%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYN382^5 : 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 : n026.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 11:43:17 EDT 2022

% Result   : Theorem 0.13s 0.37s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   31 (   8 unt;   4 typ;   1 def)
%            Number of atoms       :   62 (   1 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  112 (  34   ~;   8   |;   0   &;  44   @)
%                                         (   8 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  13 usr;  13 con; 0-2 aty)
%                                         (   4  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   15 (   1   ^  14   !;   0   ?;  15   :)

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

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

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

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

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

thf(eigendef_eigen__4,definition,
    ( eigen__4
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ( ~ ( !! @ ( cP @ X1 ) )
             => ( cQ @ X1 @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__4])]) ).

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

thf(sP2,plain,
    ( sP2
  <=> ( cQ @ eigen__4 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( !! @ ( cP @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ~ sP3
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ~ ( cP @ eigen__4 @ eigen__0 )
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( cP @ eigen__4 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i] :
        ~ ( ~ ( !! @ ( cP @ X1 ) )
         => ( cQ @ X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

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

thf(cX2134,conjecture,
    ( sP1
   => ! [X1: $i] :
        ~ ! [X2: $i] :
            ~ ( ~ ( cP @ X2 @ X1 )
             => ( cQ @ X2 @ X1 ) ) ) ).

thf(h1,negated_conjecture,
    ~ ( sP1
     => ! [X1: $i] :
          ~ ! [X2: $i] :
              ~ ( ~ ( cP @ X2 @ X1 )
               => ( cQ @ X2 @ X1 ) ) ),
    inference(assume_negation,[status(cth)],[cX2134]) ).

thf(h2,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: $i] :
        ~ ! [X2: $i] :
            ~ ( ~ ( cP @ X2 @ X1 )
             => ( cQ @ X2 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP8,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP5
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP5
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP8
    | ~ sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP3
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP3
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP7
    | sP4 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).

thf(7,plain,
    ( ~ sP1
    | ~ sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,h2,h4]) ).

thf(9,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__0)],[h3,8,h4]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,9,h2,h3]) ).

thf(11,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[10,h0]) ).

thf(0,theorem,
    ( sP1
   => ! [X1: $i] :
        ~ ! [X2: $i] :
            ~ ( ~ ( cP @ X2 @ X1 )
             => ( cQ @ X2 @ X1 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[10,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SYN382^5 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n026.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 : Mon Jul 11 20:21:57 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.37  % SZS status Theorem
% 0.13/0.37  % Mode: mode213
% 0.13/0.37  % Inferences: 193
% 0.13/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------