%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET015-2 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n008.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 05:22:33 EDT 2022 % Result : Unsatisfiable 1.45s 1.69s % Output : Refutation 1.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET015-2 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.07/0.13 % Command : run_spass %d %s % 0.13/0.35 % Computer : n008.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Mon Jul 11 10:05:53 EDT 2022 % 0.13/0.35 % CPUTime : % 1.45/1.69 % 1.45/1.69 SPASS V 3.9 % 1.45/1.69 SPASS beiseite: Proof found. % 1.45/1.69 % SZS status Theorem % 1.45/1.69 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 1.45/1.69 SPASS derived 4167 clauses, backtracked 0 clauses, performed 0 splits and kept 3605 clauses. % 1.45/1.69 SPASS allocated 69785 KBytes. % 1.45/1.69 SPASS spent 0:00:01.27 on the problem. % 1.45/1.69 0:00:00.03 for the input. % 1.45/1.69 0:00:00.00 for the FLOTTER CNF translation. % 1.45/1.69 0:00:00.06 for inferences. % 1.45/1.69 0:00:00.00 for the backtracking. % 1.45/1.69 0:00:01.12 for the reduction. % 1.45/1.69 % 1.45/1.69 % 1.45/1.69 Here is a proof with depth 6, length 38 : % 1.45/1.69 % SZS output start Refutation % 1.45/1.69 1[0:Inp] || -> equal_sets(union(as,bs),cs)*l. % 1.45/1.69 2[0:Inp] || -> equal_sets(union(bs,as),ds)*l. % 1.45/1.69 3[0:Inp] || equal_sets(cs,ds)*l -> . % 1.45/1.69 5[0:Inp] || subset(u,v)*+ member(w,u)* -> member(w,v)*. % 1.45/1.69 6[0:Inp] || -> subset(u,v) member(member_of_1_not_of_2(u,v),u)*. % 1.45/1.69 7[0:Inp] || member(member_of_1_not_of_2(u,v),v)* -> subset(u,v). % 1.45/1.69 10[0:Inp] || member(u,v) -> member(u,union(v,w))*. % 1.45/1.69 11[0:Inp] || member(u,v) -> member(u,union(w,v))*. % 1.45/1.69 12[0:Inp] || member(u,union(v,w))* -> member(u,w) member(u,v). % 1.45/1.69 17[0:Inp] || equal_sets(u,v) -> subset(v,u)*. % 1.45/1.69 18[0:Inp] || subset(u,v)*+ subset(v,u)* -> equal_sets(u,v). % 1.45/1.69 20[0:Inp] || equal_sets(u,v)* -> equal_sets(v,u). % 1.45/1.69 26[0:Res:18.2,3.0] || subset(cs,ds)* subset(ds,cs) -> . % 1.45/1.69 59[0:Res:17.1,5.0] || equal_sets(u,v)*+ member(w,v)* -> member(w,u)*. % 1.45/1.69 164[0:Res:2.0,20.0] || -> equal_sets(ds,union(bs,as))*r. % 1.45/1.69 165[0:Res:1.0,20.0] || -> equal_sets(cs,union(as,bs))*r. % 1.45/1.69 245[0:Res:2.0,59.0] || member(u,ds) -> member(u,union(bs,as))*. % 1.45/1.69 246[0:Res:1.0,59.0] || member(u,cs) -> member(u,union(as,bs))*. % 1.45/1.69 250[0:Res:164.0,59.0] || member(u,union(bs,as))* -> member(u,ds). % 1.45/1.69 251[0:Res:165.0,59.0] || member(u,union(as,bs))* -> member(u,cs). % 1.45/1.69 267[0:Res:245.1,12.0] || member(u,ds) -> member(u,as)* member(u,bs). % 1.45/1.69 273[0:Res:246.1,12.0] || member(u,cs) -> member(u,bs) member(u,as)*. % 1.45/1.69 298[0:Res:11.1,250.0] || member(u,as)* -> member(u,ds). % 1.45/1.69 299[0:Res:10.1,250.0] || member(u,bs)* -> member(u,ds). % 1.45/1.69 407[0:Res:11.1,251.0] || member(u,bs)* -> member(u,cs). % 1.45/1.69 408[0:Res:10.1,251.0] || member(u,as)* -> member(u,cs). % 1.45/1.69 4632[0:Res:267.1,408.0] || member(u,ds) -> member(u,bs)* member(u,cs). % 1.45/1.69 4662[0:MRR:4632.1,407.0] || member(u,ds) -> member(u,cs)*. % 1.45/1.69 4719[0:Res:273.2,298.0] || member(u,cs) -> member(u,bs)* member(u,ds). % 1.45/1.69 4748[0:MRR:4719.1,299.0] || member(u,cs)* -> member(u,ds). % 1.45/1.69 4749[0:Res:4662.1,7.0] || member(member_of_1_not_of_2(u,cs),ds)* -> subset(u,cs). % 1.45/1.69 4786[0:Res:6.1,4748.0] || -> subset(cs,u) member(member_of_1_not_of_2(cs,u),ds)*. % 1.45/1.69 4949[0:Res:4786.1,7.0] || -> subset(cs,ds)* subset(cs,ds)*. % 1.45/1.69 4965[0:Obv:4949.0] || -> subset(cs,ds)*. % 1.45/1.69 4966[0:MRR:26.0,4965.0] || subset(ds,cs)* -> . % 1.45/1.69 5122[0:Res:6.1,4749.0] || -> subset(ds,cs)* subset(ds,cs)*. % 1.45/1.69 5158[0:Obv:5122.0] || -> subset(ds,cs)*. % 1.45/1.69 5159[0:MRR:5158.0,4966.0] || -> . % 1.45/1.69 % SZS output end Refutation % 1.45/1.69 Formulae used in the proof : a_union_b_is_c b_union_a_is_d prove_c_equals_d membership_in_subsets subsets_axiom1 subsets_axiom2 member_of_set1_is_member_of_union member_of_set2_is_member_of_union member_of_union_is_member_of_one_set set_equal_sets_are_subsets2 subsets_are_set_equal_sets symmetry_for_set_equal % 1.45/1.69 %------------------------------------------------------------------------------