TSTP Solution File: SET788+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET788+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n013.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 03:06:59 EDT 2024

% Result   : Theorem 277.90s 101.26s
% Output   : Refutation 277.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   57
%            Number of leaves      :    9
% Syntax   : Number of formulae    :  114 (   8 unt;   8 typ;   0 def)
%            Number of atoms       :  396 (  28 equ;   0 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives : 1278 ( 100   ~; 200   |;   8   &; 944   @)
%                                         (   6 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :  142 (   0   ^ 142   !;   0   ?; 142   :)

% Comments : 
%------------------------------------------------------------------------------
thf(equalish_type,type,
    equalish: $i > $i > $o ).

thf(a_member_of_type,type,
    a_member_of: $i > $i > $o ).

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

thf(sk2_type,type,
    sk2: $i > $i > $i ).

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

thf(sk4_type,type,
    sk4: $i ).

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

thf(sk6_type,type,
    sk6: $i ).

thf(1,conjecture,
    ( ! [A: $i,B: $i] :
        ( ( equalish @ A @ B )
      <=> ! [C: $i] :
            ( ( a_member_of @ C @ A )
          <=> ( a_member_of @ C @ B ) ) )
   => ! [A: $i,B: $i] :
        ( ( equalish @ A @ B )
      <=> ( equalish @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

thf(2,negated_conjecture,
    ~ ( ! [A: $i,B: $i] :
          ( ( equalish @ A @ B )
        <=> ! [C: $i] :
              ( ( a_member_of @ C @ A )
            <=> ( a_member_of @ C @ B ) ) )
     => ! [A: $i,B: $i] :
          ( ( equalish @ A @ B )
        <=> ( equalish @ B @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ( ( equalish @ A @ B )
           => ! [C: $i] :
                ( ( ( a_member_of @ C @ A )
                 => ( a_member_of @ C @ B ) )
                & ( ( a_member_of @ C @ B )
                 => ( a_member_of @ C @ A ) ) ) )
          & ( ! [C: $i] :
                ( ( ( a_member_of @ C @ A )
                 => ( a_member_of @ C @ B ) )
                & ( ( a_member_of @ C @ B )
                 => ( a_member_of @ C @ A ) ) )
           => ( equalish @ A @ B ) ) )
     => ! [A: $i,B: $i] :
          ( ( ( equalish @ A @ B )
           => ( equalish @ B @ A ) )
          & ( ( equalish @ B @ A )
           => ( equalish @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ~ ( ( ! [A: $i,B: $i] :
            ( ( equalish @ A @ B )
           => ( ! [C: $i] :
                  ( ( a_member_of @ C @ A )
                 => ( a_member_of @ C @ B ) )
              & ! [C: $i] :
                  ( ( a_member_of @ C @ B )
                 => ( a_member_of @ C @ A ) ) ) )
        & ! [A: $i,B: $i] :
            ( ( ! [C: $i] :
                  ( ( a_member_of @ C @ A )
                 => ( a_member_of @ C @ B ) )
              & ! [C: $i] :
                  ( ( a_member_of @ C @ B )
                 => ( a_member_of @ C @ A ) ) )
           => ( equalish @ A @ B ) ) )
     => ( ! [A: $i,B: $i] :
            ( ( equalish @ A @ B )
           => ( equalish @ B @ A ) )
        & ! [A: $i,B: $i] :
            ( ( equalish @ B @ A )
           => ( equalish @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(10,plain,
    ( ~ ( equalish @ sk4 @ sk3 )
    | ( equalish @ sk6 @ sk5 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ( a_member_of @ ( sk1 @ B @ A ) @ A )
      | ( a_member_of @ ( sk2 @ B @ A ) @ B )
      | ( equalish @ A @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(17,plain,
    ! [B: $i,A: $i] :
      ( ( a_member_of @ ( sk1 @ B @ A ) @ A )
      | ( a_member_of @ ( sk2 @ B @ A ) @ B )
      | ( equalish @ A @ B ) ),
    inference(simp,[status(thm)],[9]) ).

thf(13,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( a_member_of @ C @ A )
      | ( a_member_of @ C @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(88,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( a_member_of @ ( sk1 @ B @ A ) @ A )
      | ( equalish @ A @ B )
      | ~ ( equalish @ C @ D )
      | ( a_member_of @ E @ D )
      | ( ( a_member_of @ ( sk2 @ B @ A ) @ B )
       != ( a_member_of @ E @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[17,13]) ).

