TSTP Solution File: SEU904^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU904^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n026.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  : 300s
% DateTime : Tue May 21 03:44:12 EDT 2024

% Result   : Theorem 162.78s 28.77s
% Output   : Refutation 162.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   43
%            Number of leaves      :   21
% Syntax   : Number of formulae    :  141 (   9 unt;  20 typ;   0 def)
%            Number of atoms       :  401 (  63 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives : 1330 ( 196   ~; 226   |;  57   &; 812   @)
%                                         (   0 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   6 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   44 (  44   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  17 usr;  11 con; 0-2 aty)
%            Number of variables   :  132 (   0   ^ 132   !;   0   ?; 132   :)

% Comments : 
%------------------------------------------------------------------------------
thf(g_type,type,
    g: $tType ).

thf(b_type,type,
    b: $tType ).

thf(a_type,type,
    a: $tType ).

thf(sk1_type,type,
    sk1: g > b ).

thf(sk2_type,type,
    sk2: b > a ).

thf(sk3_type,type,
    sk3: g > $o ).

thf(sk4_type,type,
    sk4: g > g > g ).

thf(sk5_type,type,
    sk5: b > $o ).

thf(sk6_type,type,
    sk6: b > b > b ).

thf(sk7_type,type,
    sk7: a > $o ).

thf(sk8_type,type,
    sk8: a > a > a ).

thf(sk9_type,type,
    sk9: $o ).

thf(sk10_type,type,
    sk10: g ).

thf(sk11_type,type,
    sk11: g ).

thf(sk12_type,type,
    sk12: $o ).

thf(sk13_type,type,
    sk13: a ).

thf(sk14_type,type,
    sk14: a ).

thf(sk15_type,type,
    sk15: g ).

thf(sk16_type,type,
    sk16: g ).

thf(sk17_type,type,
    sk17: g ).

thf(1,conjecture,
    ! [A: g > b,B: b > a,C: g > $o,D: g > g > g,E: b > $o,F: b > b > b,G: a > $o,H: a > a > a] :
      ( ( ! [I: g,J: g] :
            ( ( ( C @ I )
              & ( C @ J ) )
           => ( C @ ( D @ I @ J ) ) )
        & ! [I: b,J: b] :
            ( ( ( E @ I )
              & ( E @ J ) )
           => ( E @ ( F @ I @ J ) ) )
        & ! [I: g] :
            ( ( C @ I )
           => ( E @ ( A @ I ) ) )
        & ! [I: g,J: g] :
            ( ( ( C @ I )
              & ( C @ J ) )
           => ( ( A @ ( D @ I @ J ) )
              = ( F @ ( A @ I ) @ ( A @ J ) ) ) )
        & ! [I: b,J: b] :
            ( ( ( E @ I )
              & ( E @ J ) )
           => ( E @ ( F @ I @ J ) ) )
        & ! [I: a,J: a] :
            ( ( ( G @ I )
              & ( G @ J ) )
           => ( G @ ( H @ I @ J ) ) )
        & ! [I: b] :
            ( ( E @ I )
           => ( G @ ( B @ I ) ) )
        & ! [I: b,J: b] :
            ( ( ( E @ I )
              & ( E @ J ) )
           => ( ( B @ ( F @ I @ J ) )
              = ( H @ ( B @ I ) @ ( B @ J ) ) ) ) )
     => ( ! [I: g,J: g] :
            ( ( ( C @ I )
              & ( C @ J ) )
           => ( C @ ( D @ I @ J ) ) )
        & ! [I: a,J: a] :
            ( ( ( G @ I )
              & ( G @ J ) )
           => ( G @ ( H @ I @ J ) ) )
        & ! [I: g] :
            ( ( C @ I )
           => ( G @ ( B @ ( A @ I ) ) ) )
        & ! [I: g,J: g] :
            ( ( ( C @ I )
              & ( C @ J ) )
           => ( ( B @ ( A @ ( D @ I @ J ) ) )
              = ( H @ ( B @ ( A @ I ) ) @ ( B @ ( A @ J ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM126_pme) ).

