TSTP Solution File: NUM094-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM094-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 : Mon Jul 18 14:24:04 EDT 2022
% Result : Unsatisfiable 53.95s 54.18s
% Output : Refutation 55.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : NUM094-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.02/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.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 : Thu Jul 7 08:44:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 53.95/54.18
% 53.95/54.18 SPASS V 3.9
% 53.95/54.18 SPASS beiseite: Proof found.
% 53.95/54.18 % SZS status Theorem
% 53.95/54.18 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 53.95/54.18 SPASS derived 84200 clauses, backtracked 19060 clauses, performed 48 splits and kept 49530 clauses.
% 53.95/54.18 SPASS allocated 131621 KBytes.
% 53.95/54.18 SPASS spent 0:0:53.71 on the problem.
% 53.95/54.18 0:00:00.04 for the input.
% 53.95/54.18 0:00:00.00 for the FLOTTER CNF translation.
% 53.95/54.18 0:00:00.96 for inferences.
% 53.95/54.18 0:00:05.31 for the backtracking.
% 53.95/54.18 0:0:46.29 for the reduction.
% 53.95/54.18
% 53.95/54.18
% 53.95/54.18 Here is a proof with depth 6, length 182 :
% 53.95/54.18 % SZS output start Refutation
% 53.95/54.18 1[0:Inp] || -> well_ordering(xr,y__dfg)*.
% 53.95/54.18 2[0:Inp] || -> section(xr,w__dfg,y__dfg)*.
% 53.95/54.18 3[0:Inp] || member(least(xr,intersection(complement(w__dfg),y__dfg)),y__dfg)* -> .
% 53.95/54.18 4[0:Inp] || equal(w__dfg,y__dfg)** -> .
% 53.95/54.18 5[0:Inp] || member(u,v)*+ subclass(v,w)* -> member(u,w)*.
% 53.95/54.18 6[0:Inp] || -> subclass(u,v) member(not_subclass_element(u,v),u)*.
% 53.95/54.18 7[0:Inp] || member(not_subclass_element(u,v),v)* -> subclass(u,v).
% 53.95/54.18 8[0:Inp] || -> subclass(u,universal_class)*.
% 53.95/54.18 11[0:Inp] || subclass(u,v)*+ subclass(v,u)* -> equal(v,u).
% 53.95/54.18 13[0:Inp] || member(u,universal_class) -> member(u,unordered_pair(u,v))*.
% 53.95/54.18 15[0:Inp] || -> member(unordered_pair(u,v),universal_class)*.
% 53.95/54.18 16[0:Inp] || -> equal(unordered_pair(u,u),singleton(u))**.
% 53.95/54.18 17[0:Inp] || -> equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v))**.
% 53.95/54.18 18[0:Inp] || member(ordered_pair(u,v),cross_product(w,x))* -> member(u,w).
% 53.95/54.18 19[0:Inp] || member(ordered_pair(u,v),cross_product(w,x))* -> member(v,x).
% 53.95/54.18 21[0:Inp] || member(u,cross_product(v,w))*+ -> equal(ordered_pair(first(u),second(u)),u)**.
% 53.95/54.18 26[0:Inp] || member(u,intersection(v,w))* -> member(u,w).
% 53.95/54.18 27[0:Inp] || member(u,v) member(u,w) -> member(u,intersection(w,v))*.
% 53.95/54.18 28[0:Inp] || member(u,v) member(u,complement(v))* -> .
% 53.95/54.18 29[0:Inp] || member(u,universal_class) -> member(u,v) member(u,complement(v))*.
% 53.95/54.18 66[0:Inp] function(u) || -> subclass(u,cross_product(universal_class,universal_class))*.
% 53.95/54.18 70[0:Inp] || -> equal(u,null_class) member(regular(u),u)*.
% 53.95/54.18 108[0:Inp] || -> equal(intersection(complement(compose(element_relation,complement(identity_relation))),element_relation),singleton_relation)**.
% 53.95/54.18 128[0:Inp] || subclass(u,v)*+ well_ordering(w,v)* -> equal(u,null_class) member(least(w,u),u)*.
% 53.95/54.18 135[0:Inp] || section(u,v,w)* -> subclass(v,w).
% 53.95/54.18 138[0:Inp] || member(u,ordinal_numbers)* -> well_ordering(element_relation,u).
% 53.95/54.18 143[0:Inp] || -> equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals)**.
