TSTP Solution File: SEU466^1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU466^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.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 03:37:44 EDT 2024

% Result   : Theorem 92.59s 31.67s
% Output   : Refutation 92.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   45 (  18 unt;  13 typ;   2 def)
%            Number of atoms       :  107 (  29 equ;   0 cnn)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :  776 (  38   ~;  16   |;  75   &; 524   @)
%                                         (   0 <=>; 123  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  158 ( 158   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  19 usr;  12 con; 0-3 aty)
%            Number of variables   :  351 ( 108   ^ 243   !;   0   ?; 351   :)

% Comments : 
%------------------------------------------------------------------------------
thf(idem_type,type,
    idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).

thf(idem_def,definition,
    ( idem
    = ( ^ [A: ( $i > $i > $o ) > $i > $i > $o] :
        ! [B: $i > $i > $o] :
          ( ( A @ ( A @ B ) )
          = ( A @ B ) ) ) ) ).

thf(tc_type,type,
    tc: ( $i > $i > $o ) > $i > $i > $o ).

thf(tc_def,definition,
    ( tc
    = ( ^ [A: $i > $i > $o,B: $i,C: $i] :
        ! [D: $i > $i > $o] :
          ( ( ( trans @ D )
            & ( subrel @ A @ D ) )
         => ( D @ B @ C ) ) ) ) ).

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

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

thf(sk25_type,type,
    sk25: $i ).

thf(sk26_type,type,
    sk26: $i ).

thf(sk27_type,type,
    sk27: $i > $i > $o ).

thf(sk31_type,type,
    sk31: ( $i > $i > $o ) > $i ).

thf(sk32_type,type,
    sk32: ( $i > $i > $o ) > $i ).

thf(sk52_type,type,
    sk52: $i ).

thf(sk53_type,type,
    sk53: $i ).

thf(sk59_type,type,
    sk59: ( $i > $i > $o ) > $i ).

thf(sk60_type,type,
    sk60: ( $i > $i > $o ) > $i ).

thf(1,conjecture,
    idem @ tc,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_op_is_idempotent) ).

