%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : NUM016-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n009.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 : 600s % DateTime : Mon Jul 18 14:23:40 EDT 2022 % Result : Unsatisfiable 0.19s 0.41s % Output : Refutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : NUM016-1 : TPTP v8.1.0. Released v1.0.0. % 0.08/0.13 % Command : run_spass %d %s % 0.13/0.33 % Computer : n009.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Tue Jul 5 20:43:22 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.41 % 0.19/0.41 SPASS V 3.9 % 0.19/0.41 SPASS beiseite: Proof found. % 0.19/0.41 % SZS status Theorem % 0.19/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.19/0.41 SPASS derived 20 clauses, backtracked 0 clauses, performed 0 splits and kept 24 clauses. % 0.19/0.41 SPASS allocated 75603 KBytes. % 0.19/0.41 SPASS spent 0:00:00.06 on the problem. % 0.19/0.41 0:00:00.04 for the input. % 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation. % 0.19/0.41 0:00:00.00 for inferences. % 0.19/0.41 0:00:00.00 for the backtracking. % 0.19/0.41 0:00:00.00 for the reduction. % 0.19/0.41 % 0.19/0.41 % 0.19/0.41 Here is a proof with depth 4, length 16 : % 0.19/0.41 % SZS output start Refutation % 0.19/0.41 1[0:Inp] || less(u,u)* -> . % 0.19/0.41 2[0:Inp] || less(u,v)*+ less(v,u)* -> . % 0.19/0.41 6[0:Inp] || -> less(u,factorial_plus_one(u))*. % 0.19/0.41 7[0:Inp] || divides(u,factorial_plus_one(v)) -> less(v,u)*. % 0.19/0.41 8[0:Inp] || -> prime(u) divides(prime_divisor(u),u)*l. % 0.19/0.41 9[0:Inp] || -> prime(u) prime(prime_divisor(u))*. % 0.19/0.41 10[0:Inp] || -> prime(u) less(prime_divisor(u),u)*. % 0.19/0.41 12[0:Inp] prime(u) || less(a,u) -> less(factorial_plus_one(a),u)*. % 0.19/0.41 14[0:Res:6.0,12.1] prime(factorial_plus_one(a)) || -> less(factorial_plus_one(a),factorial_plus_one(a))*. % 0.19/0.41 16[0:MRR:14.1,1.0] prime(factorial_plus_one(a)) || -> . % 0.19/0.41 23[0:Res:10.1,2.0] || less(u,prime_divisor(u))* -> prime(u). % 0.19/0.41 26[0:Res:12.2,23.0] prime(prime_divisor(factorial_plus_one(a))) || less(a,prime_divisor(factorial_plus_one(a)))* -> prime(factorial_plus_one(a)). % 0.19/0.41 28[0:MRR:26.0,26.2,9.1,16.0] || less(a,prime_divisor(factorial_plus_one(a)))* -> . % 0.19/0.41 38[0:Res:7.1,28.0] || divides(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a))*l -> . % 0.19/0.41 39[0:Res:8.1,38.0] || -> prime(factorial_plus_one(a))*. % 0.19/0.41 41[0:MRR:39.0,16.0] || -> . % 0.19/0.41 % SZS output end Refutation % 0.19/0.41 Formulae used in the proof : nothing_is_less_than_itself numbers_are_different a_prime_is_less_than_the_next_one divisor_is_smaller division_by_prime_divisor prime_divsiors smaller_prime_divisors prove_there_is_another_prime % 0.19/0.41 %------------------------------------------------------------------------------