% 53.95/54.18 151[0:Inp] || member(u,recursion_equation_functions(v))* -> function(v).
% 53.95/54.18 167[0:Res:1.0,128.0] || subclass(u,y__dfg) -> equal(u,null_class) member(least(xr,u),u)*.
% 53.95/54.18 171[0:Res:11.2,4.0] || subclass(w__dfg,y__dfg)* subclass(y__dfg,w__dfg) -> .
% 53.95/54.18 177[0:Res:2.0,135.0] || -> subclass(w__dfg,y__dfg)*.
% 53.95/54.18 182[0:Res:26.1,3.0] || member(least(xr,intersection(complement(w__dfg),y__dfg)),intersection(u,y__dfg))* -> .
% 53.95/54.18 185[0:MRR:171.0,177.0] || subclass(y__dfg,w__dfg)* -> .
% 53.95/54.18 197[0:SpR:16.0,15.0] || -> member(singleton(u),universal_class)*.
% 53.95/54.18 202[0:Res:70.1,138.0] || -> equal(null_class,ordinal_numbers) well_ordering(element_relation,regular(ordinal_numbers))*.
% 53.95/54.18 203[1:Spt:202.0] || -> equal(null_class,ordinal_numbers)**.
% 53.95/54.18 207[1:Rew:203.0,70.0] || -> equal(u,ordinal_numbers) member(regular(u),u)*.
% 53.95/54.18 211[1:Rew:203.0,167.1] || subclass(u,y__dfg) -> equal(u,ordinal_numbers) member(least(xr,u),u)*.
% 53.95/54.18 231[1:Res:207.1,151.0] || -> equal(recursion_equation_functions(u),ordinal_numbers)** function(u).
% 53.95/54.18 233[1:Rew:231.0,151.0] || member(u,ordinal_numbers)*+ -> function(v)*.
% 53.95/54.18 264[1:Res:6.1,233.0] || -> subclass(ordinal_numbers,u)* function(v)*.
% 53.95/54.18 268[2:Spt:264.1] || -> function(u)*.
% 53.95/54.18 269[2:MRR:66.0,268.0] || -> subclass(u,cross_product(universal_class,universal_class))*.
% 53.95/54.18 370[0:Res:6.1,28.1] || member(not_subclass_element(complement(u),v),u)* -> subclass(complement(u),v).
% 53.95/54.18 379[0:SpL:108.0,26.0] || member(u,singleton_relation)* -> member(u,element_relation).
% 53.95/54.18 383[0:Res:6.1,26.0] || -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),v)*.
% 53.95/54.18 833[0:SpL:143.0,26.0] || member(u,limit_ordinals)* -> member(u,ordinal_numbers).
% 53.95/54.18 1035[0:SpR:17.0,15.0] || -> member(ordered_pair(u,v),universal_class)*.
% 53.95/54.18 1036[0:SpR:17.0,13.1] || member(singleton(u),universal_class) -> member(singleton(u),ordered_pair(u,v))*.
% 53.95/54.18 1040[0:MRR:1036.0,197.0] || -> member(singleton(u),ordered_pair(u,v))*.
% 53.95/54.18 1383[0:Res:8.0,11.0] || subclass(universal_class,u)* -> equal(universal_class,u).
% 53.95/54.18 1432[2:Res:269.0,1383.0] || -> equal(cross_product(universal_class,universal_class),universal_class)**.
% 53.95/54.18 1934[0:Res:1035.0,5.0] || subclass(universal_class,u) -> member(ordered_pair(v,w),u)*.
% 53.95/54.18 1960[2:SpL:1432.0,19.0] || member(ordered_pair(u,v),universal_class)* -> member(v,universal_class).
% 53.95/54.18 1962[2:MRR:1960.0,1035.0] || -> member(u,universal_class)*.
% 53.95/54.18 2924[2:SpL:1432.0,21.0] || member(u,universal_class) -> equal(ordered_pair(first(u),second(u)),u)**.
% 53.95/54.18 2932[2:MRR:2924.0,1962.0] || -> equal(ordered_pair(first(u),second(u)),u)**.
% 53.95/54.18 2983[2:SpR:2932.0,1040.0] || -> member(singleton(first(u)),u)*.
% 53.95/54.18 3029[2:Res:2983.0,28.1] || member(singleton(first(complement(u))),u)* -> .
% 53.95/54.18 3037[2:UnC:3029.0,1962.0] || -> .
