TSTP Solution File: SET239-6 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET239-6 : 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 15:30:37 EDT 2009
% Result : Unsatisfiable 2.2s
% Output : Refutation 2.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 9 unt; 0 def)
% Number of atoms : 13 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 6 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 15 ( 4 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(intersection1,plain,
! [A,B,C] :
( ~ member(A,intersection(B,C))
| member(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET239-6.tptp',unknown),
[] ).
cnf(175094888,plain,
( ~ member(A,intersection(B,C))
| member(A,B) ),
inference(rewrite,[status(thm)],[intersection1]),
[] ).
fof(prove_restriction_alternate_defn2_2,plain,
~ member(z,xr),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET239-6.tptp',unknown),
[] ).
cnf(176109128,plain,
~ member(z,xr),
inference(rewrite,[status(thm)],[prove_restriction_alternate_defn2_2]),
[] ).
cnf(197759096,plain,
~ member(z,intersection(xr,A)),
inference(resolution,[status(thm)],[175094888,176109128]),
[] ).
fof(restriction1,plain,
! [A,B,C] : $equal(intersection(A,cross_product(B,C)),restrict(A,B,C)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET239-6.tptp',unknown),
[] ).
cnf(175149440,plain,
$equal(intersection(A,cross_product(B,C)),restrict(A,B,C)),
inference(rewrite,[status(thm)],[restriction1]),
[] ).
cnf(210478080,plain,
~ member(z,restrict(xr,A,B)),
inference(paramodulation,[status(thm)],[197759096,175149440,theory(equality)]),
[] ).
fof(prove_restriction_alternate_defn2_1,plain,
member(z,restrict(xr,x,y)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET239-6.tptp',unknown),
[] ).
cnf(176100800,plain,
member(z,restrict(xr,x,y)),
inference(rewrite,[status(thm)],[prove_restriction_alternate_defn2_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[210478080,176100800]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(intersection1,plain,(~member(A,intersection(B,C))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET239-6.tptp',unknown),[]).
%
% cnf(175094888,plain,(~member(A,intersection(B,C))|member(A,B)),inference(rewrite,[status(thm)],[intersection1]),[]).
%
% fof(prove_restriction_alternate_defn2_2,plain,(~member(z,xr)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET239-6.tptp',unknown),[]).
%
% cnf(176109128,plain,(~member(z,xr)),inference(rewrite,[status(thm)],[prove_restriction_alternate_defn2_2]),[]).
%
% cnf(197759096,plain,(~member(z,intersection(xr,A))),inference(resolution,[status(thm)],[175094888,176109128]),[]).
%
% fof(restriction1,plain,($equal(intersection(A,cross_product(B,C)),restrict(A,B,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET239-6.tptp',unknown),[]).
%
% cnf(175149440,plain,($equal(intersection(A,cross_product(B,C)),restrict(A,B,C))),inference(rewrite,[status(thm)],[restriction1]),[]).
%
% cnf(210478080,plain,(~member(z,restrict(xr,A,B))),inference(paramodulation,[status(thm)],[197759096,175149440,theory(equality)]),[]).
%
% fof(prove_restriction_alternate_defn2_1,plain,(member(z,restrict(xr,x,y))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET239-6.tptp',unknown),[]).
%
% cnf(176100800,plain,(member(z,restrict(xr,x,y))),inference(rewrite,[status(thm)],[prove_restriction_alternate_defn2_1]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[210478080,176100800]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------