TSTP Solution File: SEV221^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV221^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n014.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
% DateTime : Tue Mar 30 22:05:09 EDT 2021

% Result   : Theorem 25.98s
% Output   : Proof 25.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   63
% Syntax   : Number of formulae    :   72 (  13 unt;   7 typ;   4 def)
%            Number of atoms       :  194 (  21 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  306 ( 112   ~;  35   |;   0   &;  85   @)
%                                         (  25 <=>;  49  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   35 (  33 usr;  29 con; 0-2 aty)
%            Number of variables   :   41 (  18   ^  23   !;   0   ?;  41   :)

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

thf(ty_eigen__2,type,
    eigen__2: a > $o ).

thf(ty_eigen__1,type,
    eigen__1: a > $o ).

thf(ty_eigen__0,type,
    eigen__0: a ).

thf(ty_cZ,type,
    cZ: a > $o ).

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

thf(ty_cW,type,
    cW: ( a > $o ) > $o ).

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

thf(eigendef_eigen__3,definition,
    ( eigen__3
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ( cW @ X1 )
           => ( eigen__1
             != ( ^ [X2: a] :
                    ~ ( ( cZ @ X2 )
                     => ~ ( X1 @ X2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ~ ! [X2: a > $o] :
                  ( ( cW @ X2 )
                 => ( X1
                   != ( ^ [X3: a] :
                          ~ ( ( cZ @ X3 )
                           => ~ ( X2 @ X3 ) ) ) ) )
           => ~ ( X1 @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__1
      @ ^ [X1: a] :
          ( ( ~ ( ~ ! [X2: a > $o] :
                      ( ( cW @ X2 )
                     => ~ ( X2 @ X1 ) )
               => ~ ( cZ @ X1 ) ) )
         != ( ~ ! [X2: a > $o] :
                  ( ~ ! [X3: a > $o] :
                        ( ( cW @ X3 )
                       => ( X2
                         != ( ^ [X4: a] :
                                ~ ( ( cZ @ X4 )
                                 => ~ ( X3 @ X4 ) ) ) ) )
                 => ~ ( X2 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__0
      @ ^ [X1: a > $o] :
          ~ ( ( cW @ X1 )
           => ~ ( X1 @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ( ~ ( ~ ! [X1: a > $o] :
                  ( ( cW @ X1 )
                 => ~ ( X1 @ eigen__0 ) )
           => ~ ( cZ @ eigen__0 ) ) )
      = ( ~ ! [X1: a > $o] :
              ( ~ ! [X2: a > $o] :
                    ( ( cW @ X2 )
                   => ( X1
                     != ( ^ [X3: a] :
                            ~ ( ( cZ @ X3 )
                             => ~ ( X2 @ X3 ) ) ) ) )
             => ~ ( X1 @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ( ( cZ @ eigen__0 )
     => ~ ( eigen__2 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: a > $o] :
        ( ~ ! [X2: a > $o] :
              ( ( cW @ X2 )
             => ( X1
               != ( ^ [X3: a] :
                      ~ ( ( cZ @ X3 )
                       => ~ ( X2 @ X3 ) ) ) ) )
       => ~ ( X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( cZ @ eigen__0 )
     => ~ ( eigen__3 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: a] :
        ( ( eigen__1 @ X1 )
        = ( ~ ( ( cZ @ X1 )
             => ~ ( eigen__3 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: a > $o] :
        ( ( cW @ X1 )
       => ( ( ^ [X2: a] :
                ~ ( ( cZ @ X2 )
                 => ~ ( eigen__2 @ X2 ) ) )
         != ( ^ [X2: a] :
                ~ ( ( cZ @ X2 )
                 => ~ ( X1 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( eigen__1 @ eigen__0 )
      = ( ~ sP5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ( ^ [X1: a] :
            ~ ( ( cZ @ X1 )
             => ~ ( eigen__2 @ X1 ) ) )
      = ( ^ [X1: a] :
            ~ ( ( cZ @ X1 )
             => ~ ( eigen__2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( cW @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP2
     => ( eigen__1
       != ( ^ [X1: a] :
              ~ ( ( cZ @ X1 )
               => ~ ( eigen__3 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ~ ! [X1: a > $o] :
            ( ( cW @ X1 )
           => ( eigen__1
             != ( ^ [X2: a] :
                    ~ ( ( cZ @ X2 )
                     => ~ ( X1 @ X2 ) ) ) ) )
     => ~ ( eigen__1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ~ ! [X1: a > $o] :
            ( ( cW @ X1 )
           => ~ ( X1 @ eigen__0 ) )
     => ~ ( cZ @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: a > $o] :
        ( ( cW @ X1 )
       => ~ ( X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( eigen__1
      = ( ^ [X1: a] :
            ~ ( ( cZ @ X1 )
             => ~ ( eigen__3 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( eigen__1 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

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

thf(sP18,plain,
    ( sP18
  <=> ( cZ @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( sP2
     => ~ ( eigen__3 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ! [X1: a > $o] :
        ( ( cW @ X1 )
       => ( eigen__1
         != ( ^ [X2: a] :
                ~ ( ( cZ @ X2 )
                 => ~ ( X1 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( sP10
     => ~ ( eigen__2 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( eigen__3 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( sP10
     => ~ sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( ~ sP7
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( eigen__2 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(cTHM61_pme,conjecture,
    sP17 ).

thf(h2,negated_conjecture,
    ~ sP17,
    inference(assume_negation,[status(cth)],[cTHM61_pme]) ).

thf(1,plain,
    sP9,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP7
    | sP23 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP23
    | ~ sP10
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP3
    | ~ sP18
    | ~ sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP24
    | sP7
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP4
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP5
    | sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP5
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP8
    | ~ sP16
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP6
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP14
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP19
    | ~ sP2
    | ~ sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP15
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( sP11
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( sP11
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( sP20
    | ~ sP11 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(17,plain,
    ( sP21
    | sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( sP21
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP12
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( sP12
    | ~ sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP14
    | ~ sP21 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(22,plain,
    ( ~ sP13
    | sP14
    | ~ sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( sP4
    | ~ sP12 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(24,plain,
    ( sP13
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
    ( sP13
    | ~ sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
    ( sP1
    | sP13
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( sP1
    | ~ sP13
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(28,plain,
    ( sP17
    | ~ sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).

thf(29,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,h2]) ).

thf(30,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[29,h1]) ).

thf(31,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[30,h0]) ).

thf(0,theorem,
    sP17,
    inference(contra,[status(thm),contra(discharge,[h2])],[29,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV221^5 : TPTP v7.5.0. 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 : n014.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 : Fri Mar 26 14:33:37 EDT 2021
% 0.13/0.34  % CPUTime  : 
% 25.98/26.31  % SZS status Theorem
% 25.98/26.31  % Mode: mode454
% 25.98/26.31  % Inferences: 423
% 25.98/26.31  % SZS output start Proof
% See solution above
% 25.98/26.31  % SZS output end Proof
%------------------------------------------------------------------------------