thf(89,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( a_member_of @ ( sk1 @ B @ C ) @ C )
      | ( equalish @ C @ B )
      | ~ ( equalish @ B @ A )
      | ( a_member_of @ ( sk2 @ B @ C ) @ A ) ),
    inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( D )),bind(E,$thf( sk2 @ F @ G ))]]) ).

thf(96,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( a_member_of @ ( sk1 @ B @ C ) @ C )
      | ( equalish @ C @ B )
      | ~ ( equalish @ B @ A )
      | ( a_member_of @ ( sk2 @ B @ C ) @ A ) ),
    inference(simp,[status(thm)],[89]) ).

thf(161,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ sk4 @ sk3 )
      | ( a_member_of @ ( sk1 @ B @ C ) @ C )
      | ( equalish @ C @ B )
      | ( a_member_of @ ( sk2 @ B @ C ) @ A )
      | ( ( equalish @ sk6 @ sk5 )
       != ( equalish @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[10,96]) ).

thf(162,plain,
    ! [A: $i] :
      ( ~ ( equalish @ sk4 @ sk3 )
      | ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
      | ( equalish @ A @ sk6 )
      | ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(167,plain,
    ! [A: $i] :
      ( ~ ( equalish @ sk4 @ sk3 )
      | ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
      | ( equalish @ A @ sk6 )
      | ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 ) ),
    inference(simp,[status(thm)],[162]) ).

thf(5,plain,
    ( ( equalish @ sk3 @ sk4 )
    | ( equalish @ sk6 @ sk5 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(153,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ( a_member_of @ ( sk1 @ B @ C ) @ C )
      | ( equalish @ C @ B )
      | ( a_member_of @ ( sk2 @ B @ C ) @ A )
      | ( ( equalish @ sk6 @ sk5 )
       != ( equalish @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5,96]) ).

thf(154,plain,
    ! [A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
      | ( equalish @ A @ sk6 )
      | ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(169,plain,
    ! [A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
      | ( equalish @ A @ sk6 )
      | ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 ) ),
    inference(simp,[status(thm)],[154]) ).

thf(6,plain,
    ! [B: $i,A: $i] :
      ( ( a_member_of @ ( sk1 @ B @ A ) @ A )
      | ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
      | ( equalish @ A @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ( a_member_of @ ( sk1 @ B @ A ) @ A )
      | ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
      | ( equalish @ A @ B ) ),
    inference(simp,[status(thm)],[6]) ).

thf(219,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
      | ( equalish @ A @ sk6 )
      | ( a_member_of @ ( sk1 @ C @ B ) @ B )
      | ( equalish @ B @ C )
      | ( ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 )
       != ( a_member_of @ ( sk2 @ C @ B ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[169,16]) ).

thf(220,plain,
    ( ( equalish @ sk3 @ sk4 )
    | ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
    | ( equalish @ sk5 @ sk6 )
    | ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
    | ( equalish @ sk5 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[219:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 )),bind(C,$thf( sk6 ))]]) ).

thf(229,plain,
    ( ( equalish @ sk3 @ sk4 )
    | ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
    | ( equalish @ sk5 @ sk6 ) ),
    inference(simp,[status(thm)],[220]) ).

thf(7,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( a_member_of @ C @ B )
      | ( a_member_of @ C @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(19,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ A @ B )
      | ~ ( a_member_of @ C @ B )
      | ( a_member_of @ C @ A ) ),
    inference(simp,[status(thm)],[7]) ).

thf(474,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ~ ( a_member_of @ C @ B )
      | ( a_member_of @ C @ A )
      | ( ( equalish @ sk6 @ sk5 )
       != ( equalish @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5,19]) ).

thf(475,plain,
    ! [A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ~ ( a_member_of @ A @ sk5 )
      | ( a_member_of @ A @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[474:[bind(A,$thf( sk6 )),bind(B,$thf( sk5 ))]]) ).

thf(536,plain,
    ! [A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ~ ( a_member_of @ A @ sk5 )
      | ( a_member_of @ A @ sk6 ) ),
    inference(simp,[status(thm)],[475]) ).

thf(1498,plain,
    ! [A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ( equalish @ sk5 @ sk6 )
      | ( a_member_of @ A @ sk6 )
      | ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
       != ( a_member_of @ A @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[229,536]) ).

thf(1499,plain,
    ( ( equalish @ sk3 @ sk4 )
    | ( equalish @ sk5 @ sk6 )
    | ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[1498:[bind(A,$thf( sk1 @ sk6 @ sk5 ))]]) ).

