%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU603^2 : 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 : n025.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 13:54:07 EDT 2022

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

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
    eigen__2: $i ).

thf(ty_eigen__1,type,
    eigen__1: $i ).

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

thf(ty_dsetconstr,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

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

thf(sP1,plain,
    ( sP1
  <=> ( in @ eigen__2
      @ ( dsetconstr @ eigen__0
        @ ^ [X1: $i] :
            ~ ( in @ X1 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ( ( in @ X1
          @ ( dsetconstr @ eigen__0
            @ ^ [X2: $i] :
                ~ ( in @ X2 @ eigen__1 ) ) )
       => ~ ( in @ X1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ ( dsetconstr @ eigen__0 @ X1 ) )
       => ( X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i,X2: $i > $o,X3: $i] :
        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
       => ( X2 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( in @ eigen__2 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP1
     => ~ sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(def_dsetconstrER,definition,
    dsetconstrER = sP4 ).

thf(def_setminus,definition,
    ( setminus
    = ( ^ [X1: $i,X2: $i] :
          ( dsetconstr @ X1
          @ ^ [X3: $i] :
              ~ ( in @ X3 @ X2 ) ) ) ) ).

thf(setminusER,conjecture,
    ( sP4
   => ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3
          @ ( dsetconstr @ X1
            @ ^ [X4: $i] :
                ~ ( in @ X4 @ X2 ) ) )
       => ~ ( in @ X3 @ X2 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP4
     => ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3
            @ ( dsetconstr @ X1
              @ ^ [X4: $i] :
                  ~ ( in @ X4 @ X2 ) ) )
         => ~ ( in @ X3 @ X2 ) ) ),
    inference(assume_negation,[status(cth)],[setminusER]) ).

thf(h1,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3
          @ ( dsetconstr @ X1
            @ ^ [X4: $i] :
                ~ ( in @ X4 @ X2 ) ) )
       => ~ ( in @ X3 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ( in @ X2
          @ ( dsetconstr @ eigen__0
            @ ^ [X3: $i] :
                ~ ( in @ X3 @ X1 ) ) )
       => ~ ( in @ X2 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP4
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP2
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP6
    | ~ sP1
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h4,h3,h1,h2,h0])],[1,2,3,4,h1,h6,h7]) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h4,h3,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,5,h6,h7]) ).

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,6,h5]) ).

thf(8,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,7,h4]) ).

thf(9,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,8,h3]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,9,h1,h2]) ).

thf(0,theorem,
    ( sP4
   => ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3
          @ ( dsetconstr @ X1
            @ ^ [X4: $i] :
                ~ ( in @ X4 @ X2 ) ) )
       => ~ ( in @ X3 @ X2 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU603^2 : TPTP v8.1.0. Released v3.7.0.
% 0.10/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n025.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 Jun 18 23:05:28 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
%------------------------------------------------------------------------------