%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU501^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n028.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 : Tue Jul 19 13:52:31 EDT 2022

% Result   : Theorem 0.13s 0.36s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
    eigen__1: $o ).

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

thf(ty_emptyset,type,
    emptyset: $i ).

thf(ty_in,type,
    in: $i > $i > $o ).

thf(sP1,plain,
    ( sP1
  <=> ( in @ eigen__0 @ emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ~ ( in @ X1 @ emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(def_emptysetAx,definition,
    emptysetAx = sP2 ).

thf(emptysetE,conjecture,
    ( sP2
   => ! [X1: $i] :
        ( ( in @ X1 @ emptyset )
       => ! [X2: $o] : X2 ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP2
     => ! [X1: $i] :
          ( ( in @ X1 @ emptyset )
         => ! [X2: $o] : X2 ) ),
    inference(assume_negation,[status(cth)],[emptysetE]) ).

thf(h1,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ emptyset )
       => ! [X2: $o] : X2 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP1
     => ! [X1: $o] : X1 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ! [X1: $o] : X1,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ eigen__1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP2
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h6,h4,h5,h3,h1,h2,h0])],[1,h1,h4]) ).

thf(3,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,2,h6]) ).

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h1,h2,h0]),tab_negimp(discharge,[h4,h5])],[h3,3,h4,h5]) ).

thf(5,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,4,h3]) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,5,h1,h2]) ).

thf(0,theorem,
    ( sP2
   => ! [X1: $i] :
        ( ( in @ X1 @ emptyset )
       => ! [X2: $o] : X2 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU501^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % 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 : Sat Jun 18 22:20:59 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.36  % SZS status Theorem
% 0.13/0.36  % Mode: mode213
% 0.13/0.36  % Inferences: 3
% 0.13/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------