%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET096-7 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n023.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 05:23:59 EDT 2022 % Result : Unsatisfiable 0.47s 0.66s % Output : Refutation 0.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET096-7 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.03/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n023.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 09:21:10 EDT 2022 % 0.13/0.34 % CPUTime : % 0.47/0.66 % 0.47/0.66 SPASS V 3.9 % 0.47/0.66 SPASS beiseite: Proof found. % 0.47/0.66 % SZS status Theorem % 0.47/0.66 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.47/0.66 SPASS derived 1298 clauses, backtracked 0 clauses, performed 1 splits and kept 716 clauses. % 0.47/0.66 SPASS allocated 77466 KBytes. % 0.47/0.66 SPASS spent 0:00:00.30 on the problem. % 0.47/0.66 0:00:00.04 for the input. % 0.47/0.66 0:00:00.00 for the FLOTTER CNF translation. % 0.47/0.66 0:00:00.02 for inferences. % 0.47/0.66 0:00:00.01 for the backtracking. % 0.47/0.66 0:00:00.19 for the reduction. % 0.47/0.66 % 0.47/0.66 % 0.47/0.66 Here is a proof with depth 3, length 17 : % 0.47/0.66 % SZS output start Refutation % 0.47/0.66 34[0:Inp] || member(u,singleton(v))* -> equal(u,v). % 0.47/0.66 48[0:Inp] || member(u,v)* -> subclass(singleton(u),v). % 0.47/0.66 49[0:Inp] || -> subclass(x__dfg,singleton(y__dfg))*r. % 0.47/0.66 50[0:Inp] || equal(null_class,x__dfg)** -> . % 0.47/0.66 51[0:Inp] || equal(singleton(y__dfg),x__dfg)** -> . % 0.47/0.66 52[0:Inp] || member(u,v)* subclass(v,w)* -> member(u,w)*. % 0.47/0.66 58[0:Inp] || subclass(u,v)* subclass(v,u)* -> equal(v,u). % 0.47/0.66 117[0:Inp] || -> equal(u,null_class) member(regular(u),u)*. % 0.47/0.66 164[0:Res:117.0,50.0] || -> member(regular(x__dfg),x__dfg)*. % 0.47/0.66 201[0:Res:49.0,58.0] || subclass(singleton(y__dfg),x__dfg)*l -> equal(singleton(y__dfg),x__dfg). % 0.47/0.66 202[0:Res:49.0,52.0] || member(u,x__dfg) -> member(u,singleton(y__dfg))*. % 0.47/0.66 207[0:MRR:201.1,51.0] || subclass(singleton(y__dfg),x__dfg)*l -> . % 0.47/0.66 278[0:Res:202.1,34.0] || member(u,x__dfg)* -> equal(u,y__dfg). % 0.47/0.66 283[0:Res:164.0,278.0] || -> equal(regular(x__dfg),y__dfg)**. % 0.47/0.66 288[0:Rew:283.0,164.0] || -> member(y__dfg,x__dfg)*. % 0.47/0.66 1741[0:Res:288.0,48.0] || -> subclass(singleton(y__dfg),x__dfg)*l. % 0.47/0.66 1766[0:MRR:1741.0,207.0] || -> . % 0.47/0.66 % SZS output end Refutation % 0.47/0.66 Formulae used in the proof : only_member_in_singleton property_of_singletons2 prove_two_subsets_of_singleton_1 prove_two_subsets_of_singleton_2 prove_two_subsets_of_singleton_3 subclass_members subclass_implies_equal regularity1 % 0.47/0.66 %------------------------------------------------------------------------------