%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET013-1 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n006.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 : Tue Jul 19 05:22:27 EDT 2022 % Result : Unsatisfiable 0.42s 0.59s % Output : Refutation 0.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SET013-1 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.12/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n006.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 : Sun Jul 10 09:35:21 EDT 2022 % 0.13/0.35 % CPUTime : % 0.42/0.59 % 0.42/0.59 SPASS V 3.9 % 0.42/0.59 SPASS beiseite: Proof found. % 0.42/0.59 % SZS status Theorem % 0.42/0.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.42/0.59 SPASS derived 1189 clauses, backtracked 0 clauses, performed 0 splits and kept 1010 clauses. % 0.42/0.59 SPASS allocated 64816 KBytes. % 0.42/0.59 SPASS spent 0:00:00.22 on the problem. % 0.42/0.59 0:00:00.03 for the input. % 0.42/0.59 0:00:00.00 for the FLOTTER CNF translation. % 0.42/0.59 0:00:00.02 for inferences. % 0.42/0.59 0:00:00.00 for the backtracking. % 0.42/0.59 0:00:00.14 for the reduction. % 0.42/0.59 % 0.42/0.59 % 0.42/0.59 Here is a proof with depth 3, length 16 : % 0.42/0.59 % SZS output start Refutation % 0.42/0.59 1[0:Inp] || equal_sets(intersection(as,bs),intersection(bs,as))*l -> . % 0.42/0.59 4[0:Inp] || -> subset(u,v) member(member_of_1_not_of_2(u,v),u)*. % 0.42/0.59 5[0:Inp] || member(member_of_1_not_of_2(u,v),v)* -> subset(u,v). % 0.42/0.59 11[0:Inp] || member(u,v) member(u,w) -> member(u,intersection(w,v))*. % 0.42/0.59 12[0:Inp] || member(u,intersection(v,w))* -> member(u,v). % 0.42/0.59 13[0:Inp] || member(u,intersection(v,w))* -> member(u,w). % 0.42/0.59 16[0:Inp] || subset(u,v)*+ subset(v,u)* -> equal_sets(u,v). % 0.42/0.59 24[0:Res:16.2,1.0] || subset(intersection(as,bs),intersection(bs,as))* subset(intersection(bs,as),intersection(as,bs)) -> . % 0.42/0.59 33[0:Res:4.1,13.0] || -> subset(intersection(u,v),w) member(member_of_1_not_of_2(intersection(u,v),w),v)*. % 0.42/0.59 34[0:Res:4.1,12.0] || -> subset(intersection(u,v),w) member(member_of_1_not_of_2(intersection(u,v),w),u)*. % 0.42/0.59 109[0:Res:11.2,5.0] || member(member_of_1_not_of_2(u,intersection(v,w)),w)*+ member(member_of_1_not_of_2(u,intersection(v,w)),v)* -> subset(u,intersection(v,w)). % 0.42/0.59 374[0:Res:34.1,109.0] || member(member_of_1_not_of_2(intersection(u,v),intersection(w,u)),w)* -> subset(intersection(u,v),intersection(w,u)) subset(intersection(u,v),intersection(w,u)). % 0.42/0.59 378[0:Obv:374.1] || member(member_of_1_not_of_2(intersection(u,v),intersection(w,u)),w)* -> subset(intersection(u,v),intersection(w,u)). % 0.42/0.59 1463[0:Res:33.1,378.0] || -> subset(intersection(u,v),intersection(v,u))* subset(intersection(u,v),intersection(v,u))*. % 0.42/0.59 1469[0:Obv:1463.0] || -> subset(intersection(u,v),intersection(v,u))*. % 0.42/0.59 1470[0:MRR:24.1,24.0,1469.0] || -> . % 0.42/0.59 % SZS output end Refutation % 0.42/0.59 Formulae used in the proof : prove_commutativity subsets_axiom1 subsets_axiom2 member_of_both_is_member_of_intersection member_of_intersection_is_member_of_set1 member_of_intersection_is_member_of_set2 subsets_are_set_equal_sets % 0.42/0.59 %------------------------------------------------------------------------------