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Vampire---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire---5.0.1
% Problem  : SEU706^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n010.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 08:30:52 AM UTC 2026

% Result   : Theorem 0.22s 0.27s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   64 (  21 unt;   0 typ;   0 def)
%            Number of atoms       :  532 ( 192 equ;   0 cnn)
%            Maximal formula atoms :    8 (   8 avg)
%            Number of connectives :  469 (  49   ~;  58   |;  48   &; 265   @)
%                                         (   7 <=>;  37  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   31 (  27 usr;  18 con; 0-4 aty)
%                                         (   0  !!;   5  ??;   0 @@+;   0 @@-)
%            Number of variables   :  119 (  12   ^;  87   !;  20   ?; 119   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(func_def_0,type,
    in: $i > $i > $o ).

thf(func_def_2,type,
    setadjoin: $i > $i > $i ).

thf(func_def_3,type,
    setunion: $i > $i ).

thf(func_def_4,type,
    uniqinunit: $o ).

thf(func_def_6,type,
    in__Cong: $o ).

thf(func_def_7,type,
    setadjoin__Cong: $o ).

thf(func_def_8,type,
    setunion__Cong: $o ).

thf(func_def_9,type,
    setunionsingleton: $o ).

thf(func_def_10,type,
    singleton: $i > $o ).

thf(func_def_13,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_14,type,
    vAND: $o > $o > $o ).

thf(func_def_15,type,
    db0: 
      !>[X0: $tType] : X0 ).

thf(func_def_16,type,
    db1: 
      !>[X0: $tType] : X0 ).

thf(func_def_17,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_18,type,
    vLAM: 
      !>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).

thf(func_def_34,type,
    sK15: $i > $i ).

thf(f1,axiom,
    ( uniqinunit
    = ( ! [X0: $i,X1: $i] :
          ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
         => ( X0 = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).

thf(f2,axiom,
    ! [X1: $i,X0: $i] :
      ( ( ( X0 = X1 )
       => ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( in @ X2 @ X0 )
            <=> ( in @ X3 @ X1 ) ) ) )
      = in__Cong ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).

thf(f5,axiom,
    ( setunionsingleton
    = ( ! [X0: $i] :
          ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
          = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).

thf(f6,axiom,
    ( singleton
    = ( ^ [X0: $i] :
        ? [X1: $i] :
          ( ( in @ X1 @ X0 )
          & ( X0
            = ( setadjoin @ X1 @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).

thf(f7,conjecture,
    ( uniqinunit
   => ( in__Cong
     => ( setadjoin__Cong
       => ( setunion__Cong
         => ( setunionsingleton
           => ! [X0: $i] :
                ( ( singleton @ X0 )
               => ! [X1: $i] :
                    ( ( in @ X1 @ X0 )
                   => ( ( setunion @ X0 )
                      = X1 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq) ).

thf(f8,negated_conjecture,
    ~ ( uniqinunit
     => ( in__Cong
       => ( setadjoin__Cong
         => ( setunion__Cong
           => ( setunionsingleton
             => ! [X0: $i] :
                  ( ( singleton @ X0 )
                 => ! [X1: $i] :
                      ( ( in @ X1 @ X0 )
                     => ( ( setunion @ X0 )
                        = X1 ) ) ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f7]) ).

thf(f9,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( X0 = X1 )
       => ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( in @ X2 @ X1 )
            <=> ( in @ X3 @ X0 ) ) ) )
      = in__Cong ),
    inference(rectify,[],[f2]) ).

thf(f10,plain,
    ( ! [X0: $i,X1: $i] :
        ( ( X0 = X1 )
       => ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( in @ X3 @ X0 )
              = ( in @ X2 @ X1 ) ) ) )
  <=> ( in__Cong = $true ) ),
    inference(fool_elimination,[],[f9]) ).

thf(f12,plain,
    ( ! [X0: $i] :
        ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
        = X0 )
  <=> ( setunionsingleton = $true ) ),
    inference(fool_elimination,[],[f5]) ).

thf(f13,plain,
    ( singleton
    = ( ^ [X0: $i] :
        ? [X1: $i] :
          ( ( in @ X1 @ X0 )
          & ( X0
            = ( setadjoin @ X1 @ emptyset ) ) ) ) ),
    inference(rectify,[],[f6]) ).

thf(f14,plain,
    ( singleton
    = ( ^ [Y0: $i] :
          ( ?? @ $i
          @ ^ [Y1: $i] :
              ( ( ( setadjoin @ Y1 @ emptyset )
                = Y0 )
              & ( in @ Y1 @ Y0 ) ) ) ) ),
    inference(fool_elimination,[],[f13]) ).

