TSTP Solution File: SEV261^5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEV261^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 04:10:15 EDT 2024

% Result   : Theorem 67.47s 11.16s
% Output   : Refutation 67.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   33
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  134 (   9 unt;  16 typ;   0 def)
%            Number of atoms       :  638 ( 152 equ;   0 cnn)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  584 ( 151   ~; 235   |;  42   &; 141   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   56 (  56   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;  10 con; 0-2 aty)
%            Number of variables   :  215 ( 135   ^  67   !;  13   ?; 215   :)

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

thf(sk1_type,type,
    sk1: $o ).

thf(sk2_type,type,
    sk2: a > $o ).

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

thf(sk4_type,type,
    sk4: a > $o ).

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

thf(sk6_type,type,
    sk6: ( a > $o ) > $o ).

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

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

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

thf(sk10_type,type,
    sk10: a > $o ).

thf(sk17_type,type,
    sk17: a ).

thf(sk20_type,type,
    sk20: a ).

thf(sk21_type,type,
    sk21: a > $o ).

thf(sk23_type,type,
    sk23: a ).

thf(sk43_type,type,
    sk43: a ).

thf(1,conjecture,
    ( ! [A: a > $o] :
        ( ( A
          = ( ^ [B: a] : $false ) )
       => ( ( A
            = ( ^ [B: a] : $false ) )
          | ( A
            = ( ^ [B: a] : ~ $false ) ) ) )
    & ! [A: a > $o] :
        ( ( A
          = ( ^ [B: a] : ~ $false ) )
       => ( ( A
            = ( ^ [B: a] : $false ) )
          | ( A
            = ( ^ [B: a] : ~ $false ) ) ) )
    & ! [A: ( a > $o ) > $o,B: a > $o] :
        ( ( ! [C: a > $o] :
              ( ( A @ C )
             => ( ( C
                  = ( ^ [D: a] : $false ) )
                | ( C
                  = ( ^ [D: a] : ~ $false ) ) ) )
          & ( B
            = ( ^ [C: a] :
                ? [D: a > $o] :
                  ( ( A @ D )
                  & ( D @ C ) ) ) ) )
       => ( ( B
            = ( ^ [C: a] : $false ) )
          | ( B
            = ( ^ [C: a] : ~ $false ) ) ) )
    & ! [A: a > $o,B: a > $o,C: a > $o] :
        ( ( ( ( A
              = ( ^ [D: a] : $false ) )
            | ( A
              = ( ^ [D: a] : ~ $false ) ) )
          & ( ( B
              = ( ^ [D: a] : $false ) )
            | ( B
              = ( ^ [D: a] : ~ $false ) ) )
          & ( C
            = ( ^ [D: a] :
                  ( ( A @ D )
                  & ( B @ D ) ) ) ) )
       => ( ( C
            = ( ^ [D: a] : $false ) )
          | ( C
            = ( ^ [D: a] : ~ $false ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cINDISCRETE_TOPOLOGY_pme) ).