thf(2,negated_conjecture,
    ~ ( idem @ tc ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(4,plain,
    ( ( ^ [A: $i,B: $i] :
        ! [C: $i > $i > $o] :
          ( ( ! [D: $i,E: $i,F: $i] :
                ( ( ( C @ D @ E )
                  & ( C @ E @ F ) )
               => ( C @ D @ F ) )
            & ! [D: $i,E: $i] :
                ( ! [F: $i > $i > $o] :
                    ( ( ! [G: $i,H: $i,I: $i] :
                          ( ( ( F @ G @ H )
                            & ( F @ H @ I ) )
                         => ( F @ G @ I ) )
                      & ! [G: $i,H: $i] :
                          ( ( sk1 @ G @ H )
                         => ( F @ G @ H ) ) )
                   => ( F @ D @ E ) )
               => ( C @ D @ E ) ) )
         => ( C @ A @ B ) ) )
   != ( ^ [A: $i,B: $i] :
        ! [C: $i > $i > $o] :
          ( ( ! [D: $i,E: $i,F: $i] :
                ( ( ( C @ D @ E )
                  & ( C @ E @ F ) )
               => ( C @ D @ F ) )
            & ! [D: $i,E: $i] :
                ( ( sk1 @ D @ E )
               => ( C @ D @ E ) ) )
         => ( C @ A @ B ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ^ [A: $i,B: $i] :
        ! [C: $i > $i > $o] :
          ( ( ! [D: $i,E: $i,F: $i] :
                ( ( ( C @ D @ E )
                  & ( C @ E @ F ) )
               => ( C @ D @ F ) )
            & ! [D: $i,E: $i] :
                ( ! [F: $i > $i > $o] :
                    ( ( ! [G: $i,H: $i,I: $i] :
                          ( ( ( F @ G @ H )
                            & ( F @ H @ I ) )
                         => ( F @ G @ I ) )
                      & ! [G: $i,H: $i] :
                          ( ( sk1 @ G @ H )
                         => ( F @ G @ H ) ) )
                   => ( F @ D @ E ) )
               => ( C @ D @ E ) ) )
         => ( C @ A @ B ) ) )
   != ( ^ [A: $i,B: $i] :
        ! [C: $i > $i > $o] :
          ( ( ! [D: $i,E: $i,F: $i] :
                ( ( ( C @ D @ E )
                  & ( C @ E @ F ) )
               => ( C @ D @ F ) )
            & ! [D: $i,E: $i] :
                ( ( sk1 @ D @ E )
               => ( C @ D @ E ) ) )
         => ( C @ A @ B ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ^ [A: $i,B: $i,C: $i > $i > $o] :
          ( ( ! [D: $i,E: $i,F: $i] :
                ( ( ( C @ D @ E )
                  & ( C @ E @ F ) )
               => ( C @ D @ F ) )
            & ! [D: $i,E: $i] :
                ( ! [F: $i > $i > $o] :
                    ( ( ! [G: $i,H: $i,I: $i] :
                          ( ( ( F @ G @ H )
                            & ( F @ H @ I ) )
                         => ( F @ G @ I ) )
                      & ! [G: $i,H: $i] :
                          ( ( sk1 @ G @ H )
                         => ( F @ G @ H ) ) )
                   => ( F @ D @ E ) )
               => ( C @ D @ E ) ) )
         => ( C @ A @ B ) ) )
   != ( ^ [A: $i,B: $i,C: $i > $i > $o] :
          ( ( ! [D: $i,E: $i,F: $i] :
                ( ( ( C @ D @ E )
                  & ( C @ E @ F ) )
               => ( C @ D @ F ) )
            & ! [D: $i,E: $i] :
                ( ( sk1 @ D @ E )
               => ( C @ D @ E ) ) )
         => ( C @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ( ^ [A: $i,B: $i,C: $i > $i > $o] :
            ( ! [D: $i,E: $i,F: $i] :
                ( ( ( C @ D @ E )
                  & ( C @ E @ F ) )
               => ( C @ D @ F ) )
            & ! [D: $i,E: $i] :
                ( ! [F: $i > $i > $o] :
                    ( ( ! [G: $i,H: $i,I: $i] :
                          ( ( ( F @ G @ H )
                            & ( F @ H @ I ) )
                         => ( F @ G @ I ) )
                      & ! [G: $i,H: $i] :
                          ( ( sk1 @ G @ H )
                         => ( F @ G @ H ) ) )
                   => ( F @ D @ E ) )
               => ( C @ D @ E ) ) ) )
     != ( ^ [A: $i,B: $i,C: $i > $i > $o] :
            ( ! [D: $i,E: $i,F: $i] :
                ( ( ( C @ D @ E )
                  & ( C @ E @ F ) )
               => ( C @ D @ F ) )
            & ! [D: $i,E: $i] :
                ( ( sk1 @ D @ E )
               => ( C @ D @ E ) ) ) ) )
    | ( ( ^ [A: $i,B: $i,C: $i > $i > $o] : ( C @ A @ B ) )
     != ( ^ [A: $i,B: $i,C: $i > $i > $o] : ( C @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[6]) ).

