%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO357^5 : 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 19:31:36 EDT 2022

% Result   : Theorem 1.95s 2.21s
% Output   : Proof 1.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   35 (   8 unt;   6 typ;   1 def)
%            Number of atoms       :   65 (   1 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   83 (  30   ~;  13   |;   0   &;  13   @)
%                                         (  11 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  17 usr;  17 con; 0-2 aty)
%            Number of variables   :    5 (   1   ^   4   !;   0   ?;   5   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_atype,type,
    atype: $tType ).

thf(ty_a,type,
    a: $o ).

thf(ty_v,type,
    v: atype ).

thf(ty_b,type,
    b: $o ).

thf(ty_eigen__0,type,
    eigen__0: atype > $o ).

thf(ty_u,type,
    u: atype ).

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: atype > $o] :
          ~ ( ( X1 @ u )
           => ( X1 @ v ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: atype > $o] :
        ( ~ ( ( ~ a
             => ~ a )
           => ~ ( X1 @ u ) )
       => ~ ( ( ~ b
             => ~ b )
           => ~ ( X1 @ v ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

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

thf(sP4,plain,
    ( sP4
  <=> ( eigen__0 @ v ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( ~ a
       => ~ a )
     => ~ sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ~ sP5
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: atype > $o] :
        ( ( X1 @ u )
       => ( X1 @ v ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP1
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

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

thf(sP10,plain,
    ( sP10
  <=> ( sP3
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> a ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(cE2LEIBEQ2_pme,conjecture,
    sP8 ).

thf(h1,negated_conjecture,
    ~ sP8,
    inference(assume_negation,[status(cth)],[cE2LEIBEQ2_pme]) ).

thf(1,plain,
    ( sP2
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP9
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP9
    | ~ sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP5
    | ~ sP9
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP6
    | sP5
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP1
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP10
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP10
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP7
    | ~ sP10 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(10,plain,
    ( sP8
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP8
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

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

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

thf(0,theorem,
    sP8,
    inference(contra,[status(thm),contra(discharge,[h1])],[12,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO357^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % 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 : Fri Jul  8 16:23:40 EDT 2022
% 0.20/0.34  % CPUTime  : 
% 1.95/2.21  % SZS status Theorem
% 1.95/2.21  % Mode: mode506
% 1.95/2.21  % Inferences: 40896
% 1.95/2.21  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------