%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET013-2 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n025.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 05:22:28 EDT 2022 % Result : Unsatisfiable 1.67s 1.84s % Output : Refutation 1.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET013-2 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.03/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n025.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 08:02:01 EDT 2022 % 0.13/0.34 % CPUTime : % 1.67/1.84 % 1.67/1.84 SPASS V 3.9 % 1.67/1.84 SPASS beiseite: Proof found. % 1.67/1.84 % SZS status Theorem % 1.67/1.84 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 1.67/1.84 SPASS derived 4667 clauses, backtracked 0 clauses, performed 0 splits and kept 4224 clauses. % 1.67/1.84 SPASS allocated 70628 KBytes. % 1.67/1.84 SPASS spent 0:00:01.38 on the problem. % 1.67/1.84 0:00:00.04 for the input. % 1.67/1.84 0:00:00.00 for the FLOTTER CNF translation. % 1.67/1.84 0:00:00.07 for inferences. % 1.67/1.84 0:00:00.00 for the backtracking. % 1.67/1.84 0:00:01.23 for the reduction. % 1.67/1.84 % 1.67/1.84 % 1.67/1.84 Here is a proof with depth 6, length 38 : % 1.67/1.84 % SZS output start Refutation % 1.67/1.84 1[0:Inp] || -> equal_sets(intersection(as,bs),cs)*l. % 1.67/1.84 2[0:Inp] || -> equal_sets(intersection(bs,as),ds)*l. % 1.67/1.84 3[0:Inp] || equal_sets(cs,ds)*l -> . % 1.67/1.84 5[0:Inp] || subset(u,v)*+ member(w,u)* -> member(w,v)*. % 1.67/1.84 6[0:Inp] || -> subset(u,v) member(member_of_1_not_of_2(u,v),u)*. % 1.67/1.84 7[0:Inp] || member(member_of_1_not_of_2(u,v),v)* -> subset(u,v). % 1.67/1.84 13[0:Inp] || member(u,v) member(u,w) -> member(u,intersection(w,v))*. % 1.67/1.84 14[0:Inp] || member(u,intersection(v,w))* -> member(u,v). % 1.67/1.84 15[0:Inp] || member(u,intersection(v,w))* -> member(u,w). % 1.67/1.84 17[0:Inp] || equal_sets(u,v) -> subset(v,u)*. % 1.67/1.84 18[0:Inp] || subset(u,v)*+ subset(v,u)* -> equal_sets(u,v). % 1.67/1.84 20[0:Inp] || equal_sets(u,v)* -> equal_sets(v,u). % 1.67/1.84 26[0:Res:18.2,3.0] || subset(cs,ds)* subset(ds,cs) -> . % 1.67/1.84 59[0:Res:17.1,5.0] || equal_sets(u,v)*+ member(w,v)* -> member(w,u)*. % 1.67/1.84 164[0:Res:2.0,20.0] || -> equal_sets(ds,intersection(bs,as))*r. % 1.67/1.84 165[0:Res:1.0,20.0] || -> equal_sets(cs,intersection(as,bs))*r. % 1.67/1.84 245[0:Res:2.0,59.0] || member(u,ds) -> member(u,intersection(bs,as))*. % 1.67/1.84 246[0:Res:1.0,59.0] || member(u,cs) -> member(u,intersection(as,bs))*. % 1.67/1.84 250[0:Res:164.0,59.0] || member(u,intersection(bs,as))* -> member(u,ds). % 1.67/1.84 251[0:Res:165.0,59.0] || member(u,intersection(as,bs))* -> member(u,cs). % 1.67/1.84 267[0:Res:245.1,14.0] || member(u,ds) -> member(u,bs)*. % 1.67/1.84 268[0:Res:245.1,15.0] || member(u,ds) -> member(u,as)*. % 1.67/1.84 303[0:Res:246.1,14.0] || member(u,cs) -> member(u,as)*. % 1.67/1.84 304[0:Res:246.1,15.0] || member(u,cs) -> member(u,bs)*. % 1.67/1.84 326[0:Res:13.2,250.0] || member(u,as)* member(u,bs) -> member(u,ds). % 1.67/1.84 333[0:Res:13.2,251.0] || member(u,bs) member(u,as)* -> member(u,cs). % 1.67/1.84 5266[0:Res:303.1,326.0] || member(u,cs) member(u,bs)* -> member(u,ds). % 1.67/1.84 5312[0:MRR:5266.1,304.1] || member(u,cs)* -> member(u,ds). % 1.67/1.84 5313[0:Res:6.1,5312.0] || -> subset(cs,u) member(member_of_1_not_of_2(cs,u),ds)*. % 1.67/1.84 5357[0:Res:5313.1,7.0] || -> subset(cs,ds)* subset(cs,ds)*. % 1.67/1.84 5375[0:Obv:5357.0] || -> subset(cs,ds)*. % 1.67/1.84 5376[0:MRR:26.0,5375.0] || subset(ds,cs)* -> . % 1.67/1.84 5399[0:Res:268.1,333.1] || member(u,ds) member(u,bs)* -> member(u,cs). % 1.67/1.84 5444[0:MRR:5399.1,267.1] || member(u,ds) -> member(u,cs)*. % 1.67/1.84 5561[0:Res:5444.1,7.0] || member(member_of_1_not_of_2(u,cs),ds)* -> subset(u,cs). % 1.67/1.84 5659[0:Res:6.1,5561.0] || -> subset(ds,cs)* subset(ds,cs)*. % 1.67/1.84 5693[0:Obv:5659.0] || -> subset(ds,cs)*. % 1.67/1.84 5694[0:MRR:5693.0,5376.0] || -> . % 1.67/1.84 % SZS output end Refutation % 1.67/1.84 Formulae used in the proof : intersection_of_a_and_b_is_c intersection_of_b_and_a_is_d prove_c_equals_d membership_in_subsets 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 set_equal_sets_are_subsets2 subsets_are_set_equal_sets symmetry_for_set_equal % 1.67/1.84 %------------------------------------------------------------------------------