%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM016-2 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.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 : Tue May 5 04:52:43 PM UTC 2026
% Result : Unsatisfiable 1.24s 1.71s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 22 ( 7 unt; 7 nHn; 13 RR)
% Number of literals : 39 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 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 : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(numbers_are_different,axiom,
( ~ less(X1,X2)
| ~ less(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',numbers_are_different) ).
cnf(smaller_prime_divisors,axiom,
( prime(X1)
| less(prime_divisor(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_prime_divisors) ).
cnf(nothing_is_less_than_itself,axiom,
~ less(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).
cnf(prove_there_is_another_prime,negated_conjecture,
( less(factorial_plus_one(a),X1)
| ~ prime(X1)
| ~ less(a,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_another_prime) ).
cnf(a_prime_is_less_than_the_next_one,axiom,
less(X1,factorial_plus_one(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).
cnf(prime_divsiors,axiom,
( prime(X1)
| prime(prime_divisor(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_divsiors) ).
cnf(divisor_is_smaller,axiom,
( less(X2,X1)
| ~ divides(X1,factorial_plus_one(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_is_smaller) ).
cnf(division_by_prime_divisor,axiom,
( prime(X1)
| divides(prime_divisor(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',division_by_prime_divisor) ).
cnf(c_0_8,axiom,
( ~ less(X1,X2)
| ~ less(X2,X1) ),
numbers_are_different ).
cnf(c_0_9,axiom,
( prime(X1)
| less(prime_divisor(X1),X1) ),
smaller_prime_divisors ).
cnf(c_0_10,axiom,
~ less(X1,X1),
nothing_is_less_than_itself ).
cnf(c_0_11,negated_conjecture,
( less(factorial_plus_one(a),X1)
| ~ prime(X1)
| ~ less(a,X1) ),
prove_there_is_another_prime ).
cnf(c_0_12,axiom,
less(X1,factorial_plus_one(X1)),
a_prime_is_less_than_the_next_one ).
cnf(c_0_13,plain,
( prime(X1)
| ~ less(X1,prime_divisor(X1)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
~ prime(factorial_plus_one(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_15,negated_conjecture,
( ~ prime(prime_divisor(factorial_plus_one(a)))
| ~ less(a,prime_divisor(factorial_plus_one(a))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_14]) ).
cnf(c_0_16,axiom,
( prime(X1)
| prime(prime_divisor(X1)) ),
prime_divsiors ).
cnf(c_0_17,axiom,
( less(X2,X1)
| ~ divides(X1,factorial_plus_one(X2)) ),
divisor_is_smaller ).
cnf(c_0_18,axiom,
( prime(X1)
| divides(prime_divisor(X1),X1) ),
division_by_prime_divisor ).
cnf(c_0_19,negated_conjecture,
~ less(a,prime_divisor(factorial_plus_one(a))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_14]) ).
cnf(c_0_20,plain,
( prime(factorial_plus_one(X1))
| less(X1,prime_divisor(factorial_plus_one(X1))) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM016-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n017.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:04:42 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.24/1.71 % Version : CSE_E---1.7
% 1.24/1.71 % Problem : theBenchmark.p
% 1.24/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.24/1.71 % SZS output start CNFRefutation
% See solution above
% 1.24/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------