TSTP Solution File: SET931+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET931+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n020.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 03:07:25 EDT 2024

% Result   : Theorem 8.88s 2.81s
% Output   : Refutation 8.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   95 (  13 unt;  12 typ;   0 def)
%            Number of atoms       :  246 ( 154 equ;   0 cnn)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  641 ( 140   ~;  98   |;  39   &; 348   @)
%                                         (   4 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;  10 con; 0-2 aty)
%            Number of variables   :  106 (   0   ^ 106   !;   0   ?; 106   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_difference_type,type,
    set_difference: $i > $i > $i ).

thf(unordered_pair_type,type,
    unordered_pair: $i > $i > $i ).

thf(empty_set_type,type,
    empty_set: $i ).

thf(singleton_type,type,
    singleton: $i > $i ).

thf(subset_type,type,
    subset: $i > $i > $o ).

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

thf(sk2_type,type,
    sk2: $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(sk7_type,type,
    sk7: $i ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( set_difference @ A @ ( unordered_pair @ B @ C ) )
        = empty_set )
    <=> ~ ( ( A != empty_set )
          & ( A
           != ( singleton @ B ) )
          & ( A
           != ( singleton @ C ) )
          & ( A
           != ( unordered_pair @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( ( set_difference @ A @ ( unordered_pair @ B @ C ) )
          = empty_set )
      <=> ~ ( ( A != empty_set )
            & ( A
             != ( singleton @ B ) )
            & ( A
             != ( singleton @ C ) )
            & ( A
             != ( unordered_pair @ B @ C ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(10,plain,
    ~ ! [A: $i,B: $i,C: $i] :
        ( ( ( ( set_difference @ A @ ( unordered_pair @ B @ C ) )
            = empty_set )
         => ~ ( ( A != empty_set )
              & ( A
               != ( singleton @ B ) )
              & ( A
               != ( singleton @ C ) )
              & ( A
               != ( unordered_pair @ B @ C ) ) ) )
        & ( ~ ( ( A != empty_set )
              & ( A
               != ( singleton @ B ) )
              & ( A
               != ( singleton @ C ) )
              & ( A
               != ( unordered_pair @ B @ C ) ) )
         => ( ( set_difference @ A @ ( unordered_pair @ B @ C ) )
            = empty_set ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(11,plain,
    ~ ( ! [A: $i,B: $i,C: $i] :
          ( ( ( set_difference @ A @ ( unordered_pair @ B @ C ) )
            = empty_set )
         => ~ ( ( A != empty_set )
              & ( A
               != ( singleton @ B ) )
              & ( A
               != ( singleton @ C ) )
              & ( A
               != ( unordered_pair @ B @ C ) ) ) )
      & ! [A: $i,B: $i,C: $i] :
          ( ~ ( ( A != empty_set )
              & ( A
               != ( singleton @ B ) )
              & ( A
               != ( singleton @ C ) )
              & ( A
               != ( unordered_pair @ B @ C ) ) )
         => ( ( set_difference @ A @ ( unordered_pair @ B @ C ) )
            = empty_set ) ) ),
    inference(miniscope,[status(thm)],[10]) ).

thf(14,plain,
    ( ( ( set_difference @ sk2 @ ( unordered_pair @ sk3 @ sk4 ) )
      = empty_set )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[11]) ).

thf(19,plain,
    ( ( ( set_difference @ sk2 @ ( unordered_pair @ sk3 @ sk4 ) )
      = empty_set )
    | ~ sk1 ),
    inference(lifteq,[status(thm)],[14]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( ( set_difference @ A @ B )
        = empty_set )
    <=> ( subset @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).

thf(53,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( set_difference @ A @ B )
          = empty_set )
       => ( subset @ A @ B ) )
      & ( ( subset @ A @ B )
       => ( ( set_difference @ A @ B )
          = empty_set ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(54,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( set_difference @ A @ B )
          = empty_set )
       => ( subset @ A @ B ) )
    & ! [A: $i,B: $i] :
        ( ( subset @ A @ B )
       => ( ( set_difference @ A @ B )
          = empty_set ) ) ),
    inference(miniscope,[status(thm)],[53]) ).

