_clock=0.
% 0.83/1.09  
% 0.83/1.09  ============================== end of statistics =====================
% 0.83/1.09  
% 0.83/1.09  ============================== end of search =========================
% 0.83/1.09  
% 0.83/1.09  THEOREM PROVED
% 0.83/1.09  % SZS status Unsatisfiable
% 0.83/1.09  
% 0.83/1.09  Exiting with 1 proof.
% 0.83/1.09  
% 0.83/1.09  Process 14652 exit (max_proofs) Thu Jun  9 04:18:53 2022
% 0.83/1.09  Prover9 interrupted
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