% 53.95/54.18 3038[2:Spt:3037.0,264.0] || -> subclass(ordinal_numbers,u)*.
% 53.95/54.18 3039[2:Res:3038.0,11.0] || subclass(u,ordinal_numbers)* -> equal(u,ordinal_numbers).
% 53.95/54.18 3243[0:Res:66.1,1383.0] function(universal_class) || -> equal(cross_product(universal_class,universal_class),universal_class)**.
% 53.95/54.18 4179[0:Res:1934.1,18.0] || subclass(universal_class,cross_product(u,v))*+ -> member(w,u)*.
% 53.95/54.18 4249[0:Res:66.1,4179.0] function(universal_class) || -> member(u,universal_class)*.
% 53.95/54.18 6016[0:Res:27.2,5.0] || member(u,v)* member(u,w)* subclass(intersection(w,v),x)*+ -> member(u,x)*.
% 53.95/54.18 9956[0:Res:383.1,7.0] || -> subclass(intersection(u,v),v)* subclass(intersection(u,v),v)*.
% 53.95/54.18 9961[0:Obv:9956.0] || -> subclass(intersection(u,v),v)*.
% 53.95/54.18 33985[0:Res:8.0,6016.2] || member(u,v)* member(u,w)* -> member(u,universal_class)*.
% 53.95/54.18 33992[0:Con:33985.1] || member(u,v)*+ -> member(u,universal_class)*.
% 53.95/54.18 34068[0:Res:6.1,33992.0] || -> subclass(u,v) member(not_subclass_element(u,v),universal_class)*.
% 53.95/54.18 35193[0:Res:34068.1,370.0] || -> subclass(complement(universal_class),u)* subclass(complement(universal_class),u)*.
% 53.95/54.18 35201[0:Obv:35193.0] || -> subclass(complement(universal_class),u)*.
% 53.95/54.18 47022[2:Res:35201.0,3039.0] || -> equal(complement(universal_class),ordinal_numbers)**.
% 53.95/54.18 47059[2:SpL:47022.0,28.1] || member(u,universal_class) member(u,ordinal_numbers)* -> .
% 53.95/54.18 47063[2:MRR:47059.0,33992.1] || member(u,ordinal_numbers)* -> .
% 53.95/54.18 58307[1:Res:211.2,182.0] || subclass(intersection(complement(w__dfg),y__dfg),y__dfg)* -> equal(intersection(complement(w__dfg),y__dfg),ordinal_numbers).
% 53.95/54.18 58310[1:MRR:58307.0,9961.0] || -> equal(intersection(complement(w__dfg),y__dfg),ordinal_numbers)**.
% 53.95/54.18 58331[1:SpR:58310.0,27.2] || member(u,y__dfg) member(u,complement(w__dfg))* -> member(u,ordinal_numbers).
% 53.95/54.18 58341[2:MRR:58331.2,47063.0] || member(u,y__dfg) member(u,complement(w__dfg))* -> .
% 53.95/54.18 58397[2:Res:29.2,58341.1] || member(u,universal_class)* member(u,y__dfg) -> member(u,w__dfg).
% 53.95/54.18 58423[2:MRR:58397.0,33992.1] || member(u,y__dfg) -> member(u,w__dfg)*.
% 53.95/54.18 58431[2:Res:58423.1,7.0] || member(not_subclass_element(u,w__dfg),y__dfg)* -> subclass(u,w__dfg).
% 53.95/54.18 58507[2:Res:6.1,58431.0] || -> subclass(y__dfg,w__dfg)* subclass(y__dfg,w__dfg)*.
% 53.95/54.18 58511[2:Obv:58507.0] || -> subclass(y__dfg,w__dfg)*.
% 53.95/54.18 58512[2:MRR:58511.0,185.0] || -> .
% 53.95/54.18 58516[1:Spt:58512.0,202.0,203.0] || equal(null_class,ordinal_numbers)** -> .
% 53.95/54.18 58517[1:Spt:58512.0,202.1] || -> well_ordering(element_relation,regular(ordinal_numbers))*.
% 53.95/54.18 58658[0:Res:70.1,379.0] || -> equal(null_class,singleton_relation) member(regular(singleton_relation),element_relation)*.
% 53.95/54.18 58665[0:Res:70.1,833.0] || -> equal(null_class,limit_ordinals) member(regular(limit_ordinals),ordinal_numbers)*.