thf(56,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ A @ B )
       != empty_set )
      | ( subset @ A @ B ) ),
    inference(cnf,[status(esa)],[54]) ).

thf(59,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ A @ B )
       != empty_set )
      | ( subset @ A @ B ) ),
    inference(lifteq,[status(thm)],[56]) ).

thf(323,plain,
    ! [B: $i,A: $i] :
      ( ~ sk1
      | ( subset @ A @ B )
      | ( ( set_difference @ sk2 @ ( unordered_pair @ sk3 @ sk4 ) )
       != ( set_difference @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[19,59]) ).

thf(324,plain,
    ( ~ sk1
    | ( subset @ sk2 @ ( unordered_pair @ sk3 @ sk4 ) ) ),
    inference(pattern_uni,[status(thm)],[323:[bind(A,$thf( sk2 )),bind(B,$thf( unordered_pair @ sk3 @ sk4 ))]]) ).

thf(12,plain,
    ( sk1
    | ( sk5 = empty_set )
    | ( sk5
      = ( singleton @ sk6 ) )
    | ( sk5
      = ( singleton @ sk7 ) )
    | ( sk5
      = ( unordered_pair @ sk6 @ sk7 ) ) ),
    inference(cnf,[status(esa)],[11]) ).

thf(22,plain,
    ( ( sk5 = empty_set )
    | ( ( singleton @ sk6 )
      = sk5 )
    | ( ( singleton @ sk7 )
      = sk5 )
    | ( ( unordered_pair @ sk6 @ sk7 )
      = sk5 )
    | sk1 ),
    inference(lifteq,[status(thm)],[12]) ).

thf(8,axiom,
    ! [A: $i,B: $i] : ( subset @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(51,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(52,plain,
    ! [A: $i] : ( subset @ A @ A ),
    inference(cnf,[status(esa)],[51]) ).

thf(55,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ( ( set_difference @ A @ B )
        = empty_set ) ),
    inference(cnf,[status(esa)],[54]) ).

thf(57,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ A @ B )
        = empty_set )
      | ~ ( subset @ A @ B ) ),
    inference(lifteq,[status(thm)],[55]) ).

thf(58,plain,
    ! [B: $i,A: $i] :
      ( ( ( set_difference @ A @ B )
        = empty_set )
      | ~ ( subset @ A @ B ) ),
    inference(simp,[status(thm)],[57]) ).

thf(16,plain,
    ( sk1
    | ( ( set_difference @ sk5 @ ( unordered_pair @ sk6 @ sk7 ) )
     != empty_set ) ),
    inference(cnf,[status(esa)],[11]) ).

thf(24,plain,
    ( ( ( set_difference @ sk5 @ ( unordered_pair @ sk6 @ sk7 ) )
     != empty_set )
    | sk1 ),
    inference(lifteq,[status(thm)],[16]) ).

thf(260,plain,
    ! [B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | sk1
      | ( ( set_difference @ A @ B )
       != ( set_difference @ sk5 @ ( unordered_pair @ sk6 @ sk7 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[58,24]) ).

thf(261,plain,
    ( ~ ( subset @ sk5 @ ( unordered_pair @ sk6 @ sk7 ) )
    | sk1 ),
    inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( sk5 )),bind(B,$thf( unordered_pair @ sk6 @ sk7 ))]]) ).

thf(268,plain,
    ! [A: $i] :
      ( sk1
      | ( ( subset @ A @ A )
       != ( subset @ sk5 @ ( unordered_pair @ sk6 @ sk7 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[52,261]) ).

thf(290,plain,
    ! [A: $i] :
      ( sk1
      | ( A != sk5 )
      | ( A
       != ( unordered_pair @ sk6 @ sk7 ) ) ),
    inference(simp,[status(thm)],[268]) ).

thf(291,plain,
    ( sk1
    | ( ( unordered_pair @ sk6 @ sk7 )
     != sk5 ) ),
    inference(simp,[status(thm)],[290]) ).

thf(313,plain,
    ( ( sk5 = empty_set )
    | ( ( singleton @ sk6 )
      = sk5 )
    | ( ( singleton @ sk7 )
      = sk5 )
    | sk1
    | ( ( unordered_pair @ sk6 @ sk7 )
     != ( unordered_pair @ sk6 @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[22,291]) ).

