TSTP Solution File: SEV452^1 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SEV452^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% 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 : Mon Jun 24 16:00:18 EDT 2024

% Result   : Theorem 272.80s 45.91s
% Output   : Refutation 272.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   54 (  25 unt;   0 typ;   0 def)
%            Number of atoms       :  253 (  51 equ;   0 cnn)
%            Maximal formula atoms :    7 (   4 avg)
%            Number of connectives :  650 (  61   ~;  46   |;  17   &; 526   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   7 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  111 ( 111   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-4 aty)
%            Number of variables   :  202 (  36   ^ 166   !;   0   ?; 202   :)

% Comments : 
%------------------------------------------------------------------------------
thf('\'const/sets/INTER\'_type',type,
    '\'const/sets/INTER\'': 
      !>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).

thf('\'const/sets/IN\'_type',type,
    '\'const/sets/IN\'': 
      !>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).

thf(skt1_type,type,
    skt1: $tType ).

thf(sk1_type,type,
    sk1: skt1 > $o ).

thf(sk2_type,type,
    sk2: skt1 ).

thf(3,axiom,
    ! [TA: $tType,A: TA > $o,B: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ B @ A )
      = ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).

thf(9,plain,
    ! [TA: $tType,A: TA > $o,B: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ B @ A )
      = ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,plain,
    ! [TA: $tType,B: TA,A: TA > $o] :
      ( ( '\'const/sets/IN\'' @ TA @ B @ A )
      = ( A @ B ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(11,plain,
    ! [TA: $tType,B: TA,A: TA > $o] :
      ( ( '\'const/sets/IN\'' @ TA @ B @ A )
      = ( A @ B ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(4,axiom,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
      = ( ( '\'const/sets/IN\'' @ TA @ C @ A )
        & ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_INTER_') ).

thf(12,plain,
    ! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
      ( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
      = ( ( '\'const/sets/IN\'' @ TA @ C @ A )
        & ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(13,plain,
    ! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
      ( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
      = ( ( '\'const/sets/IN\'' @ TA @ C @ A )
        & ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
    inference(cnf,[status(esa)],[12]) ).

thf(14,plain,
    ! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
      ( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
      = ( ( '\'const/sets/IN\'' @ TA @ C @ A )
        & ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
    inference(lifteq,[status(thm)],[13]) ).

thf(134,plain,
    ! [TA: $tType,TB: $tType,E: TB,D: TB > $o,C: TB > $o,B: TA,A: TA > $o] :
      ( ( ( '\'const/sets/IN\'' @ TA @ B @ A )
        = ( ( '\'const/sets/IN\'' @ TB @ E @ C )
          & ( '\'const/sets/IN\'' @ TB @ E @ D ) ) )
      | ( ( A @ B )
       != ( '\'const/sets/IN\'' @ TB @ E @ ( '\'const/sets/INTER\'' @ TB @ C @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,14]) ).

thf(140,plain,
    ! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
      ( ( ( '\'const/sets/IN\'' @ TA @ A
          @ ^ [G: TA] :
              ( '\'const/sets/IN\'' @ TB @ ( D @ G )
              @ ^ [H: TB] : ( '\'const/sets/INTER\'' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
        = ( ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ B )
          & ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ C ) ) )
      | ( ( E @ A )
       != ( ^ [G: TB] : B ) )
      | ( ( F @ A )
       != ( ^ [G: TB] : C ) ) ),
    inference(pre_uni,[status(thm)],[134:[bind(A,$thf( ^ [I: TA] : ( '\'const/sets/IN\'' @ TB @ ( F @ I ) @ ^ [J: TB] : ( '\'const/sets/INTER\'' @ TB @ ( H @ I @ J ) @ ( I @ I @ J ) @ J ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( F @ B ))]]) ).