thf(10,plain,
    ( ( ^ [A: $i,B: $i,C: $i > $i > $o] :
          ( ! [D: $i,E: $i,F: $i] :
              ( ( ( C @ D @ E )
                & ( C @ E @ F ) )
             => ( C @ D @ F ) )
          & ! [D: $i,E: $i] :
              ( ! [F: $i > $i > $o] :
                  ( ( ! [G: $i,H: $i,I: $i] :
                        ( ( ( F @ G @ H )
                          & ( F @ H @ I ) )
                       => ( F @ G @ I ) )
                    & ! [G: $i,H: $i] :
                        ( ( sk1 @ G @ H )
                       => ( F @ G @ H ) ) )
                 => ( F @ D @ E ) )
             => ( C @ D @ E ) ) ) )
   != ( ^ [A: $i,B: $i,C: $i > $i > $o] :
          ( ! [D: $i,E: $i,F: $i] :
              ( ( ( C @ D @ E )
                & ( C @ E @ F ) )
             => ( C @ D @ F ) )
          & ! [D: $i,E: $i] :
              ( ( sk1 @ D @ E )
             => ( C @ D @ E ) ) ) ) ),
    inference(simp,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ( ^ [A: $i,B: $i,C: $i > $i > $o] :
          ! [D: $i,E: $i,F: $i] :
            ( ( ( C @ D @ E )
              & ( C @ E @ F ) )
           => ( C @ D @ F ) ) )
     != ( ^ [A: $i,B: $i,C: $i > $i > $o] :
          ! [D: $i,E: $i,F: $i] :
            ( ( ( C @ D @ E )
              & ( C @ E @ F ) )
           => ( C @ D @ F ) ) ) )
    | ( ( ^ [A: $i,B: $i,C: $i > $i > $o] :
          ! [D: $i,E: $i] :
            ( ! [F: $i > $i > $o] :
                ( ( ! [G: $i,H: $i,I: $i] :
                      ( ( ( F @ G @ H )
                        & ( F @ H @ I ) )
                     => ( F @ G @ I ) )
                  & ! [G: $i,H: $i] :
                      ( ( sk1 @ G @ H )
                     => ( F @ G @ H ) ) )
               => ( F @ D @ E ) )
           => ( C @ D @ E ) ) )
     != ( ^ [A: $i,B: $i,C: $i > $i > $o] :
          ! [D: $i,E: $i] :
            ( ( sk1 @ D @ E )
           => ( C @ D @ E ) ) ) ) ),
    inference(simp,[status(thm)],[10]) ).

thf(13,plain,
    ( ( ^ [A: $i,B: $i,C: $i > $i > $o] :
        ! [D: $i,E: $i] :
          ( ! [F: $i > $i > $o] :
              ( ( ! [G: $i,H: $i,I: $i] :
                    ( ( ( F @ G @ H )
                      & ( F @ H @ I ) )
                   => ( F @ G @ I ) )
                & ! [G: $i,H: $i] :
                    ( ( sk1 @ G @ H )
                   => ( F @ G @ H ) ) )
             => ( F @ D @ E ) )
         => ( C @ D @ E ) ) )
   != ( ^ [A: $i,B: $i,C: $i > $i > $o] :
        ! [D: $i,E: $i] :
          ( ( sk1 @ D @ E )
         => ( C @ D @ E ) ) ) ),
    inference(simp,[status(thm)],[11]) ).

thf(14,plain,
    ( ( ^ [A: $i,B: $i,C: $i > $i > $o,D: $i] :
        ! [E: $i] :
          ( ! [F: $i > $i > $o] :
              ( ( ! [G: $i,H: $i,I: $i] :
                    ( ( ( F @ G @ H )
                      & ( F @ H @ I ) )
                   => ( F @ G @ I ) )
                & ! [G: $i,H: $i] :
                    ( ( sk1 @ G @ H )
                   => ( F @ G @ H ) ) )
             => ( F @ D @ E ) )
         => ( C @ D @ E ) ) )
   != ( ^ [A: $i,B: $i,C: $i > $i > $o,D: $i] :
        ! [E: $i] :
          ( ( sk1 @ D @ E )
         => ( C @ D @ E ) ) ) ),
    inference(simp,[status(thm)],[13]) ).

