%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM016-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Fri Jul 25 12:27:30 PM UTC 2025
% Result : Unsatisfiable 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named prove_there_is_another_prime)
% Comments :
%------------------------------------------------------------------------------
cnf(7,plain,
( ~ less(a,X0)
| ~ prime(X0)
| less(factorial_plus_one(a),X0) ),
inference(cnf,[status(esa)],[prove_there_is_another_prime]) ).
cnf(l0,plain,
( ~ less(a,factorial_plus_one(a))
| ~ prime(factorial_plus_one(a))
| less(factorial_plus_one(a),factorial_plus_one(a)) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(5,plain,
( prime(X0)
| prime(prime_divisor(X0)) ),
inference(cnf,[status(esa)],[prime_divsiors]) ).
cnf(l1,plain,
( prime(factorial_plus_one(a))
| prime(prime_divisor(factorial_plus_one(a))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(1,plain,
( ~ less(X0,X1)
| ~ less(X1,X0) ),
inference(cnf,[status(esa)],[numbers_are_different]) ).
cnf(l4,plain,
( ~ less(factorial_plus_one(a),factorial_plus_one(a))
| ~ less(factorial_plus_one(a),factorial_plus_one(a)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(2,plain,
less(X0,factorial_plus_one(X0)),
inference(cnf,[status(esa)],[a_prime_is_less_than_the_next_one]) ).
cnf(l2,plain,
less(a,factorial_plus_one(a)),
inference(instantiation,[status(thm)],[2]) ).
cnf(l3,plain,
( ~ less(a,prime_divisor(factorial_plus_one(a)))
| ~ prime(prime_divisor(factorial_plus_one(a)))
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l6,plain,
( ~ less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
| ~ less(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(3,plain,
( ~ divides(X0,factorial_plus_one(X1))
| less(X1,X0) ),
inference(cnf,[status(esa)],[divisor_is_smaller]) ).
cnf(l7,plain,
( ~ divides(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a))
| less(a,prime_divisor(factorial_plus_one(a))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(4,plain,
( divides(prime_divisor(X0),X0)
| prime(X0) ),
inference(cnf,[status(esa)],[division_by_prime_divisor]) ).
cnf(l10,plain,
( divides(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a))
| prime(factorial_plus_one(a)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(6,plain,
( less(prime_divisor(X0),X0)
| prime(X0) ),
inference(cnf,[status(esa)],[smaller_prime_divisors]) ).
cnf(l11,plain,
( less(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a))
| prime(factorial_plus_one(a)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l4,l2,l3,l6,l7,l10,l11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM016-2 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 21 10:13:04 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 4
% 0.13/0.35 % launching worker at depth: 5
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.35 % SZS status Theorem for theBenchmark
% 0.13/0.35 % launching worker at depth: 10
% 0.13/0.35 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------