TSTP Solution File: SET013-4 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET013-4 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 15:23:27 EDT 2009
% Result : Unsatisfiable 291.9s
% Output : Refutation 291.9s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 10 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 24 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 2 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_c_equals_d,plain,
~ $equal(ds,cs),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
[] ).
cnf(168163360,plain,
~ $equal(ds,cs),
inference(rewrite,[status(thm)],[prove_c_equals_d]),
[] ).
fof(extensionality2,plain,
! [A,B] :
( member(f1(A,B),A)
| member(f1(A,B),B)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
[] ).
cnf(168107536,plain,
( member(f1(A,B),A)
| member(f1(A,B),B)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[extensionality2]),
[] ).
cnf(176122736,plain,
( member(f1(cs,ds),cs)
| member(f1(cs,ds),ds) ),
inference(resolution,[status(thm)],[168163360,168107536]),
[] ).
fof(intersection1,plain,
! [A,B,C] :
( ~ member(A,intersection(B,C))
| member(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
[] ).
cnf(168124776,plain,
( ~ member(A,intersection(B,C))
| member(A,B) ),
inference(rewrite,[status(thm)],[intersection1]),
[] ).
fof(intersection_of_a_and_b_is_c,plain,
$equal(intersection(as,bs),cs),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
[] ).
cnf(168084936,plain,
$equal(intersection(as,bs),cs),
inference(rewrite,[status(thm)],[intersection_of_a_and_b_is_c]),
[] ).
cnf(176470344,plain,
( ~ member(A,cs)
| member(A,as) ),
inference(paramodulation,[status(thm)],[168124776,168084936,theory(equality)]),
[] ).
cnf(179922136,plain,
( member(f1(cs,ds),ds)
| member(f1(cs,ds),as) ),
inference(resolution,[status(thm)],[176122736,176470344]),
[] ).
fof(intersection2,plain,
! [A,B,C] :
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
[] ).
cnf(168129072,plain,
( ~ member(A,intersection(B,C))
| member(A,C) ),
inference(rewrite,[status(thm)],[intersection2]),
[] ).
fof(intersection_of_b_and_a_is_d,plain,
$equal(intersection(bs,as),ds),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
[] ).
cnf(168158736,plain,
$equal(intersection(bs,as),ds),
inference(rewrite,[status(thm)],[intersection_of_b_and_a_is_d]),
[] ).
cnf(176791128,plain,
( ~ member(A,ds)
| member(A,as) ),
inference(paramodulation,[status(thm)],[168129072,168158736,theory(equality)]),
[] ).
cnf(277974664,plain,
member(f1(cs,ds),as),
inference(resolution,[status(thm)],[179922136,176791128]),
[] ).
cnf(176490664,plain,
( ~ member(A,ds)
| member(A,bs) ),
inference(paramodulation,[status(thm)],[168124776,168158736,theory(equality)]),
[] ).
cnf(179931672,plain,
( member(f1(cs,ds),cs)
| member(f1(cs,ds),bs) ),
inference(resolution,[status(thm)],[176122736,176490664]),
[] ).
cnf(176786544,plain,
( ~ member(A,cs)
| member(A,bs) ),
inference(paramodulation,[status(thm)],[168129072,168084936,theory(equality)]),
[] ).
cnf(278158976,plain,
member(f1(cs,ds),bs),
inference(resolution,[status(thm)],[179931672,176786544]),
[] ).
fof(intersection3,plain,
! [A,B,C] :
( member(A,intersection(B,C))
| ~ member(A,B)
| ~ member(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
[] ).
cnf(168136072,plain,
( member(A,intersection(B,C))
| ~ member(A,B)
| ~ member(A,C) ),
inference(rewrite,[status(thm)],[intersection3]),
[] ).
cnf(182647648,plain,
( member(A,cs)
| ~ member(A,as)
| ~ member(A,bs) ),
inference(paramodulation,[status(thm)],[168136072,168084936,theory(equality)]),
[] ).
cnf(595690400,plain,
member(f1(cs,ds),cs),
inference(forward_subsumption_resolution__resolution,[status(thm)],[179931672,182647648,277974664]),
[] ).
cnf(182655632,plain,
( member(A,ds)
| ~ member(A,bs)
| ~ member(A,as) ),
inference(paramodulation,[status(thm)],[168136072,168158736,theory(equality)]),
[] ).
fof(extensionality3,plain,
! [A,B] :
( ~ member(f1(A,B),A)
| ~ member(f1(A,B),B)
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
[] ).
cnf(168115160,plain,
( ~ member(f1(A,B),A)
| ~ member(f1(A,B),B)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[extensionality3]),
[] ).
cnf(176081504,plain,
( ~ member(f1(cs,ds),cs)
| ~ member(f1(cs,ds),ds) ),
inference(resolution,[status(thm)],[168115160,168163360]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[277974664,278158976,595690400,182655632,176081504]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 290 seconds
% START OF PROOF SEQUENCE
% fof(prove_c_equals_d,plain,(~$equal(ds,cs)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
%
% cnf(168163360,plain,(~$equal(ds,cs)),inference(rewrite,[status(thm)],[prove_c_equals_d]),[]).
