TSTP Solution File: SET984+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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 Apr 30 20:40:50 EDT 2024

% Result   : Theorem 0.20s 0.40s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   67 (  17 unt;   0 def)
%            Number of atoms       :  158 (  80 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  140 (  49   ~;  67   |;  12   &)
%                                         (   8 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   8 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   88 (  84   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [A,B] : subset(A,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B] :
      ( cartesian_product2(A,B) = empty_set
    <=> ( A = empty_set
        | B = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A,B,C,D] :
      ( cartesian_product2(A,B) = cartesian_product2(C,D)
     => ( A = empty_set
        | B = empty_set
        | ( A = C
          & B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,conjecture,
    ! [A,B,C,D] :
      ( subset(cartesian_product2(A,B),cartesian_product2(C,D))
     => ( cartesian_product2(A,B) = empty_set
        | ( subset(A,C)
          & subset(B,D) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( subset(cartesian_product2(A,B),cartesian_product2(C,D))
       => ( cartesian_product2(A,B) = empty_set
          | ( subset(A,C)
            & subset(B,D) ) ) ),
    inference(negated_conjecture,[status(cth)],[f10]) ).

fof(f12,axiom,
    ! [A,B] : subset(set_intersection2(A,B),A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [A,B] :
      ( subset(A,B)
     => set_intersection2(A,B) = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f22,plain,
    ! [A] : subset(A,A),
    inference(miniscoping,[status(esa)],[f6]) ).

fof(f23,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f24,plain,
    ! [A,B] :
      ( ( cartesian_product2(A,B) != empty_set
        | A = empty_set
        | B = empty_set )
      & ( cartesian_product2(A,B) = empty_set
        | ( A != empty_set
          & B != empty_set ) ) ),
    inference(NNF_transformation,[status(esa)],[f7]) ).

fof(f25,plain,
    ( ! [A,B] :
        ( cartesian_product2(A,B) != empty_set
        | A = empty_set
        | B = empty_set )
    & ! [A,B] :
        ( cartesian_product2(A,B) = empty_set
        | ( A != empty_set
          & B != empty_set ) ) ),
    inference(miniscoping,[status(esa)],[f24]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( cartesian_product2(X0,X1) = empty_set
      | X0 != empty_set ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( cartesian_product2(X0,X1) = empty_set
      | X1 != empty_set ),
    inference(cnf_transformation,[status(esa)],[f25]) ).

fof(f29,plain,
    ! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f30,plain,
    ! [A,B,C,D] :
      ( cartesian_product2(A,B) != cartesian_product2(C,D)
      | A = empty_set
      | B = empty_set
      | ( A = C
        & B = D ) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f31,plain,
    ! [X0,X1,X2,X3] :
      ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
      | X0 = empty_set
      | X1 = empty_set
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f32,plain,
    ! [X0,X1,X2,X3] :
      ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
      | X0 = empty_set
      | X1 = empty_set
      | X1 = X3 ),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f33,plain,
    ? [A,B,C,D] :
      ( subset(cartesian_product2(A,B),cartesian_product2(C,D))
      & cartesian_product2(A,B) != empty_set
      & ( ~ subset(A,C)
        | ~ subset(B,D) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f11]) ).

fof(f34,plain,
    ( subset(cartesian_product2(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
    & cartesian_product2(sk0_2,sk0_3) != empty_set
    & ( ~ subset(sk0_2,sk0_4)
      | ~ subset(sk0_3,sk0_5) ) ),
    inference(skolemization,[status(esa)],[f33]) ).

fof(f35,plain,
    subset(cartesian_product2(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5)),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f36,plain,
    cartesian_product2(sk0_2,sk0_3) != empty_set,
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f37,plain,
    ( ~ subset(sk0_2,sk0_4)
    | ~ subset(sk0_3,sk0_5) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f38,plain,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f39,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | set_intersection2(A,B) = A ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | set_intersection2(X0,X1) = X0 ),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f41,plain,
    ( spl0_0
  <=> subset(sk0_2,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f43,plain,
    ( ~ subset(sk0_2,sk0_4)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f41]) ).

fof(f44,plain,
    ( spl0_1
  <=> subset(sk0_3,sk0_5) ),
    introduced(split_symbol_definition) ).

fof(f46,plain,
    ( ~ subset(sk0_3,sk0_5)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f44]) ).

fof(f47,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f37,f41,f44]) ).

fof(f48,plain,
    sk0_2 != empty_set,
    inference(resolution,[status(thm)],[f27,f36]) ).

fof(f49,plain,
    sk0_3 != empty_set,
    inference(resolution,[status(thm)],[f28,f36]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | set_intersection2(X1,X0) = X0 ),
    inference(paramodulation,[status(thm)],[f14,f40]) ).

fof(f91,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( cartesian_product2(X0,X1) != set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))
      | X0 = empty_set
      | X1 = empty_set
      | X1 = set_intersection2(X3,X5) ),
    inference(paramodulation,[status(thm)],[f29,f32]) ).

fof(f93,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( cartesian_product2(X0,X1) != set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))
      | X0 = empty_set
      | X1 = empty_set
      | X0 = set_intersection2(X2,X4) ),
    inference(paramodulation,[status(thm)],[f29,f31]) ).

