TSTP Solution File: SEU805^2 by Lash---1.13

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%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU805^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n001.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 : Thu Aug 31 17:33:05 EDT 2023

% Result   : Theorem 0.19s 0.44s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   48
% Syntax   : Number of formulae    :   58 (  18 unt;   5 typ;   5 def)
%            Number of atoms       :  150 (  25 equ;   3 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  263 (  70   ~;  16   |;   3   &; 108   @)
%                                         (  16 <=>;  50  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   29 (  26 usr;  26 con; 0-2 aty)
%            Number of variables   :   50 (   8   ^;  37   !;   5   ?;  50   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_emptyset,type,
    emptyset: $i ).

thf(ty_eigen__2,type,
    eigen__2: $i ).

thf(ty_binintersect,type,
    binintersect: $i > $i > $i ).

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

thf(ty_eigen__0,type,
    eigen__0: $i ).

thf(h0,assumption,
    ! [X1: $i > $o,X2: $i] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( in @ X1 @ eigen__0 )
           => ~ ! [X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ~ ( in @ X2 @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( eigen__0 = emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( in @ eigen__2 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( binintersect @ eigen__2 @ eigen__0 )
      = emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( sP2
     => ~ sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i] :
        ~ ( in @ X1 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i] :
        ( ~ ! [X2: $i] :
              ~ ( in @ X2 @ X1 )
       => ~ ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ~ ! [X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ~ ( in @ X3 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ~ sP5
     => ~ ! [X1: $i] :
            ( ( in @ X1 @ eigen__0 )
           => ~ ! [X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ~ ( in @ X2 @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ eigen__2 )
           => ~ ( in @ X2 @ X1 ) )
       => ( ( binintersect @ eigen__2 @ X1 )
          = emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__2 )
       => ~ ( in @ X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP2
     => ~ sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
           => ~ ( in @ X3 @ X2 ) )
       => ( ( binintersect @ X1 @ X2 )
          = emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( ( binintersect @ X1 @ eigen__0 )
         != emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ~ sP1
     => ~ sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ~ ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ~ ( in @ X2 @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i] :
        ( ( X1 != emptyset )
       => ~ ! [X2: $i] :
              ~ ( in @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( sP9
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(def_foundationAx,definition,
    ( foundationAx
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ? [X2: $i] : ( in @ X2 @ X1 )
          @ ? [X2: $i] :
              ( ( in @ X2 @ X1 )
              & ( (~)
                @ ? [X3: $i] :
                    ( ( in @ X3 @ X2 )
                    & ( in @ X3 @ X1 ) ) ) ) ) ) ) ).

thf(def_nonempty,definition,
    ( nonempty
    = ( ^ [X1: $i] : ( (~) @ ( X1 = emptyset ) ) ) ) ).

thf(def_nonemptyE1,definition,
    ( nonemptyE1
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( nonempty @ X1 )
          @ ? [X2: $i] : ( in @ X2 @ X1 ) ) ) ) ).

thf(def_disjointsetsI1,definition,
    ( disjointsetsI1
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( (~)
            @ ? [X3: $i] :
                ( ( in @ X3 @ X1 )
                & ( in @ X3 @ X2 ) ) )
          @ ( ( binintersect @ X1 @ X2 )
            = emptyset ) ) ) ) ).

thf(foundation2,conjecture,
    ( sP6
   => ( sP15
     => ( sP11
       => ! [X1: $i] :
            ( ( X1 != emptyset )
           => ~ ! [X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ( ( binintersect @ X2 @ X1 )
                   != emptyset ) ) ) ) ) ) ).

thf(h1,negated_conjecture,
    ~ ( sP6
     => ( sP15
       => ( sP11
         => ! [X1: $i] :
              ( ( X1 != emptyset )
             => ~ ! [X2: $i] :
                    ( ( in @ X2 @ X1 )
                   => ( ( binintersect @ X2 @ X1 )
                     != emptyset ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[foundation2]) ).

thf(h2,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP15
     => ( sP11
       => ! [X1: $i] :
            ( ( X1 != emptyset )
           => ~ ! [X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ( ( binintersect @ X2 @ X1 )
                   != emptyset ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP15,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( sP11
     => ! [X1: $i] :
          ( ( X1 != emptyset )
         => ~ ! [X2: $i] :
                ( ( in @ X2 @ X1 )
               => ( ( binintersect @ X2 @ X1 )
                 != emptyset ) ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP11,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ! [X1: $i] :
        ( ( X1 != emptyset )
       => ~ ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( ( binintersect @ X2 @ X1 )
               != emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( ~ sP1
     => ~ sP12 ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP12,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP16
    | ~ sP9
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP8
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP4
    | ~ sP2
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP12
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP11
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP10
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP10
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP14
    | ~ sP10 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(9,plain,
    ( ~ sP7
    | sP5
    | ~ sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP13
    | sP1
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP15
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP6
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h9,h10,h8,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h2,h4,h6,h9,h10]) ).

thf(14,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,13,h9,h10]) ).

thf(15,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__0)],[h7,14,h8]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,15,h6,h7]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,16,h4,h5]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,17,h2,h3]) ).

thf(19,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[18,h0]) ).

thf(0,theorem,
    ( sP6
   => ( sP15
     => ( sP11
       => ! [X1: $i] :
            ( ( X1 != emptyset )
           => ~ ! [X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ( ( binintersect @ X2 @ X1 )
                   != emptyset ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[18,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU805^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n001.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug 24 02:04:40 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.44  % SZS status Theorem
% 0.19/0.44  % Mode: cade22grackle2xfee4
% 0.19/0.44  % Steps: 320
% 0.19/0.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------