TSTP Solution File: SET974+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET974+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n016.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 03:07:29 EDT 2024

% Result   : Theorem 58.60s 9.17s
% Output   : Refutation 58.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   58 (  12 unt;  12 typ;   0 def)
%            Number of atoms       :  115 (  16 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  576 (  46   ~;  34   |;  18   &; 475   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   6 con; 0-5 aty)
%            Number of variables   :  142 (   0   ^ 127   !;  15   ?; 142   :)

% Comments : 
%------------------------------------------------------------------------------
thf(disjoint_type,type,
    disjoint: $i > $i > $o ).

thf(cartesian_product2_type,type,
    cartesian_product2: $i > $i > $i ).

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

thf(set_intersection2_type,type,
    set_intersection2: $i > $i > $i ).

thf(ordered_pair_type,type,
    ordered_pair: $i > $i > $i ).

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

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

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

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

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

thf(sk8_type,type,
    sk8: $i > $i > $i > $i > $i > $i ).

thf(sk9_type,type,
    sk9: $i > $i > $i ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( disjoint @ A @ B )
        | ( disjoint @ C @ D ) )
     => ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( ( disjoint @ A @ B )
          | ( disjoint @ C @ D ) )
       => ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(14,plain,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( ( disjoint @ A @ B )
          | ( disjoint @ C @ D ) )
       => ( disjoint @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(15,plain,
    ~ ( disjoint @ ( cartesian_product2 @ sk1 @ sk3 ) @ ( cartesian_product2 @ sk2 @ sk4 ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( ~ ( disjoint @ A @ B )
          & ! [C: $i] :
              ~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
      & ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
          & ( disjoint @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).

thf(47,plain,
    ! [A: $i,B: $i] :
      ( ~ ( ~ ( disjoint @ A @ B )
          & ! [C: $i] :
              ~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
      & ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
          & ( disjoint @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(48,plain,
    ( ~ ? [A: $i,B: $i] :
          ( ~ ( disjoint @ A @ B )
          & ~ ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) ) )
    & ~ ? [A: $i,B: $i] :
          ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
          & ( disjoint @ A @ B ) ) ),
    inference(miniscope,[status(thm)],[47]) ).

thf(50,plain,
    ! [B: $i,A: $i] :
      ( ( disjoint @ A @ B )
      | ( in @ ( sk9 @ B @ A ) @ ( set_intersection2 @ A @ B ) ) ),
    inference(cnf,[status(esa)],[48]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
        & ! [F: $i,G: $i] :
            ~ ( ( A
                = ( ordered_pair @ F @ G ) )
              & ( in @ F @ ( set_intersection2 @ B @ D ) )
              & ( in @ G @ ( set_intersection2 @ C @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).

thf(41,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ~ ( ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
        & ! [F: $i,G: $i] :
            ~ ( ( A
                = ( ordered_pair @ F @ G ) )
              & ( in @ F @ ( set_intersection2 @ B @ D ) )
              & ( in @ G @ ( set_intersection2 @ C @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(42,plain,
    ~ ? [A: $i,B: $i,C: $i,D: $i,E: $i] :
        ( ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
        & ~ ? [F: $i,G: $i] :
              ( ( A
                = ( ordered_pair @ F @ G ) )
              & ( in @ F @ ( set_intersection2 @ B @ D ) )
              & ( in @ G @ ( set_intersection2 @ C @ E ) ) ) ),
    inference(miniscope,[status(thm)],[41]) ).

thf(44,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
      | ( in @ ( sk7 @ E @ D @ C @ B @ A ) @ ( set_intersection2 @ B @ D ) ) ),
    inference(cnf,[status(esa)],[42]) ).

thf(264,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( disjoint @ A @ B )
      | ( in @ ( sk7 @ G @ F @ E @ D @ C ) @ ( set_intersection2 @ D @ F ) )
      | ( ( in @ ( sk9 @ B @ A ) @ ( set_intersection2 @ A @ B ) )
       != ( in @ C @ ( set_intersection2 @ ( cartesian_product2 @ D @ E ) @ ( cartesian_product2 @ F @ G ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[50,44]) ).

thf(265,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( disjoint @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
      | ( in @ ( sk7 @ D @ C @ B @ A @ ( sk9 @ ( cartesian_product2 @ C @ D ) @ ( cartesian_product2 @ A @ B ) ) ) @ ( set_intersection2 @ A @ C ) ) ),
    inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( cartesian_product2 @ J @ K )),bind(B,$thf( cartesian_product2 @ L @ M )),bind(C,$thf( sk9 @ ( cartesian_product2 @ L @ M ) @ ( cartesian_product2 @ J @ K ) )),bind(D,$thf( J )),bind(E,$thf( K )),bind(F,$thf( L )),bind(G,$thf( M ))]]) ).

