%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : NUM016-1 : 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 14:50:32 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   20 (   6 unt;   0 def)
%            Number of atoms       :   36 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   30 (  14   ~;  16   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 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   :   22 (   0 sgn  10   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/NUM016-1.tptp',unknown),
    [] ).

cnf(153970960,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/NUM016-1.tptp',unknown),
    [] ).

cnf(153977288,plain,
    ( prime(A)
    | divides(prime_divisor(A),A) ),
    inference(rewrite,[status(thm)],[division_by_prime_divisor]),
    [] ).

cnf(161977624,plain,
    ( less(A,prime_divisor(factorial_plus_one(A)))
    | prime(factorial_plus_one(A)) ),
    inference(resolution,[status(thm)],[153970960,153977288]),
    [] ).

fof(prime_divsiors,plain,
    ! [A] :
      ( prime(A)
      | prime(prime_divisor(A)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-1.tptp',unknown),
    [] ).

cnf(153982008,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/NUM016-1.tptp',unknown),
    [] ).

cnf(153961272,plain,
    less(A,factorial_plus_one(A)),
    inference(rewrite,[status(thm)],[a_prime_is_less_than_the_next_one]),
    [] ).

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/NUM016-1.tptp',unknown),
    [] ).

cnf(153998768,plain,
    ( ~ prime(A)
    | ~ less(a,A)
    | less(factorial_plus_one(a),A) ),
    inference(rewrite,[status(thm)],[prove_there_is_another_prime]),
    [] ).

fof(nothing_is_less_than_itself,plain,
    ! [A] : ~ less(A,A),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-1.tptp',unknown),
    [] ).

cnf(153933208,plain,
    ~ less(A,A),
    inference(rewrite,[status(thm)],[nothing_is_less_than_itself]),
    [] ).

cnf(161823152,plain,
    ~ prime(factorial_plus_one(a)),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[153961272,153998768,153933208]),
    [] ).

fof(numbers_are_different,plain,
    ! [A,B] :
      ( ~ less(A,B)
      | ~ less(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-1.tptp',unknown),
    [] ).

cnf(153938984,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/NUM016-1.tptp',unknown),
    [] ).

cnf(153930744,plain,
    ( prime(A)
    | less(prime_divisor(A),A) ),
    inference(rewrite,[status(thm)],[smaller_prime_divisors]),
    [] ).

cnf(161928776,plain,
    ( ~ less(A,prime_divisor(A))
    | prime(A) ),
    inference(resolution,[status(thm)],[153938984,153930744]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[161977624,153982008,161823152,153998768,161928776]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(divisor_is_smaller,plain,(~divides(A,factorial_plus_one(B))|less(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-1.tptp',unknown),[]).
% 
% cnf(153970960,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/NUM016-1.tptp',unknown),[]).
% 
% cnf(153977288,plain,(prime(A)|divides(prime_divisor(A),A)),inference(rewrite,[status(thm)],[division_by_prime_divisor]),[]).
% 
% cnf(161977624,plain,(less(A,prime_divisor(factorial_plus_one(A)))|prime(factorial_plus_one(A))),inference(resolution,[status(thm)],[153970960,153977288]),[]).
% 
% fof(prime_divsiors,plain,(prime(A)|prime(prime_divisor(A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-1.tptp',unknown),[]).
% 
% cnf(153982008,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/NUM016-1.tptp',unknown),[]).
% 
% cnf(153961272,plain,(less(A,factorial_plus_one(A))),inference(rewrite,[status(thm)],[a_prime_is_less_than_the_next_one]),[]).
% 
% 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/NUM016-1.tptp',unknown),[]).
% 
% cnf(153998768,plain,(~prime(A)|~less(a,A)|less(factorial_plus_one(a),A)),inference(rewrite,[status(thm)],[prove_there_is_another_prime]),[]).
% 
% fof(nothing_is_less_than_itself,plain,(~less(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-1.tptp',unknown),[]).
% 
% cnf(153933208,plain,(~less(A,A)),inference(rewrite,[status(thm)],[nothing_is_less_than_itself]),[]).
% 
% cnf(161823152,plain,(~prime(factorial_plus_one(a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[153961272,153998768,153933208]),[]).
% 
% fof(numbers_are_different,plain,(~less(A,B)|~less(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM016-1.tptp',unknown),[]).
% 
% cnf(153938984,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/NUM016-1.tptp',unknown),[]).
% 
% cnf(153930744,plain,(prime(A)|less(prime_divisor(A),A)),inference(rewrite,[status(thm)],[smaller_prime_divisors]),[]).
% 
% cnf(161928776,plain,(~less(A,prime_divisor(A))|prime(A)),inference(resolution,[status(thm)],[153938984,153930744]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[161977624,153982008,161823152,153998768,161928776]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------