TSTP Solution File: SET071-7 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET071-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 05:23:33 EDT 2022
% Result : Unsatisfiable 0.19s 0.54s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET071-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 23:29:56 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.54
% 0.19/0.54 SPASS V 3.9
% 0.19/0.54 SPASS beiseite: Proof found.
% 0.19/0.54 % SZS status Theorem
% 0.19/0.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.54 SPASS derived 978 clauses, backtracked 0 clauses, performed 1 splits and kept 494 clauses.
% 0.19/0.54 SPASS allocated 76934 KBytes.
% 0.19/0.54 SPASS spent 0:00:00.19 on the problem.
% 0.19/0.54 0:00:00.04 for the input.
% 0.19/0.54 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.54 0:00:00.01 for inferences.
% 0.19/0.54 0:00:00.00 for the backtracking.
% 0.19/0.54 0:00:00.11 for the reduction.
% 0.19/0.54
% 0.19/0.54
% 0.19/0.54 Here is a proof with depth 3, length 31 :
% 0.19/0.54 % SZS output start Refutation
% 0.19/0.54 6[0:Inp] || subclass(u,v)* subclass(v,w)* -> subclass(u,w)*.
% 0.19/0.54 14[0:Inp] || subclass(u,null_class)* -> equal(u,null_class).
% 0.19/0.54 19[0:Inp] || -> subclass(singleton(u),unordered_pair(v,u))*r.
% 0.19/0.54 20[0:Inp] || -> member(u,universal_class) equal(unordered_pair(v,u),singleton(v))**.
% 0.19/0.54 21[0:Inp] || -> member(u,universal_class) equal(unordered_pair(u,v),singleton(v))**.
% 0.19/0.54 22[0:Inp] || equal(unordered_pair(x__dfg,y__dfg),null_class)** -> .
% 0.19/0.54 23[0:Inp] || member(x__dfg,universal_class)* -> .
% 0.19/0.54 24[0:Inp] || member(y__dfg,universal_class)* -> .
% 0.19/0.54 25[0:Inp] || member(u,v)* subclass(v,w)* -> member(u,w)*.
% 0.19/0.54 28[0:Inp] || -> subclass(u,universal_class)*.
% 0.19/0.54 32[0:Inp] || member(u,unordered_pair(v,w))* -> equal(u,w) equal(u,v).
% 0.19/0.54 36[0:Inp] || -> equal(unordered_pair(u,u),singleton(u))**.
% 0.19/0.54 90[0:Inp] || -> equal(u,null_class) member(regular(u),u)*.
% 0.19/0.54 121[0:Res:21.0,24.0] || -> equal(unordered_pair(y__dfg,u),singleton(u))**.
% 0.19/0.54 131[0:Res:20.0,23.0] || -> equal(unordered_pair(u,x__dfg),singleton(u))**.
% 0.19/0.54 132[0:Res:21.0,23.0] || -> equal(unordered_pair(x__dfg,u),singleton(u))**.
% 0.19/0.54 139[0:Res:25.2,23.0] || subclass(u,universal_class) member(x__dfg,u)* -> .
% 0.19/0.54 140[0:Res:14.1,22.0] || subclass(unordered_pair(x__dfg,y__dfg),null_class)*l -> .
% 0.19/0.54 158[0:Rew:132.0,140.0] || subclass(singleton(y__dfg),null_class)*l -> .
% 0.19/0.54 160[0:MRR:139.0,28.0] || member(x__dfg,u)* -> .
% 0.19/0.54 180[0:SpR:131.0,121.0] || -> equal(singleton(y__dfg),singleton(x__dfg))**.
% 0.19/0.54 183[0:Rew:180.0,158.0] || subclass(singleton(x__dfg),null_class)*l -> .
% 0.19/0.54 432[0:SpR:131.0,19.0] || -> subclass(singleton(x__dfg),singleton(u))*.
% 0.19/0.54 447[0:NCh:6.2,6.0,432.0,183.0] || equal(singleton(u),null_class)** -> .
% 0.19/0.54 1281[0:SpL:36.0,32.0] || member(u,singleton(v))* -> equal(u,v) equal(u,v).
% 0.19/0.54 1294[0:Obv:1281.1] || member(u,singleton(v))* -> equal(u,v).
% 0.19/0.54 1302[0:Res:90.1,1294.0] || -> equal(singleton(u),null_class) equal(regular(singleton(u)),u)**.
% 0.19/0.54 1307[0:MRR:1302.0,447.0] || -> equal(regular(singleton(u)),u)**.
% 0.19/0.54 1310[0:SpR:1307.0,90.1] || -> equal(singleton(u),null_class) member(u,singleton(u))*.
% 0.19/0.54 1335[0:MRR:1310.0,447.0] || -> member(u,singleton(u))*.
% 0.19/0.54 1336[0:UnC:1335.0,160.0] || -> .
% 0.19/0.54 % SZS output end Refutation
% 0.19/0.54 Formulae used in the proof : transitivity_of_subclass corollary_of_null_class_is_subclass singleton_in_unordered_pair2 unordered_pair_equals_singleton1 unordered_pair_equals_singleton2 prove_null_unordered_pair_1 prove_null_unordered_pair_2 prove_null_unordered_pair_3 subclass_members class_elements_are_sets unordered_pair_member singleton_set regularity1
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