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Leo-III---1.8.0.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SEV387^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:37:13 AM UTC 2026

% Result   : Theorem 3.79s 1.72s
% Output   : Refutation 3.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   36 (  13 unt;   0 typ;   3 def)
%            Number of atoms       :  439 (  39 equ;   0 cnn)
%            Maximal formula atoms :  124 (  12 avg)
%            Number of connectives :  974 ( 191   ~; 172   |; 217   &; 394   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   34 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   31 (  16   ^;  12   !;   0   ?;  31   :)
%                                         (   0  !>;   0  ?*;   0  @-;   3  @+)

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

thf(sk1_decl,type,
    sk1: a > $o ).

thf(sk2_decl,type,
    sk2: a > $o ).

thf(sk3_decl,type,
    sk3: a > $o ).

thf(sk4_decl,type,
    sk4: a ).

thf(sk5_decl,type,
    sk5: $o ).

thf(sk1_def,definition,
    ( sk1
    = ( @+[A: a > $o] :
          ~ ! [B: a > $o,C: a > $o] :
              ( ( ^ [D: a] :
                    ( ( A @ D )
                    & ( ( ( B @ D )
                        & ~ ( C @ D ) )
                      | ( ( C @ D )
                        & ~ ( B @ D ) ) ) ) )
              = ( ^ [D: a] :
                    ( ( ( A @ D )
                      & ( B @ D )
                      & ~ ( ( A @ D )
                          & ( C @ D ) ) )
                    | ( ( A @ D )
                      & ( C @ D )
                      & ~ ( ( A @ D )
                          & ( B @ D ) ) ) ) ) ) ) ) ).

thf(sk2_def,definition,
    ( sk2
    = ( @+[A: a > $o] :
          ~ ! [B: a > $o] :
              ( ( ^ [C: a] :
                    ( ( sk1 @ C )
                    & ( ( ( A @ C )
                        & ~ ( B @ C ) )
                      | ( ( B @ C )
                        & ~ ( A @ C ) ) ) ) )
              = ( ^ [C: a] :
                    ( ( ( sk1 @ C )
                      & ( A @ C )
                      & ~ ( ( sk1 @ C )
                          & ( B @ C ) ) )
                    | ( ( sk1 @ C )
                      & ( B @ C )
                      & ~ ( ( sk1 @ C )
                          & ( A @ C ) ) ) ) ) ) ) ) ).

thf(sk3_def,definition,
    ( sk3
    = ( @+[A: a > $o] :
          ( ( ^ [B: a] :
                ( ( sk1 @ B )
                & ( ( ( sk2 @ B )
                    & ~ ( A @ B ) )
                  | ( ( A @ B )
                    & ~ ( sk2 @ B ) ) ) ) )
         != ( ^ [B: a] :
                ( ( ( sk1 @ B )
                  & ( sk2 @ B )
                  & ~ ( ( sk1 @ B )
                      & ( A @ B ) ) )
                | ( ( sk1 @ B )
                  & ( A @ B )
                  & ~ ( ( sk1 @ B )
                      & ( sk2 @ B ) ) ) ) ) ) ) ) ).

thf(1,conjecture,
    ! [A: a > $o,B: a > $o,C: a > $o] :
      ( ( ^ [D: a] :
            ( ( A @ D )
            & ( ( ( B @ D )
                & ~ ( C @ D ) )
              | ( ( C @ D )
                & ~ ( B @ D ) ) ) ) )
      = ( ^ [D: a] :
            ( ( ( A @ D )
              & ( B @ D )
              & ~ ( ( A @ D )
                  & ( C @ D ) ) )
            | ( ( A @ D )
              & ( C @ D )
              & ~ ( ( A @ D )
                  & ( B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM44_pme) ).

