%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:17:49 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.53s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 10 ~; 13 |; 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 : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ less(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).
fof(f5,axiom,
! [X0,X1] :
( ~ divides(X0,X1)
| ~ less(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',small_divides_large) ).
fof(f6,axiom,
! [X0] : less(X0,factorial_plus_one(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).
fof(f7,axiom,
! [X0,X1] :
( ~ divides(X0,factorial_plus_one(X1))
| less(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_is_smaller) ).
fof(f8,axiom,
! [X0] :
( prime(X0)
| divides(prime_divisor(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',division_by_prime_divisor) ).
fof(f9,axiom,
! [X0] :
( prime(prime_divisor(X0))
| prime(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_divsiors) ).
fof(f12,negated_conjecture,
! [X0] :
( ~ prime(X0)
| ~ less(a,X0)
| less(factorial_plus_one(a),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_another_prime) ).
fof(f14,plain,
! [X0] :
( ~ less(a,prime_divisor(X0))
| prime(X0)
| less(factorial_plus_one(a),prime_divisor(X0)) ),
inference(resolution,[],[f9,f12]) ).
fof(f17,plain,
! [X0] :
( ~ less(a,X0)
| divides(prime_divisor(X0),X0)
| less(factorial_plus_one(a),X0) ),
inference(resolution,[],[f8,f12]) ).
fof(f19,plain,
( divides(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a))
| less(factorial_plus_one(a),factorial_plus_one(a)) ),
inference(resolution,[],[f17,f6]) ).
fof(f20,plain,
divides(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a)),
inference(forward_subsumption_resolution,[],[f19,f1]) ).
fof(f22,plain,
less(a,prime_divisor(factorial_plus_one(a))),
inference(resolution,[],[f20,f7]) ).
fof(f23,plain,
~ less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))),
inference(resolution,[],[f20,f5]) ).
fof(f26,plain,
( prime(factorial_plus_one(a))
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
inference(resolution,[],[f22,f14]) ).
fof(f30,plain,
prime(factorial_plus_one(a)),
inference(forward_subsumption_resolution,[],[f26,f23]) ).
fof(f35,plain,
( ~ less(a,factorial_plus_one(a))
| less(factorial_plus_one(a),factorial_plus_one(a)) ),
inference(resolution,[],[f30,f12]) ).
fof(f36,plain,
less(factorial_plus_one(a),factorial_plus_one(a)),
inference(forward_subsumption_resolution,[],[f35,f6]) ).
fof(f37,plain,
$false,
inference(forward_subsumption_resolution,[],[f36,f1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.17/0.43 % Computer : n019.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 27 18:39:48 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.21/0.49 Running first-order model finding
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.53 % (3330240)Will run a generic schedule for satisfiability detection.
% 0.21/0.53 % (3330245)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=242941423_3000 on theBenchmark for (3000ds/0Mi)
% 0.21/0.53 % TRYING [1]
% 0.21/0.53 % TRYING [2]
% 0.21/0.53 % TRYING [3]
% 0.21/0.53 % TRYING [4]
% 0.21/0.53 % TRYING [5]
% 0.21/0.53 % TRYING [6]
% 0.21/0.53 % (3330250)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2815865617:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.21/0.53 % TRYING [7]
% 0.21/0.53 % (3330250) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3330240-3330250"...
% 0.21/0.53 % TRYING [8]
% 0.21/0.53 % (3330250)...printing done.
% 0.21/0.53 % TRYING [9]
% 0.21/0.53 % (3330250)Refutation found. Thanks to Tanya!
% 0.21/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53 % (3330250)------------------------------
% 0.21/0.53 % (3330250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.53 % (3330250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.53 % (3330250)CaDiCaL version: 2.1.3
% 0.21/0.53 % (3330250)Termination reason: Refutation
% 0.21/0.53 % (3330250)Time elapsed: 0.002 s
% 0.21/0.53 % (3330250)Peak memory usage: 11 MB
% 0.21/0.53 % (3330250)Instructions burned: 1 (million)
% 0.21/0.53 % (3330240)Success in time 0.028 s
% 0.21/0.53 % Vampire exiting
%------------------------------------------------------------------------------