TSTP Solution File: SEU681^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU681^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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  : 300s
% DateTime : Tue May 21 03:43:19 EDT 2024

% Result   : Theorem 58.59s 9.75s
% Output   : Refutation 58.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   55 (  11 unt;  14 typ;   3 def)
%            Number of atoms       :  145 (  26 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  543 (  55   ~;  45   |;   6   &; 396   @)
%                                         (   0 <=>;  41  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   8 con; 0-3 aty)
%            Number of variables   :  112 (   3   ^ 103   !;   6   ?; 112   :)

% Comments : 
%------------------------------------------------------------------------------
thf(in_type,type,
    in: $i > $i > $o ).

thf(subset_type,type,
    subset: $i > $i > $o ).

thf(subsetE_type,type,
    subsetE: $o ).

thf(subsetE_def,definition,
    ( subsetE
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( subset @ A @ B )
         => ( ( in @ C @ A )
           => ( in @ C @ B ) ) ) ) ) ).

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

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

thf(cartprodmempair1_type,type,
    cartprodmempair1: $o ).

thf(cartprodmempair1_def,definition,
    ( cartprodmempair1
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( cartprod @ A @ B ) )
         => ? [D: $i] :
              ( ( in @ D @ A )
              & ? [E: $i] :
                  ( ( in @ E @ B )
                  & ( C
                    = ( kpair @ D @ E ) ) ) ) ) ) ) ).

thf(breln_type,type,
    breln: $i > $i > $i > $o ).

thf(breln_def,definition,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).

thf(sk1_type,type,
    sk1: $i > $i > $i > $i ).

thf(sk2_type,type,
    sk2: $i > $i > $i > $i ).

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $i ).

thf(sk5_type,type,
    sk5: $i ).

thf(sk6_type,type,
    sk6: $i > $o ).

thf(sk7_type,type,
    sk7: $i ).

thf(1,conjecture,
    ( subsetE
   => ( cartprodmempair1
     => ! [A: $i,B: $i,C: $i] :
          ( ( breln @ A @ B @ C )
         => ! [D: $i > $o] :
              ( ! [E: $i] :
                  ( ( in @ E @ A )
                 => ! [F: $i] :
                      ( ( in @ F @ B )
                     => ( ( in @ ( kpair @ E @ F ) @ C )
                       => ( D @ ( kpair @ E @ F ) ) ) ) )
             => ! [E: $i] :
                  ( ( in @ E @ C )
                 => ( D @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).

thf(2,negated_conjecture,
    ~ ( subsetE
     => ( cartprodmempair1
       => ! [A: $i,B: $i,C: $i] :
            ( ( breln @ A @ B @ C )
           => ! [D: $i > $o] :
                ( ! [E: $i] :
                    ( ( in @ E @ A )
                   => ! [F: $i] :
                        ( ( in @ F @ B )
                       => ( ( in @ ( kpair @ E @ F ) @ C )
                         => ( D @ ( kpair @ E @ F ) ) ) ) )
               => ! [E: $i] :
                    ( ( in @ E @ C )
                   => ( D @ E ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i,C: $i] :
          ( ( subset @ A @ B )
         => ( ( in @ C @ A )
           => ( in @ C @ B ) ) )
     => ( ! [A: $i,B: $i,C: $i] :
            ( ( in @ C @ ( cartprod @ A @ B ) )
           => ? [D: $i] :
                ( ( in @ D @ A )
                & ? [E: $i] :
                    ( ( in @ E @ B )
                    & ( C
                      = ( kpair @ D @ E ) ) ) ) )
       => ! [A: $i,B: $i,C: $i] :
            ( ( subset @ C @ ( cartprod @ A @ B ) )
           => ! [D: $i > $o] :
                ( ! [E: $i] :
                    ( ( in @ E @ A )
                   => ! [F: $i] :
                        ( ( in @ F @ B )
                       => ( ( in @ ( kpair @ E @ F ) @ C )
                         => ( D @ ( kpair @ E @ F ) ) ) ) )
               => ! [E: $i] :
                    ( ( in @ E @ C )
                   => ( D @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ! [C: $i] :
              ( ( in @ C @ A )
             => ( in @ C @ B ) ) )
     => ( ! [A: $i,B: $i,C: $i] :
            ( ( in @ C @ ( cartprod @ A @ B ) )
           => ? [D: $i] :
                ( ( in @ D @ A )
                & ? [E: $i] :
                    ( ( in @ E @ B )
                    & ( C
                      = ( kpair @ D @ E ) ) ) ) )
       => ! [A: $i,B: $i,C: $i] :
            ( ( subset @ C @ ( cartprod @ A @ B ) )
           => ! [D: $i > $o] :
                ( ! [E: $i] :
                    ( ( in @ E @ A )
                   => ! [F: $i] :
                        ( ( in @ F @ B )
                       => ( ( in @ ( kpair @ E @ F ) @ C )
                         => ( D @ ( kpair @ E @ F ) ) ) ) )
               => ! [E: $i] :
                    ( ( in @ E @ C )
                   => ( D @ E ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(11,plain,
    subset @ sk5 @ ( cartprod @ sk3 @ sk4 ),
    inference(cnf,[status(esa)],[4]) ).

