TSTP Solution File: SET580^3 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SET580^3 : TPTP v8.1.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n008.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 04:54:03 EDT 2022

% Result   : Theorem 0.13s 0.36s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
    eigen__2: $i ).

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

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

thf(sP1,plain,
    ( sP1
  <=> ( eigen__0 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( eigen__1 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(def_in,definition,
    ( in
    = ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).

thf(def_is_a,definition,
    ( is_a
    = ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).

thf(def_emptyset,definition,
    ( emptyset
    = ( ^ [X1: $i] : $false ) ) ).

thf(def_unord_pair,definition,
    ( unord_pair
    = ( ^ [X1: $i,X2: $i,X3: $i] :
          ( ( X3 != X1 )
         => ( X3 = X2 ) ) ) ) ).

thf(def_singleton,definition,
    ( singleton
    = ( ^ [X1: $i,X2: $i] : ( X2 = X1 ) ) ) ).

thf(def_union,definition,
    ( union
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ~ ( X1 @ X3 )
         => ( X2 @ X3 ) ) ) ) ).

thf(def_excl_union,definition,
    ( excl_union
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ( ( X1 @ X3 )
           => ( X2 @ X3 ) )
         => ~ ( ~ ( X1 @ X3 )
             => ~ ( X2 @ X3 ) ) ) ) ) ).

thf(def_intersection,definition,
    ( intersection
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ~ ( ( X1 @ X3 )
           => ~ ( X2 @ X3 ) ) ) ) ).

thf(def_setminus,definition,
    ( setminus
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ~ ( ( X1 @ X3 )
           => ( X2 @ X3 ) ) ) ) ).

thf(def_complement,definition,
    ( complement
    = ( ^ [X1: $i > $o,X2: $i] :
          ~ ( X1 @ X2 ) ) ) ).

thf(def_disjoint,definition,
    ( disjoint
    = ( ^ [X1: $i > $o,X2: $i > $o] :
          ( ( intersection @ X1 @ X2 )
          = emptyset ) ) ) ).

thf(def_subset,definition,
    ( subset
    = ( ^ [X1: $i > $o,X2: $i > $o] :
        ! [X3: $i] :
          ( ( X1 @ X3 )
         => ( X2 @ X3 ) ) ) ) ).

thf(def_meets,definition,
    ( meets
    = ( ^ [X1: $i > $o,X2: $i > $o] :
          ~ ! [X3: $i] :
              ( ( X1 @ X3 )
             => ~ ( X2 @ X3 ) ) ) ) ).

thf(def_misses,definition,
    ( misses
    = ( ^ [X1: $i > $o,X2: $i > $o] :
        ! [X3: $i] :
          ( ( X1 @ X3 )
         => ~ ( X2 @ X3 ) ) ) ) ).

thf(thm,conjecture,
    ! [X1: $i > $o,X2: $i > $o,X3: $i] :
      ( ( ( ( X1 @ X3 )
         => ( X2 @ X3 ) )
       => ~ ( ~ ( X1 @ X3 )
           => ~ ( X2 @ X3 ) ) )
      = ( ( X1 @ X3 )
        = ( ~ ( X2 @ X3 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i > $o,X2: $i > $o,X3: $i] :
        ( ( ( ( X1 @ X3 )
           => ( X2 @ X3 ) )
         => ~ ( ~ ( X1 @ X3 )
             => ~ ( X2 @ X3 ) ) )
        = ( ( X1 @ X3 )
          = ( ~ ( X2 @ X3 ) ) ) ),
    inference(assume_negation,[status(cth)],[thm]) ).

thf(h1,assumption,
    ~ ! [X1: $i > $o,X2: $i] :
        ( ( ( ( eigen__0 @ X2 )
           => ( X1 @ X2 ) )
         => ~ ( ~ ( eigen__0 @ X2 )
             => ~ ( X1 @ X2 ) ) )
        = ( ( eigen__0 @ X2 )
          = ( ~ ( X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: $i] :
        ( ( ( ( eigen__0 @ X1 )
           => ( eigen__1 @ X1 ) )
         => ~ ( ~ ( eigen__0 @ X1 )
             => ~ ( eigen__1 @ X1 ) ) )
        = ( ( eigen__0 @ X1 )
          = ( ~ ( eigen__1 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ( ( sP1
     => sP2 )
   => ~ ( ~ sP1
       => ~ sP2 ) )
 != ( sP1
    = ( ~ sP2 ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ( ( sP1
     => sP2 )
   => ~ ( ~ sP1
       => ~ sP2 ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ( sP1
    = ( ~ sP2 ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( ( sP1
       => sP2 )
     => ~ ( ~ sP1
         => ~ sP2 ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP1
 != ( ~ sP2 ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( sP1
     => sP2 ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ( ~ sP1
     => ~ sP2 ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h13,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h10,h11,h10,h11,h8,h4,h5,h3,h2,h1,h0])],[h11,h11]) ).

thf(2,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h12,h13,h10,h11,h8,h4,h5,h3,h2,h1,h0])],[h10,h12]) ).

thf(3,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h10,h11,h8,h4,h5,h3,h2,h1,h0]),tab_be(discharge,[h10,h11]),tab_be(discharge,[h12,h13])],[h5,1,2,h10,h11,h12,h13]) ).