thf(2,negated_conjecture,
    ~ ! [A: g > b,B: b > a,C: g > $o,D: g > g > g,E: b > $o,F: b > b > b,G: a > $o,H: a > a > a] :
        ( ( ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( C @ ( D @ I @ J ) ) )
          & ! [I: b,J: b] :
              ( ( ( E @ I )
                & ( E @ J ) )
             => ( E @ ( F @ I @ J ) ) )
          & ! [I: g] :
              ( ( C @ I )
             => ( E @ ( A @ I ) ) )
          & ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( ( A @ ( D @ I @ J ) )
                = ( F @ ( A @ I ) @ ( A @ J ) ) ) )
          & ! [I: b,J: b] :
              ( ( ( E @ I )
                & ( E @ J ) )
             => ( E @ ( F @ I @ J ) ) )
          & ! [I: a,J: a] :
              ( ( ( G @ I )
                & ( G @ J ) )
             => ( G @ ( H @ I @ J ) ) )
          & ! [I: b] :
              ( ( E @ I )
             => ( G @ ( B @ I ) ) )
          & ! [I: b,J: b] :
              ( ( ( E @ I )
                & ( E @ J ) )
             => ( ( B @ ( F @ I @ J ) )
                = ( H @ ( B @ I ) @ ( B @ J ) ) ) ) )
       => ( ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( C @ ( D @ I @ J ) ) )
          & ! [I: a,J: a] :
              ( ( ( G @ I )
                & ( G @ J ) )
             => ( G @ ( H @ I @ J ) ) )
          & ! [I: g] :
              ( ( C @ I )
             => ( G @ ( B @ ( A @ I ) ) ) )
          & ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( ( B @ ( A @ ( D @ I @ J ) ) )
                = ( H @ ( B @ ( A @ I ) ) @ ( B @ ( A @ J ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: g > b,B: b > a,C: g > $o,D: g > g > g,E: b > $o,F: b > b > b,G: a > $o,H: a > a > a] :
        ( ( ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( C @ ( D @ I @ J ) ) )
          & ! [I: b,J: b] :
              ( ( ( E @ I )
                & ( E @ J ) )
             => ( E @ ( F @ I @ J ) ) )
          & ! [I: g] :
              ( ( C @ I )
             => ( E @ ( A @ I ) ) )
          & ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( ( A @ ( D @ I @ J ) )
                = ( F @ ( A @ I ) @ ( A @ J ) ) ) )
          & ! [I: b,J: b] :
              ( ( ( E @ I )
                & ( E @ J ) )
             => ( E @ ( F @ I @ J ) ) )
          & ! [I: a,J: a] :
              ( ( ( G @ I )
                & ( G @ J ) )
             => ( G @ ( H @ I @ J ) ) )
          & ! [I: b] :
              ( ( E @ I )
             => ( G @ ( B @ I ) ) )
          & ! [I: b,J: b] :
              ( ( ( E @ I )
                & ( E @ J ) )
             => ( ( B @ ( F @ I @ J ) )
                = ( H @ ( B @ I ) @ ( B @ J ) ) ) ) )
       => ( ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( C @ ( D @ I @ J ) ) )
          & ! [I: a,J: a] :
              ( ( ( G @ I )
                & ( G @ J ) )
             => ( G @ ( H @ I @ J ) ) )
          & ! [I: g] :
              ( ( C @ I )
             => ( G @ ( B @ ( A @ I ) ) ) )
          & ! [I: g,J: g] :
              ( ( ( C @ I )
                & ( C @ J ) )
             => ( ( B @ ( A @ ( D @ I @ J ) ) )
                = ( H @ ( B @ ( A @ I ) ) @ ( B @ ( A @ J ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(16,plain,
    ! [B: g,A: g] :
      ( ~ ( sk3 @ A )
      | ~ ( sk3 @ B )
      | ( ( sk1 @ ( sk4 @ A @ B ) )
        = ( sk6 @ ( sk1 @ A ) @ ( sk1 @ B ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(30,plain,
    ! [B: g,A: g] :
      ( ( ( sk6 @ ( sk1 @ A ) @ ( sk1 @ B ) )
        = ( sk1 @ ( sk4 @ A @ B ) ) )
      | ~ ( sk3 @ A )
      | ~ ( sk3 @ B ) ),
    inference(lifteq,[status(thm)],[16]) ).

thf(31,plain,
    ! [B: g,A: g] :
      ( ( ( sk6 @ ( sk1 @ A ) @ ( sk1 @ B ) )
        = ( sk1 @ ( sk4 @ A @ B ) ) )
      | ~ ( sk3 @ A )
      | ~ ( sk3 @ B ) ),
    inference(simp,[status(thm)],[30]) ).

thf(20,plain,
    ! [B: b,A: b] :
      ( ~ ( sk5 @ A )
      | ~ ( sk5 @ B )
      | ( ( sk2 @ ( sk6 @ A @ B ) )
        = ( sk8 @ ( sk2 @ A ) @ ( sk2 @ B ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(25,plain,
    ! [B: b,A: b] :
      ( ( ( sk8 @ ( sk2 @ A ) @ ( sk2 @ B ) )
        = ( sk2 @ ( sk6 @ A @ B ) ) )
      | ~ ( sk5 @ A )
      | ~ ( sk5 @ B ) ),
    inference(lifteq,[status(thm)],[20]) ).

