TSTP Solution File: SYN036^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYN036^5 : 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 : n011.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 11:40:36 EDT 2022

% Result   : Theorem 1.95s 2.20s
% Output   : Proof 1.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  110
% Syntax   : Number of formulae    :  122 (  15 unt;  11 typ;   8 def)
%            Number of atoms       :  318 (  40 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  314 ( 101   ~;  84   |;   0   &;  73   @)
%                                         (  40 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   55 (  52 usr;  52 con; 0-2 aty)
%                                         (   3  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   36 (   8   ^  28   !;   0   ?;  36   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
    eigen__6: $i ).

thf(ty_eigen__2,type,
    eigen__2: $i ).

thf(ty_cP,type,
    cP: $i > $o ).

thf(ty_eigen__7,type,
    eigen__7: $i ).

thf(ty_eigen__1,type,
    eigen__1: $i ).

thf(ty_eigen__15,type,
    eigen__15: $i ).

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

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

thf(ty_eigen__5,type,
    eigen__5: $i ).

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

thf(ty_cQ,type,
    cQ: $i > $o ).

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

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

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ( cQ @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(eigendef_eigen__15,definition,
    ( eigen__15
    = ( eps__0
      @ ^ [X1: $i] :
          ( ( cQ @ eigen__0 )
         != ( cQ @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__15])]) ).

thf(eigendef_eigen__6,definition,
    ( eigen__6
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ( cP @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__6])]) ).

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ! [X2: $i] :
                ( ( cP @ X1 )
                = ( cP @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(eigendef_eigen__4,definition,
    ( eigen__4
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ! [X2: $i] :
                ( ( cQ @ X1 )
                = ( cQ @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__4])]) ).

thf(eigendef_eigen__7,definition,
    ( eigen__7
    = ( eps__0
      @ ^ [X1: $i] :
          ( ( cP @ eigen__0 )
         != ( cP @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__7])]) ).

thf(eigendef_eigen__5,definition,
    ( eigen__5
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( cQ @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__5])]) ).

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

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

thf(sP3,plain,
    ( sP3
  <=> ( ( ( cP @ eigen__2 )
        = sP2 )
     => ~ ( cP @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i] :
        ~ ! [X2: $i] :
            ( ( cQ @ X1 )
            = ( cQ @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( cQ @ eigen__0 )
      = ( cQ @ eigen__15 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( cP @ eigen__7 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( cQ @ eigen__4 )
      = ( cQ @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ( ( cQ @ eigen__0 )
        = ( cQ @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $o] :
        ( ( X1
          = ( cP @ eigen__6 ) )
       => X1 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( !! @ cQ ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ( cP @ eigen__6 )
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( cP @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: $i] :
        ( sP12
        = ( cP @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ( sP12
        = ( cP @ eigen__6 ) )
     => sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $o] :
        ( ( X1 = sP2 )
       => ~ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: $o > $o] :
        ( ( X1 @ ( cP @ eigen__6 ) )
       => ! [X2: $o] :
            ( ( X2
              = ( cP @ eigen__6 ) )
           => ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( cQ @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( ( cQ @ eigen__4 )
      = ( cQ @ eigen__5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: $i] :
        ( ( cP @ eigen__0 )
        = ( cP @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( sP12 = sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $o,X2: $o > $o] :
        ( ( X2 @ X1 )
       => ! [X3: $o] :
            ( ( X3 = X1 )
           => ( X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( ( ~ sP4 )
      = ( ( ~ sP1 )
        = sP10 ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( cP @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( cQ @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( ( ~ sP1 )
      = sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( cQ @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( ( ~ ! [X1: $i] :
              ~ ( cQ @ X1 ) )
      = ( !! @ cP ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( !! @ cP ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( sP12
      = ( cP @ eigen__6 ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ! [X1: $i] :
        ~ ( cQ @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( ( ( ~ ! [X1: $i] :
                ~ ! [X2: $i] :
                    ( ( cP @ X1 )
                    = ( cP @ X2 ) ) )
        = sP27 )
      = sP22 ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( ~ sP2
     => sP15 ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ! [X1: $i] :
        ( sP26
        = ( cQ @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ( sP23 = sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ( ( ~ ! [X1: $i] :
              ~ ! [X2: $i] :
                  ( ( cP @ X1 )
                  = ( cP @ X2 ) ) )
      = sP27 ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( cP @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ! [X1: $i] :
        ~ ! [X2: $i] :
            ( ( cP @ X1 )
            = ( cP @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ( cQ @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ( cQ @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ! [X1: $o > $o] :
        ( ( X1 @ sP2 )
       => ! [X2: $o] :
            ( ( X2 = sP2 )
           => ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(cX2129,conjecture,
    sP31 ).

