TSTP Solution File: SEV017^5 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV017^5 : 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 : n021.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 18:04:28 EDT 2022

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

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

thf(ty_eigen__2,type,
    eigen__2: a ).

thf(ty_eigen__1,type,
    eigen__1: a ).

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

thf(ty_eigen__3,type,
    eigen__3: a ).

thf(sP1,plain,
    ( sP1
  <=> ( eigen__0 @ eigen__2 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ! [X1: a,X2: a] :
        ( ~ ( ( eigen__0 @ eigen__1 @ X1 )
           => ~ ( eigen__0 @ X1 @ X2 ) )
       => ( eigen__0 @ eigen__1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: a] :
        ( ~ ( ( eigen__0 @ eigen__1 @ eigen__2 )
           => ~ ( eigen__0 @ eigen__2 @ X1 ) )
       => ( eigen__0 @ eigen__1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( eigen__0 @ eigen__1 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( eigen__0 @ eigen__1 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ~ sP2
     => sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: a,X2: a,X3: a] :
        ( ~ ( ( eigen__0 @ X1 @ X2 )
           => ~ ( eigen__0 @ X2 @ X3 ) )
       => ( eigen__0 @ X1 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(cTHM514_pme,conjecture,
    ! [X1: a > a > $o] :
      ( ~ ( ~ ( ! [X2: a] : ( X1 @ X2 @ X2 )
             => ~ ! [X2: a,X3: a] :
                    ( ( X1 @ X2 @ X3 )
                   => ( X1 @ X3 @ X2 ) ) )
         => ~ ! [X2: a,X3: a,X4: a] :
                ( ~ ( ( X1 @ X2 @ X3 )
                   => ~ ( X1 @ X3 @ X4 ) )
               => ( X1 @ X2 @ X4 ) ) )
     => ! [X2: a,X3: a,X4: a] :
          ( ( X1 @ X2 @ X3 )
         => ( ( X1 @ X3 @ X4 )
           => ( X1 @ X2 @ X4 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a > a > $o] :
        ( ~ ( ~ ( ! [X2: a] : ( X1 @ X2 @ X2 )
               => ~ ! [X2: a,X3: a] :
                      ( ( X1 @ X2 @ X3 )
                     => ( X1 @ X3 @ X2 ) ) )
           => ~ ! [X2: a,X3: a,X4: a] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) )
       => ! [X2: a,X3: a,X4: a] :
            ( ( X1 @ X2 @ X3 )
           => ( ( X1 @ X3 @ X4 )
             => ( X1 @ X2 @ X4 ) ) ) ),
    inference(assume_negation,[status(cth)],[cTHM514_pme]) ).

thf(h1,assumption,
    ~ ( ~ ( ~ ( ! [X1: a] : ( eigen__0 @ X1 @ X1 )
             => ~ ! [X1: a,X2: a] :
                    ( ( eigen__0 @ X1 @ X2 )
                   => ( eigen__0 @ X2 @ X1 ) ) )
         => ~ sP8 )
     => ! [X1: a,X2: a,X3: a] :
          ( ( eigen__0 @ X1 @ X2 )
         => ( ( eigen__0 @ X2 @ X3 )
           => ( eigen__0 @ X1 @ X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( ~ ( ! [X1: a] : ( eigen__0 @ X1 @ X1 )
         => ~ ! [X1: a,X2: a] :
                ( ( eigen__0 @ X1 @ X2 )
               => ( eigen__0 @ X2 @ X1 ) ) )
     => ~ sP8 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: a,X2: a,X3: a] :
        ( ( eigen__0 @ X1 @ X2 )
       => ( ( eigen__0 @ X2 @ X3 )
         => ( eigen__0 @ X1 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( ! [X1: a] : ( eigen__0 @ X1 @ X1 )
     => ~ ! [X1: a,X2: a] :
            ( ( eigen__0 @ X1 @ X2 )
           => ( eigen__0 @ X2 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP8,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ! [X1: a] : ( eigen__0 @ X1 @ X1 ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ! [X1: a,X2: a] :
      ( ( eigen__0 @ X1 @ X2 )
     => ( eigen__0 @ X2 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ! [X1: a,X2: a] :
        ( ( eigen__0 @ eigen__1 @ X1 )
       => ( ( eigen__0 @ X1 @ X2 )
         => ( eigen__0 @ eigen__1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ! [X1: a] :
        ( sP5
       => ( ( eigen__0 @ eigen__2 @ X1 )
         => ( eigen__0 @ eigen__1 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ ( sP5
     => ( sP1
       => sP6 ) ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ ( sP1
     => sP6 ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP8
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP4
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP7
    | sP2
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP2
    | ~ sP5
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,h5,h11,h13,h14]) ).

thf(7,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h12,h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h13,h14])],[h12,6,h13,h14]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h10,h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,7,h11,h12]) ).

thf(9,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h9,h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__3)],[h9,8,h10]) ).

thf(10,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h8,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__2)],[h8,9,h9]) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__1)],[h3,10,h8]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h4,11,h6,h7]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h2,12,h4,h5]) ).

thf(14,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,13,h2,h3]) ).

thf(15,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,14,h1]) ).

thf(0,theorem,
    ! [X1: a > a > $o] :
      ( ~ ( ~ ( ! [X2: a] : ( X1 @ X2 @ X2 )
             => ~ ! [X2: a,X3: a] :
                    ( ( X1 @ X2 @ X3 )
                   => ( X1 @ X3 @ X2 ) ) )
         => ~ ! [X2: a,X3: a,X4: a] :
                ( ~ ( ( X1 @ X2 @ X3 )
                   => ~ ( X1 @ X3 @ X4 ) )
               => ( X1 @ X2 @ X4 ) ) )
     => ! [X2: a,X3: a,X4: a] :
          ( ( X1 @ X2 @ X3 )
         => ( ( X1 @ X3 @ X4 )
           => ( X1 @ X2 @ X4 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV017^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n021.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Tue Jun 28 12:14:41 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.36  % SZS status Theorem
% 0.13/0.36  % Mode: mode213
% 0.13/0.36  % Inferences: 4
% 0.13/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------