%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SET086^1 : TPTP v8.1.0. Released v3.6.0.
% 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 04:50:55 EDT 2022

% Result   : Theorem 0.17s 0.35s
% Output   : Proof 0.17s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] : ( X1 != eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(def_in,definition,
    ( in
    = ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).

thf(def_is_a,definition,
    ( is_a
    = ( ^ [X1: $i,X2: $i > $o] : ( X2 @ X1 ) ) ) ).

thf(def_emptyset,definition,
    ( emptyset
    = ( ^ [X1: $i] : $false ) ) ).

thf(def_unord_pair,definition,
    ( unord_pair
    = ( ^ [X1: $i,X2: $i,X3: $i] :
          ( ( X3 != X1 )
         => ( X3 = X2 ) ) ) ) ).

thf(def_singleton,definition,
    ( singleton
    = ( ^ [X1: $i,X2: $i] : ( X2 = X1 ) ) ) ).

thf(def_union,definition,
    ( union
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ~ ( X1 @ X3 )
         => ( X2 @ X3 ) ) ) ) ).

thf(def_excl_union,definition,
    ( excl_union
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ( ( X1 @ X3 )
           => ( X2 @ X3 ) )
         => ~ ( ~ ( X1 @ X3 )
             => ~ ( X2 @ X3 ) ) ) ) ) ).

thf(def_intersection,definition,
    ( intersection
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ~ ( ( X1 @ X3 )
           => ~ ( X2 @ X3 ) ) ) ) ).

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

thf(def_complement,definition,
    ( complement
    = ( ^ [X1: $i > $o,X2: $i] :
          ~ ( X1 @ X2 ) ) ) ).

thf(def_disjoint,definition,
    ( disjoint
    = ( ^ [X1: $i > $o,X2: $i > $o] :
          ( ( intersection @ X1 @ X2 )
          = emptyset ) ) ) ).

thf(def_subset,definition,
    ( subset
    = ( ^ [X1: $i > $o,X2: $i > $o] :
        ! [X3: $i] :
          ( ( X1 @ X3 )
         => ( X2 @ X3 ) ) ) ) ).

thf(def_meets,definition,
    ( meets
    = ( ^ [X1: $i > $o,X2: $i > $o] :
          ~ ! [X3: $i] :
              ( ( X1 @ X3 )
             => ~ ( X2 @ X3 ) ) ) ) ).

thf(def_misses,definition,
    ( misses
    = ( ^ [X1: $i > $o,X2: $i > $o] :
        ! [X3: $i] :
          ( ( X1 @ X3 )
         => ~ ( X2 @ X3 ) ) ) ) ).

thf(thm,conjecture,
    ! [X1: $i] :
      ~ ! [X2: $i] : ( X2 != X1 ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i] :
        ~ ! [X2: $i] : ( X2 != X1 ),
    inference(assume_negation,[status(cth)],[thm]) ).

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

thf(1,plain,
    sP1,
    inference(prop_rule,[status(thm)],]) ).

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

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

thf(4,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,3,h1]) ).

thf(0,theorem,
    ! [X1: $i] :
      ~ ! [X2: $i] : ( X2 != X1 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[4,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET086^1 : TPTP v8.1.0. Released v3.6.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32  % Computer : n025.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Sat Jul  9 16:48:45 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.17/0.35  % SZS status Theorem
% 0.17/0.35  % Mode: mode213
% 0.17/0.35  % Inferences: 5
% 0.17/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------