thf(h1,negated_conjecture,
    ~ sP31,
    inference(assume_negation,[status(cth)],[cX2129]) ).

thf(1,plain,
    ( ~ sP30
    | ~ sP39 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP10
    | sP39 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP5
    | ~ sP38
    | ~ sP39 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP5
    | sP38
    | sP39 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP8
    | ~ sP5 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).

thf(6,plain,
    ( ~ sP28
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP1
    | ~ sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP34
    | ~ sP23
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP34
    | sP23
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP19
    | ~ sP34 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).

thf(11,plain,
    ( ~ sP18
    | ~ sP26
    | sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP33
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP13
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP3
    | ~ sP20
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP15
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP32
    | sP2
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP40
    | sP32 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP21
    | sP40 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP7
    | sP26
    | ~ sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP33
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP13
    | sP29 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP14
    | ~ sP29
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP9
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP11
    | ~ sP36
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP16
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP21
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(27,plain,
    ( sP1
    | sP36 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).

thf(28,plain,
    ( sP10
    | ~ sP24 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).

thf(29,plain,
    ( sP25
    | sP1
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(30,plain,
    ( sP25
    | ~ sP1
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(31,plain,
    ( sP22
    | sP4
    | ~ sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(32,plain,
    ( sP22
    | ~ sP4
    | sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(33,plain,
    sP21,
    inference(eq_ind_sym,[status(thm)],]) ).

thf(34,plain,
    ( sP4
    | sP33 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).

thf(35,plain,
    ( ~ sP10
    | sP38 ),
    inference(all_rule,[status(thm)],]) ).

thf(36,plain,
    ( ~ sP1
    | ~ sP23 ),
    inference(all_rule,[status(thm)],]) ).

thf(37,plain,
    ( ~ sP25
    | sP1
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(38,plain,
    ( ~ sP25
    | ~ sP1
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(39,plain,
    ( ~ sP4
    | ~ sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(40,plain,
    ( ~ sP22
    | sP4
    | sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(41,plain,
    ( ~ sP22
    | ~ sP4
    | ~ sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(42,plain,
    ( sP28
    | ~ sP2 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(43,plain,
    ( sP27
    | sP30
    | ~ sP28 ),
    inference(prop_rule,[status(thm)],]) ).

thf(44,plain,
    ( sP27
    | ~ sP30
    | sP28 ),
    inference(prop_rule,[status(thm)],]) ).

thf(45,plain,
    ( ~ sP35
    | sP37
    | sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(46,plain,
    ( ~ sP35
    | ~ sP37
    | ~ sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(47,plain,
    ( sP37
    | sP13 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(48,plain,
    ( sP30
    | sP17 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(49,plain,
    ( ~ sP28
    | sP23 ),
    inference(all_rule,[status(thm)],]) ).

thf(50,plain,
    ( ~ sP30
    | ~ sP38 ),
    inference(all_rule,[status(thm)],]) ).

thf(51,plain,
    ( ~ sP27
    | sP30
    | sP28 ),
    inference(prop_rule,[status(thm)],]) ).

thf(52,plain,
    ( ~ sP27
    | ~ sP30
    | ~ sP28 ),
    inference(prop_rule,[status(thm)],]) ).

thf(53,plain,
    ( ~ sP37
    | ~ sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(54,plain,
    ( sP35
    | sP37
    | ~ sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(55,plain,
    ( sP35
    | ~ sP37
    | sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(56,plain,
    ( sP31
    | ~ sP35
    | ~ sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(57,plain,
    ( sP31
    | sP35
    | sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(58,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,h1]) ).

thf(59,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[58,h0]) ).

thf(0,theorem,
    sP31,
    inference(contra,[status(thm),contra(discharge,[h1])],[58,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYN036^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n011.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 Jul 12 03:33:58 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 1.95/2.20  % SZS status Theorem
% 1.95/2.20  % Mode: mode506
% 1.95/2.20  % Inferences: 20535
% 1.95/2.20  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------