TSTP Solution File: SET971+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET971+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 15:43:02 EDT 2009
% Result : Theorem 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 12 unt; 0 def)
% Number of atoms : 19 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 2 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t28_xboole_1,plain,
! [A,B] :
( ~ subset(A,B)
| $equal(set_intersection2(A,B),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET971+1.tptp',unknown),
[] ).
cnf(141454592,plain,
( ~ subset(A,B)
| $equal(set_intersection2(A,B),A) ),
inference(rewrite,[status(thm)],[t28_xboole_1]),
[] ).
fof(t124_zfmisc_1,plain,
( subset(a,b)
& subset(c,d)
& ~ $equal(set_intersection2(cartesian_product2(a,d),cartesian_product2(b,c)),cartesian_product2(a,c)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET971+1.tptp',unknown),
[] ).
cnf(141441392,plain,
subset(c,d),
inference(rewrite,[status(thm)],[t124_zfmisc_1]),
[] ).
cnf(154547112,plain,
$equal(set_intersection2(c,d),c),
inference(resolution,[status(thm)],[141454592,141441392]),
[] ).
fof(commutativity_k3_xboole_0,plain,
! [B,A] : $equal(set_intersection2(B,A),set_intersection2(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET971+1.tptp',unknown),
[] ).
cnf(141292920,plain,
$equal(set_intersection2(B,A),set_intersection2(A,B)),
inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),
[] ).
cnf(154689032,plain,
$equal(c,set_intersection2(d,c)),
inference(paramodulation,[status(thm)],[154547112,141292920,theory(equality)]),
[] ).
fof(t123_zfmisc_1,plain,
! [A,C,B,D] : $equal(set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),cartesian_product2(set_intersection2(A,B),set_intersection2(C,D))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET971+1.tptp',unknown),
[] ).
cnf(141345448,plain,
$equal(set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),cartesian_product2(set_intersection2(A,B),set_intersection2(C,D))),
inference(rewrite,[status(thm)],[t123_zfmisc_1]),
[] ).
cnf(155127704,plain,
$equal(set_intersection2(cartesian_product2(A,d),cartesian_product2(B,c)),cartesian_product2(set_intersection2(A,B),c)),
inference(paramodulation,[status(thm)],[154689032,141345448,theory(equality)]),
[] ).
cnf(141433960,plain,
~ $equal(set_intersection2(cartesian_product2(a,d),cartesian_product2(b,c)),cartesian_product2(a,c)),
inference(rewrite,[status(thm)],[t124_zfmisc_1]),
[] ).
cnf(141448368,plain,
subset(a,b),
inference(rewrite,[status(thm)],[t124_zfmisc_1]),
[] ).
cnf(154528560,plain,
$equal(set_intersection2(a,b),a),
inference(resolution,[status(thm)],[141454592,141448368]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[155127704,141433960,154528560,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t28_xboole_1,plain,(~subset(A,B)|$equal(set_intersection2(A,B),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET971+1.tptp',unknown),[]).
%
% cnf(141454592,plain,(~subset(A,B)|$equal(set_intersection2(A,B),A)),inference(rewrite,[status(thm)],[t28_xboole_1]),[]).
%
% fof(t124_zfmisc_1,plain,((subset(a,b)&subset(c,d)&~$equal(set_intersection2(cartesian_product2(a,d),cartesian_product2(b,c)),cartesian_product2(a,c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET971+1.tptp',unknown),[]).
%
% cnf(141441392,plain,(subset(c,d)),inference(rewrite,[status(thm)],[t124_zfmisc_1]),[]).
%
% cnf(154547112,plain,($equal(set_intersection2(c,d),c)),inference(resolution,[status(thm)],[141454592,141441392]),[]).
%
% fof(commutativity_k3_xboole_0,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET971+1.tptp',unknown),[]).
%
% cnf(141292920,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),[]).
%
% cnf(154689032,plain,($equal(c,set_intersection2(d,c))),inference(paramodulation,[status(thm)],[154547112,141292920,theory(equality)]),[]).
%
% fof(t123_zfmisc_1,plain,($equal(set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET971+1.tptp',unknown),[]).
%
% cnf(141345448,plain,($equal(set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)))),inference(rewrite,[status(thm)],[t123_zfmisc_1]),[]).
%
% cnf(155127704,plain,($equal(set_intersection2(cartesian_product2(A,d),cartesian_product2(B,c)),cartesian_product2(set_intersection2(A,B),c))),inference(paramodulation,[status(thm)],[154689032,141345448,theory(equality)]),[]).
%
% cnf(141433960,plain,(~$equal(set_intersection2(cartesian_product2(a,d),cartesian_product2(b,c)),cartesian_product2(a,c))),inference(rewrite,[status(thm)],[t124_zfmisc_1]),[]).
%
% cnf(141448368,plain,(subset(a,b)),inference(rewrite,[status(thm)],[t124_zfmisc_1]),[]).
%
% cnf(154528560,plain,($equal(set_intersection2(a,b),a)),inference(resolution,[status(thm)],[141454592,141448368]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[155127704,141433960,154528560,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------