%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n007.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 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 12 unt; 2 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 21 ~; 25 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 13 ( 0 sgn 13 !; 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(X0,X1)
| ~ less(X1,X0) ),
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] :
( prime(X0)
| divides(prime_divisor(X0),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] :
( prime(X0)
| less(prime_divisor(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',smaller_prime_divisors) ).
fof(f8,negated_conjecture,
! [X0] :
( ~ prime(X0)
| ~ less(a,X0)
| less(factorial_plus_one(a),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_another_prime) ).
fof(f9,plain,
! [X0] :
( ~ less(a,prime_divisor(X0))
| prime(X0)
| less(factorial_plus_one(a),prime_divisor(X0)) ),
inference(resolution,[],[f6,f8]) ).
fof(f11,plain,
! [X0] :
( ~ less(a,X0)
| divides(prime_divisor(X0),X0)
| less(factorial_plus_one(a),X0) ),
inference(resolution,[],[f5,f8]) ).
fof(f12,plain,
( divides(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a))
| less(factorial_plus_one(a),factorial_plus_one(a)) ),
inference(resolution,[],[f11,f3]) ).
fof(f13,plain,
divides(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a)),
inference(forward_subsumption_resolution,[],[f12,f1]) ).
fof(f14,plain,
! [X0] :
( ~ less(a,X0)
| less(prime_divisor(X0),X0)
| less(factorial_plus_one(a),X0) ),
inference(resolution,[],[f7,f8]) ).
fof(f15,plain,
less(a,prime_divisor(factorial_plus_one(a))),
inference(resolution,[],[f4,f13]) ).
fof(f16,plain,
( prime(factorial_plus_one(a))
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
inference(resolution,[],[f15,f9]) ).
fof(f20,definition,
( spl0_1
<=> less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f22,plain,
( less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f29,definition,
( spl0_3
<=> prime(factorial_plus_one(a)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f31,plain,
( prime(factorial_plus_one(a))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f16,f29,f20]) ).
fof(f34,plain,
( less(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a))
| less(factorial_plus_one(a),factorial_plus_one(a)) ),
inference(resolution,[],[f14,f3]) ).
fof(f35,plain,
less(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a)),
inference(forward_subsumption_resolution,[],[f34,f1]) ).
fof(f41,plain,
( ~ less(a,factorial_plus_one(a))
| less(factorial_plus_one(a),factorial_plus_one(a))
| ~ spl0_3 ),
inference(resolution,[],[f31,f8]) ).
fof(f42,plain,
( less(factorial_plus_one(a),factorial_plus_one(a))
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f41,f3]) ).
fof(f43,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f42,f1]) ).
fof(f44,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f43]) ).
fof(f45,plain,
~ less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))),
inference(resolution,[],[f35,f2]) ).
fof(f46,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f45,f22]) ).
fof(f47,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f46]) ).
cnf(s2,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f32]) ).
cnf(s4,plain,
~ spl0_3,
inference(sat_conversion,[],[f44]) ).
cnf(s5,plain,
~ spl0_1,
inference(sat_conversion,[],[f47]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s4,s5]) ).
fof(f48,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM016-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 18:37:40 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.45 % (1705491)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (1705501)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1681293755:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (1705501) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1705491-1705501"...
% 0.11/0.45 % (1705501)...printing done.
% 0.11/0.45 % (1705501)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (1705501)------------------------------
% 0.11/0.45 % (1705501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (1705501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (1705501)CaDiCaL version: 2.1.3
% 0.11/0.45 % (1705501)Termination reason: Refutation
% 0.11/0.45 % (1705501)Time elapsed: 0.001 s
% 0.11/0.45 % (1705501)Peak memory usage: 12 MB
% 0.11/0.45 % (1705501)Instructions burned: 1 (million)
% 0.11/0.45 % (1705491)Success in time 0.039 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------