thf(16,plain,
    ( ( ^ [A: $i,B: $i,C: $i > $i > $o,D: $i,E: $i] :
          ( ! [F: $i > $i > $o] :
              ( ( ! [G: $i,H: $i,I: $i] :
                    ( ( ( F @ G @ H )
                      & ( F @ H @ I ) )
                   => ( F @ G @ I ) )
                & ! [G: $i,H: $i] :
                    ( ( sk1 @ G @ H )
                   => ( F @ G @ H ) ) )
             => ( F @ D @ E ) )
         => ( C @ D @ E ) ) )
   != ( ^ [A: $i,B: $i,C: $i > $i > $o,D: $i,E: $i] :
          ( ( sk1 @ D @ E )
         => ( C @ D @ E ) ) ) ),
    inference(simp,[status(thm)],[14]) ).

thf(18,plain,
    ( ( ( ^ [A: $i,B: $i,C: $i > $i > $o,D: $i,E: $i] :
          ! [F: $i > $i > $o] :
            ( ( ! [G: $i,H: $i,I: $i] :
                  ( ( ( F @ G @ H )
                    & ( F @ H @ I ) )
                 => ( F @ G @ I ) )
              & ! [G: $i,H: $i] :
                  ( ( sk1 @ G @ H )
                 => ( F @ G @ H ) ) )
           => ( F @ D @ E ) ) )
     != ( ^ [A: $i,B: $i,C: $i > $i > $o] : sk1 ) )
    | ( ( ^ [A: $i,B: $i,C: $i > $i > $o] : C )
     != ( ^ [A: $i,B: $i,C: $i > $i > $o] : C ) ) ),
    inference(simp,[status(thm)],[16]) ).

thf(20,plain,
    ( ( ^ [A: $i,B: $i,C: $i > $i > $o,D: $i,E: $i] :
        ! [F: $i > $i > $o] :
          ( ( ! [G: $i,H: $i,I: $i] :
                ( ( ( F @ G @ H )
                  & ( F @ H @ I ) )
               => ( F @ G @ I ) )
            & ! [G: $i,H: $i] :
                ( ( sk1 @ G @ H )
               => ( F @ G @ H ) ) )
         => ( F @ D @ E ) ) )
   != ( ^ [A: $i,B: $i,C: $i > $i > $o] : sk1 ) ),
    inference(simp,[status(thm)],[18]) ).

thf(21,plain,
    ( ( ! [A: $i > $i > $o] :
          ( ( ! [B: $i,C: $i,D: $i] :
                ( ( ( A @ B @ C )
                  & ( A @ C @ D ) )
               => ( A @ B @ D ) )
            & ! [B: $i,C: $i] :
                ( ( sk1 @ B @ C )
               => ( A @ B @ C ) ) )
         => ( A @ sk25 @ sk26 ) ) )
   != ( sk1 @ sk25 @ sk26 ) ),
    inference(func_ext,[status(esa)],[20]) ).

thf(22,plain,
    ( ~ ! [A: $i > $i > $o] :
          ( ( ! [B: $i,C: $i,D: $i] :
                ( ( ( A @ B @ C )
                  & ( A @ C @ D ) )
               => ( A @ B @ D ) )
            & ! [B: $i,C: $i] :
                ( ( sk1 @ B @ C )
               => ( A @ B @ C ) ) )
         => ( A @ sk25 @ sk26 ) )
    | ~ ( sk1 @ sk25 @ sk26 ) ),
    inference(bool_ext,[status(thm)],[21]) ).

thf(24,plain,
    ( ~ ( sk1 @ sk25 @ sk26 )
    | ~ ( sk27 @ sk25 @ sk26 ) ),
    inference(cnf,[status(esa)],[22]) ).

