%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO520^1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n007.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 19:33:11 EDT 2022

% Result   : Unsatisfiable 0.12s 0.36s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   11 (   3 unt;   2 typ;   0 def)
%            Number of atoms       :   16 (   0 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   22 (   6   ~;   2   |;   0   &;   9   @)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   5 con; 0-1 aty)
%                                         (   1  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :    3 (   1   ^   2   !;   0   ?;   3   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_p,type,
    p: $i > $o ).

thf(ty_eps,type,
    eps: ( $i > $o ) > $i ).

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

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

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

thf(1,plain,
    ( ~ sP2
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(epschoice,axiom,
    ! [X1: $i > $o] :
      ( ~ ! [X2: $i] :
            ~ ( X1 @ X2 )
     => ( X1 @ ( eps @ X1 ) ) ) ).

thf(2,plain,
    ( ~ sP1
    | sP2 ),
    inference(choice_rule,[status(thm)],[epschoice]) ).

thf(ax1,axiom,
    sP1 ).

thf(ax2,axiom,
    ~ sP3 ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm)],[1,2,ax1,ax2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYO520^1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Jul  8 18:29:30 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.36  % SZS status Unsatisfiable
% 0.12/0.36  % Mode: mode213
% 0.12/0.36  % Inferences: 6
% 0.12/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------