%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET015-1 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n029.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 05:22:32 EDT 2022 % Result : Unsatisfiable 0.18s 0.53s % Output : Refutation 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET015-1 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.03/0.12 % Command : run_spass %d %s % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jul 10 13:08:01 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.53 % 0.18/0.53 SPASS V 3.9 % 0.18/0.53 SPASS beiseite: Proof found. % 0.18/0.53 % SZS status Theorem % 0.18/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.18/0.53 SPASS derived 965 clauses, backtracked 0 clauses, performed 0 splits and kept 798 clauses. % 0.18/0.53 SPASS allocated 64480 KBytes. % 0.18/0.53 SPASS spent 0:00:00.17 on the problem. % 0.18/0.53 0:00:00.03 for the input. % 0.18/0.53 0:00:00.00 for the FLOTTER CNF translation. % 0.18/0.53 0:00:00.02 for inferences. % 0.18/0.53 0:00:00.00 for the backtracking. % 0.18/0.53 0:00:00.10 for the reduction. % 0.18/0.53 % 0.18/0.53 % 0.18/0.53 Here is a proof with depth 3, length 16 : % 0.18/0.53 % SZS output start Refutation % 0.18/0.53 1[0:Inp] || equal_sets(union(as,bs),union(bs,as))*l -> . % 0.18/0.53 4[0:Inp] || -> subset(u,v) member(member_of_1_not_of_2(u,v),u)*. % 0.18/0.53 5[0:Inp] || member(member_of_1_not_of_2(u,v),v)* -> subset(u,v). % 0.18/0.53 8[0:Inp] || member(u,v) -> member(u,union(v,w))*. % 0.18/0.53 9[0:Inp] || member(u,v) -> member(u,union(w,v))*. % 0.18/0.53 10[0:Inp] || member(u,union(v,w))* -> member(u,w) member(u,v). % 0.18/0.53 16[0:Inp] || subset(u,v)*+ subset(v,u)* -> equal_sets(u,v). % 0.18/0.53 24[0:Res:16.2,1.0] || subset(union(as,bs),union(bs,as))* subset(union(bs,as),union(as,bs)) -> . % 0.18/0.53 31[0:Res:9.1,5.0] || member(member_of_1_not_of_2(u,union(v,w)),w)* -> subset(u,union(v,w)). % 0.18/0.53 32[0:Res:8.1,5.0] || member(member_of_1_not_of_2(u,union(v,w)),v)* -> subset(u,union(v,w)). % 0.18/0.53 72[0:Res:4.1,10.0] || -> subset(union(u,v),w) member(member_of_1_not_of_2(union(u,v),w),v)* member(member_of_1_not_of_2(union(u,v),w),u)*. % 0.18/0.53 320[0:Res:72.2,31.0] || -> subset(union(u,v),union(w,u)) member(member_of_1_not_of_2(union(u,v),union(w,u)),v)* subset(union(u,v),union(w,u)). % 0.18/0.53 325[0:Obv:320.0] || -> member(member_of_1_not_of_2(union(u,v),union(w,u)),v)* subset(union(u,v),union(w,u)). % 0.18/0.53 1154[0:Res:325.0,32.0] || -> subset(union(u,v),union(v,u))* subset(union(u,v),union(v,u))*. % 0.18/0.53 1156[0:Obv:1154.0] || -> subset(union(u,v),union(v,u))*. % 0.18/0.53 1157[0:MRR:24.1,24.0,1156.0] || -> . % 0.18/0.53 % SZS output end Refutation % 0.18/0.53 Formulae used in the proof : prove_commutativity 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 subsets_are_set_equal_sets % 0.18/0.53 %------------------------------------------------------------------------------