TSTP Solution File: SET977+1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET977+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 15:43:11 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 60 ( 28 ~; 24 |; 8 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 11 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t129_zfmisc_1,plain,
! [D,B,A,C] :
( ( $equal(D,B)
| ~ in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) )
& ( in(A,C)
| ~ in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) )
& ( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
| ~ in(A,C)
| ~ $equal(D,B) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET977+1.tptp',unknown),
[] ).
cnf(159954888,plain,
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
| ~ in(A,C)
| ~ $equal(D,B) ),
inference(rewrite,[status(thm)],[t129_zfmisc_1]),
[] ).
fof(t128_zfmisc_1,plain,
! [B,D,A,C] :
( ( in(B,D)
| ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) )
& ( $equal(C,A)
| ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) )
& ( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
| ~ $equal(C,A)
| ~ in(B,D) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET977+1.tptp',unknown),
[] ).
cnf(159931680,plain,
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
| ~ $equal(C,A)
| ~ in(B,D) ),
inference(rewrite,[status(thm)],[t128_zfmisc_1]),
[] ).
fof(d1_xboole_0,plain,
! [A,B] :
( ( ~ $equal(empty_set,A)
| ~ in(B,A) )
& ( $equal(empty_set,A)
| in(b(A,B),A) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET977+1.tptp',unknown),
[] ).
cnf(159879928,plain,
( $equal(empty_set,A)
| in(b(A,B),A) ),
inference(rewrite,[status(thm)],[d1_xboole_0]),
[] ).
fof(t130_zfmisc_1,plain,
( ( ~ $equal(empty_set,a)
| $equal(cartesian_product2(a,singleton(b)),empty_set) )
& ( $equal(cartesian_product2(singleton(b),a),empty_set)
| $equal(cartesian_product2(a,singleton(b)),empty_set) )
& ( ~ $equal(empty_set,a)
| ~ $equal(empty_set,a) )
& ( $equal(cartesian_product2(singleton(b),a),empty_set)
| ~ $equal(empty_set,a) ) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET977+1.tptp',unknown),
[] ).
cnf(160051024,plain,
~ $equal(empty_set,a),
inference(rewrite,[status(thm)],[t130_zfmisc_1]),
[] ).
cnf(173147968,plain,
in(b(a,A),a),
inference(resolution,[status(thm)],[159879928,160051024]),
[] ).
cnf(173249504,plain,
( in(ordered_pair(A,b(a,C)),cartesian_product2(singleton(B),a))
| ~ $equal(B,A) ),
inference(resolution,[status(thm)],[159931680,173147968]),
[] ).
cnf(177246824,plain,
in(ordered_pair(A,b(a,B)),cartesian_product2(singleton(A),a)),
inference(equality_resolution,[status(thm)],[173249504]),
[] ).
cnf(159886520,plain,
( ~ $equal(empty_set,A)
| ~ in(B,A) ),
inference(rewrite,[status(thm)],[d1_xboole_0]),
[] ).
cnf(173690528,plain,
~ in(A,empty_set),
inference(equality_resolution,[status(thm)],[159886520]),
[] ).
cnf(160055832,plain,
( $equal(cartesian_product2(singleton(b),a),empty_set)
| $equal(cartesian_product2(a,singleton(b)),empty_set) ),
inference(rewrite,[status(thm)],[t130_zfmisc_1]),
[] ).
cnf(173752720,plain,
( ~ in(A,cartesian_product2(singleton(b),a))
| $equal(cartesian_product2(a,singleton(b)),empty_set) ),
inference(paramodulation,[status(thm)],[173690528,160055832,theory(equality)]),
[] ).
cnf(177768968,plain,
$equal(cartesian_product2(a,singleton(b)),empty_set),
inference(resolution,[status(thm)],[177246824,173752720]),
[] ).
cnf(177864848,plain,
~ in(A,cartesian_product2(a,singleton(b))),
inference(paramodulation,[status(thm)],[177768968,173690528,theory(equality)]),
[] ).
cnf(179019328,plain,
( ~ in(A,a)
| ~ $equal(b,B) ),
inference(resolution,[status(thm)],[159954888,177864848]),
[] ).
cnf(179249256,plain,
~ in(A,a),
inference(equality_resolution,[status(thm)],[179019328]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[179249256,173147968]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t129_zfmisc_1,plain,((($equal(D,B)|~in(ordered_pair(A,B),cartesian_product2(C,singleton(D))))&(in(A,C)|~in(ordered_pair(A,B),cartesian_product2(C,singleton(D))))&(in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))|~in(A,C)|~$equal(D,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET977+1.tptp',unknown),[]).
