%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : NUM015-1 : TPTP v3.4.2. Released v1.0.0.
% 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 14:50:30 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 18 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 21 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(divisor2,plain,
! [A] :
( prime(A)
| less(divisor(A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),
[] ).
cnf(164586408,plain,
( prime(A)
| less(divisor(A),A) ),
inference(rewrite,[status(thm)],[divisor2]),
[] ).
fof(prove_a_has_prime_divisor,plain,
! [A] :
( ~ prime(A)
| ~ divides(A,a) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),
[] ).
cnf(164614424,plain,
( ~ prime(A)
| ~ divides(A,a) ),
inference(rewrite,[status(thm)],[prove_a_has_prime_divisor]),
[] ).
fof(divide_self,plain,
! [A] : divides(A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),
[] ).
cnf(164562728,plain,
divides(A,A),
inference(rewrite,[status(thm)],[divide_self]),
[] ).
cnf(172403816,plain,
~ prime(a),
inference(resolution,[status(thm)],[164614424,164562728]),
[] ).
cnf(172506192,plain,
less(divisor(a),a),
inference(resolution,[status(thm)],[164586408,172403816]),
[] ).
fof(divisor1,plain,
! [A] :
( prime(A)
| less(n1,divisor(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),
[] ).
cnf(164582280,plain,
( prime(A)
| less(n1,divisor(A)) ),
inference(rewrite,[status(thm)],[divisor1]),
[] ).
cnf(172498488,plain,
less(n1,divisor(a)),
inference(resolution,[status(thm)],[164582280,172403816]),
[] ).
fof(factor1,plain,
! [A] :
( ~ less(n1,A)
| ~ less(A,a)
| prime(factor_of(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),
[] ).
cnf(164594256,plain,
( ~ less(n1,A)
| ~ less(A,a)
| prime(factor_of(A)) ),
inference(rewrite,[status(thm)],[factor1]),
[] ).
cnf(173058824,plain,
prime(factor_of(divisor(a))),
inference(forward_subsumption_resolution__resolution,[status(thm)],[172506192,172498488,164594256]),
[] ).
fof(transitive_divide,plain,
! [A,B,C] :
( ~ divides(A,B)
| ~ divides(B,C)
| divides(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),
[] ).
cnf(164571032,plain,
( ~ divides(A,B)
| ~ divides(B,C)
| divides(A,C) ),
inference(rewrite,[status(thm)],[transitive_divide]),
[] ).
fof(prime,plain,
! [A] :
( prime(A)
| divides(divisor(A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),
[] ).
cnf(164577512,plain,
( prime(A)
| divides(divisor(A),A) ),
inference(rewrite,[status(thm)],[prime]),
[] ).
cnf(172485776,plain,
divides(divisor(a),a),
inference(resolution,[status(thm)],[164577512,172403816]),
[] ).
cnf(172641144,plain,
( ~ divides(A,divisor(a))
| divides(A,a) ),
inference(resolution,[status(thm)],[164571032,172485776]),
[] ).
fof(factor2,plain,
! [A] :
( ~ less(n1,A)
| ~ less(A,a)
| divides(factor_of(A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),
[] ).
cnf(164603384,plain,
( ~ less(n1,A)
| ~ less(A,a)
| divides(factor_of(A),A) ),
inference(rewrite,[status(thm)],[factor2]),
[] ).
cnf(173558568,plain,
divides(factor_of(divisor(a)),a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[172506192,172498488,172641144,164603384]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[173058824,164614424,173558568]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(divisor2,plain,(prime(A)|less(divisor(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),[]).
%
% cnf(164586408,plain,(prime(A)|less(divisor(A),A)),inference(rewrite,[status(thm)],[divisor2]),[]).
%
% fof(prove_a_has_prime_divisor,plain,(~prime(A)|~divides(A,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),[]).
%
% cnf(164614424,plain,(~prime(A)|~divides(A,a)),inference(rewrite,[status(thm)],[prove_a_has_prime_divisor]),[]).
%
% fof(divide_self,plain,(divides(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),[]).
%
% cnf(164562728,plain,(divides(A,A)),inference(rewrite,[status(thm)],[divide_self]),[]).
%
% cnf(172403816,plain,(~prime(a)),inference(resolution,[status(thm)],[164614424,164562728]),[]).
%
% cnf(172506192,plain,(less(divisor(a),a)),inference(resolution,[status(thm)],[164586408,172403816]),[]).
%
% fof(divisor1,plain,(prime(A)|less(n1,divisor(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),[]).
%
% cnf(164582280,plain,(prime(A)|less(n1,divisor(A))),inference(rewrite,[status(thm)],[divisor1]),[]).
%
% cnf(172498488,plain,(less(n1,divisor(a))),inference(resolution,[status(thm)],[164582280,172403816]),[]).
%
% fof(factor1,plain,(~less(n1,A)|~less(A,a)|prime(factor_of(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),[]).
%
% cnf(164594256,plain,(~less(n1,A)|~less(A,a)|prime(factor_of(A))),inference(rewrite,[status(thm)],[factor1]),[]).
%
% cnf(173058824,plain,(prime(factor_of(divisor(a)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[172506192,172498488,164594256]),[]).
%
% fof(transitive_divide,plain,(~divides(A,B)|~divides(B,C)|divides(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),[]).
%
% cnf(164571032,plain,(~divides(A,B)|~divides(B,C)|divides(A,C)),inference(rewrite,[status(thm)],[transitive_divide]),[]).
%
% fof(prime,plain,(prime(A)|divides(divisor(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),[]).
%
% cnf(164577512,plain,(prime(A)|divides(divisor(A),A)),inference(rewrite,[status(thm)],[prime]),[]).
%
% cnf(172485776,plain,(divides(divisor(a),a)),inference(resolution,[status(thm)],[164577512,172403816]),[]).
%
% cnf(172641144,plain,(~divides(A,divisor(a))|divides(A,a)),inference(resolution,[status(thm)],[164571032,172485776]),[]).
%
% fof(factor2,plain,(~less(n1,A)|~less(A,a)|divides(factor_of(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM015-1.tptp',unknown),[]).
%
% cnf(164603384,plain,(~less(n1,A)|~less(A,a)|divides(factor_of(A),A)),inference(rewrite,[status(thm)],[factor2]),[]).
%
% cnf(173558568,plain,(divides(factor_of(divisor(a)),a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[172506192,172498488,172641144,164603384]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[173058824,164614424,173558568]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------