TSTP Solution File: SEU165+3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SEU165+3 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 15:50:32 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 4 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 79 ( 29 ~; 37 |; 13 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 4 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(l55_zfmisc_1,plain,
! [B,D,A,C] :
( ( in(B,D)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ) ),
file('/tmp/SystemOnTPTP26354/SEU165+3.p',unknown),
[] ).
cnf(172853416,plain,
( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ),
inference(rewrite,[status(thm)],[l55_zfmisc_1]),
[] ).
cnf(172859160,plain,
( in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(rewrite,[status(thm)],[l55_zfmisc_1]),
[] ).
fof(t106_zfmisc_1,plain,
( ( in(ordered_pair(a,b),cartesian_product2(c,d))
| in(ordered_pair(a,b),cartesian_product2(c,d))
| in(a,c) )
& ( ~ in(a,c)
| in(ordered_pair(a,b),cartesian_product2(c,d))
| in(a,c) )
& ( in(ordered_pair(a,b),cartesian_product2(c,d))
| ~ in(b,d)
| in(a,c) )
& ( ~ in(a,c)
| ~ in(b,d)
| in(a,c) )
& ( in(ordered_pair(a,b),cartesian_product2(c,d))
| in(ordered_pair(a,b),cartesian_product2(c,d))
| in(b,d) )
& ( ~ in(a,c)
| in(ordered_pair(a,b),cartesian_product2(c,d))
| in(b,d) )
& ( in(ordered_pair(a,b),cartesian_product2(c,d))
| ~ in(b,d)
| in(b,d) )
& ( ~ in(a,c)
| ~ in(b,d)
| in(b,d) )
& ( in(ordered_pair(a,b),cartesian_product2(c,d))
| in(ordered_pair(a,b),cartesian_product2(c,d))
| ~ in(ordered_pair(a,b),cartesian_product2(c,d)) )
& ( ~ in(a,c)
| in(ordered_pair(a,b),cartesian_product2(c,d))
| ~ in(ordered_pair(a,b),cartesian_product2(c,d)) )
& ( in(ordered_pair(a,b),cartesian_product2(c,d))
| ~ in(b,d)
| ~ in(ordered_pair(a,b),cartesian_product2(c,d)) )
& ( ~ in(a,c)
| ~ in(b,d)
| ~ in(ordered_pair(a,b),cartesian_product2(c,d)) ) ),
file('/tmp/SystemOnTPTP26354/SEU165+3.p',unknown),
[] ).
cnf(172842304,plain,
( in(ordered_pair(a,b),cartesian_product2(c,d))
| in(b,d) ),
inference(rewrite,[status(thm)],[t106_zfmisc_1]),
[] ).
cnf(172846336,plain,
( in(ordered_pair(a,b),cartesian_product2(c,d))
| in(a,c) ),
inference(rewrite__forward_subsumption_resolution,[status(thm)],[t106_zfmisc_1,172842304]),
[] ).
cnf(188930464,plain,
in(a,c),
inference(resolution,[status(thm)],[172859160,172846336]),
[] ).
cnf(191368520,plain,
( in(ordered_pair(a,A),cartesian_product2(c,B))
| ~ in(A,B) ),
inference(resolution,[status(thm)],[172853416,188930464]),
[] ).
cnf(172824424,plain,
( ~ in(a,c)
| ~ in(b,d)
| ~ in(ordered_pair(a,b),cartesian_product2(c,d)) ),
inference(rewrite,[status(thm)],[t106_zfmisc_1]),
[] ).
cnf(193400520,plain,
~ in(b,d),
inference(forward_subsumption_resolution__resolution,[status(thm)],[191368520,172824424,188930464]),
[] ).
cnf(172863176,plain,
( in(B,D)
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(rewrite,[status(thm)],[l55_zfmisc_1]),
[] ).
cnf(189264576,plain,
in(b,d),
inference(resolution,[status(thm)],[172863176,172842304]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[193400520,189264576]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l55_zfmisc_1,plain,(((in(B,D)|~in(ordered_pair(A,B),cartesian_product2(C,D)))&(in(A,C)|~in(ordered_pair(A,B),cartesian_product2(C,D)))&(in(ordered_pair(A,B),cartesian_product2(C,D))|~in(A,C)|~in(B,D)))),file('/tmp/SystemOnTPTP26354/SEU165+3.p',unknown),[]).
