%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : HEN009-4 : TPTP v8.1.0. Bugfixed v1.2.1. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n016.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 : Sat Jul 16 13:03:11 EDT 2022 % Result : Unsatisfiable 0.18s 0.54s % Output : Refutation 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : HEN009-4 : TPTP v8.1.0. Bugfixed v1.2.1. % 0.08/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n016.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Fri Jul 1 14:17:57 EDT 2022 % 0.12/0.34 % CPUTime : % 0.18/0.54 % 0.18/0.54 SPASS V 3.9 % 0.18/0.54 SPASS beiseite: Proof found. % 0.18/0.54 % SZS status Theorem % 0.18/0.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.18/0.54 SPASS derived 1221 clauses, backtracked 0 clauses, performed 0 splits and kept 343 clauses. % 0.18/0.54 SPASS allocated 64166 KBytes. % 0.18/0.54 SPASS spent 0:00:00.18 on the problem. % 0.18/0.54 0:00:00.04 for the input. % 0.18/0.54 0:00:00.00 for the FLOTTER CNF translation. % 0.18/0.54 0:00:00.01 for inferences. % 0.18/0.54 0:00:00.00 for the backtracking. % 0.18/0.54 0:00:00.11 for the reduction. % 0.18/0.54 % 0.18/0.54 % 0.18/0.54 Here is a proof with depth 2, length 13 : % 0.18/0.54 % SZS output start Refutation % 0.18/0.54 3[0:Inp] || -> equal(divide(u,u),zero)**. % 0.18/0.54 6[0:Inp] || less_equal(divide(u,v),w)*+ -> less_equal(divide(u,w),v)*. % 0.18/0.54 7[0:Inp] || less_equal(u,v) -> less_equal(divide(w,v),divide(w,u))*. % 0.18/0.54 9[0:Inp] || equal(divide(identity,divide(identity,divide(identity,a))),divide(identity,a))** -> . % 0.18/0.54 11[0:Inp] || equal(divide(u,v),zero)** -> less_equal(u,v). % 0.18/0.54 15[0:Inp] || less_equal(u,v)*+ less_equal(v,u)* -> equal(v,u). % 0.18/0.54 18[0:Res:15.2,9.0] || less_equal(divide(identity,a),divide(identity,divide(identity,divide(identity,a)))) less_equal(divide(identity,divide(identity,divide(identity,a))),divide(identity,a))*l -> . % 0.18/0.54 59[0:SpL:3.0,11.0] || equal(zero,zero)* -> less_equal(u,u)*. % 0.18/0.54 63[0:Obv:59.0] || -> less_equal(u,u)*. % 0.18/0.54 405[0:Res:63.0,6.0] || -> less_equal(divide(u,divide(u,v)),v)*l. % 0.18/0.54 435[0:MRR:18.1,405.0] || less_equal(divide(identity,a),divide(identity,divide(identity,divide(identity,a))))*r -> . % 0.18/0.54 1689[0:Res:7.1,435.0] || less_equal(divide(identity,divide(identity,a)),a)*l -> . % 0.18/0.54 1696[0:MRR:1689.0,405.0] || -> . % 0.18/0.54 % SZS output end Refutation % 0.18/0.54 Formulae used in the proof : x_divide_x_is_zero property_of_divide1 property_of_divide2 prove_this quotient_less_equal2 less_equal_and_equal % 0.18/0.54 %------------------------------------------------------------------------------