%
% fof(extensionality2,plain,(member(f1(A,B),A)|member(f1(A,B),B)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
%
% cnf(168107536,plain,(member(f1(A,B),A)|member(f1(A,B),B)|$equal(B,A)),inference(rewrite,[status(thm)],[extensionality2]),[]).
%
% cnf(176122736,plain,(member(f1(cs,ds),cs)|member(f1(cs,ds),ds)),inference(resolution,[status(thm)],[168163360,168107536]),[]).
%
% fof(intersection1,plain,(~member(A,intersection(B,C))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
%
% cnf(168124776,plain,(~member(A,intersection(B,C))|member(A,B)),inference(rewrite,[status(thm)],[intersection1]),[]).
%
% fof(intersection_of_a_and_b_is_c,plain,($equal(intersection(as,bs),cs)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
%
% cnf(168084936,plain,($equal(intersection(as,bs),cs)),inference(rewrite,[status(thm)],[intersection_of_a_and_b_is_c]),[]).
%
% cnf(176470344,plain,(~member(A,cs)|member(A,as)),inference(paramodulation,[status(thm)],[168124776,168084936,theory(equality)]),[]).
%
% cnf(179922136,plain,(member(f1(cs,ds),ds)|member(f1(cs,ds),as)),inference(resolution,[status(thm)],[176122736,176470344]),[]).
%
% fof(intersection2,plain,(~member(A,intersection(B,C))|member(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
%
% cnf(168129072,plain,(~member(A,intersection(B,C))|member(A,C)),inference(rewrite,[status(thm)],[intersection2]),[]).
%
% fof(intersection_of_b_and_a_is_d,plain,($equal(intersection(bs,as),ds)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
%
% cnf(168158736,plain,($equal(intersection(bs,as),ds)),inference(rewrite,[status(thm)],[intersection_of_b_and_a_is_d]),[]).
%
% cnf(176791128,plain,(~member(A,ds)|member(A,as)),inference(paramodulation,[status(thm)],[168129072,168158736,theory(equality)]),[]).
%
% cnf(277974664,plain,(member(f1(cs,ds),as)),inference(resolution,[status(thm)],[179922136,176791128]),[]).
%
% cnf(176490664,plain,(~member(A,ds)|member(A,bs)),inference(paramodulation,[status(thm)],[168124776,168158736,theory(equality)]),[]).
%
% cnf(179931672,plain,(member(f1(cs,ds),cs)|member(f1(cs,ds),bs)),inference(resolution,[status(thm)],[176122736,176490664]),[]).
%
% cnf(176786544,plain,(~member(A,cs)|member(A,bs)),inference(paramodulation,[status(thm)],[168129072,168084936,theory(equality)]),[]).
%
% cnf(278158976,plain,(member(f1(cs,ds),bs)),inference(resolution,[status(thm)],[179931672,176786544]),[]).
%
% fof(intersection3,plain,(member(A,intersection(B,C))|~member(A,B)|~member(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
%
% cnf(168136072,plain,(member(A,intersection(B,C))|~member(A,B)|~member(A,C)),inference(rewrite,[status(thm)],[intersection3]),[]).
%
% cnf(182647648,plain,(member(A,cs)|~member(A,as)|~member(A,bs)),inference(paramodulation,[status(thm)],[168136072,168084936,theory(equality)]),[]).
%
% cnf(595690400,plain,(member(f1(cs,ds),cs)),inference(forward_subsumption_resolution__resolution,[status(thm)],[179931672,182647648,277974664]),[]).
%
% cnf(182655632,plain,(member(A,ds)|~member(A,bs)|~member(A,as)),inference(paramodulation,[status(thm)],[168136072,168158736,theory(equality)]),[]).
%
% fof(extensionality3,plain,(~member(f1(A,B),A)|~member(f1(A,B),B)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
%
% cnf(168115160,plain,(~member(f1(A,B),A)|~member(f1(A,B),B)|$equal(B,A)),inference(rewrite,[status(thm)],[extensionality3]),[]).
%
% cnf(176081504,plain,(~member(f1(cs,ds),cs)|~member(f1(cs,ds),ds)),inference(resolution,[status(thm)],[168115160,168163360]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[277974664,278158976,595690400,182655632,176081504]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------