TSTP Solution File: SEU736^2 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU736^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n032.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  : 600s
% DateTime : Tue Jul 19 13:59:54 EDT 2022

% Result   : Theorem 0.13s 0.33s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_subset,type,
    subset: $i > $i > $o ).

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

thf(ty_eigen__1,type,
    eigen__1: $i ).

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

thf(ty_setminus,type,
    setminus: $i > $i > $i ).

thf(ty_eigen__3,type,
    eigen__3: $i ).

thf(ty_powerset,type,
    powerset: $i > $i ).

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

thf(sP1,plain,
    ( sP1
  <=> ( in @ eigen__3 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( subset @ eigen__1 @ ( setminus @ eigen__0 @ eigen__2 ) )
     => ( sP1
       => ~ ( in @ eigen__3 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X3: $i] :
            ( ( in @ X3 @ ( powerset @ X1 ) )
           => ! [X4: $i] :
                ( ( in @ X4 @ X1 )
               => ( ( subset @ X2 @ ( setminus @ X1 @ X3 ) )
                 => ( ( in @ X4 @ X3 )
                   => ~ ( in @ X4 @ X2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( in @ eigen__1 @ ( powerset @ eigen__0 ) )
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ( ( subset @ eigen__1 @ ( setminus @ eigen__0 @ X1 ) )
               => ( ( in @ X2 @ X1 )
                 => ~ ( in @ X2 @ eigen__1 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( in @ eigen__3 @ eigen__0 )
     => ( ~ ( in @ eigen__3 @ eigen__1 )
       => ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( ~ ( in @ X1 @ eigen__1 )
         => ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( in @ eigen__2 @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( in @ eigen__3 @ eigen__0 )
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( in @ eigen__1 @ ( powerset @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ~ ( in @ eigen__3 @ eigen__1 )
     => ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP7
     => ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ( ( subset @ eigen__1 @ ( setminus @ eigen__0 @ eigen__2 ) )
           => ( ( in @ X1 @ eigen__2 )
             => ~ ( in @ X1 @ eigen__1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( in @ eigen__3 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ( ( subset @ eigen__1 @ ( setminus @ eigen__0 @ X1 ) )
             => ( ( in @ X2 @ X1 )
               => ~ ( in @ X2 @ eigen__1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ eigen__0 )
               => ( ( subset @ X1 @ ( setminus @ eigen__0 @ X2 ) )
                 => ( ( in @ X3 @ X2 )
                   => ~ ( in @ X3 @ X1 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( sP1
     => ~ sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( in @ eigen__3 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( in @ eigen__3 @ ( setminus @ eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ X1 )
       => ( ~ ( in @ X3 @ X2 )
         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ eigen__0 )
       => ( ~ ( in @ X2 @ X1 )
         => ( in @ X2 @ ( setminus @ eigen__0 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( subset @ eigen__1 @ ( setminus @ eigen__0 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( sP20
         => ( ( in @ X1 @ eigen__2 )
           => ~ ( in @ X1 @ eigen__1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(def_setminusI,definition,
    setminusI = sP18 ).

thf(def_contrasubsetT,definition,
    contrasubsetT = sP3 ).

thf(contraSubsetComplement,conjecture,
    ( sP18
   => ( sP3
     => ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
         => ! [X3: $i] :
              ( ( in @ X3 @ ( powerset @ X1 ) )
             => ( ( subset @ X2 @ ( setminus @ X1 @ X3 ) )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X1 )
                   => ( ( in @ X4 @ X3 )
                     => ( in @ X4 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP18
     => ( sP3
       => ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( powerset @ X1 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ ( powerset @ X1 ) )
               => ( ( subset @ X2 @ ( setminus @ X1 @ X3 ) )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ X1 )
                     => ( ( in @ X4 @ X3 )
                       => ( in @ X4 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[contraSubsetComplement]) ).

