%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM016-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 : Fri Sep 25 02:18:32 PM UTC 2026
% Result : Unsatisfiable 1.60s 0.80s
% Output : Proof 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 27 ~; 37 |; 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 : 43 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,axiom,
( less(Y,X)
| ~ divides(X,factorial_plus_one(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor_is_smaller) ).
fof(f3_nnf,plain,
! [X,Y] :
( less(Y,X)
| ~ divides(X,factorial_plus_one(Y)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( less(Y,X)
| ~ divides(X,factorial_plus_one(Y)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( less(X1,X0)
| ~ divides(X0,factorial_plus_one(X1)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(f4,axiom,
( divides(prime_divisor(X),X)
| prime(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',division_by_prime_divisor) ).
fof(f4_nnf,plain,
! [X] :
( divides(prime_divisor(X),X)
| prime(X) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] :
( divides(prime_divisor(X),X)
| prime(X) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( divides(prime_divisor(X0),X0)
| prime(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p11,plain,
( prime(factorial_plus_one(X0))
| less(X0,prime_divisor(factorial_plus_one(X0))) ),
inference(resolution,[status(thm)],[c3,c4]) ).
cnf(f5,axiom,
( prime(prime_divisor(X))
| prime(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_divsiors) ).
fof(f5_nnf,plain,
! [X] :
( prime(prime_divisor(X))
| prime(X) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] :
( prime(prime_divisor(X))
| prime(X) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( prime(prime_divisor(X0))
| prime(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f7,negated_conjecture,
( less(factorial_plus_one(a),X)
| ~ less(a,X)
| ~ prime(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_another_prime) ).
fof(f7_nnf,plain,
! [X] :
( less(factorial_plus_one(a),X)
| ~ less(a,X)
| ~ prime(X) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X] :
( less(factorial_plus_one(a),X)
| ~ less(a,X)
| ~ prime(X) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( less(factorial_plus_one(a),X0)
| ~ less(a,X0)
| ~ prime(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p8,plain,
( less(factorial_plus_one(a),prime_divisor(X0))
| ~ less(a,prime_divisor(X0))
| prime(X0) ),
inference(resolution,[status(thm)],[c5,c7]) ).
cnf(p13,plain,
( less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
| prime(factorial_plus_one(a))
| prime(factorial_plus_one(a)) ),
inference(resolution,[status(thm)],[p11,p8]) ).
cnf(p14,plain,
( less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
| prime(factorial_plus_one(a)) ),
inference(factoring,[status(thm)],[p13]) ).
cnf(f6,axiom,
( less(prime_divisor(X),X)
| prime(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',smaller_prime_divisors) ).
fof(f6_nnf,plain,
! [X] :
( less(prime_divisor(X),X)
| prime(X) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] :
( less(prime_divisor(X),X)
| prime(X) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( less(prime_divisor(X0),X0)
| prime(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f1,axiom,
( ~ less(Y,X)
| ~ less(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',numbers_are_different) ).
fof(f1_nnf,plain,
! [X,Y] :
( ~ less(Y,X)
| ~ less(X,Y) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( ~ less(Y,X)
| ~ less(X,Y) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p10,plain,
( ~ less(X0,prime_divisor(X0))
| prime(X0) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(p16,plain,
( prime(factorial_plus_one(a))
| prime(factorial_plus_one(a)) ),
inference(resolution,[status(thm)],[p14,p10]) ).
cnf(p17,plain,
prime(factorial_plus_one(a)),
inference(factoring,[status(thm)],[p16]) ).
cnf(p18,plain,
( less(factorial_plus_one(a),factorial_plus_one(a))
| ~ less(a,factorial_plus_one(a)) ),
inference(resolution,[status(thm)],[p17,c7]) ).
cnf(f2,axiom,
less(X,factorial_plus_one(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).
fof(f2_nnf,plain,
! [X] : less(X,factorial_plus_one(X)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : less(X,factorial_plus_one(X)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
less(X0,factorial_plus_one(X0)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p19,plain,
less(factorial_plus_one(a),factorial_plus_one(a)),
inference(resolution,[status(thm)],[p18,c2]) ).
cnf(f0,axiom,
~ less(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).
fof(f0_nnf,plain,
! [X] : ~ less(X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : ~ less(X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
~ less(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p20,plain,
$false,
inference(resolution,[status(thm)],[p19,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM016-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 02:40:13 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.60/0.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.60/0.80 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------