%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM079-1 : 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 : Mon Jul 18 14:24:00 EDT 2022

% Result   : Timeout 299.82s 300.43s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : NUM079-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.13/0.14  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n011.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Tue Jul  5 14:09:37 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 299.82/300.43  
% 299.82/300.43  SPASS V 3.9 
% 299.82/300.43  SPASS beiseite: Ran out of time.
% 299.82/300.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 299.82/300.43  SPASS derived 181230 clauses, backtracked 25346 clauses, performed 70 splits and kept 81923 clauses.
% 299.82/300.43  SPASS allocated 233309 KBytes.
% 299.82/300.43  SPASS spent	0:05:00.07 on the problem.
% 299.82/300.43  		0:00:00.04 for the input.
% 299.82/300.43  		0:00:00.00 for the FLOTTER CNF translation.
% 299.82/300.43  		0:00:02.91 for inferences.
% 299.82/300.43  		0:0:12.90 for the backtracking.
% 299.82/300.43  		0:4:39.71 for the reduction.
% 299.82/300.43  
% 299.82/300.43  
% 299.82/300.43   The set of clauses at termination is :
% 299.82/300.43  161035[10:Rew:160202.0,150481.0] || member(u,intersection(power_class(successor_relation),complement(v)))* member(u,union(image(element_relation,universal_class),v)) -> .
% 299.82/300.43  222482[24:Rew:204010.0,222393.0] ||  -> equal(segment(u,v,kind_1_ordinals),segment(u,v,universal_class))**.
% 299.82/300.43  231598[24:Res:8.1,222619.0] || equal(u,ordered_pair(kind_1_ordinals,v))*+ -> member(successor_relation,u)*.
% 299.82/300.43  231194[10:Res:8.1,221320.0] || equal(regular(unordered_pair(ordered_pair(u,v),w)),universal_class)** -> .
% 299.82/300.43  230662[10:Res:8.1,219386.0] || equal(regular(unordered_pair(u,ordered_pair(v,w))),universal_class)** -> .
% 299.82/300.43  189411[15:Rew:189339.1,184856.2] || member(u,universal_class) subclass(domain_relation,omega) -> equal(integer_of(ordered_pair(u,successor_relation)),ordered_pair(u,successor_relation))**.
% 299.82/300.43  228737[10:MRR:228721.2,185225.0] || equal(singleton(u),v)* equal(v,universal_class) -> .
% 299.82/300.43  228736[10:MRR:228720.2,185225.0] || equal(singleton(u),v)*+ subclass(universal_class,v)* -> .
% 299.82/300.43  224912[25:SpR:224739.1,45.0] function(u) ||  -> equal(union(u,successor_relation),successor(u))**.
% 299.82/300.43  231621[15:MRR:231620.0,100.0] || equal(sum_class(range_of(singleton(successor_relation))),successor_relation)** -> .
% 299.82/300.43  184011[14:MRR:183978.2,160227.0] || equal(sum_class(range_of(singleton(u))),u) member(singleton(singleton(singleton(u))),cross_product(universal_class,universal_class))* -> .
% 299.82/300.43  222619[24:Res:222332.0,3.0] || subclass(ordered_pair(kind_1_ordinals,u),v)* -> member(successor_relation,v).
% 299.82/300.43  221327[10:Res:8.1,217590.0] || equal(regular(unordered_pair(unordered_pair(u,v),w)),universal_class)** -> .
% 299.82/300.43  231219[12:Res:185430.1,231184.0] || equal(complement(regular(unordered_pair(regular(element_relation),u))),successor_relation)** -> .
% 299.82/300.43  231211[10:Res:185430.1,231183.0] || equal(complement(regular(unordered_pair(regular(domain_relation),u))),successor_relation)** -> .
% 299.82/300.43  155802[3:Res:1495.2,141576.1] || member(u,universal_class) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(u,rest_of(u)),ordinal_numbers)* -> .
% 299.82/300.43  231203[10:Res:185430.1,231182.0] || equal(complement(regular(unordered_pair(regular(rest_relation),u))),successor_relation)** -> .
% 299.82/300.43  231218[12:Res:8.1,231184.0] || equal(regular(unordered_pair(regular(element_relation),u)),universal_class)** -> .
% 299.82/300.43  231210[10:Res:8.1,231183.0] || equal(regular(unordered_pair(regular(domain_relation),u)),universal_class)** -> .
% 299.82/300.43  231202[10:Res:8.1,231182.0] || equal(regular(unordered_pair(regular(rest_relation),u)),universal_class)** -> .
% 299.82/300.43  10029[0:SpR:511.0,45.0] ||  -> equal(complement(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))),successor(image(element_relation,complement(u))))**.
% 299.82/300.43  231184[12:SpL:209433.0,221320.0] || subclass(universal_class,regular(unordered_pair(regular(element_relation),u)))* -> .
% 299.82/300.43  231183[10:SpL:201355.0,221320.0] || subclass(universal_class,regular(unordered_pair(regular(domain_relation),u)))* -> .
% 299.82/300.43  231182[10:SpL:199964.0,221320.0] || subclass(universal_class,regular(unordered_pair(regular(rest_relation),u)))* -> .
% 299.82/300.43  221320[10:SpL:15.0,217590.0] || subclass(universal_class,regular(unordered_pair(ordered_pair(u,v),w)))* -> .
% 299.82/300.43  10028[0:SpR:511.0,115.0] ||  -> equal(complement(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))),symmetrization_of(image(element_relation,complement(u))))**.
% 299.82/300.43  219396[10:Res:8.1,217589.0] || equal(regular(unordered_pair(u,unordered_pair(v,w))),universal_class)** -> .
% 299.82/300.43  230725[12:MRR:230724.2,209559.0] || equal(regular(element_relation),u)* equal(u,universal_class) -> .
% 299.82/300.43  230719[10:MRR:230718.2,201541.0] || equal(regular(domain_relation),u)* equal(u,universal_class) -> .
% 299.82/300.43  230701[10:MRR:230700.2,200297.0] || equal(regular(rest_relation),u)* equal(u,universal_class) -> .
% 299.82/300.43  160972[10:Rew:160202.0,150480.1] || member(u,universal_class) -> member(u,image(element_relation,power_class(successor_relation)))* member(u,power_class(image(element_relation,universal_class))).
% 299.82/300.43  230695[12:MRR:230691.2,209559.0] || equal(regular(element_relation),u) subclass(universal_class,u)* -> .
% 299.82/300.43  230686[10:MRR:230682.2,201541.0] || equal(regular(domain_relation),u) subclass(universal_class,u)* -> .
% 299.82/300.43  230677[10:MRR:230673.2,200297.0] || equal(regular(rest_relation),u) subclass(universal_class,u)* -> .
% 299.82/300.43  230694[12:Res:185430.1,230652.0] || equal(complement(regular(unordered_pair(u,regular(element_relation)))),successor_relation)** -> .
% 299.82/300.43  163539[10:Rew:160202.0,162827.1,160305.0,162827.1,160305.0,162827.0] ||  -> subclass(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u) member(not_subclass_element(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u),kind_1_ordinals)*.
% 299.82/300.43  230685[10:Res:185430.1,230651.0] || equal(complement(regular(unordered_pair(u,regular(domain_relation)))),successor_relation)** -> .
% 299.82/300.43  230676[10:Res:185430.1,230650.0] || equal(complement(regular(unordered_pair(u,regular(rest_relation)))),successor_relation)** -> .
% 299.82/300.43  230693[12:Res:8.1,230652.0] || equal(regular(unordered_pair(u,regular(element_relation))),universal_class)** -> .
% 299.82/300.43  230684[10:Res:8.1,230651.0] || equal(regular(unordered_pair(u,regular(domain_relation))),universal_class)** -> .
% 299.82/300.43  192570[10:Res:54.0,162356.0] || subclass(universal_class,u)+ well_ordering(omega,u)* -> equal(integer_of(ordered_pair(omega,least(omega,universal_class))),successor_relation)**.
% 299.82/300.43  230675[10:Res:8.1,230650.0] || equal(regular(unordered_pair(u,regular(rest_relation))),universal_class)** -> .
% 299.82/300.43  230652[12:SpL:209433.0,219386.0] || subclass(universal_class,regular(unordered_pair(u,regular(element_relation))))* -> .
% 299.82/300.43  230651[10:SpL:201355.0,219386.0] || subclass(universal_class,regular(unordered_pair(u,regular(domain_relation))))* -> .
% 299.82/300.43  230650[10:SpL:199964.0,219386.0] || subclass(universal_class,regular(unordered_pair(u,regular(rest_relation))))* -> .
% 299.82/300.43  157905[6:Res:1479.2,148657.1] || member(u,universal_class) subclass(universal_class,complement(compose(element_relation,universal_class)))*+ member(sum_class(u),element_relation)* -> .
% 299.82/300.43  219386[10:SpL:15.0,217589.0] || subclass(universal_class,regular(unordered_pair(u,ordered_pair(v,w))))* -> .
% 299.82/300.43  230608[15:Res:8.1,230172.1] || equal(u,domain_relation) equal(complement(u),domain_relation)** -> .
% 299.82/300.43  230498[10:Res:8.1,229049.0] || equal(singleton(u),kind_1_ordinals)**+ -> equal(regular(ordinal_numbers),u)*.
% 299.82/300.43  230287[25:SoR:224788.0,73.1] one_to_one(least(u,omega)) || well_ordering(u,omega)* -> .
% 299.82/300.43  157904[6:Res:1478.2,148657.1] || member(u,universal_class) subclass(universal_class,complement(compose(element_relation,universal_class)))*+ member(power_class(u),element_relation)* -> .
% 299.82/300.43  230284[25:SoR:224787.0,73.1] one_to_one(least(u,omega)) || well_ordering(u,universal_class)* -> .
% 299.82/300.43  230281[25:SoR:224786.0,73.1] one_to_one(least(u,rest_relation)) || well_ordering(u,rest_relation)* -> .
% 299.82/300.43  230278[25:SoR:224785.0,73.1] one_to_one(least(u,rest_relation)) || well_ordering(u,universal_class)* -> .
% 299.82/300.43  230242[25:SoR:224784.0,73.1] one_to_one(least(u,universal_class)) || well_ordering(u,universal_class)* -> .
% 299.82/300.43  164286[10:Res:163149.1,1320.1] inductive(sum_class(range_of(successor_relation))) || member(range_of(successor_relation),ordinal_numbers)* -> equal(sum_class(range_of(successor_relation)),range_of(successor_relation)).
% 299.82/300.43  230239[25:SoR:224783.0,73.1] one_to_one(least(u,ordinal_numbers)) || well_ordering(u,kind_1_ordinals)* -> .
% 299.82/300.43  230610[15:Res:100.0,230172.1] || equal(complement(cross_product(universal_class,universal_class)),domain_relation)** -> .
% 299.82/300.43  230172[15:Res:8.1,222296.1] || equal(complement(u),domain_relation) subclass(domain_relation,u)* -> .
% 299.82/300.43  229849[20:Res:8.1,221538.0] || equal(u,complement(singleton(omega)))*+ -> member(successor_relation,u)*.
% 299.82/300.43  161960[10:Rew:160202.0,146174.1] || member(cross_product(universal_class,cross_product(universal_class,universal_class)),ordinal_numbers)* -> equal(segment(element_relation,composition_function,least(element_relation,composition_function)),successor_relation).
% 299.82/300.43  229800[10:Res:221521.1,26.1] || member(u,singleton(omega))* -> equal(integer_of(u),successor_relation).
% 299.82/300.43  229049[10:Res:228991.1,2151.0] || subclass(kind_1_ordinals,singleton(u))* -> equal(regular(ordinal_numbers),u).
% 299.82/300.43  227642[10:SpR:30.0,227524.0] ||  -> equal(intersection(complement(kind_1_ordinals),restrict(ordinal_numbers,u,v)),successor_relation)**.
% 299.82/300.43  226753[10:SpR:30.0,226634.0] ||  -> equal(intersection(restrict(ordinal_numbers,u,v),complement(kind_1_ordinals)),successor_relation)**.
% 299.82/300.43  162952[10:Rew:160202.0,155795.2] || member(complement(kind_1_ordinals),universal_class) member(apply(choice,complement(kind_1_ordinals)),ordinal_numbers)* -> equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.43  224788[25:MRR:224675.2,3567.0] function(least(u,omega)) || well_ordering(u,omega)* -> .
% 299.82/300.43  224787[25:MRR:224674.2,3567.0] function(least(u,omega)) || well_ordering(u,universal_class)* -> .
% 299.82/300.43  224786[25:MRR:224673.2,3567.0] function(least(u,rest_relation)) || well_ordering(u,rest_relation)* -> .
% 299.82/300.43  224785[25:MRR:224672.2,3567.0] function(least(u,rest_relation)) || well_ordering(u,universal_class)* -> .
% 299.82/300.43  9647[0:Res:1481.2,595.0] || subclass(u,restrict(v,w,x))*+ -> subclass(u,y) member(not_subclass_element(u,y),v)*.
% 299.82/300.43  224784[25:MRR:224671.2,3567.0] function(least(u,universal_class)) || well_ordering(u,universal_class)* -> .
% 299.82/300.43  224783[25:MRR:224670.2,3567.0] function(least(u,ordinal_numbers)) || well_ordering(u,kind_1_ordinals)* -> .
% 299.82/300.43  223309[24:SpL:222479.0,21.0] || member(ordered_pair(u,universal_class),element_relation)* -> member(u,kind_1_ordinals).
% 299.82/300.43  223072[25:SoR:222758.0,160511.2] single_valued_class(singleton(u)) || equal(singleton(u),successor_relation)** -> .
% 299.82/300.43  203327[6:Rew:203192.0,10422.0] ||  -> equal(cantor(restrict(cross_product(u,singleton(v)),w,x)),segment(cross_product(w,x),u,v))**.
% 299.82/300.43  230177[15:Res:8.1,230174.0] || equal(singleton(domain_relation),domain_relation)** -> equal(singleton(domain_relation),successor_relation).
% 299.82/300.43  230174[15:Res:218373.0,222296.1] || subclass(domain_relation,singleton(domain_relation))* -> equal(singleton(domain_relation),successor_relation).
% 299.82/300.43  222296[15:MRR:222272.1,160214.0] || subclass(domain_relation,u) subclass(domain_relation,complement(u))* -> .
% 299.82/300.43  222140[10:Res:221525.0,3670.1] || equal(complement(complement(singleton(ordered_pair(u,v)))),universal_class)** -> .
% 299.82/300.43  9529[0:Rew:161.0,9461.0] ||  -> subclass(symmetric_difference(u,v),w) member(not_subclass_element(symmetric_difference(u,v),w),complement(intersection(u,v)))*.
% 299.82/300.43  221538[20:Res:221515.0,3.0] || subclass(complement(singleton(omega)),u)* -> member(successor_relation,u).
% 299.82/300.43  229836[26:MRR:229835.1,160217.0] || equal(omega,universal_class)** -> .
% 299.82/300.43  229834[26:Spt:229827.0] ||  -> equal(integer_of(omega),successor_relation)**.
% 299.82/300.43  221521[10:MRR:221453.0,185582.0] ||  -> equal(integer_of(u),successor_relation) member(u,complement(singleton(omega)))*.
% 299.82/300.43  161696[10:Rew:160202.0,146143.0] ||  -> equal(restrict(u,v,w),successor_relation) member(regular(restrict(u,v,w)),cross_product(v,w))*.
% 299.82/300.43  229733[15:Res:8.1,222241.0] || equal(singleton(ordered_pair(singleton(singleton(successor_relation)),u)),domain_relation)** -> .
% 299.82/300.43  223168[24:Res:222372.0,191095.1] || equal(complement(complement(singleton(ordered_pair(kind_1_ordinals,u)))),omega)** -> .
% 299.82/300.43  223165[24:Res:222372.0,206958.1] || equal(complement(complement(singleton(ordered_pair(kind_1_ordinals,u)))),kind_1_ordinals)** -> .
% 299.82/300.43  222243[10:Res:181213.1,222147.0] || equal(singleton(ordered_pair(successor_relation,u)),singleton(singleton(successor_relation)))** -> .
% 299.82/300.43  206164[10:Res:203330.1,160435.1] inductive(cantor(restrict(u,v,w))) || section(u,w,v)* -> member(successor_relation,w).
% 299.82/300.43  229740[15:Res:8.1,229730.0] || equal(singleton(singleton(singleton(singleton(singleton(successor_relation))))),domain_relation)** -> .
% 299.82/300.43  229730[15:SpL:1005.0,222241.0] || subclass(domain_relation,singleton(singleton(singleton(singleton(singleton(successor_relation))))))* -> .
% 299.82/300.43  222241[15:Res:189485.1,222147.0] || subclass(domain_relation,singleton(ordered_pair(singleton(singleton(successor_relation)),u)))* -> .
% 299.82/300.43  222158[10:SpL:1005.0,222139.0] || subclass(complement(singleton(singleton(singleton(singleton(u))))),successor_relation)* -> .
% 299.82/300.43  29643[0:Res:8.1,1487.1] || equal(u,complement(v))*+ member(w,universal_class)* -> member(w,v)* member(w,u)*.
% 299.82/300.43  221791[20:Res:221522.0,191095.1] || equal(complement(complement(singleton(ordered_pair(universal_class,u)))),omega)** -> .
% 299.82/300.43  221788[10:Res:221522.0,206958.1] || equal(complement(complement(singleton(ordered_pair(universal_class,u)))),kind_1_ordinals)** -> .
% 299.82/300.43  229323[15:Res:8.1,228237.1] || equal(domain_relation,ordinal_numbers) equal(complement(kind_1_ordinals),domain_relation)** -> .
% 299.82/300.43  229319[25:SoR:225424.0,73.1] one_to_one(first(regular(element_relation))) || member(successor_relation,element_relation)* -> .
% 299.82/300.43  143792[0:Res:1481.2,159.0] || subclass(u,omega) -> subclass(u,v) equal(integer_of(not_subclass_element(u,v)),not_subclass_element(u,v))**.
% 299.82/300.43  229291[25:SoR:225423.0,73.1] one_to_one(first(regular(domain_relation))) || member(successor_relation,domain_relation)* -> .
% 299.82/300.43  229288[25:SoR:225422.0,73.1] one_to_one(first(regular(rest_relation))) || member(successor_relation,rest_relation)* -> .
% 299.82/300.43  229069[25:SoR:229059.0,160511.2] single_valued_class(regular(ordinal_numbers)) || equal(regular(ordinal_numbers),successor_relation)** -> .
% 299.82/300.43  229066[15:MRR:229054.0,6.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(ordinal_numbers)),successor_relation)**.
% 299.82/300.43  9368[0:Res:322.1,26.1] || member(not_subclass_element(intersection(u,complement(v)),w),v)* -> subclass(intersection(u,complement(v)),w).
% 299.82/300.43  229065[15:MRR:229053.0,6.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(ordinal_numbers)),successor_relation)**.
% 299.82/300.43  228893[25:SoR:225056.0,73.1] one_to_one(first(regular(element_relation))) ||  -> member(successor_relation,regular(element_relation))*.
% 299.82/300.43  228890[25:SoR:225055.0,73.1] one_to_one(first(regular(domain_relation))) ||  -> member(successor_relation,regular(domain_relation))*.
% 299.82/300.43  228887[25:SoR:225054.0,73.1] one_to_one(first(regular(rest_relation))) ||  -> member(successor_relation,regular(rest_relation))*.
% 299.82/300.43  9482[0:Res:340.1,26.1] || member(not_subclass_element(intersection(complement(u),v),w),u)* -> subclass(intersection(complement(u),v),w).
% 299.82/300.43  228762[15:Res:8.1,222294.1] || equal(complement(rest_relation),domain_relation) subclass(rest_relation,domain_relation)* -> .
% 299.82/300.43  228237[15:Res:8.1,221688.1] || equal(complement(kind_1_ordinals),domain_relation) subclass(domain_relation,ordinal_numbers)* -> .
% 299.82/300.43  225424[25:SpL:224739.1,209662.0] function(first(regular(element_relation))) || member(successor_relation,element_relation)* -> .
% 299.82/300.43  10194[0:Rew:1933.0,10172.0] ||  -> subclass(symmetric_difference(u,inverse(u)),v) member(not_subclass_element(symmetric_difference(u,inverse(u)),v),symmetrization_of(u))*.
% 299.82/300.43  225423[25:SpL:224739.1,201590.0] function(first(regular(domain_relation))) || member(successor_relation,domain_relation)* -> .
% 299.82/300.43  225422[25:SpL:224739.1,200393.0] function(first(regular(rest_relation))) || member(successor_relation,rest_relation)* -> .
% 299.82/300.43  229228[10:Res:229170.0,3.0] || subclass(universal_class,u) -> member(regular(ordinal_numbers),u)*.
% 299.82/300.43  229170[10:Res:6.0,229012.0] ||  -> member(regular(ordinal_numbers),universal_class)*.
% 299.82/300.43  10258[0:Rew:1934.0,10234.0] ||  -> subclass(symmetric_difference(u,singleton(u)),v) member(not_subclass_element(symmetric_difference(u,singleton(u)),v),successor(u))*.
% 299.82/300.43  229064[10:MRR:229055.0,6.0] || equal(rest_of(regular(ordinal_numbers)),successor(regular(ordinal_numbers)))** -> .
% 299.82/300.43  229062[10:MRR:229058.0,6.0] || equal(singleton(regular(ordinal_numbers)),successor_relation)** -> .
% 299.82/300.43  229061[15:MRR:229057.0,6.0] || equal(successor(regular(ordinal_numbers)),successor_relation)** -> .
% 299.82/300.43  160789[10:Rew:160202.0,146000.1] || subclass(u,symmetric_difference(v,w)) -> equal(u,successor_relation) member(regular(u),union(v,w))*.
% 299.82/300.43  229060[15:MRR:229056.0,6.0] ||  -> equal(cantor(regular(ordinal_numbers)),successor_relation)**.
% 299.82/300.43  229067[25:SoR:229059.0,73.1] one_to_one(regular(ordinal_numbers)) ||  -> .