thf(2,negated_conjecture,
    ~ ( ! [A: a > $o] :
          ( ( A
            = ( ^ [B: a] : $false ) )
         => ( ( A
              = ( ^ [B: a] : $false ) )
            | ( A
              = ( ^ [B: a] : ~ $false ) ) ) )
      & ! [A: a > $o] :
          ( ( A
            = ( ^ [B: a] : ~ $false ) )
         => ( ( A
              = ( ^ [B: a] : $false ) )
            | ( A
              = ( ^ [B: a] : ~ $false ) ) ) )
      & ! [A: ( a > $o ) > $o,B: a > $o] :
          ( ( ! [C: a > $o] :
                ( ( A @ C )
               => ( ( C
                    = ( ^ [D: a] : $false ) )
                  | ( C
                    = ( ^ [D: a] : ~ $false ) ) ) )
            & ( B
              = ( ^ [C: a] :
                  ? [D: a > $o] :
                    ( ( A @ D )
                    & ( D @ C ) ) ) ) )
         => ( ( B
              = ( ^ [C: a] : $false ) )
            | ( B
              = ( ^ [C: a] : ~ $false ) ) ) )
      & ! [A: a > $o,B: a > $o,C: a > $o] :
          ( ( ( ( A
                = ( ^ [D: a] : $false ) )
              | ( A
                = ( ^ [D: a] : ~ $false ) ) )
            & ( ( B
                = ( ^ [D: a] : $false ) )
              | ( B
                = ( ^ [D: a] : ~ $false ) ) )
            & ( C
              = ( ^ [D: a] :
                    ( ( A @ D )
                    & ( B @ D ) ) ) ) )
         => ( ( C
              = ( ^ [D: a] : $false ) )
            | ( C
              = ( ^ [D: a] : ~ $false ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: a > $o] :
          ( ( A
            = ( ^ [B: a] : $false ) )
         => ( ( A
              = ( ^ [B: a] : $false ) )
            | ( A
              = ( ^ [B: a] : $true ) ) ) )
      & ! [A: a > $o] :
          ( ( A
            = ( ^ [B: a] : $true ) )
         => ( ( A
              = ( ^ [B: a] : $false ) )
            | ( A
              = ( ^ [B: a] : $true ) ) ) )
      & ! [A: ( a > $o ) > $o,B: a > $o] :
          ( ( ! [C: a > $o] :
                ( ( A @ C )
               => ( ( C
                    = ( ^ [D: a] : $false ) )
                  | ( C
                    = ( ^ [D: a] : $true ) ) ) )
            & ( B
              = ( ^ [C: a] :
                  ? [D: a > $o] :
                    ( ( A @ D )
                    & ( D @ C ) ) ) ) )
         => ( ( B
              = ( ^ [C: a] : $false ) )
            | ( B
              = ( ^ [C: a] : $true ) ) ) )
      & ! [A: a > $o,B: a > $o,C: a > $o] :
          ( ( ( ( A
                = ( ^ [D: a] : $false ) )
              | ( A
                = ( ^ [D: a] : $true ) ) )
            & ( ( B
                = ( ^ [D: a] : $false ) )
              | ( B
                = ( ^ [D: a] : $true ) ) )
            & ( C
              = ( ^ [D: a] :
                    ( ( A @ D )
                    & ( B @ D ) ) ) ) )
         => ( ( C
              = ( ^ [D: a] : $false ) )
            | ( C
              = ( ^ [D: a] : $true ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(9,plain,
    ( sk1
    | sk3
    | ( sk7
      = ( ^ [A: a] :
          ? [B: a > $o] :
            ( ( sk6 @ B )
            & ( B @ A ) ) ) )
    | ~ sk5 ),
    inference(cnf,[status(esa)],[3]) ).

thf(23,plain,
    ( ( sk7
      = ( ^ [A: a] :
          ? [B: a > $o] :
            ( ( sk6 @ B )
            & ( B @ A ) ) ) )
    | sk1
    | sk3
    | ~ sk5 ),
    inference(lifteq,[status(thm)],[9]) ).

thf(18,plain,
    ( sk1
    | ( sk4
      = ( ^ [A: a] : $true ) )
    | ~ sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(28,plain,
    ( ( sk4
      = ( ^ [A: a] : $true ) )
    | sk1
    | ~ sk3 ),
    inference(lifteq,[status(thm)],[18]) ).

thf(11,plain,
    ( ( sk2
      = ( ^ [A: a] : $false ) )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(30,plain,
    ( ( sk2
      = ( ^ [A: a] : $false ) )
    | ~ sk1 ),
    inference(lifteq,[status(thm)],[11]) ).

thf(17,plain,
    ( ( sk2
     != ( ^ [A: a] : $false ) )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[3]) ).

thf(25,plain,
    ( ( sk2
     != ( ^ [A: a] : $false ) )
    | ~ sk1 ),
    inference(lifteq,[status(thm)],[17]) ).