thf(9,plain,
    in @ sk7 @ sk5,
    inference(cnf,[status(esa)],[4]) ).

thf(8,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ~ ( in @ C @ A )
      | ( in @ C @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(80,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( subset @ A @ B )
      | ( in @ C @ B )
      | ( ( in @ sk7 @ sk5 )
       != ( in @ C @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[9,8]) ).

thf(81,plain,
    ! [A: $i] :
      ( ~ ( subset @ sk5 @ A )
      | ( in @ sk7 @ A ) ),
    inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( sk5 )),bind(B,$thf( B )),bind(C,$thf( sk7 ))]]) ).

thf(102,plain,
    ! [A: $i] :
      ( ~ ( subset @ sk5 @ A )
      | ( in @ sk7 @ A ) ),
    inference(simp,[status(thm)],[81]) ).

thf(113,plain,
    ! [A: $i] :
      ( ( in @ sk7 @ A )
      | ( ( subset @ sk5 @ ( cartprod @ sk3 @ sk4 ) )
       != ( subset @ sk5 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[11,102]) ).

thf(114,plain,
    in @ sk7 @ ( cartprod @ sk3 @ sk4 ),
    inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( cartprod @ sk3 @ sk4 ))]]) ).

thf(10,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( cartprod @ A @ B ) )
      | ( C
        = ( kpair @ ( sk1 @ C @ B @ A ) @ ( sk2 @ C @ B @ A ) ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(14,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( kpair @ ( sk1 @ C @ B @ A ) @ ( sk2 @ C @ B @ A ) )
        = C )
      | ~ ( in @ C @ ( cartprod @ A @ B ) ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(15,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( kpair @ ( sk1 @ C @ B @ A ) @ ( sk2 @ C @ B @ A ) )
        = C )
      | ~ ( in @ C @ ( cartprod @ A @ B ) ) ),
    inference(simp,[status(thm)],[14]) ).

thf(145,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( kpair @ ( sk1 @ C @ B @ A ) @ ( sk2 @ C @ B @ A ) )
        = C )
      | ( ( in @ sk7 @ ( cartprod @ sk3 @ sk4 ) )
       != ( in @ C @ ( cartprod @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[114,15]) ).

thf(146,plain,
    ( ( kpair @ ( sk1 @ sk7 @ sk4 @ sk3 ) @ ( sk2 @ sk7 @ sk4 @ sk3 ) )
    = sk7 ),
    inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 )),bind(C,$thf( sk7 ))]]) ).

thf(5,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ sk3 )
      | ~ ( in @ B @ sk4 )
      | ~ ( in @ ( kpair @ A @ B ) @ sk5 )
      | ( sk6 @ ( kpair @ A @ B ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ sk3 )
      | ~ ( in @ B @ sk4 )
      | ~ ( in @ ( kpair @ A @ B ) @ sk5 )
      | ( sk6 @ ( kpair @ A @ B ) ) ),
    inference(simp,[status(thm)],[5]) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ sk3 )
      | ~ ( in @ B @ sk4 )
      | ( sk6 @ ( kpair @ A @ B ) )
      | ( ( in @ ( kpair @ A @ B ) @ sk5 )
       != ( in @ sk7 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[9,13]) ).

thf(37,plain,
    ! [B: $i,A: $i] :
      ( ( sk6 @ ( kpair @ A @ B ) )
      | ~ ( in @ A @ sk3 )
      | ~ ( in @ B @ sk4 )
      | ( ( kpair @ A @ B )
       != sk7 )
      | ( sk5 != sk5 ) ),
    inference(simp,[status(thm)],[26]) ).

thf(43,plain,
    ! [B: $i,A: $i] :
      ( ( sk6 @ ( kpair @ A @ B ) )
      | ~ ( in @ A @ sk3 )
      | ~ ( in @ B @ sk4 )
      | ( ( kpair @ A @ B )
       != sk7 ) ),
    inference(simp,[status(thm)],[37]) ).