% 299.82/300.43  229059[25:MRR:229052.1,6.0] function(regular(ordinal_numbers)) ||  -> .
% 299.82/300.43  228991[10:MRR:228979.1,184560.0] || subclass(kind_1_ordinals,u) -> member(regular(ordinal_numbers),u)*.
% 299.82/300.43  160788[10:Rew:160202.0,146001.2] || subclass(u,v)*+ subclass(v,w)* -> equal(u,successor_relation) member(regular(u),w)*.
% 299.82/300.43  225056[25:SpR:224739.1,209506.0] function(first(regular(element_relation))) ||  -> member(successor_relation,regular(element_relation))*.
% 299.82/300.43  225055[25:SpR:224739.1,201484.0] function(first(regular(domain_relation))) ||  -> member(successor_relation,regular(domain_relation))*.
% 299.82/300.43  225054[25:SpR:224739.1,200240.0] function(first(regular(rest_relation))) ||  -> member(successor_relation,regular(rest_relation))*.
% 299.82/300.43  224810[25:SoR:224725.0,160511.2] single_valued_class(power_class(successor_relation)) || equal(power_class(successor_relation),successor_relation)** -> .
% 299.82/300.43  161243[10:Rew:160202.0,146049.3] inductive(not_well_ordering(u,v)) || connected(u,v) -> well_ordering(u,v)* member(successor_relation,v).
% 299.82/300.43  223107[24:SpR:222331.0,161194.0] ||  -> equal(intersection(successor(kind_1_ordinals),universal_class),symmetric_difference(complement(kind_1_ordinals),universal_class))**.
% 299.82/300.43  223097[24:SpR:222331.0,183453.0] ||  -> equal(symmetric_difference(symmetric_difference(universal_class,kind_1_ordinals),complement(successor(kind_1_ordinals))),successor_relation)**.
% 299.82/300.43  222295[15:MRR:222271.1,160214.0] || equal(rest_relation,domain_relation) subclass(domain_relation,complement(rest_relation))* -> .
% 299.82/300.43  222294[15:MRR:222270.1,160214.0] || subclass(rest_relation,domain_relation) subclass(domain_relation,complement(rest_relation))* -> .
% 299.82/300.43  161611[10:Rew:160202.0,146169.1] || equal(u,v) -> equal(unordered_pair(v,u),successor_relation) equal(regular(unordered_pair(v,u)),v)**.
% 299.82/300.43  222225[12:SpL:209433.0,222147.0] || member(singleton(first(regular(element_relation))),singleton(regular(element_relation)))* -> .
% 299.82/300.43  222224[10:SpL:201355.0,222147.0] || member(singleton(first(regular(domain_relation))),singleton(regular(domain_relation)))* -> .
% 299.82/300.43  222223[10:SpL:199964.0,222147.0] || member(singleton(first(regular(rest_relation))),singleton(regular(rest_relation)))* -> .
% 299.82/300.43  228473[12:Res:222128.0,3670.1] || equal(complement(complement(singleton(regular(element_relation)))),universal_class)** -> .
% 299.82/300.43  161711[10:Rew:160202.0,146157.1] || subclass(u,v) -> equal(intersection(w,u),successor_relation) member(regular(intersection(w,u)),v)*.
% 299.82/300.43  222128[12:SpR:209433.0,221525.0] ||  -> member(singleton(first(regular(element_relation))),complement(singleton(regular(element_relation))))*.
% 299.82/300.43  228456[10:Res:222127.0,3670.1] || equal(complement(complement(singleton(regular(domain_relation)))),universal_class)** -> .
% 299.82/300.43  222127[10:SpR:201355.0,221525.0] ||  -> member(singleton(first(regular(domain_relation))),complement(singleton(regular(domain_relation))))*.
% 299.82/300.43  228252[10:Res:222126.0,3670.1] || equal(complement(complement(singleton(regular(rest_relation)))),universal_class)** -> .
% 299.82/300.43  161722[10:Rew:160202.0,146161.1] || subclass(u,v) -> equal(intersection(u,w),successor_relation) member(regular(intersection(u,w)),v)*.
% 299.82/300.43  222126[10:SpR:199964.0,221525.0] ||  -> member(singleton(first(regular(rest_relation))),complement(singleton(regular(rest_relation))))*.
% 299.82/300.43  221973[10:Res:181213.1,221891.0] || equal(singleton(singleton(singleton(successor_relation))),singleton(singleton(successor_relation)))** -> .
% 299.82/300.43  221884[10:Res:221523.0,3670.1] || equal(complement(complement(singleton(singleton(singleton(successor_relation))))),universal_class)** -> .
% 299.82/300.43  221688[15:MRR:221683.1,160214.0] || subclass(domain_relation,ordinal_numbers) subclass(domain_relation,complement(kind_1_ordinals))* -> .
% 299.82/300.43  161869[10:Rew:160202.0,146156.2] inductive(domain_of(restrict(u,v,w))) || section(u,w,v)* -> member(successor_relation,w).
% 299.82/300.43  221582[11:Res:221516.0,168534.1] || equal(complement(complement(singleton(singleton(successor_relation)))),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  221581[10:Res:221516.0,163205.1] || equal(complement(complement(singleton(singleton(successor_relation)))),successor(successor_relation))** -> .
% 299.82/300.43  221579[10:Res:221516.0,163207.1] || equal(complement(complement(singleton(singleton(successor_relation)))),singleton(successor_relation))** -> .
% 299.82/300.43  221578[11:Res:221516.0,179992.1] || equal(complement(complement(singleton(singleton(successor_relation)))),inverse(successor_relation))** -> .
% 299.82/300.43  161875[10:Rew:160202.0,146158.0] ||  -> equal(intersection(u,intersection(v,w)),successor_relation) member(regular(intersection(u,intersection(v,w))),w)*.
% 299.82/300.43  227646[10:SpR:195339.0,227524.0] ||  -> equal(intersection(complement(kind_1_ordinals),intersection(u,ordinal_numbers)),successor_relation)**.
% 299.82/300.43  227794[10:Rew:160223.0,227738.0] ||  -> equal(union(kind_1_ordinals,complement(ordinal_numbers)),universal_class)**.
% 299.82/300.43  227655[10:SpR:139600.0,227524.0] ||  -> equal(intersection(complement(kind_1_ordinals),complement(complement(ordinal_numbers))),successor_relation)**.
% 299.82/300.43  227524[10:Obv:227503.0] ||  -> equal(intersection(complement(kind_1_ordinals),intersection(ordinal_numbers,u)),successor_relation)**.
% 299.82/300.43  161874[10:Rew:160202.0,146159.0] ||  -> equal(intersection(u,intersection(v,w)),successor_relation) member(regular(intersection(u,intersection(v,w))),v)*.
% 299.82/300.43  227340[25:SoR:224780.0,73.1] one_to_one(not_subclass_element(u,v)) ||  -> subclass(u,v)*.
% 299.82/300.43  224780[25:MRR:224660.2,3567.0] function(not_subclass_element(u,v)) ||  -> subclass(u,v)*.
% 299.82/300.43  226453[25:SoR:224779.0,73.1] function(u) one_to_one(apply(u,v)) ||  -> .
% 299.82/300.43  224913[25:SpR:224739.1,1004.0] function(u) ||  -> member(successor_relation,ordered_pair(u,v))*.
% 299.82/300.43  161881[10:Rew:160202.0,146162.0] ||  -> equal(intersection(intersection(u,v),w),successor_relation) member(regular(intersection(intersection(u,v),w)),v)*.
% 299.82/300.43  226757[10:SpR:195339.0,226634.0] ||  -> equal(intersection(intersection(u,ordinal_numbers),complement(kind_1_ordinals)),successor_relation)**.
% 299.82/300.43  226899[10:Rew:160223.0,226844.0] ||  -> equal(union(complement(ordinal_numbers),kind_1_ordinals),universal_class)**.
% 299.82/300.43  226766[10:SpR:139600.0,226634.0] ||  -> equal(intersection(complement(complement(ordinal_numbers)),complement(kind_1_ordinals)),successor_relation)**.
% 299.82/300.43  226634[10:Obv:226616.0] ||  -> equal(intersection(intersection(ordinal_numbers,u),complement(kind_1_ordinals)),successor_relation)**.
% 299.82/300.43  161880[10:Rew:160202.0,146163.0] ||  -> equal(intersection(intersection(u,v),w),successor_relation) member(regular(intersection(intersection(u,v),w)),u)*.
% 299.82/300.43  224779[25:MRR:224659.2,3567.0] function(apply(u,v)) function(u) ||  -> .
% 299.82/300.43  226446[25:SoR:224778.0,73.1] one_to_one(rest_of(u)) || member(u,universal_class)* -> .
% 299.82/300.43  226443[25:SoR:224777.0,73.1] one_to_one(sum_class(u)) || member(u,universal_class)* -> .
% 299.82/300.43  226440[25:SoR:224775.0,73.1] one_to_one(power_class(u)) || equal(successor_relation,u)* -> .
% 299.82/300.43  226354[25:Rew:226350.1,30721.2] one_to_one(u) || subclass(range_of(inverse(u)),v) -> maps(inverse(u),universal_class,v)*.
% 299.82/300.43  226437[25:SoR:224774.0,73.1] one_to_one(power_class(u)) || member(u,universal_class)* -> .
% 299.82/300.43  226351[25:SoR:224638.0,73.1] one_to_one(inverse(u)) ||  -> equal(range_of(u),universal_class)**.
% 299.82/300.43  224778[25:MRR:224658.2,3567.0] function(rest_of(u)) || member(u,universal_class)* -> .
% 299.82/300.43  224777[25:MRR:224657.2,3567.0] function(sum_class(u)) || member(u,universal_class)* -> .
% 299.82/300.43  226366[25:Rew:226351.1,226357.2] one_to_one(inverse(u)) || subclass(universal_class,v) -> maps(inverse(u),universal_class,v)*.
% 299.82/300.43  224775[25:MRR:224643.2,3567.0] function(power_class(u)) || equal(successor_relation,u)* -> .
% 299.82/300.43  224774[25:MRR:224642.2,3567.0] function(power_class(u)) || member(u,universal_class)* -> .
% 299.82/300.43  226350[25:SoR:224638.0,74.1] one_to_one(u) ||  -> equal(range_of(u),universal_class)**.
% 299.82/300.43  224638[25:SpR:224236.1,203285.0] function(inverse(u)) ||  -> equal(range_of(u),universal_class)**.
% 299.82/300.43  9128[0:Res:1479.2,595.0] || member(u,universal_class) subclass(universal_class,restrict(v,w,x))*+ -> member(sum_class(u),v)*.
% 299.82/300.43  226335[25:SoR:224287.0,73.1] one_to_one(complement(cross_product(singleton(singleton(u)),universal_class))) ||  -> .
% 299.82/300.43  224287[25:Res:222777.1,194074.0] function(complement(cross_product(singleton(singleton(u)),universal_class))) ||  -> .
% 299.82/300.43  223226[24:Res:168384.1,222450.0] || equal(singleton(ordered_pair(kind_1_ordinals,u)),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  223225[24:Res:163169.1,222450.0] || equal(singleton(ordered_pair(kind_1_ordinals,u)),successor(successor_relation))** -> .
% 299.82/300.43  223224[24:Res:163171.1,222450.0] || equal(singleton(ordered_pair(kind_1_ordinals,u)),singleton(successor_relation))** -> .
% 299.82/300.43  223223[24:Res:179843.1,222450.0] || equal(singleton(ordered_pair(kind_1_ordinals,u)),inverse(successor_relation))** -> .
% 299.82/300.43  222627[24:Res:222332.0,168534.1] || equal(complement(ordered_pair(kind_1_ordinals,u)),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  222626[24:Res:222332.0,163205.1] || equal(complement(ordered_pair(kind_1_ordinals,u)),successor(successor_relation))** -> .
% 299.82/300.43  203658[10:Rew:203192.0,160584.1] || member(u,universal_class) -> member(u,cantor(v))* equal(apply(v,u),sum_class(range_of(successor_relation))).
% 299.82/300.43  222624[24:Res:222332.0,163207.1] || equal(complement(ordered_pair(kind_1_ordinals,u)),singleton(successor_relation))** -> .
% 299.82/300.43  222623[24:Res:222332.0,179992.1] || equal(complement(ordered_pair(kind_1_ordinals,u)),inverse(successor_relation))** -> .
% 299.82/300.43  226084[25:SoR:224776.0,73.1] one_to_one(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))) ||  -> .
% 299.82/300.43  225989[25:SoR:224290.0,73.1] one_to_one(complement(cross_product(singleton(regular(element_relation)),universal_class))) ||  -> .
% 299.82/300.43  189386[15:Rew:189339.1,28095.2] || member(u,universal_class) subclass(domain_relation,intersection(v,w))*+ -> member(ordered_pair(u,successor_relation),w)*.
% 299.82/300.43  225986[25:SoR:224289.0,73.1] one_to_one(complement(cross_product(singleton(regular(domain_relation)),universal_class))) ||  -> .
% 299.82/300.43  225983[25:SoR:224288.0,73.1] one_to_one(complement(cross_product(singleton(regular(rest_relation)),universal_class))) ||  -> .
% 299.82/300.43  225980[25:SoR:224285.0,73.1] one_to_one(complement(cross_product(singleton(power_class(successor_relation)),universal_class))) ||  -> .
% 299.82/300.43  224776[25:MRR:224654.1,3567.0] function(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))) ||  -> .
% 299.82/300.43  189381[15:Rew:189339.1,28094.2] || member(u,universal_class) subclass(domain_relation,intersection(v,w))*+ -> member(ordered_pair(u,successor_relation),v)*.
% 299.82/300.43  224290[25:Res:222777.1,209469.0] function(complement(cross_product(singleton(regular(element_relation)),universal_class))) ||  -> .
% 299.82/300.43  224289[25:Res:222777.1,201396.0] function(complement(cross_product(singleton(regular(domain_relation)),universal_class))) ||  -> .
% 299.82/300.43  224288[25:Res:222777.1,200006.0] function(complement(cross_product(singleton(regular(rest_relation)),universal_class))) ||  -> .
% 299.82/300.43  224285[25:Res:222777.1,194078.0] function(complement(cross_product(singleton(power_class(successor_relation)),universal_class))) ||  -> .
% 299.82/300.43  161867[10:Rew:160202.0,146155.2] || well_ordering(u,universal_class) member(least(u,complement(v)),v)* -> equal(complement(v),successor_relation).
% 299.82/300.43  223104[24:SpR:222331.0,161203.0] ||  -> equal(union(symmetric_difference(universal_class,kind_1_ordinals),successor(kind_1_ordinals)),universal_class)**.
% 299.82/300.43  223103[24:SpR:222331.0,161204.0] ||  -> equal(union(successor(kind_1_ordinals),symmetric_difference(universal_class,kind_1_ordinals)),universal_class)**.
% 299.82/300.43  223102[24:SpR:222331.0,161205.0] ||  -> equal(symmetric_difference(symmetric_difference(universal_class,kind_1_ordinals),successor(kind_1_ordinals)),universal_class)**.
% 299.82/300.43  223101[24:SpR:222331.0,161206.0] ||  -> equal(symmetric_difference(successor(kind_1_ordinals),symmetric_difference(universal_class,kind_1_ordinals)),universal_class)**.
% 299.82/300.43  3627[0:SpL:1005.0,98.0] || member(ordered_pair(u,singleton(singleton(singleton(v)))),composition_function)* -> equal(compose(u,singleton(v)),v).
% 299.82/300.43  223100[24:SpR:222331.0,162964.0] ||  -> equal(intersection(symmetric_difference(universal_class,kind_1_ordinals),successor(kind_1_ordinals)),successor_relation)**.
% 299.82/300.43  223099[24:SpR:222331.0,162965.0] ||  -> equal(intersection(successor(kind_1_ordinals),symmetric_difference(universal_class,kind_1_ordinals)),successor_relation)**.
% 299.82/300.43  222440[24:SpL:222326.0,193819.0] || member(kind_1_ordinals,cantor(complement(cross_product(successor_relation,universal_class))))* -> .
% 299.82/300.43  225544[25:Res:160274.1,225443.1] function(u) ||  -> equal(integer_of(u),successor_relation)**.
% 299.82/300.43  28281[0:Res:1495.2,2151.0] || member(u,universal_class) subclass(rest_relation,singleton(v))*+ -> equal(ordered_pair(u,rest_of(u)),v)*.
% 299.82/300.43  225500[25:SoR:224740.0,73.1] one_to_one(regular(u)) ||  -> equal(u,successor_relation)*.
% 299.82/300.43  225443[25:MRR:224930.2,160227.0] function(u) || member(u,universal_class)* -> .
% 299.82/300.43  224905[25:SoR:224486.1,73.1] function(u) one_to_one(cantor(u)) ||  -> .
% 299.82/300.43  224740[25:MRR:224646.2,3567.0] function(regular(u)) ||  -> equal(u,successor_relation)*.
% 299.82/300.43  28304[0:Res:1495.2,95.0] || member(u,universal_class) subclass(rest_relation,compose_class(v))*+ -> equal(compose(v,u),rest_of(u))**.
% 299.82/300.43  224739[25:MRR:224626.2,3567.0] function(u) ||  -> equal(singleton(u),successor_relation)**.
% 299.82/300.43  224486[25:MRR:224485.2,153242.0] function(u) function(cantor(u)) ||  -> .
% 299.82/300.43  224899[25:SoR:224782.0,73.1] one_to_one(complement(cross_product(singleton(omega),universal_class))) ||  -> .
% 299.82/300.43  224896[25:SoR:224743.0,73.1] one_to_one(regular(complement(complement(symmetrization_of(successor_relation))))) ||  -> .
% 299.82/300.43  224312[25:Rew:224236.1,204959.2] function(restrict(u,v,universal_class)) || subclass(image(u,v),cantor(cantor(w))) equal(cantor(cantor(x)),universal_class) -> compatible(restrict(u,v,universal_class),x,w)*.
% 299.82/300.43  224782[25:Obv:224703.1] function(complement(cross_product(singleton(omega),universal_class))) ||  -> .
% 299.82/300.43  224743[25:MRR:224650.1,3567.0] function(regular(complement(complement(symmetrization_of(successor_relation))))) ||  -> .
% 299.82/300.43  224861[25:SoR:224738.0,73.1] one_to_one(regular(complement(power_class(successor_relation)))) ||  -> .
% 299.82/300.43  224858[25:SoR:224737.0,73.1] one_to_one(regular(complement(power_class(universal_class)))) ||  -> .
% 299.82/300.43  224321[25:Rew:224236.1,204924.2] function(u) || subclass(range_of(u),cantor(segment(v,w,x))) equal(cantor(cantor(y)),universal_class) -> compatible(u,y,restrict(v,w,singleton(x)))*.
% 299.82/300.43  224855[25:SoR:224736.0,73.1] one_to_one(regular(complement(successor(successor_relation)))) ||  -> .
% 299.82/300.43  224738[25:MRR:224649.1,3567.0] function(regular(complement(power_class(successor_relation)))) ||  -> .
% 299.82/300.43  224737[25:MRR:224648.1,3567.0] function(regular(complement(power_class(universal_class)))) ||  -> .
% 299.82/300.43  224736[25:MRR:224647.1,3567.0] function(regular(complement(successor(successor_relation)))) ||  -> .
% 299.82/300.43  224316[25:Rew:224236.1,204842.2] function(u) || subclass(range_of(u),cantor(sum_class(v))) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,restrict(element_relation,universal_class,v))*.
% 299.82/300.43  224847[25:SoR:224735.0,73.1] one_to_one(unordered_pair(u,v)) ||  -> .
% 299.82/300.43  224844[25:SoR:224734.0,73.1] one_to_one(ordered_pair(u,v)) ||  -> .
% 299.82/300.43  224735[25:MRR:224656.1,3567.0] function(unordered_pair(u,v)) ||  -> .
% 299.82/300.43  224734[25:MRR:224655.1,3567.0] function(ordered_pair(u,v)) ||  -> .
% 299.82/300.43  224317[25:Rew:224236.1,204820.2] function(u) || subclass(range_of(u),range_of(v)) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,flip(cross_product(v,universal_class)))*.
% 299.82/300.43  224836[25:SoR:224733.0,73.1] one_to_one(regular(symmetrization_of(successor_relation))) ||  -> .
% 299.82/300.43  224733[25:MRR:224645.1,3567.0] function(regular(symmetrization_of(successor_relation))) ||  -> .
% 299.82/300.43  224821[25:SoR:224728.0,73.1] one_to_one(regular(element_relation)) ||  -> .
% 299.82/300.43  224818[25:SoR:224727.0,73.1] one_to_one(regular(domain_relation)) ||  -> .
% 299.82/300.43  224318[25:Rew:224236.1,204803.2] function(u) || subclass(range_of(u),cantor(range_of(v)))*+ equal(cantor(cantor(w)),universal_class) -> compatible(u,w,inverse(v))*.
% 299.82/300.43  224811[25:SoR:224726.0,73.1] one_to_one(regular(rest_relation)) ||  -> .
% 299.82/300.43  224808[25:SoR:224725.0,73.1] one_to_one(power_class(successor_relation)) ||  -> .
% 299.82/300.43  224728[25:MRR:224653.1,3567.0] function(regular(element_relation)) ||  -> .
% 299.82/300.43  224727[25:MRR:224652.1,3567.0] function(regular(domain_relation)) ||  -> .
% 299.82/300.43  224319[25:Rew:224236.1,204780.2] function(u) || equal(cantor(cantor(v)),range_of(u)) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,v)*.
% 299.82/300.43  224726[25:MRR:224651.1,3567.0] function(regular(rest_relation)) ||  -> .
% 299.82/300.43  224725[25:MRR:224641.1,3567.0] function(power_class(successor_relation)) ||  -> .
% 299.82/300.43  224753[25:SSi:224752.0,80.1] operation(u) ||  -> .
% 299.82/300.43  224805[25:SoR:224724.0,73.1] one_to_one(omega) ||  -> .
% 299.82/300.43  224754[25:MRR:88.1,224753.0] || homomorphism(u,v,w)* -> .