thf(39,plain,
    ( ~ sk1
    | ( sk2 != sk2 ) ),
    inference(paramod_ordered,[status(thm)],[30,25]) ).

thf(40,plain,
    ~ sk1,
    inference(pattern_uni,[status(thm)],[39:[]]) ).

thf(64,plain,
    ( ( sk4
      = ( ^ [A: a] : $true ) )
    | $false
    | ~ sk3 ),
    inference(rewrite,[status(thm)],[28,40]) ).

thf(65,plain,
    ( ( sk4
      = ( ^ [A: a] : $true ) )
    | ~ sk3 ),
    inference(simp,[status(thm)],[64]) ).

thf(10,plain,
    ( sk1
    | ( sk4
     != ( ^ [A: a] : $true ) )
    | ~ sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(20,plain,
    ( ( sk4
     != ( ^ [A: a] : $true ) )
    | sk1
    | ~ sk3 ),
    inference(lifteq,[status(thm)],[10]) ).

thf(47,plain,
    ( ( sk4
     != ( ^ [A: a] : $true ) )
    | $false
    | ~ sk3 ),
    inference(rewrite,[status(thm)],[20,40]) ).

thf(48,plain,
    ( ( sk4
     != ( ^ [A: a] : $true ) )
    | ~ sk3 ),
    inference(simp,[status(thm)],[47]) ).

thf(67,plain,
    ( ~ sk3
    | ( sk4 != sk4 ) ),
    inference(paramod_ordered,[status(thm)],[65,48]) ).

thf(68,plain,
    ~ sk3,
    inference(pattern_uni,[status(thm)],[67:[]]) ).

thf(91,plain,
    ( ( sk7
      = ( ^ [A: a] :
          ? [B: a > $o] :
            ( ( sk6 @ B )
            & ( B @ A ) ) ) )
    | $false
    | $false
    | ~ sk5 ),
    inference(rewrite,[status(thm)],[23,68,40]) ).

thf(92,plain,
    ( ( sk7
      = ( ^ [A: a] :
          ? [B: a > $o] :
            ( ( sk6 @ B )
            & ( B @ A ) ) ) )
    | ~ sk5 ),
    inference(simp,[status(thm)],[91]) ).

thf(16,plain,
    ( sk1
    | sk3
    | ( sk7
     != ( ^ [A: a] : $false ) )
    | ~ sk5 ),
    inference(cnf,[status(esa)],[3]) ).

thf(29,plain,
    ( ( sk7
     != ( ^ [A: a] : $false ) )
    | sk1
    | sk3
    | ~ sk5 ),
    inference(lifteq,[status(thm)],[16]) ).

thf(58,plain,
    ( ( sk7
     != ( ^ [A: a] : $false ) )
    | $false
    | sk3
    | ~ sk5 ),
    inference(rewrite,[status(thm)],[29,40]) ).

thf(59,plain,
    ( ( sk7
     != ( ^ [A: a] : $false ) )
    | sk3
    | ~ sk5 ),
    inference(simp,[status(thm)],[58]) ).

thf(79,plain,
    ( ( sk7
     != ( ^ [A: a] : $false ) )
    | $false
    | ~ sk5 ),
    inference(rewrite,[status(thm)],[59,68]) ).

thf(80,plain,
    ( ( sk7
     != ( ^ [A: a] : $false ) )
    | ~ sk5 ),
    inference(simp,[status(thm)],[79]) ).

thf(94,plain,
    ( ~ sk5
    | ( ( ^ [A: a] :
          ? [B: a > $o] :
            ( ( sk6 @ B )
            & ( B @ A ) ) )
     != ( ^ [A: a] : $false ) )
    | ( sk7 != sk7 ) ),
    inference(paramod_ordered,[status(thm)],[92,80]) ).

thf(95,plain,
    ( ~ sk5
    | ( ( ^ [A: a] :
          ? [B: a > $o] :
            ( ( sk6 @ B )
            & ( B @ A ) ) )
     != ( ^ [A: a] : $false ) ) ),
    inference(pattern_uni,[status(thm)],[94:[]]) ).

