%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : HEN008-4 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n007.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 13:03:09 EDT 2022 % Result : Unsatisfiable 0.20s 0.55s % Output : Refutation 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : HEN008-4 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n007.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 : 600 % 0.13/0.34 % DateTime : Fri Jul 1 13:05:24 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.55 % 0.20/0.55 SPASS V 3.9 % 0.20/0.55 SPASS beiseite: Proof found. % 0.20/0.55 % SZS status Theorem % 0.20/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.20/0.55 SPASS derived 1545 clauses, backtracked 0 clauses, performed 0 splits and kept 428 clauses. % 0.20/0.55 SPASS allocated 64438 KBytes. % 0.20/0.55 SPASS spent 0:00:00.20 on the problem. % 0.20/0.55 0:00:00.04 for the input. % 0.20/0.55 0:00:00.00 for the FLOTTER CNF translation. % 0.20/0.55 0:00:00.01 for inferences. % 0.20/0.55 0:00:00.00 for the backtracking. % 0.20/0.55 0:00:00.12 for the reduction. % 0.20/0.55 % 0.20/0.55 % 0.20/0.55 Here is a proof with depth 5, length 29 : % 0.20/0.55 % SZS output start Refutation % 0.20/0.55 2[0:Inp] || -> equal(divide(zero,u),zero)**. % 0.20/0.55 3[0:Inp] || -> equal(divide(u,u),zero)**. % 0.20/0.55 6[0:Inp] || less_equal(divide(u,v),w)*+ -> less_equal(divide(u,w),v)*. % 0.20/0.55 8[0:Inp] || -> less_equal(a,b)*r. % 0.20/0.55 9[0:Inp] || less_equal(divide(a,c),divide(b,c))*r -> . % 0.20/0.55 10[0:Inp] || less_equal(u,v) -> equal(divide(u,v),zero)**. % 0.20/0.55 11[0:Inp] || equal(divide(u,v),zero)** -> less_equal(u,v). % 0.20/0.55 12[0:Inp] || -> less_equal(divide(u,v),u)*l. % 0.20/0.55 13[0:Inp] || -> less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v))*l. % 0.20/0.55 14[0:Inp] || -> less_equal(zero,u)*. % 0.20/0.55 15[0:Inp] || less_equal(u,v)*+ less_equal(v,u)* -> equal(v,u). % 0.20/0.55 56[0:SpL:3.0,11.0] || equal(zero,zero)* -> less_equal(u,u)*. % 0.20/0.55 60[0:Obv:56.0] || -> less_equal(u,u)*. % 0.20/0.55 106[0:Res:14.0,15.0] || less_equal(u,zero)* -> equal(u,zero). % 0.20/0.55 236[0:SpL:10.1,6.0] || less_equal(u,v)* less_equal(zero,w) -> less_equal(divide(u,w),v)*. % 0.20/0.55 240[0:Res:60.0,6.0] || -> less_equal(divide(u,divide(u,v)),v)*l. % 0.20/0.55 241[0:Res:13.0,6.0] || -> less_equal(divide(divide(u,v),divide(divide(u,w),v)),divide(w,v))*l. % 0.20/0.55 269[0:MRR:236.1,14.0] || less_equal(u,v)*+ -> less_equal(divide(u,w),v)*. % 0.20/0.55 376[0:Res:240.0,106.0] || -> equal(divide(u,divide(u,zero)),zero)**. % 0.20/0.55 487[0:SpL:376.0,11.0] || equal(zero,zero) -> less_equal(u,divide(u,zero))*r. % 0.20/0.55 490[0:Obv:487.0] || -> less_equal(u,divide(u,zero))*r. % 0.20/0.55 542[0:Res:490.0,15.0] || less_equal(divide(u,zero),u)*l -> equal(divide(u,zero),u). % 0.20/0.55 596[0:MRR:542.0,12.0] || -> equal(divide(u,zero),u)**. % 0.20/0.55 1894[0:Res:8.0,269.0] || -> less_equal(divide(a,u),b)*l. % 0.20/0.55 1950[0:Res:1894.0,6.0] || -> less_equal(divide(a,b),u)*. % 0.20/0.55 2051[0:Res:1950.0,106.0] || -> equal(divide(a,b),zero)**. % 0.20/0.55 2174[0:SpR:2051.0,241.0] || -> less_equal(divide(divide(a,u),divide(zero,u)),divide(b,u))*l. % 0.20/0.55 2194[0:Rew:596.0,2174.0,2.0,2174.0] || -> less_equal(divide(a,u),divide(b,u))*r. % 0.20/0.55 2195[0:UnC:2194.0,9.0] || -> . % 0.20/0.55 % SZS output end Refutation % 0.20/0.55 Formulae used in the proof : zero_divide_anything_is_zero x_divide_x_is_zero property_of_divide1 a_LE_b prove_a_divide_c_LE_b_divide_c quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal % 0.20/0.55 %------------------------------------------------------------------------------