thf(7,plain,
    ( ( ! [A: $i > $i > $o] :
          ( ( ! [B: $i,C: $i,D: $i] :
                ( ( ( A @ B @ C )
                  & ( A @ C @ D ) )
               => ( A @ B @ D ) )
            & ! [B: $i,C: $i] :
                ( ! [D: $i > $i > $o] :
                    ( ( ! [E: $i,F: $i,G: $i] :
                          ( ( ( D @ E @ F )
                            & ( D @ F @ G ) )
                         => ( D @ E @ G ) )
                      & ! [E: $i,F: $i] :
                          ( ( sk1 @ E @ F )
                         => ( D @ E @ F ) ) )
                   => ( D @ B @ C ) )
               => ( A @ B @ C ) ) )
         => ( A @ sk2 @ sk3 ) ) )
   != ( ! [A: $i > $i > $o] :
          ( ( ! [B: $i,C: $i,D: $i] :
                ( ( ( A @ B @ C )
                  & ( A @ C @ D ) )
               => ( A @ B @ D ) )
            & ! [B: $i,C: $i] :
                ( ( sk1 @ B @ C )
               => ( A @ B @ C ) ) )
         => ( A @ sk2 @ sk3 ) ) ) ),
    inference(func_ext,[status(esa)],[5]) ).

thf(15,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [C: $i > $i > $o] :
              ( ( ! [D: $i,E: $i,F: $i] :
                    ( ( ( C @ D @ E )
                      & ( C @ E @ F ) )
                   => ( C @ D @ F ) )
                & ! [D: $i,E: $i] :
                    ( ( sk1 @ D @ E )
                   => ( C @ D @ E ) ) )
             => ( C @ A @ B ) )
         => ( sk12 @ A @ B ) ) )
   != ( ! [A: $i,B: $i] :
          ( ( sk1 @ A @ B )
         => ( sk12 @ A @ B ) ) ) ),
    inference(func_ext,[status(esa)],[13]) ).

thf(117,plain,
    ( ( ^ [A: $i] :
        ! [B: $i] :
          ( ! [C: $i > $i > $o] :
              ( ( ! [D: $i,E: $i,F: $i] :
                    ( ( ( C @ D @ E )
                      & ( C @ E @ F ) )
                   => ( C @ D @ F ) )
                & ! [D: $i,E: $i] :
                    ( ( sk1 @ D @ E )
                   => ( C @ D @ E ) ) )
             => ( C @ A @ B ) )
         => ( sk12 @ A @ B ) ) )
   != ( ^ [A: $i] :
        ! [B: $i] :
          ( ( sk1 @ A @ B )
         => ( sk12 @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[15]) ).

thf(140,plain,
    ( ( ^ [A: $i,B: $i] :
          ( ! [C: $i > $i > $o] :
              ( ( ! [D: $i,E: $i,F: $i] :
                    ( ( ( C @ D @ E )
                      & ( C @ E @ F ) )
                   => ( C @ D @ F ) )
                & ! [D: $i,E: $i] :
                    ( ( sk1 @ D @ E )
                   => ( C @ D @ E ) ) )
             => ( C @ A @ B ) )
         => ( sk12 @ A @ B ) ) )
   != ( ^ [A: $i,B: $i] :
          ( ( sk1 @ A @ B )
         => ( sk12 @ A @ B ) ) ) ),
    inference(simp,[status(thm)],[117]) ).

thf(141,plain,
    ( ( ( ^ [A: $i,B: $i] :
          ! [C: $i > $i > $o] :
            ( ( ! [D: $i,E: $i,F: $i] :
                  ( ( ( C @ D @ E )
                    & ( C @ E @ F ) )
                 => ( C @ D @ F ) )
              & ! [D: $i,E: $i] :
                  ( ( sk1 @ D @ E )
                 => ( C @ D @ E ) ) )
           => ( C @ A @ B ) ) )
     != sk1 )
    | ( sk12 != sk12 ) ),
    inference(simp,[status(thm)],[140]) ).

thf(142,plain,
    ( ( ^ [A: $i,B: $i] :
        ! [C: $i > $i > $o] :
          ( ( ! [D: $i,E: $i,F: $i] :
                ( ( ( C @ D @ E )
                  & ( C @ E @ F ) )
               => ( C @ D @ F ) )
            & ! [D: $i,E: $i] :
                ( ( sk1 @ D @ E )
               => ( C @ D @ E ) ) )
         => ( C @ A @ B ) ) )
   != sk1 ),
    inference(simp,[status(thm)],[141]) ).