thf(280,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( disjoint @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
      | ( in @ ( sk7 @ D @ C @ B @ A @ ( sk9 @ ( cartesian_product2 @ C @ D ) @ ( cartesian_product2 @ A @ B ) ) ) @ ( set_intersection2 @ A @ C ) ) ),
    inference(simp,[status(thm)],[265]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( set_intersection2 @ A @ B )
      = ( set_intersection2 @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

thf(22,plain,
    ! [A: $i,B: $i] :
      ( ( set_intersection2 @ A @ B )
      = ( set_intersection2 @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(23,plain,
    ! [B: $i,A: $i] :
      ( ( set_intersection2 @ A @ B )
      = ( set_intersection2 @ B @ A ) ),
    inference(cnf,[status(esa)],[22]) ).

thf(24,plain,
    ! [B: $i,A: $i] :
      ( ( set_intersection2 @ A @ B )
      = ( set_intersection2 @ B @ A ) ),
    inference(lifteq,[status(thm)],[23]) ).

thf(253,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( disjoint @ C @ D )
      | ( in @ ( sk9 @ D @ C ) @ ( set_intersection2 @ B @ A ) )
      | ( ( set_intersection2 @ A @ B )
       != ( set_intersection2 @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[24,50]) ).

thf(254,plain,
    ! [B: $i,A: $i] :
      ( ( disjoint @ A @ B )
      | ( in @ ( sk9 @ B @ A ) @ ( set_intersection2 @ B @ A ) ) ),
    inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).

thf(1281,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( disjoint @ C @ D )
      | ( in @ ( sk9 @ D @ C ) @ ( set_intersection2 @ B @ A ) )
      | ( ( set_intersection2 @ A @ B )
       != ( set_intersection2 @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[24,254]) ).

thf(1282,plain,
    ! [B: $i,A: $i] :
      ( ( disjoint @ B @ A )
      | ( in @ ( sk9 @ A @ B ) @ ( set_intersection2 @ B @ A ) ) ),
    inference(pattern_uni,[status(thm)],[1281:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).

thf(45,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
      | ( in @ ( sk8 @ E @ D @ C @ B @ A ) @ ( set_intersection2 @ C @ E ) ) ),
    inference(cnf,[status(esa)],[42]) ).

thf(16,plain,
    ( ( disjoint @ sk1 @ sk2 )
    | ( disjoint @ sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[14]) ).

thf(49,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( set_intersection2 @ A @ B ) )
      | ~ ( disjoint @ A @ B ) ),
    inference(cnf,[status(esa)],[48]) ).

thf(51,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( set_intersection2 @ A @ B ) )
      | ~ ( disjoint @ A @ B ) ),
    inference(simp,[status(thm)],[49]) ).

thf(88,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( disjoint @ sk1 @ sk2 )
      | ~ ( in @ C @ ( set_intersection2 @ A @ B ) )
      | ( ( disjoint @ sk3 @ sk4 )
       != ( disjoint @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[16,51]) ).

thf(89,plain,
    ! [A: $i] :
      ( ( disjoint @ sk1 @ sk2 )
      | ~ ( in @ A @ ( set_intersection2 @ sk3 @ sk4 ) ) ),
    inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(95,plain,
    ! [A: $i] :
      ( ( disjoint @ sk1 @ sk2 )
      | ~ ( in @ A @ ( set_intersection2 @ sk3 @ sk4 ) ) ),
    inference(simp,[status(thm)],[89]) ).

thf(331,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( set_intersection2 @ ( cartesian_product2 @ B @ C ) @ ( cartesian_product2 @ D @ E ) ) )
      | ( disjoint @ sk1 @ sk2 )
      | ( ( in @ ( sk8 @ E @ D @ C @ B @ A ) @ ( set_intersection2 @ C @ E ) )
       != ( in @ F @ ( set_intersection2 @ sk3 @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[45,95]) ).

thf(332,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( set_intersection2 @ ( cartesian_product2 @ B @ sk3 ) @ ( cartesian_product2 @ A @ sk4 ) ) )
      | ( disjoint @ sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[331:[bind(A,$thf( K )),bind(B,$thf( J )),bind(C,$thf( sk3 )),bind(D,$thf( H )),bind(E,$thf( sk4 )),bind(F,$thf( sk8 @ sk4 @ H @ sk3 @ J @ K ))]]) ).

thf(345,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( set_intersection2 @ ( cartesian_product2 @ B @ sk3 ) @ ( cartesian_product2 @ A @ sk4 ) ) )
      | ( disjoint @ sk1 @ sk2 ) ),
    inference(simp,[status(thm)],[332]) ).

thf(6789,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( disjoint @ B @ A )
      | ( disjoint @ sk1 @ sk2 )
      | ( ( in @ ( sk9 @ A @ B ) @ ( set_intersection2 @ B @ A ) )
       != ( in @ E @ ( set_intersection2 @ ( cartesian_product2 @ D @ sk3 ) @ ( cartesian_product2 @ C @ sk4 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1282,345]) ).

