%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SEU162+3 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 15:50:17 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 4 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 41 ( 18 ~; 19 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t83_xboole_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| $equal(set_difference(A,B),A) )
& ( disjoint(A,B)
| ~ $equal(set_difference(A,B),A) ) ),
file('/tmp/SystemOnTPTP10469/SEU162+3.p',unknown),
[] ).
cnf(153814616,plain,
( ~ disjoint(A,B)
| $equal(set_difference(A,B),A) ),
inference(rewrite,[status(thm)],[t83_xboole_1]),
[] ).
fof(symmetry_r1_xboole_0,plain,
! [A,B] :
( ~ disjoint(A,B)
| disjoint(B,A) ),
file('/tmp/SystemOnTPTP10469/SEU162+3.p',unknown),
[] ).
cnf(153714064,plain,
( ~ disjoint(A,B)
| disjoint(B,A) ),
inference(rewrite,[status(thm)],[symmetry_r1_xboole_0]),
[] ).
fof(l28_zfmisc_1,plain,
! [A,B] :
( in(A,B)
| disjoint(singleton(A),B) ),
file('/tmp/SystemOnTPTP10469/SEU162+3.p',unknown),
[] ).
cnf(153695112,plain,
( in(A,B)
| disjoint(singleton(A),B) ),
inference(rewrite,[status(thm)],[l28_zfmisc_1]),
[] ).
cnf(164251816,plain,
( disjoint(A,singleton(B))
| in(B,A) ),
inference(resolution,[status(thm)],[153714064,153695112]),
[] ).
cnf(164501360,plain,
( $equal(set_difference(A,singleton(B)),A)
| in(B,A) ),
inference(resolution,[status(thm)],[153814616,164251816]),
[] ).
fof(t65_zfmisc_1,plain,
( ( ~ in(b,a)
| $equal(set_difference(a,singleton(b)),a) )
& ( ~ $equal(set_difference(a,singleton(b)),a)
| $equal(set_difference(a,singleton(b)),a) )
& ( ~ in(b,a)
| in(b,a) )
& ( ~ $equal(set_difference(a,singleton(b)),a)
| in(b,a) ) ),
file('/tmp/SystemOnTPTP10469/SEU162+3.p',unknown),
[] ).
cnf(153795200,plain,
( ~ in(b,a)
| $equal(set_difference(a,singleton(b)),a) ),
inference(rewrite,[status(thm)],[t65_zfmisc_1]),
[] ).
cnf(165438200,plain,
$equal(set_difference(a,singleton(b)),a),
inference(resolution,[status(thm)],[164501360,153795200]),
[] ).
cnf(153789208,plain,
( ~ $equal(set_difference(a,singleton(b)),a)
| in(b,a) ),
inference(rewrite,[status(thm)],[t65_zfmisc_1]),
[] ).
cnf(165429664,plain,
in(b,a),
inference(resolution,[status(thm)],[164501360,153789208]),
[] ).
fof(l25_zfmisc_1,plain,
! [A,B] :
( ~ disjoint(singleton(A),B)
| ~ in(A,B) ),
file('/tmp/SystemOnTPTP10469/SEU162+3.p',unknown),
[] ).
cnf(153688496,plain,
( ~ disjoint(singleton(A),B)
| ~ in(A,B) ),
inference(rewrite,[status(thm)],[l25_zfmisc_1]),
[] ).
cnf(165493008,plain,
~ disjoint(singleton(b),a),
inference(resolution,[status(thm)],[165429664,153688496]),
[] ).
cnf(153805648,plain,
( disjoint(A,B)
| ~ $equal(set_difference(A,B),A) ),
inference(rewrite,[status(thm)],[t83_xboole_1]),
[] ).
cnf(164430656,plain,
( ~ $equal(set_difference(A,B),A)
| disjoint(B,A) ),
inference(resolution,[status(thm)],[153805648,153714064]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[165438200,165493008,164430656]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t83_xboole_1,plain,(((~disjoint(A,B)|$equal(set_difference(A,B),A))&(disjoint(A,B)|~$equal(set_difference(A,B),A)))),file('/tmp/SystemOnTPTP10469/SEU162+3.p',unknown),[]).
%
% cnf(153814616,plain,(~disjoint(A,B)|$equal(set_difference(A,B),A)),inference(rewrite,[status(thm)],[t83_xboole_1]),[]).
%
% fof(symmetry_r1_xboole_0,plain,(~disjoint(A,B)|disjoint(B,A)),file('/tmp/SystemOnTPTP10469/SEU162+3.p',unknown),[]).
%
% cnf(153714064,plain,(~disjoint(A,B)|disjoint(B,A)),inference(rewrite,[status(thm)],[symmetry_r1_xboole_0]),[]).
%
% fof(l28_zfmisc_1,plain,(in(A,B)|disjoint(singleton(A),B)),file('/tmp/SystemOnTPTP10469/SEU162+3.p',unknown),[]).
%
% cnf(153695112,plain,(in(A,B)|disjoint(singleton(A),B)),inference(rewrite,[status(thm)],[l28_zfmisc_1]),[]).
%
% cnf(164251816,plain,(disjoint(A,singleton(B))|in(B,A)),inference(resolution,[status(thm)],[153714064,153695112]),[]).
%
% cnf(164501360,plain,($equal(set_difference(A,singleton(B)),A)|in(B,A)),inference(resolution,[status(thm)],[153814616,164251816]),[]).
%
% fof(t65_zfmisc_1,plain,(((~in(b,a)|$equal(set_difference(a,singleton(b)),a))&(~$equal(set_difference(a,singleton(b)),a)|$equal(set_difference(a,singleton(b)),a))&(~in(b,a)|in(b,a))&(~$equal(set_difference(a,singleton(b)),a)|in(b,a)))),file('/tmp/SystemOnTPTP10469/SEU162+3.p',unknown),[]).
%
% cnf(153795200,plain,(~in(b,a)|$equal(set_difference(a,singleton(b)),a)),inference(rewrite,[status(thm)],[t65_zfmisc_1]),[]).
%
% cnf(165438200,plain,($equal(set_difference(a,singleton(b)),a)),inference(resolution,[status(thm)],[164501360,153795200]),[]).
%
% cnf(153789208,plain,(~$equal(set_difference(a,singleton(b)),a)|in(b,a)),inference(rewrite,[status(thm)],[t65_zfmisc_1]),[]).
%
% cnf(165429664,plain,(in(b,a)),inference(resolution,[status(thm)],[164501360,153789208]),[]).
%
% fof(l25_zfmisc_1,plain,(~disjoint(singleton(A),B)|~in(A,B)),file('/tmp/SystemOnTPTP10469/SEU162+3.p',unknown),[]).
%
% cnf(153688496,plain,(~disjoint(singleton(A),B)|~in(A,B)),inference(rewrite,[status(thm)],[l25_zfmisc_1]),[]).
%
% cnf(165493008,plain,(~disjoint(singleton(b),a)),inference(resolution,[status(thm)],[165429664,153688496]),[]).
%
% cnf(153805648,plain,(disjoint(A,B)|~$equal(set_difference(A,B),A)),inference(rewrite,[status(thm)],[t83_xboole_1]),[]).
%
% cnf(164430656,plain,(~$equal(set_difference(A,B),A)|disjoint(B,A)),inference(resolution,[status(thm)],[153805648,153714064]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[165438200,165493008,164430656]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------