%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SEU167+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 15:50:37 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 12 ~; 9 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t118_zfmisc_1,plain,
! [C,A,B] :
( ( subset(cartesian_product2(C,A),cartesian_product2(C,B))
| ~ subset(A,B) )
& ( subset(cartesian_product2(A,C),cartesian_product2(B,C))
| ~ subset(A,B) ) ),
file('/tmp/SystemOnTPTP4402/SEU167+1.p',unknown),
[] ).
cnf(172028752,plain,
( subset(cartesian_product2(C,A),cartesian_product2(C,B))
| ~ subset(A,B) ),
inference(rewrite,[status(thm)],[t118_zfmisc_1]),
[] ).
fof(t119_zfmisc_1,plain,
( subset(a,b)
& subset(c,d)
& ~ subset(cartesian_product2(a,c),cartesian_product2(b,d)) ),
file('/tmp/SystemOnTPTP4402/SEU167+1.p',unknown),
[] ).
cnf(172106176,plain,
subset(c,d),
inference(rewrite,[status(thm)],[t119_zfmisc_1]),
[] ).
cnf(185372432,plain,
subset(cartesian_product2(A,c),cartesian_product2(A,d)),
inference(resolution,[status(thm)],[172028752,172106176]),
[] ).
fof(t1_xboole_1,plain,
! [A,B,C] :
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
file('/tmp/SystemOnTPTP4402/SEU167+1.p',unknown),
[] ).
cnf(172120192,plain,
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(rewrite,[status(thm)],[t1_xboole_1]),
[] ).
cnf(172094824,plain,
~ subset(cartesian_product2(a,c),cartesian_product2(b,d)),
inference(rewrite,[status(thm)],[t119_zfmisc_1]),
[] ).
cnf(185250456,plain,
( ~ subset(cartesian_product2(a,c),A)
| ~ subset(A,cartesian_product2(b,d)) ),
inference(resolution,[status(thm)],[172120192,172094824]),
[] ).
cnf(172018888,plain,
( subset(cartesian_product2(A,C),cartesian_product2(B,C))
| ~ subset(A,B) ),
inference(rewrite,[status(thm)],[t118_zfmisc_1]),
[] ).
cnf(172113168,plain,
subset(a,b),
inference(rewrite,[status(thm)],[t119_zfmisc_1]),
[] ).
cnf(185157224,plain,
subset(cartesian_product2(a,A),cartesian_product2(b,A)),
inference(resolution,[status(thm)],[172018888,172113168]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[185372432,185250456,185157224]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t118_zfmisc_1,plain,(((subset(cartesian_product2(C,A),cartesian_product2(C,B))|~subset(A,B))&(subset(cartesian_product2(A,C),cartesian_product2(B,C))|~subset(A,B)))),file('/tmp/SystemOnTPTP4402/SEU167+1.p',unknown),[]).
%
% cnf(172028752,plain,(subset(cartesian_product2(C,A),cartesian_product2(C,B))|~subset(A,B)),inference(rewrite,[status(thm)],[t118_zfmisc_1]),[]).
%
% fof(t119_zfmisc_1,plain,((subset(a,b)&subset(c,d)&~subset(cartesian_product2(a,c),cartesian_product2(b,d)))),file('/tmp/SystemOnTPTP4402/SEU167+1.p',unknown),[]).
%
% cnf(172106176,plain,(subset(c,d)),inference(rewrite,[status(thm)],[t119_zfmisc_1]),[]).
%
% cnf(185372432,plain,(subset(cartesian_product2(A,c),cartesian_product2(A,d))),inference(resolution,[status(thm)],[172028752,172106176]),[]).
%
% fof(t1_xboole_1,plain,(~subset(A,B)|~subset(B,C)|subset(A,C)),file('/tmp/SystemOnTPTP4402/SEU167+1.p',unknown),[]).
%
% cnf(172120192,plain,(~subset(A,B)|~subset(B,C)|subset(A,C)),inference(rewrite,[status(thm)],[t1_xboole_1]),[]).
%
% cnf(172094824,plain,(~subset(cartesian_product2(a,c),cartesian_product2(b,d))),inference(rewrite,[status(thm)],[t119_zfmisc_1]),[]).
%
% cnf(185250456,plain,(~subset(cartesian_product2(a,c),A)|~subset(A,cartesian_product2(b,d))),inference(resolution,[status(thm)],[172120192,172094824]),[]).
%
% cnf(172018888,plain,(subset(cartesian_product2(A,C),cartesian_product2(B,C))|~subset(A,B)),inference(rewrite,[status(thm)],[t118_zfmisc_1]),[]).
%
% cnf(172113168,plain,(subset(a,b)),inference(rewrite,[status(thm)],[t119_zfmisc_1]),[]).
%
% cnf(185157224,plain,(subset(cartesian_product2(a,A),cartesian_product2(b,A))),inference(resolution,[status(thm)],[172018888,172113168]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[185372432,185250456,185157224]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------