TSTP Solution File: SET974+1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET974+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art08.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 15:43:05 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   16 (   6 unt;   0 def)
%            Number of atoms       :   38 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   41 (  19   ~;  16   |;   6   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-5 aty)
%            Number of variables   :   30 (   8 sgn   8   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t104_zfmisc_1,plain,
    ! [A,B,C,D,E] :
      ( ( in(f(A,B,C,D,E),set_intersection2(B,D))
        | ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) )
      & ( in(g(A,B,C,D,E),set_intersection2(C,E))
        | ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) )
      & ( $equal(ordered_pair(f(A,B,C,D,E),g(A,B,C,D,E)),A)
        | ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET974+1.tptp',unknown),
    [] ).

cnf(142763240,plain,
    ( in(f(A,B,C,D,E),set_intersection2(B,D))
    | ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
    inference(rewrite,[status(thm)],[t104_zfmisc_1]),
    [] ).

cnf(142757440,plain,
    ( in(g(A,B,C,D,E),set_intersection2(C,E))
    | ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) ),
    inference(rewrite,[status(thm)],[t104_zfmisc_1]),
    [] ).

fof(t4_xboole_0,plain,
    ! [A,B,D] :
      ( ( disjoint(A,B)
        | in(c_nn_1(A,B),set_intersection2(A,B)) )
      & ( ~ in(D,set_intersection2(A,B))
        | ~ disjoint(A,B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET974+1.tptp',unknown),
    [] ).

cnf(142888504,plain,
    ( disjoint(A,B)
    | in(c_nn_1(A,B),set_intersection2(A,B)) ),
    inference(rewrite,[status(thm)],[t4_xboole_0]),
    [] ).

fof(t127_zfmisc_1,plain,
    ( ( ~ disjoint(cartesian_product2(a,c),cartesian_product2(b,d))
      | disjoint(a,b) )
    & ( disjoint(c,d)
      | disjoint(a,b) )
    & ( ~ disjoint(cartesian_product2(a,c),cartesian_product2(b,d))
      | ~ disjoint(cartesian_product2(a,c),cartesian_product2(b,d)) )
    & ( disjoint(c,d)
      | ~ disjoint(cartesian_product2(a,c),cartesian_product2(b,d)) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET974+1.tptp',unknown),
    [] ).

cnf(142856424,plain,
    ~ disjoint(cartesian_product2(a,c),cartesian_product2(b,d)),
    inference(rewrite,[status(thm)],[t127_zfmisc_1]),
    [] ).

cnf(156040216,plain,
    in(c_nn_1(cartesian_product2(a,c),cartesian_product2(b,d)),set_intersection2(cartesian_product2(a,c),cartesian_product2(b,d))),
    inference(resolution,[status(thm)],[142888504,142856424]),
    [] ).

cnf(156102944,plain,
    in(g(c_nn_1(cartesian_product2(a,c),cartesian_product2(b,d)),a,c,b,d),set_intersection2(c,d)),
    inference(resolution,[status(thm)],[142757440,156040216]),
    [] ).

cnf(142878552,plain,
    ( ~ in(D,set_intersection2(A,B))
    | ~ disjoint(A,B) ),
    inference(rewrite,[status(thm)],[t4_xboole_0]),
    [] ).

cnf(142861160,plain,
    ( disjoint(c,d)
    | disjoint(a,b) ),
    inference(rewrite,[status(thm)],[t127_zfmisc_1]),
    [] ).

cnf(156381512,plain,
    ( ~ in(B,set_intersection2(c,d))
    | disjoint(a,b) ),
    inference(resolution,[status(thm)],[142878552,142861160]),
    [] ).

cnf(156481872,plain,
    ( ~ in(B,set_intersection2(c,d))
    | ~ in(D,set_intersection2(a,b)) ),
    inference(resolution,[status(thm)],[156381512,142878552]),
    [] ).

