%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : HEN010-4 : 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 13:03:13 EDT 2022 % Result : Unsatisfiable 0.20s 0.48s % Output : Refutation 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : HEN010-4 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : run_spass %d %s % 0.12/0.34 % Computer : n007.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 : Fri Jul 1 14:16:39 EDT 2022 % 0.12/0.34 % CPUTime : % 0.20/0.48 % 0.20/0.48 SPASS V 3.9 % 0.20/0.48 SPASS beiseite: Proof found. % 0.20/0.48 % SZS status Theorem % 0.20/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.48 SPASS derived 749 clauses, backtracked 0 clauses, performed 0 splits and kept 223 clauses. % 0.20/0.48 SPASS allocated 63747 KBytes. % 0.20/0.48 SPASS spent 0:00:00.12 on the problem. % 0.20/0.48 0:00:00.03 for the input. % 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation. % 0.20/0.48 0:00:00.01 for inferences. % 0.20/0.48 0:00:00.00 for the backtracking. % 0.20/0.48 0:00:00.06 for the reduction. % 0.20/0.48 % 0.20/0.48 % 0.20/0.48 Here is a proof with depth 5, length 24 : % 0.20/0.48 % SZS output start Refutation % 0.20/0.48 3[0:Inp] || -> equal(divide(u,u),zero)**. % 0.20/0.48 6[0:Inp] || less_equal(divide(u,v),w)*+ -> less_equal(divide(u,w),v)*. % 0.20/0.48 9[0:Inp] || -> equal(divide(identity,divide(identity,divide(identity,u))),divide(identity,u))**. % 0.20/0.48 10[0:Inp] || equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a))** -> . % 0.20/0.48 12[0:Inp] || equal(divide(u,v),zero)** -> less_equal(u,v). % 0.20/0.48 13[0:Inp] || -> less_equal(divide(u,v),u)*l. % 0.20/0.48 14[0:Inp] || -> less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v))*l. % 0.20/0.48 15[0:Inp] || -> less_equal(zero,u)*. % 0.20/0.48 16[0:Inp] || less_equal(u,v)*+ less_equal(v,u)* -> equal(v,u). % 0.20/0.48 19[0:Res:16.2,10.0] || less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a)))) less_equal(divide(divide(identity,a),divide(identity,divide(identity,a))),divide(identity,a))*l -> . % 0.20/0.48 20[0:MRR:19.1,13.0] || less_equal(divide(identity,a),divide(divide(identity,a),divide(identity,divide(identity,a))))*r -> . % 0.20/0.48 66[0:SpL:3.0,12.0] || equal(zero,zero)* -> less_equal(u,u)*. % 0.20/0.48 72[0:Obv:66.0] || -> less_equal(u,u)*. % 0.20/0.48 82[0:SpR:3.0,14.0] || -> less_equal(divide(divide(u,v),zero),divide(divide(u,v),v))*. % 0.20/0.48 126[0:Res:15.0,16.0] || less_equal(u,zero)* -> equal(u,zero). % 0.20/0.48 434[0:Res:72.0,6.0] || -> less_equal(divide(u,divide(u,v)),v)*l. % 0.20/0.48 482[0:Res:434.0,126.0] || -> equal(divide(u,divide(u,zero)),zero)**. % 0.20/0.48 523[0:SpL:482.0,12.0] || equal(zero,zero) -> less_equal(u,divide(u,zero))*r. % 0.20/0.48 526[0:Obv:523.0] || -> less_equal(u,divide(u,zero))*r. % 0.20/0.48 536[0:Res:526.0,16.0] || less_equal(divide(u,zero),u)*l -> equal(divide(u,zero),u). % 0.20/0.48 574[0:MRR:536.0,13.0] || -> equal(divide(u,zero),u)**. % 0.20/0.48 586[0:Rew:574.0,82.0] || -> less_equal(divide(u,v),divide(divide(u,v),v))*r. % 0.20/0.48 975[0:SpR:9.0,586.0] || -> less_equal(divide(identity,u),divide(divide(identity,u),divide(identity,divide(identity,u))))*r. % 0.20/0.48 1003[0:UnC:975.0,20.0] || -> . % 0.20/0.48 % SZS output end Refutation % 0.20/0.48 Formulae used in the proof : x_divide_x_is_zero property_of_divide1 one_inversion_equals_three prove_property_of_inversion quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal % 0.20/0.48 %------------------------------------------------------------------------------