% 299.82/300.43  224724[25:MRR:224640.1,3567.0] function(omega) ||  -> .
% 299.82/300.43  224236[25:Res:222777.1,1312.0] function(u) ||  -> equal(cantor(u),universal_class)**.
% 299.82/300.43  224320[25:Rew:224236.1,204781.2] function(u) || subclass(range_of(u),cantor(cantor(v)))*+ equal(cantor(cantor(w)),universal_class) -> compatible(u,w,v)*.
% 299.82/300.43  224525[25:SoR:224286.0,73.1] one_to_one(complement(cross_product(singleton(successor_relation),universal_class))) ||  -> .
% 299.82/300.43  224314[25:Rew:224236.1,203300.2] function(u) || subclass(range_of(u),v) -> maps(u,universal_class,v)*.
% 299.82/300.43  224286[25:Res:222777.1,199779.0] function(complement(cross_product(singleton(successor_relation),universal_class))) ||  -> .
% 299.82/300.43  223252[24:Rew:183965.0,223243.0] ||  -> equal(ordinal_add(u,kind_1_ordinals),ordinal_add(u,universal_class))**.
% 299.82/300.43  34427[0:MRR:28532.0,34189.1] ||  -> member(not_subclass_element(u,image(element_relation,complement(v))),power_class(v))* subclass(u,image(element_relation,complement(v))).
% 299.82/300.43  222750[25:MRR:160230.2,222730.0] single_valued_class(singleton(u)) ||  -> member(u,universal_class)*.
% 299.82/300.43  222479[24:Rew:181083.0,222380.0] ||  -> equal(ordered_pair(u,kind_1_ordinals),ordered_pair(u,universal_class))**.
% 299.82/300.43  222476[24:Rew:181082.0,222378.0] ||  -> equal(apply(u,kind_1_ordinals),apply(u,universal_class))**.
% 299.82/300.43  223221[24:Res:191074.1,222450.0] || equal(singleton(ordered_pair(kind_1_ordinals,u)),omega)** -> .
% 299.82/300.43  223220[24:Res:206947.1,222450.0] || equal(singleton(ordered_pair(kind_1_ordinals,u)),kind_1_ordinals)** -> .
% 299.82/300.43  222628[24:Res:222332.0,191095.1] || equal(complement(ordered_pair(kind_1_ordinals,u)),omega)** -> .
% 299.82/300.43  222625[24:Res:222332.0,206958.1] || equal(complement(ordered_pair(kind_1_ordinals,u)),kind_1_ordinals)** -> .
% 299.82/300.43  223228[24:Res:160271.1,222450.0] inductive(singleton(ordered_pair(kind_1_ordinals,u))) ||  -> .
% 299.82/300.43  222450[24:SpL:222326.0,222147.0] || member(successor_relation,singleton(ordered_pair(kind_1_ordinals,u)))* -> .
% 299.82/300.43  222372[24:SpR:222326.0,221525.0] ||  -> member(successor_relation,complement(singleton(ordered_pair(kind_1_ordinals,u))))*.
% 299.82/300.43  223096[24:SpR:222331.0,160369.0] ||  -> subclass(complement(successor(kind_1_ordinals)),symmetric_difference(universal_class,kind_1_ordinals))*.
% 299.82/300.43  222474[24:Rew:160223.0,222335.0] ||  -> subclass(symmetric_difference(complement(kind_1_ordinals),universal_class),successor(kind_1_ordinals))*.
% 299.82/300.43  222331[24:SpR:222326.0,45.0] ||  -> equal(union(kind_1_ordinals,successor_relation),successor(kind_1_ordinals))**.
% 299.82/300.43  222645[15:Res:8.1,222595.0] || equal(rest_of(u),domain_relation)** -> .
% 299.82/300.43  223069[25:SoR:222758.0,73.1] one_to_one(singleton(u)) ||  -> .
% 299.82/300.43  222758[25:MRR:222751.1,222757.1] function(singleton(u)) ||  -> .
% 299.82/300.43  222872[25:SoR:222730.0,73.1] one_to_one(successor_relation) ||  -> .
% 299.82/300.43  222746[25:MRR:160234.1,222730.0] one_to_one(subset_relation) ||  -> .
% 299.82/300.43  222745[25:MRR:160235.1,222730.0] function(subset_relation) ||  -> .
% 299.82/300.43  222744[25:MRR:160236.1,222730.0] single_valued_class(subset_relation) ||  -> .
% 299.82/300.43  222743[25:MRR:160241.1,222730.0] one_to_one(singleton_relation) ||  -> .
% 299.82/300.43  222742[25:MRR:160242.1,222730.0] function(singleton_relation) ||  -> .
% 299.82/300.43  222741[25:MRR:160244.1,222730.0] single_valued_class(singleton_relation) ||  -> .
% 299.82/300.43  222740[25:MRR:164254.1,222730.0] function(identity_relation) ||  -> .
% 299.82/300.43  222739[25:MRR:164401.1,222730.0] one_to_one(identity_relation) ||  -> .
% 299.82/300.43  222738[25:MRR:183962.1,222730.0] single_valued_class(union_of_range_map) ||  -> .
% 299.82/300.43  222737[25:MRR:184023.1,222730.0] function(union_of_range_map) ||  -> .
% 299.82/300.43  222736[25:MRR:184024.1,222730.0] one_to_one(union_of_range_map) ||  -> .
% 299.82/300.43  222734[25:MRR:6330.1,222730.0] single_valued_class(successor_relation) ||  -> .
% 299.82/300.43  222747[25:MRR:160239.1,222730.0] inductive(recursion_equation_functions(u)) ||  -> .
% 299.82/300.43  222733[25:MRR:160243.1,222730.0] single_valued_class(identity_relation) ||  -> .
% 299.82/300.43  222730[25:MRR:165323.1,222729.1] function(successor_relation) ||  -> .
% 299.82/300.43  222595[15:MRR:203307.1,222593.1] || subclass(domain_relation,rest_of(u))* -> .
% 299.82/300.43  222332[24:SpR:222326.0,1004.0] ||  -> member(successor_relation,ordered_pair(kind_1_ordinals,u))*.
% 299.82/300.43  222603[24:Res:160274.1,222472.0] ||  -> equal(integer_of(kind_1_ordinals),successor_relation)**.
% 299.82/300.43  222472[24:MRR:222348.1,160227.0] || member(kind_1_ordinals,universal_class)* -> .
% 299.82/300.43  222326[24:Spt:221477.0] ||  -> equal(singleton(kind_1_ordinals),successor_relation)**.
% 299.82/300.43  222324[22:Res:8.1,222242.0] || equal(singleton(ordered_pair(successor_relation,u)),kind_1_ordinals)** -> .
% 299.82/300.43  222242[22:Res:218867.1,222147.0] || subclass(kind_1_ordinals,singleton(ordered_pair(successor_relation,u)))* -> .
% 299.82/300.43  222292[15:MRR:222269.0,160214.0] || subclass(domain_relation,complement(domain_relation))* -> .
% 299.82/300.43  189380[15:Rew:189339.1,28091.2] || member(u,universal_class) subclass(domain_relation,complement(v)) member(ordered_pair(u,successor_relation),v)* -> .
% 299.82/300.43  222147[10:Res:221525.0,26.1] || member(singleton(u),singleton(ordered_pair(u,v)))* -> .
% 299.82/300.43  222155[12:SpL:209433.0,222139.0] || subclass(complement(singleton(regular(element_relation))),successor_relation)* -> .
% 299.82/300.43  222154[10:SpL:201355.0,222139.0] || subclass(complement(singleton(regular(domain_relation))),successor_relation)* -> .
% 299.82/300.43  222153[10:SpL:199964.0,222139.0] || subclass(complement(singleton(regular(rest_relation))),successor_relation)* -> .
% 299.82/300.43  155810[3:Res:322.1,141576.1] || member(not_subclass_element(intersection(u,complement(kind_1_ordinals)),v),ordinal_numbers)* -> subclass(intersection(u,complement(kind_1_ordinals)),v).
% 299.82/300.43  222139[10:Res:221525.0,185065.1] || subclass(complement(singleton(ordered_pair(u,v))),successor_relation)* -> .
% 299.82/300.43  222149[10:Res:221525.0,211446.0] || well_ordering(universal_class,complement(singleton(ordered_pair(successor_relation,u))))* -> .
% 299.82/300.43  221525[10:MRR:221479.0,185218.0] ||  -> member(singleton(u),complement(singleton(ordered_pair(u,v))))*.
% 299.82/300.43  221846[11:Res:168384.1,221783.0] || equal(singleton(ordered_pair(universal_class,u)),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  155808[3:Res:340.1,141576.1] || member(not_subclass_element(intersection(complement(kind_1_ordinals),u),v),ordinal_numbers)* -> subclass(intersection(complement(kind_1_ordinals),u),v).
% 299.82/300.43  221845[10:Res:163169.1,221783.0] || equal(singleton(ordered_pair(universal_class,u)),successor(successor_relation))** -> .
% 299.82/300.43  221844[10:Res:163171.1,221783.0] || equal(singleton(ordered_pair(universal_class,u)),singleton(successor_relation))** -> .
% 299.82/300.43  221843[11:Res:179843.1,221783.0] || equal(singleton(ordered_pair(universal_class,u)),inverse(successor_relation))** -> .
% 299.82/300.43  221976[22:Res:8.1,221972.0] || equal(singleton(singleton(singleton(successor_relation))),kind_1_ordinals)** -> .
% 299.82/300.43  986[0:SpL:208.0,26.1] || member(u,image(element_relation,power_class(v))) member(u,power_class(image(element_relation,complement(v))))* -> .
% 299.82/300.43  221972[22:Res:218867.1,221891.0] || subclass(kind_1_ordinals,singleton(singleton(singleton(successor_relation))))* -> .
% 299.82/300.43  221891[10:Res:221523.0,26.1] || member(singleton(successor_relation),singleton(singleton(singleton(successor_relation))))* -> .
% 299.82/300.43  221883[10:Res:221523.0,185065.1] || subclass(complement(singleton(singleton(singleton(successor_relation)))),successor_relation)* -> .
% 299.82/300.43  221584[10:Res:221516.0,160258.1] || equal(complement(complement(singleton(singleton(successor_relation)))),universal_class)** -> .
% 299.82/300.43  33515[0:MRR:33507.1,191.0] || member(u,universal_class) member(singleton(u),u)*+ -> member(singleton(singleton(singleton(u))),element_relation)*.
% 299.82/300.43  221583[20:Res:221516.0,191095.1] || equal(complement(complement(singleton(singleton(successor_relation)))),omega)** -> .
% 299.82/300.43  221580[10:Res:221516.0,206958.1] || equal(complement(complement(singleton(singleton(successor_relation)))),kind_1_ordinals)** -> .
% 299.82/300.43  221546[20:Res:221515.0,168534.1] || equal(complement(complement(singleton(omega))),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  221545[20:Res:221515.0,163205.1] || equal(complement(complement(singleton(omega))),successor(successor_relation))** -> .
% 299.82/300.43  163147[10:MRR:5892.2,160227.0] || equal(successor(singleton(u)),u) member(singleton(singleton(singleton(u))),cross_product(universal_class,universal_class))* -> .
% 299.82/300.43  221543[20:Res:221515.0,163207.1] || equal(complement(complement(singleton(omega))),singleton(successor_relation))** -> .
% 299.82/300.43  221542[20:Res:221515.0,179992.1] || equal(complement(complement(singleton(omega))),inverse(successor_relation))** -> .
% 299.82/300.43  221524[10:MRR:221463.1,185111.0] || well_ordering(universal_class,complement(singleton(singleton(singleton(successor_relation)))))* -> .
% 299.82/300.43  221523[10:MRR:221462.0,185111.0] ||  -> member(singleton(successor_relation),complement(singleton(singleton(singleton(successor_relation)))))*.
% 299.82/300.43  160703[10:Rew:160202.0,158101.2] || subclass(u,complement(compose(element_relation,universal_class)))* member(regular(u),element_relation) -> equal(u,successor_relation).
% 299.82/300.43  221841[20:Res:191074.1,221783.0] || equal(singleton(ordered_pair(universal_class,u)),omega)** -> .
% 299.82/300.43  221840[10:Res:206947.1,221783.0] || equal(singleton(ordered_pair(universal_class,u)),kind_1_ordinals)** -> .
% 299.82/300.43  221848[10:Res:160271.1,221783.0] inductive(singleton(ordered_pair(universal_class,u))) ||  -> .
% 299.82/300.43  221783[10:Res:221522.0,26.1] || member(successor_relation,singleton(ordered_pair(universal_class,u)))* -> .
% 299.82/300.43  161795[10:Rew:160202.0,146154.1] || member(regular(image(element_relation,complement(u))),power_class(u))* -> equal(image(element_relation,complement(u)),successor_relation).
% 299.82/300.43  221522[10:MRR:221486.0,185218.0] ||  -> member(successor_relation,complement(singleton(ordered_pair(universal_class,u))))*.
% 299.82/300.43  221599[11:Res:168384.1,221575.0] || equal(singleton(singleton(successor_relation)),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  221598[10:Res:163169.1,221575.0] || equal(singleton(singleton(successor_relation)),successor(successor_relation))** -> .
% 299.82/300.43  221597[10:Res:163171.1,221575.0] || equal(singleton(singleton(successor_relation)),singleton(successor_relation))** -> .
% 299.82/300.43  161949[10:Rew:160202.0,148514.0] ||  -> equal(intersection(omega,u),successor_relation) equal(integer_of(regular(intersection(omega,u))),regular(intersection(omega,u)))**.
% 299.82/300.43  221596[11:Res:179843.1,221575.0] || equal(singleton(singleton(successor_relation)),inverse(successor_relation))** -> .
% 299.82/300.43  221565[6:Obv:221562.0] ||  -> subclass(complement(compose(element_relation,universal_class)),complement(element_relation))*.
% 299.82/300.43  221548[20:Res:221515.0,160258.1] || equal(complement(complement(singleton(omega))),universal_class)** -> .
% 299.82/300.43  221547[20:Res:221515.0,191095.1] || equal(complement(complement(singleton(omega))),omega)** -> .
% 299.82/300.43  161951[10:Rew:160202.0,148516.0] ||  -> equal(intersection(u,omega),successor_relation) equal(integer_of(regular(intersection(u,omega))),regular(intersection(u,omega)))**.
% 299.82/300.43  221544[20:Res:221515.0,206958.1] || equal(complement(complement(singleton(omega))),kind_1_ordinals)** -> .
% 299.82/300.43  221520[12:MRR:221473.1,209383.0] || well_ordering(universal_class,complement(singleton(regular(element_relation))))* -> .
% 299.82/300.43  221519[10:MRR:221472.1,201238.0] || well_ordering(universal_class,complement(singleton(regular(domain_relation))))* -> .
% 299.82/300.43  221518[10:MRR:221471.1,199854.0] || well_ordering(universal_class,complement(singleton(regular(rest_relation))))* -> .
% 299.82/300.43  189406[15:Rew:189339.1,184835.2] || member(u,universal_class) subclass(domain_relation,complement(kind_1_ordinals)) member(ordered_pair(u,successor_relation),ordinal_numbers)* -> .
% 299.82/300.43  221517[10:MRR:221460.1,185111.0] || well_ordering(universal_class,complement(singleton(singleton(successor_relation))))* -> .
% 299.82/300.43  221594[20:Res:191074.1,221575.0] || equal(singleton(singleton(successor_relation)),omega)** -> .
% 299.82/300.43  221593[10:Res:206947.1,221575.0] || equal(singleton(singleton(successor_relation)),kind_1_ordinals)** -> .
% 299.82/300.43  221601[10:Res:160271.1,221575.0] inductive(singleton(singleton(successor_relation))) ||  -> .
% 299.82/300.43  185698[10:Res:136.1,161945.1] inductive(u) || member(u,ordinal_numbers)*+ -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.43  221575[10:Res:221516.0,26.1] || member(successor_relation,singleton(singleton(successor_relation)))* -> .
% 299.82/300.43  221557[20:Res:168384.1,221539.0] || equal(symmetrization_of(successor_relation),singleton(omega))** -> .
% 299.82/300.43  221556[20:Res:163169.1,221539.0] || equal(successor(successor_relation),singleton(omega))** -> .
% 299.82/300.43  221555[20:Res:163171.1,221539.0] || equal(singleton(omega),singleton(successor_relation))** -> .
% 299.82/300.43  162951[10:Rew:160202.0,159509.2] || well_ordering(u,universal_class) member(least(u,complement(kind_1_ordinals)),ordinal_numbers)* -> equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.43  221554[20:Res:179843.1,221539.0] || equal(inverse(successor_relation),singleton(omega))** -> .
% 299.82/300.43  221516[10:MRR:221461.0,185111.0] ||  -> member(successor_relation,complement(singleton(singleton(successor_relation))))*.
% 299.82/300.43  221552[20:Res:191074.1,221539.0] || equal(singleton(omega),omega)** -> .
% 299.82/300.43  221551[20:Res:206947.1,221539.0] || equal(singleton(omega),kind_1_ordinals)** -> .
% 299.82/300.43  157891[6:Res:4.1,148657.1] || member(not_subclass_element(complement(compose(element_relation,universal_class)),u),element_relation)* -> subclass(complement(compose(element_relation,universal_class)),u).
% 299.82/300.43  221559[20:Res:160271.1,221539.0] inductive(singleton(omega)) ||  -> .
% 299.82/300.43  221539[20:Res:221515.0,26.1] || member(successor_relation,singleton(omega))* -> .
% 299.82/300.43  221515[20:MRR:221451.0,185582.0] ||  -> member(successor_relation,complement(singleton(omega)))*.
% 299.82/300.43  218373[10:Obv:218349.0] ||  -> subclass(u,complement(singleton(u)))* equal(singleton(u),successor_relation).
% 299.82/300.43  149509[6:Rew:149379.0,56493.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),cantor(u))* subclass(universal_class,intersection(y__dfg,ordinal_numbers)) -> .
% 299.82/300.43  221341[10:Res:185430.1,221319.0] || equal(complement(regular(unordered_pair(singleton(u),v))),successor_relation)** -> .
% 299.82/300.43  221340[10:Res:8.1,221319.0] || equal(regular(unordered_pair(singleton(u),v)),universal_class)** -> .
% 299.82/300.43  221350[10:Res:185430.1,221330.0] || equal(complement(regular(unordered_pair(successor_relation,u))),successor_relation)** -> .
% 299.82/300.43  221349[10:Res:8.1,221330.0] || equal(regular(unordered_pair(successor_relation,u)),universal_class)** -> .
% 299.82/300.43  190697[19:Spt:163621.0,163621.1,163621.3] inductive(u) || well_ordering(v,u)*+ -> member(least(v,range_of(successor_relation)),range_of(successor_relation))*.
% 299.82/300.43  221330[10:SpL:181056.0,221319.0] || subclass(universal_class,regular(unordered_pair(successor_relation,u)))* -> .
% 299.82/300.43  221319[10:SpL:14.0,217590.0] || subclass(universal_class,regular(unordered_pair(singleton(u),v)))* -> .
% 299.82/300.43  217590[10:MRR:217554.0,217554.2,13.0,188711.0] || subclass(universal_class,regular(unordered_pair(unordered_pair(u,v),w)))* -> .
% 299.82/300.43  220898[10:Res:185430.1,219813.0] || equal(complement(regular(singleton(ordered_pair(u,v)))),successor_relation)** -> .
% 299.82/300.43  163341[10:Rew:160202.0,160623.0] ||  -> equal(cross_product(u,universal_class),successor_relation) equal(image(regular(cross_product(u,universal_class)),u),range_of(successor_relation))**.
% 299.82/300.43  163369[10:Rew:160305.0,162787.0] ||  -> equal(power_class(intersection(complement(singleton(successor_relation)),complement(range_of(successor_relation)))),complement(image(element_relation,kind_1_ordinals)))**.
% 299.82/300.43  193730[10:SpR:161319.0,44.0] ||  -> equal(image(complement(cross_product(u,universal_class)),u),range_of(successor_relation))**.
% 299.82/300.43  219819[10:Res:185430.1,219389.0] || equal(complement(regular(singleton(unordered_pair(u,v)))),successor_relation)** -> .
% 299.82/300.43  219547[10:Res:185430.1,219385.0] || equal(complement(regular(unordered_pair(u,singleton(v)))),successor_relation)** -> .
% 299.82/300.43  166982[10:MRR:166965.0,160214.0] || equal(unordered_pair(successor_relation,u),range_of(successor_relation)) -> inductive(unordered_pair(successor_relation,u))*.
% 299.82/300.43  221065[23:Res:8.1,220407.0] || equal(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),complement(kind_1_ordinals))** -> .
% 299.82/300.43  220883[23:Res:220417.0,193015.0] ||  -> equal(cantor(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),successor_relation)**.
% 299.82/300.43  220407[23:MRR:196235.1,220405.0] || subclass(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),complement(kind_1_ordinals))* -> .
% 299.82/300.43  166981[10:MRR:166964.0,160214.0] || equal(unordered_pair(u,successor_relation),range_of(successor_relation)) -> inductive(unordered_pair(u,successor_relation))*.
% 299.82/300.43  195625[10:Res:163149.1,195436.0] inductive(complement(range_of(successor_relation))) ||  -> equal(range_of(successor_relation),successor_relation)**.
% 299.82/300.43  163294[10:Rew:160305.0,162806.0] || member(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(u,kind_1_ordinals).
% 299.82/300.43  201466[20:MRR:201435.2,166685.1] one_to_one(range_of(successor_relation)) || equal(range_of(successor_relation),omega)** -> .
% 299.82/300.43  163219[10:Rew:160305.0,162780.0] ||  -> subclass(symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation))),kind_1_ordinals)*.
% 299.82/300.43  168373[11:Res:168372.0,163256.1] || equal(range_of(successor_relation),symmetrization_of(successor_relation)) -> inductive(symmetrization_of(successor_relation))*.
% 299.82/300.43  3834[0:Res:8.1,1322.1] inductive(u) || equal(omega,u)* -> equal(u,omega).
