%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET012-2 : TPTP v8.1.0. Bugfixed v2.1.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n017.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 0.21s 0.50s % Output : Refutation 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SET012-2 : TPTP v8.1.0. Bugfixed v2.1.0. % 0.08/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n017.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 : Mon Jul 11 05:31:18 EDT 2022 % 0.13/0.35 % CPUTime : % 0.21/0.50 % 0.21/0.50 SPASS V 3.9 % 0.21/0.50 SPASS beiseite: Proof found. % 0.21/0.50 % SZS status Theorem % 0.21/0.50 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.21/0.50 SPASS derived 701 clauses, backtracked 0 clauses, performed 0 splits and kept 584 clauses. % 0.21/0.50 SPASS allocated 64000 KBytes. % 0.21/0.50 SPASS spent 0:00:00.14 on the problem. % 0.21/0.50 0:00:00.03 for the input. % 0.21/0.50 0:00:00.00 for the FLOTTER CNF translation. % 0.21/0.50 0:00:00.01 for inferences. % 0.21/0.50 0:00:00.00 for the backtracking. % 0.21/0.50 0:00:00.07 for the reduction. % 0.21/0.50 % 0.21/0.50 % 0.21/0.50 Here is a proof with depth 7, length 32 : % 0.21/0.50 % SZS output start Refutation % 0.21/0.50 1[0:Inp] || -> equal_sets(complement(a),b)*l. % 0.21/0.50 2[0:Inp] || -> equal_sets(complement(b),c)*l. % 0.21/0.50 3[0:Inp] || equal_sets(a,c)*l -> . % 0.21/0.50 5[0:Inp] || subset(u,v)*+ member(w,u)* -> member(w,v)*. % 0.21/0.50 6[0:Inp] || -> subset(u,v) member(member_of_1_not_of_2(u,v),u)*. % 0.21/0.50 7[0:Inp] || member(member_of_1_not_of_2(u,v),v)* -> subset(u,v). % 0.21/0.50 8[0:Inp] || -> member(u,v) member(u,complement(v))*. % 0.21/0.50 9[0:Inp] || member(u,v) member(u,complement(v))* -> . % 0.21/0.50 17[0:Inp] || equal_sets(u,v) -> subset(v,u)*. % 0.21/0.50 18[0:Inp] || subset(u,v)*+ subset(v,u)* -> equal_sets(u,v). % 0.21/0.50 20[0:Inp] || equal_sets(u,v)* -> equal_sets(v,u). % 0.21/0.50 21[0:Inp] || equal_sets(u,v)* equal_sets(v,w)* -> equal_sets(u,w)*. % 0.21/0.50 25[0:Res:20.1,3.0] || equal_sets(c,a)*r -> . % 0.21/0.50 29[0:Res:6.1,9.1] || member(member_of_1_not_of_2(complement(u),v),u)* -> subset(complement(u),v). % 0.21/0.50 30[0:Res:8.1,7.0] || -> member(member_of_1_not_of_2(u,complement(v)),v)* subset(u,complement(v)). % 0.21/0.50 59[0:Res:17.1,5.0] || equal_sets(u,v)*+ member(w,v)* -> member(w,u)*. % 0.21/0.50 164[0:Res:2.0,20.0] || -> equal_sets(c,complement(b))*r. % 0.21/0.50 165[0:Res:1.0,20.0] || -> equal_sets(b,complement(a))*r. % 0.21/0.50 246[0:Res:1.0,59.0] || member(u,b) -> member(u,complement(a))*. % 0.21/0.50 251[0:Res:165.0,59.0] || member(u,complement(a))* -> member(u,b). % 0.21/0.50 273[0:Res:246.1,9.1] || member(u,b) member(u,a)* -> . % 0.21/0.50 310[0:Res:8.1,251.0] || -> member(u,a)* member(u,b). % 0.21/0.50 317[0:Res:310.0,7.0] || -> member(member_of_1_not_of_2(u,a),b)* subset(u,a). % 0.21/0.50 335[0:Res:6.1,273.1] || member(member_of_1_not_of_2(a,u),b)* -> subset(a,u). % 0.21/0.50 351[0:Res:317.0,29.0] || -> subset(complement(b),a)* subset(complement(b),a)*. % 0.21/0.50 352[0:Obv:351.0] || -> subset(complement(b),a)*. % 0.21/0.50 353[0:Res:352.0,18.0] || subset(a,complement(b))* -> equal_sets(complement(b),a). % 0.21/0.50 483[0:Res:30.0,335.0] || -> subset(a,complement(b))* subset(a,complement(b))*. % 0.21/0.50 486[0:Obv:483.0] || -> subset(a,complement(b))*. % 0.21/0.50 487[0:MRR:353.0,486.0] || -> equal_sets(complement(b),a)*l. % 0.21/0.50 831[0:OCh:21.1,21.0,487.0,164.0] || -> equal_sets(c,a)*r. % 0.21/0.50 835[0:MRR:831.0,25.0] || -> . % 0.21/0.50 % SZS output end Refutation % 0.21/0.50 Formulae used in the proof : complement_of_a_is_b complement_of_b_is_c prove_a_equals_c membership_in_subsets subsets_axiom1 subsets_axiom2 member_of_set_or_complement not_member_of_set_and_complement set_equal_sets_are_subsets2 subsets_are_set_equal_sets symmetry_for_set_equal transitivity_for_set_equal % 0.21/0.50 %------------------------------------------------------------------------------