↑ Up

Leo-III---1.8.0.THM-Ref.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SEV229^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:37:02 AM UTC 2026

% Result   : Theorem 8.16s 3.15s
% Output   : Refutation 7.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   76 (   9 unt;   0 typ;   3 def)
%            Number of atoms       :  404 (  83 equ;   0 cnn)
%            Maximal formula atoms :   28 (   5 avg)
%            Number of connectives :  762 ( 189   ~; 212   |;  25   &; 312   @)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   61 (   8   ^;  50   !;   0   ?;  61   :)
%                                         (   0  !>;   0  ?*;   0  @-;   3  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(cE_decl,type,
    cE: a > $o ).

thf(cD_decl,type,
    cD: a > $o ).

thf(sk1_decl,type,
    sk1: a > $o ).

thf(sk2_decl,type,
    sk2: a ).

thf(sk3_decl,type,
    sk3: a ).

thf(sk4_decl,type,
    sk4: a ).

thf(sk2_def,definition,
    ( sk2
    = ( @+[A: a] :
          ~ ( ( sk1 @ A )
           => ( ( cD @ A )
              & ( cE @ A ) ) ) ) ) ).

thf(sk3_def,definition,
    ( sk3
    = ( @+[A: a] :
          ~ ( ( sk1 @ A )
           => ( cD @ A ) ) ) ) ).

thf(sk4_def,definition,
    ( sk4
    = ( @+[A: a] :
          ~ ( ( sk1 @ A )
           => ( cE @ A ) ) ) ) ).

thf(1,conjecture,
    ( ( ^ [A: a > $o] :
        ! [B: a] :
          ( ( A @ B )
         => ( ( cD @ B )
            & ( cE @ B ) ) ) )
    = ( ^ [A: a > $o] :
          ( ! [B: a] :
              ( ( A @ B )
             => ( cD @ B ) )
          & ! [B: a] :
              ( ( A @ B )
             => ( cE @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5209_pme) ).

thf(2,negated_conjecture,
    ( ( ^ [A: a > $o] :
        ! [B: a] :
          ( ( A @ B )
         => ( ( cD @ B )
            & ( cE @ B ) ) ) )
   != ( ^ [A: a > $o] :
          ( ! [B: a] :
              ( ( A @ B )
             => ( cD @ B ) )
          & ! [B: a] :
              ( ( A @ B )
             => ( cE @ B ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ^ [A: a > $o] :
        ! [B: a] :
          ( ( A @ B )
         => ( ( cD @ B )
            & ( cE @ B ) ) ) )
   != ( ^ [A: a > $o] :
          ( ! [B: a] :
              ( ( A @ B )
             => ( cD @ B ) )
          & ! [B: a] :
              ( ( A @ B )
             => ( cE @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ^ [A: a > $o] :
        ! [B: a] :
          ( ( A @ B )
         => ( ( cD @ B )
            & ( cE @ B ) ) ) )
   != ( ^ [A: a > $o] :
          ( ! [B: a] :
              ( ( A @ B )
             => ( cD @ B ) )
          & ! [B: a] :
              ( ( A @ B )
             => ( cE @ B ) ) ) ) ),
    inference(lifteq,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [A: a] :
          ( ( sk1 @ A )
         => ( ( cD @ A )
            & ( cE @ A ) ) ) )
   != ( ! [A: a] :
          ( ( sk1 @ A )
         => ( cD @ A ) )
      & ! [A: a] :
          ( ( sk1 @ A )
         => ( cE @ A ) ) ) ),
    inference(func_ext,[status(esa)],[4]) ).

