TSTP Solution File: NUM016-2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM016-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n007.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 Aug 31 10:26:09 EDT 2023

% Result   : Unsatisfiable 0.21s 0.58s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   28 (   7 unt;   6 typ;   0 def)
%            Number of atoms       :   39 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   34 (  17   ~;  17   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   5   >;   2   *;   0   +;   0  <<)
%            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;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    less: ( $i * $i ) > $o ).

tff(decl_23,type,
    factorial_plus_one: $i > $i ).

tff(decl_24,type,
    divides: ( $i * $i ) > $o ).

tff(decl_25,type,
    prime: $i > $o ).

tff(decl_26,type,
    prime_divisor: $i > $i ).

tff(decl_27,type,
    a: $i ).

cnf(numbers_are_different,axiom,
    ( ~ less(X1,X2)
    | ~ less(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',numbers_are_different) ).

cnf(smaller_prime_divisors,axiom,
    ( prime(X1)
    | less(prime_divisor(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',smaller_prime_divisors) ).

cnf(nothing_is_less_than_itself,axiom,
    ~ less(X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).

cnf(prove_there_is_another_prime,negated_conjecture,
    ( less(factorial_plus_one(a),X1)
    | ~ prime(X1)
    | ~ less(a,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_another_prime) ).

cnf(a_prime_is_less_than_the_next_one,axiom,
    less(X1,factorial_plus_one(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).

cnf(prime_divsiors,axiom,
    ( prime(X1)
    | prime(prime_divisor(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_divsiors) ).

cnf(divisor_is_smaller,axiom,
    ( less(X2,X1)
    | ~ divides(X1,factorial_plus_one(X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor_is_smaller) ).

cnf(division_by_prime_divisor,axiom,
    ( prime(X1)
    | divides(prime_divisor(X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',division_by_prime_divisor) ).

cnf(c_0_8,axiom,
    ( ~ less(X1,X2)
    | ~ less(X2,X1) ),
    numbers_are_different ).

cnf(c_0_9,axiom,
    ( prime(X1)
    | less(prime_divisor(X1),X1) ),
    smaller_prime_divisors ).

cnf(c_0_10,axiom,
    ~ less(X1,X1),
    nothing_is_less_than_itself ).

cnf(c_0_11,negated_conjecture,
    ( less(factorial_plus_one(a),X1)
    | ~ prime(X1)
    | ~ less(a,X1) ),
    prove_there_is_another_prime ).

cnf(c_0_12,axiom,
    less(X1,factorial_plus_one(X1)),
    a_prime_is_less_than_the_next_one ).

cnf(c_0_13,plain,
    ( prime(X1)
    | ~ less(X1,prime_divisor(X1)) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    ~ prime(factorial_plus_one(a)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).

cnf(c_0_15,negated_conjecture,
    ( ~ prime(prime_divisor(factorial_plus_one(a)))
    | ~ less(a,prime_divisor(factorial_plus_one(a))) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_14]) ).

cnf(c_0_16,axiom,
    ( prime(X1)
    | prime(prime_divisor(X1)) ),
    prime_divsiors ).

cnf(c_0_17,axiom,
    ( less(X2,X1)
    | ~ divides(X1,factorial_plus_one(X2)) ),
    divisor_is_smaller ).

cnf(c_0_18,axiom,
    ( prime(X1)
    | divides(prime_divisor(X1),X1) ),
    division_by_prime_divisor ).

cnf(c_0_19,negated_conjecture,
    ~ less(a,prime_divisor(factorial_plus_one(a))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_14]) ).

cnf(c_0_20,plain,
    ( prime(factorial_plus_one(X1))
    | less(X1,prime_divisor(factorial_plus_one(X1))) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_14]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : NUM016-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri Aug 25 12:53:26 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 0.21/0.58  % Version  : CSE_E---1.5
% 0.21/0.58  % Problem  : theBenchmark.p
% 0.21/0.58  % Proof found
% 0.21/0.58  % SZS status Theorem for theBenchmark.p
% 0.21/0.58  % SZS output start Proof
% See solution above
% 0.21/0.58  % Total time : 0.004000 s
% 0.21/0.58  % SZS output end Proof
% 0.21/0.58  % Total time : 0.007000 s
%------------------------------------------------------------------------------