thf(98,plain,
    ( ? [A: a > $o] :
        ( ( sk6 @ A )
        & ( A @ sk20 ) )
    | ~ sk5 ),
    inference(func_ext,[status(esa)],[95]) ).

thf(102,plain,
    ( ~ sk5
    | ( sk6 @ sk21 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(5,plain,
    ( sk1
    | sk3
    | ( sk7
     != ( ^ [A: a] : $true ) )
    | ~ sk5 ),
    inference(cnf,[status(esa)],[3]) ).

thf(19,plain,
    ( ( sk7
     != ( ^ [A: a] : $true ) )
    | sk1
    | sk3
    | ~ sk5 ),
    inference(lifteq,[status(thm)],[5]) ).

thf(50,plain,
    ( ( sk7
     != ( ^ [A: a] : $true ) )
    | $false
    | sk3
    | ~ sk5 ),
    inference(rewrite,[status(thm)],[19,40]) ).

thf(51,plain,
    ( ( sk7
     != ( ^ [A: a] : $true ) )
    | sk3
    | ~ sk5 ),
    inference(simp,[status(thm)],[50]) ).

thf(73,plain,
    ( ( sk7
     != ( ^ [A: a] : $true ) )
    | $false
    | ~ sk5 ),
    inference(rewrite,[status(thm)],[51,68]) ).

thf(74,plain,
    ( ( sk7
     != ( ^ [A: a] : $true ) )
    | ~ sk5 ),
    inference(simp,[status(thm)],[73]) ).

thf(96,plain,
    ( ~ sk5
    | ( ( ^ [A: a] :
          ? [B: a > $o] :
            ( ( sk6 @ B )
            & ( B @ A ) ) )
     != ( ^ [A: a] : $true ) )
    | ( sk7 != sk7 ) ),
    inference(paramod_ordered,[status(thm)],[92,74]) ).

thf(97,plain,
    ( ~ sk5
    | ( ( ^ [A: a] :
          ? [B: a > $o] :
            ( ( sk6 @ B )
            & ( B @ A ) ) )
     != ( ^ [A: a] : $true ) ) ),
    inference(pattern_uni,[status(thm)],[96:[]]) ).

thf(103,plain,
    ( ~ ? [A: a > $o] :
          ( ( sk6 @ A )
          & ( A @ sk22 ) )
    | ~ sk5 ),
    inference(func_ext,[status(esa)],[97]) ).

thf(106,plain,
    ! [A: a > $o] :
      ( ~ sk5
      | ~ ( sk6 @ A )
      | ~ ( A @ sk22 ) ),
    inference(cnf,[status(esa)],[103]) ).

thf(112,plain,
    ! [A: a > $o] :
      ( ~ sk5
      | ~ ( sk6 @ A )
      | ( ( sk6 @ sk21 )
       != ( A @ sk22 ) ) ),
    inference(paramod_ordered,[status(thm)],[102,106]) ).

thf(141,plain,
    ( ~ sk5
    | ~ ( sk6
        @ ^ [A: a] : ( sk6 @ sk21 ) ) ),
    inference(pre_uni,[status(thm)],[112:[bind(A,$thf( ^ [B: a] : ( sk6 @ sk21 ) ))]]) ).

thf(232,plain,
    ( ~ sk5
    | ( ( sk6
        @ ^ [A: a] : ( sk6 @ sk21 ) )
     != ( sk6 @ sk21 ) ) ),
    inference(paramod_ordered,[status(thm)],[102,141]) ).

thf(239,plain,
    ( ~ sk5
    | ( ( ^ [A: a] : ( sk6 @ sk21 ) )
     != sk21 ) ),
    inference(simp,[status(thm)],[232]) ).

thf(601,plain,
    ( ( ( sk6 @ sk21 )
     != ( sk21 @ sk43 ) )
    | ~ sk5 ),
    inference(func_ext,[status(esa)],[239]) ).