thf(f15,plain,
    ( uniqinunit
    = ( ! [X0: $i,X1: $i] :
          ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
         => ( X0 = X1 ) ) ) ),
    inference(rectify,[],[f1]) ).

thf(f16,plain,
    ( ! [X0: $i,X1: $i] :
        ( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
          = $true )
       => ( X0 = X1 ) )
  <=> ( uniqinunit = $true ) ),
    inference(fool_elimination,[],[f15]) ).

thf(f17,plain,
    ~ ( uniqinunit
     => ( in__Cong
       => ( setadjoin__Cong
         => ( setunion__Cong
           => ( setunionsingleton
             => ! [X0: $i] :
                  ( ( singleton @ X0 )
                 => ! [X1: $i] :
                      ( ( in @ X1 @ X0 )
                     => ( ( setunion @ X0 )
                        = X1 ) ) ) ) ) ) ) ),
    inference(rectify,[],[f8]) ).

thf(f18,plain,
    ~ ( ( uniqinunit = $true )
     => ( ( in__Cong = $true )
       => ( ( setadjoin__Cong = $true )
         => ( ( setunion__Cong = $true )
           => ( ( setunionsingleton = $true )
             => ! [X0: $i] :
                  ( ( ( singleton @ X0 )
                    = $true )
                 => ! [X1: $i] :
                      ( ( ( in @ X1 @ X0 )
                        = $true )
                     => ( ( setunion @ X0 )
                        = X1 ) ) ) ) ) ) ) ),
    inference(fool_elimination,[],[f17]) ).

thf(f21,plain,
    ( ( uniqinunit = $true )
  <=> ! [X0: $i,X1: $i] :
        ( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
         != $true )
        | ( X0 = X1 ) ) ),
    inference(ennf_transformation,[],[f16]) ).

thf(f23,plain,
    ( ? [X0: $i] :
        ( ( ( singleton @ X0 )
          = $true )
        & ? [X1: $i] :
            ( ( ( setunion @ X0 )
             != X1 )
            & ( ( in @ X1 @ X0 )
              = $true ) ) )
    & ( setunionsingleton = $true )
    & ( setunion__Cong = $true )
    & ( setadjoin__Cong = $true )
    & ( in__Cong = $true )
    & ( uniqinunit = $true ) ),
    inference(ennf_transformation,[],[f18]) ).

thf(f24,plain,
    ( ( setunionsingleton = $true )
    & ( setunion__Cong = $true )
    & ( in__Cong = $true )
    & ( setadjoin__Cong = $true )
    & ? [X0: $i] :
        ( ( ( singleton @ X0 )
          = $true )
        & ? [X1: $i] :
            ( ( ( setunion @ X0 )
             != X1 )
            & ( ( in @ X1 @ X0 )
              = $true ) ) )
    & ( uniqinunit = $true ) ),
    inference(flattening,[],[f23]) ).

thf(f26,plain,
    ( ( in__Cong = $true )
  <=> ! [X1: $i,X0: $i] :
        ( ( X0 != X1 )
        | ! [X2: $i,X3: $i] :
            ( ( X2 != X3 )
            | ( ( in @ X3 @ X0 )
              = ( in @ X2 @ X1 ) ) ) ) ),
    inference(ennf_transformation,[],[f10]) ).

thf(f27,plain,
    ( ( ( in__Cong = $true )
      | ? [X1: $i,X0: $i] :
          ( ( X0 = X1 )
          & ? [X2: $i,X3: $i] :
              ( ( X2 = X3 )
              & ( ( in @ X3 @ X0 )
               != ( in @ X2 @ X1 ) ) ) ) )
    & ( ! [X1: $i,X0: $i] :
          ( ( X0 != X1 )
          | ! [X2: $i,X3: $i] :
              ( ( X2 != X3 )
              | ( ( in @ X3 @ X0 )
                = ( in @ X2 @ X1 ) ) ) )
      | ( in__Cong != $true ) ) ),
    inference(nnf_transformation,[],[f26]) ).

thf(f28,plain,
    ( ( ( in__Cong = $true )
      | ? [X0: $i,X1: $i] :
          ( ( X0 = X1 )
          & ? [X2: $i,X3: $i] :
              ( ( X2 = X3 )
              & ( ( in @ X2 @ X0 )
               != ( in @ X3 @ X1 ) ) ) ) )
    & ( ! [X4: $i,X5: $i] :
          ( ( X4 != X5 )
          | ! [X6: $i,X7: $i] :
              ( ( X6 != X7 )
              | ( ( in @ X7 @ X5 )
                = ( in @ X6 @ X4 ) ) ) )
      | ( in__Cong != $true ) ) ),
    inference(rectify,[],[f27]) ).