thf(h1,assumption,
    sP18,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP3
     => ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
         => ! [X3: $i] :
              ( ( in @ X3 @ ( powerset @ X1 ) )
             => ( ( subset @ X2 @ ( setminus @ X1 @ X3 ) )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X1 )
                   => ( ( in @ X4 @ X3 )
                     => ( in @ X4 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
       => ! [X3: $i] :
            ( ( in @ X3 @ ( powerset @ X1 ) )
           => ( ( subset @ X2 @ ( setminus @ X1 @ X3 ) )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X1 )
                 => ( ( in @ X4 @ X3 )
                   => ( in @ X4 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ ( powerset @ eigen__0 ) )
           => ( ( subset @ X1 @ ( setminus @ eigen__0 @ X2 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ eigen__0 )
                 => ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ ( setminus @ eigen__0 @ X1 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( sP9
     => ! [X1: $i] :
          ( ( in @ X1 @ ( powerset @ eigen__0 ) )
         => ( ( subset @ eigen__1 @ ( setminus @ eigen__0 @ X1 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ eigen__0 )
               => ( ( in @ X2 @ X1 )
                 => ( in @ X2 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__0 ) )
       => ( ( subset @ eigen__1 @ ( setminus @ eigen__0 @ X1 ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ eigen__0 )
             => ( ( in @ X2 @ X1 )
               => ( in @ X2 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ( sP7
     => ( sP20
       => ! [X1: $i] :
            ( ( in @ X1 @ eigen__0 )
           => ( ( in @ X1 @ eigen__2 )
             => ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ ( sP20
     => ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ( ( in @ X1 @ eigen__2 )
           => ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h12,assumption,
    sP20,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( ( in @ X1 @ eigen__2 )
         => ( in @ X1 @ ( setminus @ eigen__0 @ eigen__1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ ( sP16
     => ( sP1
       => sP17 ) ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    sP16,
    introduced(assumption,[]) ).

thf(h16,assumption,
    ~ ( sP1
     => sP17 ),
    introduced(assumption,[]) ).

thf(h17,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ sP17,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP19
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP6
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP5
    | ~ sP16
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP10
    | sP12
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP18
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP21
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP8
    | ~ sP16
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP2
    | ~ sP20
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP15
    | ~ sP1
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP13
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP11
    | ~ sP7
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP3
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP14
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP4
    | ~ sP9
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h17,h18,h15,h16,h14,h12,h13,h10,h11,h9,h7,h8,h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h1,h3,h7,h10,h12,h15,h17,h18]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h12,h13,h10,h11,h9,h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h16,15,h17,h18]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h10,h11,h9,h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,16,h15,h16]) ).

thf(18,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h12,h13,h10,h11,h9,h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,17,h14]) ).

thf(19,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,18,h12,h13]) ).

thf(20,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,19,h10,h11]) ).

thf(21,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,20,h9]) ).

thf(22,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,21,h7,h8]) ).

thf(23,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,22,h6]) ).

thf(24,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h4,23,h5]) ).

thf(25,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,24,h3,h4]) ).

thf(26,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,25,h1,h2]) ).

thf(0,theorem,
    ( sP18
   => ( sP3
     => ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
         => ! [X3: $i] :
              ( ( in @ X3 @ ( powerset @ X1 ) )
             => ( ( subset @ X2 @ ( setminus @ X1 @ X3 ) )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X1 )
                   => ( ( in @ X4 @ X3 )
                     => ( in @ X4 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[26,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.10  % Problem  : SEU736^2 : TPTP v8.1.0. Released v3.7.0.
% 0.01/0.10  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.29  % Computer : n032.cluster.edu
% 0.10/0.29  % Model    : x86_64 x86_64
% 0.10/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29  % Memory   : 8042.1875MB
% 0.10/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29  % CPULimit : 300
% 0.10/0.29  % WCLimit  : 600
% 0.10/0.29  % DateTime : Mon Jun 20 02:19:18 EDT 2022
% 0.10/0.29  % CPUTime  : 
% 0.13/0.33  % SZS status Theorem
% 0.13/0.33  % Mode: mode213
% 0.13/0.33  % Inferences: 8
% 0.13/0.33  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------