TSTP Solution File: SET983+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET983+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n018.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 : Wed May 31 12:35:39 EDT 2023

% Result   : Theorem 0.07s 0.28s
% Output   : CNFRefutation 0.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   19 (   8 unt;   0 def)
%            Number of atoms       :   75 (  10 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :   88 (  32   ~;  30   |;  22   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-3 aty)
%            Number of variables   :   57 (;  50   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A,B,C] :
      ( C = set_intersection2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,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(f8,conjecture,
    ! [A,B,C,D,E] :
      ( ( in(A,cartesian_product2(B,C))
        & in(A,cartesian_product2(D,E)) )
     => in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,negated_conjecture,
    ~ ! [A,B,C,D,E] :
        ( ( in(A,cartesian_product2(B,C))
          & in(A,cartesian_product2(D,E)) )
       => in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
    inference(negated_conjecture,[status(cth)],[f8]) ).

fof(f13,plain,
    ! [A,B,C] :
      ( ( C != set_intersection2(A,B)
        | ! [D] :
            ( ( ~ in(D,C)
              | ( in(D,A)
                & in(D,B) ) )
            & ( in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) ) ) )
      & ( C = set_intersection2(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) )
            & ( in(D,C)
              | ( in(D,A)
                & in(D,B) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f14,plain,
    ( ! [A,B,C] :
        ( C != set_intersection2(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | ( in(D,A)
                & in(D,B) ) )
          & ! [D] :
              ( in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) ) ) )
    & ! [A,B,C] :
        ( C = set_intersection2(A,B)
        | ? [D] :
            ( ( ~ in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) )
            & ( in(D,C)
              | ( in(D,A)
                & in(D,B) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f15,plain,
    ( ! [A,B,C] :
        ( C != set_intersection2(A,B)
        | ( ! [D] :
              ( ~ in(D,C)
              | ( in(D,A)
                & in(D,B) ) )
          & ! [D] :
              ( in(D,C)
              | ~ in(D,A)
              | ~ in(D,B) ) ) )
    & ! [A,B,C] :
        ( C = set_intersection2(A,B)
        | ( ( ~ in(sk0_0(C,B,A),C)
            | ~ in(sk0_0(C,B,A),A)
            | ~ in(sk0_0(C,B,A),B) )
          & ( in(sk0_0(C,B,A),C)
            | ( in(sk0_0(C,B,A),A)
              & in(sk0_0(C,B,A),B) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f14]) ).

fof(f18,plain,
    ! [X0,X1,X2,X3] :
      ( X0 != set_intersection2(X1,X2)
      | in(X3,X0)
      | ~ in(X3,X1)
      | ~ in(X3,X2) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f28,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)],[f7]) ).

fof(f29,plain,
    ? [A,B,C,D,E] :
      ( in(A,cartesian_product2(B,C))
      & in(A,cartesian_product2(D,E))
      & ~ in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f30,plain,
    ( in(sk0_3,cartesian_product2(sk0_4,sk0_5))
    & in(sk0_3,cartesian_product2(sk0_6,sk0_7))
    & ~ in(sk0_3,cartesian_product2(set_intersection2(sk0_4,sk0_6),set_intersection2(sk0_5,sk0_7))) ),
    inference(skolemization,[status(esa)],[f29]) ).

fof(f31,plain,
    in(sk0_3,cartesian_product2(sk0_4,sk0_5)),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f32,plain,
    in(sk0_3,cartesian_product2(sk0_6,sk0_7)),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f33,plain,
    ~ in(sk0_3,cartesian_product2(set_intersection2(sk0_4,sk0_6),set_intersection2(sk0_5,sk0_7))),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( in(X0,set_intersection2(X1,X2))
      | ~ in(X0,X1)
      | ~ in(X0,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f18]) ).

fof(f43,plain,
    ! [X0] :
      ( in(sk0_3,set_intersection2(X0,cartesian_product2(sk0_6,sk0_7)))
      | ~ in(sk0_3,X0) ),
    inference(resolution,[status(thm)],[f36,f32]) ).

fof(f47,plain,
    in(sk0_3,set_intersection2(cartesian_product2(sk0_4,sk0_5),cartesian_product2(sk0_6,sk0_7))),
    inference(resolution,[status(thm)],[f43,f31]) ).

fof(f60,plain,
    ~ in(sk0_3,set_intersection2(cartesian_product2(sk0_4,sk0_5),cartesian_product2(sk0_6,sk0_7))),
    inference(backward_demodulation,[status(thm)],[f28,f33]) ).

fof(f61,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f60,f47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SET983+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26  % Computer : n018.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Tue May 30 10:24:10 EDT 2023
% 0.07/0.26  % CPUTime  : 
% 0.07/0.27  % Drodi V3.5.1
% 0.07/0.28  % Refutation found
% 0.07/0.28  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.28  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.28  % Elapsed time: 0.015040 seconds
% 0.07/0.28  % CPU time: 0.021762 seconds
% 0.07/0.28  % Memory used: 14.311 MB
%------------------------------------------------------------------------------