TSTP Solution File: SEV258^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV258^5 : TPTP v8.1.0. Released v4.0.0.
% 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 18:05:36 EDT 2022

% Result   : Theorem 0.13s 0.37s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_eigen__6,type,
    eigen__6: a > $o ).

thf(ty_eigen__2,type,
    eigen__2: ( a > $o ) > $o ).

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

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

thf(ty_eigen__4,type,
    eigen__4: a > $o ).

thf(ty_eigen__5,type,
    eigen__5: a > $o ).

thf(ty_eigen__3,type,
    eigen__3: a > $o ).

thf(cDISCRETE_TOPOLOGY_pme,conjecture,
    ~ ( ~ ( ~ ( ! [X1: a > $o] :
                  ( ( X1
                    = ( ^ [X2: a] : $false ) )
                 => ~ $false )
             => ~ ! [X1: a > $o] :
                    ( ( X1
                      = ( ^ [X2: a] : ~ $false ) )
                   => ~ $false ) )
         => ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
                ( ~ ( ! [X3: a > $o] :
                        ( ( X1 @ X3 )
                       => ~ $false )
                   => ( X2
                     != ( ^ [X3: a] :
                            ~ ! [X4: a > $o] :
                                ( ( X1 @ X4 )
                               => ~ ( X4 @ X3 ) ) ) ) )
               => ~ $false ) )
     => ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
            ( ~ ( ~ $false
               => ( X3
                 != ( ^ [X4: a] :
                        ~ ( ( X1 @ X4 )
                         => ~ ( X2 @ X4 ) ) ) ) )
           => ~ $false ) ) ).

thf(h0,negated_conjecture,
    ( ~ ( ~ ( ! [X1: a > $o] :
                ( ( X1
                  = ( ^ [X2: a] : $false ) )
               => ~ $false )
           => ~ ! [X1: a > $o] :
                  ( ( X1
                    = ( ^ [X2: a] : ~ $false ) )
                 => ~ $false ) )
       => ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
              ( ~ ( ! [X3: a > $o] :
                      ( ( X1 @ X3 )
                     => ~ $false )
                 => ( X2
                   != ( ^ [X3: a] :
                          ~ ! [X4: a > $o] :
                              ( ( X1 @ X4 )
                             => ~ ( X4 @ X3 ) ) ) ) )
             => ~ $false ) )
   => ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
          ( ~ ( ~ $false
             => ( X3
               != ( ^ [X4: a] :
                      ~ ( ( X1 @ X4 )
                       => ~ ( X2 @ X4 ) ) ) ) )
         => ~ $false ) ),
    inference(assume_negation,[status(cth)],[cDISCRETE_TOPOLOGY_pme]) ).

thf(h1,assumption,
    ( ~ ( ! [X1: a > $o] :
            ( ( X1
              = ( ^ [X2: a] : $false ) )
           => ~ $false )
       => ~ ! [X1: a > $o] :
              ( ( X1
                = ( ^ [X2: a] : ~ $false ) )
             => ~ $false ) )
   => ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
          ( ~ ( ! [X3: a > $o] :
                  ( ( X1 @ X3 )
                 => ~ $false )
             => ( X2
               != ( ^ [X3: a] :
                      ~ ! [X4: a > $o] :
                          ( ( X1 @ X4 )
                         => ~ ( X4 @ X3 ) ) ) ) )
         => ~ $false ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
        ( ~ ( ~ $false
           => ( X3
             != ( ^ [X4: a] :
                    ~ ( ( X1 @ X4 )
                     => ~ ( X2 @ X4 ) ) ) ) )
       => ~ $false ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ( ! [X1: a > $o] :
        ( ( X1
          = ( ^ [X2: a] : $false ) )
       => ~ $false )
   => ~ ! [X1: a > $o] :
          ( ( X1
            = ( ^ [X2: a] : ~ $false ) )
         => ~ $false ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
        ( ~ ( ! [X3: a > $o] :
                ( ( X1 @ X3 )
               => ~ $false )
           => ( X2
             != ( ^ [X3: a] :
                    ~ ! [X4: a > $o] :
                        ( ( X1 @ X4 )
                       => ~ ( X4 @ X3 ) ) ) ) )
       => ~ $false ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ! [X1: a > $o] :
        ( ( X1
          = ( ^ [X2: a] : $false ) )
       => ~ $false ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ! [X1: a > $o] :
        ( ( X1
          = ( ^ [X2: a] : ~ $false ) )
       => ~ $false ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ( ( eigen__0
        = ( ^ [X1: a] : $false ) )
     => ~ $false ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ( eigen__0
    = ( ^ [X1: a] : $false ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    $false,
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_false,[status(thm),assumptions([h8,h9,h7,h5,h3,h1,h0])],[h9]) ).

thf(2,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h5,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,1,h8,h9]) ).

thf(3,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h5,2,h7]) ).

thf(h10,assumption,
    ~ ( ( eigen__1
        = ( ^ [X1: a] : ~ $false ) )
     => ~ $false ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    ( eigen__1
    = ( ^ [X1: a] : ~ $false ) ),
    introduced(assumption,[]) ).

thf(4,plain,
    $false,
    inference(tab_false,[status(thm),assumptions([h11,h9,h10,h6,h3,h1,h0])],[h9]) ).

