%------------------------------------------------------------------------------
% File     : PyRes---1.5
% Problem  : NUM016-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s

% Computer : n032.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  : 300s
% DateTime : Thu May  9 17:35:01 EDT 2024

% Result   : Unsatisfiable 0.16s 0.47s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   18 (   6 unt;   7 nHn;  13 RR)
%            Number of literals    :   32 (   0 equ;   9 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    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   12 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(nothing_is_less_than_itself,axiom,
    ~ less(X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).

cnf(a_prime_is_less_than_the_next_one,axiom,
    less(X4,factorial_plus_one(X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).

cnf(prove_there_is_another_prime,negated_conjecture,
    ( ~ prime(X24)
    | ~ less(a,X24)
    | less(factorial_plus_one(a),X24) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_another_prime) ).

cnf(c10,plain,
    ( ~ prime(factorial_plus_one(a))
    | less(factorial_plus_one(a),factorial_plus_one(a)) ),
    inference(resolution,[status(thm)],[prove_there_is_another_prime,a_prime_is_less_than_the_next_one]) ).

cnf(numbers_are_different,axiom,
    ( ~ less(X5,X6)
    | ~ less(X6,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',numbers_are_different) ).

cnf(smaller_prime_divisors,axiom,
    ( prime(X23)
    | less(prime_divisor(X23),X23) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_prime_divisors) ).

cnf(c8,plain,
    ( prime(X25)
    | ~ less(X25,prime_divisor(X25)) ),
    inference(resolution,[status(thm)],[smaller_prime_divisors,numbers_are_different]) ).

cnf(prime_divsiors,axiom,
    ( prime(X15)
    | prime(prime_divisor(X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_divsiors) ).

cnf(c19,plain,
    ( less(factorial_plus_one(a),factorial_plus_one(a))
    | prime(prime_divisor(factorial_plus_one(a))) ),
    inference(resolution,[status(thm)],[c10,prime_divsiors]) ).

cnf(c21,plain,
    prime(prime_divisor(factorial_plus_one(a))),
    inference(resolution,[status(thm)],[c19,nothing_is_less_than_itself]) ).

cnf(divisor_is_smaller,axiom,
    ( ~ divides(X16,factorial_plus_one(X17))
    | less(X17,X16) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_is_smaller) ).

cnf(division_by_prime_divisor,axiom,
    ( prime(X22)
    | divides(prime_divisor(X22),X22) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',division_by_prime_divisor) ).

cnf(c7,plain,
    ( prime(factorial_plus_one(X30))
    | less(X30,prime_divisor(factorial_plus_one(X30))) ),
    inference(resolution,[status(thm)],[division_by_prime_divisor,divisor_is_smaller]) ).

cnf(c15,plain,
    ( prime(factorial_plus_one(a))
    | ~ prime(prime_divisor(factorial_plus_one(a)))
    | less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
    inference(resolution,[status(thm)],[c7,prove_there_is_another_prime]) ).

cnf(c24,plain,
    ( prime(factorial_plus_one(a))
    | less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
    inference(resolution,[status(thm)],[c15,c21]) ).

cnf(c31,plain,
    prime(factorial_plus_one(a)),
    inference(resolution,[status(thm)],[c24,c8]) ).

cnf(c32,plain,
    less(factorial_plus_one(a),factorial_plus_one(a)),
    inference(resolution,[status(thm)],[c31,c10]) ).

cnf(c34,plain,
    $false,
    inference(resolution,[status(thm)],[c32,nothing_is_less_than_itself]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem  : NUM016-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.11  % Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.10/0.31  % Computer : n032.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Wed May  8 16:07:22 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.16/0.47  % Version:  1.5
% 0.16/0.47  % SZS status Unsatisfiable
% 0.16/0.47  % SZS output start CNFRefutation
% See solution above
% 0.16/0.47  
% 0.16/0.47  % Initial clauses    : 12
% 0.16/0.47  % Processed clauses  : 27
% 0.16/0.47  % Factors computed   : 2
% 0.16/0.47  % Resolvents computed: 34
% 0.16/0.47  % Tautologies deleted: 2
% 0.16/0.47  % Forward subsumed   : 7
% 0.16/0.47  % Backward subsumed  : 4
% 0.16/0.47  % -------- CPU Time ---------
% 0.16/0.47  % User time          : 0.145 s
% 0.16/0.47  % System time        : 0.012 s
% 0.16/0.47  % Total time         : 0.157 s
%------------------------------------------------------------------------------