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

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

thf(4,plain,
    ( ( ^ [A: a] :
          ( ( sk1 @ A )
          & ( ( ( sk2 @ A )
              & ~ ( sk3 @ A ) )
            | ( ( sk3 @ A )
              & ~ ( sk2 @ A ) ) ) ) )
   != ( ^ [A: a] :
          ( ( ( sk1 @ A )
            & ( sk2 @ A )
            & ~ ( ( sk1 @ A )
                & ( sk3 @ A ) ) )
          | ( ( sk1 @ A )
            & ( sk3 @ A )
            & ~ ( ( sk1 @ A )
                & ( sk2 @ A ) ) ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ^ [A: a] :
          ( ( sk1 @ A )
          & ( ( ( sk2 @ A )
              & ~ ( sk3 @ A ) )
            | ( ( sk3 @ A )
              & ~ ( sk2 @ A ) ) ) ) )
   != ( ^ [A: a] :
          ( ( ( sk1 @ A )
            & ( sk2 @ A )
            & ~ ( ( sk1 @ A )
                & ( sk3 @ A ) ) )
          | ( ( sk1 @ A )
            & ( sk3 @ A )
            & ~ ( ( sk1 @ A )
                & ( sk2 @ A ) ) ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ( sk1 @ sk4 )
      & ( ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
        | ( ( sk3 @ sk4 )
          & ~ ( sk2 @ sk4 ) ) ) )
   != ( ( ( sk1 @ sk4 )
        & ( sk2 @ sk4 )
        & ~ ( ( sk1 @ sk4 )
            & ( sk3 @ sk4 ) ) )
      | ( ( sk1 @ sk4 )
        & ( sk3 @ sk4 )
        & ~ ( ( sk1 @ sk4 )
            & ( sk2 @ sk4 ) ) ) ) ),
    inference(func_ext,[status(esa)],[5]) ).

thf(8,plain,
    ( ( ( sk1 @ sk4 )
      & ( ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
        | ( ( sk3 @ sk4 )
          & ~ ( sk2 @ sk4 ) ) ) )
    | ( ( sk1 @ sk4 )
      & ( sk2 @ sk4 )
      & ~ ( ( sk1 @ sk4 )
          & ( sk3 @ sk4 ) ) )
    | ( ( sk1 @ sk4 )
      & ( sk3 @ sk4 )
      & ~ ( ( sk1 @ sk4 )
          & ( sk2 @ sk4 ) ) ) ),
    inference(bool_ext,[status(thm)],[6]) ).