thf(26,plain,
    ! [B: b,A: b] :
      ( ( ( sk8 @ ( sk2 @ A ) @ ( sk2 @ B ) )
        = ( sk2 @ ( sk6 @ A @ B ) ) )
      | ~ ( sk5 @ A )
      | ~ ( sk5 @ B ) ),
    inference(simp,[status(thm)],[25]) ).

thf(18,plain,
    ( sk9
    | sk12
    | ( sk3 @ sk15 )
    | ( ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) )
     != ( sk8 @ ( sk2 @ ( sk1 @ sk16 ) ) @ ( sk2 @ ( sk1 @ sk17 ) ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(29,plain,
    ( ( ( sk8 @ ( sk2 @ ( sk1 @ sk16 ) ) @ ( sk2 @ ( sk1 @ sk17 ) ) )
     != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) )
    | sk9
    | sk12
    | ( sk3 @ sk15 ) ),
    inference(lifteq,[status(thm)],[18]) ).

thf(21,plain,
    ( sk9
    | ( sk7 @ sk13 )
    | ~ sk12 ),
    inference(cnf,[status(esa)],[3]) ).

thf(17,plain,
    ( ( sk3 @ sk10 )
    | ~ sk9 ),
    inference(cnf,[status(esa)],[3]) ).

thf(23,plain,
    ( ( sk3 @ sk11 )
    | ~ sk9 ),
    inference(cnf,[status(esa)],[3]) ).

thf(9,plain,
    ! [B: g,A: g] :
      ( ~ ( sk3 @ A )
      | ~ ( sk3 @ B )
      | ( sk3 @ ( sk4 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ( ~ ( sk3 @ ( sk4 @ sk10 @ sk11 ) )
    | ~ sk9 ),
    inference(cnf,[status(esa)],[3]) ).

thf(59,plain,
    ! [B: g,A: g] :
      ( ~ ( sk3 @ A )
      | ~ ( sk3 @ B )
      | ~ sk9
      | ( ( sk3 @ ( sk4 @ A @ B ) )
       != ( sk3 @ ( sk4 @ sk10 @ sk11 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[9,12]) ).

thf(60,plain,
    ( ~ ( sk3 @ sk10 )
    | ~ ( sk3 @ sk11 )
    | ~ sk9 ),
    inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( sk10 )),bind(B,$thf( sk11 ))]]) ).

thf(93,plain,
    ( ~ sk9
    | ~ ( sk3 @ sk10 )
    | ( ( sk3 @ sk11 )
     != ( sk3 @ sk11 ) ) ),
    inference(paramod_ordered,[status(thm)],[23,60]) ).

thf(94,plain,
    ( ~ sk9
    | ~ ( sk3 @ sk10 ) ),
    inference(pattern_uni,[status(thm)],[93:[]]) ).

thf(108,plain,
    ( ~ sk9
    | ( ( sk3 @ sk10 )
     != ( sk3 @ sk10 ) ) ),
    inference(paramod_ordered,[status(thm)],[17,94]) ).

thf(109,plain,
    ~ sk9,
    inference(pattern_uni,[status(thm)],[108:[]]) ).

thf(130,plain,
    ( $false
    | ( sk7 @ sk13 )
    | ~ sk12 ),
    inference(rewrite,[status(thm)],[21,109]) ).

thf(131,plain,
    ( ( sk7 @ sk13 )
    | ~ sk12 ),
    inference(simp,[status(thm)],[130]) ).

thf(6,plain,
    ( sk9
    | ( sk7 @ sk14 )
    | ~ sk12 ),
    inference(cnf,[status(esa)],[3]) ).

thf(128,plain,
    ( $false
    | ( sk7 @ sk14 )
    | ~ sk12 ),
    inference(rewrite,[status(thm)],[6,109]) ).

thf(129,plain,
    ( ( sk7 @ sk14 )
    | ~ sk12 ),
    inference(simp,[status(thm)],[128]) ).

thf(13,plain,
    ! [B: a,A: a] :
      ( ~ ( sk7 @ A )
      | ~ ( sk7 @ B )
      | ( sk7 @ ( sk8 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(27,plain,
    ! [B: a,A: a] :
      ( ~ ( sk7 @ A )
      | ~ ( sk7 @ B )
      | ( sk7 @ ( sk8 @ A @ B ) ) ),
    inference(simp,[status(thm)],[13]) ).

thf(5,plain,
    ( sk9
    | ~ ( sk7 @ ( sk8 @ sk13 @ sk14 ) )
    | ~ sk12 ),
    inference(cnf,[status(esa)],[3]) ).

thf(124,plain,
    ( $false
    | ~ ( sk7 @ ( sk8 @ sk13 @ sk14 ) )
    | ~ sk12 ),
    inference(rewrite,[status(thm)],[5,109]) ).

