TSTP Solution File: NUM016-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : NUM016-2 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 14:50:35 EDT 2009
% Result : Unsatisfiable 0.0s
% Output : Refutation 0.0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 11 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 14 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 20 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_there_is_another_prime,plain,
! [A] :
( ~ prime(A)
| ~ less(a,A)
| less(factorial_plus_one(a),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),
[] ).
cnf(156125744,plain,
( ~ prime(A)
| ~ less(a,A)
| less(factorial_plus_one(a),A) ),
inference(rewrite,[status(thm)],[prove_there_is_another_prime]),
[] ).
fof(prime_divsiors,plain,
! [A] :
( prime(A)
| prime(prime_divisor(A)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),
[] ).
cnf(156112936,plain,
( prime(A)
| prime(prime_divisor(A)) ),
inference(rewrite,[status(thm)],[prime_divsiors]),
[] ).
fof(a_prime_is_less_than_the_next_one,plain,
! [A] : less(A,factorial_plus_one(A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),
[] ).
cnf(156091248,plain,
less(A,factorial_plus_one(A)),
inference(rewrite,[status(thm)],[a_prime_is_less_than_the_next_one]),
[] ).
fof(nothing_is_less_than_itself,plain,
! [A] : ~ less(A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),
[] ).
cnf(156080752,plain,
~ less(A,A),
inference(rewrite,[status(thm)],[nothing_is_less_than_itself]),
[] ).
cnf(163922520,plain,
~ prime(factorial_plus_one(a)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[156091248,156125744,156080752]),
[] ).
cnf(163950464,plain,
prime(prime_divisor(factorial_plus_one(a))),
inference(resolution,[status(thm)],[156112936,163922520]),
[] ).
cnf(163995272,plain,
( ~ less(a,prime_divisor(factorial_plus_one(a)))
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
inference(resolution,[status(thm)],[156125744,163950464]),
[] ).
fof(divisor_is_smaller,plain,
! [A,B] :
( ~ divides(A,factorial_plus_one(B))
| less(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),
[] ).
cnf(156097640,plain,
( ~ divides(A,factorial_plus_one(B))
| less(B,A) ),
inference(rewrite,[status(thm)],[divisor_is_smaller]),
[] ).
fof(division_by_prime_divisor,plain,
! [A] :
( prime(A)
| divides(prime_divisor(A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),
[] ).
cnf(156104064,plain,
( prime(A)
| divides(prime_divisor(A),A) ),
inference(rewrite,[status(thm)],[division_by_prime_divisor]),
[] ).
cnf(163961512,plain,
divides(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a)),
inference(resolution,[status(thm)],[156104064,163922520]),
[] ).
cnf(164003360,plain,
less(a,prime_divisor(factorial_plus_one(a))),
inference(resolution,[status(thm)],[156097640,163961512]),
[] ).
cnf(164023792,plain,
less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))),
inference(resolution,[status(thm)],[163995272,164003360]),
[] ).
fof(numbers_are_different,plain,
! [A,B] :
( ~ less(A,B)
| ~ less(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),
[] ).
cnf(156086528,plain,
( ~ less(A,B)
| ~ less(B,A) ),
inference(rewrite,[status(thm)],[numbers_are_different]),
[] ).
fof(smaller_prime_divisors,plain,
! [A] :
( prime(A)
| less(prime_divisor(A),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),
[] ).
cnf(156117656,plain,
( prime(A)
| less(prime_divisor(A),A) ),
inference(rewrite,[status(thm)],[smaller_prime_divisors]),
[] ).
cnf(163969360,plain,
less(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a)),
inference(resolution,[status(thm)],[156117656,163922520]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[164023792,156086528,163969360]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_there_is_another_prime,plain,(~prime(A)|~less(a,A)|less(factorial_plus_one(a),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),[]).
%
% cnf(156125744,plain,(~prime(A)|~less(a,A)|less(factorial_plus_one(a),A)),inference(rewrite,[status(thm)],[prove_there_is_another_prime]),[]).
%
% fof(prime_divsiors,plain,(prime(A)|prime(prime_divisor(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),[]).
%
% cnf(156112936,plain,(prime(A)|prime(prime_divisor(A))),inference(rewrite,[status(thm)],[prime_divsiors]),[]).
%
% fof(a_prime_is_less_than_the_next_one,plain,(less(A,factorial_plus_one(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),[]).
%
% cnf(156091248,plain,(less(A,factorial_plus_one(A))),inference(rewrite,[status(thm)],[a_prime_is_less_than_the_next_one]),[]).
%
% fof(nothing_is_less_than_itself,plain,(~less(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),[]).
%
% cnf(156080752,plain,(~less(A,A)),inference(rewrite,[status(thm)],[nothing_is_less_than_itself]),[]).
%
% cnf(163922520,plain,(~prime(factorial_plus_one(a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[156091248,156125744,156080752]),[]).
%
% cnf(163950464,plain,(prime(prime_divisor(factorial_plus_one(a)))),inference(resolution,[status(thm)],[156112936,163922520]),[]).
%
% cnf(163995272,plain,(~less(a,prime_divisor(factorial_plus_one(a)))|less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))),inference(resolution,[status(thm)],[156125744,163950464]),[]).
%
% fof(divisor_is_smaller,plain,(~divides(A,factorial_plus_one(B))|less(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),[]).
%
% cnf(156097640,plain,(~divides(A,factorial_plus_one(B))|less(B,A)),inference(rewrite,[status(thm)],[divisor_is_smaller]),[]).
%
% fof(division_by_prime_divisor,plain,(prime(A)|divides(prime_divisor(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),[]).
%
% cnf(156104064,plain,(prime(A)|divides(prime_divisor(A),A)),inference(rewrite,[status(thm)],[division_by_prime_divisor]),[]).
%
% cnf(163961512,plain,(divides(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a))),inference(resolution,[status(thm)],[156104064,163922520]),[]).
%
% cnf(164003360,plain,(less(a,prime_divisor(factorial_plus_one(a)))),inference(resolution,[status(thm)],[156097640,163961512]),[]).
%
% cnf(164023792,plain,(less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))),inference(resolution,[status(thm)],[163995272,164003360]),[]).
%
% fof(numbers_are_different,plain,(~less(A,B)|~less(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),[]).
%
% cnf(156086528,plain,(~less(A,B)|~less(B,A)),inference(rewrite,[status(thm)],[numbers_are_different]),[]).
%
% fof(smaller_prime_divisors,plain,(prime(A)|less(prime_divisor(A),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-2.tptp',unknown),[]).
%
% cnf(156117656,plain,(prime(A)|less(prime_divisor(A),A)),inference(rewrite,[status(thm)],[smaller_prime_divisors]),[]).
%
% cnf(163969360,plain,(less(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a))),inference(resolution,[status(thm)],[156117656,163922520]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[164023792,156086528,163969360]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------