%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM016-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 14:23:40 EDT 2022

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   14 (   4 unt;   4 nHn;  14 RR)
%            Number of literals    :   26 (   0 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ less(u,u),
    file('NUM016-2.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ less(u,v)
    | ~ less(v,u) ),
    file('NUM016-2.p',unknown),
    [] ).

cnf(3,axiom,
    less(u,factorial_plus_one(u)),
    file('NUM016-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ divides(u,factorial_plus_one(v))
    | less(v,u) ),
    file('NUM016-2.p',unknown),
    [] ).

cnf(5,axiom,
    ( prime(u)
    | divides(prime_divisor(u),u) ),
    file('NUM016-2.p',unknown),
    [] ).

cnf(6,axiom,
    ( prime(u)
    | prime(prime_divisor(u)) ),
    file('NUM016-2.p',unknown),
    [] ).

cnf(7,axiom,
    ( prime(u)
    | less(prime_divisor(u),u) ),
    file('NUM016-2.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ prime(u)
    | ~ less(a,u)
    | less(factorial_plus_one(a),u) ),
    file('NUM016-2.p',unknown),
    [] ).

cnf(9,plain,
    ( ~ prime(factorial_plus_one(a))
    | less(factorial_plus_one(a),factorial_plus_one(a)) ),
    inference(res,[status(thm),theory(equality)],[3,8]),
    [iquote('0:Res:3.0,8.1')] ).

cnf(11,plain,
    ~ prime(factorial_plus_one(a)),
    inference(mrr,[status(thm)],[9,1]),
    [iquote('0:MRR:9.1,1.0')] ).

cnf(16,plain,
    ( prime(factorial_plus_one(u))
    | less(u,prime_divisor(factorial_plus_one(u))) ),
    inference(res,[status(thm),theory(equality)],[5,4]),
    [iquote('0:Res:5.1,4.0')] ).

cnf(19,plain,
    ( ~ less(u,prime_divisor(u))
    | prime(u) ),
    inference(res,[status(thm),theory(equality)],[7,2]),
    [iquote('0:Res:7.1,2.0')] ).

cnf(23,plain,
    ( ~ prime(prime_divisor(factorial_plus_one(a)))
    | ~ less(a,prime_divisor(factorial_plus_one(a)))
    | prime(factorial_plus_one(a)) ),
    inference(res,[status(thm),theory(equality)],[8,19]),
    [iquote('0:Res:8.2,19.0')] ).

cnf(24,plain,
    $false,
    inference(mrr,[status(thm)],[23,6,16,11]),
    [iquote('0:MRR:23.0,23.1,23.2,6.1,16.1,11.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM016-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jul  6 16:37:04 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.41  
% 0.19/0.41  SPASS V 3.9 
% 0.19/0.41  SPASS beiseite: Proof found.
% 0.19/0.41  % SZS status Theorem
% 0.19/0.41  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.41  SPASS derived 10 clauses, backtracked 0 clauses, performed 0 splits and kept 15 clauses.
% 0.19/0.41  SPASS allocated 75591 KBytes.
% 0.19/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.41  		0:00:00.04 for the input.
% 0.19/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41  		0:00:00.00 for inferences.
% 0.19/0.41  		0:00:00.00 for the backtracking.
% 0.19/0.41  		0:00:00.00 for the reduction.
% 0.19/0.41  
% 0.19/0.41  
% 0.19/0.41  Here is a proof with depth 2, length 14 :
% 0.19/0.41  % SZS output start Refutation
% See solution above
% 0.19/0.41  Formulae used in the proof : nothing_is_less_than_itself numbers_are_different a_prime_is_less_than_the_next_one divisor_is_smaller division_by_prime_divisor prime_divsiors smaller_prime_divisors prove_there_is_another_prime
% 0.19/0.41  
%------------------------------------------------------------------------------