thf(2333,plain,
    ( ~ sk5
    | ~ ( sk21 @ sk43 )
    | ( ( sk6 @ sk21 )
     != ( sk6 @ sk21 ) ) ),
    inference(paramod_ordered,[status(thm)],[102,601]) ).

thf(2334,plain,
    ( ~ sk5
    | ~ ( sk21 @ sk43 ) ),
    inference(pattern_uni,[status(thm)],[2333:[]]) ).

thf(6,plain,
    ( sk1
    | sk3
    | sk5
    | ( sk10
     != ( ^ [A: a] : $false ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(22,plain,
    ( ( sk10
     != ( ^ [A: a] : $false ) )
    | sk1
    | sk3
    | sk5 ),
    inference(lifteq,[status(thm)],[6]) ).

thf(81,plain,
    ( ( sk10
     != ( ^ [A: a] : $false ) )
    | $false
    | $false
    | sk5 ),
    inference(rewrite,[status(thm)],[22,68,40]) ).

thf(82,plain,
    ( ( sk10
     != ( ^ [A: a] : $false ) )
    | sk5 ),
    inference(simp,[status(thm)],[81]) ).

thf(83,plain,
    ( ( sk10 @ sk17 )
    | sk5 ),
    inference(func_ext,[status(esa)],[82]) ).

thf(8,plain,
    ( sk1
    | sk3
    | sk5
    | ( sk10
      = ( ^ [A: a] :
            ( ( sk8 @ A )
            & ( sk9 @ A ) ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(31,plain,
    ( ( ( ^ [A: a] :
            ( ( sk8 @ A )
            & ( sk9 @ A ) ) )
      = sk10 )
    | sk1
    | sk3
    | sk5 ),
    inference(lifteq,[status(thm)],[8]) ).

thf(61,plain,
    ( ( ( ^ [A: a] :
            ( ( sk8 @ A )
            & ( sk9 @ A ) ) )
      = sk10 )
    | $false
    | sk3
    | sk5 ),
    inference(rewrite,[status(thm)],[31,40]) ).

thf(62,plain,
    ( ( ( ^ [A: a] :
            ( ( sk8 @ A )
            & ( sk9 @ A ) ) )
      = sk10 )
    | sk3
    | sk5 ),
    inference(simp,[status(thm)],[61]) ).

thf(75,plain,
    ( ( ( ^ [A: a] :
            ( ( sk8 @ A )
            & ( sk9 @ A ) ) )
      = sk10 )
    | $false
    | sk5 ),
    inference(rewrite,[status(thm)],[62,68]) ).

thf(76,plain,
    ( ( ( ^ [A: a] :
            ( ( sk8 @ A )
            & ( sk9 @ A ) ) )
      = sk10 )
    | sk5 ),
    inference(simp,[status(thm)],[75]) ).

thf(90,plain,
    ! [A: a] :
      ( ( ( ( sk8 @ A )
          & ( sk9 @ A ) )
        = ( sk10 @ A ) )
      | sk5 ),
    inference(func_ext,[status(esa)],[76]) ).

thf(248,plain,
    ! [A: a] :
      ( sk5
      | ( ( sk8 @ A )
        & ( sk9 @ A ) )
      | ~ ( sk10 @ A ) ),
    inference(bool_ext,[status(thm)],[90]) ).

thf(251,plain,
    ! [A: a] :
      ( ~ ( sk10 @ A )
      | ( sk9 @ A )
      | sk5 ),
    inference(cnf,[status(esa)],[248]) ).

thf(1934,plain,
    ! [A: a] :
      ( sk5
      | ( sk9 @ A )
      | ( ( sk10 @ sk17 )
       != ( sk10 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[83,251]) ).

thf(1935,plain,
    ( sk5
    | ( sk9 @ sk17 ) ),
    inference(pattern_uni,[status(thm)],[1934:[bind(A,$thf( sk17 ))]]) ).