thf(6,plain,
    ( ~ ! [A: a] :
          ( ( sk1 @ A )
         => ( ( cD @ A )
            & ( cE @ A ) ) )
    | ~ ( ! [A: a] :
            ( ( sk1 @ A )
           => ( cD @ A ) )
        & ! [A: a] :
            ( ( sk1 @ A )
           => ( cE @ A ) ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ( sk1 @ sk2 )
      | ( sk1 @ sk3 )
      | ( sk1 @ sk4 ) )
    & ( ( sk1 @ sk2 )
      | ( sk1 @ sk3 )
      | ~ ( cE @ sk4 ) )
    & ( ( sk1 @ sk2 )
      | ~ ( cD @ sk3 )
      | ( sk1 @ sk4 ) )
    & ( ( sk1 @ sk2 )
      | ~ ( cD @ sk3 )
      | ~ ( cE @ sk4 ) )
    & ( ~ ( cD @ sk2 )
      | ~ ( cE @ sk2 )
      | ( sk1 @ sk3 )
      | ( sk1 @ sk4 ) )
    & ( ~ ( cD @ sk2 )
      | ~ ( cE @ sk2 )
      | ( sk1 @ sk3 )
      | ~ ( cE @ sk4 ) )
    & ( ~ ( cD @ sk2 )
      | ~ ( cE @ sk2 )
      | ~ ( cD @ sk3 )
      | ( sk1 @ sk4 ) )
    & ( ~ ( cD @ sk2 )
      | ~ ( cE @ sk2 )
      | ~ ( cD @ sk3 )
      | ~ ( cE @ sk4 ) ) ),
    inference(cnf,[status(esa)],[6]) ).

thf(10,plain,
    ( ~ ( cD @ sk2 )
    | ~ ( cE @ sk2 )
    | ~ ( cD @ sk3 )
    | ( sk1 @ sk4 ) ),
    inference(cnfConj,[status(thm)],[8]) ).

thf(11,plain,
    ( ( sk1 @ sk2 )
    | ( sk1 @ sk3 )
    | ~ ( cE @ sk4 ) ),
    inference(cnfConj,[status(thm)],[8]) ).

thf(24,plain,
    ( ( sk1 @ sk2 )
    | ~ ( cE @ sk4 )
    | ( ( sk1 @ sk3 )
     != ( sk1 @ sk2 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[11]) ).

thf(26,plain,
    ( ( sk1 @ sk2 )
    | ~ ( cE @ sk4 )
    | ( sk3 != sk2 ) ),
    inference(simp,[status(thm)],[24]) ).

thf(7,plain,
    ( ! [A: a] :
        ( ( sk1 @ A )
       => ( ( cD @ A )
          & ( cE @ A ) ) )
    | ( ! [A: a] :
          ( ( sk1 @ A )
         => ( cD @ A ) )
      & ! [A: a] :
          ( ( sk1 @ A )
         => ( cE @ A ) ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(17,plain,
    ! [C: a,B: a,A: a] :
      ( ( ~ ( sk1 @ A )
        | ( cD @ A )
        | ~ ( sk1 @ B )
        | ( cD @ B ) )
      & ( ~ ( sk1 @ A )
        | ( cD @ A )
        | ~ ( sk1 @ C )
        | ( cE @ C ) )
      & ( ~ ( sk1 @ A )
        | ( cE @ A )
        | ~ ( sk1 @ B )
        | ( cD @ B ) )
      & ( ~ ( sk1 @ A )
        | ( cE @ A )
        | ~ ( sk1 @ C )
        | ( cE @ C ) ) ),
    inference(cnf,[status(esa)],[7]) ).

thf(18,plain,
    ! [B: a,A: a] :
      ( ~ ( sk1 @ A )
      | ( cD @ A )
      | ~ ( sk1 @ B )
      | ( cD @ B ) ),
    inference(cnfConj,[status(thm)],[17]) ).

thf(151,plain,
    ! [B: a,A: a] :
      ( ~ ( sk1 @ A )
      | ( cD @ A )
      | ( cD @ B )
      | ( ( sk1 @ B )
       != ( sk1 @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[18]) ).

thf(152,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( cD @ A )
      | ( cD @ A ) ),
    inference(pattern_uni,[status(thm)],[151:[bind(A,$thf( B ))]]) ).

thf(160,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( cD @ A ) ),
    inference(simp,[status(thm)],[152]) ).

thf(188,plain,
    ! [A: a] :
      ( ~ ( cE @ sk4 )
      | ( sk3 != sk2 )
      | ~ $true
      | ( cD @ A )
      | ( ( sk1 @ sk2 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[26,160]) ).

thf(189,plain,
    ! [A: a] :
      ( ~ ( cE @ sk4 )
      | ( sk3 != sk2 )
      | ( cD @ A )
      | ( ( sk1 @ sk2 )
       != ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[188]) ).

thf(190,plain,
    ( ~ ( cE @ sk4 )
    | ( sk3 != sk2 )
    | ( cD @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[189:[bind(A,$thf( sk2 ))]]) ).