thf(f29,plain,
    ( ( ( in__Cong = $true )
      | ( ( sK1 = sK0 )
        & ( sK2 = sK3 )
        & ( ( in @ sK3 @ sK1 )
         != ( in @ sK2 @ sK0 ) ) ) )
    & ( ! [X4: $i,X5: $i] :
          ( ( X4 != X5 )
          | ! [X6: $i,X7: $i] :
              ( ( X6 != X7 )
              | ( ( in @ X7 @ X5 )
                = ( in @ X6 @ X4 ) ) ) )
      | ( in__Cong != $true ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f28]) ).

thf(f33,plain,
    ( ( setunionsingleton = $true )
    & ( setunion__Cong = $true )
    & ( in__Cong = $true )
    & ( setadjoin__Cong = $true )
    & ( $true
      = ( singleton @ sK6 ) )
    & ( ( setunion @ sK6 )
     != sK7 )
    & ( ( in @ sK7 @ sK6 )
      = $true )
    & ( uniqinunit = $true ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f24]) ).

thf(f34,plain,
    ( ( ! [X0: $i] :
          ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
          = X0 )
      | ( setunionsingleton != $true ) )
    & ( ( setunionsingleton = $true )
      | ? [X0: $i] :
          ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
         != X0 ) ) ),
    inference(nnf_transformation,[],[f12]) ).

thf(f35,plain,
    ( ( ! [X0: $i] :
          ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
          = X0 )
      | ( setunionsingleton != $true ) )
    & ( ( setunionsingleton = $true )
      | ? [X1: $i] :
          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
         != X1 ) ) ),
    inference(rectify,[],[f34]) ).

thf(f36,plain,
    ( ( ! [X0: $i] :
          ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
          = X0 )
      | ( setunionsingleton != $true ) )
    & ( ( setunionsingleton = $true )
      | ( sK8
       != ( setunion @ ( setadjoin @ sK8 @ emptyset ) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8)],[f35]) ).

thf(f40,plain,
    ( ( ( uniqinunit = $true )
      | ? [X0: $i,X1: $i] :
          ( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
            = $true )
          & ( X0 != X1 ) ) )
    & ( ! [X0: $i,X1: $i] :
          ( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
           != $true )
          | ( X0 = X1 ) )
      | ( uniqinunit != $true ) ) ),
    inference(nnf_transformation,[],[f21]) ).

thf(f41,plain,
    ( ( ( uniqinunit = $true )
      | ? [X0: $i,X1: $i] :
          ( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
            = $true )
          & ( X0 != X1 ) ) )
    & ( ! [X2: $i,X3: $i] :
          ( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
           != $true )
          | ( X2 = X3 ) )
      | ( uniqinunit != $true ) ) ),
    inference(rectify,[],[f40]) ).

thf(f42,plain,
    ( ( ( uniqinunit = $true )
      | ( ( $true
          = ( in @ sK13 @ ( setadjoin @ sK14 @ emptyset ) ) )
        & ( sK13 != sK14 ) ) )
    & ( ! [X2: $i,X3: $i] :
          ( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
           != $true )
          | ( X2 = X3 ) )
      | ( uniqinunit != $true ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f41]) ).

thf(f43,plain,
    ! [X6: $i,X7: $i,X4: $i,X5: $i] :
      ( ( X4 != X5 )
      | ( X6 != X7 )
      | ( ( in @ X7 @ X5 )
        = ( in @ X6 @ X4 ) )
      | ( in__Cong != $true ) ),
    inference(cnf_transformation,[],[f29]) ).

thf(f47,plain,
    ( singleton
    = ( ^ [Y0: $i] :
          ( ?? @ $i
          @ ^ [Y1: $i] :
              ( ( ( setadjoin @ Y1 @ emptyset )
                = Y0 )
              & ( in @ Y1 @ Y0 ) ) ) ) ),
    inference(cnf_transformation,[],[f14]) ).

thf(f51,plain,
    uniqinunit = $true,
    inference(cnf_transformation,[],[f33]) ).

thf(f52,plain,
    ( ( in @ sK7 @ sK6 )
    = $true ),
    inference(cnf_transformation,[],[f33]) ).