% 299.82/300.43  168390[11:Res:168387.0,163256.1] || equal(range_of(successor_relation),inverse(successor_relation)) -> inductive(inverse(successor_relation))*.
% 299.82/300.43  166971[10:Res:160414.0,163256.1] || equal(range_of(successor_relation),singleton(successor_relation)) -> inductive(singleton(successor_relation))*.
% 299.82/300.43  207120[10:MRR:207112.2,166685.1] one_to_one(range_of(successor_relation)) || equal(range_of(successor_relation),kind_1_ordinals)** -> .
% 299.82/300.43  166685[10:SoR:164882.0,73.1] one_to_one(range_of(successor_relation)) || member(successor_relation,cross_product(universal_class,universal_class))* -> .
% 299.82/300.43  218483[10:Res:163149.1,217932.0] inductive(complement(kind_1_ordinals)) ||  -> subclass(range_of(successor_relation),complement(ordinal_numbers))*.
% 299.82/300.43  207118[10:SoR:164295.0,207001.1] || equal(range_of(successor_relation),kind_1_ordinals)** -> equal(range_of(successor_relation),omega).
% 299.82/300.43  166988[10:SoR:164295.0,166950.1] || equal(range_of(successor_relation),universal_class)** -> equal(range_of(successor_relation),omega).
% 299.82/300.43  185973[10:Res:185646.1,164877.0] || equal(complement(range_of(successor_relation)),successor_relation)** -> inductive(range_of(successor_relation)).
% 299.82/300.43  220897[10:Res:8.1,219813.0] || equal(regular(singleton(ordered_pair(u,v))),universal_class)** -> .
% 299.82/300.43  219818[10:Res:8.1,219389.0] || equal(regular(singleton(unordered_pair(u,v))),universal_class)** -> .
% 299.82/300.43  220910[12:Res:185430.1,220890.0] || equal(complement(regular(singleton(regular(element_relation)))),successor_relation)** -> .
% 299.82/300.43  163153[10:Rew:160305.0,3842.1] inductive(image(successor_relation,omega)) ||  -> equal(range_of(successor_relation),omega)**.
% 299.82/300.43  220906[10:Res:185430.1,220889.0] || equal(complement(regular(singleton(regular(domain_relation)))),successor_relation)** -> .
% 299.82/300.43  220902[10:Res:185430.1,220888.0] || equal(complement(regular(singleton(regular(rest_relation)))),successor_relation)** -> .
% 299.82/300.43  220909[12:Res:8.1,220890.0] || equal(regular(singleton(regular(element_relation))),universal_class)** -> .
% 299.82/300.43  220905[10:Res:8.1,220889.0] || equal(regular(singleton(regular(domain_relation))),universal_class)** -> .
% 299.82/300.43  220901[10:Res:8.1,220888.0] || equal(regular(singleton(regular(rest_relation))),universal_class)** -> .
% 299.82/300.43  220890[12:SpL:209433.0,219813.0] || subclass(universal_class,regular(singleton(regular(element_relation))))* -> .
% 299.82/300.43  220889[10:SpL:201355.0,219813.0] || subclass(universal_class,regular(singleton(regular(domain_relation))))* -> .
% 299.82/300.43  220888[10:SpL:199964.0,219813.0] || subclass(universal_class,regular(singleton(regular(rest_relation))))* -> .
% 299.82/300.43  219813[10:SpL:15.0,219389.0] || subclass(universal_class,regular(singleton(ordered_pair(u,v))))* -> .
% 299.82/300.43  220417[23:Res:220406.0,34067.0] ||  -> member(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),universal_class)*.
% 299.82/300.43  163580[10:Rew:160305.0,162235.2] inductive(u) || well_ordering(v,u)*+ -> equal(segment(v,range_of(successor_relation),least(v,range_of(successor_relation))),successor_relation)**.
% 299.82/300.43  203270[10:Rew:203192.0,160639.1] || member(u,universal_class) -> member(u,cantor(v)) equal(image(v,singleton(u)),range_of(successor_relation))**.
% 299.82/300.43  168389[11:MRR:163397.1,168387.0] || subclass(range_of(successor_relation),successor_relation)* -> inductive(inverse(successor_relation)).
% 299.82/300.43  163458[10:Rew:160305.0,162858.0] ||  -> equal(intersection(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals),symmetric_difference(singleton(successor_relation),range_of(successor_relation)))**.
% 299.82/300.43  160304[10:Rew:160202.0,146019.1] || asymmetric(u,universal_class) -> equal(image(intersection(u,inverse(u)),universal_class),range_of(successor_relation))**.
% 299.82/300.43  168405[11:Res:160354.1,168389.0] || equal(range_of(successor_relation),successor_relation) -> inductive(inverse(successor_relation))*.
% 299.82/300.43  164295[10:SSi:164289.0,52.0] inductive(range_of(successor_relation)) ||  -> equal(range_of(successor_relation),omega)**.
% 299.82/300.43  163335[10:Rew:160305.0,163150.1] inductive(u) || subclass(u,range_of(successor_relation))* -> equal(range_of(successor_relation),u).
% 299.82/300.43  191132[20:Res:191074.1,164877.0] || equal(range_of(successor_relation),omega) -> inductive(range_of(successor_relation))*.
% 299.82/300.43  164877[10:Res:314.0,163257.1] || member(successor_relation,range_of(successor_relation))* -> inductive(range_of(successor_relation)).
% 299.82/300.43  160345[10:Rew:160202.0,148539.0] ||  -> equal(apply(successor_relation,u),sum_class(range_of(successor_relation)))**.
% 299.82/300.43  163256[10:Rew:160305.0,160259.0] || equal(range_of(successor_relation),u) member(successor_relation,u)* -> inductive(u).
% 299.82/300.43  206778[10:Res:160354.1,206703.0] || equal(range_of(successor_relation),successor_relation)** -> inductive(kind_1_ordinals).
% 299.82/300.43  206703[10:MRR:163287.1,206690.0] || subclass(range_of(successor_relation),ordinal_numbers)* -> inductive(kind_1_ordinals).
% 299.82/300.43  206717[10:Res:206690.0,163256.1] || equal(range_of(successor_relation),kind_1_ordinals)** -> inductive(kind_1_ordinals).
% 299.82/300.43  206779[10:Res:8.1,206703.0] || equal(range_of(successor_relation),ordinal_numbers)** -> inductive(kind_1_ordinals).
% 299.82/300.43  163177[10:Rew:160305.0,160408.0] ||  -> subclass(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),kind_1_ordinals)*.
% 299.82/300.43  160305[10:Rew:160202.0,146206.0] ||  -> equal(image(successor_relation,u),range_of(successor_relation))**.
% 299.82/300.43  184004[14:MRR:183977.1,160227.0] || equal(sum_class(range_of(successor_relation)),successor_relation)** -> .
% 299.82/300.43  163257[10:Rew:160305.0,160270.1] || member(successor_relation,u) subclass(range_of(successor_relation),u)* -> inductive(u).
% 299.82/300.43  220405[23:Spt:220369.0,163508.0,219663.0] || equal(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),successor_relation)** -> .
% 299.82/300.43  163149[10:Rew:160305.0,50.1] inductive(u) ||  -> subclass(range_of(successor_relation),u)*.
% 299.82/300.43  163176[10:Rew:160305.0,160405.0] ||  -> equal(union(singleton(successor_relation),range_of(successor_relation)),kind_1_ordinals)**.
% 299.82/300.43  220406[23:Spt:220369.0,163508.1] ||  -> member(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals)*.
% 299.82/300.43  219546[10:Res:8.1,219385.0] || equal(regular(unordered_pair(u,singleton(v))),universal_class)** -> .
% 299.82/300.43  219389[10:SpL:14.0,217589.0] || subclass(universal_class,regular(singleton(unordered_pair(u,v))))* -> .
% 299.82/300.43  219652[10:Res:185430.1,219542.0] || equal(complement(regular(singleton(singleton(u)))),successor_relation)** -> .
% 299.82/300.43  219554[10:Res:185430.1,219537.0] || equal(complement(regular(unordered_pair(u,successor_relation))),successor_relation)** -> .
% 299.82/300.43  219651[10:Res:8.1,219542.0] || equal(regular(singleton(singleton(u))),universal_class)** -> .
% 299.82/300.43  219553[10:Res:8.1,219537.0] || equal(regular(unordered_pair(u,successor_relation)),universal_class)** -> .
% 299.82/300.43  219542[10:SpL:14.0,219385.0] || subclass(universal_class,regular(singleton(singleton(u))))* -> .
% 299.82/300.43  219559[10:Res:185430.1,219549.0] || equal(complement(regular(singleton(successor_relation))),successor_relation)** -> .
% 299.82/300.43  978[0:Res:4.1,595.0] ||  -> subclass(restrict(u,v,w),x) member(not_subclass_element(restrict(u,v,w),x),u)*.
% 299.82/300.43  219558[10:Res:8.1,219549.0] || equal(regular(singleton(successor_relation)),universal_class)** -> .
% 299.82/300.43  219549[10:SpL:14.0,219537.0] || subclass(universal_class,regular(singleton(successor_relation)))* -> .
% 299.82/300.43  219537[10:SpL:181056.0,219385.0] || subclass(universal_class,regular(unordered_pair(u,successor_relation)))* -> .
% 299.82/300.43  219385[10:SpL:14.0,217589.0] || subclass(universal_class,regular(unordered_pair(u,singleton(v))))* -> .
% 299.82/300.43  6832[0:Res:4.1,1952.0] ||  -> subclass(symmetric_difference(u,v),w) member(not_subclass_element(symmetric_difference(u,v),w),union(u,v))*.
% 299.82/300.43  217589[10:MRR:217555.0,217555.2,13.0,188662.0] || subclass(universal_class,regular(unordered_pair(u,unordered_pair(v,w))))* -> .
% 299.82/300.43  219376[22:Res:8.1,218911.0] || equal(singleton(u),kind_1_ordinals)**+ -> equal(singleton(successor_relation),u)*.
% 299.82/300.43  218911[22:Res:218867.1,2151.0] || subclass(kind_1_ordinals,singleton(u))* -> equal(singleton(successor_relation),u).
% 299.82/300.43  218872[22:Res:218867.1,3670.1] || subclass(kind_1_ordinals,u)* equal(complement(u),universal_class) -> .
% 299.82/300.43  9640[0:Res:1481.2,24.0] || subclass(u,intersection(v,w))*+ -> subclass(u,x) member(not_subclass_element(u,x),w)*.
% 299.82/300.43  218628[3:Con:218624.0] || member(u,complement(kind_1_ordinals))* -> member(u,complement(ordinal_numbers)).
% 299.82/300.43  218473[3:Res:8.1,217932.0] || equal(complement(kind_1_ordinals),u) -> subclass(u,complement(ordinal_numbers))*.
% 299.82/300.43  218926[22:Res:8.1,218871.0] || equal(u,kind_1_ordinals) subclass(u,successor_relation)* -> .
% 299.82/300.43  218912[22:Res:218867.1,185639.1] || subclass(kind_1_ordinals,u)* equal(successor_relation,u) -> .
% 299.82/300.43  9639[0:Res:1481.2,23.0] || subclass(u,intersection(v,w))*+ -> subclass(u,x) member(not_subclass_element(u,x),v)*.
% 299.82/300.43  218871[22:Res:218867.1,185065.1] || subclass(kind_1_ordinals,u)*+ subclass(u,successor_relation)* -> .
% 299.82/300.43  218867[22:Res:218858.0,3.0] || subclass(kind_1_ordinals,u) -> member(singleton(successor_relation),u)*.
% 299.82/300.43  218869[22:Res:218858.0,211446.0] || well_ordering(universal_class,kind_1_ordinals)* -> .
% 299.82/300.43  218858[22:Spt:218776.0] ||  -> member(singleton(successor_relation),kind_1_ordinals)*.
% 299.82/300.43  9380[0:Res:322.1,2151.0] ||  -> subclass(intersection(u,singleton(v)),w) equal(not_subclass_element(intersection(u,singleton(v)),w),v)**.
% 299.82/300.43  218513[10:Res:218490.0,160435.1] inductive(symmetric_difference(universal_class,kind_1_ordinals)) ||  -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.43  218493[3:Res:89275.1,217932.0] ||  -> member(u,kind_1_ordinals) subclass(singleton(u),complement(ordinal_numbers))*.
% 299.82/300.43  218481[3:Res:9424.0,217932.0] ||  -> subclass(restrict(complement(kind_1_ordinals),u,v),complement(ordinal_numbers))*.
% 299.82/300.43  9494[0:Res:340.1,2151.0] ||  -> subclass(intersection(singleton(u),v),w) equal(not_subclass_element(intersection(singleton(u),v),w),u)**.
% 299.82/300.43  218501[10:Res:218497.0,160435.1] inductive(regular(kind_1_ordinals)) ||  -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.43  218477[3:Res:53.1,217932.0] inductive(complement(kind_1_ordinals)) ||  -> subclass(omega,complement(ordinal_numbers))*.
% 299.82/300.43  218485[3:Res:9395.0,217932.0] ||  -> subclass(intersection(u,complement(kind_1_ordinals)),complement(ordinal_numbers))*.
% 299.82/300.43  218475[3:Res:9509.0,217932.0] ||  -> subclass(intersection(complement(kind_1_ordinals),u),complement(ordinal_numbers))*.
% 299.82/300.43  9636[0:Res:1481.2,26.1] || subclass(u,complement(v)) member(not_subclass_element(u,w),v)* -> subclass(u,w).
% 299.82/300.43  218494[3:Res:107233.0,217932.0] ||  -> subclass(complement(complement(complement(kind_1_ordinals))),complement(ordinal_numbers))*.
% 299.82/300.43  218490[3:Res:114856.0,217932.0] ||  -> subclass(symmetric_difference(universal_class,kind_1_ordinals),complement(ordinal_numbers))*.
% 299.82/300.43  218497[10:MRR:218495.0,184563.0] ||  -> subclass(regular(kind_1_ordinals),complement(ordinal_numbers))*.
% 299.82/300.43  217932[3:Obv:217927.1] || subclass(u,complement(kind_1_ordinals))* -> subclass(u,complement(ordinal_numbers)).
% 299.82/300.43  9587[0:Res:1476.1,594.0] || subclass(universal_class,restrict(u,v,w))*+ -> member(unordered_pair(x,y),cross_product(v,w))*.
% 299.82/300.43  218372[10:MRR:218338.1,185595.0] ||  -> subclass(regular(image(element_relation,universal_class)),power_class(successor_relation))*.
% 299.82/300.43  218371[13:MRR:218337.1,185593.0] ||  -> subclass(regular(image(element_relation,successor_relation)),power_class(universal_class))*.
% 299.82/300.43  218370[10:MRR:218330.1,217612.0] ||  -> subclass(regular(complement(singleton(successor_relation))),successor(successor_relation))*.
% 299.82/300.43  160796[10:Rew:160202.0,146003.1] || subclass(u,restrict(v,w,x))* -> equal(u,successor_relation) member(regular(u),v).
% 299.82/300.43  218368[12:MRR:218361.1,177130.0] || well_ordering(universal_class,complement(element_relation))* -> .
% 299.82/300.43  218367[10:MRR:218360.1,159406.0] || well_ordering(universal_class,complement(domain_relation))* -> .
% 299.82/300.43  218366[10:MRR:218359.1,160372.0] || well_ordering(universal_class,complement(rest_relation))* -> .
% 299.82/300.43  218298[10:Obv:218285.0] ||  -> subclass(regular(u),complement(u))* equal(u,successor_relation).
% 299.82/300.43  160698[10:Rew:160202.0,159689.2] || member(not_subclass_element(regular(u),v),u)* -> subclass(regular(u),v) equal(u,successor_relation).
% 299.82/300.43  217539[20:Res:8.1,217421.1] || equal(ordinal_numbers,y__dfg) equal(singleton(ordinal_numbers),omega)** -> .
% 299.82/300.43  217909[10:Res:185430.1,217574.0] || equal(complement(regular(ordered_pair(u,v))),successor_relation)** -> .
% 299.82/300.43  161690[10:Rew:160202.0,146141.0] ||  -> equal(symmetric_difference(u,v),successor_relation) member(regular(symmetric_difference(u,v)),complement(intersection(u,v)))*.
% 299.82/300.43  217908[10:Res:8.1,217574.0] || equal(regular(ordered_pair(u,v)),universal_class)** -> .
% 299.82/300.43  217671[10:Res:185430.1,217599.0] || equal(complement(ordered_pair(u,v)),successor_relation)** -> .
% 299.82/300.43  217604[10:Res:185430.1,217584.0] || equal(complement(unordered_pair(u,v)),successor_relation)** -> .
% 299.82/300.43  161451[10:Rew:160202.0,146152.1] || well_ordering(u,universal_class) -> equal(singleton(v),successor_relation) equal(least(u,singleton(v)),v)**.
% 299.82/300.43  217918[12:Res:185430.1,217902.0] || equal(complement(regular(regular(element_relation))),successor_relation)** -> .
% 299.82/300.43  217915[10:Res:185430.1,217901.0] || equal(complement(regular(regular(domain_relation))),successor_relation)** -> .
% 299.82/300.43  217912[10:Res:185430.1,217900.0] || equal(complement(regular(regular(rest_relation))),successor_relation)** -> .
% 299.82/300.43  28300[0:Res:1495.2,17.0] || member(u,universal_class) subclass(rest_relation,cross_product(v,w))*+ -> member(rest_of(u),w)*.
% 299.82/300.43  217917[12:Res:8.1,217902.0] || equal(regular(regular(element_relation)),universal_class)** -> .
% 299.82/300.43  217914[10:Res:8.1,217901.0] || equal(regular(regular(domain_relation)),universal_class)** -> .
% 299.82/300.43  217911[10:Res:8.1,217900.0] || equal(regular(regular(rest_relation)),universal_class)** -> .
% 299.82/300.43  155811[3:Res:1481.2,141576.1] || subclass(u,complement(kind_1_ordinals)) member(not_subclass_element(u,v),ordinal_numbers)* -> subclass(u,v).
% 299.82/300.43  217902[12:SpL:209433.0,217574.0] || subclass(universal_class,regular(regular(element_relation)))* -> .
% 299.82/300.43  217901[10:SpL:201355.0,217574.0] || subclass(universal_class,regular(regular(domain_relation)))* -> .
% 299.82/300.43  217900[10:SpL:199964.0,217574.0] || subclass(universal_class,regular(regular(rest_relation)))* -> .
% 299.82/300.43  217574[10:MRR:217559.1,160315.0] || subclass(universal_class,regular(ordered_pair(u,v)))* -> .
% 299.82/300.43  39022[0:Rew:55.0,39011.2] || section(element_relation,u,universal_class)*+ subclass(u,sum_class(u))* -> equal(sum_class(u),u).
% 299.82/300.43  217670[10:Res:8.1,217599.0] || equal(ordered_pair(u,v),universal_class)** -> .
% 299.82/300.43  217603[10:Res:8.1,217584.0] || equal(unordered_pair(u,v),universal_class)** -> .
% 299.82/300.43  217680[12:Res:185430.1,217664.0] || equal(complement(regular(element_relation)),successor_relation)** -> .
% 299.82/300.43  217677[10:Res:185430.1,217663.0] || equal(complement(regular(domain_relation)),successor_relation)** -> .
% 299.82/300.43  9121[0:Res:1479.2,23.0] || member(u,universal_class) subclass(universal_class,intersection(v,w))*+ -> member(sum_class(u),v)*.
% 299.82/300.43  217674[10:Res:185430.1,217662.0] || equal(complement(regular(rest_relation)),successor_relation)** -> .
% 299.82/300.43  217679[12:Res:8.1,217664.0] || equal(regular(element_relation),universal_class)** -> .
% 299.82/300.43  217676[10:Res:8.1,217663.0] || equal(regular(domain_relation),universal_class)** -> .
% 299.82/300.43  217673[10:Res:8.1,217662.0] || equal(regular(rest_relation),universal_class)** -> .
% 299.82/300.43  9122[0:Res:1479.2,24.0] || member(u,universal_class) subclass(universal_class,intersection(v,w))*+ -> member(sum_class(u),w)*.
% 299.82/300.43  217664[12:SpL:209433.0,217599.0] || subclass(universal_class,regular(element_relation))* -> .
% 299.82/300.43  217663[10:SpL:201355.0,217599.0] || subclass(universal_class,regular(domain_relation))* -> .
% 299.82/300.43  217662[10:SpL:199964.0,217599.0] || subclass(universal_class,regular(rest_relation))* -> .
% 299.82/300.43  217599[10:SpL:15.0,217584.0] || subclass(universal_class,ordered_pair(u,v))* -> .
% 299.82/300.43  1089[0:Rew:57.0,1075.1] || member(not_subclass_element(power_class(u),v),image(element_relation,complement(u)))* -> subclass(power_class(u),v).
% 299.82/300.43  217612[10:Res:185430.1,217598.0] || equal(complement(singleton(u)),successor_relation)** -> .
% 299.82/300.43  217611[10:Res:8.1,217598.0] || equal(singleton(u),universal_class)** -> .
% 299.82/300.43  217598[10:SpL:14.0,217584.0] || subclass(universal_class,singleton(u))* -> .
% 299.82/300.43  217584[10:MRR:217583.1,185246.0] || subclass(universal_class,unordered_pair(u,v))* -> .
% 299.82/300.43  160697[10:Rew:160202.0,159693.2] || subclass(universal_class,regular(u)) member(unordered_pair(v,w),u)* -> equal(u,successor_relation).
% 299.82/300.43  217421[20:Res:217226.1,195493.1] || equal(singleton(ordinal_numbers),omega) subclass(ordinal_numbers,y__dfg)* -> .
% 299.82/300.43  217439[20:MRR:217402.1,185591.0] || equal(singleton(regular(complement(singleton(successor_relation)))),omega)** -> .
% 299.82/300.43  217435[20:Res:217226.1,197074.0] || equal(singleton(regular(complement(successor(successor_relation)))),omega)** -> .
% 299.82/300.43  217420[20:Res:217226.1,160407.0] || equal(singleton(intersection(y__dfg,ordinal_numbers)),omega)** -> .