thf(9,plain,
    ( ~ ( cD @ sk2 )
    | ~ ( cE @ sk2 )
    | ~ ( cD @ sk3 )
    | ~ ( cE @ sk4 ) ),
    inference(cnfConj,[status(thm)],[8]) ).

thf(27,plain,
    ( ~ ( cD @ sk2 )
    | ~ ( cE @ sk2 )
    | ~ ( cE @ sk4 )
    | ( ( cD @ sk3 )
     != ( cD @ sk2 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[9]) ).

thf(29,plain,
    ( ~ ( cD @ sk2 )
    | ~ ( cE @ sk2 )
    | ~ ( cE @ sk4 )
    | ( sk3 != sk2 ) ),
    inference(simp,[status(thm)],[27]) ).

thf(276,plain,
    ( ~ ( cE @ sk4 )
    | ( sk3 != sk2 )
    | ~ $true
    | ~ ( cE @ sk2 )
    | ~ ( cE @ sk4 )
    | ( sk3 != sk2 )
    | ( ( cD @ sk2 )
     != ( cD @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[190,29]) ).

thf(277,plain,
    ( ~ ( cE @ sk4 )
    | ( sk3 != sk2 )
    | ~ ( cE @ sk2 )
    | ( ( cD @ sk2 )
     != ( cD @ sk2 ) ) ),
    inference(simp,[status(thm)],[276]) ).

thf(278,plain,
    ( ~ ( cE @ sk4 )
    | ( sk3 != sk2 )
    | ~ ( cE @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[277:[]]) ).

thf(395,plain,
    ( ( sk3 != sk2 )
    | ~ ( cE @ sk2 )
    | ( ( cE @ sk4 )
     != ( cE @ sk2 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[278]) ).

thf(397,plain,
    ( ( sk3 != sk2 )
    | ~ ( cE @ sk2 )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[395]) ).

thf(16,plain,
    ( ( sk1 @ sk2 )
    | ( sk1 @ sk3 )
    | ( sk1 @ sk4 ) ),
    inference(cnfConj,[status(thm)],[8]) ).

thf(30,plain,
    ( ( sk1 @ sk2 )
    | ( sk1 @ sk3 )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk2 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[16]) ).

thf(33,plain,
    ( ( sk1 @ sk2 )
    | ( sk1 @ sk3 )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[30]) ).

thf(39,plain,
    ( ( sk1 @ sk2 )
    | ( sk4 != sk2 )
    | ( ( sk1 @ sk3 )
     != ( sk1 @ sk2 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[33]) ).

thf(41,plain,
    ( ( sk1 @ sk2 )
    | ( sk4 != sk2 )
    | ( sk3 != sk2 ) ),
    inference(simp,[status(thm)],[39]) ).

thf(203,plain,
    ! [A: a] :
      ( ( sk4 != sk2 )
      | ( sk3 != sk2 )
      | ~ $true
      | ( cD @ A )
      | ( ( sk1 @ sk2 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[41,160]) ).

thf(204,plain,
    ! [A: a] :
      ( ( sk4 != sk2 )
      | ( sk3 != sk2 )
      | ( cD @ A )
      | ( ( sk1 @ sk2 )
       != ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[203]) ).

thf(205,plain,
    ( ( sk4 != sk2 )
    | ( sk3 != sk2 )
    | ( cD @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( sk2 ))]]) ).

thf(32,plain,
    ( ( sk1 @ sk2 )
    | ( sk1 @ sk3 )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk2 ) ) ),
    inference(simp,[status(thm)],[30]) ).

thf(31,plain,
    ( ( sk1 @ sk2 )
    | ( sk1 @ sk3 )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk3 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[16]) ).

thf(35,plain,
    ( ( sk1 @ sk2 )
    | ( sk1 @ sk3 )
    | ( sk4 != sk3 ) ),
    inference(simp,[status(thm)],[31]) ).

thf(42,plain,
    ( ( sk1 @ sk2 )
    | ( sk4 != sk3 )
    | ( ( sk1 @ sk3 )
     != ( sk1 @ sk2 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[35]) ).

thf(44,plain,
    ( ( sk1 @ sk2 )
    | ( sk4 != sk3 )
    | ( sk3 != sk2 ) ),
    inference(simp,[status(thm)],[42]) ).