thf(f53,plain,
    ( ( setunion @ sK6 )
   != sK7 ),
    inference(cnf_transformation,[],[f33]) ).

thf(f54,plain,
    ( $true
    = ( singleton @ sK6 ) ),
    inference(cnf_transformation,[],[f33]) ).

thf(f56,plain,
    in__Cong = $true,
    inference(cnf_transformation,[],[f33]) ).

thf(f58,plain,
    setunionsingleton = $true,
    inference(cnf_transformation,[],[f33]) ).

thf(f60,plain,
    ! [X0: $i] :
      ( ( setunionsingleton != $true )
      | ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
        = X0 ) ),
    inference(cnf_transformation,[],[f36]) ).

thf(f65,plain,
    ! [X2: $i,X3: $i] :
      ( ( uniqinunit != $true )
      | ( X2 = X3 )
      | ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
       != $true ) ),
    inference(cnf_transformation,[],[f42]) ).

thf(f69,plain,
    ! [X6: $i,X7: $i,X5: $i] :
      ( ( X6 != X7 )
      | ( ( in @ X7 @ X5 )
        = ( in @ X6 @ X5 ) )
      | ( in__Cong != $true ) ),
    inference(equality_resolution,[],[f43]) ).

thf(f70,plain,
    ! [X7: $i,X5: $i] :
      ( ( ( in @ X7 @ X5 )
        = ( in @ X7 @ X5 ) )
      | ( in__Cong != $true ) ),
    inference(equality_resolution,[],[f69]) ).

thf(f74,plain,
    ! [X7: $i,X5: $i] :
      ( ( ( in @ X7 @ X5 )
        = $true )
      | ( $false
        = ( in @ X7 @ X5 ) )
      | ( in__Cong != $true ) ),
    inference(iff_proxy_clausification,[],[f70]) ).

thf(f83,plain,
    ! [X0: $i] :
      ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
      = X0 ),
    inference(forward_subsumption_resolution,[],[f60,f58]) ).

thf(f84,plain,
    ! [X2: $i,X3: $i] :
      ( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
       != $true )
      | ( X2 = X3 ) ),
    inference(forward_subsumption_resolution,[],[f65,f51]) ).

thf(f85,plain,
    ! [X7: $i,X5: $i] :
      ( ( ( in @ X7 @ X5 )
        = $true )
      | ( $false
        = ( in @ X7 @ X5 ) ) ),
    inference(forward_subsumption_resolution,[],[f74,f56]) ).

thf(f86,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
        = $false )
      | ( X0 = X1 )
      | ( $true != $true ) ),
    inference(superposition,[],[f84,f85]) ).

thf(f88,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
        = $false )
      | ( X0 = X1 ) ),
    inference(trivial_inequality_removal,[],[f86]) ).

thf(f93,plain,
    ! [X1: $i] :
      ( ( ^ [Y0: $i] :
            ( ?? @ $i
            @ ^ [Y1: $i] :
                ( ( ( setadjoin @ Y1 @ emptyset )
                  = Y0 )
                & ( in @ Y1 @ Y0 ) ) )
        @ X1 )
      = ( singleton @ X1 ) ),
    inference(argument_congruence,[],[f47]) ).

thf(f94,plain,
    ! [X1: $i] :
      ( ( $false
        = ( singleton @ X1 ) )
      | ( ( ^ [Y0: $i] :
              ( ?? @ $i
              @ ^ [Y1: $i] :
                  ( ( ( setadjoin @ Y1 @ emptyset )
                    = Y0 )
                  & ( in @ Y1 @ Y0 ) ) )
          @ X1 )
        = $true ) ),
    inference(iff_proxy_clausification,[],[f93]) ).

thf(f101,plain,
    ! [X1: $i] :
      ( ( ( ?? @ $i
          @ ^ [Y0: $i] :
              ( ( ( setadjoin @ Y0 @ emptyset )
                = X1 )
              & ( in @ Y0 @ X1 ) ) )
        = $true )
      | ( $false
        = ( singleton @ X1 ) ) ),
    inference(beta-eta_normalization,[],[f94]) ).

thf(f102,plain,
    ! [X1: $i] :
      ( ( ( ^ [Y0: $i] :
              ( ( ( setadjoin @ Y0 @ emptyset )
                = X1 )
              & ( in @ Y0 @ X1 ) )
          @ ( sK15 @ X1 ) )
        = $true )
      | ( $false
        = ( singleton @ X1 ) ) ),
    inference(sigma_proxy_clausification,[],[f101]) ).

