%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO527^1 : 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 : n020.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 19:33:14 EDT 2022

% Result   : Theorem 33.25s 33.52s
% Output   : Proof 33.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   21 (   8 unt;   4 typ;   1 def)
%            Number of atoms       :   31 (   1 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   45 (  12   ~;   4   |;   0   &;  23   @)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   8 con; 0-2 aty)
%            Number of variables   :   12 (   1   ^   8   !;   0   ?;  12   :)
%                                         (   0  !>;   0  ?*;   0  @-;   3  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

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

thf(ty_r,type,
    r: a > b > $o ).

thf(ty_eigen__38,type,
    eigen__38: a ).

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

thf(eigendef_eigen__38,definition,
    ( eigen__38
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( r @ X1
            @ @+[X2: b] : ( r @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__38])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: a] :
        ~ ! [X2: b] :
            ~ ( r @ X1 @ X2 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( r @ eigen__38
      @ @+[X1: b] : ( r @ eigen__38 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: a > b] :
        ~ ! [X2: a] : ( r @ X2 @ ( X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: b] :
        ~ ( r @ eigen__38 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: a] :
        ( r @ X1
        @ @+[X2: b] : ( r @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(skolem,conjecture,
    ~ sP3 ).

thf(h1,negated_conjecture,
    sP3,
    inference(assume_negation,[status(cth)],[skolem]) ).

thf(1,plain,
    ( ~ sP1
    | ~ sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP2
    | sP4 ),
    inference(choice_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP5
    | ~ sP2 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__38]) ).

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

thf(rtotal,axiom,
    sP1 ).

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

thf(6,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[5,h0]) ).

thf(0,theorem,
    ~ sP3,
    inference(contra,[status(thm),contra(discharge,[h1])],[5,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SYO527^1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33  % Computer : n020.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sat Jul  9 09:42:28 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 33.25/33.52  % SZS status Theorem
% 33.25/33.52  % Mode: mode448
% 33.25/33.52  % Inferences: 1152
% 33.25/33.52  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------