%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO559^1 : 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 : 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 19:33:25 EDT 2022

% Result   : Theorem 1.99s 2.31s
% Output   : Proof 1.99s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_epso,type,
    epso: ( $o > $o ) > $o ).

thf(ty_epsoo,type,
    epsoo: ( ( $o > $o ) > $o ) > $o > $o ).

thf(sP1,plain,
    ( sP1
  <=> ( epsoo @ epso @ $false ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

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

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $o] :
        ~ ( epsoo @ epso @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP3
      = ( ~ sP5 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

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

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

thf(sP9,plain,
    ( sP9
  <=> ( epso
      @ ^ [X1: $o] : X1 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP1
     => sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

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

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

thf(c,conjecture,
    sP10 ).

thf(h0,negated_conjecture,
    ~ sP10,
    inference(assume_negation,[status(cth)],[c]) ).

thf(1,plain,
    ( ~ sP7
    | ~ sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(choiceaxo,axiom,
    ! [X1: $o > $o] :
      ( ~ ! [X2: $o] :
            ~ ( X1 @ X2 )
     => ( X1 @ ( epso @ X1 ) ) ) ).

thf(2,plain,
    ( sP9
    | sP7 ),
    inference(choice_rule,[status(thm)],[choiceaxo]) ).

thf(3,plain,
    ( ~ sP12
    | ~ sP9 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(5,plain,
    ( sP6
    | ~ sP3
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    sP11,
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP4
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP2
    | sP8
    | ~ sP11
    | ~ sP6 ),
    inference(mating_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP2
    | sP4 ),
    inference(choice_rule,[status(thm)],[choiceaxo]) ).

thf(choiceaxoo,axiom,
    ! [X1: ( $o > $o ) > $o] :
      ( ~ ! [X2: $o > $o] :
            ~ ( X1 @ X2 )
     => ( X1 @ ( epsoo @ X1 ) ) ) ).

thf(10,plain,
    ( sP3
    | sP12 ),
    inference(choice_rule,[status(thm)],[choiceaxoo]) ).

thf(11,plain,
    ( sP10
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP10
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(0,theorem,
    sP10,
    inference(contra,[status(thm),contra(discharge,[h0])],[13,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SYO559^1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n026.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 : Sat Jul  9 01:16:55 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.99/2.31  % SZS status Theorem
% 1.99/2.31  % Mode: mode506
% 1.99/2.31  % Inferences: 58311
% 1.99/2.31  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------