%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET095-7 : 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 : Tue Jul 19 05:23:57 EDT 2022 % Result : Unsatisfiable 0.19s 0.44s % Output : Refutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET095-7 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.11/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n018.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 05:22:57 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.44 % 0.19/0.44 SPASS V 3.9 % 0.19/0.44 SPASS beiseite: Proof found. % 0.19/0.44 % SZS status Theorem % 0.19/0.44 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.19/0.44 SPASS derived 17 clauses, backtracked 0 clauses, performed 0 splits and kept 147 clauses. % 0.19/0.44 SPASS allocated 75799 KBytes. % 0.19/0.44 SPASS spent 0:00:00.08 on the problem. % 0.19/0.44 0:00:00.04 for the input. % 0.19/0.44 0:00:00.00 for the FLOTTER CNF translation. % 0.19/0.44 0:00:00.00 for inferences. % 0.19/0.44 0:00:00.00 for the backtracking. % 0.19/0.44 0:00:00.01 for the reduction. % 0.19/0.44 % 0.19/0.44 % 0.19/0.44 Here is a proof with depth 2, length 8 : % 0.19/0.44 % SZS output start Refutation % 0.19/0.44 28[0:Inp] || member(u,v)* member(w,v)* -> subclass(unordered_pair(w,u),v)*. % 0.19/0.44 48[0:Inp] || -> member(x__dfg,y__dfg)*. % 0.19/0.44 49[0:Inp] || subclass(singleton(x__dfg),y__dfg)*l -> . % 0.19/0.44 61[0:Inp] || -> equal(unordered_pair(u,u),singleton(u))**. % 0.19/0.44 155[0:Res:48.0,28.1] || member(u,y__dfg) -> subclass(unordered_pair(u,x__dfg),y__dfg)*l. % 0.19/0.44 161[0:Res:48.0,155.0] || -> subclass(unordered_pair(x__dfg,x__dfg),y__dfg)*l. % 0.19/0.44 165[0:Rew:61.0,161.0] || -> subclass(singleton(x__dfg),y__dfg)*l. % 0.19/0.44 166[0:MRR:165.0,49.0] || -> . % 0.19/0.44 % SZS output end Refutation % 0.19/0.44 Formulae used in the proof : unordered_pair_is_subset prove_property_of_singletons2_1 prove_property_of_singletons2_2 singleton_set % 0.19/0.44 %------------------------------------------------------------------------------