%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : HEN007-4 : TPTP v8.1.0. Released v1.0.0. % 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 13:03:07 EDT 2022 % Result : Unsatisfiable 0.44s 0.66s % Output : Refutation 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : HEN007-4 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.12 % 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 13:22:57 EDT 2022 % 0.12/0.33 % CPUTime : % 0.44/0.66 % 0.44/0.66 SPASS V 3.9 % 0.44/0.66 SPASS beiseite: Proof found. % 0.44/0.66 % SZS status Theorem % 0.44/0.66 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.44/0.66 SPASS derived 2333 clauses, backtracked 0 clauses, performed 0 splits and kept 525 clauses. % 0.44/0.66 SPASS allocated 65095 KBytes. % 0.44/0.66 SPASS spent 0:00:00.31 on the problem. % 0.44/0.66 0:00:00.04 for the input. % 0.44/0.66 0:00:00.00 for the FLOTTER CNF translation. % 0.44/0.66 0:00:00.03 for inferences. % 0.44/0.66 0:00:00.00 for the backtracking. % 0.44/0.66 0:00:00.23 for the reduction. % 0.44/0.66 % 0.44/0.66 % 0.44/0.66 Here is a proof with depth 6, length 29 : % 0.44/0.66 % SZS output start Refutation % 0.44/0.66 3[0:Inp] || -> equal(divide(u,u),zero)**. % 0.44/0.66 5[0:Inp] || less_equal(u,v)* less_equal(v,w)* -> less_equal(u,w)*. % 0.44/0.66 6[0:Inp] || less_equal(divide(u,v),w)*+ -> less_equal(divide(u,w),v)*. % 0.44/0.66 7[0:Inp] || -> less_equal(a,b)*r. % 0.44/0.66 8[0:Inp] || less_equal(divide(c,b),divide(c,a))*l -> . % 0.44/0.66 9[0:Inp] || less_equal(u,v) -> equal(divide(u,v),zero)**. % 0.44/0.66 10[0:Inp] || equal(divide(u,v),zero)** -> less_equal(u,v). % 0.44/0.66 11[0:Inp] || -> less_equal(divide(u,v),u)*l. % 0.44/0.66 12[0:Inp] || -> less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v))*l. % 0.44/0.66 13[0:Inp] || -> less_equal(zero,u)*. % 0.44/0.66 14[0:Inp] || less_equal(u,v)*+ less_equal(v,u)* -> equal(v,u). % 0.44/0.66 56[0:SpL:3.0,10.0] || equal(zero,zero)* -> less_equal(u,u)*. % 0.44/0.66 60[0:Obv:56.0] || -> less_equal(u,u)*. % 0.44/0.66 91[0:Res:13.0,14.0] || less_equal(u,zero)* -> equal(u,zero). % 0.44/0.66 155[0:SpL:9.1,6.0] || less_equal(u,v)* less_equal(zero,w) -> less_equal(divide(u,w),v)*. % 0.44/0.66 158[0:Res:60.0,6.0] || -> less_equal(divide(u,divide(u,v)),v)*l. % 0.44/0.66 174[0:MRR:155.1,13.0] || less_equal(u,v)*+ -> less_equal(divide(u,w),v)*. % 0.44/0.66 186[0:Res:158.0,91.0] || -> equal(divide(u,divide(u,zero)),zero)**. % 0.44/0.66 213[0:SpL:186.0,10.0] || equal(zero,zero) -> less_equal(u,divide(u,zero))*r. % 0.44/0.66 215[0:Obv:213.0] || -> less_equal(u,divide(u,zero))*r. % 0.44/0.66 222[0:Res:215.0,14.0] || less_equal(divide(u,zero),u)*l -> equal(divide(u,zero),u). % 0.44/0.66 233[0:MRR:222.0,11.0] || -> equal(divide(u,zero),u)**. % 0.44/0.66 1522[0:Res:7.0,174.0] || -> less_equal(divide(a,u),b)*l. % 0.44/0.66 1573[0:Res:1522.0,6.0] || -> less_equal(divide(a,b),u)*. % 0.44/0.66 1620[0:Res:1573.0,91.0] || -> equal(divide(a,b),zero)**. % 0.44/0.66 1777[0:SpR:1620.0,12.0] || -> less_equal(divide(divide(u,b),zero),divide(divide(u,a),b))*l. % 0.44/0.66 1798[0:Rew:233.0,1777.0] || -> less_equal(divide(u,b),divide(divide(u,a),b))*r. % 0.44/0.66 3337[0:OCh:5.1,5.0,1798.0,11.0] || -> less_equal(divide(u,b),divide(u,a))*l. % 0.44/0.66 3367[0:UnC:3337.0,8.0] || -> . % 0.44/0.66 % SZS output end Refutation % 0.44/0.66 Formulae used in the proof : x_divide_x_is_zero transitivity_of_less_equal property_of_divide1 a_LE_b prove_c_divide_b_LE_c_divide_a quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal % 0.44/0.66 %------------------------------------------------------------------------------