TSTP Solution File: SEU938^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU938^5 : 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 : 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 : Tue Jul 19 14:10:56 EDT 2022

% Result   : Timeout 290.22s 287.80s
% Output   : None 
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   52
% Syntax   : Number of formulae    :   59 (  15 unt;   5 typ;   2 def)
%            Number of atoms       :  119 (  22 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  251 (  50   ~;  28   |;   0   &; 111   @)
%                                         (  22 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   42 (  42   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   31 (  29 usr;  27 con; 0-2 aty)
%            Number of variables   :   49 (  23   ^  26   !;   0   ?;  49   :)

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

thf(ty_h,type,
    h: $i > $i ).

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

thf(ty_b,type,
    b: $i ).

thf(ty_eigen__4,type,
    eigen__4: $i > $i ).

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: ( $i > $i ) > $o] :
          ~ ( ~ ( ( X1
                  @ ^ [X2: $i] : ( h @ ( h @ a ) ) )
               => ~ ! [X2: $i > $i] :
                      ( ( X1 @ X2 )
                     => ( X1
                        @ ^ [X3: $i] : ( h @ ( h @ a ) ) ) ) )
           => ( X1
              @ ^ [X2: $i] : ( h @ ( h @ a ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

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

thf(eigendef_eigen__4,definition,
    ( eigen__4
    = ( eps__1
      @ ^ [X1: $i > $i] :
          ~ ( ( a
              = ( X1 @ b ) )
           => ( a
              = ( h @ ( h @ a ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__4])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ~ ( ( ( h @ a )
            = a )
         => ( ( h @ b )
            = a ) )
     => ~ ! [X1: $i > $i,X2: $i > $i] :
            ( ! [X3: $i] :
                ( ( X1 @ X3 )
                = ( X2 @ X3 ) )
           => ( X1 = X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( h @ b )
      = a ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: ( $i > $i ) > $o] :
        ( ~ ( ( X1
              @ ^ [X2: $i] : ( h @ ( h @ a ) ) )
           => ~ ! [X2: $i > $i] :
                  ( ( X1 @ X2 )
                 => ( X1
                    @ ^ [X3: $i] : ( h @ ( h @ a ) ) ) ) )
       => ( X1
          @ ^ [X2: $i] : ( h @ ( h @ a ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( a
        = ( h @ ( h @ a ) ) )
     => ~ ! [X1: $i > $i] :
            ( ( a
              = ( X1 @ b ) )
           => ( a
              = ( h @ ( h @ a ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i > $i] :
        ( ( a
          = ( X1 @ b ) )
       => ( a
          = ( h @ ( h @ a ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( h @ a )
      = a ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( eigen__0
        @ ^ [X1: $i] : ( h @ ( h @ a ) ) )
     => ~ ! [X1: $i > $i] :
            ( ( eigen__0 @ X1 )
           => ( eigen__0
              @ ^ [X2: $i] : ( h @ ( h @ a ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( h @ ( h @ a ) )
      = ( h @ a ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: ( $i > $i ) > $o] :
        ( ~ ( ( X1
              @ ^ [X2: $i] : ( h @ ( h @ a ) ) )
           => ~ ! [X2: $i > $i] :
                  ( ( X1 @ X2 )
                 => ( X1
                    @ ^ [X3: $i] : ( h @ ( h @ a ) ) ) ) )
       => ( X1
          @ ^ [X2: $i] : X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ~ sP4
     => ( a = b ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( a
      = ( h @ ( h @ a ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i > $i,X2: $i > $i] :
        ( ! [X3: ( $i > $i ) > $o] :
            ( ~ ( ( X3 @ X1 )
               => ~ ! [X4: $i > $i] :
                      ( ( X3 @ X4 )
                     => ( X3
                        @ ^ [X5: $i] : ( X1 @ ( X4 @ X5 ) ) ) ) )
           => ( X3
              @ ^ [X4: $i] : ( X2 @ ( X1 @ X4 ) ) ) )
       => ! [X3: ( $i > $i ) > $o] :
            ( ~ ( ( X3 @ X1 )
               => ~ ! [X4: $i > $i] :
                      ( ( X3 @ X4 )
                     => ( X3
                        @ ^ [X5: $i] : ( X1 @ ( X4 @ X5 ) ) ) ) )
           => ( X3 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( a
        = ( eigen__4 @ b ) )
     => sP11 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( a = b ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( ~ sP1
     => ~ sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( ~ sP7
     => ( eigen__0
        @ ^ [X1: $i] : ( h @ ( h @ a ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: $i > $i] :
        ( ! [X2: ( $i > $i ) > $o] :
            ( ~ ( ( X2
                  @ ^ [X3: $i] : ( h @ ( h @ a ) ) )
               => ~ ! [X3: $i > $i] :
                      ( ( X2 @ X3 )
                     => ( X2
                        @ ^ [X4: $i] : ( h @ ( h @ a ) ) ) ) )
           => ( X2
              @ ^ [X3: $i] : ( X1 @ ( h @ ( h @ a ) ) ) ) )
       => ! [X2: ( $i > $i ) > $o] :
            ( ~ ( ( X2
                  @ ^ [X3: $i] : ( h @ ( h @ a ) ) )
               => ~ ! [X3: $i > $i] :
                      ( ( X2 @ X3 )
                     => ( X2
                        @ ^ [X4: $i] : ( h @ ( h @ a ) ) ) ) )
           => ( X2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

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

thf(sP19,plain,
    ( sP19
  <=> ( sP6
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( sP3
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( eigen__0
      @ ^ [X1: $i] : ( h @ ( h @ a ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( ( h @ a )
      = ( h @ b ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(cTHM196_pme,conjecture,
    sP15 ).

thf(h2,negated_conjecture,
    ~ sP15,
    inference(assume_negation,[status(cth)],[cTHM196_pme]) ).

thf(1,plain,
    ( ~ sP10
    | sP4
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP8
    | sP11
    | ~ sP6
    | ~ sP18 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP13
    | ~ sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    sP18,
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP8
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP9
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP20
    | ~ sP3
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP5
    | ~ sP13 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).

thf(9,plain,
    ( ~ sP4
    | ~ sP11
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP7
    | sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP16
    | ~ sP21 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP16
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( sP3
    | ~ sP16 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(14,plain,
    ( ~ sP17
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP12
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( sP22
    | ~ sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP6
    | sP2
    | ~ sP22
    | ~ sP6 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(18,plain,
    ( sP19
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP19
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( sP1
    | ~ sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP15
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( sP15
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,h2]) ).

thf(24,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[23,h1]) ).

thf(25,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[24,h0]) ).

thf(0,theorem,
    sP15,
    inference(contra,[status(thm),contra(discharge,[h2])],[23,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU938^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n016.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 : Sat Jun 18 22:59:53 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 290.22/287.80  % SZS status Theorem
% 290.22/287.80  % Mode: mode469
% 290.22/287.80  % Inferences: 4596
% 290.22/287.80  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------