TSTP Solution File: ALG006-1 by Prover9---1109a

View Problem - Process Solution

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% File     : Prover9---1109a
% Problem  : ALG006-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n032.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 17:53:34 EDT 2022

% Result   : Unsatisfiable 0.62s 0.95s
% Output   : Refutation 0.62s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : ALG006-1 : TPTP v8.1.0. Released v2.2.0.
% 0.05/0.09  % Command  : tptp2X_and_run_prover9 %d %s
% 0.09/0.29  % Computer : n032.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 600
% 0.09/0.29  % DateTime : Thu Jun  9 06:25:37 EDT 2022
% 0.09/0.29  % CPUTime  : 
% 0.62/0.95  ============================== Prover9 ===============================
% 0.62/0.95  Prover9 (32) version 2009-11A, November 2009.
% 0.62/0.95  Process 21203 was started by sandbox2 on n032.cluster.edu,
% 0.62/0.95  Thu Jun  9 06:25:38 2022
% 0.62/0.95  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21050_n032.cluster.edu".
% 0.62/0.95  ============================== end of head ===========================
% 0.62/0.95  
% 0.62/0.95  ============================== INPUT =================================
% 0.62/0.95  
% 0.62/0.95  % Reading from file /tmp/Prover9_21050_n032.cluster.edu
% 0.62/0.95  
% 0.62/0.95  set(prolog_style_variables).
% 0.62/0.95  set(auto2).
% 0.62/0.95      % set(auto2) -> set(auto).
% 0.62/0.95      % set(auto) -> set(auto_inference).
% 0.62/0.95      % set(auto) -> set(auto_setup).
% 0.62/0.95      % set(auto_setup) -> set(predicate_elim).
% 0.62/0.95      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.62/0.95      % set(auto) -> set(auto_limits).
% 0.62/0.95      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.62/0.95      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.62/0.95      % set(auto) -> set(auto_denials).
% 0.62/0.95      % set(auto) -> set(auto_process).
% 0.62/0.95      % set(auto2) -> assign(new_constants, 1).
% 0.62/0.95      % set(auto2) -> assign(fold_denial_max, 3).
% 0.62/0.95      % set(auto2) -> assign(max_weight, "200.000").
% 0.62/0.95      % set(auto2) -> assign(max_hours, 1).
% 0.62/0.95      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.62/0.95      % set(auto2) -> assign(max_seconds, 0).
% 0.62/0.95      % set(auto2) -> assign(max_minutes, 5).
% 0.62/0.95      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.62/0.95      % set(auto2) -> set(sort_initial_sos).
% 0.62/0.95      % set(auto2) -> assign(sos_limit, -1).
% 0.62/0.95      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.62/0.95      % set(auto2) -> assign(max_megs, 400).
% 0.62/0.95      % set(auto2) -> assign(stats, some).
% 0.62/0.95      % set(auto2) -> clear(echo_input).
% 0.62/0.95      % set(auto2) -> set(quiet).
% 0.62/0.95      % set(auto2) -> clear(print_initial_clauses).
% 0.62/0.95      % set(auto2) -> clear(print_given).
% 0.62/0.95  assign(lrs_ticks,-1).
% 0.62/0.95  assign(sos_limit,10000).
% 0.62/0.95  assign(order,kbo).
% 0.62/0.95  set(lex_order_vars).
% 0.62/0.95  clear(print_given).
% 0.62/0.95  
% 0.62/0.95  % formulas(sos).  % not echoed (4 formulas)
% 0.62/0.95  
% 0.62/0.95  ============================== end of input ==========================
% 0.62/0.95  
% 0.62/0.95  % From the command line: assign(max_seconds, 300).
% 0.62/0.95  
% 0.62/0.95  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.62/0.95  
% 0.62/0.95  % Formulas that are not ordinary clauses:
% 0.62/0.95  
% 0.62/0.95  ============================== end of process non-clausal formulas ===
% 0.62/0.95  
% 0.62/0.95  ============================== PROCESS INITIAL CLAUSES ===============
% 0.62/0.95  
% 0.62/0.95  ============================== PREDICATE ELIMINATION =================
% 0.62/0.95  
% 0.62/0.95  ============================== end predicate elimination =============
% 0.62/0.95  
% 0.62/0.95  Auto_denials:
% 0.62/0.95    % copying label prove_set_difference_3_simplified to answer in negative clause
% 0.62/0.95  
% 0.62/0.95  Term ordering decisions:
% 0.62/0.95  Function symbol KB weights:  a=1. b=1. c=1. difference=1.
% 0.62/0.95  
% 0.62/0.95  ============================== end of process initial clauses ========
% 0.62/0.95  
% 0.62/0.95  ============================== CLAUSES FOR SEARCH ====================
% 0.62/0.95  
% 0.62/0.95  ============================== end of clauses for search =============
% 0.62/0.95  
% 0.62/0.95  ============================== SEARCH ================================
% 0.62/0.95  