thf(24,plain,
    ( ( ( sk1 @ sk4 )
      | ( sk1 @ sk4 )
      | sk5 )
    & ( ( sk1 @ sk4 )
      | ( sk2 @ sk4 )
      | sk5 )
    & ( ( sk1 @ sk4 )
      | ~ ( sk1 @ sk4 )
      | ~ ( sk3 @ sk4 )
      | sk5 )
    & ( ( sk1 @ sk4 )
      | ~ sk5
      | ( sk1 @ sk4 ) )
    & ( ( sk1 @ sk4 )
      | ~ sk5
      | ( sk3 @ sk4 ) )
    & ( ( sk1 @ sk4 )
      | ~ sk5
      | ~ ( sk1 @ sk4 )
      | ~ ( sk2 @ sk4 ) )
    & ( ( sk2 @ sk4 )
      | ( sk3 @ sk4 )
      | ( sk1 @ sk4 )
      | sk5 )
    & ( ( sk2 @ sk4 )
      | ( sk3 @ sk4 )
      | ( sk2 @ sk4 )
      | sk5 )
    & ( ( sk2 @ sk4 )
      | ( sk3 @ sk4 )
      | ~ ( sk1 @ sk4 )
      | ~ ( sk3 @ sk4 )
      | sk5 )
    & ( ( sk2 @ sk4 )
      | ( sk3 @ sk4 )
      | ~ sk5
      | ( sk1 @ sk4 ) )
    & ( ( sk2 @ sk4 )
      | ( sk3 @ sk4 )
      | ~ sk5
      | ( sk3 @ sk4 ) )
    & ( ( sk2 @ sk4 )
      | ( sk3 @ sk4 )
      | ~ sk5
      | ~ ( sk1 @ sk4 )
      | ~ ( sk2 @ sk4 ) )
    & ( ( sk2 @ sk4 )
      | ~ ( sk2 @ sk4 )
      | ( sk1 @ sk4 )
      | sk5 )
    & ( ( sk2 @ sk4 )
      | ~ ( sk2 @ sk4 )
      | ( sk2 @ sk4 )
      | sk5 )
    & ( ( sk2 @ sk4 )
      | ~ ( sk2 @ sk4 )
      | ~ ( sk1 @ sk4 )
      | ~ ( sk3 @ sk4 )
      | sk5 )
    & ( ( sk2 @ sk4 )
      | ~ ( sk2 @ sk4 )
      | ~ sk5
      | ( sk1 @ sk4 ) )
    & ( ( sk2 @ sk4 )
      | ~ ( sk2 @ sk4 )
      | ~ sk5
      | ( sk3 @ sk4 ) )
    & ( ( sk2 @ sk4 )
      | ~ ( sk2 @ sk4 )
      | ~ sk5
      | ~ ( sk1 @ sk4 )
      | ~ ( sk2 @ sk4 ) )
    & ( ~ ( sk3 @ sk4 )
      | ( sk3 @ sk4 )
      | ( sk1 @ sk4 )
      | sk5 )
    & ( ~ ( sk3 @ sk4 )
      | ( sk3 @ sk4 )
      | ( sk2 @ sk4 )
      | sk5 )
    & ( ~ ( sk3 @ sk4 )
      | ( sk3 @ sk4 )
      | ~ ( sk1 @ sk4 )
      | ~ ( sk3 @ sk4 )
      | sk5 )
    & ( ~ ( sk3 @ sk4 )
      | ( sk3 @ sk4 )
      | ~ sk5
      | ( sk1 @ sk4 ) )
    & ( ~ ( sk3 @ sk4 )
      | ( sk3 @ sk4 )
      | ~ sk5
      | ( sk3 @ sk4 ) )
    & ( ~ ( sk3 @ sk4 )
      | ( sk3 @ sk4 )
      | ~ sk5
      | ~ ( sk1 @ sk4 )
      | ~ ( sk2 @ sk4 ) )
    & ( ~ ( sk3 @ sk4 )
      | ~ ( sk2 @ sk4 )
      | ( sk1 @ sk4 )
      | sk5 )
    & ( ~ ( sk3 @ sk4 )
      | ~ ( sk2 @ sk4 )
      | ( sk2 @ sk4 )
      | sk5 )
    & ( ~ ( sk3 @ sk4 )
      | ~ ( sk2 @ sk4 )
      | ~ ( sk1 @ sk4 )
      | ~ ( sk3 @ sk4 )
      | sk5 )
    & ( ~ ( sk3 @ sk4 )
      | ~ ( sk2 @ sk4 )
      | ~ sk5
      | ( sk1 @ sk4 ) )
    & ( ~ ( sk3 @ sk4 )
      | ~ ( sk2 @ sk4 )
      | ~ sk5
      | ( sk3 @ sk4 ) )
    & ( ~ ( sk3 @ sk4 )
      | ~ ( sk2 @ sk4 )
      | ~ sk5
      | ~ ( sk1 @ sk4 )
      | ~ ( sk2 @ sk4 ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(44,plain,
    ( ( sk1 @ sk4 )
    | ~ sk5
    | ( sk1 @ sk4 ) ),
    inference(cnfConj,[status(thm)],[24]) ).

thf(60,plain,
    ( ( sk1 @ sk4 )
    | ~ sk5 ),
    inference(simp,[status(thm)],[44]) ).

thf(28,plain,
    ( ( sk1 @ sk4 )
    | ( sk1 @ sk4 )
    | sk5 ),
    inference(cnfConj,[status(thm)],[24]) ).

thf(58,plain,
    ( ( sk1 @ sk4 )
    | sk5 ),
    inference(simp,[status(thm)],[28]) ).

thf(65,plain,
    ( sk5
    | ( ( $true
        & ( ( ( sk2 @ sk4 )
            & ~ ( sk3 @ sk4 ) )
          | ( ( sk3 @ sk4 )
            & ~ ( sk2 @ sk4 ) ) ) )
     != ( ( ( sk1 @ sk4 )
          & ( sk2 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk3 @ sk4 ) ) )
        | ( ( sk1 @ sk4 )
          & ( sk3 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk2 @ sk4 ) ) ) ) )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[58,6]) ).