% 299.82/300.43  161380[10:Rew:160202.0,146147.1] || member(regular(intersection(u,complement(v))),v)* -> equal(intersection(u,complement(v)),successor_relation).
% 299.82/300.43  217226[20:Res:191074.1,217209.0] || equal(singleton(u),omega) -> member(u,singleton(successor_relation))*.
% 299.82/300.43  217399[10:Res:8.1,217258.1] || equal(ordinal_numbers,y__dfg) equal(singleton(ordinal_numbers),kind_1_ordinals)** -> .
% 299.82/300.43  217258[10:Res:217225.1,195493.1] || equal(singleton(ordinal_numbers),kind_1_ordinals) subclass(ordinal_numbers,y__dfg)* -> .
% 299.82/300.43  217275[10:MRR:217239.1,185591.0] || equal(singleton(regular(complement(singleton(successor_relation)))),kind_1_ordinals)** -> .
% 299.82/300.43  161700[10:Rew:160202.0,146150.1] || member(regular(intersection(complement(u),v)),u)* -> equal(intersection(complement(u),v),successor_relation).
% 299.82/300.43  217272[10:Res:217225.1,197074.0] || equal(singleton(regular(complement(successor(successor_relation)))),kind_1_ordinals)** -> .
% 299.82/300.43  217257[10:Res:217225.1,160407.0] || equal(singleton(intersection(y__dfg,ordinal_numbers)),kind_1_ordinals)** -> .
% 299.82/300.43  217225[10:Res:206947.1,217209.0] || equal(singleton(u),kind_1_ordinals) -> member(u,singleton(successor_relation))*.
% 299.82/300.43  217233[10:Res:160271.1,217209.0] inductive(singleton(u)) ||  -> member(u,singleton(successor_relation))*.
% 299.82/300.43  189417[15:Rew:189339.1,28128.2] || member(u,universal_class) subclass(domain_relation,compose_class(v))*+ -> equal(compose(v,u),successor_relation)**.
% 299.82/300.43  217209[10:Res:89275.1,206660.0] || member(successor_relation,singleton(u))*+ -> member(u,singleton(successor_relation))*.
% 299.82/300.43  206660[10:SpL:194805.1,206268.0] || subclass(u,complement(singleton(successor_relation)))* member(successor_relation,u) -> .
% 299.82/300.43  206542[10:MRR:206529.1,206430.0] || subclass(complement(complement(successor(successor_relation))),u)* -> member(successor_relation,u).
% 299.82/300.43  206105[10:SpL:185605.1,206094.0] || equal(successor_relation,u) equal(power_class(u),successor(successor_relation))** -> .
% 299.82/300.43  189383[15:Rew:189339.1,28105.2] || member(u,universal_class) subclass(domain_relation,singleton(v))*+ -> equal(ordered_pair(u,successor_relation),v)*.
% 299.82/300.43  206081[10:Res:160268.1,163205.1] || equal(u,universal_class) equal(complement(u),successor(successor_relation))** -> .
% 299.82/300.43  206075[20:Res:191074.1,163205.1] || equal(u,omega) equal(complement(u),successor(successor_relation))** -> .
% 299.82/300.43  206046[10:Res:8.1,163071.0] || equal(singleton(u),domain_relation)**+ -> equal(ordered_pair(successor_relation,successor_relation),u)*.
% 299.82/300.43  205672[10:Res:205375.1,185066.0] || equal(sum_class(u),successor_relation) subclass(universal_class,sum_class(u))* -> .
% 299.82/300.43  205626[10:Res:205359.1,185066.0] || equal(inverse(u),successor_relation) subclass(universal_class,inverse(u))* -> .
% 299.82/300.43  205568[10:Res:205036.1,185066.0] || equal(range_of(u),successor_relation) subclass(universal_class,range_of(u))* -> .
% 299.82/300.43  205567[10:Res:205036.1,188823.0] || equal(range_of(u),successor_relation) member(successor_relation,range_of(u))* -> .
% 299.82/300.43  205566[10:Res:205036.1,188825.1] || equal(range_of(u),successor_relation)** equal(range_of(u),universal_class) -> .
% 299.82/300.43  9118[0:Res:1479.2,26.1] || member(u,universal_class) subclass(universal_class,complement(v))*+ member(sum_class(u),v)* -> .
% 299.82/300.43  202881[11:Res:160268.1,168534.1] || equal(u,universal_class) equal(complement(u),symmetrization_of(successor_relation))* -> .
% 299.82/300.43  202875[20:Res:191074.1,168534.1] || equal(u,omega) equal(complement(u),symmetrization_of(successor_relation))* -> .
% 299.82/300.43  202516[10:SpR:202485.1,41.0] || equal(rest_of(inverse(u)),successor_relation)** -> equal(range_of(u),successor_relation).
% 299.82/300.43  9069[0:Res:1476.1,307.0] || subclass(universal_class,image(element_relation,complement(u)))*+ member(unordered_pair(v,w),power_class(u))* -> .
% 299.82/300.43  216969[10:Obv:216967.1] || equal(compose_class(successor_relation),domain_relation) -> transitive(successor_relation,u)*.
% 299.82/300.43  202307[10:Res:8.1,163107.0] || equal(compose_class(u),domain_relation) -> equal(compose(u,successor_relation),successor_relation)**.
% 299.82/300.43  216847[10:MRR:216839.1,314.0] || equal(complement(u),successor_relation) -> member(regular(domain_relation),u)*.
% 299.82/300.43  163343[10:Rew:160202.0,160688.1] || member(apply(choice,regular(u)),u)* -> equal(regular(u),successor_relation) equal(u,successor_relation).
% 299.82/300.43  201376[6:Res:201231.1,183398.0] || subclass(universal_class,complement(complement(u)))* -> member(regular(domain_relation),u).
% 299.82/300.43  201372[6:Res:201231.1,26.1] || subclass(universal_class,complement(u))* member(regular(domain_relation),u) -> .
% 299.82/300.43  201224[6:Res:195720.1,154493.0] || equal(sum_class(u),universal_class) -> member(regular(domain_relation),sum_class(u))*.
% 299.82/300.43  201223[6:Res:195710.1,154493.0] || equal(inverse(u),universal_class) -> member(regular(domain_relation),inverse(u))*.
% 299.82/300.43  143767[0:Res:1479.2,159.0] || member(u,universal_class) subclass(universal_class,omega) -> equal(integer_of(sum_class(u)),sum_class(u))**.
% 299.82/300.43  201220[6:Res:8.1,154493.0] || equal(u,cross_product(universal_class,universal_class)) -> member(regular(domain_relation),u)*.
% 299.82/300.43  200931[10:Res:200802.1,185066.0] || equal(cantor(u),successor_relation) subclass(universal_class,cantor(u))* -> .
% 299.82/300.43  200890[10:MRR:200806.2,3567.0] || equal(cantor(u),successor_relation)** equal(cantor(u),universal_class) -> .
% 299.82/300.43  216465[10:MRR:216457.1,314.0] || equal(complement(u),successor_relation) -> member(regular(rest_relation),u)*.
% 299.82/300.43  199986[6:Res:199848.1,183398.0] || subclass(universal_class,complement(complement(u)))* -> member(regular(rest_relation),u).
% 299.82/300.43  199982[6:Res:199848.1,26.1] || subclass(universal_class,complement(u))* member(regular(rest_relation),u) -> .
% 299.82/300.43  199971[14:Res:160362.0,184789.0] || member(u,universal_class) -> equal(singleton(sum_class(range_of(u))),successor_relation)**.
% 299.82/300.43  143766[0:Res:1478.2,159.0] || member(u,universal_class) subclass(universal_class,omega) -> equal(integer_of(power_class(u)),power_class(u))**.
% 299.82/300.43  199970[14:Res:160274.1,184789.0] || member(u,universal_class) -> equal(integer_of(sum_class(range_of(u))),successor_relation)**.
% 299.82/300.43  216184[6:Res:314.0,199959.0] || well_ordering(universal_class,cross_product(universal_class,universal_class))* -> .
% 299.82/300.43  155799[3:Res:1479.2,141576.1] || member(u,universal_class) subclass(universal_class,complement(kind_1_ordinals))*+ member(sum_class(u),ordinal_numbers)* -> .
% 299.82/300.43  199959[6:Res:199831.0,6045.0] || subclass(cross_product(universal_class,universal_class),u)* well_ordering(universal_class,u) -> .
% 299.82/300.43  199834[6:Res:195720.1,153518.0] || equal(sum_class(u),universal_class) -> member(regular(rest_relation),sum_class(u))*.
% 299.82/300.43  199833[6:Res:195710.1,153518.0] || equal(inverse(u),universal_class) -> member(regular(rest_relation),inverse(u))*.
% 299.82/300.43  199830[6:Res:8.1,153518.0] || equal(u,cross_product(universal_class,universal_class)) -> member(regular(rest_relation),u)*.
% 299.82/300.43  163027[10:Rew:160202.0,158258.1] || member(regular(intersection(complement(kind_1_ordinals),u)),ordinal_numbers)* -> equal(intersection(complement(kind_1_ordinals),u),successor_relation).
% 299.82/300.43  199026[11:SpL:31.0,199013.0] || equal(restrict(complement(inverse(successor_relation)),u,v),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  198998[11:SpL:31.0,198982.0] || subclass(symmetrization_of(successor_relation),restrict(complement(inverse(successor_relation)),u,v))* -> .
% 299.82/300.43  216020[10:Rew:113504.0,215960.0,160223.0,215960.0] ||  -> equal(symmetric_difference(ordinal_numbers,complement(kind_1_ordinals)),union(ordinal_numbers,complement(kind_1_ordinals)))**.
% 299.82/300.43  215951[10:Obv:215946.0] ||  -> equal(intersection(ordinal_numbers,complement(kind_1_ordinals)),successor_relation)**.
% 299.82/300.43  163029[10:Rew:160202.0,158449.1] || member(regular(intersection(u,complement(kind_1_ordinals))),ordinal_numbers)* -> equal(intersection(u,complement(kind_1_ordinals)),successor_relation).
% 299.82/300.43  198799[10:SpL:30.0,198728.0] || equal(restrict(complement(singleton(successor_relation)),u,v),successor(successor_relation))** -> .
% 299.82/300.43  198706[10:SpL:30.0,198694.0] || subclass(successor(successor_relation),restrict(complement(singleton(successor_relation)),u,v))* -> .
% 299.82/300.43  155798[3:Res:1478.2,141576.1] || member(u,universal_class) subclass(universal_class,complement(kind_1_ordinals))*+ member(power_class(u),ordinal_numbers)* -> .
% 299.82/300.43  197082[10:Res:197071.0,3.0] || subclass(universal_class,u) -> member(regular(complement(successor(successor_relation))),u)*.
% 299.82/300.43  215835[10:Res:314.0,197069.0] || well_ordering(universal_class,complement(singleton(successor_relation)))* -> .
% 299.82/300.43  161860[10:Rew:160202.0,148473.1] || subclass(omega,intersection(y__dfg,ordinal_numbers)) -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation)**.
% 299.82/300.43  197069[10:Res:197034.0,6045.0] || subclass(complement(singleton(successor_relation)),u)* well_ordering(universal_class,u) -> .
% 299.82/300.43  195870[10:Res:195720.1,161271.0] || equal(sum_class(u),universal_class) -> equal(complement(sum_class(u)),successor_relation)**.
% 299.82/300.43  195847[6:Res:195720.1,5754.0] || equal(sum_class(u),universal_class) -> section(element_relation,sum_class(u),universal_class)*.
% 299.82/300.43  195836[10:Res:195720.1,185343.1] || equal(sum_class(u),universal_class) equal(sum_class(u),successor_relation)** -> .
% 299.82/300.43  163021[10:Rew:160202.0,157900.1] || member(regular(complement(compose(element_relation,universal_class))),element_relation)* -> equal(complement(compose(element_relation,universal_class)),successor_relation).
% 299.82/300.43  195835[6:Res:195720.1,183.1] || equal(sum_class(u),universal_class) well_ordering(element_relation,sum_class(u))* -> .
% 299.82/300.43  195811[10:Res:195710.1,161271.0] || equal(inverse(u),universal_class) -> equal(complement(inverse(u)),successor_relation)**.
% 299.82/300.43  195788[6:Res:195710.1,5754.0] || equal(inverse(u),universal_class) -> section(element_relation,inverse(u),universal_class)*.
% 299.82/300.43  215242[11:MRR:215241.1,198997.0] || member(not_subclass_element(symmetrization_of(successor_relation),successor_relation),symmetric_difference(universal_class,inverse(successor_relation)))* -> .
% 299.82/300.43  40234[0:Obv:40215.1] || member(not_subclass_element(u,intersection(v,u)),v)* -> subclass(u,intersection(v,u)).
% 299.82/300.43  195777[10:Res:195710.1,185343.1] || equal(inverse(u),universal_class) equal(inverse(u),successor_relation)** -> .
% 299.82/300.43  195776[6:Res:195710.1,183.1] || equal(inverse(u),universal_class) well_ordering(element_relation,inverse(u))* -> .
% 299.82/300.43  214963[10:Obv:214962.1] || equal(inverse(successor_relation),universal_class) -> connected(successor_relation,u)*.
% 299.82/300.43  9649[0:Res:1481.2,2151.0] || subclass(u,singleton(v))*+ -> subclass(u,w) equal(not_subclass_element(u,w),v)*.
% 299.82/300.43  214842[10:Res:8.1,214832.0] || equal(inverse(successor_relation),universal_class) -> equal(symmetrization_of(successor_relation),universal_class)**.
% 299.82/300.43  214832[10:Res:214812.1,1312.0] || subclass(universal_class,inverse(successor_relation))* -> equal(symmetrization_of(successor_relation),universal_class).
% 299.82/300.43  161697[10:Rew:160202.0,146144.0] ||  -> equal(restrict(u,v,w),successor_relation) member(regular(restrict(u,v,w)),u)*.
% 299.82/300.43  195403[2:SpR:194805.1,142543.0] || subclass(universal_class,complement(u))* -> equal(symmetric_difference(universal_class,u),universal_class).
% 299.82/300.43  194544[11:Res:168384.1,183398.0] || equal(complement(complement(u)),symmetrization_of(successor_relation))** -> member(successor_relation,u).
% 299.82/300.43  194543[10:Res:163169.1,183398.0] || equal(complement(complement(u)),successor(successor_relation))** -> member(successor_relation,u).
% 299.82/300.43  194542[10:Res:163171.1,183398.0] || equal(complement(complement(u)),singleton(successor_relation))** -> member(successor_relation,u).
% 299.82/300.43  204452[6:Rew:203335.0,150813.0] ||  -> equal(symmetric_difference(segment(u,v,w),universal_class),symmetric_difference(universal_class,segment(u,v,w)))**.
% 299.82/300.43  194541[11:Res:179843.1,183398.0] || equal(complement(complement(u)),inverse(successor_relation))** -> member(successor_relation,u).
% 299.82/300.43  214453[21:Res:214433.0,186157.0] || equal(singleton(regular(complement(complement(symmetrization_of(successor_relation))))),successor_relation)** -> .
% 299.82/300.43  30984[0:Res:1032.1,23.0] || member(u,universal_class) -> member(u,union(v,w))* member(u,complement(v)).
% 299.82/300.43  214451[21:Res:214433.0,189419.0] || equal(successor(regular(complement(complement(symmetrization_of(successor_relation))))),successor_relation)** -> .
% 299.82/300.43  214450[21:Res:214433.0,193015.0] ||  -> equal(cantor(regular(complement(complement(symmetrization_of(successor_relation))))),successor_relation)**.
% 299.82/300.43  214433[21:Res:214356.0,34067.0] ||  -> member(regular(complement(complement(symmetrization_of(successor_relation)))),universal_class)*.
% 299.82/300.43  214356[21:MRR:201738.0,214355.0] ||  -> member(regular(complement(complement(symmetrization_of(successor_relation)))),inverse(successor_relation))*.
% 299.82/300.43  30985[0:Res:1032.1,24.0] || member(u,universal_class) -> member(u,union(v,w))* member(u,complement(w)).
% 299.82/300.43  214355[21:MRR:214339.1,208804.0] || equal(complement(complement(symmetrization_of(successor_relation))),successor_relation)** -> .
% 299.82/300.43  194540[10:Res:185646.1,183398.0] || equal(complement(complement(complement(u))),successor_relation)** -> member(successor_relation,u).
% 299.82/300.43  214277[10:MRR:214269.1,314.0] || equal(complement(u),successor_relation) -> member(power_class(successor_relation),u)*.
% 299.82/300.43  194520[10:Res:187500.1,183398.0] || subclass(universal_class,complement(complement(u)))* -> member(power_class(successor_relation),u).
% 299.82/300.43  3485[0:Res:1476.1,3.0] || subclass(universal_class,u)*+ subclass(u,v)* -> member(unordered_pair(w,x),v)*.
% 299.82/300.43  194513[10:Res:185647.1,183398.0] || equal(complement(complement(complement(u))),successor_relation)** -> member(omega,u).
% 299.82/300.43  214151[20:Res:193270.1,141576.1] || equal(symmetric_difference(universal_class,kind_1_ordinals),omega)** member(successor_relation,ordinal_numbers) -> .
% 299.82/300.43  214165[21:Res:193270.1,208804.0] || equal(symmetric_difference(universal_class,inverse(successor_relation)),omega)** -> .
% 299.82/300.43  214164[20:Res:193270.1,206271.0] || equal(symmetric_difference(universal_class,successor(successor_relation)),omega)** -> .
% 299.82/300.43  6842[0:Res:1476.1,1952.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(unordered_pair(w,x),union(u,v))*.
% 299.82/300.43  193270[20:SpL:142543.0,191100.0] || equal(symmetric_difference(universal_class,u),omega) -> member(successor_relation,complement(u))*.
% 299.82/300.43  193155[17:Res:188729.1,193015.0] || well_ordering(u,universal_class) -> equal(cantor(least(u,omega)),successor_relation)**.
% 299.82/300.43  193154[17:Res:188737.1,193015.0] || well_ordering(u,omega) -> equal(cantor(least(u,omega)),successor_relation)**.
% 299.82/300.43  193153[15:Res:110382.1,193015.0] || well_ordering(u,universal_class) -> equal(cantor(least(u,rest_relation)),successor_relation)**.
% 299.82/300.43  10288[0:Res:8.1,1485.1] || equal(u,unordered_pair(v,w))*+ member(v,universal_class) -> member(v,u)*.
% 299.82/300.43  193152[15:Res:110388.1,193015.0] || well_ordering(u,rest_relation) -> equal(cantor(least(u,rest_relation)),successor_relation)**.
% 299.82/300.43  193151[15:Res:110623.1,193015.0] || well_ordering(u,universal_class) -> equal(cantor(least(u,universal_class)),successor_relation)**.
% 299.82/300.43  193150[15:Res:184599.1,193015.0] || well_ordering(u,kind_1_ordinals) -> equal(cantor(least(u,ordinal_numbers)),successor_relation)**.
% 299.82/300.43  192320[20:Res:168384.1,191095.1] || equal(u,symmetrization_of(successor_relation))*+ equal(complement(u),omega)** -> .
% 299.82/300.43  10385[0:Res:8.1,1484.1] || equal(u,unordered_pair(v,w))*+ member(w,universal_class) -> member(w,u)*.
% 299.82/300.43  192319[20:Res:163169.1,191095.1] || equal(u,successor(successor_relation)) equal(complement(u),omega)** -> .
% 299.82/300.43  192318[20:Res:163171.1,191095.1] || equal(u,singleton(successor_relation)) equal(complement(u),omega)** -> .
% 299.82/300.43  192317[20:Res:179843.1,191095.1] || equal(u,inverse(successor_relation)) equal(complement(u),omega)** -> .
% 299.82/300.43  191656[15:Rew:160370.0,191653.1] || equal(successor(u),successor_relation) -> equal(union(u,successor_relation),successor_relation)**.
% 299.82/300.43  160802[10:Rew:160202.0,146004.1] || subclass(u,intersection(v,w))* -> equal(u,successor_relation) member(regular(u),w).
% 299.82/300.43  191631[15:Res:120366.1,189419.0] || member(u,universal_class) equal(successor(rest_of(u)),successor_relation)** -> .
% 299.82/300.43  191628[15:Res:56.1,189419.0] || member(u,universal_class) equal(successor(sum_class(u)),successor_relation)** -> .
% 299.82/300.43  191623[15:Res:58.1,189419.0] || member(u,universal_class) equal(successor(power_class(u)),successor_relation)** -> .
% 299.82/300.43  191622[15:Res:186499.1,189419.0] || equal(successor_relation,u) equal(successor(power_class(u)),successor_relation)** -> .
% 299.82/300.43  160801[10:Rew:160202.0,146005.1] || subclass(u,intersection(v,w))* -> equal(u,successor_relation) member(regular(u),v).
% 299.82/300.43  161691[10:Rew:160202.0,146142.0] ||  -> equal(symmetric_difference(u,v),successor_relation) member(regular(symmetric_difference(u,v)),union(u,v))*.
% 299.82/300.43  213296[15:Res:8.1,213195.0] || equal(u,domain_relation) equal(complement(u),universal_class)** -> .
% 299.82/300.43  28123[0:Res:1496.2,16.0] || member(u,universal_class)* subclass(domain_relation,cross_product(v,w))*+ -> member(u,v)*.
% 299.82/300.43  213298[15:Res:100.0,213195.0] || equal(complement(cross_product(universal_class,universal_class)),universal_class)** -> .
% 299.82/300.43  213195[15:Res:189485.1,3670.1] || subclass(domain_relation,u)* equal(complement(u),universal_class) -> .
% 299.82/300.43  213260[15:Res:8.1,213194.0] || equal(u,domain_relation) subclass(u,successor_relation)* -> .
% 299.82/300.43  213194[15:Res:189485.1,185065.1] || subclass(domain_relation,u)*+ subclass(u,successor_relation)* -> .
% 299.82/300.43  28299[0:Res:1495.2,16.0] || member(u,universal_class)* subclass(rest_relation,cross_product(v,w))*+ -> member(u,v)*.