thf(314,plain,
    ( ( sk5 = empty_set )
    | ( ( singleton @ sk6 )
      = sk5 )
    | ( ( singleton @ sk7 )
      = sk5 )
    | sk1 ),
    inference(pattern_uni,[status(thm)],[313:[]]) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( subset @ A @ ( unordered_pair @ B @ C ) )
    <=> ~ ( ( A != empty_set )
          & ( A
           != ( singleton @ B ) )
          & ( A
           != ( singleton @ C ) )
          & ( A
           != ( unordered_pair @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).

thf(30,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( subset @ A @ ( unordered_pair @ B @ C ) )
       => ~ ( ( A != empty_set )
            & ( A
             != ( singleton @ B ) )
            & ( A
             != ( singleton @ C ) )
            & ( A
             != ( unordered_pair @ B @ C ) ) ) )
      & ( ~ ( ( A != empty_set )
            & ( A
             != ( singleton @ B ) )
            & ( A
             != ( singleton @ C ) )
            & ( A
             != ( unordered_pair @ B @ C ) ) )
       => ( subset @ A @ ( unordered_pair @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(31,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( ( subset @ A @ ( unordered_pair @ B @ C ) )
       => ~ ( ( A != empty_set )
            & ( A
             != ( singleton @ B ) )
            & ( A
             != ( singleton @ C ) )
            & ( A
             != ( unordered_pair @ B @ C ) ) ) )
    & ! [A: $i,B: $i,C: $i] :
        ( ~ ( ( A != empty_set )
            & ( A
             != ( singleton @ B ) )
            & ( A
             != ( singleton @ C ) )
            & ( A
             != ( unordered_pair @ B @ C ) ) )
       => ( subset @ A @ ( unordered_pair @ B @ C ) ) ) ),
    inference(miniscope,[status(thm)],[30]) ).

thf(32,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( singleton @ C ) )
      | ( subset @ A @ ( unordered_pair @ B @ C ) ) ),
    inference(cnf,[status(esa)],[31]) ).

thf(42,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( singleton @ C ) )
      | ( subset @ A @ ( unordered_pair @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[32]) ).

thf(43,plain,
    ! [B: $i,A: $i] : ( subset @ ( singleton @ B ) @ ( unordered_pair @ A @ B ) ),
    inference(simp,[status(thm)],[42]) ).

thf(274,plain,
    ! [B: $i,A: $i] :
      ( sk1
      | ( ( subset @ ( singleton @ B ) @ ( unordered_pair @ A @ B ) )
       != ( subset @ sk5 @ ( unordered_pair @ sk6 @ sk7 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[43,261]) ).

thf(288,plain,
    ! [B: $i,A: $i] :
      ( sk1
      | ( ( singleton @ B )
       != sk5 )
      | ( ( unordered_pair @ A @ B )
       != ( unordered_pair @ sk6 @ sk7 ) ) ),
    inference(simp,[status(thm)],[274]) ).

thf(540,plain,
    ! [B: $i,A: $i] :
      ( sk1
      | ( ( singleton @ B )
       != sk5 )
      | ( A != sk6 )
      | ( B != sk7 ) ),
    inference(simp,[status(thm)],[288]) ).

thf(568,plain,
    ( sk1
    | ( ( singleton @ sk7 )
     != sk5 ) ),
    inference(simp,[status(thm)],[540]) ).

thf(578,plain,
    ( ( sk5 = empty_set )
    | ( ( singleton @ sk6 )
      = sk5 )
    | sk1
    | ( ( singleton @ sk7 )
     != ( singleton @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[314,568]) ).

thf(579,plain,
    ( ( sk5 = empty_set )
    | ( ( singleton @ sk6 )
      = sk5 )
    | sk1 ),
    inference(pattern_uni,[status(thm)],[578:[]]) ).

thf(36,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( singleton @ B ) )
      | ( subset @ A @ ( unordered_pair @ B @ C ) ) ),
    inference(cnf,[status(esa)],[31]) ).

thf(40,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( singleton @ B ) )
      | ( subset @ A @ ( unordered_pair @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[36]) ).