thf(12,plain,
    ~ ( sk6 @ sk7 ),
    inference(cnf,[status(esa)],[4]) ).

thf(3226,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ sk3 )
      | ~ ( in @ B @ sk4 )
      | ( ( kpair @ A @ B )
       != sk7 )
      | ( ( sk6 @ ( kpair @ A @ B ) )
       != ( sk6 @ sk7 ) ) ),
    inference(paramod_ordered,[status(thm)],[43,12]) ).

thf(3333,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ sk3 )
      | ~ ( in @ B @ sk4 )
      | ( ( kpair @ A @ B )
       != sk7 )
      | ( ( kpair @ A @ B )
       != sk7 ) ),
    inference(simp,[status(thm)],[3226]) ).

thf(3361,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ sk3 )
      | ~ ( in @ B @ sk4 )
      | ( ( kpair @ A @ B )
       != sk7 ) ),
    inference(simp,[status(thm)],[3333]) ).

thf(5566,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ sk3 )
      | ~ ( in @ B @ sk4 )
      | ( ( kpair @ ( sk1 @ sk7 @ sk4 @ sk3 ) @ ( sk2 @ sk7 @ sk4 @ sk3 ) )
       != ( kpair @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[146,3361]) ).

thf(5567,plain,
    ( ~ ( in @ ( sk1 @ sk7 @ sk4 @ sk3 ) @ sk3 )
    | ~ ( in @ ( sk2 @ sk7 @ sk4 @ sk3 ) @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[5566:[bind(A,$thf( sk1 @ sk7 @ sk4 @ sk3 )),bind(B,$thf( sk2 @ sk7 @ sk4 @ sk3 ))]]) ).

thf(7,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( cartprod @ A @ B ) )
      | ( in @ ( sk1 @ C @ B @ A ) @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(17,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( cartprod @ A @ B ) )
      | ( in @ ( sk1 @ C @ B @ A ) @ A ) ),
    inference(simp,[status(thm)],[7]) ).

thf(362,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ ( sk1 @ C @ B @ A ) @ A )
      | ( ( in @ sk7 @ ( cartprod @ sk3 @ sk4 ) )
       != ( in @ C @ ( cartprod @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[114,17]) ).

thf(363,plain,
    in @ ( sk1 @ sk7 @ sk4 @ sk3 ) @ sk3,
    inference(pattern_uni,[status(thm)],[362:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 )),bind(C,$thf( sk7 ))]]) ).

thf(6,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( cartprod @ A @ B ) )
      | ( in @ ( sk2 @ C @ B @ A ) @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(16,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( cartprod @ A @ B ) )
      | ( in @ ( sk2 @ C @ B @ A ) @ B ) ),
    inference(simp,[status(thm)],[6]) ).

thf(141,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ ( sk2 @ C @ B @ A ) @ B )
      | ( ( in @ sk7 @ ( cartprod @ sk3 @ sk4 ) )
       != ( in @ C @ ( cartprod @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[114,16]) ).

thf(142,plain,
    in @ ( sk2 @ sk7 @ sk4 @ sk3 ) @ sk4,
    inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 )),bind(C,$thf( sk7 ))]]) ).

thf(6068,plain,
    ( ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[5567,363,142]) ).

thf(6069,plain,
    $false,
    inference(simp,[status(thm)],[6068]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEU681^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13  % Command  : run_Leo-III %s %d
% 0.12/0.33  % Computer : n007.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  : 300
% 0.12/0.33  % DateTime : Sun May 19 15:32:24 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.99/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.16/1.07  % [INFO] 	 Parsing done (141ms). 
% 1.30/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.41  % [INFO] 	 nitpick registered as external prover. 
% 1.67/1.42  % [INFO] 	 Scanning for conjecture ... 
% 2.05/1.54  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.05/1.58  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.05/1.58  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.05/1.58  % [INFO] 	 Type checking passed. 
% 2.05/1.59  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 58.59/9.73  % [INFO] 	 Killing All external provers ... 
% 58.59/9.74  % Time passed: 9250ms (effective reasoning time: 8640ms)
% 58.59/9.74  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 58.59/9.74  % Axioms used in derivation (0): 
% 58.59/9.74  % No. of inferences in proof: 38
% 58.59/9.75  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9250 ms resp. 8640 ms w/o parsing
% 58.59/9.86  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 58.59/9.86  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------