thf(23,plain,
    ( ! [A: $i > $i > $o] :
        ( ( ! [B: $i,C: $i,D: $i] :
              ( ( ( A @ B @ C )
                & ( A @ C @ D ) )
             => ( A @ B @ D ) )
          & ! [B: $i,C: $i] :
              ( ( sk1 @ B @ C )
             => ( A @ B @ C ) ) )
       => ( A @ sk25 @ sk26 ) )
    | ( sk1 @ sk25 @ sk26 ) ),
    inference(bool_ext,[status(thm)],[21]) ).

thf(28,plain,
    ! [A: $i > $i > $o] :
      ( ( sk1 @ sk25 @ sk26 )
      | ( A @ ( sk28 @ A ) @ ( sk29 @ A ) )
      | ( sk1 @ ( sk31 @ A ) @ ( sk32 @ A ) )
      | ( A @ sk25 @ sk26 ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(118,plain,
    ( ~ ! [A: $i,B: $i] :
          ( ! [C: $i > $i > $o] :
              ( ( ! [D: $i,E: $i,F: $i] :
                    ( ( ( C @ D @ E )
                      & ( C @ E @ F ) )
                   => ( C @ D @ F ) )
                & ! [D: $i,E: $i] :
                    ( ( sk1 @ D @ E )
                   => ( C @ D @ E ) ) )
             => ( C @ A @ B ) )
         => ( sk12 @ A @ B ) )
    | ~ ! [A: $i,B: $i] :
          ( ( sk1 @ A @ B )
         => ( sk12 @ A @ B ) ) ),
    inference(bool_ext,[status(thm)],[15]) ).

thf(123,plain,
    ! [A: $i > $i > $o] :
      ( ~ ( sk12 @ ( sk59 @ A ) @ ( sk60 @ A ) )
      | ~ ( sk12 @ sk52 @ sk53 ) ),
    inference(cnf,[status(esa)],[118]) ).

thf(143,plain,
    ! [A: $i > $i > $o] :
      ( ~ ( sk12 @ sk52 @ sk53 )
      | ( ( sk12 @ ( sk59 @ A ) @ ( sk60 @ A ) )
       != ( sk12 @ sk52 @ sk53 ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[123]) ).

thf(145,plain,
    ! [A: $i > $i > $o] :
      ( ~ ( sk12 @ sk52 @ sk53 )
      | ( ( sk59 @ A )
       != sk52 )
      | ( ( sk60 @ A )
       != sk53 ) ),
    inference(simp,[status(thm)],[143]) ).

thf(456,plain,
    $false,
    inference(cvc4,[status(thm)],[5,24,14,20,13,7,140,3,16,15,10,142,6,117,28,21,123,145]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU466^1 : TPTP v8.2.0. Released v3.6.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n024.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sun May 19 16:43:39 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.99/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.53/1.02  % [INFO] 	 Parsing done (144ms). 
% 1.53/1.02  % [INFO] 	 Running in sequential loop mode. 
% 2.03/1.25  % [INFO] 	 eprover registered as external prover. 
% 2.03/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 2.03/1.26  % [INFO] 	 Scanning for conjecture ... 
% 2.33/1.37  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.33/1.39  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.33/1.39  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.33/1.39  % [INFO] 	 Type checking passed. 
% 2.33/1.39  % [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 ... 
% 92.59/31.66  % External prover 'cvc4' found a proof!
% 92.59/31.66  % [INFO] 	 Killing All external provers ... 
% 92.59/31.66  % Time passed: 31131ms (effective reasoning time: 30636ms)
% 92.59/31.66  % 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)>
% 92.59/31.66  % Axioms used in derivation (0): 
% 92.59/31.66  % No. of inferences in proof: 30
% 92.59/31.67  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 31131 ms resp. 30636 ms w/o parsing
% 92.66/31.72  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 92.66/31.72  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------