thf(141,plain,
    ! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
      ( ( ( '\'const/sets/IN\'' @ TA @ A
          @ ^ [G: TA] :
              ( '\'const/sets/IN\'' @ TB @ ( D @ G )
              @ ^ [H: TB] : ( '\'const/sets/INTER\'' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
        = ( ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ B )
          & ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ C ) ) )
      | ( ( E @ A )
       != ( ^ [G: TB] : B ) )
      | ( ( F @ A )
       != ( ^ [G: TB] : C ) ) ),
    inference(pre_uni,[status(thm)],[140:[]]) ).

thf(153,plain,
    ! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
      ( ( ( '\'const/sets/IN\'' @ TA @ A
          @ ^ [G: TA] :
              ( '\'const/sets/IN\'' @ TB @ ( D @ G )
              @ ^ [H: TB] : ( '\'const/sets/INTER\'' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
        = ( ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ B )
          & ( '\'const/sets/IN\'' @ TB @ ( D @ A ) @ C ) ) )
      | ( ( E @ A )
       != ( ^ [G: TB] : B ) )
      | ( ( F @ A )
       != ( ^ [G: TB] : C ) ) ),
    inference(simp,[status(thm)],[141]) ).

thf(128,plain,
    ! [TA: $tType,TB: $tType,E: TB,D: TB > $o,C: TB > $o,B: TA,A: TA > $o] :
      ( ( ( A @ B )
        = ( ( '\'const/sets/IN\'' @ TB @ E @ C )
          & ( '\'const/sets/IN\'' @ TB @ E @ D ) ) )
      | ( ( '\'const/sets/IN\'' @ TA @ B @ A )
       != ( '\'const/sets/IN\'' @ TB @ E @ ( '\'const/sets/INTER\'' @ TB @ C @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,14]) ).

thf(129,plain,
    ! [TB: $tType,C: TB > $o,B: TB > $o,A: TB] :
      ( ( ( '\'const/sets/IN\'' @ TB @ A @ B )
        & ( '\'const/sets/IN\'' @ TB @ A @ C ) )
      = ( '\'const/sets/INTER\'' @ TB @ B @ C @ A ) ),
    inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( '\'const/sets/INTER\'' @ TB @ C @ D )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind_type(TA,$thf( TB ))]]) ).

thf(149,plain,
    ! [TA: $tType,C: TA > $o,B: TA > $o,A: TA] :
      ( ( ( '\'const/sets/IN\'' @ TA @ A @ B )
        & ( '\'const/sets/IN\'' @ TA @ A @ C ) )
      = ( '\'const/sets/INTER\'' @ TA @ B @ C @ A ) ),
    inference(simp,[status(thm)],[129]) ).

thf(8013,plain,
    ! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
      ( ( ( '\'const/sets/IN\'' @ TA @ A
          @ ^ [G: TA] :
              ( '\'const/sets/IN\'' @ TB @ ( D @ G )
              @ ^ [H: TB] : ( '\'const/sets/INTER\'' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
        = ( '\'const/sets/INTER\'' @ TB @ B @ C @ ( D @ A ) ) )
      | ( ( E @ A )
       != ( ^ [G: TB] : B ) )
      | ( ( F @ A )
       != ( ^ [G: TB] : C ) ) ),
    inference(rewrite,[status(thm)],[153,149]) ).

thf(1,conjecture,
    ! [TA: $tType,A: TA > $o] :
      ( ( '\'const/sets/INTER\'' @ TA @ A @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INTER_IDEMPOT_') ).

thf(2,negated_conjecture,
    ~ ! [TA: $tType,A: TA > $o] :
        ( ( '\'const/sets/INTER\'' @ TA @ A @ A )
        = A ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(6,plain,
    ~ ! [TA: $tType,A: TA > $o] :
        ( ( '\'const/sets/INTER\'' @ TA @ A @ A )
        = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(7,plain,
    ( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 )
   != sk1 ),
    inference(cnf,[status(esa)],[6]) ).

thf(8,plain,
    ( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 )
   != sk1 ),
    inference(lifteq,[status(thm)],[7]) ).

thf(18,plain,
    ( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2 )
   != ( sk1 @ sk2 ) ),
    inference(func_ext,[status(esa)],[8]) ).