% 299.82/300.43  189485[15:Res:189478.0,3.0] || subclass(domain_relation,u) -> member(singleton(singleton(singleton(successor_relation))),u)*.
% 299.82/300.43  213117[10:Res:188444.1,141576.1] || equal(symmetric_difference(universal_class,kind_1_ordinals),universal_class)** member(successor_relation,ordinal_numbers) -> .
% 299.82/300.43  213131[21:Res:188444.1,208804.0] || equal(symmetric_difference(universal_class,inverse(successor_relation)),universal_class)** -> .
% 299.82/300.43  213130[10:Res:188444.1,206271.0] || equal(symmetric_difference(universal_class,successor(successor_relation)),universal_class)** -> .
% 299.82/300.43  160800[10:Rew:160202.0,146006.2] || subclass(u,complement(v))* member(regular(u),v) -> equal(u,successor_relation).
% 299.82/300.43  188444[10:SpL:142543.0,160566.0] || equal(symmetric_difference(universal_class,u),universal_class) -> member(successor_relation,complement(u))*.
% 299.82/300.43  188189[10:Res:120366.1,186157.0] || member(u,universal_class) equal(singleton(rest_of(u)),successor_relation)** -> .
% 299.82/300.43  188186[10:Res:56.1,186157.0] || member(u,universal_class) equal(singleton(sum_class(u)),successor_relation)** -> .
% 299.82/300.43  161277[10:Rew:160202.0,146138.0] ||  -> equal(intersection(u,singleton(v)),successor_relation) equal(regular(intersection(u,singleton(v))),v)**.
% 299.82/300.43  188181[10:Res:58.1,186157.0] || member(u,universal_class) equal(singleton(power_class(u)),successor_relation)** -> .
% 299.82/300.43  188180[10:Res:186499.1,186157.0] || equal(successor_relation,u) equal(singleton(power_class(u)),successor_relation)** -> .
% 299.82/300.43  187767[10:Res:187500.1,26.1] || subclass(universal_class,complement(u))* member(power_class(successor_relation),u) -> .
% 299.82/300.43  161284[10:Rew:160202.0,146140.0] ||  -> equal(intersection(singleton(u),v),successor_relation) equal(regular(intersection(singleton(u),v)),u)**.
% 299.82/300.43  186044[10:Rew:57.0,186039.0] || equal(power_class(u),successor_relation) member(omega,power_class(u))* -> .
% 299.82/300.43  186009[10:Res:185647.1,26.1] || equal(complement(complement(u)),successor_relation)** member(omega,u) -> .
% 299.82/300.43  185977[10:Rew:57.0,185965.0] || equal(power_class(u),successor_relation) member(successor_relation,power_class(u))* -> .
% 299.82/300.43  212822[15:MRR:212795.0,209313.0] || member(second(regular(element_relation)),cantor(first(regular(element_relation))))* -> .
% 299.82/300.43  212821[15:MRR:212794.0,201221.0] || member(second(regular(domain_relation)),cantor(first(regular(domain_relation))))* -> .
% 299.82/300.43  212820[15:MRR:212793.0,199831.0] || member(second(regular(rest_relation)),cantor(first(regular(rest_relation))))* -> .
% 299.82/300.43  203931[15:Rew:203192.0,186272.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* member(v,cantor(u)) -> .
% 299.82/300.43  212521[10:MRR:163366.1,212520.0] || member(not_subclass_element(image(element_relation,universal_class),successor_relation),power_class(successor_relation))* -> .
% 299.82/300.43  212516[13:MRR:163365.1,212514.0] || member(not_subclass_element(image(element_relation,successor_relation),successor_relation),power_class(universal_class))* -> .
% 299.82/300.43  212674[10:Res:212652.0,186157.0] || equal(singleton(regular(complement(power_class(successor_relation)))),successor_relation)** -> .
% 299.82/300.43  203662[6:Rew:203192.0,28298.2] || member(u,universal_class) subclass(rest_relation,rest_of(v))*+ -> member(u,cantor(v))*.
% 299.82/300.43  212672[15:Res:212652.0,189419.0] || equal(successor(regular(complement(power_class(successor_relation)))),successor_relation)** -> .
% 299.82/300.43  212567[13:Res:212548.0,186157.0] || equal(singleton(regular(complement(power_class(universal_class)))),successor_relation)** -> .
% 299.82/300.43  212565[15:Res:212548.0,189419.0] || equal(successor(regular(complement(power_class(universal_class)))),successor_relation)** -> .
% 299.82/300.43  212671[15:Res:212652.0,193015.0] ||  -> equal(cantor(regular(complement(power_class(successor_relation)))),successor_relation)**.
% 299.82/300.43  212652[10:Res:212518.0,34067.0] ||  -> member(regular(complement(power_class(successor_relation))),universal_class)*.
% 299.82/300.43  212518[10:MRR:163315.1,212517.0] ||  -> member(regular(complement(power_class(successor_relation))),image(element_relation,universal_class))*.
% 299.82/300.43  212564[15:Res:212548.0,193015.0] ||  -> equal(cantor(regular(complement(power_class(universal_class)))),successor_relation)**.
% 299.82/300.43  203281[6:Rew:203192.0,1074.1] || member(singleton(singleton(singleton(u))),rest_of(v))* -> member(singleton(u),cantor(v)).
% 299.82/300.43  212548[13:Res:212515.0,34067.0] ||  -> member(regular(complement(power_class(universal_class))),universal_class)*.
% 299.82/300.43  212515[13:MRR:201767.1,212512.0] ||  -> member(regular(complement(power_class(universal_class))),image(element_relation,successor_relation))*.
% 299.82/300.43  212520[10:MRR:184948.1,212517.0] || subclass(image(element_relation,universal_class),successor_relation)* -> .
% 299.82/300.43  212517[10:MRR:212504.1,160460.0] || equal(complement(power_class(successor_relation)),successor_relation)** -> .
% 299.82/300.43  5858[0:Res:191.0,127.0] || subclass(universal_class,u)+ well_ordering(v,u)* -> member(least(v,universal_class),universal_class)*.
% 299.82/300.43  212514[13:MRR:184947.1,212512.0] || subclass(image(element_relation,successor_relation),successor_relation)* -> .
% 299.82/300.43  212512[13:MRR:212503.1,180583.0] || equal(complement(power_class(universal_class)),successor_relation)** -> .
% 299.82/300.43  185935[10:Res:185646.1,26.1] || equal(complement(complement(u)),successor_relation)** member(successor_relation,u) -> .
% 299.82/300.43  185801[10:Res:185430.1,30433.1] || equal(complement(complement(u)),successor_relation)** subclass(universal_class,u) -> .
% 299.82/300.43  185794[10:Res:185430.1,3888.0] || equal(complement(u),successor_relation)** equal(complement(u),universal_class) -> .
% 299.82/300.43  185628[10:Rew:113504.0,185432.1] || equal(complement(u),successor_relation) -> equal(symmetric_difference(universal_class,u),successor_relation)**.
% 299.82/300.43  185434[10:SpR:185302.1,183420.0] || equal(complement(u),successor_relation) -> equal(symmetric_difference(u,universal_class),successor_relation)**.
% 299.82/300.43  185433[10:SpR:185302.1,139600.0] || equal(complement(u),successor_relation) -> equal(intersection(u,universal_class),universal_class)**.
% 299.82/300.43  160799[10:Rew:160202.0,146412.1] || subclass(u,omega) -> equal(u,successor_relation) equal(integer_of(regular(u)),regular(u))**.
% 299.82/300.43  184637[10:SpR:163198.1,142543.0] || subclass(complement(u),successor_relation)* -> equal(symmetric_difference(universal_class,u),successor_relation).
% 299.82/300.43  212122[10:Res:8.1,212118.0] || equal(regular(kind_1_ordinals),ordinal_numbers)** -> equal(regular(kind_1_ordinals),successor_relation).
% 299.82/300.43  212118[10:Obv:212115.1] || subclass(regular(kind_1_ordinals),ordinal_numbers)* -> equal(regular(kind_1_ordinals),successor_relation).
% 299.82/300.43  212099[10:MRR:212088.2,184563.0] || member(regular(regular(kind_1_ordinals)),ordinal_numbers)* -> equal(regular(kind_1_ordinals),successor_relation).
% 299.82/300.43  163312[10:Rew:160202.0,160699.1] || member(regular(regular(u)),u)* -> equal(regular(u),successor_relation) equal(u,successor_relation).
% 299.82/300.43  212060[3:Res:184090.1,141576.1] || equal(symmetric_difference(universal_class,kind_1_ordinals),universal_class)** member(omega,ordinal_numbers) -> .
% 299.82/300.43  184090[2:SpL:142543.0,1510.0] || equal(symmetric_difference(universal_class,u),universal_class) -> member(omega,complement(u))*.
% 299.82/300.43  212004[11:Res:183759.1,185639.1] || subclass(inverse(successor_relation),u)* equal(successor_relation,u) -> .
% 299.82/300.43  161375[10:Rew:160202.0,146090.1] inductive(intersection(complement(u),complement(v))) || member(successor_relation,union(u,v))* -> .
% 299.82/300.43  212012[11:Res:183759.1,168466.0] || subclass(inverse(successor_relation),complement(inverse(successor_relation)))* -> .
% 299.82/300.43  183759[11:Res:183734.0,3.0] || subclass(inverse(successor_relation),u) -> member(regular(symmetrization_of(successor_relation)),u)*.
% 299.82/300.43  183456[10:SpR:57.0,183420.0] ||  -> equal(symmetric_difference(image(element_relation,complement(u)),complement(power_class(u))),successor_relation)**.
% 299.82/300.43  183453[10:SpR:160367.0,183420.0] ||  -> equal(symmetric_difference(symmetric_difference(universal_class,u),complement(union(u,successor_relation))),successor_relation)**.
% 299.82/300.43  9948[0:SpR:115.0,505.0] ||  -> equal(power_class(intersection(complement(u),complement(inverse(u)))),complement(image(element_relation,symmetrization_of(u))))**.
% 299.82/300.43  182324[11:Res:168384.1,160258.1] || equal(u,symmetrization_of(successor_relation))*+ equal(complement(u),universal_class)** -> .
% 299.82/300.43  182321[11:Res:179843.1,160258.1] || equal(u,inverse(successor_relation)) equal(complement(u),universal_class)** -> .
% 299.82/300.43  9949[0:SpR:45.0,505.0] ||  -> equal(power_class(intersection(complement(u),complement(singleton(u)))),complement(image(element_relation,successor(u))))**.
% 299.82/300.43  181213[10:SpL:181067.0,6210.0] || equal(u,singleton(singleton(successor_relation))) -> member(singleton(successor_relation),u)*.
% 299.82/300.43  211579[10:Res:89275.1,181153.0] ||  -> member(singleton(successor_relation),u) member(singleton(successor_relation),complement(u))*.
% 299.82/300.43  160705[10:Rew:160202.0,158100.2] || subclass(u,complement(kind_1_ordinals))* member(regular(u),ordinal_numbers) -> equal(u,successor_relation).
% 299.82/300.43  181153[10:Res:181060.0,3.0] || subclass(singleton(singleton(successor_relation)),u)* -> member(singleton(successor_relation),u).
% 299.82/300.43  161505[10:Rew:160202.0,146136.1] || member(regular(power_class(u)),image(element_relation,complement(u)))* -> equal(power_class(u),successor_relation).
% 299.82/300.43  211484[10:Res:192947.1,211446.0] || equal(complement(u),successor_relation) well_ordering(universal_class,u)* -> .
% 299.82/300.43  211448[10:Res:89275.1,181149.0] || well_ordering(universal_class,complement(u))* -> member(singleton(successor_relation),u).
% 299.82/300.43  211485[10:Res:114897.1,211446.0] || equal(u,universal_class) well_ordering(universal_class,u)* -> .
% 299.82/300.43  211513[10:MRR:211496.0,191.0] || well_ordering(universal_class,unordered_pair(u,singleton(successor_relation)))* -> .
% 299.82/300.43  157895[6:Res:1476.1,148657.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))*+ member(unordered_pair(u,v),element_relation)* -> .
% 299.82/300.43  211512[10:MRR:211495.0,191.0] || well_ordering(universal_class,unordered_pair(singleton(successor_relation),u))* -> .
% 299.82/300.43  211500[10:Res:1004.0,211446.0] || well_ordering(universal_class,ordered_pair(successor_relation,u))* -> .
% 299.82/300.43  211446[10:Res:6219.1,181149.0] || member(singleton(successor_relation),u)* well_ordering(universal_class,u) -> .
% 299.82/300.43  187490[10:MRR:163520.0,187489.0] || member(apply(choice,power_class(successor_relation)),image(element_relation,universal_class))* -> equal(power_class(successor_relation),successor_relation).
% 299.82/300.43  211450[10:Res:160272.1,181149.0] || well_ordering(universal_class,omega) -> equal(integer_of(singleton(successor_relation)),successor_relation)**.
% 299.82/300.43  211445[10:Res:314.0,181149.0] || well_ordering(universal_class,singleton(singleton(successor_relation)))* -> .
% 299.82/300.43  181149[10:Res:181060.0,6045.0] || subclass(singleton(singleton(successor_relation)),u)* well_ordering(universal_class,u) -> .
% 299.82/300.43  211297[10:SpR:181056.0,181073.0] ||  -> equal(unordered_pair(successor_relation,unordered_pair(universal_class,successor_relation)),ordered_pair(universal_class,universal_class))**.
% 299.82/300.43  181073[10:SpR:181056.0,15.0] ||  -> equal(unordered_pair(successor_relation,unordered_pair(universal_class,singleton(u))),ordered_pair(universal_class,u))**.
% 299.82/300.43  161257[10:Rew:160202.0,159919.1] one_to_one(image(successor_relation,cross_product(universal_class,universal_class))) || member(successor_relation,cross_product(universal_class,universal_class))* -> .
% 299.82/300.43  211275[13:Res:314.0,180584.0] || well_ordering(universal_class,image(element_relation,successor_relation))* -> .
% 299.82/300.43  180584[13:Res:180583.0,6045.0] || subclass(image(element_relation,successor_relation),u)* well_ordering(universal_class,u) -> .
% 299.82/300.43  211092[11:Res:160271.1,179992.1] inductive(u) || equal(complement(u),inverse(successor_relation))** -> .
% 299.82/300.43  211101[11:Res:206681.0,179992.1] || equal(complement(union(singleton(successor_relation),u)),inverse(successor_relation))** -> .
% 299.82/300.43  211100[11:Res:207189.0,179992.1] || equal(complement(union(u,singleton(successor_relation))),inverse(successor_relation))** -> .
% 299.82/300.43  211094[11:Res:206541.0,179992.1] || equal(complement(complement(complement(successor(successor_relation)))),inverse(successor_relation))** -> .
% 299.82/300.43  211109[11:MRR:211063.0,160214.0] || equal(complement(unordered_pair(u,successor_relation)),inverse(successor_relation))** -> .
% 299.82/300.43  211108[11:MRR:211062.0,160214.0] || equal(complement(unordered_pair(successor_relation,u)),inverse(successor_relation))** -> .
% 299.82/300.43  31076[2:Res:314.0,5832.1] inductive(u) || well_ordering(v,u) -> member(least(v,u),u)*.
% 299.82/300.43  211098[11:Res:181063.0,179992.1] || equal(complement(ordered_pair(universal_class,u)),inverse(successor_relation))** -> .
% 299.82/300.43  211079[11:Res:206684.0,179992.1] || equal(complement(successor(singleton(successor_relation))),inverse(successor_relation))** -> .
% 299.82/300.43  211077[11:Res:206682.0,179992.1] || equal(complement(symmetrization_of(singleton(successor_relation))),inverse(successor_relation))** -> .
% 299.82/300.43  211076[11:Res:168372.0,179992.1] || equal(complement(symmetrization_of(successor_relation)),inverse(successor_relation))** -> .
% 299.82/300.43  161445[10:Rew:160202.0,146069.1] || well_ordering(u,v) -> equal(v,successor_relation) member(least(u,v),v)*.
% 299.82/300.43  211106[13:Rew:160322.0,211082.0] || equal(power_class(universal_class),inverse(successor_relation))** -> .
% 299.82/300.43  211105[11:Rew:160328.0,211081.0] || equal(power_class(successor_relation),inverse(successor_relation))** -> .
% 299.82/300.43  211103[11:Res:206690.0,179992.1] || equal(complement(kind_1_ordinals),inverse(successor_relation))** -> .
% 299.82/300.43  211099[20:Res:191039.0,179992.1] || equal(complement(omega),inverse(successor_relation))** -> .
% 299.82/300.43  31282[0:Res:6.0,5829.0] || well_ordering(u,universal_class)+ -> subclass(v,w)* member(least(u,v),v)*.
% 299.82/300.43  179992[11:Res:179843.1,26.1] || equal(complement(u),inverse(successor_relation)) member(successor_relation,u)* -> .
% 299.82/300.43  211028[15:SpR:1005.0,210293.1] || subclass(rest_relation,domain_relation) -> member(singleton(singleton(singleton(successor_relation))),rest_relation)*.
% 299.82/300.43  211024[15:SpR:181056.0,210293.1] || subclass(rest_relation,domain_relation) -> member(ordered_pair(successor_relation,successor_relation),rest_relation)*.
% 299.82/300.43  210293[15:MRR:210261.1,191.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(singleton(u),successor_relation),rest_relation)*.
% 299.82/300.43  3492[0:Res:1476.1,595.0] || subclass(universal_class,restrict(u,v,w))*+ -> member(unordered_pair(x,y),u)*.
% 299.82/300.43  210318[12:Res:8.1,209469.0] || equal(cantor(complement(cross_product(singleton(regular(element_relation)),universal_class))),universal_class)** -> .
% 299.82/300.43  1504[0:Res:1006.0,3.0] || subclass(ordered_pair(u,v),w) -> member(unordered_pair(u,singleton(v)),w)*.
% 299.82/300.43  210209[15:MRR:210181.1,209309.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(regular(element_relation),successor_relation),rest_relation)*.
% 299.82/300.43  210174[15:MRR:210146.1,201216.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(regular(domain_relation),successor_relation),rest_relation)*.
% 299.82/300.43  210139[15:MRR:210111.1,199826.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(regular(rest_relation),successor_relation),rest_relation)*.
% 299.82/300.43  210899[15:MRR:210892.0,107556.2] || subclass(rest_relation,u) well_ordering(universal_class,u)* -> .
% 299.82/300.43  161502[10:Rew:160202.0,146072.1] || well_ordering(u,v) -> equal(segment(u,v,least(u,v)),successor_relation)**.
% 299.82/300.43  210104[15:MRR:210074.1,187489.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(power_class(successor_relation),successor_relation),rest_relation)*.
% 299.82/300.43  209905[15:Res:183757.0,189421.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(symmetrization_of(successor_relation))),successor_relation)**.
% 299.82/300.43  209786[15:Res:183757.0,189420.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(symmetrization_of(successor_relation))),successor_relation)**.
% 299.82/300.43  31069[2:Res:6.0,5832.1] inductive(u) || well_ordering(v,universal_class) -> member(least(v,u),u)*.
% 299.82/300.43  209680[12:Res:161493.2,209662.0] inductive(element_relation) ||  -> equal(integer_of(singleton(first(regular(element_relation)))),successor_relation)**.
% 299.82/300.43  209566[14:MRR:209543.1,209313.0] || equal(sum_class(range_of(first(regular(element_relation)))),second(regular(element_relation)))** -> .
% 299.82/300.43  210742[15:Res:8.1,210479.0] || equal(rotate(u),domain_relation)** equal(successor_relation,u) -> .
% 299.82/300.43  210739[15:Res:8.1,210401.0] || equal(flip(u),domain_relation)** equal(successor_relation,u) -> .
% 299.82/300.43  1486[0:Res:305.1,3.0] || member(u,universal_class) subclass(singleton(u),v)* -> member(u,v).
% 299.82/300.43  210479[15:Res:189564.1,185639.1] || subclass(domain_relation,rotate(u))* equal(successor_relation,u) -> .
% 299.82/300.43  210401[15:Res:189563.1,185639.1] || subclass(domain_relation,flip(u))* equal(successor_relation,u) -> .
% 299.82/300.43  210737[15:Res:8.1,210493.0] || equal(rotate(cross_product(universal_class,universal_class)),domain_relation)** -> .
% 299.82/300.43  210493[15:AED:1.0,210460.1] || subclass(domain_relation,rotate(cross_product(universal_class,universal_class)))* -> .
% 299.82/300.43  34429[0:MRR:1081.0,34189.1] ||  -> member(not_subclass_element(complement(complement(u)),v),u)* subclass(complement(complement(u)),v).
% 299.82/300.43  210632[15:Res:8.1,210492.0] || equal(rotate(rest_of(u)),domain_relation)** -> .
% 299.82/300.43  210618[15:Res:8.1,210491.0] || equal(rotate(compose_class(u)),domain_relation)** -> .
% 299.82/300.43  210492[15:AED:1.0,210455.1] || subclass(domain_relation,rotate(rest_of(u)))* -> .
% 299.82/300.43  210491[15:AED:1.0,210461.1] || subclass(domain_relation,rotate(compose_class(u)))* -> .
% 299.82/300.43  160804[10:Rew:160202.0,146007.1] || subclass(u,singleton(v))* -> equal(u,successor_relation) equal(regular(u),v).
% 299.82/300.43  210504[15:Res:8.1,210490.0] || equal(rotate(composition_function),domain_relation)** -> .
% 299.82/300.43  210502[15:Res:8.1,210489.0] || equal(rotate(domain_relation),domain_relation)** -> .
% 299.82/300.43  210500[15:Res:8.1,210488.0] || equal(rotate(rest_relation),domain_relation)** -> .
% 299.82/300.43  210498[15:Res:8.1,210446.0] || equal(rotate(successor_relation),domain_relation)** -> .
% 299.82/300.43  149475[6:Rew:149379.0,56491.1] || member(u,cantor(v))*+ subclass(universal_class,w)* -> member(u,w)*.