thf(1943,plain,
    ! [A: a] :
      ( sk5
      | ( ( sk8 @ A )
        = ( sk10 @ A ) )
      | ( ( sk9 @ sk17 )
       != ( sk9 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1935,90]) ).

thf(1944,plain,
    ( sk5
    | ( ( sk10 @ sk17 )
      = ( sk8 @ sk17 ) ) ),
    inference(pattern_uni,[status(thm)],[1943:[bind(A,$thf( sk17 ))]]) ).

thf(2061,plain,
    ( sk5
    | ( sk8 @ sk17 )
    | ( ( sk10 @ sk17 )
     != ( sk10 @ sk17 ) ) ),
    inference(paramod_ordered,[status(thm)],[1944,83]) ).

thf(2062,plain,
    ( sk5
    | ( sk8 @ sk17 ) ),
    inference(pattern_uni,[status(thm)],[2061:[]]) ).

thf(12,plain,
    ( sk1
    | sk3
    | sk5
    | ( sk8
      = ( ^ [A: a] : $false ) )
    | ( sk8
      = ( ^ [A: a] : $true ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(26,plain,
    ( ( sk8
      = ( ^ [A: a] : $false ) )
    | ( sk8
      = ( ^ [A: a] : $true ) )
    | sk1
    | sk3
    | sk5 ),
    inference(lifteq,[status(thm)],[12]) ).

thf(43,plain,
    ( ( sk8
      = ( ^ [A: a] : $false ) )
    | ( sk8
      = ( ^ [A: a] : $true ) )
    | $false
    | sk3
    | sk5 ),
    inference(rewrite,[status(thm)],[26,40]) ).

thf(44,plain,
    ( ( sk8
      = ( ^ [A: a] : $false ) )
    | ( sk8
      = ( ^ [A: a] : $true ) )
    | sk3
    | sk5 ),
    inference(simp,[status(thm)],[43]) ).

thf(45,plain,
    ! [B: a,A: a] :
      ( ~ ( sk8 @ A )
      | ( sk8 @ B )
      | sk3
      | sk5 ),
    inference(func_ext,[status(esa)],[44]) ).

thf(263,plain,
    ! [B: a,A: a] :
      ( ~ ( sk8 @ A )
      | ( sk8 @ B )
      | $false
      | sk5 ),
    inference(rewrite,[status(thm)],[45,68]) ).

thf(264,plain,
    ! [B: a,A: a] :
      ( ~ ( sk8 @ A )
      | ( sk8 @ B )
      | sk5 ),
    inference(simp,[status(thm)],[263]) ).

thf(2070,plain,
    ! [B: a,A: a] :
      ( sk5
      | ( sk8 @ B )
      | ( ( sk8 @ sk17 )
       != ( sk8 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2062,264]) ).

thf(2071,plain,
    ! [A: a] :
      ( sk5
      | ( sk8 @ A ) ),
    inference(pattern_uni,[status(thm)],[2070:[bind(A,$thf( sk17 ))]]) ).

thf(2077,plain,
    ! [A: a] :
      ( sk5
      | ( sk8 @ A ) ),
    inference(simp,[status(thm)],[2071]) ).

thf(15,plain,
    ( sk1
    | sk3
    | sk5
    | ( sk9
      = ( ^ [A: a] : $false ) )
    | ( sk9
      = ( ^ [A: a] : $true ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(33,plain,
    ( ( sk9
      = ( ^ [A: a] : $false ) )
    | ( sk9
      = ( ^ [A: a] : $true ) )
    | sk1
    | sk3
    | sk5 ),
    inference(lifteq,[status(thm)],[15]) ).

thf(172,plain,
    ( ( sk9
      = ( ^ [A: a] : $false ) )
    | ( sk9
      = ( ^ [A: a] : $true ) )
    | $false
    | $false
    | sk5 ),
    inference(rewrite,[status(thm)],[33,68,40]) ).

thf(173,plain,
    ( ( sk9
      = ( ^ [A: a] : $false ) )
    | ( sk9
      = ( ^ [A: a] : $true ) )
    | sk5 ),
    inference(simp,[status(thm)],[172]) ).

