%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : NUM022-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n008.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 14:23:43 EDT 2022 % Result : Unsatisfiable 0.20s 0.41s % Output : Refutation 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM022-1 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.12 % Command : run_spass %d %s % 0.12/0.34 % Computer : n008.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Wed Jul 6 00:13:23 EDT 2022 % 0.12/0.34 % CPUTime : % 0.20/0.41 % 0.20/0.41 SPASS V 3.9 % 0.20/0.41 SPASS beiseite: Proof found. % 0.20/0.41 % SZS status Theorem % 0.20/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.20/0.41 SPASS derived 14 clauses, backtracked 0 clauses, performed 0 splits and kept 16 clauses. % 0.20/0.41 SPASS allocated 63096 KBytes. % 0.20/0.41 SPASS spent 0:00:00.06 on the problem. % 0.20/0.41 0:00:00.03 for the input. % 0.20/0.41 0:00:00.00 for the FLOTTER CNF translation. % 0.20/0.41 0:00:00.00 for inferences. % 0.20/0.41 0:00:00.00 for the backtracking. % 0.20/0.41 0:00:00.00 for the reduction. % 0.20/0.41 % 0.20/0.41 % 0.20/0.41 Here is a proof with depth 3, length 15 : % 0.20/0.41 % SZS output start Refutation % 0.20/0.41 1[0:Inp] || equalish(u,v)* equalish(v,w)* -> equalish(u,w)*. % 0.20/0.41 2[0:Inp] || -> less(a,b)*l. % 0.20/0.41 3[0:Inp] || -> divides(b,d)*. % 0.20/0.41 4[0:Inp] || less(a,d)*l -> . % 0.20/0.41 5[0:Inp] || less(u,v)* less(v,w)* -> less(u,w)*. % 0.20/0.41 6[0:Inp] || equalish(add(successor(u),v),w)* -> less(v,w). % 0.20/0.41 7[0:Inp] || less(u,v) -> equalish(add(successor(predecessor_of_1st_minus_2nd(v,u)),u),v)*l. % 0.20/0.41 8[0:Inp] || divides(u,v)* -> equalish(u,v) less(u,v). % 0.20/0.41 12[0:Res:6.1,4.0] || equalish(add(successor(u),a),d)*l -> . % 0.20/0.41 13[0:NCh:5.2,5.0,4.0,2.0] || less(b,d)*l -> . % 0.20/0.41 16[0:Res:3.0,8.0] || -> equalish(b,d) less(b,d)*l. % 0.20/0.41 19[0:MRR:16.1,13.0] || -> equalish(b,d)*l. % 0.20/0.41 22[0:NCh:1.2,1.0,7.1,12.0] || less(a,u)* equalish(u,d) -> . % 0.20/0.41 24[0:Res:2.0,22.0] || equalish(b,d)*l -> . % 0.20/0.41 26[0:MRR:24.0,19.0] || -> . % 0.20/0.41 % SZS output end Refutation % 0.20/0.41 Formulae used in the proof : transitivity a_less_than_b b_divides_d prove_a_less_than_d transitivity_of_less smaller_number less_lemma divides_only_less_or_equal % 0.20/0.41 %------------------------------------------------------------------------------