% 53.95/54.18 58667[2:Spt:58658.0] || -> equal(null_class,singleton_relation)**.
% 53.95/54.18 58677[2:Rew:58667.0,70.0] || -> equal(u,singleton_relation) member(regular(u),u)*.
% 53.95/54.18 58687[2:Rew:58667.0,167.1] || subclass(u,y__dfg) -> equal(u,singleton_relation) member(least(xr,u),u)*.
% 53.95/54.18 58858[0:Res:6.1,151.0] || -> subclass(recursion_equation_functions(u),v)* function(u).
% 53.95/54.18 58908[2:Res:58677.1,151.0] || -> equal(recursion_equation_functions(u),singleton_relation)** function(u).
% 55.22/55.43 58911[2:Rew:58908.0,151.0] || member(u,singleton_relation)*+ -> function(v)*.
% 55.22/55.43 58912[2:Rew:58908.0,58858.0] || -> subclass(singleton_relation,u)* function(v)*.
% 55.22/55.43 58921[3:Spt:58912.1] || -> function(u)*.
% 55.22/55.43 58934[3:MRR:4249.0,58921.0] || -> member(u,universal_class)*.
% 55.22/55.43 58935[3:MRR:3243.0,58921.0] || -> equal(cross_product(universal_class,universal_class),universal_class)**.
% 55.22/55.43 59454[3:SpL:58935.0,21.0] || member(u,universal_class) -> equal(ordered_pair(first(u),second(u)),u)**.
% 55.22/55.43 59477[3:MRR:59454.0,58934.0] || -> equal(ordered_pair(first(u),second(u)),u)**.
% 55.22/55.43 59662[3:SpR:59477.0,1040.0] || -> member(singleton(first(u)),u)*.
% 55.22/55.43 59725[3:Res:59662.0,28.1] || member(singleton(first(complement(u))),u)* -> .
% 55.22/55.43 59743[3:UnC:59725.0,58934.0] || -> .
% 55.22/55.43 59744[3:Spt:59743.0,58912.0] || -> subclass(singleton_relation,u)*.
% 55.22/55.43 59747[3:Res:59744.0,11.0] || subclass(u,singleton_relation)* -> equal(u,singleton_relation).
% 55.22/55.43 59790[2:SoR:4249.0,58911.1] || member(u,singleton_relation)* -> member(v,universal_class)*.
% 55.22/55.43 59906[3:Res:35201.0,59747.0] || -> equal(complement(universal_class),singleton_relation)**.
% 55.22/55.43 59944[3:SpL:59906.0,28.1] || member(u,universal_class) member(u,singleton_relation)* -> .
% 55.22/55.43 59948[3:MRR:59944.0,59790.1] || member(u,singleton_relation)* -> .
% 55.22/55.43 71171[2:Res:58687.2,182.0] || subclass(intersection(complement(w__dfg),y__dfg),y__dfg)* -> equal(intersection(complement(w__dfg),y__dfg),singleton_relation).
% 55.22/55.43 71175[2:MRR:71171.0,9961.0] || -> equal(intersection(complement(w__dfg),y__dfg),singleton_relation)**.
% 55.22/55.43 71194[2:SpR:71175.0,27.2] || member(u,y__dfg) member(u,complement(w__dfg))* -> member(u,singleton_relation).
% 55.22/55.43 71204[3:MRR:71194.2,59948.0] || member(u,y__dfg) member(u,complement(w__dfg))* -> .
% 55.22/55.43 71226[3:Res:29.2,71204.1] || member(u,universal_class)* member(u,y__dfg) -> member(u,w__dfg).
% 55.22/55.43 71254[3:MRR:71226.0,33992.1] || member(u,y__dfg) -> member(u,w__dfg)*.
% 55.22/55.43 71280[3:Res:71254.1,7.0] || member(not_subclass_element(u,w__dfg),y__dfg)* -> subclass(u,w__dfg).
% 55.22/55.43 71336[3:Res:6.1,71280.0] || -> subclass(y__dfg,w__dfg)* subclass(y__dfg,w__dfg)*.
% 55.22/55.43 71340[3:Obv:71336.0] || -> subclass(y__dfg,w__dfg)*.
% 55.22/55.43 71341[3:MRR:71340.0,185.0] || -> .
% 55.22/55.43 71345[2:Spt:71341.0,58658.0,58667.0] || equal(null_class,singleton_relation)** -> .
