%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU528^2 : 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 : n024.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 13:52:51 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

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

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

thf(ty_setadjoin,type,
    setadjoin: $i > $i > $i ).

thf(sP1,plain,
    ( sP1
  <=> ( eigen__0 = eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i,X2: $i] :
        ( ( X1 = X2 )
       => ( X2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( in @ eigen__1 @ ( setadjoin @ eigen__0 @ emptyset ) )
     => ( eigen__1 = eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( eigen__1 = eigen__0 )
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
       => ( X1 = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( in @ eigen__1 @ ( setadjoin @ eigen__0 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i] :
        ( ( eigen__1 = X1 )
       => ( X1 = eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ( ( in @ eigen__1 @ ( setadjoin @ X1 @ emptyset ) )
       => ( eigen__1 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( eigen__1 = eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(def_uniqinunit,definition,
    uniqinunit = sP5 ).

thf(notinsingleton,conjecture,
    ( sP5
   => ! [X1: $i,X2: $i] :
        ( ( X1 != X2 )
       => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP5
     => ! [X1: $i,X2: $i] :
          ( ( X1 != X2 )
         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
    inference(assume_negation,[status(cth)],[notinsingleton]) ).

thf(h1,assumption,
    sP5,
    introduced(assumption,[]) ).

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

thf(h3,assumption,
    ~ ! [X1: $i] :
        ( ( eigen__0 != X1 )
       => ~ ( in @ X1 @ ( setadjoin @ eigen__0 @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( ~ sP1
     => ~ sP6 ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP5
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP8
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP3
    | ~ sP6
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP4
    | ~ sP9
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP7
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP2
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    sP2,
    inference(eq_sym,[status(thm)],]) ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h3,h1,h2,h0])],[1,2,3,4,5,6,7,h1,h5,h6]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h3,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,8,h5,h6]) ).

thf(10,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h1,h2,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,9,h4]) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,10,h3]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,11,h1,h2]) ).

thf(0,theorem,
    ( sP5
   => ! [X1: $i,X2: $i] :
        ( ( X1 != X2 )
       => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU528^2 : TPTP v8.1.0. Released v3.7.0.
% 0.06/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n024.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 : Sun Jun 19 10:23:32 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.36  % SZS status Theorem
% 0.12/0.36  % Mode: mode213
% 0.12/0.36  % Inferences: 3
% 0.12/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------