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a_member_of @ ( sk1 @ B @ A ) @ B )
      | ( a_member_of @ ( sk2 @ B @ A ) @ B )
      | ( equalish @ A @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(18,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a_member_of @ ( sk1 @ B @ A ) @ B )
      | ( a_member_of @ ( sk2 @ B @ A ) @ B )
      | ( equalish @ A @ B ) ),
    inference(simp,[status(thm)],[12]) ).

thf(1715,plain,
    ! [B: $i,A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ( equalish @ sk5 @ sk6 )
      | ( a_member_of @ ( sk2 @ B @ A ) @ B )
      | ( equalish @ A @ B )
      | ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk6 )
       != ( a_member_of @ ( sk1 @ B @ A ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1499,18]) ).

thf(1716,plain,
    ( ( equalish @ sk3 @ sk4 )
    | ( equalish @ sk5 @ sk6 )
    | ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6 )
    | ( equalish @ sk5 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[1715:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(1747,plain,
    ( ( equalish @ sk3 @ sk4 )
    | ( equalish @ sk5 @ sk6 )
    | ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6 ) ),
    inference(simp,[status(thm)],[1716]) ).

thf(80,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ~ ( a_member_of @ C @ A )
      | ( a_member_of @ C @ B )
      | ( ( equalish @ sk6 @ sk5 )
       != ( equalish @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5,13]) ).

thf(81,plain,
    ! [A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ~ ( a_member_of @ A @ sk6 )
      | ( a_member_of @ A @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( sk6 )),bind(B,$thf( sk5 ))]]) ).

thf(92,plain,
    ! [A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ~ ( a_member_of @ A @ sk6 )
      | ( a_member_of @ A @ sk5 ) ),
    inference(simp,[status(thm)],[81]) ).

thf(1766,plain,
    ! [A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ( equalish @ sk5 @ sk6 )
      | ( a_member_of @ A @ sk5 )
      | ( ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6 )
       != ( a_member_of @ A @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[1747,92]) ).

thf(1767,plain,
    ( ( equalish @ sk3 @ sk4 )
    | ( equalish @ sk5 @ sk6 )
    | ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[1766:[bind(A,$thf( sk2 @ sk6 @ sk5 ))]]) ).

thf(14,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a_member_of @ ( sk1 @ B @ A ) @ B )
      | ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
      | ( equalish @ A @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(15,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a_member_of @ ( sk1 @ B @ A ) @ B )
      | ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
      | ( equalish @ A @ B ) ),
    inference(simp,[status(thm)],[14]) ).

thf(1721,plain,
    ! [B: $i,A: $i] :
      ( ( equalish @ sk3 @ sk4 )
      | ( equalish @ sk5 @ sk6 )
      | ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
      | ( equalish @ A @ B )
      | ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk6 )
       != ( a_member_of @ ( sk1 @ B @ A ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1499,15]) ).

thf(1722,plain,
    ( ( equalish @ sk3 @ sk4 )
    | ( equalish @ sk5 @ sk6 )
    | ~ ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5 )
    | ( equalish @ sk5 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[1721:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(1749,plain,
    ( ( equalish @ sk3 @ sk4 )
    | ( equalish @ sk5 @ sk6 )
    | ~ ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5 ) ),
    inference(simp,[status(thm)],[1722]) ).

thf(1903,plain,
    ( ( equalish @ sk3 @ sk4 )
    | ( equalish @ sk5 @ sk6 )
    | ( ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5 )
     != ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[1767,1749]) ).

thf(1904,plain,
    ( ( equalish @ sk3 @ sk4 )
    | ( equalish @ sk5 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[1903:[]]) ).

thf(8,plain,
    ( ( equalish @ sk3 @ sk4 )
    | ~ ( equalish @ sk5 @ sk6 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(1966,plain,
    ( ( equalish @ sk3 @ sk4 )
    | ( ( equalish @ sk5 @ sk6 )
     != ( equalish @ sk5 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[1904,8]) ).

thf(1967,plain,
    equalish @ sk3 @ sk4,
    inference(pattern_uni,[status(thm)],[1966:[]]) ).