thf(66,plain,
    ( sk5
    | ( ( ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
        | ( ( sk3 @ sk4 )
          & ~ ( sk2 @ sk4 ) ) )
     != ( ( ( sk1 @ sk4 )
          & ( sk2 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk3 @ sk4 ) ) )
        | ( ( sk1 @ sk4 )
          & ( sk3 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk2 @ sk4 ) ) ) ) )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk4 ) ) ),
    inference(simp,[status(thm)],[65]) ).

thf(67,plain,
    ( sk5
    | ( ( ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
        | ( ( sk3 @ sk4 )
          & ~ ( sk2 @ sk4 ) ) )
     != ( ( ( sk1 @ sk4 )
          & ( sk2 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk3 @ sk4 ) ) )
        | ( ( sk1 @ sk4 )
          & ( sk3 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk2 @ sk4 ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[66:[]]) ).

thf(140,plain,
    ( sk5
    | sk5
    | ( ( ( $true
          & ( sk2 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk3 @ sk4 ) ) )
        | ( ( sk1 @ sk4 )
          & ( sk3 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk2 @ sk4 ) ) ) )
     != ( ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
        | ( ( sk3 @ sk4 )
          & ~ ( sk2 @ sk4 ) ) ) )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[58,67]) ).

thf(141,plain,
    ( sk5
    | ( ( ( ( sk2 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk3 @ sk4 ) ) )
        | ( ( sk1 @ sk4 )
          & ( sk3 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk2 @ sk4 ) ) ) )
     != ( ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
        | ( ( sk3 @ sk4 )
          & ~ ( sk2 @ sk4 ) ) ) )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk4 ) ) ),
    inference(simp,[status(thm)],[140]) ).

thf(142,plain,
    ( sk5
    | ( ( ( ( sk2 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk3 @ sk4 ) ) )
        | ( ( sk1 @ sk4 )
          & ( sk3 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk2 @ sk4 ) ) ) )
     != ( ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
        | ( ( sk3 @ sk4 )
          & ~ ( sk2 @ sk4 ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[141:[]]) ).

thf(210,plain,
    ( sk5
    | sk5
    | ( ( ( ( sk2 @ sk4 )
          & ~ ( $true
              & ( sk3 @ sk4 ) ) )
        | ( ( sk1 @ sk4 )
          & ( sk3 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk2 @ sk4 ) ) ) )
     != ( ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
        | ( ( sk3 @ sk4 )
          & ~ ( sk2 @ sk4 ) ) ) )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[58,142]) ).

thf(211,plain,
    ( sk5
    | ( ( ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
        | ( ( sk1 @ sk4 )
          & ( sk3 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk2 @ sk4 ) ) ) )
     != ( ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
        | ( ( sk3 @ sk4 )
          & ~ ( sk2 @ sk4 ) ) ) )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk4 ) ) ),
    inference(simp,[status(thm)],[210]) ).

thf(212,plain,
    ( sk5
    | ( ( ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
        | ( ( sk1 @ sk4 )
          & ( sk3 @ sk4 )
          & ~ ( ( sk1 @ sk4 )
              & ( sk2 @ sk4 ) ) ) )
     != ( ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
        | ( ( sk3 @ sk4 )
          & ~ ( sk2 @ sk4 ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[211:[]]) ).

thf(258,plain,
    ( sk5
    | ( ( ( sk2 @ sk4 )
        & ~ ( sk3 @ sk4 ) )
     != ( ( sk2 @ sk4 )
        & ~ ( sk3 @ sk4 ) ) )
    | ( ( ( sk1 @ sk4 )
        & ( sk3 @ sk4 )
        & ~ ( ( sk1 @ sk4 )
            & ( sk2 @ sk4 ) ) )
     != ( ( sk3 @ sk4 )
        & ~ ( sk2 @ sk4 ) ) ) ),
    inference(simp,[status(thm)],[212]) ).

thf(279,plain,
    ( sk5
    | ( ( ( sk1 @ sk4 )
        & ( sk3 @ sk4 )
        & ~ ( ( sk1 @ sk4 )
            & ( sk2 @ sk4 ) ) )
     != ( ( sk3 @ sk4 )
        & ~ ( sk2 @ sk4 ) ) ) ),
    inference(simp,[status(thm)],[258]) ).