thf(41,plain,
    ! [B: $i,A: $i] : ( subset @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) ),
    inference(simp,[status(thm)],[40]) ).

thf(269,plain,
    ! [B: $i,A: $i] :
      ( sk1
      | ( ( subset @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
       != ( subset @ sk5 @ ( unordered_pair @ sk6 @ sk7 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[41,261]) ).

thf(285,plain,
    ! [B: $i,A: $i] :
      ( sk1
      | ( ( singleton @ A )
       != sk5 )
      | ( ( unordered_pair @ A @ B )
       != ( unordered_pair @ sk6 @ sk7 ) ) ),
    inference(simp,[status(thm)],[269]) ).

thf(509,plain,
    ! [B: $i,A: $i] :
      ( sk1
      | ( ( singleton @ A )
       != sk5 )
      | ( A != sk6 )
      | ( B != sk7 ) ),
    inference(simp,[status(thm)],[285]) ).

thf(538,plain,
    ( sk1
    | ( ( singleton @ sk6 )
     != sk5 ) ),
    inference(simp,[status(thm)],[509]) ).

thf(584,plain,
    ( ( sk5 = empty_set )
    | sk1
    | ( ( singleton @ sk6 )
     != ( singleton @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[579,538]) ).

thf(585,plain,
    ( ( sk5 = empty_set )
    | sk1 ),
    inference(pattern_uni,[status(thm)],[584:[]]) ).

thf(34,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != empty_set )
      | ( subset @ A @ ( unordered_pair @ B @ C ) ) ),
    inference(cnf,[status(esa)],[31]) ).

thf(44,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != empty_set )
      | ( subset @ A @ ( unordered_pair @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[34]) ).

thf(45,plain,
    ! [B: $i,A: $i] : ( subset @ empty_set @ ( unordered_pair @ A @ B ) ),
    inference(simp,[status(thm)],[44]) ).

thf(270,plain,
    ! [B: $i,A: $i] :
      ( sk1
      | ( ( subset @ empty_set @ ( unordered_pair @ A @ B ) )
       != ( subset @ sk5 @ ( unordered_pair @ sk6 @ sk7 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[45,261]) ).

thf(286,plain,
    ! [B: $i,A: $i] :
      ( sk1
      | ( sk5 != empty_set )
      | ( ( unordered_pair @ A @ B )
       != ( unordered_pair @ sk6 @ sk7 ) ) ),
    inference(simp,[status(thm)],[270]) ).

thf(441,plain,
    ! [B: $i,A: $i] :
      ( sk1
      | ( sk5 != empty_set )
      | ( A != sk6 )
      | ( B != sk7 ) ),
    inference(simp,[status(thm)],[286]) ).

thf(465,plain,
    ( sk1
    | ( sk5 != empty_set ) ),
    inference(simp,[status(thm)],[441]) ).

thf(607,plain,
    ( sk1
    | ( sk5 != sk5 ) ),
    inference(paramod_ordered,[status(thm)],[585,465]) ).

thf(608,plain,
    sk1,
    inference(pattern_uni,[status(thm)],[607:[]]) ).

thf(614,plain,
    ( ~ $true
    | ( subset @ sk2 @ ( unordered_pair @ sk3 @ sk4 ) ) ),
    inference(rewrite,[status(thm)],[324,608]) ).

thf(615,plain,
    subset @ sk2 @ ( unordered_pair @ sk3 @ sk4 ),
    inference(simp,[status(thm)],[614]) ).

thf(33,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset @ A @ ( unordered_pair @ B @ C ) )
      | ( A = empty_set )
      | ( A
        = ( singleton @ B ) )
      | ( A
        = ( singleton @ C ) )
      | ( A
        = ( unordered_pair @ B @ C ) ) ),
    inference(cnf,[status(esa)],[31]) ).

thf(37,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = empty_set )
      | ( A
        = ( singleton @ B ) )
      | ( A
        = ( singleton @ C ) )
      | ( A
        = ( unordered_pair @ B @ C ) )
      | ~ ( subset @ A @ ( unordered_pair @ B @ C ) ) ),
    inference(lifteq,[status(thm)],[33]) ).

