%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM015-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of clauses : 32 ( 8 unt; 11 nHn; 28 RR)
% Number of literals : 64 ( 0 equ; 26 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(divide_self,axiom,
divides(X,X) ).
cnf(transitive_divide,axiom,
( ~ divides(X,Y)
| ~ divides(Y,Z)
| divides(X,Z) ) ).
cnf(prime,axiom,
( prime(X)
| divides(divisor(X),X) ) ).
cnf(divisor1,axiom,
( prime(X)
| less(n1,divisor(X)) ) ).
cnf(divisor2,axiom,
( prime(X)
| less(divisor(X),X) ) ).
cnf(factor1,axiom,
( ~ less(n1,X)
| ~ less(X,a)
| prime(factor_of(X)) ) ).
cnf(factor2,axiom,
( ~ less(n1,X)
| ~ less(X,a)
| divides(factor_of(X),X) ) ).
cnf(prove_a_has_prime_divisor,negated_conjecture,
( ~ prime(X)
| ~ divides(X,a) ) ).
cnf(refute_0_0,plain,
( ~ divides(factor_of(divisor(a)),a)
| ~ prime(factor_of(divisor(a))) ),
inference(subst,[],[prove_a_has_prime_divisor:[bind(X,$fot(factor_of(divisor(a))))]]) ).
cnf(refute_0_1,plain,
( divides(divisor(a),a)
| prime(a) ),
inference(subst,[],[prime:[bind(X,$fot(a))]]) ).
cnf(refute_0_2,plain,
( less(n1,divisor(a))
| prime(a) ),
inference(subst,[],[divisor1:[bind(X,$fot(a))]]) ).
cnf(refute_0_3,plain,
( less(divisor(a),a)
| prime(a) ),
inference(subst,[],[divisor2:[bind(X,$fot(a))]]) ).
cnf(refute_0_4,plain,
( ~ less(divisor(a),a)
| ~ less(n1,divisor(a))
| divides(factor_of(divisor(a)),divisor(a)) ),
inference(subst,[],[factor2:[bind(X,$fot(divisor(a)))]]) ).
cnf(refute_0_5,plain,
( ~ less(n1,divisor(a))
| divides(factor_of(divisor(a)),divisor(a))
| prime(a) ),
inference(resolve,[$cnf( less(divisor(a),a) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
divides(a,a),
inference(subst,[],[divide_self:[bind(X,$fot(a))]]) ).
cnf(refute_0_7,plain,
( ~ divides(a,a)
| ~ prime(a) ),
inference(subst,[],[prove_a_has_prime_divisor:[bind(X,$fot(a))]]) ).
cnf(refute_0_8,plain,
~ prime(a),
inference(resolve,[$cnf( divides(a,a) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ less(n1,divisor(a))
| divides(factor_of(divisor(a)),divisor(a)) ),
inference(resolve,[$cnf( prime(a) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( divides(factor_of(divisor(a)),divisor(a))
| prime(a) ),
inference(resolve,[$cnf( less(n1,divisor(a)) )],[refute_0_2,refute_0_9]) ).
cnf(refute_0_11,plain,
divides(factor_of(divisor(a)),divisor(a)),
inference(resolve,[$cnf( prime(a) )],[refute_0_10,refute_0_8]) ).
cnf(refute_0_12,plain,
( ~ divides(divisor(a),X_9)
| ~ divides(factor_of(divisor(a)),divisor(a))
| divides(factor_of(divisor(a)),X_9) ),
inference(subst,[],[transitive_divide:[bind(X,$fot(factor_of(divisor(a)))),bind(Y,$fot(divisor(a))),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_13,plain,
( ~ divides(divisor(a),X_9)
| divides(factor_of(divisor(a)),X_9) ),
inference(resolve,[$cnf( divides(factor_of(divisor(a)),divisor(a)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ divides(divisor(a),a)
| divides(factor_of(divisor(a)),a) ),
inference(subst,[],[refute_0_13:[bind(X_9,$fot(a))]]) ).
cnf(refute_0_15,plain,
( divides(factor_of(divisor(a)),a)
| prime(a) ),
inference(resolve,[$cnf( divides(divisor(a),a) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
divides(factor_of(divisor(a)),a),
inference(resolve,[$cnf( prime(a) )],[refute_0_15,refute_0_8]) ).
cnf(refute_0_17,plain,
~ prime(factor_of(divisor(a))),
inference(resolve,[$cnf( divides(factor_of(divisor(a)),a) )],[refute_0_16,refute_0_0]) ).
cnf(refute_0_18,plain,
( ~ less(divisor(a),a)
| ~ less(n1,divisor(a))
| prime(factor_of(divisor(a))) ),
inference(subst,[],[factor1:[bind(X,$fot(divisor(a)))]]) ).
cnf(refute_0_19,plain,
( ~ less(n1,divisor(a))
| prime(a)
| prime(factor_of(divisor(a))) ),
inference(resolve,[$cnf( less(divisor(a),a) )],[refute_0_3,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ less(n1,divisor(a))
| prime(factor_of(divisor(a))) ),
inference(resolve,[$cnf( prime(a) )],[refute_0_19,refute_0_8]) ).
cnf(refute_0_21,plain,
( prime(a)
| prime(factor_of(divisor(a))) ),
inference(resolve,[$cnf( less(n1,divisor(a)) )],[refute_0_2,refute_0_20]) ).
cnf(refute_0_22,plain,
prime(factor_of(divisor(a))),
inference(resolve,[$cnf( prime(a) )],[refute_0_21,refute_0_8]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( prime(factor_of(divisor(a))) )],[refute_0_22,refute_0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM015-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jul 6 14:30:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35
%------------------------------------------------------------------------------