TSTP Solution File: SET050-6 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET050-6 : 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 15:25:35 EDT 2009
% Result : Unsatisfiable 6.3s
% Output : Refutation 6.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% 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 : 21 ( 13 ~; 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 : 24 ( 8 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_corollary_1_to_unordered_pair_1,plain,
member(ordered_pair(x,y),cross_product(u,v)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET050-6.tptp',unknown),
[] ).
cnf(151350568,plain,
member(ordered_pair(x,y),cross_product(u,v)),
inference(rewrite,[status(thm)],[prove_corollary_1_to_unordered_pair_1]),
[] ).
fof(cartesian_product1,plain,
! [A,B,C,D] :
( ~ member(ordered_pair(A,B),cross_product(C,D))
| member(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET050-6.tptp',unknown),
[] ).
cnf(150513632,plain,
( ~ member(ordered_pair(A,B),cross_product(C,D))
| member(A,C) ),
inference(rewrite,[status(thm)],[cartesian_product1]),
[] ).
fof(class_elements_are_sets,plain,
! [A] : subclass(A,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET050-6.tptp',unknown),
[] ).
cnf(150423032,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/SET050-6.tptp',unknown),
[] ).
cnf(150392672,plain,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subclass_members]),
[] ).
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/SET050-6.tptp',unknown),
[] ).
cnf(150478520,plain,
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
inference(rewrite,[status(thm)],[unordered_pair2]),
[] ).
fof(prove_corollary_1_to_unordered_pair_2,plain,
~ member(x,unordered_pair(x,y)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET050-6.tptp',unknown),
[] ).
cnf(151355456,plain,
~ member(x,unordered_pair(x,y)),
inference(rewrite,[status(thm)],[prove_corollary_1_to_unordered_pair_2]),
[] ).
cnf(170722776,plain,
~ member(x,universal_class),
inference(resolution,[status(thm)],[150478520,151355456]),
[] ).
cnf(177418704,plain,
~ member(x,A),
inference(forward_subsumption_resolution__resolution,[status(thm)],[150423032,150392672,170722776]),
[] ).
cnf(177540176,plain,
~ member(ordered_pair(x,A),cross_product(B,C)),
inference(resolution,[status(thm)],[150513632,177418704]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[151350568,177540176]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 6 seconds
% START OF PROOF SEQUENCE
% fof(prove_corollary_1_to_unordered_pair_1,plain,(member(ordered_pair(x,y),cross_product(u,v))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET050-6.tptp',unknown),[]).
%
% cnf(151350568,plain,(member(ordered_pair(x,y),cross_product(u,v))),inference(rewrite,[status(thm)],[prove_corollary_1_to_unordered_pair_1]),[]).
%
% fof(cartesian_product1,plain,(~member(ordered_pair(A,B),cross_product(C,D))|member(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET050-6.tptp',unknown),[]).
%
% cnf(150513632,plain,(~member(ordered_pair(A,B),cross_product(C,D))|member(A,C)),inference(rewrite,[status(thm)],[cartesian_product1]),[]).
%
% fof(class_elements_are_sets,plain,(subclass(A,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET050-6.tptp',unknown),[]).
%
% cnf(150423032,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/SET050-6.tptp',unknown),[]).
%
% cnf(150392672,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
%
% fof(unordered_pair2,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET050-6.tptp',unknown),[]).
%
% cnf(150478520,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),inference(rewrite,[status(thm)],[unordered_pair2]),[]).
%
% fof(prove_corollary_1_to_unordered_pair_2,plain,(~member(x,unordered_pair(x,y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET050-6.tptp',unknown),[]).
%
% cnf(151355456,plain,(~member(x,unordered_pair(x,y))),inference(rewrite,[status(thm)],[prove_corollary_1_to_unordered_pair_2]),[]).
%
% cnf(170722776,plain,(~member(x,universal_class)),inference(resolution,[status(thm)],[150478520,151355456]),[]).
%
% cnf(177418704,plain,(~member(x,A)),inference(forward_subsumption_resolution__resolution,[status(thm)],[150423032,150392672,170722776]),[]).
%
% cnf(177540176,plain,(~member(ordered_pair(x,A),cross_product(B,C))),inference(resolution,[status(thm)],[150513632,177418704]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[151350568,177540176]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------