%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM014-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 14:23:39 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 7 unt; 1 nHn; 12 RR)
% Number of literals : 23 ( 0 equ; 13 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 : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
product(u,u,square(u)),
file('NUM014-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(u,v,w)
| divides(u,w) ),
file('NUM014-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ prime(u)
| ~ divides(u,v)
| ~ product(w,x,v)
| divides(u,x)
| divides(u,w) ),
file('NUM014-1.p',unknown),
[] ).
cnf(5,axiom,
prime(a),
file('NUM014-1.p',unknown),
[] ).
cnf(6,axiom,
product(a,square(c),square(b)),
file('NUM014-1.p',unknown),
[] ).
cnf(7,axiom,
~ divides(a,b),
file('NUM014-1.p',unknown),
[] ).
cnf(10,plain,
( ~ prime(a)
| ~ product(b,u,v)
| ~ divides(a,v)
| divides(a,u) ),
inference(res,[status(thm),theory(equality)],[4,7]),
[iquote('0:Res:4.3,7.0')] ).
cnf(12,plain,
( ~ divides(a,u)
| ~ product(b,v,u)
| divides(a,v) ),
inference(mrr,[status(thm)],[10,5]),
[iquote('0:MRR:10.0,5.0')] ).
cnf(13,plain,
( ~ divides(a,u)
| ~ product(b,b,u) ),
inference(res,[status(thm),theory(equality)],[12,7]),
[iquote('0:Res:12.2,7.0')] ).
cnf(17,plain,
divides(a,square(b)),
inference(res,[status(thm),theory(equality)],[6,3]),
[iquote('0:Res:6.0,3.0')] ).
cnf(18,plain,
~ divides(a,square(b)),
inference(res,[status(thm),theory(equality)],[1,13]),
[iquote('0:Res:1.0,13.1')] ).
cnf(19,plain,
$false,
inference(mrr,[status(thm)],[18,17]),
[iquote('0:MRR:18.0,17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM014-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n016.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 12:42:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 14 clauses.
% 0.19/0.41 SPASS allocated 75593 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.04 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 3, length 12 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : square divides remainder a_is_prime a_equals_b_squared_by_c_squared prove_a_divides_b
% 0.19/0.41
%------------------------------------------------------------------------------