TSTP Solution File: SEU515^2 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU515^2 : 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 : n015.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 13:52:41 EDT 2022

% Result   : Theorem 0.19s 0.52s
% Output   : Proof 0.19s
% 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 ).

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

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

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

thf(ty_setadjoin,type,
    setadjoin: $i > $i > $i ).

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

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

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

thf(sP4,plain,
    ( sP4
  <=> ( eigen__2 = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> eigen__3 ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( setadjoin @ eigen__0 @ X1 ) )
        = ( ( X2 != eigen__0 )
         => ( in @ X2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

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

thf(sP8,plain,
    ( sP8
  <=> ( in @ eigen__2 @ ( setadjoin @ eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ~ sP4
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(def_setadjoinAx,definition,
    setadjoinAx = sP3 ).

thf(setadjoinE,conjecture,
    ( sP3
   => ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
       => ! [X4: $o] :
            ( ( ( X3 = X1 )
             => X4 )
           => ( ( ( in @ X3 @ X2 )
               => X4 )
             => X4 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP3
     => ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
         => ! [X4: $o] :
              ( ( ( X3 = X1 )
               => X4 )
             => ( ( ( in @ X3 @ X2 )
                 => X4 )
               => X4 ) ) ) ),
    inference(assume_negation,[status(cth)],[setadjoinE]) ).

thf(h1,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
       => ! [X4: $o] :
            ( ( ( X3 = X1 )
             => X4 )
           => ( ( ( in @ X3 @ X2 )
               => X4 )
             => X4 ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( setadjoin @ eigen__0 @ X1 ) )
       => ! [X3: $o] :
            ( ( ( X2 = eigen__0 )
             => X3 )
           => ( ( ( in @ X2 @ X1 )
               => X3 )
             => X3 ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ ( setadjoin @ eigen__0 @ eigen__1 ) )
       => ! [X2: $o] :
            ( ( ( X1 = eigen__0 )
             => X2 )
           => ( ( ( in @ X1 @ eigen__1 )
               => X2 )
             => X2 ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( sP8
     => ! [X1: $o] :
          ( ( sP4
           => X1 )
         => ( ( sP1
             => X1 )
           => X1 ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP8,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ! [X1: $o] :
        ( ( sP4
         => X1 )
       => ( ( sP1
           => X1 )
         => X1 ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( ( sP4
       => sP5 )
     => ( ( sP1
         => sP5 )
       => sP5 ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ( sP4
   => sP5 ),
    introduced(assumption,[]) ).

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

thf(h11,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(h12,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ( sP1
   => sP5 ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

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

thf(1,plain,
    ( ~ sP9
    | sP4
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | ~ sP8
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP7
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(5,plain,
    ( ~ sP3
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h15,h13,h14,h11,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0])],[1,2,3,4,5,h1,h6,h11,h15]) ).

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

thf(8,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h13,h14,h11,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h12])],[h13,6,7,h15,h12]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h10,8,h13,h14]) ).

thf(10,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h15,h13,h14,h12,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0])],[h12,h14]) ).

thf(11,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h12,h13,h14,h12,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0])],[h12,h14]) ).

thf(12,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h13,h14,h12,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0]),tab_imp(discharge,[h15]),tab_imp(discharge,[h12])],[h13,10,11,h15,h12]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h12,h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h10,12,h13,h14]) ).

thf(14,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h4,h3,h1,h2,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h9,9,13,h11,h12]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,14,h9,h10]) ).

thf(16,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h4,h3,h1,h2,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,15,h8]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,16,h6,h7]) ).

thf(18,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,17,h5]) ).

thf(19,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,18,h4]) ).

thf(20,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,19,h3]) ).

thf(21,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,20,h1,h2]) ).

thf(0,theorem,
    ( sP3
   => ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
       => ! [X4: $o] :
            ( ( ( X3 = X1 )
             => X4 )
           => ( ( ( in @ X3 @ X2 )
               => X4 )
             => X4 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU515^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n015.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 : Sun Jun 19 22:47:45 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.52  % SZS status Theorem
% 0.19/0.52  % Mode: mode213
% 0.19/0.52  % Inferences: 2254
% 0.19/0.52  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------