thf(1998,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( a_member_of @ ( sk1 @ B @ C ) @ C )
      | ( equalish @ C @ B )
      | ( a_member_of @ ( sk2 @ B @ C ) @ A )
      | ( ( equalish @ sk3 @ sk4 )
       != ( equalish @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1967,96]) ).

thf(1999,plain,
    ! [A: $i] :
      ( ( a_member_of @ ( sk1 @ sk3 @ A ) @ A )
      | ( equalish @ A @ sk3 )
      | ( a_member_of @ ( sk2 @ sk3 @ A ) @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[1998:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 ))]]) ).

thf(2027,plain,
    ! [A: $i] :
      ( ( a_member_of @ ( sk1 @ sk3 @ A ) @ A )
      | ( equalish @ A @ sk3 )
      | ( a_member_of @ ( sk2 @ sk3 @ A ) @ sk4 ) ),
    inference(simp,[status(thm)],[1999]) ).

thf(2058,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( a_member_of @ ( sk1 @ sk3 @ A ) @ A )
      | ( equalish @ A @ sk3 )
      | ( a_member_of @ ( sk1 @ C @ B ) @ B )
      | ( equalish @ B @ C )
      | ( ( a_member_of @ ( sk2 @ sk3 @ A ) @ sk4 )
       != ( a_member_of @ ( sk2 @ C @ B ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2027,16]) ).

thf(2059,plain,
    ( ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk4 )
    | ( equalish @ sk4 @ sk3 )
    | ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk4 )
    | ( equalish @ sk4 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[2058:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 )),bind(C,$thf( sk3 ))]]) ).

thf(2104,plain,
    ( ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk4 )
    | ( equalish @ sk4 @ sk3 ) ),
    inference(simp,[status(thm)],[2059]) ).

thf(1994,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( a_member_of @ C @ B )
      | ( a_member_of @ C @ A )
      | ( ( equalish @ sk3 @ sk4 )
       != ( equalish @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1967,19]) ).

thf(1995,plain,
    ! [A: $i] :
      ( ~ ( a_member_of @ A @ sk4 )
      | ( a_member_of @ A @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[1994:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(2026,plain,
    ! [A: $i] :
      ( ~ ( a_member_of @ A @ sk4 )
      | ( a_member_of @ A @ sk3 ) ),
    inference(simp,[status(thm)],[1995]) ).

thf(2251,plain,
    ! [A: $i] :
      ( ( equalish @ sk4 @ sk3 )
      | ( a_member_of @ A @ sk3 )
      | ( ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk4 )
       != ( a_member_of @ A @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[2104,2026]) ).

thf(2252,plain,
    ( ( equalish @ sk4 @ sk3 )
    | ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[2251:[bind(A,$thf( sk1 @ sk3 @ sk4 ))]]) ).

thf(2302,plain,
    ! [B: $i,A: $i] :
      ( ( equalish @ sk4 @ sk3 )
      | ( a_member_of @ ( sk2 @ B @ A ) @ B )
      | ( equalish @ A @ B )
      | ( ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk3 )
       != ( a_member_of @ ( sk1 @ B @ A ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2252,18]) ).

thf(2303,plain,
    ( ( equalish @ sk4 @ sk3 )
    | ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk3 )
    | ( equalish @ sk4 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[2302:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 ))]]) ).

thf(2327,plain,
    ( ( equalish @ sk4 @ sk3 )
    | ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk3 ) ),
    inference(simp,[status(thm)],[2303]) ).

thf(1989,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( a_member_of @ C @ A )
      | ( a_member_of @ C @ B )
      | ( ( equalish @ sk3 @ sk4 )
       != ( equalish @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1967,13]) ).

thf(1990,plain,
    ! [A: $i] :
      ( ~ ( a_member_of @ A @ sk3 )
      | ( a_member_of @ A @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[1989:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(2025,plain,
    ! [A: $i] :
      ( ~ ( a_member_of @ A @ sk3 )
      | ( a_member_of @ A @ sk4 ) ),
    inference(simp,[status(thm)],[1990]) ).

thf(2307,plain,
    ! [B: $i,A: $i] :
      ( ( equalish @ sk4 @ sk3 )
      | ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
      | ( equalish @ A @ B )
      | ( ( a_member_of @ ( sk1 @ sk3 @ sk4 ) @ sk3 )
       != ( a_member_of @ ( sk1 @ B @ A ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2252,15]) ).

