TSTP Solution File: SYO513^1 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO513^1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n016.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 : Thu Jul 21 19:33:08 EDT 2022

% Result   : Theorem 9.72s 9.99s
% Output   : Proof 9.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   46
% Syntax   : Number of formulae    :   54 (  13 unt;   3 typ;   3 def)
%            Number of atoms       :  136 (  19 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  124 (  42   ~;  31   |;   0   &;  26   @)
%                                         (  19 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  24 usr;  24 con; 0-2 aty)
%            Number of variables   :   23 (  11   ^  12   !;   0   ?;  23   :)

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

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

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

thf(h0,assumption,
    ! [X1: $o > $o,X2: $o] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__3,definition,
    ( eigen__3
    = ( eps__0
      @ ^ [X1: $o] :
          ~ ~ ( eigen__2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(h1,assumption,
    ! [X1: ( $o > $o ) > $o,X2: $o > $o] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__1 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__1
      @ ^ [X1: $o > $o] :
          ~ ( ~ ! [X2: $o] :
                  ~ ( X1 @ X2 )
           => ( X1
              @ ( ( ^ [X2: $o] : X2 )
                = X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(eigendef_eigen__4,definition,
    ( eigen__4
    = ( eps__0
      @ ^ [X1: $o] :
          ( X1
         != ( eigen__2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__4])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $o > $o] :
        ( ~ ! [X2: $o] :
              ~ ( X1 @ X2 )
       => ( X1
          @ ( ( ^ [X2: $o] : X2 )
            = X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ( eigen__4
      = ( eigen__2 @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> eigen__4 ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $o] :
        ~ ( eigen__2 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP4
      = ( ( ^ [X1: $o] : X1 )
        = eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( sP2 = sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $o] :
        ( X1
        = ( eigen__2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( eigen__2 @ ~ $false ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP2
      = ( ( ^ [X1: $o] : X1 )
        = eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ~ sP5
     => ( eigen__2
        @ ( ( ^ [X1: $o] : X1 )
          = eigen__2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( eigen__2
      @ ( ( ^ [X1: $o] : X1 )
        = eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( ~ $false )
      = ( ( ^ [X1: $o] : X1 )
        = eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( eigen__2 @ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( ( ^ [X1: $o] : X1 )
      = eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: ( $o > $o ) > $o] :
        ~ ! [X2: $o > $o] :
            ( ~ ! [X3: $o] :
                  ~ ( X2 @ X3 )
           => ( X2 @ ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ( ~ $false )
      = sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( eigen__2 @ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(choiceo,conjecture,
    ~ sP16 ).

thf(h2,negated_conjecture,
    sP16,
    inference(assume_negation,[status(cth)],[choiceo]) ).

thf(1,plain,
    ( sP13
    | sP19
    | ~ sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP9
    | sP12
    | ~ sP13 ),
    inference(mating_rule,[status(thm)],]) ).

thf(3,plain,
    ~ sP19,
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP17
    | sP19
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP8
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP15
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP6
    | sP4
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP14
    | sP12
    | ~ sP6 ),
    inference(mating_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP7
    | ~ sP2
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP18
    | sP14
    | ~ sP7 ),
    inference(mating_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP3
    | ~ sP4
    | ~ sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP3
    | sP4
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( sP8
    | ~ sP3 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).

thf(14,plain,
    ( sP15
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( sP10
    | sP2
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP18
    | sP12
    | ~ sP10 ),
    inference(mating_rule,[status(thm)],]) ).

thf(17,plain,
    ( sP5
    | sP18 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(18,plain,
    ( sP11
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP11
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( sP1
    | ~ sP11 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).

thf(21,plain,
    ( ~ sP16
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,h2]) ).

thf(23,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[22,h1]) ).

thf(24,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[23,h0]) ).

thf(0,theorem,
    ~ sP16,
    inference(contra,[status(thm),contra(discharge,[h2])],[22,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SYO513^1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n016.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.33  % CPULimit : 300
% 0.18/0.33  % WCLimit  : 600
% 0.18/0.33  % DateTime : Fri Jul  8 23:21:54 EDT 2022
% 0.18/0.33  % CPUTime  : 
% 9.72/9.99  % SZS status Theorem
% 9.72/9.99  % Mode: mode495
% 9.72/9.99  % Inferences: 59
% 9.72/9.99  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------