thf(185,plain,
    ! [A: a] :
      ( ( sk1 @ sk2 )
      | ~ ( cE @ sk4 )
      | ~ $true
      | ( cD @ A )
      | ( ( sk1 @ sk3 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[11,160]) ).

thf(186,plain,
    ! [A: a] :
      ( ( sk1 @ sk2 )
      | ~ ( cE @ sk4 )
      | ( cD @ A )
      | ( ( sk1 @ sk3 )
       != ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[185]) ).

thf(187,plain,
    ( ( sk1 @ sk2 )
    | ~ ( cE @ sk4 )
    | ( cD @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( sk3 ))]]) ).

thf(13,plain,
    ( ( sk1 @ sk2 )
    | ~ ( cD @ sk3 )
    | ( sk1 @ sk4 ) ),
    inference(cnfConj,[status(thm)],[8]) ).

thf(200,plain,
    ! [A: a] :
      ( ( sk1 @ sk2 )
      | ~ ( cD @ sk3 )
      | ~ $true
      | ( cD @ A )
      | ( ( sk1 @ sk4 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[13,160]) ).

thf(201,plain,
    ! [A: a] :
      ( ( sk1 @ sk2 )
      | ~ ( cD @ sk3 )
      | ( cD @ A )
      | ( ( sk1 @ sk4 )
       != ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[200]) ).

thf(202,plain,
    ( ( sk1 @ sk2 )
    | ~ ( cD @ sk3 )
    | ( cD @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[201:[bind(A,$thf( sk4 ))]]) ).

thf(14,plain,
    ( ~ ( cD @ sk2 )
    | ~ ( cE @ sk2 )
    | ( sk1 @ sk3 )
    | ( sk1 @ sk4 ) ),
    inference(cnfConj,[status(thm)],[8]) ).

thf(182,plain,
    ! [A: a] :
      ( ( sk1 @ sk2 )
      | ( sk1 @ sk3 )
      | ~ $true
      | ( cD @ A )
      | ( ( sk1 @ sk4 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[16,160]) ).

thf(183,plain,
    ! [A: a] :
      ( ( sk1 @ sk2 )
      | ( sk1 @ sk3 )
      | ( cD @ A )
      | ( ( sk1 @ sk4 )
       != ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[182]) ).

thf(184,plain,
    ( ( sk1 @ sk2 )
    | ( sk1 @ sk3 )
    | ( cD @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( sk4 ))]]) ).

thf(194,plain,
    ! [A: a] :
      ( ( sk1 @ sk2 )
      | ( sk4 != sk2 )
      | ~ $true
      | ( cD @ A )
      | ( ( sk1 @ sk3 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[33,160]) ).

thf(195,plain,
    ! [A: a] :
      ( ( sk1 @ sk2 )
      | ( sk4 != sk2 )
      | ( cD @ A )
      | ( ( sk1 @ sk3 )
       != ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[194]) ).

thf(196,plain,
    ( ( sk1 @ sk2 )
    | ( sk4 != sk2 )
    | ( cD @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( sk3 ))]]) ).

thf(28,plain,
    ( ~ ( cD @ sk2 )
    | ~ ( cE @ sk2 )
    | ~ ( cE @ sk4 )
    | ( ( cD @ sk3 )
     != ( cD @ sk2 ) ) ),
    inference(simp,[status(thm)],[27]) ).

thf(36,plain,
    ( ( sk1 @ sk2 )
    | ~ ( cD @ sk3 )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk2 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[13]) ).

thf(38,plain,
    ( ( sk1 @ sk2 )
    | ~ ( cD @ sk3 )
    | ( sk4 != sk2 ) ),
    inference(simp,[status(thm)],[36]) ).

thf(12,plain,
    ( ( sk1 @ sk2 )
    | ~ ( cD @ sk3 )
    | ~ ( cE @ sk4 ) ),
    inference(cnfConj,[status(thm)],[8]) ).

thf(179,plain,
    ! [A: a] :
      ( ( sk1 @ sk2 )
      | ( sk4 != sk3 )
      | ~ $true
      | ( cD @ A )
      | ( ( sk1 @ sk3 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[35,160]) ).

thf(180,plain,
    ! [A: a] :
      ( ( sk1 @ sk2 )
      | ( sk4 != sk3 )
      | ( cD @ A )
      | ( ( sk1 @ sk3 )
       != ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[179]) ).

