%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : NUM015-1 : 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 14:23:39 EDT 2022 % Result : Unsatisfiable 0.13s 0.40s % Output : Refutation 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : NUM015-1 : TPTP v8.1.0. Released v1.0.0. % 0.10/0.12 % Command : run_spass %d %s % 0.13/0.32 % Computer : n009.cluster.edu % 0.13/0.32 % Model : x86_64 x86_64 % 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.32 % Memory : 8042.1875MB % 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.32 % CPULimit : 300 % 0.13/0.32 % WCLimit : 600 % 0.13/0.32 % DateTime : Wed Jul 6 14:29:22 EDT 2022 % 0.13/0.33 % CPUTime : % 0.13/0.40 % 0.13/0.40 SPASS V 3.9 % 0.13/0.40 SPASS beiseite: Proof found. % 0.13/0.40 % SZS status Theorem % 0.13/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.13/0.40 SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 16 clauses. % 0.13/0.40 SPASS allocated 75594 KBytes. % 0.13/0.40 SPASS spent 0:00:00.06 on the problem. % 0.13/0.40 0:00:00.04 for the input. % 0.13/0.40 0:00:00.00 for the FLOTTER CNF translation. % 0.13/0.40 0:00:00.00 for inferences. % 0.13/0.40 0:00:00.00 for the backtracking. % 0.13/0.40 0:00:00.00 for the reduction. % 0.13/0.40 % 0.13/0.40 % 0.13/0.40 Here is a proof with depth 4, length 15 : % 0.13/0.40 % SZS output start Refutation % 0.13/0.40 1[0:Inp] || -> divides(u,u)*. % 0.13/0.40 2[0:Inp] || divides(u,v)* divides(v,w)* -> divides(u,w)*. % 0.13/0.40 3[0:Inp] || -> prime(u) divides(divisor(u),u)*l. % 0.13/0.40 4[0:Inp] || -> prime(u) less(n1,divisor(u))*. % 0.13/0.40 5[0:Inp] || -> prime(u) less(divisor(u),u)*. % 0.13/0.40 6[0:Inp] || less(u,a) less(n1,u) -> prime(factor_of(u))*. % 0.13/0.40 7[0:Inp] || less(u,a)*+ less(n1,u)* -> divides(factor_of(u),u). % 0.13/0.40 9[0:Inp] prime(u) || divides(u,a)* -> . % 0.13/0.40 10[0:Res:1.0,9.1] prime(a) || -> . % 0.13/0.40 21[0:Res:5.1,7.0] || less(n1,divisor(a))* -> prime(a) divides(factor_of(divisor(a)),divisor(a)). % 0.13/0.40 22[0:MRR:21.0,21.1,4.1,10.0] || -> divides(factor_of(divisor(a)),divisor(a))*l. % 0.13/0.40 23[0:NCh:2.2,2.0,22.0,9.1] prime(factor_of(divisor(a))) || divides(divisor(a),a)*l -> . % 0.13/0.40 24[0:SoR:23.0,6.2] || divides(divisor(a),a) less(n1,divisor(a)) less(divisor(a),a)* -> . % 0.13/0.40 25[0:Res:5.1,24.2] || divides(divisor(a),a) less(n1,divisor(a))* -> prime(a). % 0.13/0.40 26[0:MRR:25.0,25.1,25.2,3.1,4.1,10.0] || -> . % 0.13/0.40 % SZS output end Refutation % 0.13/0.40 Formulae used in the proof : divide_self transitive_divide prime divisor1 divisor2 factor1 factor2 prove_a_has_prime_divisor % 0.13/0.40 %------------------------------------------------------------------------------