%
% cnf(172853416,plain,(in(ordered_pair(A,B),cartesian_product2(C,D))|~in(A,C)|~in(B,D)),inference(rewrite,[status(thm)],[l55_zfmisc_1]),[]).
%
% cnf(172859160,plain,(in(A,C)|~in(ordered_pair(A,B),cartesian_product2(C,D))),inference(rewrite,[status(thm)],[l55_zfmisc_1]),[]).
%
% fof(t106_zfmisc_1,plain,(((in(ordered_pair(a,b),cartesian_product2(c,d))|in(ordered_pair(a,b),cartesian_product2(c,d))|in(a,c))&(~in(a,c)|in(ordered_pair(a,b),cartesian_product2(c,d))|in(a,c))&(in(ordered_pair(a,b),cartesian_product2(c,d))|~in(b,d)|in(a,c))&(~in(a,c)|~in(b,d)|in(a,c))&(in(ordered_pair(a,b),cartesian_product2(c,d))|in(ordered_pair(a,b),cartesian_product2(c,d))|in(b,d))&(~in(a,c)|in(ordered_pair(a,b),cartesian_product2(c,d))|in(b,d))&(in(ordered_pair(a,b),cartesian_product2(c,d))|~in(b,d)|in(b,d))&(~in(a,c)|~in(b,d)|in(b,d))&(in(ordered_pair(a,b),cartesian_product2(c,d))|in(ordered_pair(a,b),cartesian_product2(c,d))|~in(ordered_pair(a,b),cartesian_product2(c,d)))&(~in(a,c)|in(ordered_pair(a,b),cartesian_product2(c,d))|~in(ordered_pair(a,b),cartesian_product2(c,d)))&(in(ordered_pair(a,b),cartesian_product2(c,d))|~in(b,d)|~in(ordered_pair(a,b),cartesian_product2(c,d)))&(~in(a,c)|~in(b,d)|~in(ordered_pair(a,b),cartesian_product2(c,d))))),file('/tmp/SystemOnTPTP26354/SEU165+3.p',unknown),[]).
%
% cnf(172842304,plain,(in(ordered_pair(a,b),cartesian_product2(c,d))|in(b,d)),inference(rewrite,[status(thm)],[t106_zfmisc_1]),[]).
%
% cnf(172846336,plain,(in(ordered_pair(a,b),cartesian_product2(c,d))|in(a,c)),inference(rewrite__forward_subsumption_resolution,[status(thm)],[t106_zfmisc_1,172842304]),[]).
%
% cnf(188930464,plain,(in(a,c)),inference(resolution,[status(thm)],[172859160,172846336]),[]).
%
% cnf(191368520,plain,(in(ordered_pair(a,A),cartesian_product2(c,B))|~in(A,B)),inference(resolution,[status(thm)],[172853416,188930464]),[]).
%
% cnf(172824424,plain,(~in(a,c)|~in(b,d)|~in(ordered_pair(a,b),cartesian_product2(c,d))),inference(rewrite,[status(thm)],[t106_zfmisc_1]),[]).
%
% cnf(193400520,plain,(~in(b,d)),inference(forward_subsumption_resolution__resolution,[status(thm)],[191368520,172824424,188930464]),[]).
%
% cnf(172863176,plain,(in(B,D)|~in(ordered_pair(A,B),cartesian_product2(C,D))),inference(rewrite,[status(thm)],[l55_zfmisc_1]),[]).
%
% cnf(189264576,plain,(in(b,d)),inference(resolution,[status(thm)],[172863176,172842304]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[193400520,189264576]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------