%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU682^2 : 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 13:56:32 EDT 2022

% Result   : Theorem 1.97s 2.16s
% Output   : Proof 1.97s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_subset,type,
    subset: $i > $i > $o ).

thf(ty_cartprod,type,
    cartprod: $i > $i > $i ).

thf(ty_kpair,type,
    kpair: $i > $i > $i ).

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

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
       => ! [X4: $i > $o] :
            ( ! [X5: $i] :
                ( ( in @ X5 @ X1 )
               => ! [X6: $i] :
                    ( ( in @ X6 @ X2 )
                   => ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
                     => ( X4 @ ( kpair @ X5 @ X6 ) ) ) ) )
           => ! [X5: $i] :
                ( ( in @ X5 @ X3 )
               => ( X4 @ X5 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(def_breln,definition,
    ( breln
    = ( ^ [X1: $i,X2: $i,X3: $i] : ( subset @ X3 @ ( cartprod @ X1 @ X2 ) ) ) ) ).

thf(def_brelnall1,definition,
    ( brelnall1
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( breln @ X1 @ X2 @ X3 )
         => ! [X4: $i > $o] :
              ( ! [X5: $i] :
                  ( ( in @ X5 @ X1 )
                 => ! [X6: $i] :
                      ( ( in @ X6 @ X2 )
                     => ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
                       => ( X4 @ ( kpair @ X5 @ X6 ) ) ) ) )
             => ! [X5: $i] :
                  ( ( in @ X5 @ X3 )
                 => ( X4 @ X5 ) ) ) ) ) ) ).

thf(brelnall2,conjecture,
    sP2 ).

thf(h0,negated_conjecture,
    ~ sP2,
    inference(assume_negation,[status(cth)],[brelnall2]) ).

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

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

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

thf(0,theorem,
    sP2,
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU682^2 : 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
% 0.12/0.33  % Computer : n024.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jun 19 05:08:17 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.97/2.16  % SZS status Theorem
% 1.97/2.16  % Mode: mode506
% 1.97/2.16  % Inferences: 1
% 1.97/2.16  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------