TSTP Solution File: SYO094^5 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO094^5 : 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 : n023.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 19:30:16 EDT 2022

% Result   : Theorem 0.14s 0.38s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   35 (  11 unt;   4 typ;   2 def)
%            Number of atoms       :   64 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   83 (  22   ~;   8   |;   0   &;  31   @)
%                                         (   8 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;  13 con; 0-2 aty)
%            Number of variables   :    9 (   2   ^   7   !;   0   ?;   9   :)

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

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

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

thf(ty_cR,type,
    cR: $i > $i > $o ).

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

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( cR @ eigen__0 @ eigen__0 )
           => ( cR @ X1 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

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

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

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

thf(sP3,plain,
    ( sP3
  <=> ( ( cR @ eigen__0 @ eigen__0 )
     => ( cR @ eigen__1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

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

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i] :
        ~ ! [X2: $i] :
            ( ( cR @ X1 @ X1 )
           => ( cR @ X2 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( sP5
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ( sP5
       => ( cR @ X1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(cTHM55A,conjecture,
    ( ( ~ sP1
     => sP2 )
   => ~ sP6 ) ).

thf(h1,negated_conjecture,
    ~ ( ( ~ sP1
       => sP2 )
     => ~ sP6 ),
    inference(assume_negation,[status(cth)],[cTHM55A]) ).

thf(h2,assumption,
    ( ~ sP1
   => sP2 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP3
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP8
    | ~ sP3 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(3,plain,
    ( ~ sP6
    | ~ sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP1
    | ~ sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h2,h3,h1,h0])],[1,2,3,4,h4,h3]) ).

thf(6,plain,
    ( ~ sP2
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP7
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP8
    | ~ sP7 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(9,plain,
    ( ~ sP6
    | ~ sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h5,h2,h3,h1,h0])],[6,7,8,9,h5,h3]) ).

thf(11,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h2,h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h2,5,10,h4,h5]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,11,h2,h3]) ).

thf(13,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0]) ).

thf(0,theorem,
    ( ( ~ sP1
     => sP2 )
   => ~ sP6 ),
    inference(contra,[status(thm),contra(discharge,[h1])],[12,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SYO094^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sat Jul  9 02:49:26 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.38  % SZS status Theorem
% 0.14/0.38  % Mode: mode213
% 0.14/0.38  % Inferences: 16
% 0.14/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------