thf(309,plain,
    ( sk5
    | sk5
    | ( ( $true
        & ( sk3 @ sk4 )
        & ~ ( ( sk1 @ sk4 )
            & ( sk2 @ sk4 ) ) )
     != ( ( sk3 @ sk4 )
        & ~ ( sk2 @ sk4 ) ) )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[58,279]) ).

thf(310,plain,
    ( sk5
    | ( ( ( sk3 @ sk4 )
        & ~ ( ( sk1 @ sk4 )
            & ( sk2 @ sk4 ) ) )
     != ( ( sk3 @ sk4 )
        & ~ ( sk2 @ sk4 ) ) )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk4 ) ) ),
    inference(simp,[status(thm)],[309]) ).

thf(311,plain,
    ( sk5
    | ( ( ( sk3 @ sk4 )
        & ~ ( ( sk1 @ sk4 )
            & ( sk2 @ sk4 ) ) )
     != ( ( sk3 @ sk4 )
        & ~ ( sk2 @ sk4 ) ) ) ),
    inference(pattern_uni,[status(thm)],[310:[]]) ).

thf(801,plain,
    ( sk5
    | sk5
    | ( ( ( sk3 @ sk4 )
        & ~ ( $true
            & ( sk2 @ sk4 ) ) )
     != ( ( sk3 @ sk4 )
        & ~ ( sk2 @ sk4 ) ) )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[58,311]) ).

thf(802,plain,
    ( sk5
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk4 ) ) ),
    inference(simp,[status(thm)],[801]) ).

thf(803,plain,
    sk5,
    inference(pattern_uni,[status(thm)],[802:[]]) ).

thf(825,plain,
    ( ( sk1 @ sk4 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[60,803]) ).

thf(826,plain,
    sk1 @ sk4,
    inference(simp,[status(thm)],[825]) ).

thf(829,plain,
    ( ( $true
      & ( ( ( sk2 @ sk4 )
          & ~ ( sk3 @ sk4 ) )
        | ( ( sk3 @ sk4 )
          & ~ ( sk2 @ sk4 ) ) ) )
   != ( ( $true
        & ( sk2 @ sk4 )
        & ~ ( $true
            & ( sk3 @ sk4 ) ) )
      | ( $true
        & ( sk3 @ sk4 )
        & ~ ( $true
            & ( sk2 @ sk4 ) ) ) ) ),
    inference(rewrite,[status(thm)],[6,826]) ).

thf(830,plain,
    $false,
    inference(simp,[status(thm)],[829]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01  % Problem  : SEV387^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.08/0.12  % Computer : n012.cluster.edu
% 0.08/0.12  % Model    : x86_64 x86_64
% 0.08/0.12  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.12  % Memory   : 8046.5625MB
% 0.08/0.12  % OS       : Linux 6.8.0-71-generic
% 0.08/0.13  % CPULimit : 300
% 0.08/0.13  % WCLimit  : 300
% 0.08/0.13  % DateTime : Tue Sep 29 15:43:18 UTC 2026
% 0.08/0.13  % CPUTime  : 
% 0.08/0.13  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.56/0.44  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 0.72/0.54  % [INFO] 	 Parsing done (99ms). 
% 0.72/0.55  % [INFO] 	 Running in sequential loop mode. 
% 0.98/0.75  % [INFO] 	 eprover registered as external prover. 
% 0.98/0.75  % [INFO] 	 Scanning for conjecture ... 
% 0.98/0.79  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.18/0.81  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.18/0.81  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.18/0.82  % [INFO] 	 Type checking passed. 
% 1.18/0.82  % [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 ... 
% 3.79/1.72  % [INFO] 	 Killing All external provers ... 
% 3.79/1.72  % Time passed: 1507ms (effective reasoning time: 1161ms)
% 3.79/1.72  % 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)>
% 3.79/1.72  % Axioms used in derivation (0): 
% 3.79/1.72  % No. of inferences in proof: 33
% 3.79/1.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1507 ms resp. 1161 ms w/o parsing
% 3.79/1.76  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.79/1.76  % [INFO] 	 Killing All external provers ... 
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