% 299.82/300.43  210490[15:AED:1.0,210467.1] || subclass(domain_relation,rotate(composition_function))* -> .
% 299.82/300.43  210489[15:AED:1.0,210477.1] || subclass(domain_relation,rotate(domain_relation))* -> .
% 299.82/300.43  210488[15:AED:1.0,210453.1] || subclass(domain_relation,rotate(rest_relation))* -> .
% 299.82/300.43  210446[15:Res:189564.1,160227.0] || subclass(domain_relation,rotate(successor_relation))* -> .
% 299.82/300.43  189564[15:Rew:189513.0,28144.1] || subclass(domain_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,successor_relation),w),u)*.
% 299.82/300.43  210414[15:Res:8.1,210409.0] || equal(flip(element_relation),domain_relation)** -> .
% 299.82/300.43  210412[15:Res:8.1,210373.0] || equal(flip(successor_relation),domain_relation)** -> .
% 299.82/300.43  210409[15:MRR:210389.1,160227.0] || subclass(domain_relation,flip(element_relation))* -> .
% 299.82/300.43  210373[15:Res:189563.1,160227.0] || subclass(domain_relation,flip(successor_relation))* -> .
% 299.82/300.43  189563[15:Rew:189513.0,28145.1] || subclass(domain_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,w),successor_relation),u)*.
% 299.82/300.43  209505[12:Res:8.1,209311.0] || equal(cross_product(universal_class,universal_class),ordinal_numbers) -> member(regular(element_relation),kind_1_ordinals)*.
% 299.82/300.43  209472[12:Res:209377.1,159.0] || subclass(universal_class,omega) -> equal(integer_of(regular(element_relation)),regular(element_relation))**.
% 299.82/300.43  209469[12:Res:209377.1,193819.0] || subclass(universal_class,cantor(complement(cross_product(singleton(regular(element_relation)),universal_class))))* -> .
% 299.82/300.43  209468[12:Res:209377.1,183723.0] || subclass(universal_class,symmetrization_of(successor_relation)) -> member(regular(element_relation),inverse(successor_relation))*.
% 299.82/300.43  143095[2:SSi:143068.1,52.0] inductive(u) || well_ordering(v,u)*+ -> member(least(v,omega),omega)*.
% 299.82/300.43  209451[12:Res:209377.1,141576.1] || subclass(universal_class,complement(kind_1_ordinals))* member(regular(element_relation),ordinal_numbers) -> .
% 299.82/300.43  209715[12:Res:8.1,209655.0] || equal(u,regular(element_relation)) well_ordering(universal_class,u)* -> .
% 299.82/300.43  209872[15:Res:191.0,189421.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(singleton(u)),successor_relation)**.
% 299.82/300.43  209753[15:Res:191.0,189420.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(singleton(u)),successor_relation)**.
% 299.82/300.43  3499[0:Res:1476.1,159.0] || subclass(universal_class,omega) -> equal(integer_of(unordered_pair(u,v)),unordered_pair(u,v))**.
% 299.82/300.43  209914[15:Res:209309.0,189421.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(element_relation)),successor_relation)**.
% 299.82/300.43  209912[15:Res:201216.0,189421.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(domain_relation)),successor_relation)**.
% 299.82/300.43  209910[15:Res:199826.0,189421.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(rest_relation)),successor_relation)**.
% 299.82/300.43  209878[15:Res:187489.0,189421.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(power_class(successor_relation)),successor_relation)**.
% 299.82/300.43  209831[15:MRR:209805.1,54.0] || equal(rest_relation,domain_relation) -> member(ordered_pair(omega,successor_relation),rest_relation)*.
% 299.82/300.43  209795[15:Res:209309.0,189420.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(element_relation)),successor_relation)**.
% 299.82/300.43  209793[15:Res:201216.0,189420.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(domain_relation)),successor_relation)**.
% 299.82/300.43  143798[4:MRR:143773.1,3094.0] || well_ordering(u,universal_class) -> equal(integer_of(least(u,omega)),least(u,omega))**.
% 299.82/300.43  209791[15:Res:199826.0,189420.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(rest_relation)),successor_relation)**.
% 299.82/300.43  209759[15:Res:187489.0,189420.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(power_class(successor_relation)),successor_relation)**.
% 299.82/300.43  209880[15:Res:160214.0,189421.0] || subclass(rest_relation,domain_relation)* -> equal(rest_of(successor_relation),successor_relation).
% 299.82/300.43  209879[15:Res:54.0,189421.0] || subclass(rest_relation,domain_relation)* -> equal(rest_of(omega),successor_relation).
% 299.82/300.43  189421[15:Rew:189339.1,28296.2] || member(u,universal_class)*+ subclass(rest_relation,domain_relation)* -> equal(rest_of(u),successor_relation).
% 299.82/300.43  209803[15:Res:8.1,209760.0] || equal(rest_relation,domain_relation) -> equal(rest_of(omega),successor_relation)**.
% 299.82/300.43  209760[15:Res:54.0,189420.0] || subclass(domain_relation,rest_relation)* -> equal(rest_of(omega),successor_relation).
% 299.82/300.43  209716[12:Res:314.0,209655.0] || well_ordering(universal_class,regular(element_relation))* -> .
% 299.82/300.43  189420[15:Rew:189339.1,28133.2] || member(u,universal_class)*+ subclass(domain_relation,rest_relation)* -> equal(rest_of(u),successor_relation).
% 299.82/300.43  209655[12:Res:209506.0,6045.0] || subclass(regular(element_relation),u)* well_ordering(universal_class,u) -> .
% 299.82/300.43  209701[12:Res:185430.1,209558.0] || equal(complement(complement(unordered_pair(u,regular(element_relation)))),successor_relation)** -> .
% 299.82/300.43  209693[12:Res:185430.1,209547.0] || equal(complement(complement(unordered_pair(regular(element_relation),u))),successor_relation)** -> .
% 299.82/300.43  209565[12:MRR:209544.1,209313.0] || equal(successor(first(regular(element_relation))),second(regular(element_relation)))** -> .
% 299.82/300.43  209558[12:SpL:209433.0,30584.0] || subclass(universal_class,complement(unordered_pair(u,regular(element_relation))))* -> .
% 299.82/300.43  209557[12:SpL:209433.0,30645.0] || equal(complement(unordered_pair(u,regular(element_relation))),universal_class)** -> .
% 299.82/300.43  209547[12:SpL:209433.0,30614.0] || subclass(universal_class,complement(unordered_pair(regular(element_relation),u)))* -> .
% 299.82/300.43  209546[12:SpL:209433.0,30656.0] || equal(complement(unordered_pair(regular(element_relation),u)),universal_class)** -> .
% 299.82/300.43  3836[0:Res:137.1,1322.1] inductive(sum_class(omega)) || member(omega,ordinal_numbers)* -> equal(sum_class(omega),omega).
% 299.82/300.43  209527[12:SpL:209433.0,185803.0] || equal(complement(complement(singleton(regular(element_relation)))),successor_relation)** -> .
% 299.82/300.43  209559[12:SpL:209433.0,188646.0] || equal(unordered_pair(u,regular(element_relation)),successor_relation)** -> .
% 299.82/300.43  209545[12:SpL:209433.0,188713.0] || equal(unordered_pair(regular(element_relation),u),successor_relation)** -> .
% 299.82/300.43  209662[12:MRR:209660.1,177130.0] || member(singleton(first(regular(element_relation))),element_relation)* -> .
% 299.82/300.43  5762[0:Res:64.1,5754.0] function(sum_class(cross_product(universal_class,universal_class))) ||  -> section(element_relation,cross_product(universal_class,universal_class),universal_class)*.
% 299.82/300.43  209526[12:SpL:209433.0,30556.0] || equal(complement(singleton(regular(element_relation))),universal_class)** -> .
% 299.82/300.43  209525[12:SpL:209433.0,30537.0] || subclass(universal_class,complement(singleton(regular(element_relation))))* -> .
% 299.82/300.43  209524[12:SpL:209433.0,185804.0] || equal(complement(complement(regular(element_relation))),successor_relation)** -> .
% 299.82/300.43  209506[12:SpR:209433.0,1004.0] ||  -> member(singleton(first(regular(element_relation))),regular(element_relation))*.
% 299.82/300.43  161676[10:Rew:160202.0,148481.1] || member(complement(omega),universal_class) -> equal(integer_of(apply(choice,complement(omega))),successor_relation)**.
% 299.82/300.43  209528[12:SpL:209433.0,185068.0] || subclass(singleton(regular(element_relation)),successor_relation)* -> .
% 299.82/300.43  209523[12:SpL:209433.0,3898.0] || equal(complement(regular(element_relation)),universal_class)** -> .
% 299.82/300.43  209522[12:SpL:209433.0,30448.0] || subclass(universal_class,complement(regular(element_relation)))* -> .
% 299.82/300.43  209540[12:SpL:209433.0,160313.0] || subclass(regular(element_relation),successor_relation)* -> .
% 299.82/300.43  204366[6:Rew:203192.0,203323.1] || member(u,cantor(u)) -> member(ordered_pair(u,cantor(u)),element_relation)*.
% 299.82/300.43  209539[12:SpL:209433.0,160315.0] || equal(regular(element_relation),successor_relation)** -> .
% 299.82/300.43  209433[12:Res:209313.0,19.0] ||  -> equal(ordered_pair(first(regular(element_relation)),second(regular(element_relation))),regular(element_relation))**.
% 299.82/300.43  209311[12:Res:159952.1,177133.0] || subclass(cross_product(universal_class,universal_class),ordinal_numbers)* -> member(regular(element_relation),kind_1_ordinals).
% 299.82/300.43  209377[12:Res:209309.0,3.0] || subclass(universal_class,u) -> member(regular(element_relation),u)*.
% 299.82/300.43  209379[12:Res:209309.0,163137.0] || equal(rest_of(regular(element_relation)),successor(regular(element_relation)))** -> .
% 299.82/300.43  209383[12:Res:209309.0,186157.0] || equal(singleton(regular(element_relation)),successor_relation)** -> .
% 299.82/300.43  209381[15:Res:209309.0,189419.0] || equal(successor(regular(element_relation)),successor_relation)** -> .
% 299.82/300.43  209313[12:Res:314.0,177133.0] ||  -> member(regular(element_relation),cross_product(universal_class,universal_class))*.
% 299.82/300.43  209380[15:Res:209309.0,193015.0] ||  -> equal(cantor(regular(element_relation)),successor_relation)**.
% 299.82/300.43  209309[12:Res:6.0,177133.0] ||  -> member(regular(element_relation),universal_class)*.
% 299.82/300.43  204942[10:Rew:203192.0,203333.3] || section(u,v,w) well_ordering(x,v) -> equal(cantor(restrict(u,w,v)),successor_relation) member(least(x,cantor(restrict(u,w,v))),cantor(restrict(u,w,v)))*.
% 299.82/300.43  177133[12:MRR:161680.1,177130.0] || subclass(cross_product(universal_class,universal_class),u)* -> member(regular(element_relation),u).
% 299.82/300.43  209285[9:Res:314.0,157925.0] || well_ordering(universal_class,image(element_relation,universal_class))* -> .
% 299.82/300.43  203275[6:Rew:203192.0,6043.0] || member(u,cantor(v)) equal(restrict(v,u,universal_class),least(rest_of(v),w))*+ member(u,w)* subclass(w,x)* well_ordering(rest_of(v),x)* -> .
% 299.82/300.43  157925[9:Res:157923.0,6045.0] || subclass(image(element_relation,universal_class),u)* well_ordering(universal_class,u) -> .
% 299.82/300.43  48083[0:Res:968.1,47745.0] || member(u,cantor(u))*+ subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.43  209153[20:Res:8.1,209135.1] || equal(complement(element_relation),universal_class) equal(rest_of(successor_relation),omega)** -> .
% 299.82/300.43  209149[10:Res:8.1,209134.1] || equal(complement(element_relation),universal_class) equal(rest_of(successor_relation),kind_1_ordinals)** -> .
% 299.82/300.43  209135[20:Res:191074.1,47888.0] || equal(rest_of(successor_relation),omega) subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.43  209134[10:Res:206947.1,47888.0] || equal(rest_of(successor_relation),kind_1_ordinals) subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.43  47888[0:Res:34085.1,3514.1] || member(u,rest_of(u))*+ subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.43  163218[10:Rew:160202.0,162774.1] ||  -> member(u,complement(singleton(successor_relation))) subclass(singleton(u),successor(successor_relation))*.
% 299.82/300.43  162872[10:Rew:160202.0,159725.0] || equal(u,singleton(successor_relation)) equal(complement(u),universal_class)** -> .
% 299.82/300.43  208945[10:Res:160271.1,163207.1] inductive(u) || equal(complement(u),singleton(successor_relation))** -> .
% 299.82/300.43  208954[10:Res:206681.0,163207.1] || equal(complement(union(singleton(successor_relation),u)),singleton(successor_relation))** -> .
% 299.82/300.43  208953[10:Res:207189.0,163207.1] || equal(complement(union(u,singleton(successor_relation))),singleton(successor_relation))** -> .
% 299.82/300.43  203332[10:Rew:203192.0,162529.2] || section(u,v,w) well_ordering(x,v) -> equal(segment(x,cantor(restrict(u,w,v)),least(x,cantor(restrict(u,w,v)))),successor_relation)**.
% 299.82/300.43  208947[10:Res:206541.0,163207.1] || equal(complement(complement(complement(successor(successor_relation)))),singleton(successor_relation))** -> .
% 299.82/300.43  208962[10:MRR:208916.0,160214.0] || equal(complement(unordered_pair(u,successor_relation)),singleton(successor_relation))** -> .
% 299.82/300.43  208961[10:MRR:208915.0,160214.0] || equal(complement(unordered_pair(successor_relation,u)),singleton(successor_relation))** -> .
% 299.82/300.43  208951[10:Res:181063.0,163207.1] || equal(complement(ordered_pair(universal_class,u)),singleton(successor_relation))** -> .
% 299.82/300.43  208932[10:Res:206684.0,163207.1] || equal(complement(successor(singleton(successor_relation))),singleton(successor_relation))** -> .
% 299.82/300.43  208930[10:Res:206682.0,163207.1] || equal(complement(symmetrization_of(singleton(successor_relation))),singleton(successor_relation))** -> .
% 299.82/300.43  208929[11:Res:168372.0,163207.1] || equal(complement(symmetrization_of(successor_relation)),singleton(successor_relation))** -> .
% 299.82/300.43  208959[13:Rew:160322.0,208935.0] || equal(power_class(universal_class),singleton(successor_relation))** -> .
% 299.82/300.43  208958[10:Rew:160328.0,208934.0] || equal(power_class(successor_relation),singleton(successor_relation))** -> .
% 299.82/300.43  208956[10:Res:206690.0,163207.1] || equal(complement(kind_1_ordinals),singleton(successor_relation))** -> .
% 299.82/300.43  208952[20:Res:191039.0,163207.1] || equal(complement(omega),singleton(successor_relation))** -> .
% 299.82/300.43  163207[10:Rew:160202.0,160559.0] || equal(complement(u),singleton(successor_relation)) member(successor_relation,u)* -> .
% 299.82/300.43  162918[10:Rew:160202.0,159724.0] || equal(u,successor(successor_relation)) equal(complement(u),universal_class)** -> .
% 299.82/300.43  183719[10:SpL:183391.0,5884.0] || equal(symmetrization_of(successor_relation),universal_class) -> member(singleton(u),inverse(successor_relation))*.
% 299.82/300.43  208845[10:SoR:208218.0,73.1] one_to_one(successor(singleton(successor_relation))) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.43  203276[6:Rew:203192.0,5916.0] || member(u,cantor(v)) equal(restrict(v,u,universal_class),w)*+ subclass(rest_of(v),x)* -> member(ordered_pair(u,w),x)*.
% 299.82/300.43  208841[10:SoR:208210.0,73.1] one_to_one(symmetrization_of(singleton(successor_relation))) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.43  161107[10:Rew:160202.0,159775.1] inductive(complement(inverse(identity_relation))) || equal(symmetrization_of(successor_relation),universal_class)** -> .
% 299.82/300.43  185442[10:SpR:185302.1,160336.0] || equal(complement(inverse(successor_relation)),successor_relation)** -> equal(symmetrization_of(successor_relation),universal_class).
% 299.82/300.43  208218[10:Res:64.1,206737.0] function(successor(singleton(successor_relation))) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.43  208210[10:Res:64.1,206723.0] function(symmetrization_of(singleton(successor_relation))) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.43  163188[10:Rew:160202.0,160335.1] || equal(symmetrization_of(successor_relation),universal_class) -> member(omega,inverse(successor_relation))*.
% 299.82/300.43  208825[21:Res:163171.1,208804.0] || equal(complement(inverse(successor_relation)),singleton(successor_relation))** -> .
% 299.82/300.43  208804[21:Spt:208802.0,207528.0,208779.0] || member(successor_relation,complement(inverse(successor_relation)))* -> .
% 299.82/300.43  208807[21:MRR:166945.1,208804.0] inductive(complement(symmetrization_of(successor_relation))) ||  -> .
% 299.82/300.43  208806[21:MRR:162978.1,208804.0] inductive(complement(symmetrization_of(identity_relation))) ||  -> .
% 299.82/300.43  208805[21:Spt:208802.0,207528.1] ||  -> subclass(successor(successor_relation),symmetrization_of(successor_relation))*.
% 299.82/300.43  206965[10:Res:206947.1,24.0] || equal(intersection(u,v),kind_1_ordinals)** -> member(successor_relation,v).
% 299.82/300.43  206964[10:Res:206947.1,23.0] || equal(intersection(u,v),kind_1_ordinals)** -> member(successor_relation,u).
% 299.82/300.43  208282[10:SpL:185605.1,208271.0] || equal(successor_relation,u) equal(power_class(u),kind_1_ordinals)** -> .
% 299.82/300.43  208257[10:Res:160268.1,206958.1] || equal(u,universal_class) equal(complement(u),kind_1_ordinals)** -> .
% 299.82/300.43  208251[20:Res:191074.1,206958.1] || equal(u,omega) equal(complement(u),kind_1_ordinals)** -> .
% 299.82/300.43  208250[10:Res:206947.1,206958.1] || equal(u,kind_1_ordinals) equal(complement(u),kind_1_ordinals)** -> .
% 299.82/300.43  206609[6:Res:64.1,203329.1] function(cantor(restrict(u,v,cross_product(universal_class,universal_class)))) || subclass(cross_product(universal_class,universal_class),v) -> section(u,cross_product(universal_class,universal_class),v)*.
% 299.82/300.43  208216[10:Res:8.1,206737.0] || equal(u,successor(singleton(successor_relation)))*+ -> member(successor_relation,u)*.
% 299.82/300.43  208208[10:Res:8.1,206723.0] || equal(u,symmetrization_of(singleton(successor_relation)))*+ -> member(successor_relation,u)*.
% 299.82/300.43  207378[10:SpL:30.0,207006.0] || equal(restrict(complement(singleton(successor_relation)),u,v),kind_1_ordinals)** -> .
% 299.82/300.43  204754[6:Rew:203192.0,203331.2] || section(u,v,w) subclass(v,cantor(restrict(u,w,v)))* -> equal(cantor(restrict(u,w,v)),v).
% 299.82/300.43  207285[10:SpL:30.0,206676.0] || equal(restrict(complement(singleton(successor_relation)),u,v),universal_class)** -> .
% 299.82/300.43  207260[20:SpL:30.0,206670.0] || equal(restrict(complement(singleton(successor_relation)),u,v),omega)** -> .
% 299.82/300.43  206997[10:Res:206947.1,160258.1] || equal(u,kind_1_ordinals) equal(complement(u),universal_class)** -> .
% 299.82/300.43  206996[20:Res:206947.1,191095.1] || equal(u,kind_1_ordinals) equal(complement(u),omega)** -> .
% 299.82/300.43  206962[10:Res:206947.1,183398.0] || equal(complement(complement(u)),kind_1_ordinals)** -> member(successor_relation,u).
% 299.82/300.43  208258[10:Res:160271.1,206958.1] inductive(u) || equal(complement(u),kind_1_ordinals)** -> .
% 299.82/300.43  208267[10:Res:206681.0,206958.1] || equal(complement(union(singleton(successor_relation),u)),kind_1_ordinals)** -> .
% 299.82/300.43  208266[10:Res:207189.0,206958.1] || equal(complement(union(u,singleton(successor_relation))),kind_1_ordinals)** -> .
% 299.82/300.43  208260[10:Res:206541.0,206958.1] || equal(complement(complement(complement(successor(successor_relation)))),kind_1_ordinals)** -> .
% 299.82/300.43  208275[10:MRR:208229.0,160214.0] || equal(complement(unordered_pair(u,successor_relation)),kind_1_ordinals)** -> .
% 299.82/300.43  208274[10:MRR:208228.0,160214.0] || equal(complement(unordered_pair(successor_relation,u)),kind_1_ordinals)** -> .
% 299.82/300.43  208264[10:Res:181063.0,206958.1] || equal(complement(ordered_pair(universal_class,u)),kind_1_ordinals)** -> .
% 299.82/300.43  208245[10:Res:206684.0,206958.1] || equal(complement(successor(singleton(successor_relation))),kind_1_ordinals)** -> .
% 299.82/300.43  208243[10:Res:206682.0,206958.1] || equal(complement(symmetrization_of(singleton(successor_relation))),kind_1_ordinals)** -> .
% 299.82/300.43  208242[11:Res:168372.0,206958.1] || equal(complement(symmetrization_of(successor_relation)),kind_1_ordinals)** -> .
% 299.82/300.43  208241[11:Res:168387.0,206958.1] || equal(complement(inverse(successor_relation)),kind_1_ordinals)** -> .
% 299.82/300.43  208272[13:Rew:160322.0,208248.0] || equal(power_class(universal_class),kind_1_ordinals)** -> .
% 299.82/300.43  208271[10:Rew:160328.0,208247.0] || equal(power_class(successor_relation),kind_1_ordinals)** -> .
% 299.82/300.43  208265[20:Res:191039.0,206958.1] || equal(complement(omega),kind_1_ordinals)** -> .