cnf(158546264,plain,
    ~ in(C,set_intersection2(a,b)),
    inference(resolution,[status(thm)],[156102944,156481872]),
    [] ).

cnf(159779184,plain,
    ~ in(A,set_intersection2(cartesian_product2(a,B),cartesian_product2(b,C))),
    inference(resolution,[status(thm)],[142763240,158546264]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[159779184,156040216]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t104_zfmisc_1,plain,(((in(f(A,B,C,D,E),set_intersection2(B,D))|~in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))))&(in(g(A,B,C,D,E),set_intersection2(C,E))|~in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))))&($equal(ordered_pair(f(A,B,C,D,E),g(A,B,C,D,E)),A)|~in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET974+1.tptp',unknown),[]).
% 
% cnf(142763240,plain,(in(f(A,B,C,D,E),set_intersection2(B,D))|~in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))),inference(rewrite,[status(thm)],[t104_zfmisc_1]),[]).
% 
% cnf(142757440,plain,(in(g(A,B,C,D,E),set_intersection2(C,E))|~in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))),inference(rewrite,[status(thm)],[t104_zfmisc_1]),[]).
% 
% fof(t4_xboole_0,plain,(((disjoint(A,B)|in(c_nn_1(A,B),set_intersection2(A,B)))&(~in(D,set_intersection2(A,B))|~disjoint(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET974+1.tptp',unknown),[]).
% 
% cnf(142888504,plain,(disjoint(A,B)|in(c_nn_1(A,B),set_intersection2(A,B))),inference(rewrite,[status(thm)],[t4_xboole_0]),[]).
% 
% fof(t127_zfmisc_1,plain,(((~disjoint(cartesian_product2(a,c),cartesian_product2(b,d))|disjoint(a,b))&(disjoint(c,d)|disjoint(a,b))&(~disjoint(cartesian_product2(a,c),cartesian_product2(b,d))|~disjoint(cartesian_product2(a,c),cartesian_product2(b,d)))&(disjoint(c,d)|~disjoint(cartesian_product2(a,c),cartesian_product2(b,d))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET974+1.tptp',unknown),[]).
% 
% cnf(142856424,plain,(~disjoint(cartesian_product2(a,c),cartesian_product2(b,d))),inference(rewrite,[status(thm)],[t127_zfmisc_1]),[]).
% 
% cnf(156040216,plain,(in(c_nn_1(cartesian_product2(a,c),cartesian_product2(b,d)),set_intersection2(cartesian_product2(a,c),cartesian_product2(b,d)))),inference(resolution,[status(thm)],[142888504,142856424]),[]).
% 
% cnf(156102944,plain,(in(g(c_nn_1(cartesian_product2(a,c),cartesian_product2(b,d)),a,c,b,d),set_intersection2(c,d))),inference(resolution,[status(thm)],[142757440,156040216]),[]).
% 
% cnf(142878552,plain,(~in(D,set_intersection2(A,B))|~disjoint(A,B)),inference(rewrite,[status(thm)],[t4_xboole_0]),[]).
% 
% cnf(142861160,plain,(disjoint(c,d)|disjoint(a,b)),inference(rewrite,[status(thm)],[t127_zfmisc_1]),[]).
% 
% cnf(156381512,plain,(~in(B,set_intersection2(c,d))|disjoint(a,b)),inference(resolution,[status(thm)],[142878552,142861160]),[]).
% 
% cnf(156481872,plain,(~in(B,set_intersection2(c,d))|~in(D,set_intersection2(a,b))),inference(resolution,[status(thm)],[156381512,142878552]),[]).
% 
% cnf(158546264,plain,(~in(C,set_intersection2(a,b))),inference(resolution,[status(thm)],[156102944,156481872]),[]).
% 
% cnf(159779184,plain,(~in(A,set_intersection2(cartesian_product2(a,B),cartesian_product2(b,C)))),inference(resolution,[status(thm)],[142763240,158546264]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[159779184,156040216]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------