% 0.62/0.95  % Starting search at 0.01 seconds.
% 0.62/0.95  
% 0.62/0.95  ============================== PROOF =================================
% 0.62/0.95  % SZS status Unsatisfiable
% 0.62/0.95  % SZS output start Refutation
% 0.62/0.95  
% 0.62/0.95  % Proof 1 at 0.02 (+ 0.00) seconds: prove_set_difference_3_simplified.
% 0.62/0.95  % Length of proof is 26.
% 0.62/0.95  % Level of proof is 13.
% 0.62/0.95  % Maximum clause weight is 23.000.
% 0.62/0.95  % Given clauses 21.
% 0.62/0.95  
% 0.62/0.95  1 difference(A,difference(B,A)) = A # label(set_difference_1) # label(axiom).  [assumption].
% 0.62/0.95  2 difference(A,difference(A,B)) = difference(B,difference(B,A)) # label(set_difference_2) # label(axiom).  [assumption].
% 0.62/0.95  3 difference(difference(A,B),C) = difference(difference(A,C),difference(B,C)) # label(set_difference_3) # label(axiom).  [assumption].
% 0.62/0.95  4 difference(difference(A,B),difference(C,B)) = difference(difference(A,C),B).  [copy(3),flip(a)].
% 0.62/0.95  5 difference(difference(a,c),b) != difference(difference(a,b),c) # label(prove_set_difference_3_simplified) # label(negated_conjecture) # answer(prove_set_difference_3_simplified).  [assumption].
% 0.62/0.95  6 difference(difference(A,B),B) = difference(A,B).  [para(1(a,1),1(a,1,2))].
% 0.62/0.95  8 difference(difference(A,A),B) = difference(B,B).  [para(1(a,1),2(a,1,2)),rewrite([6(4),4(4)]),flip(a)].
% 0.62/0.95  10 difference(difference(A,B),difference(C,A)) = difference(A,difference(B,difference(C,A))).  [para(1(a,1),4(a,1,1)),flip(a)].
% 0.62/0.95  19 difference(difference(A,A),difference(B,B)) = difference(B,B).  [para(8(a,1),1(a,1)),rewrite([4(5)])].
% 0.62/0.95  21 difference(difference(difference(A,A),B),C) = difference(C,C).  [para(8(a,1),4(a,1,1)),rewrite([10(3),1(2)]),flip(a)].
% 0.62/0.95  23 difference(difference(A,B),A) = difference(difference(B,B),A).  [para(8(a,1),4(a,1)),rewrite([4(3)]),flip(a)].
% 0.62/0.95  24 difference(difference(difference(A,A),B),C) = difference(difference(B,B),C).  [para(8(a,1),4(a,2,1)),rewrite([4(4)])].
% 0.62/0.95  28 difference(A,A) = difference(B,B).  [para(19(a,1),2(a,1,2)),rewrite([19(3),19(5),19(4)])].
% 0.62/0.95  31 difference(A,A) = c_0.  [new_symbol(28)].
% 0.62/0.95  36 difference(difference(c_0,A),B) = difference(c_0,B).  [back_rewrite(24),rewrite([31(1),31(4)])].
% 0.62/0.95  37 difference(difference(A,B),A) = difference(c_0,A).  [back_rewrite(23),rewrite([31(3)])].
% 0.62/0.95  39 difference(c_0,A) = c_0.  [back_rewrite(21),rewrite([31(1),36(3),31(3)])].
% 0.62/0.95  41 difference(difference(A,B),A) = c_0.  [back_rewrite(37),rewrite([39(4)])].
% 0.62/0.95  42 difference(A,c_0) = A.  [para(31(a,1),1(a,1,2))].
% 0.62/0.95  45 difference(A,difference(A,difference(A,B))) = difference(A,B).  [para(41(a,1),2(a,1,2)),rewrite([42(3)]),flip(a)].
% 0.62/0.95  47 difference(difference(A,difference(B,C)),B) = difference(A,B).  [para(41(a,1),4(a,1,2)),rewrite([42(3)]),flip(a)].
% 0.62/0.95  69 difference(difference(A,B),difference(difference(A,B),difference(A,difference(B,difference(C,A))))) = difference(A,difference(B,difference(C,A))).  [para(10(a,1),45(a,1,2,2)),rewrite([10(10)])].
% 0.62/0.95  77 difference(difference(A,B),difference(A,difference(B,C))) = c_0.  [para(47(a,1),41(a,1,1))].
% 0.62/0.95  82 difference(A,difference(B,difference(C,A))) = difference(A,B).  [back_rewrite(69),rewrite([77(6),42(3)]),flip(a)].
% 0.62/0.95  127 difference(difference(A,B),C) = difference(difference(A,C),B).  [para(1(a,1),82(a,1,2,2)),rewrite([4(3)])].
% 0.62/0.95  128 $F # answer(prove_set_difference_3_simplified).  [resolve(127,a,5,a)].
% 0.62/0.95  
% 0.62/0.95  % SZS output end Refutation
% 0.62/0.95  ============================== end of proof ==========================
% 0.62/0.95  
% 0.62/0.95  ============================== STATISTICS ============================
% 0.62/0.95  
% 0.62/0.95  Given=21. Generated=782. Kept=126. proofs=1.
% 0.62/0.95  Usable=16. Sos=57. Demods=69. Limbo=0, Disabled=56. Hints=0.
% 0.62/0.95  Megabytes=0.11.
% 0.62/0.95  User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.62/0.95  
% 0.62/0.95  ============================== end of statistics =====================
% 0.62/0.95  
% 0.62/0.95  ============================== end of search =========================
% 0.62/0.95  
% 0.62/0.95  THEOREM PROVED
% 0.62/0.95  % SZS status Unsatisfiable
% 0.62/0.95  
% 0.62/0.95  Exiting with 1 proof.
% 0.62/0.95  
% 0.62/0.95  Process 21203 exit (max_proofs) Thu Jun  9 06:25:38 2022
% 0.62/0.95  Prover9 interrupted
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