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,3,h10,h11]) ).

thf(5,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h10,h11,h12,h13,h9,h4,h5,h3,h2,h1,h0])],[h10,h12]) ).

thf(6,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h12,h13,h12,h13,h9,h4,h5,h3,h2,h1,h0])],[h13,h13]) ).

thf(7,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h12,h13,h9,h4,h5,h3,h2,h1,h0]),tab_be(discharge,[h10,h11]),tab_be(discharge,[h12,h13])],[h5,5,6,h10,h11,h12,h13]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h9,7,h12,h13]) ).

thf(9,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_imp(discharge,[h8]),tab_imp(discharge,[h9])],[h4,4,8,h8,h9]) ).

thf(h14,assumption,
    ( sP1
   => sP2 ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    ( ~ sP1
   => ~ sP2 ),
    introduced(assumption,[]) ).

thf(10,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h10,h11,h10,h12,h14,h15,h6,h7,h3,h2,h1,h0])],[h10,h12]) ).

thf(11,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h12,h13,h10,h12,h14,h15,h6,h7,h3,h2,h1,h0])],[h10,h12]) ).

thf(12,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h10,h12,h14,h15,h6,h7,h3,h2,h1,h0]),tab_bq(discharge,[h10,h11]),tab_bq(discharge,[h12,h13])],[h7,10,11,h10,h11,h12,h13]) ).

thf(13,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h10,h11,h11,h12,h14,h15,h6,h7,h3,h2,h1,h0])],[h10,h12]) ).

thf(14,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h12,h13,h11,h12,h14,h15,h6,h7,h3,h2,h1,h0])],[h13,h11]) ).

thf(15,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h11,h12,h14,h15,h6,h7,h3,h2,h1,h0]),tab_bq(discharge,[h10,h11]),tab_bq(discharge,[h12,h13])],[h7,13,14,h10,h11,h12,h13]) ).

thf(16,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h12,h14,h15,h6,h7,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h15,12,15,h10,h11]) ).

thf(17,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h10,h11,h10,h13,h14,h15,h6,h7,h3,h2,h1,h0])],[h13,h11]) ).

thf(18,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h12,h13,h10,h13,h14,h15,h6,h7,h3,h2,h1,h0])],[h10,h12]) ).

thf(19,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h10,h13,h14,h15,h6,h7,h3,h2,h1,h0]),tab_bq(discharge,[h10,h11]),tab_bq(discharge,[h12,h13])],[h7,17,18,h10,h11,h12,h13]) ).

thf(20,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h10,h11,h11,h13,h14,h15,h6,h7,h3,h2,h1,h0])],[h13,h11]) ).

thf(21,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h12,h13,h11,h13,h14,h15,h6,h7,h3,h2,h1,h0])],[h13,h11]) ).

thf(22,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h11,h13,h14,h15,h6,h7,h3,h2,h1,h0]),tab_bq(discharge,[h10,h11]),tab_bq(discharge,[h12,h13])],[h7,20,21,h10,h11,h12,h13]) ).

thf(23,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h13,h14,h15,h6,h7,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[h15,19,22,h10,h11]) ).

thf(24,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h14,h15,h6,h7,h3,h2,h1,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h13])],[h14,16,23,h12,h13]) ).

thf(25,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h7,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h6,24,h14,h15]) ).

thf(26,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h3,h2,h1,h0]),tab_be(discharge,[h4,h5]),tab_be(discharge,[h6,h7])],[h3,9,25,h4,h5,h6,h7]) ).

thf(27,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,26,h3]) ).

thf(28,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,27,h2]) ).

thf(29,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,28,h1]) ).

thf(0,theorem,
    ! [X1: $i > $o,X2: $i > $o,X3: $i] :
      ( ( ( ( X1 @ X3 )
         => ( X2 @ X3 ) )
       => ~ ( ~ ( X1 @ X3 )
           => ~ ( X2 @ X3 ) ) )
      = ( ( X1 @ X3 )
        = ( ~ ( X2 @ X3 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[29,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET580^3 : TPTP v8.1.0. Released v3.6.0.
% 0.07/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jul 10 03:42:38 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.36  % SZS status Theorem
% 0.13/0.36  % Mode: mode213
% 0.13/0.36  % Inferences: 0
% 0.13/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------