thf(125,plain,
    ( ~ ( sk7 @ ( sk8 @ sk13 @ sk14 ) )
    | ~ sk12 ),
    inference(simp,[status(thm)],[124]) ).

thf(374,plain,
    ! [B: a,A: a] :
      ( ~ ( sk7 @ A )
      | ~ ( sk7 @ B )
      | ~ sk12
      | ( ( sk7 @ ( sk8 @ A @ B ) )
       != ( sk7 @ ( sk8 @ sk13 @ sk14 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[27,125]) ).

thf(375,plain,
    ( ~ ( sk7 @ sk13 )
    | ~ ( sk7 @ sk14 )
    | ~ sk12 ),
    inference(pattern_uni,[status(thm)],[374:[bind(A,$thf( sk13 )),bind(B,$thf( sk14 ))]]) ).

thf(410,plain,
    ( ~ sk12
    | ~ ( sk7 @ sk13 )
    | ( ( sk7 @ sk14 )
     != ( sk7 @ sk14 ) ) ),
    inference(paramod_ordered,[status(thm)],[129,375]) ).

thf(411,plain,
    ( ~ sk12
    | ~ ( sk7 @ sk13 ) ),
    inference(pattern_uni,[status(thm)],[410:[]]) ).

thf(434,plain,
    ( ~ sk12
    | ( ( sk7 @ sk13 )
     != ( sk7 @ sk13 ) ) ),
    inference(paramod_ordered,[status(thm)],[131,411]) ).

thf(435,plain,
    ~ sk12,
    inference(pattern_uni,[status(thm)],[434:[]]) ).

thf(635,plain,
    ( ( ( sk8 @ ( sk2 @ ( sk1 @ sk16 ) ) @ ( sk2 @ ( sk1 @ sk17 ) ) )
     != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) )
    | $false
    | $false
    | ( sk3 @ sk15 ) ),
    inference(rewrite,[status(thm)],[29,435,109]) ).

thf(636,plain,
    ( ( ( sk8 @ ( sk2 @ ( sk1 @ sk16 ) ) @ ( sk2 @ ( sk1 @ sk17 ) ) )
     != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) )
    | ( sk3 @ sk15 ) ),
    inference(simp,[status(thm)],[635]) ).

thf(637,plain,
    ! [B: b,A: b] :
      ( ~ ( sk5 @ A )
      | ~ ( sk5 @ B )
      | ( ( sk2 @ ( sk6 @ A @ B ) )
       != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) )
      | ( sk3 @ sk15 )
      | ( ( sk8 @ ( sk2 @ A ) @ ( sk2 @ B ) )
       != ( sk8 @ ( sk2 @ ( sk1 @ sk16 ) ) @ ( sk2 @ ( sk1 @ sk17 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[26,636]) ).

thf(638,plain,
    ( ~ ( sk5 @ ( sk1 @ sk16 ) )
    | ~ ( sk5 @ ( sk1 @ sk17 ) )
    | ( ( sk2 @ ( sk6 @ ( sk1 @ sk16 ) @ ( sk1 @ sk17 ) ) )
     != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) )
    | ( sk3 @ sk15 ) ),
    inference(pattern_uni,[status(thm)],[637:[bind(A,$thf( sk1 @ sk16 )),bind(B,$thf( sk1 @ sk17 ))]]) ).

thf(22,plain,
    ( sk9
    | sk12
    | ( sk3 @ sk15 )
    | ( sk3 @ sk17 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(132,plain,
    ( $false
    | sk12
    | ( sk3 @ sk15 )
    | ( sk3 @ sk17 ) ),
    inference(rewrite,[status(thm)],[22,109]) ).

thf(133,plain,
    ( sk12
    | ( sk3 @ sk15 )
    | ( sk3 @ sk17 ) ),
    inference(simp,[status(thm)],[132]) ).

thf(454,plain,
    ( $false
    | ( sk3 @ sk15 )
    | ( sk3 @ sk17 ) ),
    inference(rewrite,[status(thm)],[133,435]) ).

thf(455,plain,
    ( ( sk3 @ sk15 )
    | ( sk3 @ sk17 ) ),
    inference(simp,[status(thm)],[454]) ).

thf(11,plain,
    ! [A: g] :
      ( ~ ( sk3 @ A )
      | ( sk5 @ ( sk1 @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(32,plain,
    ! [A: g] :
      ( ~ ( sk3 @ A )
      | ( sk5 @ ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[11]) ).

thf(472,plain,
    ! [A: g] :
      ( ( sk3 @ sk15 )
      | ( sk5 @ ( sk1 @ A ) )
      | ( ( sk3 @ sk17 )
       != ( sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[455,32]) ).

thf(473,plain,
    ( ( sk3 @ sk15 )
    | ( sk5 @ ( sk1 @ sk17 ) ) ),
    inference(pattern_uni,[status(thm)],[472:[bind(A,$thf( sk17 ))]]) ).

