%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM016-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:11:34 PM UTC 2026
% Result : Unsatisfiable 3.63s 1.49s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 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(f1,axiom,
! [X0] : ~ less(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).
fof(f2,axiom,
! [X0,X1] :
( ~ less(X1,X0)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',numbers_are_different) ).
fof(f3,axiom,
! [X0] : less(X0,factorial_plus_one(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).
fof(f4,axiom,
! [X0,X1] :
( ~ divides(X0,factorial_plus_one(X1))
| less(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor_is_smaller) ).
fof(f5,axiom,
! [X0] :
( divides(prime_divisor(X0),X0)
| prime(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',division_by_prime_divisor) ).
fof(f6,axiom,
! [X0] :
( prime(prime_divisor(X0))
| prime(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_divsiors) ).
fof(f7,axiom,
! [X0] :
( less(prime_divisor(X0),X0)
| prime(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',smaller_prime_divisors) ).
fof(f8,negated_conjecture,
! [X0] :
( less(factorial_plus_one(a),X0)
| ~ less(a,X0)
| ~ prime(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_another_prime) ).
fof(f9,plain,
( ~ less(a,factorial_plus_one(a))
| ~ prime(factorial_plus_one(a)) ),
inference(resolution,[],[f1,f8]) ).
fof(f10,plain,
~ prime(factorial_plus_one(a)),
inference(forward_subsumption_resolution,[],[f9,f3]) ).
fof(f11,plain,
! [X0] :
( ~ less(X0,factorial_plus_one(a))
| ~ less(a,X0)
| ~ prime(X0) ),
inference(resolution,[],[f2,f8]) ).
fof(f18,plain,
( prime(factorial_plus_one(a))
| ~ less(a,prime_divisor(factorial_plus_one(a)))
| ~ prime(prime_divisor(factorial_plus_one(a))) ),
inference(resolution,[],[f7,f11]) ).
fof(f19,plain,
( prime(factorial_plus_one(a))
| ~ less(a,prime_divisor(factorial_plus_one(a))) ),
inference(forward_subsumption_resolution,[],[f18,f6]) ).
fof(f20,plain,
~ less(a,prime_divisor(factorial_plus_one(a))),
inference(forward_subsumption_resolution,[],[f19,f10]) ).
fof(f21,plain,
! [X0] :
( less(X0,prime_divisor(factorial_plus_one(X0)))
| prime(factorial_plus_one(X0)) ),
inference(resolution,[],[f4,f5]) ).
fof(f25,plain,
prime(factorial_plus_one(a)),
inference(resolution,[],[f21,f20]) ).
fof(f26,plain,
$false,
inference(forward_subsumption_resolution,[],[f25,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM016-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 18:39:31 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.63/1.49 % (1095734)Input is clausal, will run a generic CNF schedule.
% 3.63/1.49 % (1095740)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3166695450:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.63/1.49 % (1095739)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1910713289:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.63/1.49 % (1095745)dis-21_1_sil=8000:lcm=predicate:random_seed=1030537034:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.63/1.49 % (1095744)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1177378548:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.63/1.49 % (1095742)lrs+10_1_sil=8000:sp=occurrence:random_seed=1303427756:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.63/1.49 % (1095743)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=628292191:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.63/1.49 % (1095741)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2320746620:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.63/1.49 % (1095742)First to succeed.
% 3.63/1.49 % (1095744)Also succeeded, but the first one will report.
% 3.63/1.49 % (1095743)Also succeeded, but the first one will report.
% 3.63/1.49 % (1095742)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1095734"
% 3.63/1.49 % (1095745)Also succeeded, but the first one will report.
% 3.63/1.49 % (1095742)Refutation found. Thanks to Tanya!
% 3.63/1.49 % SZS status Unsatisfiable for theBenchmark
% 3.63/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.49 % (1095742)------------------------------
% 3.63/1.49 % (1095742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.49 % (1095742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.49 % (1095742)CaDiCaL version: 2.1.3
% 3.63/1.49 % (1095742)Termination reason: Refutation
% 3.63/1.49 % (1095742)Time elapsed: 0.002 s
% 3.63/1.49 % (1095742)Peak memory usage: 87 MB
% 3.63/1.49 % (1095742)Instructions burned: 1 (million)
% 3.63/1.49 % (1095742)------------------------------
% 3.63/1.49 % (1095742)------------------------------
% 3.63/1.49 % (1095734)Success in time 0.432 s
% 3.63/1.49 % Vampire exiting
%------------------------------------------------------------------------------