TSTP Solution File: NUM016-2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM016-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.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 : Sun May 5 08:17:14 EDT 2024
% Result : Unsatisfiable 0.13s 0.34s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 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 : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,plain,
$false,
inference(subsumption_resolution,[],[f19,f10]) ).
fof(f10,plain,
~ prime(factorial_plus_one(a)),
inference(subsumption_resolution,[],[f9,f1]) ).
fof(f1,axiom,
! [X0] : ~ less(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).
fof(f9,plain,
( ~ prime(factorial_plus_one(a))
| less(factorial_plus_one(a),factorial_plus_one(a)) ),
inference(resolution,[],[f8,f3]) ).
fof(f3,axiom,
! [X0] : less(X0,factorial_plus_one(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).
fof(f8,axiom,
! [X0] :
( ~ less(a,X0)
| ~ prime(X0)
| less(factorial_plus_one(a),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_another_prime) ).
fof(f19,plain,
prime(factorial_plus_one(a)),
inference(resolution,[],[f18,f12]) ).
fof(f12,plain,
! [X0] :
( ~ less(X0,prime_divisor(X0))
| prime(X0) ),
inference(resolution,[],[f7,f2]) ).
fof(f2,axiom,
! [X0,X1] :
( ~ less(X1,X0)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',numbers_are_different) ).
fof(f7,axiom,
! [X0] :
( less(prime_divisor(X0),X0)
| prime(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_prime_divisors) ).
fof(f18,plain,
less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))),
inference(subsumption_resolution,[],[f17,f10]) ).
fof(f17,plain,
( less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
| prime(factorial_plus_one(a)) ),
inference(resolution,[],[f16,f6]) ).
fof(f6,axiom,
! [X0] :
( prime(prime_divisor(X0))
| prime(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_divsiors) ).
fof(f16,plain,
( ~ prime(prime_divisor(factorial_plus_one(a)))
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
inference(subsumption_resolution,[],[f14,f10]) ).
fof(f14,plain,
( prime(factorial_plus_one(a))
| ~ prime(prime_divisor(factorial_plus_one(a)))
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
inference(resolution,[],[f13,f8]) ).
fof(f13,plain,
! [X0] :
( less(X0,prime_divisor(factorial_plus_one(X0)))
| prime(factorial_plus_one(X0)) ),
inference(resolution,[],[f4,f5]) ).
fof(f5,axiom,
! [X0] :
( divides(prime_divisor(X0),X0)
| prime(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',division_by_prime_divisor) ).
fof(f4,axiom,
! [X0,X1] :
( ~ divides(X0,factorial_plus_one(X1))
| less(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_is_smaller) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM016-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.32 % Computer : n029.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Fri May 3 14:50:22 EDT 2024
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % (8132)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.34 % (8137)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.34 % (8137)First to succeed.
% 0.13/0.34 % (8137)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-8132"
% 0.13/0.34 % (8137)Refutation found. Thanks to Tanya!
% 0.13/0.34 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.34 % (8137)------------------------------
% 0.13/0.34 % (8137)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.34 % (8137)Termination reason: Refutation
% 0.13/0.34
% 0.13/0.34 % (8137)Memory used [KB]: 745
% 0.13/0.34 % (8137)Time elapsed: 0.002 s
% 0.13/0.34 % (8137)Instructions burned: 2 (million)
% 0.13/0.34 % (8132)Success in time 0.003 s
%------------------------------------------------------------------------------