thf(2308,plain,
    ( ( equalish @ sk4 @ sk3 )
    | ~ ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk4 )
    | ( equalish @ sk4 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[2307:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 ))]]) ).

thf(2318,plain,
    ( ( equalish @ sk4 @ sk3 )
    | ~ ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk4 ) ),
    inference(simp,[status(thm)],[2308]) ).

thf(2344,plain,
    ! [A: $i] :
      ( ~ ( a_member_of @ A @ sk3 )
      | ( equalish @ sk4 @ sk3 )
      | ( ( a_member_of @ A @ sk4 )
       != ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[2025,2318]) ).

thf(2345,plain,
    ( ~ ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk3 )
    | ( equalish @ sk4 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[2344:[bind(A,$thf( sk2 @ sk3 @ sk4 ))]]) ).

thf(2471,plain,
    ( ( equalish @ sk4 @ sk3 )
    | ( ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk3 )
     != ( a_member_of @ ( sk2 @ sk3 @ sk4 ) @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[2327,2345]) ).

thf(2472,plain,
    equalish @ sk4 @ sk3,
    inference(pattern_uni,[status(thm)],[2471:[]]) ).

thf(2732,plain,
    ! [A: $i] :
      ( ~ $true
      | ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
      | ( equalish @ A @ sk6 )
      | ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 ) ),
    inference(rewrite,[status(thm)],[167,2472]) ).

thf(2733,plain,
    ! [A: $i] :
      ( ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
      | ( equalish @ A @ sk6 )
      | ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 ) ),
    inference(simp,[status(thm)],[2732]) ).

thf(2736,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( a_member_of @ ( sk1 @ sk6 @ A ) @ A )
      | ( equalish @ A @ sk6 )
      | ( a_member_of @ ( sk1 @ C @ B ) @ B )
      | ( equalish @ B @ C )
      | ( ( a_member_of @ ( sk2 @ sk6 @ A ) @ sk5 )
       != ( a_member_of @ ( sk2 @ C @ B ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2733,16]) ).

thf(2737,plain,
    ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
    | ( equalish @ sk5 @ sk6 )
    | ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
    | ( equalish @ sk5 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[2736:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 )),bind(C,$thf( sk6 ))]]) ).

thf(2777,plain,
    ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
    | ( equalish @ sk5 @ sk6 ) ),
    inference(simp,[status(thm)],[2737]) ).

thf(11,plain,
    ( ~ ( equalish @ sk4 @ sk3 )
    | ~ ( equalish @ sk5 @ sk6 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(2510,plain,
    ( ~ $true
    | ~ ( equalish @ sk5 @ sk6 ) ),
    inference(rewrite,[status(thm)],[11,2472]) ).

thf(2511,plain,
    ~ ( equalish @ sk5 @ sk6 ),
    inference(simp,[status(thm)],[2510]) ).

thf(2795,plain,
    ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
    | $false ),
    inference(rewrite,[status(thm)],[2777,2511]) ).

thf(2796,plain,
    a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5,
    inference(simp,[status(thm)],[2795]) ).

thf(504,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ sk4 @ sk3 )
      | ~ ( a_member_of @ C @ B )
      | ( a_member_of @ C @ A )
      | ( ( equalish @ sk6 @ sk5 )
       != ( equalish @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[10,19]) ).

thf(505,plain,
    ! [A: $i] :
      ( ~ ( equalish @ sk4 @ sk3 )
      | ~ ( a_member_of @ A @ sk5 )
      | ( a_member_of @ A @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[504:[bind(A,$thf( sk6 )),bind(B,$thf( sk5 ))]]) ).

thf(535,plain,
    ! [A: $i] :
      ( ~ ( equalish @ sk4 @ sk3 )
      | ~ ( a_member_of @ A @ sk5 )
      | ( a_member_of @ A @ sk6 ) ),
    inference(simp,[status(thm)],[505]) ).

thf(2516,plain,
    ! [A: $i] :
      ( ~ $true
      | ~ ( a_member_of @ A @ sk5 )
      | ( a_member_of @ A @ sk6 ) ),
    inference(rewrite,[status(thm)],[535,2472]) ).

thf(2517,plain,
    ! [A: $i] :
      ( ~ ( a_member_of @ A @ sk5 )
      | ( a_member_of @ A @ sk6 ) ),
    inference(simp,[status(thm)],[2516]) ).

thf(2810,plain,
    ! [A: $i] :
      ( ( a_member_of @ A @ sk6 )
      | ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk5 )
       != ( a_member_of @ A @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[2796,2517]) ).

