%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : FLD069-3 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n018.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 02:28:38 EDT 2022 % Result : Unsatisfiable 0.19s 0.42s % Output : Refutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : FLD069-3 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.06/0.12 % Command : run_spass %d %s % 0.13/0.33 % Computer : n018.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon Jun 6 20:33:50 EDT 2022 % 0.13/0.33 % CPUTime : % 0.19/0.42 % 0.19/0.42 SPASS V 3.9 % 0.19/0.42 SPASS beiseite: Proof found. % 0.19/0.42 % SZS status Theorem % 0.19/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.19/0.42 SPASS derived 89 clauses, backtracked 0 clauses, performed 0 splits and kept 97 clauses. % 0.19/0.42 SPASS allocated 75730 KBytes. % 0.19/0.42 SPASS spent 0:00:00.07 on the problem. % 0.19/0.42 0:00:00.04 for the input. % 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation. % 0.19/0.42 0:00:00.00 for inferences. % 0.19/0.42 0:00:00.00 for the backtracking. % 0.19/0.42 0:00:00.01 for the reduction. % 0.19/0.42 % 0.19/0.42 % 0.19/0.42 Here is a proof with depth 3, length 15 : % 0.19/0.42 % SZS output start Refutation % 0.19/0.42 2[0:Inp] || -> defined(b)*. % 0.19/0.42 3[0:Inp] || -> less_or_equal(additive_identity,a)*r. % 0.19/0.42 4[0:Inp] || -> less_or_equal(additive_identity,b)*r. % 0.19/0.42 5[0:Inp] || sum__dfg(additive_identity,b,additive_identity)* -> . % 0.19/0.42 6[0:Inp] || -> sum__dfg(a,b,additive_identity)*. % 0.19/0.42 9[0:Inp] defined(u) || -> sum__dfg(additive_identity,u,u)*. % 0.19/0.42 27[0:Inp] || less_or_equal(u,v) less_or_equal(v,u) -> sum__dfg(additive_identity,v,u)*. % 0.19/0.42 30[0:Inp] || less_or_equal(u,v)* sum__dfg(v,w,x)* sum__dfg(u,w,y)* -> less_or_equal(y,x)*. % 0.19/0.42 56[0:Res:4.0,27.1] || less_or_equal(b,additive_identity) -> sum__dfg(additive_identity,b,additive_identity)*. % 0.19/0.42 59[0:Res:3.0,30.0] || sum__dfg(a,u,v)* sum__dfg(additive_identity,u,w)* -> less_or_equal(w,v)*. % 0.19/0.42 64[0:MRR:56.1,5.0] || less_or_equal(b,additive_identity)*l -> . % 0.19/0.42 69[0:Res:6.0,59.1] || sum__dfg(additive_identity,b,u)* -> less_or_equal(u,additive_identity). % 0.19/0.42 138[0:Res:9.1,69.0] defined(b) || -> less_or_equal(b,additive_identity)*l. % 0.19/0.42 142[0:SSi:138.0,2.0] || -> less_or_equal(b,additive_identity)*l. % 0.19/0.42 143[0:MRR:142.0,64.0] || -> . % 0.19/0.42 % SZS output end Refutation % 0.19/0.42 Formulae used in the proof : b_is_defined less_or_equal_3 less_or_equal_4 not_sum_5 sum_6 existence_of_identity_addition antisymmetry_of_order_relation compatibility_of_order_relation_and_addition % 0.19/0.42 %------------------------------------------------------------------------------