thf(181,plain,
    ( ( sk1 @ sk2 )
    | ( sk4 != sk3 )
    | ( cD @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[180:[bind(A,$thf( sk3 ))]]) ).

thf(197,plain,
    ! [A: a] :
      ( ~ ( cD @ sk3 )
      | ( sk4 != sk2 )
      | ~ $true
      | ( cD @ A )
      | ( ( sk1 @ sk2 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[38,160]) ).

thf(198,plain,
    ! [A: a] :
      ( ~ ( cD @ sk3 )
      | ( sk4 != sk2 )
      | ( cD @ A )
      | ( ( sk1 @ sk2 )
       != ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[197]) ).

thf(199,plain,
    ( ~ ( cD @ sk3 )
    | ( sk4 != sk2 )
    | ( cD @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( sk2 ))]]) ).

thf(173,plain,
    ! [A: a] :
      ( ( sk4 != sk3 )
      | ( sk3 != sk2 )
      | ~ $true
      | ( cD @ A )
      | ( ( sk1 @ sk2 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[44,160]) ).

thf(174,plain,
    ! [A: a] :
      ( ( sk4 != sk3 )
      | ( sk3 != sk2 )
      | ( cD @ A )
      | ( ( sk1 @ sk2 )
       != ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[173]) ).

thf(175,plain,
    ( ( sk4 != sk3 )
    | ( sk3 != sk2 )
    | ( cD @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[174:[bind(A,$thf( sk2 ))]]) ).

thf(15,plain,
    ( ~ ( cD @ sk2 )
    | ~ ( cE @ sk2 )
    | ( sk1 @ sk3 )
    | ~ ( cE @ sk4 ) ),
    inference(cnfConj,[status(thm)],[8]) ).

thf(176,plain,
    ! [A: a] :
      ( ~ ( cD @ sk3 )
      | ~ ( cE @ sk4 )
      | ~ $true
      | ( cD @ A )
      | ( ( sk1 @ sk2 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[12,160]) ).

thf(177,plain,
    ! [A: a] :
      ( ~ ( cD @ sk3 )
      | ~ ( cE @ sk4 )
      | ( cD @ A )
      | ( ( sk1 @ sk2 )
       != ( sk1 @ A ) ) ),
    inference(simp,[status(thm)],[176]) ).

thf(178,plain,
    ( ~ ( cD @ sk3 )
    | ~ ( cE @ sk4 )
    | ( cD @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[177:[bind(A,$thf( sk2 ))]]) ).

thf(541,plain,
    $false,
    inference(e,[status(thm)],[10,397,9,205,32,44,187,26,190,4,5,202,14,184,196,160,33,28,38,13,41,12,181,278,3,35,199,16,11,175,15,178]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEV229^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.21  % Computer : n019.cluster.edu
% 0.09/0.21  % Model    : x86_64 x86_64
% 0.09/0.21  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21  % Memory   : 8046.5625MB
% 0.09/0.21  % OS       : Linux 6.8.0-71-generic
% 0.09/0.21  % CPULimit : 300
% 0.09/0.21  % WCLimit  : 300
% 0.09/0.21  % DateTime : Tue Sep 29 15:23:17 UTC 2026
% 0.09/0.21  % CPUTime  : 
% 0.09/0.21  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.90/0.76  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.24/0.95  % [INFO] 	 Parsing done (184ms). 
% 1.24/0.96  % [INFO] 	 Running in sequential loop mode. 
% 1.85/1.37  % [INFO] 	 eprover registered as external prover. 
% 1.85/1.38  % [INFO] 	 Scanning for conjecture ... 
% 2.05/1.47  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.22/1.51  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.22/1.51  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.22/1.51  % [INFO] 	 Type checking passed. 
% 2.22/1.52  % [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 ... 
% 8.16/3.14  % External prover 'e' found a proof!
% 8.16/3.14  % [INFO] 	 Killing All external provers ... 
% 8.16/3.14  % Time passed: 2808ms (effective reasoning time: 2173ms)
% 8.16/3.14  % 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)>
% 8.16/3.15  % Axioms used in derivation (0): 
% 8.16/3.15  % No. of inferences in proof: 73
% 8.16/3.15  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2808 ms resp. 2173 ms w/o parsing
% 7.44/3.21  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.44/3.21  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------