TSTP Solution File: SET024-6 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET024-6 : TPTP v3.4.2. Bugfixed v2.1.0.
% 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 15:24:24 EDT 2009
% Result : Unsatisfiable 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 8 unt; 0 def)
% Number of atoms : 12 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 1 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_set_in_its_singleton_1,plain,
member(x,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET024-6.tptp',unknown),
[] ).
cnf(149195816,plain,
member(x,universal_class),
inference(rewrite,[status(thm)],[prove_set_in_its_singleton_1]),
[] ).
fof(unordered_pair2,plain,
! [A,B] :
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET024-6.tptp',unknown),
[] ).
cnf(149284840,plain,
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
inference(rewrite,[status(thm)],[unordered_pair2]),
[] ).
fof(prove_set_in_its_singleton_2,plain,
~ member(x,singleton(x)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET024-6.tptp',unknown),
[] ).
cnf(150144728,plain,
~ member(x,singleton(x)),
inference(rewrite,[status(thm)],[prove_set_in_its_singleton_2]),
[] ).
fof(singleton_set,plain,
! [A] : $equal(singleton(A),unordered_pair(A,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET024-6.tptp',unknown),
[] ).
cnf(149308112,plain,
$equal(singleton(A),unordered_pair(A,A)),
inference(rewrite,[status(thm)],[singleton_set]),
[] ).
cnf(162168832,plain,
~ member(x,unordered_pair(x,x)),
inference(paramodulation,[status(thm)],[150144728,149308112,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[149195816,149284840,162168832]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_set_in_its_singleton_1,plain,(member(x,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET024-6.tptp',unknown),[]).
%
% cnf(149195816,plain,(member(x,universal_class)),inference(rewrite,[status(thm)],[prove_set_in_its_singleton_1]),[]).
%
% fof(unordered_pair2,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET024-6.tptp',unknown),[]).
%
% cnf(149284840,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),inference(rewrite,[status(thm)],[unordered_pair2]),[]).
%
% fof(prove_set_in_its_singleton_2,plain,(~member(x,singleton(x))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET024-6.tptp',unknown),[]).
%
% cnf(150144728,plain,(~member(x,singleton(x))),inference(rewrite,[status(thm)],[prove_set_in_its_singleton_2]),[]).
%
% fof(singleton_set,plain,($equal(singleton(A),unordered_pair(A,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET024-6.tptp',unknown),[]).
%
% cnf(149308112,plain,($equal(singleton(A),unordered_pair(A,A))),inference(rewrite,[status(thm)],[singleton_set]),[]).
%
% cnf(162168832,plain,(~member(x,unordered_pair(x,x))),inference(paramodulation,[status(thm)],[150144728,149308112,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[149195816,149284840,162168832]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------