thf(10,plain,
    ! [A: b] :
      ( ~ ( sk5 @ A )
      | ( sk7 @ ( sk2 @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(24,plain,
    ! [A: b] :
      ( ~ ( sk5 @ A )
      | ( sk7 @ ( sk2 @ A ) ) ),
    inference(simp,[status(thm)],[10]) ).

thf(78,plain,
    ! [B: b,A: g] :
      ( ~ ( sk3 @ A )
      | ( sk7 @ ( sk2 @ B ) )
      | ( ( sk5 @ ( sk1 @ A ) )
       != ( sk5 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[32,24]) ).

thf(79,plain,
    ! [A: g] :
      ( ~ ( sk3 @ A )
      | ( sk7 @ ( sk2 @ ( sk1 @ A ) ) ) ),
    inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( C )),bind(B,$thf( sk1 @ C ))]]) ).

thf(83,plain,
    ! [A: g] :
      ( ~ ( sk3 @ A )
      | ( sk7 @ ( sk2 @ ( sk1 @ A ) ) ) ),
    inference(simp,[status(thm)],[79]) ).

thf(19,plain,
    ( sk9
    | sk12
    | ~ ( sk7 @ ( sk2 @ ( sk1 @ sk15 ) ) )
    | ( sk3 @ sk17 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(157,plain,
    ( $false
    | sk12
    | ~ ( sk7 @ ( sk2 @ ( sk1 @ sk15 ) ) )
    | ( sk3 @ sk17 ) ),
    inference(rewrite,[status(thm)],[19,109]) ).

thf(158,plain,
    ( sk12
    | ~ ( sk7 @ ( sk2 @ ( sk1 @ sk15 ) ) )
    | ( sk3 @ sk17 ) ),
    inference(simp,[status(thm)],[157]) ).

thf(174,plain,
    ! [A: g] :
      ( ~ ( sk3 @ A )
      | sk12
      | ( sk3 @ sk17 )
      | ( ( sk7 @ ( sk2 @ ( sk1 @ A ) ) )
       != ( sk7 @ ( sk2 @ ( sk1 @ sk15 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[83,158]) ).

thf(175,plain,
    ( ~ ( sk3 @ sk15 )
    | sk12
    | ( sk3 @ sk17 ) ),
    inference(pattern_uni,[status(thm)],[174:[bind(A,$thf( sk15 ))]]) ).

thf(450,plain,
    ( ~ ( sk3 @ sk15 )
    | $false
    | ( sk3 @ sk17 ) ),
    inference(rewrite,[status(thm)],[175,435]) ).

thf(451,plain,
    ( ~ ( sk3 @ sk15 )
    | ( sk3 @ sk17 ) ),
    inference(simp,[status(thm)],[450]) ).

thf(15,plain,
    ( sk9
    | sk12
    | ~ ( sk7 @ ( sk2 @ ( sk1 @ sk15 ) ) )
    | ( sk3 @ sk16 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(135,plain,
    ( $false
    | sk12
    | ~ ( sk7 @ ( sk2 @ ( sk1 @ sk15 ) ) )
    | ( sk3 @ sk16 ) ),
    inference(rewrite,[status(thm)],[15,109]) ).

thf(136,plain,
    ( sk12
    | ~ ( sk7 @ ( sk2 @ ( sk1 @ sk15 ) ) )
    | ( sk3 @ sk16 ) ),
    inference(simp,[status(thm)],[135]) ).

thf(176,plain,
    ! [A: g] :
      ( ~ ( sk3 @ A )
      | sk12
      | ( sk3 @ sk16 )
      | ( ( sk7 @ ( sk2 @ ( sk1 @ A ) ) )
       != ( sk7 @ ( sk2 @ ( sk1 @ sk15 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[83,136]) ).

thf(177,plain,
    ( ~ ( sk3 @ sk15 )
    | sk12
    | ( sk3 @ sk16 ) ),
    inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( sk15 ))]]) ).

thf(460,plain,
    ( ~ ( sk3 @ sk15 )
    | $false
    | ( sk3 @ sk16 ) ),
    inference(rewrite,[status(thm)],[177,435]) ).

thf(461,plain,
    ( ~ ( sk3 @ sk15 )
    | ( sk3 @ sk16 ) ),
    inference(simp,[status(thm)],[460]) ).

thf(608,plain,
    ! [A: g] :
      ( ~ ( sk3 @ sk15 )
      | ( sk5 @ ( sk1 @ A ) )
      | ( ( sk3 @ sk16 )
       != ( sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[461,32]) ).

thf(609,plain,
    ( ~ ( sk3 @ sk15 )
    | ( sk5 @ ( sk1 @ sk16 ) ) ),
    inference(pattern_uni,[status(thm)],[608:[bind(A,$thf( sk16 ))]]) ).

