TSTP Solution File: SEV429^1 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV429^1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n019.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 18:06:22 EDT 2022

% Result   : Timeout 292.95s 292.96s
% Output   : None 
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   37 (  10 unt;   2 typ;   1 def)
%            Number of atoms       :   79 (  29 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   95 (  19   ~;  13   |;   0   &;  42   @)
%                                         (  14 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  17 usr;  17 con; 0-2 aty)
%            Number of variables   :   22 (   1   ^  12   !;   0   ?;  22   :)
%                                         (   0  !>;   0  ?*;   0  @-;   9  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__8,type,
    eigen__8: $i ).

thf(ty_f,type,
    f: $i > $i ).

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

thf(eigendef_eigen__8,definition,
    ( eigen__8
    = ( eps__0
      @ ^ [X1: $i] :
          ( ( @+[X2: $i] :
                ( ( f @ X1 )
                = ( f @ X2 ) ) )
         != X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__8])]) ).

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

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ( ( f @ eigen__8 )
       != ( f @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( @+[X1: $i] :
            ( ( f @ eigen__8 )
            = ( f @ X1 ) ) )
      = eigen__8 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i] :
        ( ( ( f
            @ @+[X2: $i] :
                ( ( f @ eigen__8 )
                = ( f @ X2 ) ) )
          = ( f @ X1 ) )
       => ( ( @+[X2: $i] :
                ( ( f @ eigen__8 )
                = ( f @ X2 ) ) )
          = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i] :
        ( ( @+[X2: $i] :
              ( ( f @ X1 )
              = ( f @ X2 ) ) )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( ( f
          @ @+[X1: $i] :
              ( ( f @ eigen__8 )
              = ( f @ X1 ) ) )
        = ( f @ eigen__8 ) )
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( f
        @ @+[X1: $i] :
            ( ( f @ eigen__8 )
            = ( f @ X1 ) ) )
      = ( f @ eigen__8 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ( ( ( f @ eigen__8 )
          = X1 )
       => ( X1
          = ( f @ eigen__8 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( eigen__8 = eigen__8 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i,X2: $i] :
        ( ( X1 = X2 )
       => ( X2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ( ( f @ eigen__8 )
        = ( f
          @ @+[X1: $i] :
              ( ( f @ eigen__8 )
              = ( f @ X1 ) ) ) )
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i > $i] :
        ~ ! [X2: $i] :
            ( ( X1 @ ( f @ X2 ) )
            = X2 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( f @ eigen__8 )
      = ( f @ eigen__8 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ( f @ eigen__8 )
      = ( f
        @ @+[X1: $i] :
            ( ( f @ eigen__8 )
            = ( f @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(invexists,conjecture,
    ~ sP12 ).

thf(h1,negated_conjecture,
    sP12,
    inference(assume_negation,[status(cth)],[invexists]) ).

thf(1,plain,
    ( ~ sP6
    | ~ sP7
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    sP9,
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP13
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP2
    | ~ sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP11
    | ~ sP14
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP8
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP10
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP14
    | sP2 ),
    inference(choice_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP5
    | ~ sP3 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__8]) ).

thf(12,plain,
    sP10,
    inference(eq_sym,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP12
    | ~ sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(finj,axiom,
    sP1 ).

thf(14,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,finj,h1]) ).

thf(15,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[14,h0]) ).

thf(0,theorem,
    ~ sP12,
    inference(contra,[status(thm),contra(discharge,[h1])],[14,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV429^1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n019.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
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue Jun 28 08:42:54 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 292.95/292.96  % SZS status Theorem
% 292.95/292.96  % Mode: mode469
% 292.95/292.96  % Inferences: 22250
% 292.95/292.96  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------