%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU541^2 : 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 : n011.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 13:53:03 EDT 2022

% Result   : Theorem 0.12s 0.35s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
    eigen__0: $o ).

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

thf(ty_prop2set,type,
    prop2set: $o > $i ).

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

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

thf(sP2,plain,
    ( sP2
  <=> ( sP1
     => ( in @ emptyset @ ( prop2set @ sP1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $o] :
        ( X1
       => ( in @ emptyset @ ( prop2set @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( in @ emptyset @ ( prop2set @ sP1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(def_prop2setI,definition,
    prop2setI = sP3 ).

thf(def_set2prop,definition,
    ( set2prop
    = ( in @ emptyset ) ) ).

thf(prop2set2propI,conjecture,
    ( sP3
   => sP3 ) ).

thf(h0,negated_conjecture,
    ~ ( sP3
     => sP3 ),
    inference(assume_negation,[status(cth)],[prop2set2propI]) ).

thf(h1,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

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

thf(h5,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

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

thf(2,plain,
    ( ~ sP2
    | ~ sP1
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h1,h2,h0])],[1,2,h1,h4,h5]) ).

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,
    ( sP3
   => sP3 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU541^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n011.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 : Mon Jun 20 06:17:24 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.35  % SZS status Theorem
% 0.12/0.35  % Mode: mode213
% 0.12/0.35  % Inferences: 3
% 0.12/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------