thf(544,plain,
    ! [A: g] :
      ( ~ ( sk3 @ sk15 )
      | ( sk5 @ ( sk1 @ A ) )
      | ( ( sk3 @ sk17 )
       != ( sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[451,32]) ).

thf(545,plain,
    ( ~ ( sk3 @ sk15 )
    | ( sk5 @ ( sk1 @ sk17 ) ) ),
    inference(pattern_uni,[status(thm)],[544:[bind(A,$thf( sk17 ))]]) ).

thf(4,plain,
    ( sk9
    | sk12
    | ~ ( sk7 @ ( sk2 @ ( sk1 @ sk15 ) ) )
    | ( ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) )
     != ( sk8 @ ( sk2 @ ( sk1 @ sk16 ) ) @ ( sk2 @ ( sk1 @ sk17 ) ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(34,plain,
    ( ( ( sk8 @ ( sk2 @ ( sk1 @ sk16 ) ) @ ( sk2 @ ( sk1 @ sk17 ) ) )
     != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) )
    | sk9
    | sk12
    | ~ ( sk7 @ ( sk2 @ ( sk1 @ sk15 ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(908,plain,
    ( ( ( sk8 @ ( sk2 @ ( sk1 @ sk16 ) ) @ ( sk2 @ ( sk1 @ sk17 ) ) )
     != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) )
    | $false
    | $false
    | ~ ( sk7 @ ( sk2 @ ( sk1 @ sk15 ) ) ) ),
    inference(rewrite,[status(thm)],[34,435,109]) ).

thf(909,plain,
    ( ( ( sk8 @ ( sk2 @ ( sk1 @ sk16 ) ) @ ( sk2 @ ( sk1 @ sk17 ) ) )
     != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) )
    | ~ ( sk7 @ ( sk2 @ ( sk1 @ sk15 ) ) ) ),
    inference(simp,[status(thm)],[908]) ).

thf(914,plain,
    ! [A: g] :
      ( ~ ( sk3 @ A )
      | ( ( sk8 @ ( sk2 @ ( sk1 @ sk16 ) ) @ ( sk2 @ ( sk1 @ sk17 ) ) )
       != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) )
      | ( ( sk7 @ ( sk2 @ ( sk1 @ A ) ) )
       != ( sk7 @ ( sk2 @ ( sk1 @ sk15 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[83,909]) ).

thf(915,plain,
    ( ~ ( sk3 @ sk15 )
    | ( ( sk8 @ ( sk2 @ ( sk1 @ sk16 ) ) @ ( sk2 @ ( sk1 @ sk17 ) ) )
     != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[914:[bind(A,$thf( sk15 ))]]) ).

thf(981,plain,
    ! [B: b,A: b] :
      ( ~ ( sk5 @ A )
      | ~ ( sk5 @ B )
      | ~ ( sk3 @ sk15 )
      | ( ( sk2 @ ( sk6 @ A @ B ) )
       != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) )
      | ( ( sk8 @ ( sk2 @ A ) @ ( sk2 @ B ) )
       != ( sk8 @ ( sk2 @ ( sk1 @ sk16 ) ) @ ( sk2 @ ( sk1 @ sk17 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[26,915]) ).

thf(982,plain,
    ( ~ ( sk5 @ ( sk1 @ sk16 ) )
    | ~ ( sk5 @ ( sk1 @ sk17 ) )
    | ~ ( sk3 @ sk15 )
    | ( ( sk2 @ ( sk6 @ ( sk1 @ sk16 ) @ ( sk1 @ sk17 ) ) )
     != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[981:[bind(A,$thf( sk1 @ sk16 )),bind(B,$thf( sk1 @ sk17 ))]]) ).

thf(2390,plain,
    ! [B: g,A: g] :
      ( ~ ( sk3 @ A )
      | ~ ( sk3 @ B )
      | ~ ( sk5 @ ( sk1 @ sk16 ) )
      | ~ ( sk5 @ ( sk1 @ sk17 ) )
      | ~ ( sk3 @ sk15 )
      | ( ( sk2 @ ( sk1 @ ( sk4 @ A @ B ) ) )
       != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) )
      | ( ( sk6 @ ( sk1 @ A ) @ ( sk1 @ B ) )
       != ( sk6 @ ( sk1 @ sk16 ) @ ( sk1 @ sk17 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[31,982]) ).

thf(2391,plain,
    ( ~ ( sk3 @ sk16 )
    | ~ ( sk3 @ sk17 )
    | ~ ( sk5 @ ( sk1 @ sk16 ) )
    | ~ ( sk5 @ ( sk1 @ sk17 ) )
    | ~ ( sk3 @ sk15 )
    | ( ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) )
     != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[2390:[bind(A,$thf( sk16 )),bind(B,$thf( sk17 ))]]) ).

