TSTP Solution File: SET203-6 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET203-6 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 15:30:17 EDT 2009
% Result : Unsatisfiable 0.4s
% Output : Refutation 0.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 16 ( 11 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 18 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SET203-6.tptp',unknown),
[] ).
cnf(153984464,plain,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subclass_members]),
[] ).
fof(class_elements_are_sets,plain,
! [A] : subclass(A,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET203-6.tptp',unknown),
[] ).
cnf(154015688,plain,
subclass(A,universal_class),
inference(rewrite,[status(thm)],[class_elements_are_sets]),
[] ).
cnf(168999928,plain,
( ~ member(B,A)
| member(B,universal_class) ),
inference(resolution,[status(thm)],[153984464,154015688]),
[] ).
fof(prove_corollary_to_X_product_property1_1,plain,
member(u,x),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET203-6.tptp',unknown),
[] ).
cnf(155182032,plain,
member(u,x),
inference(rewrite,[status(thm)],[prove_corollary_to_X_product_property1_1]),
[] ).
cnf(171404688,plain,
member(u,universal_class),
inference(resolution,[status(thm)],[168999928,155182032]),
[] ).
fof(prove_corollary_to_X_product_property1_2,plain,
member(v,y),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET203-6.tptp',unknown),
[] ).
cnf(155185792,plain,
member(v,y),
inference(rewrite,[status(thm)],[prove_corollary_to_X_product_property1_2]),
[] ).
cnf(171414136,plain,
member(v,universal_class),
inference(resolution,[status(thm)],[168999928,155185792]),
[] ).
fof(cartesian_product3,plain,
! [A,B,C,D] :
( ~ member(A,B)
| ~ member(C,D)
| member(ordered_pair(A,C),cross_product(B,D)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET203-6.tptp',unknown),
[] ).
cnf(154128928,plain,
( ~ member(A,B)
| ~ member(C,D)
| member(ordered_pair(A,C),cross_product(B,D)) ),
inference(rewrite,[status(thm)],[cartesian_product3]),
[] ).
fof(prove_corollary_to_X_product_property1_3,plain,
~ member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET203-6.tptp',unknown),
[] ).
cnf(155189696,plain,
~ member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
inference(rewrite,[status(thm)],[prove_corollary_to_X_product_property1_3]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[171404688,171414136,154128928,155189696]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(subclass_members,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET203-6.tptp',unknown),[]).
%
% cnf(153984464,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
%
% fof(class_elements_are_sets,plain,(subclass(A,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET203-6.tptp',unknown),[]).
%
% cnf(154015688,plain,(subclass(A,universal_class)),inference(rewrite,[status(thm)],[class_elements_are_sets]),[]).
%
% cnf(168999928,plain,(~member(B,A)|member(B,universal_class)),inference(resolution,[status(thm)],[153984464,154015688]),[]).
%
% fof(prove_corollary_to_X_product_property1_1,plain,(member(u,x)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET203-6.tptp',unknown),[]).
%
% cnf(155182032,plain,(member(u,x)),inference(rewrite,[status(thm)],[prove_corollary_to_X_product_property1_1]),[]).
%
% cnf(171404688,plain,(member(u,universal_class)),inference(resolution,[status(thm)],[168999928,155182032]),[]).
%
% fof(prove_corollary_to_X_product_property1_2,plain,(member(v,y)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET203-6.tptp',unknown),[]).
%
% cnf(155185792,plain,(member(v,y)),inference(rewrite,[status(thm)],[prove_corollary_to_X_product_property1_2]),[]).
%
% cnf(171414136,plain,(member(v,universal_class)),inference(resolution,[status(thm)],[168999928,155185792]),[]).
%
% fof(cartesian_product3,plain,(~member(A,B)|~member(C,D)|member(ordered_pair(A,C),cross_product(B,D))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET203-6.tptp',unknown),[]).
%
% cnf(154128928,plain,(~member(A,B)|~member(C,D)|member(ordered_pair(A,C),cross_product(B,D))),inference(rewrite,[status(thm)],[cartesian_product3]),[]).
%
% fof(prove_corollary_to_X_product_property1_3,plain,(~member(ordered_pair(u,v),cross_product(universal_class,universal_class))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET203-6.tptp',unknown),[]).
%
% cnf(155189696,plain,(~member(ordered_pair(u,v),cross_product(universal_class,universal_class))),inference(rewrite,[status(thm)],[prove_corollary_to_X_product_property1_3]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[171404688,171414136,154128928,155189696]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------