%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SET585+3 : TPTP v8.1.0. Released v2.2.0. % 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 05:27:08 EDT 2022 % Result : Theorem 0.21s 0.45s % Output : Refutation 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SET585+3 : TPTP v8.1.0. Released v2.2.0. % 0.12/0.13 % Command : run_spass %d %s % 0.14/0.34 % Computer : n017.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 600 % 0.14/0.34 % DateTime : Sun Jul 10 13:21:18 EDT 2022 % 0.14/0.34 % CPUTime : % 0.21/0.45 % 0.21/0.45 SPASS V 3.9 % 0.21/0.45 SPASS beiseite: Proof found. % 0.21/0.45 % SZS status Theorem % 0.21/0.45 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 0.21/0.45 SPASS derived 33 clauses, backtracked 0 clauses, performed 0 splits and kept 24 clauses. % 0.21/0.45 SPASS allocated 85305 KBytes. % 0.21/0.45 SPASS spent 0:00:00.10 on the problem. % 0.21/0.45 0:00:00.04 for the input. % 0.21/0.45 0:00:00.03 for the FLOTTER CNF translation. % 0.21/0.45 0:00:00.00 for inferences. % 0.21/0.45 0:00:00.00 for the backtracking. % 0.21/0.45 0:00:00.00 for the reduction. % 0.21/0.45 % 0.21/0.45 % 0.21/0.45 Here is a proof with depth 2, length 11 : % 0.21/0.45 % SZS output start Refutation % 0.21/0.45 2[0:Inp] || -> subset(u,union(u,v))*r. % 0.21/0.45 3[0:Inp] || -> subset(intersection(u,v),u)*l. % 0.21/0.45 4[0:Inp] || -> equal(union(u,v),union(v,u))*. % 0.21/0.45 5[0:Inp] || -> equal(intersection(u,v),intersection(v,u))*. % 0.21/0.45 6[0:Inp] || subset(intersection(skc5,skc4),union(skc5,skc3))*l -> . % 0.21/0.45 13[0:Inp] || subset(u,v)* subset(v,w)* -> subset(u,w)*. % 0.21/0.45 21[0:Rew:5.0,6.0,4.0,6.0] || subset(intersection(skc4,skc5),union(skc3,skc5))*l -> . % 0.21/0.45 40[0:SpR:5.0,3.0] || -> subset(intersection(u,v),v)*l. % 0.21/0.45 42[0:SpR:4.0,2.0] || -> subset(u,union(v,u))*r. % 0.21/0.45 55[0:NCh:13.2,13.0,21.0,40.0] || subset(skc5,union(skc3,skc5))*r -> . % 0.21/0.45 57[0:MRR:55.0,42.0] || -> . % 0.21/0.45 % SZS output end Refutation % 0.21/0.45 Formulae used in the proof : subset_of_union intersection_is_subset commutativity_of_union commutativity_of_intersection prove_intersection_subset_of_union transitivity_of_subset % 0.21/0.45 %------------------------------------------------------------------------------