thf(2507,plain,
    ( ~ ( sk3 @ sk16 )
    | ~ ( sk3 @ sk17 )
    | ~ ( sk5 @ ( sk1 @ sk16 ) )
    | ~ ( sk5 @ ( sk1 @ sk17 ) )
    | ~ ( sk3 @ sk15 ) ),
    inference(simp,[status(thm)],[2391]) ).

thf(2606,plain,
    ( ~ ( sk3 @ sk15 )
    | ~ ( sk3 @ sk16 )
    | ~ ( sk3 @ sk17 )
    | ~ ( sk5 @ ( sk1 @ sk16 ) )
    | ( ( sk5 @ ( sk1 @ sk17 ) )
     != ( sk5 @ ( sk1 @ sk17 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[545,2507]) ).

thf(2607,plain,
    ( ~ ( sk3 @ sk15 )
    | ~ ( sk3 @ sk16 )
    | ~ ( sk3 @ sk17 )
    | ~ ( sk5 @ ( sk1 @ sk16 ) ) ),
    inference(pattern_uni,[status(thm)],[2606:[]]) ).

thf(2790,plain,
    ( ~ ( sk3 @ sk15 )
    | ~ ( sk3 @ sk16 )
    | ~ ( sk3 @ sk17 )
    | ( ( sk5 @ ( sk1 @ sk16 ) )
     != ( sk5 @ ( sk1 @ sk16 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[609,2607]) ).

thf(2791,plain,
    ( ~ ( sk3 @ sk15 )
    | ~ ( sk3 @ sk16 )
    | ~ ( sk3 @ sk17 ) ),
    inference(pattern_uni,[status(thm)],[2790:[]]) ).

thf(3058,plain,
    ( ~ ( sk3 @ sk15 )
    | ~ ( sk3 @ sk17 )
    | ( ( sk3 @ sk16 )
     != ( sk3 @ sk16 ) ) ),
    inference(paramod_ordered,[status(thm)],[461,2791]) ).

thf(3059,plain,
    ( ~ ( sk3 @ sk15 )
    | ~ ( sk3 @ sk17 ) ),
    inference(pattern_uni,[status(thm)],[3058:[]]) ).

thf(3195,plain,
    ( ~ ( sk3 @ sk15 )
    | ( ( sk3 @ sk17 )
     != ( sk3 @ sk17 ) ) ),
    inference(paramod_ordered,[status(thm)],[451,3059]) ).

thf(3196,plain,
    ~ ( sk3 @ sk15 ),
    inference(pattern_uni,[status(thm)],[3195:[]]) ).

thf(3331,plain,
    ( $false
    | ( sk5 @ ( sk1 @ sk17 ) ) ),
    inference(rewrite,[status(thm)],[473,3196]) ).

thf(3332,plain,
    sk5 @ ( sk1 @ sk17 ),
    inference(simp,[status(thm)],[3331]) ).

thf(14,plain,
    ( sk9
    | sk12
    | ( sk3 @ sk15 )
    | ( sk3 @ sk16 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(126,plain,
    ( $false
    | sk12
    | ( sk3 @ sk15 )
    | ( sk3 @ sk16 ) ),
    inference(rewrite,[status(thm)],[14,109]) ).

thf(127,plain,
    ( sk12
    | ( sk3 @ sk15 )
    | ( sk3 @ sk16 ) ),
    inference(simp,[status(thm)],[126]) ).

thf(149,plain,
    ! [A: g] :
      ( sk12
      | ( sk3 @ sk15 )
      | ( sk5 @ ( sk1 @ A ) )
      | ( ( sk3 @ sk16 )
       != ( sk3 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[127,32]) ).

thf(150,plain,
    ( sk12
    | ( sk3 @ sk15 )
    | ( sk5 @ ( sk1 @ sk16 ) ) ),
    inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( sk16 ))]]) ).

thf(448,plain,
    ( $false
    | ( sk3 @ sk15 )
    | ( sk5 @ ( sk1 @ sk16 ) ) ),
    inference(rewrite,[status(thm)],[150,435]) ).

thf(449,plain,
    ( ( sk3 @ sk15 )
    | ( sk5 @ ( sk1 @ sk16 ) ) ),
    inference(simp,[status(thm)],[448]) ).

thf(3287,plain,
    ( $false
    | ( sk5 @ ( sk1 @ sk16 ) ) ),
    inference(rewrite,[status(thm)],[449,3196]) ).

thf(3288,plain,
    sk5 @ ( sk1 @ sk16 ),
    inference(simp,[status(thm)],[3287]) ).