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h10,h6,h3,h1,h0]),tab_negimp(discharge,[h11,h9])],[h10,4,h11,h9]) ).

thf(6,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h6,5,h10]) ).

thf(7,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h3,3,6,h5,h6]) ).

thf(h12,assumption,
    ~ ! [X1: a > $o] :
        ( ~ ( ! [X2: a > $o] :
                ( ( eigen__2 @ X2 )
               => ~ $false )
           => ( X1
             != ( ^ [X2: a] :
                    ~ ! [X3: a > $o] :
                        ( ( eigen__2 @ X3 )
                       => ~ ( X3 @ X2 ) ) ) ) )
       => ~ $false ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ( ~ ( ! [X1: a > $o] :
              ( ( eigen__2 @ X1 )
             => ~ $false )
         => ( eigen__3
           != ( ^ [X1: a] :
                  ~ ! [X2: a > $o] :
                      ( ( eigen__2 @ X2 )
                     => ~ ( X2 @ X1 ) ) ) ) )
     => ~ $false ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ ( ! [X1: a > $o] :
          ( ( eigen__2 @ X1 )
         => ~ $false )
     => ( eigen__3
       != ( ^ [X1: a] :
              ~ ! [X2: a > $o] :
                  ( ( eigen__2 @ X2 )
                 => ~ ( X2 @ X1 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    ! [X1: a > $o] :
      ( ( eigen__2 @ X1 )
     => ~ $false ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    ( eigen__3
    = ( ^ [X1: a] :
          ~ ! [X2: a > $o] :
              ( ( eigen__2 @ X2 )
             => ~ ( X2 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(8,plain,
    $false,
    inference(tab_false,[status(thm),assumptions([h15,h16,h14,h9,h13,h12,h4,h1,h0])],[h9]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h9,h13,h12,h4,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,8,h15,h16]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h13,h12,h4,h1,h0]),tab_negimp(discharge,[h14,h9])],[h13,9,h14,h9]) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h12,h4,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__3)],[h12,10,h13]) ).

thf(12,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__2)],[h4,11,h12]) ).

thf(13,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h1,7,12,h3,h4]) ).

thf(h17,assumption,
    ~ ! [X1: a > $o,X2: a > $o] :
        ( ~ ( ~ $false
           => ( X2
             != ( ^ [X3: a] :
                    ~ ( ( eigen__4 @ X3 )
                     => ~ ( X1 @ X3 ) ) ) ) )
       => ~ $false ),
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ ! [X1: a > $o] :
        ( ~ ( ~ $false
           => ( X1
             != ( ^ [X2: a] :
                    ~ ( ( eigen__4 @ X2 )
                     => ~ ( eigen__5 @ X2 ) ) ) ) )
       => ~ $false ),
    introduced(assumption,[]) ).

thf(h19,assumption,
    ~ ( ~ ( ~ $false
         => ( eigen__6
           != ( ^ [X1: a] :
                  ~ ( ( eigen__4 @ X1 )
                   => ~ ( eigen__5 @ X1 ) ) ) ) )
     => ~ $false ),
    introduced(assumption,[]) ).

thf(h20,assumption,
    ~ ( ~ $false
     => ( eigen__6
       != ( ^ [X1: a] :
              ~ ( ( eigen__4 @ X1 )
               => ~ ( eigen__5 @ X1 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h21,assumption,
    ~ $false,
    introduced(assumption,[]) ).

thf(h22,assumption,
    ( eigen__6
    = ( ^ [X1: a] :
          ~ ( ( eigen__4 @ X1 )
           => ~ ( eigen__5 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(14,plain,
    $false,
    inference(tab_false,[status(thm),assumptions([h21,h22,h20,h9,h19,h18,h17,h2,h0])],[h9]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h20,h9,h19,h18,h17,h2,h0]),tab_negimp(discharge,[h21,h22])],[h20,14,h21,h22]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h19,h18,h17,h2,h0]),tab_negimp(discharge,[h20,h9])],[h19,15,h20,h9]) ).

thf(17,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h18,h17,h2,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__6)],[h18,16,h19]) ).

thf(18,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h17,h2,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__5)],[h17,17,h18]) ).

thf(19,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__4)],[h2,18,h17]) ).

thf(20,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,13,19,h1,h2]) ).

thf(0,theorem,
    ~ ( ~ ( ~ ( ! [X1: a > $o] :
                  ( ( X1
                    = ( ^ [X2: a] : $false ) )
                 => ~ $false )
             => ~ ! [X1: a > $o] :
                    ( ( X1
                      = ( ^ [X2: a] : ~ $false ) )
                   => ~ $false ) )
         => ~ ! [X1: ( a > $o ) > $o,X2: a > $o] :
                ( ~ ( ! [X3: a > $o] :
                        ( ( X1 @ X3 )
                       => ~ $false )
                   => ( X2
                     != ( ^ [X3: a] :
                            ~ ! [X4: a > $o] :
                                ( ( X1 @ X4 )
                               => ~ ( X4 @ X3 ) ) ) ) )
               => ~ $false ) )
     => ~ ! [X1: a > $o,X2: a > $o,X3: a > $o] :
            ( ~ ( ~ $false
               => ( X3
                 != ( ^ [X4: a] :
                        ~ ( ( X1 @ X4 )
                         => ~ ( X2 @ X4 ) ) ) ) )
           => ~ $false ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[20,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SEV258^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n008.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  : 600
% 0.13/0.35  % DateTime : Mon Jun 20 14:32:37 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.37  % SZS status Theorem
% 0.13/0.37  % Mode: mode213
% 0.13/0.37  % Inferences: 0
% 0.13/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------