% 55.22/55.43 71346[2:Spt:71341.0,58658.1] || -> member(regular(singleton_relation),element_relation)*.
% 55.22/55.43 71456[3:Spt:58665.0] || -> equal(null_class,limit_ordinals)**.
% 55.22/55.43 71474[3:Rew:71456.0,167.1] || subclass(u,y__dfg) -> equal(u,limit_ordinals) member(least(xr,u),u)*.
% 55.22/55.43 71478[3:Rew:71456.0,70.0] || -> equal(u,limit_ordinals) member(regular(u),u)*.
% 55.22/55.43 71651[3:Res:71478.1,151.0] || -> equal(recursion_equation_functions(u),limit_ordinals)** function(u).
% 55.22/55.43 71660[3:Rew:71651.0,58858.0] || -> subclass(limit_ordinals,u)* function(v)*.
% 55.22/55.43 71661[3:Rew:71651.0,151.0] || member(u,limit_ordinals)*+ -> function(v)*.
% 55.22/55.43 71669[4:Spt:71660.1] || -> function(u)*.
% 55.22/55.43 71681[4:MRR:4249.0,71669.0] || -> member(u,universal_class)*.
% 55.22/55.43 71682[4:MRR:3243.0,71669.0] || -> equal(cross_product(universal_class,universal_class),universal_class)**.
% 55.22/55.43 72209[4:SpL:71682.0,21.0] || member(u,universal_class) -> equal(ordered_pair(first(u),second(u)),u)**.
% 55.22/55.43 72232[4:MRR:72209.0,71681.0] || -> equal(ordered_pair(first(u),second(u)),u)**.
% 55.22/55.43 72345[4:SpR:72232.0,1040.0] || -> member(singleton(first(u)),u)*.
% 55.22/55.43 72410[4:Res:72345.0,28.1] || member(singleton(first(complement(u))),u)* -> .
% 55.22/55.43 72427[4:UnC:72410.0,71681.0] || -> .
% 55.22/55.43 72428[4:Spt:72427.0,71660.0] || -> subclass(limit_ordinals,u)*.
% 55.22/55.43 72430[4:Res:72428.0,11.0] || subclass(u,limit_ordinals)* -> equal(u,limit_ordinals).
% 55.22/55.43 72467[3:SoR:4249.0,71661.1] || member(u,limit_ordinals)* -> member(v,universal_class)*.
% 55.22/55.43 72558[4:Res:35201.0,72430.0] || -> equal(complement(universal_class),limit_ordinals)**.
% 55.22/55.43 72596[4:SpL:72558.0,28.1] || member(u,universal_class) member(u,limit_ordinals)* -> .
% 55.22/55.43 72600[4:MRR:72596.0,72467.1] || member(u,limit_ordinals)* -> .
% 55.22/55.43 85081[3:Res:71474.2,182.0] || subclass(intersection(complement(w__dfg),y__dfg),y__dfg)* -> equal(intersection(complement(w__dfg),y__dfg),limit_ordinals).
% 55.22/55.43 85083[3:MRR:85081.0,9961.0] || -> equal(intersection(complement(w__dfg),y__dfg),limit_ordinals)**.
% 55.22/55.43 85102[3:SpR:85083.0,27.2] || member(u,y__dfg) member(u,complement(w__dfg))* -> member(u,limit_ordinals).
% 55.22/55.43 85112[4:MRR:85102.2,72600.0] || member(u,y__dfg) member(u,complement(w__dfg))* -> .
% 55.22/55.43 85288[4:Res:29.2,85112.1] || member(u,universal_class)* member(u,y__dfg) -> member(u,w__dfg).
% 55.22/55.43 85316[4:MRR:85288.0,33992.1] || member(u,y__dfg) -> member(u,w__dfg)*.
% 55.22/55.43 85331[4:Res:85316.1,7.0] || member(not_subclass_element(u,w__dfg),y__dfg)* -> subclass(u,w__dfg).
% 55.22/55.43 85504[4:Res:6.1,85331.0] || -> subclass(y__dfg,w__dfg)* subclass(y__dfg,w__dfg)*.
% 55.22/55.43 85508[4:Obv:85504.0] || -> subclass(y__dfg,w__dfg)*.
% 55.22/55.43 85509[4:MRR:85508.0,185.0] || -> .
% 55.22/55.43 85513[3:Spt:85509.0,58665.0,71456.0] || equal(null_class,limit_ordinals)** -> .