thf(30028,plain,
    ( ~ $true
    | ~ $true
    | ( ( sk2 @ ( sk6 @ ( sk1 @ sk16 ) @ ( sk1 @ sk17 ) ) )
     != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) )
    | $false ),
    inference(rewrite,[status(thm)],[638,3332,3288,3196]) ).

thf(30029,plain,
    ( ( sk2 @ ( sk6 @ ( sk1 @ sk16 ) @ ( sk1 @ sk17 ) ) )
   != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) ),
    inference(simp,[status(thm)],[30028]) ).

thf(30031,plain,
    ! [B: g,A: g] :
      ( ~ ( sk3 @ A )
      | ~ ( sk3 @ B )
      | ( ( sk2 @ ( sk1 @ ( sk4 @ A @ B ) ) )
       != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) )
      | ( ( sk6 @ ( sk1 @ A ) @ ( sk1 @ B ) )
       != ( sk6 @ ( sk1 @ sk16 ) @ ( sk1 @ sk17 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[31,30029]) ).

thf(30032,plain,
    ( ~ ( sk3 @ sk16 )
    | ~ ( sk3 @ sk17 )
    | ( ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) )
     != ( sk2 @ ( sk1 @ ( sk4 @ sk16 @ sk17 ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[30031:[bind(A,$thf( sk16 )),bind(B,$thf( sk17 ))]]) ).

thf(30033,plain,
    ( ~ ( sk3 @ sk16 )
    | ~ ( sk3 @ sk17 ) ),
    inference(simp,[status(thm)],[30032]) ).

thf(476,plain,
    ( ( sk3 @ sk15 )
    | ( ( sk3 @ sk17 )
     != ( sk3 @ sk15 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[455]) ).

thf(477,plain,
    ( ( sk3 @ sk15 )
    | ( ( sk3 @ sk17 )
     != ( sk3 @ sk15 ) ) ),
    inference(simp,[status(thm)],[476]) ).

thf(3319,plain,
    ( $false
    | ( sk3 @ sk17 ) ),
    inference(rewrite,[status(thm)],[477,3196]) ).

thf(3320,plain,
    sk3 @ sk17,
    inference(simp,[status(thm)],[3319]) ).

thf(40,plain,
    ( sk9
    | sk12
    | ( sk3 @ sk15 )
    | ( ( sk3 @ sk16 )
     != ( sk3 @ sk15 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[14]) ).

thf(41,plain,
    ( sk9
    | sk12
    | ( sk3 @ sk15 )
    | ( ( sk3 @ sk16 )
     != ( sk3 @ sk15 ) ) ),
    inference(simp,[status(thm)],[40]) ).

thf(1021,plain,
    ( $false
    | $false
    | ( sk3 @ sk15 )
    | ( ( sk3 @ sk16 )
     != ( sk3 @ sk15 ) ) ),
    inference(rewrite,[status(thm)],[41,435,109]) ).

thf(1022,plain,
    ( ( sk3 @ sk15 )
    | ( ( sk3 @ sk16 )
     != ( sk3 @ sk15 ) ) ),
    inference(simp,[status(thm)],[1021]) ).

thf(3321,plain,
    ( $false
    | ( sk3 @ sk16 ) ),
    inference(rewrite,[status(thm)],[1022,3196]) ).

thf(3322,plain,
    sk3 @ sk16,
    inference(simp,[status(thm)],[3321]) ).

thf(30228,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[30033,3320,3322]) ).

thf(30229,plain,
    $false,
    inference(simp,[status(thm)],[30228]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SEU904^5 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.11  % Command  : run_Leo-III %s %d
% 0.12/0.31  % Computer : n026.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit : 300
% 0.12/0.31  % WCLimit  : 300
% 0.12/0.31  % DateTime : Sun May 19 18:05:09 EDT 2024
% 0.12/0.31  % CPUTime  : 
% 1.00/0.94  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.29/1.13  % [INFO] 	 Parsing done (180ms). 
% 1.29/1.14  % [INFO] 	 Running in sequential loop mode. 
% 1.97/1.50  % [INFO] 	 nitpick registered as external prover. 
% 1.97/1.51  % [INFO] 	 Scanning for conjecture ... 
% 2.28/1.63  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.28/1.68  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.28/1.68  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.28/1.69  % [INFO] 	 Type checking passed. 
% 2.28/1.70  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 162.78/28.76  % [INFO] 	 Killing All external provers ... 
% 162.78/28.77  % Time passed: 28307ms (effective reasoning time: 27625ms)
% 162.78/28.77  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 162.78/28.77  % Axioms used in derivation (0): 
% 162.78/28.77  % No. of inferences in proof: 121
% 162.78/28.77  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 28307 ms resp. 27625 ms w/o parsing
% 162.96/28.89  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 162.96/28.89  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------