thf(631,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = empty_set )
      | ( A
        = ( singleton @ B ) )
      | ( A
        = ( singleton @ C ) )
      | ( A
        = ( unordered_pair @ B @ C ) )
      | ( ( subset @ sk2 @ ( unordered_pair @ sk3 @ sk4 ) )
       != ( subset @ A @ ( unordered_pair @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[615,37]) ).

thf(632,plain,
    ( ( sk2 = empty_set )
    | ( ( singleton @ sk3 )
      = sk2 )
    | ( ( singleton @ sk4 )
      = sk2 )
    | ( ( unordered_pair @ sk3 @ sk4 )
      = sk2 ) ),
    inference(pattern_uni,[status(thm)],[631:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).

thf(17,plain,
    ( ( sk2 != empty_set )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[11]) ).

thf(21,plain,
    ( ( sk2 != empty_set )
    | ~ sk1 ),
    inference(lifteq,[status(thm)],[17]) ).

thf(624,plain,
    ( ( sk2 != empty_set )
    | ~ $true ),
    inference(rewrite,[status(thm)],[21,608]) ).

thf(625,plain,
    sk2 != empty_set,
    inference(simp,[status(thm)],[624]) ).

thf(18,plain,
    ( ( sk2
     != ( singleton @ sk3 ) )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[11]) ).

thf(23,plain,
    ( ( ( singleton @ sk3 )
     != sk2 )
    | ~ sk1 ),
    inference(lifteq,[status(thm)],[18]) ).

thf(616,plain,
    ( ( ( singleton @ sk3 )
     != sk2 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[23,608]) ).

thf(617,plain,
    ( ( singleton @ sk3 )
   != sk2 ),
    inference(simp,[status(thm)],[616]) ).

thf(15,plain,
    ( ( sk2
     != ( singleton @ sk4 ) )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[11]) ).

thf(25,plain,
    ( ( ( singleton @ sk4 )
     != sk2 )
    | ~ sk1 ),
    inference(lifteq,[status(thm)],[15]) ).

thf(620,plain,
    ( ( ( singleton @ sk4 )
     != sk2 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[25,608]) ).

thf(621,plain,
    ( ( singleton @ sk4 )
   != sk2 ),
    inference(simp,[status(thm)],[620]) ).

thf(13,plain,
    ( ( sk2
     != ( unordered_pair @ sk3 @ sk4 ) )
    | ~ sk1 ),
    inference(cnf,[status(esa)],[11]) ).

thf(20,plain,
    ( ( ( unordered_pair @ sk3 @ sk4 )
     != sk2 )
    | ~ sk1 ),
    inference(lifteq,[status(thm)],[13]) ).

thf(622,plain,
    ( ( ( unordered_pair @ sk3 @ sk4 )
     != sk2 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[20,608]) ).

thf(623,plain,
    ( ( unordered_pair @ sk3 @ sk4 )
   != sk2 ),
    inference(simp,[status(thm)],[622]) ).

thf(702,plain,
    $false,
    inference(simplifyReflect,[status(thm)],[632,625,617,621,623]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET931+1 : TPTP v8.2.0. Released v3.2.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n020.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May 20 12:49:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.96/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.20/0.98  % [INFO] 	 Parsing done (105ms). 
% 1.20/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.21  % [INFO] 	 nitpick registered as external prover. 
% 1.67/1.21  % [INFO] 	 Scanning for conjecture ... 
% 1.79/1.28  % [INFO] 	 Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ... 
% 1.79/1.30  % [INFO] 	 Axiom selection finished. Selected 7 axioms (removed 0 axioms). 
% 1.96/1.31  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.96/1.31  % [INFO] 	 Type checking passed. 
% 1.96/1.32  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 8.88/2.80  % [INFO] 	 Killing All external provers ... 
% 8.88/2.81  % Time passed: 2265ms (effective reasoning time: 1809ms)
% 8.88/2.81  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.88/2.81  % Axioms used in derivation (3): t37_xboole_1, reflexivity_r1_tarski, l46_zfmisc_1
% 8.88/2.81  % No. of inferences in proof: 83
% 8.88/2.81  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2265 ms resp. 1809 ms w/o parsing
% 8.88/2.88  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.88/2.88  % [INFO] 	 Killing All external provers ... 
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