% 55.22/55.43 85514[3:Spt:85509.0,58665.1] || -> member(regular(limit_ordinals),ordinal_numbers)*.
% 55.22/55.43 85699[0:Res:70.1,151.0] || -> equal(recursion_equation_functions(u),null_class)** function(u).
% 55.22/55.43 85711[0:Rew:85699.0,58858.0] || -> subclass(null_class,u)* function(v)*.
% 55.22/55.43 85712[0:Rew:85699.0,151.0] || member(u,null_class)*+ -> function(v)*.
% 55.22/55.43 85731[4:Spt:85711.1] || -> function(u)*.
% 55.22/55.43 85743[4:MRR:4249.0,85731.0] || -> member(u,universal_class)*.
% 55.22/55.43 85744[4:MRR:3243.0,85731.0] || -> equal(cross_product(universal_class,universal_class),universal_class)**.
% 55.22/55.43 86280[4:SpL:85744.0,21.0] || member(u,universal_class) -> equal(ordered_pair(first(u),second(u)),u)**.
% 55.22/55.43 86303[4:MRR:86280.0,85743.0] || -> equal(ordered_pair(first(u),second(u)),u)**.
% 55.22/55.43 86459[4:SpR:86303.0,1040.0] || -> member(singleton(first(u)),u)*.
% 55.22/55.43 86555[4:Res:86459.0,28.1] || member(singleton(first(complement(u))),u)* -> .
% 55.22/55.43 86573[4:UnC:86555.0,85743.0] || -> .
% 55.22/55.43 86574[4:Spt:86573.0,85711.0] || -> subclass(null_class,u)*.
% 55.22/55.43 86575[4:Res:86574.0,11.0] || subclass(u,null_class)* -> equal(u,null_class).
% 55.22/55.43 86617[0:SoR:4249.0,85712.1] || member(u,null_class)* -> member(v,universal_class)*.
% 55.22/55.43 86741[4:Res:35201.0,86575.0] || -> equal(complement(universal_class),null_class)**.
% 55.22/55.43 86775[4:SpL:86741.0,28.1] || member(u,universal_class) member(u,null_class)* -> .
% 55.22/55.43 86779[4:MRR:86775.0,86617.1] || member(u,null_class)* -> .
% 55.22/55.43 98902[0:Res:167.2,182.0] || subclass(intersection(complement(w__dfg),y__dfg),y__dfg)* -> equal(intersection(complement(w__dfg),y__dfg),null_class).
% 55.22/55.43 98905[0:MRR:98902.0,9961.0] || -> equal(intersection(complement(w__dfg),y__dfg),null_class)**.
% 55.22/55.43 98927[0:SpR:98905.0,27.2] || member(u,y__dfg) member(u,complement(w__dfg))* -> member(u,null_class).
% 55.22/55.43 98937[4:MRR:98927.2,86779.0] || member(u,y__dfg) member(u,complement(w__dfg))* -> .
% 55.22/55.43 99653[4:Res:29.2,98937.1] || member(u,universal_class)* member(u,y__dfg) -> member(u,w__dfg).
% 55.22/55.43 99686[4:MRR:99653.0,33992.1] || member(u,y__dfg) -> member(u,w__dfg)*.
% 55.22/55.43 99692[4:Res:99686.1,7.0] || member(not_subclass_element(u,w__dfg),y__dfg)* -> subclass(u,w__dfg).
% 55.22/55.43 102675[4:Res:6.1,99692.0] || -> subclass(y__dfg,w__dfg)* subclass(y__dfg,w__dfg)*.
% 55.22/55.43 102679[4:Obv:102675.0] || -> subclass(y__dfg,w__dfg)*.
% 55.22/55.43 102680[4:MRR:102679.0,185.0] || -> .
% 55.22/55.43 % SZS output end Refutation
% 55.22/55.43 Formulae used in the proof : prove_sections_property3_1 prove_sections_property3_2 prove_sections_property3_3 prove_sections_property3_4 subclass_members not_subclass_members1 not_subclass_members2 class_elements_are_sets subclass_implies_equal unordered_pair2 unordered_pairs_in_universal singleton_set ordered_pair cartesian_product1 cartesian_product2 cartesian_product4 intersection2 intersection3 complement1 complement2 function1 regularity1 compose_can_define_singleton well_ordering2 section1 ordinal_numbers1 limit_ordinals recursion_equation_functions1
% 55.22/55.43
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