thf(20,plain,
    ( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2 )
    | ( sk1 @ sk2 ) ),
    inference(bool_ext,[status(thm)],[18]) ).

thf(116,plain,
    ! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
      ( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
      | ~ ( ( '\'const/sets/IN\'' @ TA @ C @ A )
          & ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ),
    inference(bool_ext,[status(thm)],[14]) ).

thf(159,plain,
    ! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
      ( ~ ( '\'const/sets/IN\'' @ TA @ C @ A )
      | ~ ( '\'const/sets/IN\'' @ TA @ C @ B )
      | ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) ) ),
    inference(cnf,[status(esa)],[116]) ).

thf(22,plain,
    ! [TA: $tType,B: TA,A: TA > $o] :
      ( ( '\'const/sets/IN\'' @ TA @ B @ A )
      | ~ ( A @ B ) ),
    inference(bool_ext,[status(thm)],[11]) ).

thf(19,plain,
    ( ~ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2 )
    | ~ ( sk1 @ sk2 ) ),
    inference(bool_ext,[status(thm)],[18]) ).

thf(8178,plain,
    ! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
      ( ( ( E @ A )
       != ( ^ [G: TB] : B ) )
      | ( ( F @ A )
       != ( ^ [G: TB] : C ) )
      | ~ ( '\'const/sets/IN\'' @ TA @ A
          @ ^ [G: TA] :
              ( '\'const/sets/IN\'' @ TB @ ( D @ G )
              @ ^ [H: TB] : ( '\'const/sets/INTER\'' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
      | ~ ( sk1 @ sk2 )
      | ( ( '\'const/sets/INTER\'' @ TB @ B @ C @ ( D @ A ) )
       != ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[8013,19]) ).

thf(8206,plain,
    ! [TA: $tType,C: TA > skt1 > skt1 > $o,B: TA > skt1 > skt1 > $o,A: TA] :
      ( ( ( B @ A )
       != ( ^ [D: skt1] : sk1 ) )
      | ( ( C @ A )
       != ( ^ [D: skt1] : sk1 ) )
      | ~ ( '\'const/sets/IN\'' @ TA @ A
          @ ^ [D: TA] :
              ( '\'const/sets/IN\'' @ skt1 @ sk2
              @ ^ [E: skt1] : ( '\'const/sets/INTER\'' @ skt1 @ ( B @ D @ E ) @ ( C @ D @ E ) @ E ) ) )
      | ~ ( sk1 @ sk2 ) ),
    inference(pre_uni,[status(thm)],[8178:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk1 )),bind(D,$thf( ^ [G: TA] : sk2 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).

thf(8207,plain,
    ! [TA: $tType,A: TA] :
      ( ~ ( sk1 @ sk2 )
      | ~ ( '\'const/sets/IN\'' @ TA @ A
          @ ^ [B: TA] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) ) ),
    inference(pre_uni,[status(thm)],[8206:[bind(A,$thf( (>) )),bind(B,$thf( ^ [D: TA] : ^ [E: skt1] : sk1 )),bind(C,$thf( ^ [D: TA] : ^ [E: skt1] : sk1 ))]]) ).

thf(24732,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: TA,A: TA > $o] :
      ( ~ ( A @ B )
      | ~ ( sk1 @ sk2 )
      | ( ( '\'const/sets/IN\'' @ TA @ B @ A )
       != ( '\'const/sets/IN\'' @ TB @ C
          @ ^ [D: TB] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[22,8207]) ).

thf(24733,plain,
    ( ~ ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) )
    | ~ ( sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[24732:[bind(A,$thf( ^ [D: TB] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind_type(TA,$thf( TB ))]]) ).

thf(24981,plain,
    ! [TA: $tType,C: TA,B: TA > $o,A: TA > $o] :
      ( ~ ( '\'const/sets/IN\'' @ TA @ C @ A )
      | ~ ( '\'const/sets/IN\'' @ TA @ C @ B )
      | ~ ( sk1 @ sk2 )
      | ( ( '\'const/sets/IN\'' @ TA @ C @ ( '\'const/sets/INTER\'' @ TA @ A @ B ) )
       != ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[159,24733]) ).

