%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET012-1 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n016.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 05:22:26 EDT 2022 % Result : Unsatisfiable 0.19s 0.43s % Output : Refutation 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SET012-1 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.03/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n016.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 20:42:57 EDT 2022 % 0.13/0.34 % CPUTime : % 0.19/0.43 % 0.19/0.43 SPASS V 3.9 % 0.19/0.43 SPASS beiseite: Proof found. % 0.19/0.43 % SZS status Theorem % 0.19/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p % 0.19/0.43 SPASS derived 124 clauses, backtracked 0 clauses, performed 0 splits and kept 102 clauses. % 0.19/0.43 SPASS allocated 63253 KBytes. % 0.19/0.43 SPASS spent 0:00:00.07 on the problem. % 0.19/0.43 0:00:00.04 for the input. % 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation. % 0.19/0.43 0:00:00.00 for inferences. % 0.19/0.43 0:00:00.00 for the backtracking. % 0.19/0.43 0:00:00.01 for the reduction. % 0.19/0.43 % 0.19/0.43 % 0.19/0.43 Here is a proof with depth 3, length 17 : % 0.19/0.43 % SZS output start Refutation % 0.19/0.43 1[0:Inp] || equal_sets(complement(complement(a)),a)*l -> . % 0.19/0.43 4[0:Inp] || -> subset(u,v) member(member_of_1_not_of_2(u,v),u)*. % 0.19/0.43 5[0:Inp] || member(member_of_1_not_of_2(u,v),v)* -> subset(u,v). % 0.19/0.43 6[0:Inp] || -> member(u,v) member(u,complement(v))*. % 0.19/0.43 7[0:Inp] || member(u,v) member(u,complement(v))* -> . % 0.19/0.43 16[0:Inp] || subset(u,v)*+ subset(v,u)* -> equal_sets(u,v). % 0.19/0.43 24[0:Res:16.2,1.0] || subset(a,complement(complement(a))) subset(complement(complement(a)),a)* -> . % 0.19/0.43 27[0:Res:4.1,7.1] || member(member_of_1_not_of_2(complement(u),v),u)* -> subset(complement(u),v). % 0.19/0.43 28[0:Res:6.1,5.0] || -> member(member_of_1_not_of_2(u,complement(v)),v)* subset(u,complement(v)). % 0.19/0.43 36[0:Res:28.0,7.1] || member(member_of_1_not_of_2(u,complement(complement(v))),v)* -> subset(u,complement(complement(v))). % 0.19/0.43 39[0:Res:6.1,27.0] || -> member(member_of_1_not_of_2(complement(complement(u)),v),u)* subset(complement(complement(u)),v). % 0.19/0.43 70[0:Res:39.0,5.0] || -> subset(complement(complement(u)),u)* subset(complement(complement(u)),u)*. % 0.19/0.43 71[0:Obv:70.0] || -> subset(complement(complement(u)),u)*. % 0.19/0.43 72[0:MRR:24.1,71.0] || subset(a,complement(complement(a)))* -> . % 0.19/0.43 152[0:Res:4.1,36.0] || -> subset(u,complement(complement(u)))* subset(u,complement(complement(u)))*. % 0.19/0.43 156[0:Obv:152.0] || -> subset(u,complement(complement(u)))*. % 0.19/0.43 157[0:UnC:156.0,72.0] || -> . % 0.19/0.43 % SZS output end Refutation % 0.19/0.43 Formulae used in the proof : prove_involution subsets_axiom1 subsets_axiom2 member_of_set_or_complement not_member_of_set_and_complement subsets_are_set_equal_sets % 0.19/0.43 %------------------------------------------------------------------------------