thf(174,plain,
    ! [B: a,A: a] :
      ( ~ ( sk9 @ A )
      | ( sk9 @ B )
      | sk5 ),
    inference(func_ext,[status(esa)],[173]) ).

thf(1936,plain,
    ! [B: a,A: a] :
      ( sk5
      | ( sk9 @ B )
      | ( ( sk9 @ sk17 )
       != ( sk9 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1935,174]) ).

thf(1937,plain,
    ! [A: a] :
      ( sk5
      | ( sk9 @ A ) ),
    inference(pattern_uni,[status(thm)],[1936:[bind(A,$thf( sk17 ))]]) ).

thf(1945,plain,
    ! [A: a] :
      ( sk5
      | ( sk9 @ A ) ),
    inference(simp,[status(thm)],[1937]) ).

thf(3285,plain,
    ! [B: a,A: a] :
      ( sk5
      | ( ( sk8 @ B )
        = ( sk10 @ B ) )
      | ( ( sk9 @ A )
       != ( sk9 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1945,90]) ).

thf(3286,plain,
    ! [A: a] :
      ( sk5
      | ( ( sk10 @ A )
        = ( sk8 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[3285:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(13,plain,
    ( sk1
    | sk3
    | sk5
    | ( sk10
     != ( ^ [A: a] : $true ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(24,plain,
    ( ( sk10
     != ( ^ [A: a] : $true ) )
    | sk1
    | sk3
    | sk5 ),
    inference(lifteq,[status(thm)],[13]) ).

thf(165,plain,
    ( ( sk10
     != ( ^ [A: a] : $true ) )
    | $false
    | $false
    | sk5 ),
    inference(rewrite,[status(thm)],[24,68,40]) ).

thf(166,plain,
    ( ( sk10
     != ( ^ [A: a] : $true ) )
    | sk5 ),
    inference(simp,[status(thm)],[165]) ).

thf(167,plain,
    ( ~ ( sk10 @ sk23 )
    | sk5 ),
    inference(func_ext,[status(esa)],[166]) ).

thf(4677,plain,
    ! [A: a] :
      ( sk5
      | ~ ( sk8 @ A )
      | ( ( sk10 @ A )
       != ( sk10 @ sk23 ) ) ),
    inference(paramod_ordered,[status(thm)],[3286,167]) ).

thf(4678,plain,
    ( sk5
    | ~ ( sk8 @ sk23 ) ),
    inference(pattern_uni,[status(thm)],[4677:[bind(A,$thf( sk23 ))]]) ).

thf(4692,plain,
    ! [A: a] :
      ( sk5
      | ( ( sk8 @ A )
       != ( sk8 @ sk23 ) ) ),
    inference(paramod_ordered,[status(thm)],[2077,4678]) ).

thf(4693,plain,
    sk5,
    inference(pattern_uni,[status(thm)],[4692:[bind(A,$thf( sk23 ))]]) ).

thf(5072,plain,
    ( ~ $true
    | ~ ( sk21 @ sk43 ) ),
    inference(rewrite,[status(thm)],[2334,4693]) ).

thf(5073,plain,
    ~ ( sk21 @ sk43 ),
    inference(simp,[status(thm)],[5072]) ).

thf(101,plain,
    ( ~ sk5
    | ( sk21 @ sk20 ) ),
    inference(cnf,[status(esa)],[98]) ).

thf(4700,plain,
    ( ~ $true
    | ( sk21 @ sk20 ) ),
    inference(rewrite,[status(thm)],[101,4693]) ).

thf(4701,plain,
    sk21 @ sk20,
    inference(simp,[status(thm)],[4700]) ).

thf(4,plain,
    ! [A: a > $o] :
      ( sk1
      | sk3
      | ~ ( sk6 @ A )
      | ( A
        = ( ^ [B: a] : $false ) )
      | ( A
        = ( ^ [B: a] : $true ) )
      | ~ sk5 ),
    inference(cnf,[status(esa)],[3]) ).