thf(24982,plain,
    ( ~ ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 )
    | ~ ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 )
    | ~ ( sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[24981:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).

thf(25012,plain,
    ( ~ ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 )
    | ~ ( sk1 @ sk2 ) ),
    inference(simp,[status(thm)],[24982]) ).

thf(25048,plain,
    ! [TA: $tType,B: TA,A: TA > $o] :
      ( ~ ( A @ B )
      | ~ ( sk1 @ sk2 )
      | ( ( '\'const/sets/IN\'' @ TA @ B @ A )
       != ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,25012]) ).

thf(25049,plain,
    ( ~ ( sk1 @ sk2 )
    | ~ ( sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[25048:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind_type(TA,$thf( skt1 ))]]) ).

thf(25065,plain,
    ~ ( sk1 @ sk2 ),
    inference(simp,[status(thm)],[25049]) ).

thf(25591,plain,
    ( ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2 )
    | $false ),
    inference(rewrite,[status(thm)],[20,25065]) ).

thf(25592,plain,
    '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2,
    inference(simp,[status(thm)],[25591]) ).

thf(25647,plain,
    ! [TA: $tType,TB: $tType,F: TA > TB > TB > $o,E: TA > TB > TB > $o,D: TA > TB,C: TB > $o,B: TB > $o,A: TA] :
      ( ( ( E @ A )
       != ( ^ [G: TB] : B ) )
      | ( ( F @ A )
       != ( ^ [G: TB] : C ) )
      | ( '\'const/sets/IN\'' @ TA @ A
        @ ^ [G: TA] :
            ( '\'const/sets/IN\'' @ TB @ ( D @ G )
            @ ^ [H: TB] : ( '\'const/sets/INTER\'' @ TB @ ( E @ G @ H ) @ ( F @ G @ H ) @ H ) ) )
      | ( ( '\'const/sets/INTER\'' @ TB @ B @ C @ ( D @ A ) )
       != ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[8013,25592]) ).

thf(25669,plain,
    ! [TA: $tType,C: TA > skt1 > skt1 > $o,B: TA > skt1 > skt1 > $o,A: TA] :
      ( ( ( B @ A )
       != ( ^ [D: skt1] : sk1 ) )
      | ( ( C @ A )
       != ( ^ [D: skt1] : sk1 ) )
      | ( '\'const/sets/IN\'' @ TA @ A
        @ ^ [D: TA] :
            ( '\'const/sets/IN\'' @ skt1 @ sk2
            @ ^ [E: skt1] : ( '\'const/sets/INTER\'' @ skt1 @ ( B @ D @ E ) @ ( C @ D @ E ) @ E ) ) ) ),
    inference(pre_uni,[status(thm)],[25647:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk1 )),bind(D,$thf( ^ [G: TA] : sk2 )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( skt1 ))]]) ).

thf(25670,plain,
    ! [TA: $tType,A: TA] :
      ( '\'const/sets/IN\'' @ TA @ A
      @ ^ [B: TA] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) ),
    inference(pre_uni,[status(thm)],[25669:[bind(A,$thf( (>) )),bind(B,$thf( ^ [D: TA] : ^ [E: skt1] : sk1 )),bind(C,$thf( ^ [D: TA] : ^ [E: skt1] : sk1 ))]]) ).

thf(21,plain,
    ! [TA: $tType,B: TA,A: TA > $o] :
      ( ~ ( '\'const/sets/IN\'' @ TA @ B @ A )
      | ( A @ B ) ),
    inference(bool_ext,[status(thm)],[11]) ).

thf(26237,plain,
    ! [TA: $tType,TB: $tType,C: TB,B: TB > $o,A: TA] :
      ( ( B @ C )
      | ( ( '\'const/sets/IN\'' @ TA @ A
          @ ^ [D: TA] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) )
       != ( '\'const/sets/IN\'' @ TB @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[25670,21]) ).