%
% cnf(159954888,plain,(in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))|~in(A,C)|~$equal(D,B)),inference(rewrite,[status(thm)],[t129_zfmisc_1]),[]).
%
% fof(t128_zfmisc_1,plain,(((in(B,D)|~in(ordered_pair(A,B),cartesian_product2(singleton(C),D)))&($equal(C,A)|~in(ordered_pair(A,B),cartesian_product2(singleton(C),D)))&(in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|~$equal(C,A)|~in(B,D)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET977+1.tptp',unknown),[]).
%
% cnf(159931680,plain,(in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|~$equal(C,A)|~in(B,D)),inference(rewrite,[status(thm)],[t128_zfmisc_1]),[]).
%
% fof(d1_xboole_0,plain,(((~$equal(empty_set,A)|~in(B,A))&($equal(empty_set,A)|in(b(A,B),A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET977+1.tptp',unknown),[]).
%
% cnf(159879928,plain,($equal(empty_set,A)|in(b(A,B),A)),inference(rewrite,[status(thm)],[d1_xboole_0]),[]).
%
% fof(t130_zfmisc_1,plain,(((~$equal(empty_set,a)|$equal(cartesian_product2(a,singleton(b)),empty_set))&($equal(cartesian_product2(singleton(b),a),empty_set)|$equal(cartesian_product2(a,singleton(b)),empty_set))&(~$equal(empty_set,a)|~$equal(empty_set,a))&($equal(cartesian_product2(singleton(b),a),empty_set)|~$equal(empty_set,a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET977+1.tptp',unknown),[]).
%
% cnf(160051024,plain,(~$equal(empty_set,a)),inference(rewrite,[status(thm)],[t130_zfmisc_1]),[]).
%
% cnf(173147968,plain,(in(b(a,A),a)),inference(resolution,[status(thm)],[159879928,160051024]),[]).
%
% cnf(173249504,plain,(in(ordered_pair(A,b(a,C)),cartesian_product2(singleton(B),a))|~$equal(B,A)),inference(resolution,[status(thm)],[159931680,173147968]),[]).
%
% cnf(177246824,plain,(in(ordered_pair(A,b(a,B)),cartesian_product2(singleton(A),a))),inference(equality_resolution,[status(thm)],[173249504]),[]).
%
% cnf(159886520,plain,(~$equal(empty_set,A)|~in(B,A)),inference(rewrite,[status(thm)],[d1_xboole_0]),[]).
%
% cnf(173690528,plain,(~in(A,empty_set)),inference(equality_resolution,[status(thm)],[159886520]),[]).
%
% cnf(160055832,plain,($equal(cartesian_product2(singleton(b),a),empty_set)|$equal(cartesian_product2(a,singleton(b)),empty_set)),inference(rewrite,[status(thm)],[t130_zfmisc_1]),[]).
%
% cnf(173752720,plain,(~in(A,cartesian_product2(singleton(b),a))|$equal(cartesian_product2(a,singleton(b)),empty_set)),inference(paramodulation,[status(thm)],[173690528,160055832,theory(equality)]),[]).
%
% cnf(177768968,plain,($equal(cartesian_product2(a,singleton(b)),empty_set)),inference(resolution,[status(thm)],[177246824,173752720]),[]).
%
% cnf(177864848,plain,(~in(A,cartesian_product2(a,singleton(b)))),inference(paramodulation,[status(thm)],[177768968,173690528,theory(equality)]),[]).
%
% cnf(179019328,plain,(~in(A,a)|~$equal(b,B)),inference(resolution,[status(thm)],[159954888,177864848]),[]).
%
% cnf(179249256,plain,(~in(A,a)),inference(equality_resolution,[status(thm)],[179019328]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[179249256,173147968]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------