TSTP Solution File: SET013-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET013-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 05:22:27 EDT 2022
% Result : Unsatisfiable 0.42s 0.59s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET013-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.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 09:35:21 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.42/0.59
% 0.42/0.59 SPASS V 3.9
% 0.42/0.59 SPASS beiseite: Proof found.
% 0.42/0.59 % SZS status Theorem
% 0.42/0.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.42/0.59 SPASS derived 1189 clauses, backtracked 0 clauses, performed 0 splits and kept 1010 clauses.
% 0.42/0.59 SPASS allocated 64816 KBytes.
% 0.42/0.59 SPASS spent 0:00:00.22 on the problem.
% 0.42/0.59 0:00:00.03 for the input.
% 0.42/0.59 0:00:00.00 for the FLOTTER CNF translation.
% 0.42/0.59 0:00:00.02 for inferences.
% 0.42/0.59 0:00:00.00 for the backtracking.
% 0.42/0.59 0:00:00.14 for the reduction.
% 0.42/0.59
% 0.42/0.59
% 0.42/0.59 Here is a proof with depth 3, length 16 :
% 0.42/0.59 % SZS output start Refutation
% 0.42/0.59 1[0:Inp] || equal_sets(intersection(as,bs),intersection(bs,as))*l -> .
% 0.42/0.59 4[0:Inp] || -> subset(u,v) member(member_of_1_not_of_2(u,v),u)*.
% 0.42/0.59 5[0:Inp] || member(member_of_1_not_of_2(u,v),v)* -> subset(u,v).
% 0.42/0.59 11[0:Inp] || member(u,v) member(u,w) -> member(u,intersection(w,v))*.
% 0.42/0.59 12[0:Inp] || member(u,intersection(v,w))* -> member(u,v).
% 0.42/0.59 13[0:Inp] || member(u,intersection(v,w))* -> member(u,w).
% 0.42/0.59 16[0:Inp] || subset(u,v)*+ subset(v,u)* -> equal_sets(u,v).
% 0.42/0.59 24[0:Res:16.2,1.0] || subset(intersection(as,bs),intersection(bs,as))* subset(intersection(bs,as),intersection(as,bs)) -> .
% 0.42/0.59 33[0:Res:4.1,13.0] || -> subset(intersection(u,v),w) member(member_of_1_not_of_2(intersection(u,v),w),v)*.
% 0.42/0.59 34[0:Res:4.1,12.0] || -> subset(intersection(u,v),w) member(member_of_1_not_of_2(intersection(u,v),w),u)*.
% 0.42/0.59 109[0:Res:11.2,5.0] || member(member_of_1_not_of_2(u,intersection(v,w)),w)*+ member(member_of_1_not_of_2(u,intersection(v,w)),v)* -> subset(u,intersection(v,w)).
% 0.42/0.59 374[0:Res:34.1,109.0] || member(member_of_1_not_of_2(intersection(u,v),intersection(w,u)),w)* -> subset(intersection(u,v),intersection(w,u)) subset(intersection(u,v),intersection(w,u)).
% 0.42/0.59 378[0:Obv:374.1] || member(member_of_1_not_of_2(intersection(u,v),intersection(w,u)),w)* -> subset(intersection(u,v),intersection(w,u)).
% 0.42/0.59 1463[0:Res:33.1,378.0] || -> subset(intersection(u,v),intersection(v,u))* subset(intersection(u,v),intersection(v,u))*.
% 0.42/0.59 1469[0:Obv:1463.0] || -> subset(intersection(u,v),intersection(v,u))*.
% 0.42/0.59 1470[0:MRR:24.1,24.0,1469.0] || -> .
% 0.42/0.59 % SZS output end Refutation
% 0.42/0.59 Formulae used in the proof : prove_commutativity subsets_axiom1 subsets_axiom2 member_of_both_is_member_of_intersection member_of_intersection_is_member_of_set1 member_of_intersection_is_member_of_set2 subsets_are_set_equal_sets
% 0.42/0.59
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