%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET051-6 : TPTP v3.4.2. Bugfixed v2.1.0.
% 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 15:25:37 EDT 2009
% Result : Unsatisfiable 6.6s
% Output : Refutation 6.6s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 16 ( 10 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 21 ( 5 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cartesian_product2,plain,
! [A,B,C,D] :
( ~ member(ordered_pair(A,B),cross_product(C,D))
| member(B,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET051-6.tptp',unknown),
[] ).
cnf(153391680,plain,
( ~ member(ordered_pair(A,B),cross_product(C,D))
| member(B,D) ),
inference(rewrite,[status(thm)],[cartesian_product2]),
[] ).
fof(prove_corollary_2_to_unordered_pair_1,plain,
member(ordered_pair(x,y),cross_product(u,v)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET051-6.tptp',unknown),
[] ).
cnf(154219408,plain,
member(ordered_pair(x,y),cross_product(u,v)),
inference(rewrite,[status(thm)],[prove_corollary_2_to_unordered_pair_1]),
[] ).
cnf(293987352,plain,
member(y,v),
inference(resolution,[status(thm)],[153391680,154219408]),
[] ).
fof(class_elements_are_sets,plain,
! [A] : subclass(A,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET051-6.tptp',unknown),
[] ).
cnf(153291872,plain,
subclass(A,universal_class),
inference(rewrite,[status(thm)],[class_elements_are_sets]),
[] ).
fof(subclass_members,plain,
! [A,B,C] :
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET051-6.tptp',unknown),
[] ).
cnf(153261512,plain,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subclass_members]),
[] ).
fof(unordered_pair3,plain,
! [A,B] :
( ~ member(A,universal_class)
| member(A,unordered_pair(B,A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET051-6.tptp',unknown),
[] ).
cnf(153352976,plain,
( ~ member(A,universal_class)
| member(A,unordered_pair(B,A)) ),
inference(rewrite,[status(thm)],[unordered_pair3]),
[] ).
fof(prove_corollary_2_to_unordered_pair_2,plain,
~ member(y,unordered_pair(x,y)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET051-6.tptp',unknown),
[] ).
cnf(154224296,plain,
~ member(y,unordered_pair(x,y)),
inference(rewrite,[status(thm)],[prove_corollary_2_to_unordered_pair_2]),
[] ).
cnf(174423688,plain,
~ member(y,universal_class),
inference(resolution,[status(thm)],[153352976,154224296]),
[] ).
cnf(178954384,plain,
~ member(y,A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[153291872,153261512,174423688]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[293987352,178954384]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 6 seconds
% START OF PROOF SEQUENCE
% fof(cartesian_product2,plain,(~member(ordered_pair(A,B),cross_product(C,D))|member(B,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET051-6.tptp',unknown),[]).
%
% cnf(153391680,plain,(~member(ordered_pair(A,B),cross_product(C,D))|member(B,D)),inference(rewrite,[status(thm)],[cartesian_product2]),[]).
%
% fof(prove_corollary_2_to_unordered_pair_1,plain,(member(ordered_pair(x,y),cross_product(u,v))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET051-6.tptp',unknown),[]).
%
% cnf(154219408,plain,(member(ordered_pair(x,y),cross_product(u,v))),inference(rewrite,[status(thm)],[prove_corollary_2_to_unordered_pair_1]),[]).
%
% cnf(293987352,plain,(member(y,v)),inference(resolution,[status(thm)],[153391680,154219408]),[]).
%
% fof(class_elements_are_sets,plain,(subclass(A,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET051-6.tptp',unknown),[]).
%
% cnf(153291872,plain,(subclass(A,universal_class)),inference(rewrite,[status(thm)],[class_elements_are_sets]),[]).
%
% fof(subclass_members,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET051-6.tptp',unknown),[]).
%
% cnf(153261512,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
%
% fof(unordered_pair3,plain,(~member(A,universal_class)|member(A,unordered_pair(B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET051-6.tptp',unknown),[]).
%
% cnf(153352976,plain,(~member(A,universal_class)|member(A,unordered_pair(B,A))),inference(rewrite,[status(thm)],[unordered_pair3]),[]).
%
% fof(prove_corollary_2_to_unordered_pair_2,plain,(~member(y,unordered_pair(x,y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET051-6.tptp',unknown),[]).
%
% cnf(154224296,plain,(~member(y,unordered_pair(x,y))),inference(rewrite,[status(thm)],[prove_corollary_2_to_unordered_pair_2]),[]).
%
% cnf(174423688,plain,(~member(y,universal_class)),inference(resolution,[status(thm)],[153352976,154224296]),[]).
%
% cnf(178954384,plain,(~member(y,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[153291872,153261512,174423688]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[293987352,178954384]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------