TSTP Solution File: NUM016-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM016-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 12:24:06 EDT 2022
% Result : Unsatisfiable 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 29 ( 8 unt; 10 nHn; 22 RR)
% Number of literals : 54 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 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 : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(nothing_is_less_than_itself,axiom,
~ less(X,X) ).
cnf(numbers_are_different,axiom,
( ~ less(X,Y)
| ~ less(Y,X) ) ).
cnf(a_prime_is_less_than_the_next_one,axiom,
less(X,factorial_plus_one(X)) ).
cnf(divisor_is_smaller,axiom,
( ~ divides(X,factorial_plus_one(Y))
| less(Y,X) ) ).
cnf(division_by_prime_divisor,axiom,
( prime(X)
| divides(prime_divisor(X),X) ) ).
cnf(prime_divsiors,axiom,
( prime(X)
| prime(prime_divisor(X)) ) ).
cnf(smaller_prime_divisors,axiom,
( prime(X)
| less(prime_divisor(X),X) ) ).
cnf(prove_there_is_another_prime,negated_conjecture,
( ~ prime(X)
| ~ less(a,X)
| less(factorial_plus_one(a),X) ) ).
cnf(refute_0_0,plain,
( less(prime_divisor(X_9),X_9)
| prime(X_9) ),
inference(subst,[],[smaller_prime_divisors:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_1,plain,
( ~ less(X_9,prime_divisor(X_9))
| ~ less(prime_divisor(X_9),X_9) ),
inference(subst,[],[numbers_are_different:[bind(X,$fot(prime_divisor(X_9))),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_2,plain,
( ~ less(X_9,prime_divisor(X_9))
| prime(X_9) ),
inference(resolve,[$cnf( less(prime_divisor(X_9),X_9) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
| prime(factorial_plus_one(a)) ),
inference(subst,[],[refute_0_2:[bind(X_9,$fot(factorial_plus_one(a)))]]) ).
cnf(refute_0_4,plain,
( prime(factorial_plus_one(a))
| prime(prime_divisor(factorial_plus_one(a))) ),
inference(subst,[],[prime_divsiors:[bind(X,$fot(factorial_plus_one(a)))]]) ).
cnf(refute_0_5,plain,
( divides(prime_divisor(factorial_plus_one(X_7)),factorial_plus_one(X_7))
| prime(factorial_plus_one(X_7)) ),
inference(subst,[],[division_by_prime_divisor:[bind(X,$fot(factorial_plus_one(X_7)))]]) ).
cnf(refute_0_6,plain,
( ~ divides(prime_divisor(factorial_plus_one(X_7)),factorial_plus_one(X_7))
| less(X_7,prime_divisor(factorial_plus_one(X_7))) ),
inference(subst,[],[divisor_is_smaller:[bind(X,$fot(prime_divisor(factorial_plus_one(X_7)))),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_7,plain,
( less(X_7,prime_divisor(factorial_plus_one(X_7)))
| prime(factorial_plus_one(X_7)) ),
inference(resolve,[$cnf( divides(prime_divisor(factorial_plus_one(X_7)),factorial_plus_one(X_7)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( less(a,prime_divisor(factorial_plus_one(a)))
| prime(factorial_plus_one(a)) ),
inference(subst,[],[refute_0_7:[bind(X_7,$fot(a))]]) ).
cnf(refute_0_9,plain,
( ~ less(a,prime_divisor(factorial_plus_one(a)))
| ~ prime(prime_divisor(factorial_plus_one(a)))
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
inference(subst,[],[prove_there_is_another_prime:[bind(X,$fot(prime_divisor(factorial_plus_one(a))))]]) ).
cnf(refute_0_10,plain,
( ~ prime(prime_divisor(factorial_plus_one(a)))
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
| prime(factorial_plus_one(a)) ),
inference(resolve,[$cnf( less(a,prime_divisor(factorial_plus_one(a))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
less(a,factorial_plus_one(a)),
inference(subst,[],[a_prime_is_less_than_the_next_one:[bind(X,$fot(a))]]) ).
cnf(refute_0_12,plain,
( ~ less(a,factorial_plus_one(a))
| ~ prime(factorial_plus_one(a))
| less(factorial_plus_one(a),factorial_plus_one(a)) ),
inference(subst,[],[prove_there_is_another_prime:[bind(X,$fot(factorial_plus_one(a)))]]) ).
cnf(refute_0_13,plain,
( ~ prime(factorial_plus_one(a))
| less(factorial_plus_one(a),factorial_plus_one(a)) ),
inference(resolve,[$cnf( less(a,factorial_plus_one(a)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
~ less(factorial_plus_one(a),factorial_plus_one(a)),
inference(subst,[],[nothing_is_less_than_itself:[bind(X,$fot(factorial_plus_one(a)))]]) ).
cnf(refute_0_15,plain,
~ prime(factorial_plus_one(a)),
inference(resolve,[$cnf( less(factorial_plus_one(a),factorial_plus_one(a)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ prime(prime_divisor(factorial_plus_one(a)))
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
inference(resolve,[$cnf( prime(factorial_plus_one(a)) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
( less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
| prime(factorial_plus_one(a)) ),
inference(resolve,[$cnf( prime(prime_divisor(factorial_plus_one(a))) )],[refute_0_4,refute_0_16]) ).
cnf(refute_0_18,plain,
less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))),
inference(resolve,[$cnf( prime(factorial_plus_one(a)) )],[refute_0_17,refute_0_15]) ).
cnf(refute_0_19,plain,
prime(factorial_plus_one(a)),
inference(resolve,[$cnf( less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) )],[refute_0_18,refute_0_3]) ).
cnf(refute_0_20,plain,
$false,
inference(resolve,[$cnf( prime(factorial_plus_one(a)) )],[refute_0_19,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM016-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n014.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 : Tue Jul 5 20:47:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------