thf(f103,plain,
    ! [X1: $i] :
      ( ( $false
        = ( singleton @ X1 ) )
      | ( $true
        = ( ( ( setadjoin @ ( sK15 @ X1 ) @ emptyset )
            = X1 )
          & ( in @ ( sK15 @ X1 ) @ X1 ) ) ) ),
    inference(beta-eta_normalization,[],[f102]) ).

thf(f105,plain,
    ! [X1: $i] :
      ( ( ( ( setadjoin @ ( sK15 @ X1 ) @ emptyset )
          = X1 )
        = $true )
      | ( $false
        = ( singleton @ X1 ) ) ),
    inference(and_proxy_clausification,[],[f103]) ).

thf(f106,plain,
    ! [X1: $i] :
      ( ( ( setadjoin @ ( sK15 @ X1 ) @ emptyset )
        = X1 )
      | ( $false
        = ( singleton @ X1 ) ) ),
    inference(equality_proxy_clausification,[],[f105]) ).

thf(f115,plain,
    ! [X0: $i] :
      ( ( ( singleton @ X0 )
        = $false )
      | ( ( setunion @ X0 )
        = ( sK15 @ X0 ) ) ),
    inference(superposition,[],[f83,f106]) ).

thf(f116,plain,
    ( ( ( setunion @ sK6 )
      = ( sK15 @ sK6 ) )
    | ( $false = $true ) ),
    inference(superposition,[],[f115,f54]) ).

thf(f118,plain,
    ( ( setunion @ sK6 )
    = ( sK15 @ sK6 ) ),
    inference(trivial_inequality_removal,[],[f116]) ).

thf(f120,plain,
    ( ( ( setadjoin @ ( setunion @ sK6 ) @ emptyset )
      = sK6 )
    | ( $false
      = ( singleton @ sK6 ) ) ),
    inference(superposition,[],[f106,f118]) ).

thf(f122,plain,
    ( ( ( setadjoin @ ( setunion @ sK6 ) @ emptyset )
      = sK6 )
    | ( $false = $true ) ),
    inference(forward_demodulation,[],[f120,f54]) ).

thf(f123,plain,
    ( ( setadjoin @ ( setunion @ sK6 ) @ emptyset )
    = sK6 ),
    inference(trivial_inequality_removal,[],[f122]) ).

thf(f127,plain,
    ! [X0: $i] :
      ( ( ( in @ X0 @ sK6 )
        = $false )
      | ( ( setunion @ sK6 )
        = X0 ) ),
    inference(superposition,[],[f88,f123]) ).

thf(f129,plain,
    ( ( ( setunion @ sK6 )
      = sK7 )
    | ( $false = $true ) ),
    inference(superposition,[],[f127,f52]) ).

thf(f135,plain,
    ( ( setunion @ sK6 )
    = sK7 ),
    inference(trivial_inequality_removal,[],[f129]) ).

thf(f139,plain,
    $false,
    inference(forward_subsumption_resolution,[],[f135,f53]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU706^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19  % Computer : n010.cluster.edu
% 0.09/0.19  % Model    : x86_64 x86_64
% 0.09/0.19  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19  % Memory   : 8046.5625MB
% 0.09/0.19  % OS       : Linux 6.8.0-71-generic
% 0.09/0.19  % CPULimit : 300
% 0.09/0.19  % WCLimit  : 300
% 0.09/0.19  % DateTime : Tue Sep 29 14:13:18 UTC 2026
% 0.09/0.19  % CPUTime  : 
% 0.09/0.19  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22  Running higher-order theorem proving
% 0.09/0.24  Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.27  % (2917220)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27  % (2917229)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3583180452:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.27  % (2917229) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2917220-2917229"...
% 0.22/0.27  % (2917229)...printing done.
% 0.22/0.27  % (2917229)Refutation found. Thanks to Tanya!
% 0.22/0.27  % SZS status Theorem for theBenchmark
% 0.22/0.27  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28  % (2917229)------------------------------
% 0.22/0.28  % (2917229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28  % (2917229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28  % (2917229)CaDiCaL version: 2.1.3
% 0.22/0.28  % (2917229)Termination reason: Refutation
% 0.22/0.28  % (2917229)Time elapsed: 0.004 s
% 0.22/0.28  % (2917229)Peak memory usage: 12 MB
% 0.22/0.28  % (2917229)Instructions burned: 10 (million)
% 0.22/0.28  % (2917220)Success in time 0.029 s
% 0.22/0.28  % Vampire exiting
%------------------------------------------------------------------------------