thf(32,plain,
    ! [A: a > $o] :
      ( ( A
        = ( ^ [B: a] : $false ) )
      | ( A
        = ( ^ [B: a] : $true ) )
      | sk1
      | sk3
      | ~ ( sk6 @ A )
      | ~ sk5 ),
    inference(lifteq,[status(thm)],[4]) ).

thf(177,plain,
    ! [A: a > $o] :
      ( ( A
        = ( ^ [B: a] : $false ) )
      | ( A
        = ( ^ [B: a] : $true ) )
      | $false
      | $false
      | ~ ( sk6 @ A )
      | ~ sk5 ),
    inference(rewrite,[status(thm)],[32,68,40]) ).

thf(178,plain,
    ! [A: a > $o] :
      ( ( A
        = ( ^ [B: a] : $false ) )
      | ( A
        = ( ^ [B: a] : $true ) )
      | ~ ( sk6 @ A )
      | ~ sk5 ),
    inference(simp,[status(thm)],[177]) ).

thf(202,plain,
    ! [A: a > $o] :
      ( ~ sk5
      | ( A
        = ( ^ [B: a] : $false ) )
      | ( A
        = ( ^ [B: a] : $true ) )
      | ( ( sk6 @ sk21 )
       != ( sk6 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[102,178]) ).

thf(203,plain,
    ( ~ sk5
    | ( sk21
      = ( ^ [A: a] : $false ) )
    | ( sk21
      = ( ^ [A: a] : $true ) ) ),
    inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( sk21 ))]]) ).

thf(374,plain,
    ! [B: a,A: a] :
      ( ~ ( sk21 @ A )
      | ( sk21 @ B )
      | ~ sk5 ),
    inference(func_ext,[status(esa)],[203]) ).

thf(7319,plain,
    ! [B: a,A: a] :
      ( ~ ( sk21 @ A )
      | ( sk21 @ B )
      | ~ $true ),
    inference(rewrite,[status(thm)],[374,4693]) ).

thf(7320,plain,
    ! [B: a,A: a] :
      ( ~ ( sk21 @ A )
      | ( sk21 @ B ) ),
    inference(simp,[status(thm)],[7319]) ).

thf(7321,plain,
    ! [B: a,A: a] :
      ( ( sk21 @ B )
      | ( ( sk21 @ sk20 )
       != ( sk21 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4701,7320]) ).

thf(7322,plain,
    ! [A: a] : ( sk21 @ A ),
    inference(pattern_uni,[status(thm)],[7321:[bind(A,$thf( sk20 ))]]) ).

thf(7343,plain,
    ! [A: a] : ( sk21 @ A ),
    inference(simp,[status(thm)],[7322]) ).

thf(7368,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[5073,7343]) ).

thf(7369,plain,
    $false,
    inference(simp,[status(thm)],[7368]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SEV261^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun May 19 19:20:39 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 1.20/1.13  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.61/1.33  % [INFO] 	 Parsing done (197ms). 
% 1.61/1.34  % [INFO] 	 Running in sequential loop mode. 
% 2.36/1.81  % [INFO] 	 eprover registered as external prover. 
% 2.36/1.81  % [INFO] 	 cvc4 registered as external prover. 
% 2.36/1.82  % [INFO] 	 Scanning for conjecture ... 
% 2.63/1.94  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.63/1.98  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.63/1.98  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.63/1.99  % [INFO] 	 Type checking passed. 
% 2.80/1.99  % [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 ... 
% 67.47/11.14  % [INFO] 	 Killing All external provers ... 
% 67.47/11.16  % Time passed: 10610ms (effective reasoning time: 9790ms)
% 67.47/11.16  % 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)>
% 67.47/11.16  % Axioms used in derivation (0): 
% 67.47/11.16  % No. of inferences in proof: 118
% 67.47/11.16  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10610 ms resp. 9790 ms w/o parsing
% 67.47/11.23  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 67.47/11.23  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------