thf(6790,plain,
    ! [B: $i,A: $i] :
      ( ( disjoint @ ( cartesian_product2 @ A @ sk3 ) @ ( cartesian_product2 @ B @ sk4 ) )
      | ( disjoint @ sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[6789:[bind(A,$thf( cartesian_product2 @ J @ sk4 )),bind(B,$thf( cartesian_product2 @ H @ sk3 )),bind(C,$thf( J )),bind(D,$thf( H )),bind(E,$thf( sk9 @ ( cartesian_product2 @ J @ sk4 ) @ ( cartesian_product2 @ H @ sk3 ) ))]]) ).

thf(6809,plain,
    ! [B: $i,A: $i] :
      ( ( disjoint @ ( cartesian_product2 @ A @ sk3 ) @ ( cartesian_product2 @ B @ sk4 ) )
      | ( disjoint @ sk1 @ sk2 ) ),
    inference(simp,[status(thm)],[6790]) ).

thf(6852,plain,
    ! [B: $i,A: $i] :
      ( ( disjoint @ sk1 @ sk2 )
      | ( ( disjoint @ ( cartesian_product2 @ A @ sk3 ) @ ( cartesian_product2 @ B @ sk4 ) )
       != ( disjoint @ ( cartesian_product2 @ sk1 @ sk3 ) @ ( cartesian_product2 @ sk2 @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6809,15]) ).

thf(6853,plain,
    disjoint @ sk1 @ sk2,
    inference(pattern_uni,[status(thm)],[6852:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(6879,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( set_intersection2 @ A @ B ) )
      | ( ( disjoint @ sk1 @ sk2 )
       != ( disjoint @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[6853,51]) ).

thf(6880,plain,
    ! [A: $i] :
      ~ ( in @ A @ ( set_intersection2 @ sk1 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[6879:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(6886,plain,
    ! [A: $i] :
      ~ ( in @ A @ ( set_intersection2 @ sk1 @ sk2 ) ),
    inference(simp,[status(thm)],[6880]) ).

thf(6916,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( disjoint @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
      | ( ( in @ ( sk7 @ D @ C @ B @ A @ ( sk9 @ ( cartesian_product2 @ C @ D ) @ ( cartesian_product2 @ A @ B ) ) ) @ ( set_intersection2 @ A @ C ) )
       != ( in @ E @ ( set_intersection2 @ sk1 @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[280,6886]) ).

thf(6917,plain,
    ! [B: $i,A: $i] : ( disjoint @ ( cartesian_product2 @ sk1 @ B ) @ ( cartesian_product2 @ sk2 @ A ) ),
    inference(pattern_uni,[status(thm)],[6916:[bind(A,$thf( sk1 )),bind(B,$thf( P )),bind(C,$thf( sk2 )),bind(D,$thf( N )),bind(E,$thf( sk7 @ N @ sk2 @ P @ sk1 @ ( sk9 @ ( cartesian_product2 @ sk2 @ N ) @ ( cartesian_product2 @ sk1 @ P ) ) ))]]) ).

thf(6951,plain,
    ! [B: $i,A: $i] : ( disjoint @ ( cartesian_product2 @ sk1 @ B ) @ ( cartesian_product2 @ sk2 @ A ) ),
    inference(simp,[status(thm)],[6917]) ).

thf(7469,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[15,6951]) ).

thf(7470,plain,
    $false,
    inference(simp,[status(thm)],[7469]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET974+1 : TPTP v8.2.0. Released v3.2.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n016.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Mon May 20 12:34:54 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.93/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/0.98  % [INFO] 	 Parsing done (114ms). 
% 1.25/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.70/1.19  % [INFO] 	 nitpick registered as external prover. 
% 1.70/1.20  % [INFO] 	 Scanning for conjecture ... 
% 1.87/1.25  % [INFO] 	 Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ... 
% 1.87/1.27  % [INFO] 	 Axiom selection finished. Selected 11 axioms (removed 0 axioms). 
% 1.87/1.29  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.87/1.30  % [INFO] 	 Type checking passed. 
% 1.87/1.30  % [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 ... 
% 58.60/9.16  % [INFO] 	 Killing All external provers ... 
% 58.60/9.17  % Time passed: 8636ms (effective reasoning time: 8175ms)
% 58.60/9.17  % 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)>
% 58.60/9.17  % Axioms used in derivation (3): t4_xboole_0, t104_zfmisc_1, commutativity_k3_xboole_0
% 58.60/9.17  % No. of inferences in proof: 46
% 58.60/9.17  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8636 ms resp. 8175 ms w/o parsing
% 58.60/9.20  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 58.60/9.20  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------