thf(2811,plain,
    a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk6,
    inference(pattern_uni,[status(thm)],[2810:[bind(A,$thf( sk1 @ sk6 @ sk5 ))]]) ).

thf(2854,plain,
    ! [B: $i,A: $i] :
      ( ~ ( a_member_of @ ( sk2 @ B @ A ) @ A )
      | ( equalish @ A @ B )
      | ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk6 )
       != ( a_member_of @ ( sk1 @ B @ A ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2811,15]) ).

thf(2855,plain,
    ( ~ ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5 )
    | ( equalish @ sk5 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[2854:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(2846,plain,
    ! [B: $i,A: $i] :
      ( ( a_member_of @ ( sk2 @ B @ A ) @ B )
      | ( equalish @ A @ B )
      | ( ( a_member_of @ ( sk1 @ sk6 @ sk5 ) @ sk6 )
       != ( a_member_of @ ( sk1 @ B @ A ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2811,18]) ).

thf(2847,plain,
    ( ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6 )
    | ( equalish @ sk5 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[2846:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).

thf(2875,plain,
    ( ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6 )
    | $false ),
    inference(rewrite,[status(thm)],[2847,2511]) ).

thf(2876,plain,
    a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6,
    inference(simp,[status(thm)],[2875]) ).

thf(82,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( equalish @ sk4 @ sk3 )
      | ~ ( a_member_of @ C @ A )
      | ( a_member_of @ C @ B )
      | ( ( equalish @ sk6 @ sk5 )
       != ( equalish @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[10,13]) ).

thf(83,plain,
    ! [A: $i] :
      ( ~ ( equalish @ sk4 @ sk3 )
      | ~ ( a_member_of @ A @ sk6 )
      | ( a_member_of @ A @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( sk6 )),bind(B,$thf( sk5 ))]]) ).

thf(93,plain,
    ! [A: $i] :
      ( ~ ( equalish @ sk4 @ sk3 )
      | ~ ( a_member_of @ A @ sk6 )
      | ( a_member_of @ A @ sk5 ) ),
    inference(simp,[status(thm)],[83]) ).

thf(2514,plain,
    ! [A: $i] :
      ( ~ $true
      | ~ ( a_member_of @ A @ sk6 )
      | ( a_member_of @ A @ sk5 ) ),
    inference(rewrite,[status(thm)],[93,2472]) ).

thf(2515,plain,
    ! [A: $i] :
      ( ~ ( a_member_of @ A @ sk6 )
      | ( a_member_of @ A @ sk5 ) ),
    inference(simp,[status(thm)],[2514]) ).

thf(2883,plain,
    ! [A: $i] :
      ( ( a_member_of @ A @ sk5 )
      | ( ( a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk6 )
       != ( a_member_of @ A @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[2876,2515]) ).

thf(2884,plain,
    a_member_of @ ( sk2 @ sk6 @ sk5 ) @ sk5,
    inference(pattern_uni,[status(thm)],[2883:[bind(A,$thf( sk2 @ sk6 @ sk5 ))]]) ).

thf(40970,plain,
    ( ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[2855,2884,2511]) ).

thf(40971,plain,
    $false,
    inference(simp,[status(thm)],[40970]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : SET788+1 : TPTP v8.2.0. Released v3.1.0.
% 0.05/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n013.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Mon May 20 13:21:24 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.89/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.23/1.04  % [INFO] 	 Parsing done (141ms). 
% 1.23/1.05  % [INFO] 	 Running in sequential loop mode. 
% 1.69/1.40  % [INFO] 	 nitpick registered as external prover. 
% 1.69/1.40  % [INFO] 	 Scanning for conjecture ... 
% 1.91/1.48  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.91/1.51  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.91/1.51  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.91/1.52  % [INFO] 	 Type checking passed. 
% 1.91/1.52  % [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 ... 
% 277.90/101.25  % [INFO] 	 Killing All external provers ... 
% 277.90/101.25  % Time passed: 100801ms (effective reasoning time: 100194ms)
% 277.90/101.25  % 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)>
% 277.90/101.26  % Axioms used in derivation (0): 
% 277.90/101.26  % No. of inferences in proof: 106
% 277.90/101.26  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 100801 ms resp. 100194 ms w/o parsing
% 277.90/101.28  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 277.90/101.29  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------