%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM014-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %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 : 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 : 6
% Number of leaves : 6
% Syntax : Number of clauses : 15 ( 8 unt; 1 nHn; 13 RR)
% Number of literals : 29 ( 0 equ; 14 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 13 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(square,axiom,
product(X,X,square(X)) ).
cnf(divides,axiom,
( ~ product(X,Y,Z)
| divides(X,Z) ) ).
cnf(remainder,axiom,
( ~ prime(X)
| ~ product(Y,Z,U)
| ~ divides(X,U)
| divides(X,Y)
| divides(X,Z) ) ).
cnf(a_is_prime,hypothesis,
prime(a) ).
cnf(a_equals_b_squared_by_c_squared,hypothesis,
product(a,square(c),square(b)) ).
cnf(prove_a_divides_b,negated_conjecture,
~ divides(a,b) ).
cnf(refute_0_0,plain,
( ~ product(a,square(c),square(b))
| divides(a,square(b)) ),
inference(subst,[],[divides:[bind(X,$fot(a)),bind(Y,$fot(square(c))),bind(Z,$fot(square(b)))]]) ).
cnf(refute_0_1,plain,
divides(a,square(b)),
inference(resolve,[$cnf( product(a,square(c),square(b)) )],[a_equals_b_squared_by_c_squared,refute_0_0]) ).
cnf(refute_0_2,plain,
product(X_11,X_11,square(X_11)),
inference(subst,[],[square:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_3,plain,
( ~ divides(X_9,square(X_11))
| ~ prime(X_9)
| ~ product(X_11,X_11,square(X_11))
| divides(X_9,X_11) ),
inference(subst,[],[remainder:[bind(U,$fot(square(X_11))),bind(X,$fot(X_9)),bind(Y,$fot(X_11)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_4,plain,
( ~ divides(X_9,square(X_11))
| ~ prime(X_9)
| divides(X_9,X_11) ),
inference(resolve,[$cnf( product(X_11,X_11,square(X_11)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ divides(a,square(b))
| ~ prime(a)
| divides(a,b) ),
inference(subst,[],[refute_0_4:[bind(X_11,$fot(b)),bind(X_9,$fot(a))]]) ).
cnf(refute_0_6,plain,
( ~ prime(a)
| divides(a,b) ),
inference(resolve,[$cnf( divides(a,square(b)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
divides(a,b),
inference(resolve,[$cnf( prime(a) )],[a_is_prime,refute_0_6]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( divides(a,b) )],[refute_0_7,prove_a_divides_b]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM014-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n007.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 12:06:27 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
% 0.12/0.34
%------------------------------------------------------------------------------