fof(f124,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = empty_set
      | X1 = empty_set
      | X1 = set_intersection2(X2,X1)
      | ~ subset(cartesian_product2(X0,X1),cartesian_product2(X3,X2)) ),
    inference(resolution,[status(thm)],[f91,f75]) ).

fof(f154,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = empty_set
      | X1 = empty_set
      | X0 = set_intersection2(X2,X0)
      | ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
    inference(resolution,[status(thm)],[f93,f75]) ).

fof(f175,plain,
    ( spl0_11
  <=> sk0_2 = empty_set ),
    introduced(split_symbol_definition) ).

fof(f176,plain,
    ( sk0_2 = empty_set
    | ~ spl0_11 ),
    inference(component_clause,[status(thm)],[f175]) ).

fof(f178,plain,
    ( spl0_12
  <=> sk0_3 = empty_set ),
    introduced(split_symbol_definition) ).

fof(f179,plain,
    ( sk0_3 = empty_set
    | ~ spl0_12 ),
    inference(component_clause,[status(thm)],[f178]) ).

fof(f181,plain,
    ( spl0_13
  <=> sk0_3 = set_intersection2(sk0_5,sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f182,plain,
    ( sk0_3 = set_intersection2(sk0_5,sk0_3)
    | ~ spl0_13 ),
    inference(component_clause,[status(thm)],[f181]) ).

fof(f184,plain,
    ( sk0_2 = empty_set
    | sk0_3 = empty_set
    | sk0_3 = set_intersection2(sk0_5,sk0_3) ),
    inference(resolution,[status(thm)],[f124,f35]) ).

fof(f185,plain,
    ( spl0_11
    | spl0_12
    | spl0_13 ),
    inference(split_clause,[status(thm)],[f184,f175,f178,f181]) ).

fof(f199,plain,
    ( $false
    | ~ spl0_12 ),
    inference(forward_subsumption_resolution,[status(thm)],[f179,f49]) ).

fof(f200,plain,
    ~ spl0_12,
    inference(contradiction_clause,[status(thm)],[f199]) ).

fof(f201,plain,
    ( $false
    | ~ spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f176,f48]) ).

fof(f202,plain,
    ~ spl0_11,
    inference(contradiction_clause,[status(thm)],[f201]) ).

fof(f207,plain,
    ( spl0_15
  <=> subset(empty_set,empty_set) ),
    introduced(split_symbol_definition) ).

fof(f209,plain,
    ( ~ subset(empty_set,empty_set)
    | spl0_15 ),
    inference(component_clause,[status(thm)],[f207]) ).

fof(f232,plain,
    ( $false
    | spl0_15 ),
    inference(forward_subsumption_resolution,[status(thm)],[f209,f23]) ).

fof(f233,plain,
    spl0_15,
    inference(contradiction_clause,[status(thm)],[f232]) ).

fof(f235,plain,
    ( subset(sk0_3,sk0_5)
    | ~ spl0_13 ),
    inference(paramodulation,[status(thm)],[f182,f38]) ).

fof(f236,plain,
    ( $false
    | spl0_1
    | ~ spl0_13 ),
    inference(forward_subsumption_resolution,[status(thm)],[f235,f46]) ).

fof(f237,plain,
    ( spl0_1
    | ~ spl0_13 ),
    inference(contradiction_clause,[status(thm)],[f236]) ).

fof(f241,plain,
    ( spl0_20
  <=> sk0_2 = set_intersection2(sk0_4,sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f242,plain,
    ( sk0_2 = set_intersection2(sk0_4,sk0_2)
    | ~ spl0_20 ),
    inference(component_clause,[status(thm)],[f241]) ).

fof(f244,plain,
    ( sk0_2 = empty_set
    | sk0_3 = empty_set
    | sk0_2 = set_intersection2(sk0_4,sk0_2) ),
    inference(resolution,[status(thm)],[f154,f35]) ).

fof(f245,plain,
    ( spl0_11
    | spl0_12
    | spl0_20 ),
    inference(split_clause,[status(thm)],[f244,f175,f178,f241]) ).

fof(f263,plain,
    ( subset(sk0_2,sk0_4)
    | ~ spl0_20 ),
    inference(paramodulation,[status(thm)],[f242,f38]) ).

fof(f264,plain,
    ( $false
    | spl0_0
    | ~ spl0_20 ),
    inference(forward_subsumption_resolution,[status(thm)],[f263,f43]) ).

fof(f265,plain,
    ( spl0_0
    | ~ spl0_20 ),
    inference(contradiction_clause,[status(thm)],[f264]) ).

fof(f266,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f47,f185,f200,f202,f233,f237,f245,f265]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% 0.04/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n003.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 21:40:03 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.36  % Drodi V3.6.0
% 0.20/0.40  % Refutation found
% 0.20/0.40  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.42  % Elapsed time: 0.052489 seconds
% 0.20/0.42  % CPU time: 0.301238 seconds
% 0.20/0.42  % Total memory used: 61.419 MB
% 0.20/0.42  % Net memory used: 61.272 MB
%------------------------------------------------------------------------------