TSTP Solution File: SET974+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n021.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 20:40:49 EDT 2024

% Result   : Theorem 0.16s 0.33s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   42 (   8 unt;   0 def)
%            Number of atoms       :   96 (   6 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   95 (  41   ~;  32   |;  17   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-5 aty)
%            Number of variables   :  102 (  91   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A,B] :
      ( disjoint(A,B)
     => disjoint(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [A,B,C,D,E] :
      ~ ( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
        & ! [F,G] :
            ~ ( A = ordered_pair(F,G)
              & in(F,set_intersection2(B,D))
              & in(G,set_intersection2(C,E)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,conjecture,
    ! [A,B,C,D] :
      ( ( disjoint(A,B)
        | disjoint(C,D) )
     => disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( ( disjoint(A,B)
          | disjoint(C,D) )
       => disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
    inference(negated_conjecture,[status(cth)],[f11]) ).

fof(f13,axiom,
    ! [A,B] :
      ( ~ ( ~ disjoint(A,B)
          & ! [C] : ~ in(C,set_intersection2(A,B)) )
      & ~ ( ? [C] : in(C,set_intersection2(A,B))
          & disjoint(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f26,plain,
    ! [A,B] :
      ( ~ disjoint(A,B)
      | disjoint(B,A) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | disjoint(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f28,plain,
    ! [A,B,C,D,E] :
      ( ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
      | ? [F,G] :
          ( A = ordered_pair(F,G)
          & in(F,set_intersection2(B,D))
          & in(G,set_intersection2(C,E)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f29,plain,
    ! [A,B,C,D,E] :
      ( ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
      | ? [G] :
          ( ? [F] :
              ( A = ordered_pair(F,G)
              & in(F,set_intersection2(B,D)) )
          & in(G,set_intersection2(C,E)) ) ),
    inference(miniscoping,[status(esa)],[f28]) ).

fof(f30,plain,
    ! [A,B,C,D,E] :
      ( ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
      | ( A = ordered_pair(sk0_3(E,D,C,B,A),sk0_2(E,D,C,B,A))
        & in(sk0_3(E,D,C,B,A),set_intersection2(B,D))
        & in(sk0_2(E,D,C,B,A),set_intersection2(C,E)) ) ),
    inference(skolemization,[status(esa)],[f29]) ).

fof(f32,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
      | in(sk0_3(X4,X3,X2,X1,X0),set_intersection2(X1,X3)) ),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f33,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
      | in(sk0_2(X4,X3,X2,X1,X0),set_intersection2(X2,X4)) ),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f34,plain,
    ? [A,B,C,D] :
      ( ( disjoint(A,B)
        | disjoint(C,D) )
      & ~ disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f35,plain,
    ( ( disjoint(sk0_4,sk0_5)
      | disjoint(sk0_6,sk0_7) )
    & ~ disjoint(cartesian_product2(sk0_4,sk0_6),cartesian_product2(sk0_5,sk0_7)) ),
    inference(skolemization,[status(esa)],[f34]) ).

fof(f36,plain,
    ( disjoint(sk0_4,sk0_5)
    | disjoint(sk0_6,sk0_7) ),
    inference(cnf_transformation,[status(esa)],[f35]) ).

fof(f37,plain,
    ~ disjoint(cartesian_product2(sk0_4,sk0_6),cartesian_product2(sk0_5,sk0_7)),
    inference(cnf_transformation,[status(esa)],[f35]) ).

fof(f38,plain,
    ! [A,B] :
      ( ( disjoint(A,B)
        | ? [C] : in(C,set_intersection2(A,B)) )
      & ( ! [C] : ~ in(C,set_intersection2(A,B))
        | ~ disjoint(A,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f39,plain,
    ( ! [A,B] :
        ( disjoint(A,B)
        | ? [C] : in(C,set_intersection2(A,B)) )
    & ! [A,B] :
        ( ! [C] : ~ in(C,set_intersection2(A,B))
        | ~ disjoint(A,B) ) ),
    inference(miniscoping,[status(esa)],[f38]) ).

fof(f40,plain,
    ( ! [A,B] :
        ( disjoint(A,B)
        | in(sk0_8(B,A),set_intersection2(A,B)) )
    & ! [A,B] :
        ( ! [C] : ~ in(C,set_intersection2(A,B))
        | ~ disjoint(A,B) ) ),
    inference(skolemization,[status(esa)],[f39]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | in(sk0_8(X1,X0),set_intersection2(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ~ in(X0,set_intersection2(X1,X2))
      | ~ disjoint(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f43,plain,
    ( spl0_0
  <=> disjoint(sk0_4,sk0_5) ),
    introduced(split_symbol_definition) ).

fof(f44,plain,
    ( disjoint(sk0_4,sk0_5)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f43]) ).

fof(f46,plain,
    ( spl0_1
  <=> disjoint(sk0_6,sk0_7) ),
    introduced(split_symbol_definition) ).

fof(f47,plain,
    ( disjoint(sk0_6,sk0_7)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f46]) ).

fof(f49,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f36,f43,f46]) ).

fof(f68,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
      | ~ disjoint(X1,X3) ),
    inference(resolution,[status(thm)],[f32,f42]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
      | in(sk0_8(X1,X0),set_intersection2(X1,X0)) ),
    inference(paramodulation,[status(thm)],[f17,f41]) ).

fof(f127,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
      | ~ disjoint(X2,X4) ),
    inference(resolution,[status(thm)],[f33,f42]) ).

fof(f140,plain,
    ! [X0,X1,X2,X3] :
      ( ~ disjoint(X0,X1)
      | disjoint(cartesian_product2(X1,X2),cartesian_product2(X0,X3)) ),
    inference(resolution,[status(thm)],[f68,f75]) ).

fof(f147,plain,
    ( disjoint(sk0_5,sk0_4)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f44,f27]) ).

fof(f151,plain,
    ! [X0,X1,X2,X3] :
      ( ~ disjoint(X0,X1)
      | disjoint(cartesian_product2(X2,X1),cartesian_product2(X3,X0)) ),
    inference(resolution,[status(thm)],[f127,f75]) ).

fof(f159,plain,
    ~ disjoint(sk0_5,sk0_4),
    inference(resolution,[status(thm)],[f140,f37]) ).

fof(f160,plain,
    ( $false
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f159,f147]) ).

fof(f161,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f160]) ).

fof(f164,plain,
    ( disjoint(sk0_7,sk0_6)
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f47,f27]) ).

fof(f184,plain,
    ~ disjoint(sk0_7,sk0_6),
    inference(resolution,[status(thm)],[f151,f37]) ).

fof(f185,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f184,f164]) ).

fof(f186,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f185]) ).

fof(f187,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f49,f161,f186]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n021.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Mon Apr 29 21:44:25 EDT 2024
% 0.15/0.31  % CPUTime  : 
% 0.15/0.32  % Drodi V3.6.0
% 0.16/0.33  % Refutation found
% 0.16/0.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.34  % Elapsed time: 0.019082 seconds
% 0.16/0.34  % CPU time: 0.043403 seconds
% 0.16/0.34  % Total memory used: 15.182 MB
% 0.16/0.34  % Net memory used: 15.131 MB
%------------------------------------------------------------------------------