thf(26238,plain,
    '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ),
    inference(pattern_uni,[status(thm)],[26237:[bind(A,$thf( A )),bind(B,$thf( ^ [D: TB] : ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) ) )),bind(C,$thf( A )),bind_type(TA,$thf( TB ))]]) ).

thf(130,plain,
    ! [TA: $tType,TB: $tType,E: TB,D: TB > $o,C: TB > $o,B: TA,A: TA > $o] :
      ( ( ( ( '\'const/sets/IN\'' @ TB @ E @ C )
          & ( A @ B ) )
        = ( '\'const/sets/IN\'' @ TB @ E @ ( '\'const/sets/INTER\'' @ TB @ C @ D ) ) )
      | ( ( '\'const/sets/IN\'' @ TA @ B @ A )
       != ( '\'const/sets/IN\'' @ TB @ E @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[11,14]) ).

thf(131,plain,
    ! [TB: $tType,C: TB > $o,B: TB,A: TB > $o] :
      ( ( ( '\'const/sets/IN\'' @ TB @ B @ C )
        & ( A @ B ) )
      = ( '\'const/sets/IN\'' @ TB @ B @ ( '\'const/sets/INTER\'' @ TB @ C @ A ) ) ),
    inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B )),bind_type(TA,$thf( TB ))]]) ).

thf(150,plain,
    ! [TA: $tType,C: TA > $o,B: TA,A: TA > $o] :
      ( ( ( '\'const/sets/IN\'' @ TA @ B @ C )
        & ( A @ B ) )
      = ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/INTER\'' @ TA @ C @ A ) ) ),
    inference(simp,[status(thm)],[131]) ).

thf(26368,plain,
    ! [TA: $tType,C: TA > $o,B: TA,A: TA > $o] :
      ( ( ( '\'const/sets/IN\'' @ TA @ B @ C )
        & ( A @ B ) )
      | ( ( '\'const/sets/IN\'' @ skt1 @ sk2 @ ( '\'const/sets/INTER\'' @ skt1 @ sk1 @ sk1 ) )
       != ( '\'const/sets/IN\'' @ TA @ B @ ( '\'const/sets/INTER\'' @ TA @ C @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[26238,150]) ).

thf(26369,plain,
    ( ( '\'const/sets/IN\'' @ skt1 @ sk2 @ sk1 )
    & ( sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[26368:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).

thf(26397,plain,
    sk1 @ sk2,
    inference(cnf,[status(esa)],[26369]) ).

thf(26418,plain,
    $false,
    inference(rewrite,[status(thm)],[26397,25065]) ).

thf(26419,plain,
    $false,
    inference(simp,[status(thm)],[26418]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV452^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.12  % Command  : run_Leo-III %s %d SAT
% 0.13/0.33  % Computer : n022.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Fri Jun 21 19:11:40 EDT 2024
% 0.13/0.33  % CPUTime  : 
% 0.83/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.15/0.96  % [INFO] 	 Parsing done (102ms). 
% 1.15/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.43/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.43/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.73/1.21  % [INFO] 	 Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ... 
% 1.73/1.23  % [INFO] 	 Axiom selection finished. Selected 3 axioms (removed 0 axioms). 
% 1.85/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.85/1.25  % [INFO] 	 Type checking passed. 
% 1.85/1.25  % [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 ... 
% 272.80/45.91  % [INFO] 	 Killing All external provers ... 
% 272.80/45.91  % Time passed: 45380ms (effective reasoning time: 44935ms)
% 272.80/45.91  % 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)>
% 272.80/45.91  % Axioms used in derivation (2): thm/sets/IN_, thm/sets/IN_INTER_
% 272.80/45.91  % No. of inferences in proof: 54
% 272.80/45.91  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 45380 ms resp. 44935 ms w/o parsing
% 272.81/45.98  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 272.81/45.98  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------