% 299.82/300.43  206958[10:Res:206947.1,26.1] || equal(complement(u),kind_1_ordinals) member(successor_relation,u)* -> .
% 299.82/300.43  206737[10:Res:206684.0,3.0] || subclass(successor(singleton(successor_relation)),u)* -> member(successor_relation,u).
% 299.82/300.43  206723[10:Res:206682.0,3.0] || subclass(symmetrization_of(singleton(successor_relation)),u)* -> member(successor_relation,u).
% 299.82/300.43  208204[10:Res:160271.1,206644.0] inductive(restrict(complement(singleton(successor_relation)),u,v)) ||  -> .
% 299.82/300.43  206644[10:SpL:30.0,206268.0] || member(successor_relation,restrict(complement(singleton(successor_relation)),u,v))* -> .
% 299.82/300.43  203268[10:Rew:203192.0,161323.1] || member(u,universal_class) -> member(u,cantor(v)) equal(second(not_subclass_element(successor_relation,successor_relation)),range__dfg(v,u,universal_class))*.
% 299.82/300.43  207205[11:Res:207189.0,168534.1] || equal(complement(union(u,singleton(successor_relation))),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  207204[10:Res:207189.0,163205.1] || equal(complement(union(u,singleton(successor_relation))),successor(successor_relation))** -> .
% 299.82/300.43  207196[10:SpR:511.0,207189.0] ||  -> member(successor_relation,complement(intersection(power_class(u),complement(singleton(successor_relation)))))*.
% 299.82/300.43  207184[11:Res:168384.1,206269.0] || equal(intersection(u,complement(singleton(successor_relation))),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  203334[6:Rew:203192.0,5751.0] || equal(cantor(restrict(u,v,w)),w)** subclass(w,v) -> section(u,w,v).
% 299.82/300.43  207182[10:Res:163171.1,206269.0] || equal(intersection(u,complement(singleton(successor_relation))),singleton(successor_relation))** -> .
% 299.82/300.43  207181[11:Res:179843.1,206269.0] || equal(intersection(u,complement(singleton(successor_relation))),inverse(successor_relation))** -> .
% 299.82/300.43  207180[10:Res:185646.1,206269.0] || equal(complement(intersection(u,complement(singleton(successor_relation)))),successor_relation)** -> .
% 299.82/300.43  206699[11:Res:206681.0,168534.1] || equal(complement(union(singleton(successor_relation),u)),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  206698[10:Res:206681.0,163205.1] || equal(complement(union(singleton(successor_relation),u)),successor(successor_relation))** -> .
% 299.82/300.43  206688[10:SpR:509.0,206681.0] ||  -> member(successor_relation,complement(intersection(complement(singleton(successor_relation)),power_class(u))))*.
% 299.82/300.43  206675[11:Res:168384.1,206268.0] || equal(intersection(complement(singleton(successor_relation)),u),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  206673[10:Res:163171.1,206268.0] || equal(intersection(complement(singleton(successor_relation)),u),singleton(successor_relation))** -> .
% 299.82/300.43  206672[11:Res:179843.1,206268.0] || equal(intersection(complement(singleton(successor_relation)),u),inverse(successor_relation))** -> .
% 299.82/300.43  206671[10:Res:185646.1,206268.0] || equal(complement(intersection(complement(singleton(successor_relation)),u)),successor_relation)** -> .
% 299.82/300.43  207702[10:SoR:207009.0,73.1] one_to_one(kind_1_ordinals) || subclass(cross_product(universal_class,universal_class),ordinal_numbers)* -> .
% 299.82/300.43  207009[10:MRR:160065.2,207008.0] function(kind_1_ordinals) || subclass(cross_product(universal_class,universal_class),ordinal_numbers)* -> .
% 299.82/300.43  206978[10:Res:206947.1,193819.0] || equal(cantor(complement(cross_product(singleton(successor_relation),universal_class))),kind_1_ordinals)** -> .
% 299.82/300.43  206589[11:Res:206541.0,168534.1] || equal(complement(complement(complement(successor(successor_relation)))),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  206588[10:Res:206541.0,163205.1] || equal(complement(complement(complement(successor(successor_relation)))),successor(successor_relation))** -> .
% 299.82/300.43  206988[10:Res:206947.1,185639.1] || equal(u,kind_1_ordinals)* equal(successor_relation,u) -> .
% 299.82/300.43  206987[10:Res:206947.1,2151.0] || equal(singleton(u),kind_1_ordinals)** -> equal(successor_relation,u).
% 299.82/300.43  207553[10:MRR:207552.0,143555.0] || subclass(kind_1_ordinals,successor_relation)* -> .
% 299.82/300.43  206707[10:Res:206690.0,6045.0] || subclass(kind_1_ordinals,u) well_ordering(universal_class,u)* -> .
% 299.82/300.43  206226[10:Obv:206214.0] ||  -> member(successor_relation,u) subclass(successor(successor_relation),complement(u))*.
% 299.82/300.43  207207[10:Res:207189.0,160258.1] || equal(complement(union(u,singleton(successor_relation))),universal_class)** -> .
% 299.82/300.43  207206[20:Res:207189.0,191095.1] || equal(complement(union(u,singleton(successor_relation))),omega)** -> .
% 299.82/300.43  207185[10:Res:160268.1,206269.0] || equal(intersection(u,complement(singleton(successor_relation))),universal_class)** -> .
% 299.82/300.43  207179[20:Res:191074.1,206269.0] || equal(intersection(u,complement(singleton(successor_relation))),omega)** -> .
% 299.82/300.43  207178[10:Res:206947.1,206269.0] || equal(intersection(u,complement(singleton(successor_relation))),kind_1_ordinals)** -> .
% 299.82/300.43  207006[10:Res:206947.1,206268.0] || equal(intersection(complement(singleton(successor_relation)),u),kind_1_ordinals)** -> .
% 299.82/300.43  206701[10:Res:206681.0,160258.1] || equal(complement(union(singleton(successor_relation),u)),universal_class)** -> .
% 299.82/300.43  206700[20:Res:206681.0,191095.1] || equal(complement(union(singleton(successor_relation),u)),omega)** -> .
% 299.82/300.43  206676[10:Res:160268.1,206268.0] || equal(intersection(complement(singleton(successor_relation)),u),universal_class)** -> .
% 299.82/300.43  206670[20:Res:191074.1,206268.0] || equal(intersection(complement(singleton(successor_relation)),u),omega)** -> .
% 299.82/300.43  207203[10:Res:207189.0,185639.1] || equal(union(u,singleton(successor_relation)),successor_relation)** -> .
% 299.82/300.43  207186[10:Res:160271.1,206269.0] inductive(intersection(u,complement(singleton(successor_relation)))) ||  -> .
% 299.82/300.43  207189[10:MRR:207175.0,160214.0] ||  -> member(successor_relation,union(u,singleton(successor_relation)))*.
% 299.82/300.43  206269[10:Res:206224.1,198710.0] || member(successor_relation,intersection(u,complement(singleton(successor_relation))))* -> .
% 299.82/300.43  207151[10:MRR:207144.1,160215.0] || equal(kind_1_ordinals,ordinal_numbers) -> section(element_relation,successor_relation,universal_class)*.
% 299.82/300.43  207103[10:SoR:206949.0,73.1] one_to_one(kind_1_ordinals) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.43  207004[10:Res:206947.1,163173.0] || equal(kind_1_ordinals,ordinal_numbers) -> equal(sum_class(successor_relation),successor_relation)**.
% 299.82/300.43  206949[10:Res:64.1,206711.0] function(kind_1_ordinals) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.43  206740[11:Res:206684.0,168534.1] || equal(complement(successor(singleton(successor_relation))),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  206739[10:Res:206684.0,163205.1] || equal(complement(successor(singleton(successor_relation))),successor(successor_relation))** -> .
% 299.82/300.43  206726[11:Res:206682.0,168534.1] || equal(complement(symmetrization_of(singleton(successor_relation))),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  206725[10:Res:206682.0,163205.1] || equal(complement(symmetrization_of(singleton(successor_relation))),successor(successor_relation))** -> .
% 299.82/300.43  207005[10:Res:206947.1,206267.0] || equal(symmetric_difference(universal_class,singleton(successor_relation)),kind_1_ordinals)** -> .
% 299.82/300.43  207008[10:MRR:206969.1,160315.0] || equal(cross_product(u,v),kind_1_ordinals)** -> .
% 299.82/300.43  207000[10:Res:206947.1,206271.0] || equal(complement(successor(successor_relation)),kind_1_ordinals)** -> .
% 299.82/300.43  204368[6:Rew:203335.0,149381.0] ||  -> equal(intersection(segment(u,v,w),universal_class),segment(u,v,w))**.
% 299.82/300.43  206999[10:Res:206947.1,183651.0] || equal(complement(singleton(successor_relation)),kind_1_ordinals)** -> .
% 299.82/300.43  206947[10:Res:8.1,206711.0] || equal(u,kind_1_ordinals) -> member(successor_relation,u)*.
% 299.82/300.43  206711[10:Res:206690.0,3.0] || subclass(kind_1_ordinals,u)* -> member(successor_relation,u).
% 299.82/300.43  206697[10:Res:206681.0,185639.1] || equal(union(singleton(successor_relation),u),successor_relation)** -> .
% 299.82/300.43  206677[10:Res:160271.1,206268.0] inductive(intersection(complement(singleton(successor_relation)),u)) ||  -> .
% 299.82/300.43  206742[10:Res:206684.0,160258.1] || equal(complement(successor(singleton(successor_relation))),universal_class)** -> .
% 299.82/300.43  206741[20:Res:206684.0,191095.1] || equal(complement(successor(singleton(successor_relation))),omega)** -> .
% 299.82/300.43  206728[10:Res:206682.0,160258.1] || equal(complement(symmetrization_of(singleton(successor_relation))),universal_class)** -> .
% 299.82/300.43  206727[20:Res:206682.0,191095.1] || equal(complement(symmetrization_of(singleton(successor_relation))),omega)** -> .
% 299.82/300.43  206780[10:Res:163149.1,206703.0] inductive(ordinal_numbers) ||  -> inductive(kind_1_ordinals)*.
% 299.82/300.43  206724[10:Res:206682.0,185639.1] || equal(symmetrization_of(singleton(successor_relation)),successor_relation)** -> .
% 299.82/300.43  206714[11:Res:206690.0,168534.1] || equal(symmetrization_of(successor_relation),complement(kind_1_ordinals))** -> .
% 299.82/300.43  203278[6:Rew:203192.0,145.0] || member(u,cantor(v)) equal(restrict(v,u,universal_class),w) -> member(ordered_pair(u,w),rest_of(v))*.
% 299.82/300.43  206713[10:Res:206690.0,163205.1] || equal(complement(kind_1_ordinals),successor(successor_relation))** -> .
% 299.82/300.43  206716[10:Res:206690.0,160258.1] || equal(complement(kind_1_ordinals),universal_class)** -> .
% 299.82/300.43  206715[20:Res:206690.0,191095.1] || equal(complement(kind_1_ordinals),omega)** -> .
% 299.82/300.43  206684[10:SpR:45.0,206681.0] ||  -> member(successor_relation,successor(singleton(successor_relation)))*.
% 299.82/300.43  206682[10:SpR:115.0,206681.0] ||  -> member(successor_relation,symmetrization_of(singleton(successor_relation)))*.
% 299.82/300.43  206690[10:SpR:163176.0,206681.0] ||  -> member(successor_relation,kind_1_ordinals)*.
% 299.82/300.43  206681[10:MRR:206667.0,160214.0] ||  -> member(successor_relation,union(singleton(successor_relation),u))*.
% 299.82/300.43  206268[10:Res:206224.1,198694.0] || member(successor_relation,intersection(complement(singleton(successor_relation)),u))* -> .
% 299.82/300.43  203269[15:Rew:203192.0,186274.0] || member(u,cantor(v)) member(ordered_pair(v,ordered_pair(u,w)),cross_product(universal_class,cross_product(universal_class,universal_class)))* -> .
% 299.82/300.43  206591[10:Res:206541.0,160258.1] || equal(complement(complement(complement(successor(successor_relation)))),universal_class)** -> .
% 299.82/300.43  206590[20:Res:206541.0,191095.1] || equal(complement(complement(complement(successor(successor_relation)))),omega)** -> .
% 299.82/300.43  203329[6:Rew:203192.0,135.1] || subclass(u,v) subclass(cantor(restrict(w,v,u)),u)* -> section(w,u,v).
% 299.82/300.43  206446[11:Res:168384.1,206267.0] || equal(symmetric_difference(universal_class,singleton(successor_relation)),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  206444[10:Res:163171.1,206267.0] || equal(symmetric_difference(universal_class,singleton(successor_relation)),singleton(successor_relation))** -> .
% 299.82/300.43  206443[11:Res:179843.1,206267.0] || equal(symmetric_difference(universal_class,singleton(successor_relation)),inverse(successor_relation))** -> .
% 299.82/300.43  206541[10:MRR:206526.0,206430.0] ||  -> member(successor_relation,complement(complement(successor(successor_relation))))*.
% 299.82/300.43  203271[10:Rew:203192.0,160347.1] || member(u,universal_class) -> member(u,cantor(v)) equal(restrict(v,singleton(u),universal_class),successor_relation)**.
% 299.82/300.43  206519[10:Res:206438.0,2151.0] ||  -> equal(regular(complement(complement(successor(successor_relation)))),successor_relation)**.
% 299.82/300.43  206272[20:MRR:206247.1,191039.0] inductive(successor(successor_relation)) ||  -> equal(successor(successor_relation),omega)**.
% 299.82/300.43  206447[10:Res:160268.1,206267.0] || equal(symmetric_difference(universal_class,singleton(successor_relation)),universal_class)** -> .
% 299.82/300.43  206441[20:Res:191074.1,206267.0] || equal(symmetric_difference(universal_class,singleton(successor_relation)),omega)** -> .
% 299.82/300.43  206431[11:Res:179843.1,206271.0] || equal(complement(successor(successor_relation)),inverse(successor_relation))** -> .
% 299.82/300.43  206430[10:Res:185646.1,206271.0] || equal(complement(complement(successor(successor_relation))),successor_relation)** -> .
% 299.82/300.43  203272[10:Rew:203192.0,160348.0] || member(u,cantor(v)) equal(restrict(v,singleton(u),universal_class),successor_relation)** -> .
% 299.82/300.43  206448[10:Res:160271.1,206267.0] inductive(symmetric_difference(universal_class,singleton(successor_relation))) ||  -> .
% 299.82/300.43  206267[10:Res:206224.1,195551.0] || member(successor_relation,symmetric_difference(universal_class,singleton(successor_relation)))* -> .
% 299.82/300.43  206271[10:Res:206224.1,198731.0] || member(successor_relation,complement(successor(successor_relation)))* -> .
% 299.82/300.43  206224[10:Obv:206216.1] || member(successor_relation,u) -> subclass(successor(successor_relation),u)*.
% 299.82/300.43  206225[10:Obv:206217.1] || member(successor_relation,ordinal_numbers) -> subclass(successor(successor_relation),kind_1_ordinals)*.
% 299.82/300.43  163222[10:Rew:160202.0,162886.1] ||  -> subclass(successor(successor_relation),u) equal(not_subclass_element(successor(successor_relation),u),successor_relation)**.
% 299.82/300.43  206082[10:Res:160271.1,163205.1] inductive(u) || equal(complement(u),successor(successor_relation))** -> .
% 299.82/300.43  203330[6:Rew:203192.0,134.1] || section(u,v,w) -> subclass(cantor(restrict(u,w,v)),v)*.
% 299.82/300.43  206098[10:MRR:206056.0,160214.0] || equal(complement(unordered_pair(u,successor_relation)),successor(successor_relation))** -> .
% 299.82/300.43  206097[10:MRR:206055.0,160214.0] || equal(complement(unordered_pair(successor_relation,u)),successor(successor_relation))** -> .
% 299.82/300.43  206085[10:Res:181063.0,163205.1] || equal(complement(ordered_pair(universal_class,u)),successor(successor_relation))** -> .
% 299.82/300.43  206069[11:Res:168372.0,163205.1] || equal(complement(symmetrization_of(successor_relation)),successor(successor_relation))** -> .
% 299.82/300.43  203335[6:Rew:203192.0,124.0] ||  -> equal(cantor(restrict(u,v,singleton(w))),segment(u,v,w))**.
% 299.82/300.43  206068[11:Res:168387.0,163205.1] || equal(complement(inverse(successor_relation)),successor(successor_relation))** -> .
% 299.82/300.43  206095[13:Rew:160322.0,206073.0] || equal(power_class(universal_class),successor(successor_relation))** -> .
% 299.82/300.43  206094[10:Rew:160328.0,206072.0] || equal(power_class(successor_relation),successor(successor_relation))** -> .
% 299.82/300.43  206091[20:Res:191039.0,163205.1] || equal(complement(omega),successor(successor_relation))** -> .
% 299.82/300.43  204365[6:Rew:203192.0,203265.1,203192.0,203265.1] || compatible(u,v,w)* -> equal(cantor(cantor(v)),cantor(u)).
% 299.82/300.43  163205[10:Rew:160202.0,160556.0] || equal(complement(u),successor(successor_relation)) member(successor_relation,u)* -> .
% 299.82/300.43  163071[10:Rew:160202.0,159394.1] || subclass(domain_relation,singleton(u))* -> equal(ordered_pair(successor_relation,successor_relation),u).
% 299.82/300.43  160970[10:Rew:160202.0,149934.1] ||  -> member(u,image(element_relation,universal_class)) subclass(singleton(u),power_class(successor_relation))*.
% 299.82/300.43  163210[10:Rew:160202.0,161105.0] ||  -> member(u,complement(inverse(successor_relation))) subclass(singleton(u),symmetrization_of(successor_relation))*.
% 299.82/300.43  203263[6:Rew:203192.0,143.1] || member(ordered_pair(u,v),rest_of(w))* -> member(u,cantor(w)).
% 299.82/300.43  205787[14:SpR:183965.0,205291.0] ||  -> equal(intersection(ordinal_add(u,v),universal_class),ordinal_add(u,v))**.
% 299.82/300.43  205791[10:SpR:160822.1,205291.0] ||  -> equal(singleton(u),successor_relation) equal(intersection(u,universal_class),u)**.
% 299.82/300.43  205291[6:SpR:70.0,204278.0] ||  -> equal(intersection(apply(u,v),universal_class),apply(u,v))**.
% 299.82/300.43  204482[6:Rew:44.0,204122.0] ||  -> equal(intersection(image(u,v),universal_class),image(u,v))**.
% 299.82/300.43  204364[6:Rew:203192.0,203259.1] || compatible(u,v,w)*+ -> subclass(range_of(u),cantor(cantor(w)))*.
% 299.82/300.43  205375[10:Rew:204281.0,205364.0] || equal(sum_class(u),successor_relation) -> subclass(sum_class(u),v)*.
% 299.82/300.43  205374[10:Rew:204281.0,205363.0] || equal(sum_class(u),successor_relation) -> asymmetric(sum_class(u),v)*.
% 299.82/300.43  205359[10:Rew:204209.0,205348.0] || equal(inverse(u),successor_relation) -> subclass(inverse(u),v)*.
% 299.82/300.43  205358[10:Rew:204209.0,205347.0] || equal(inverse(u),successor_relation) -> asymmetric(inverse(u),v)*.
% 299.82/300.43  203286[6:Rew:203192.0,101.1] || member(ordered_pair(u,v),domain_relation)* -> equal(cantor(u),v).
% 299.82/300.43  205036[10:Rew:203285.0,205026.0] || equal(range_of(u),successor_relation) -> subclass(range_of(u),v)*.
% 299.82/300.43  205035[10:Rew:203285.0,205025.0] || equal(range_of(u),successor_relation) -> asymmetric(range_of(u),v)*.
% 299.82/300.43  205288[6:SpR:204278.0,143590.0] ||  -> equal(symmetric_difference(sum_class(u),universal_class),symmetric_difference(universal_class,sum_class(u)))**.
% 299.82/300.43  205150[6:SpR:204206.0,143590.0] ||  -> equal(symmetric_difference(inverse(u),universal_class),symmetric_difference(universal_class,inverse(u)))**.
% 299.82/300.43  203287[6:Rew:203192.0,112.1] || maps(u,v,w)* -> equal(cantor(u),v).
% 299.82/300.43  204042[6:Rew:203285.0,150117.0] ||  -> equal(symmetric_difference(range_of(u),universal_class),symmetric_difference(universal_class,range_of(u)))**.
% 299.82/300.43  203302[6:Rew:203192.0,150036.0] ||  -> equal(symmetric_difference(cantor(u),universal_class),symmetric_difference(universal_class,cantor(u)))**.
% 299.82/300.43  204281[6:Rew:204278.0,149382.0] ||  -> equal(cantor(restrict(element_relation,universal_class,u)),sum_class(u))**.
% 299.82/300.43  204209[6:Rew:204206.0,149380.0] ||  -> equal(cantor(flip(cross_product(u,universal_class))),inverse(u))**.
% 299.82/300.43  204278[6:Rew:149382.0,203328.0] ||  -> equal(intersection(sum_class(u),universal_class),sum_class(u))**.
% 299.82/300.43  204038[6:Rew:203285.0,149383.0] ||  -> equal(intersection(range_of(u),universal_class),range_of(u))**.
% 299.82/300.43  204206[6:Rew:149380.0,203284.0] ||  -> equal(intersection(inverse(u),universal_class),inverse(u))**.
% 299.82/300.43  203301[6:Rew:203192.0,149386.0] ||  -> equal(intersection(cantor(u),universal_class),cantor(u))**.
% 299.82/300.43  203285[6:Rew:203192.0,41.0] ||  -> equal(cantor(inverse(u)),range_of(u))**.
% 299.82/300.43  203192[6:MRR:52835.0,203191.0] ||  -> equal(domain_of(u),cantor(u))**.
% 299.82/300.43  203125[11:Obv:203116.1] inductive(complement(inverse(successor_relation))) ||  -> .
% 299.82/300.43  202882[11:Res:160271.1,168534.1] inductive(u) || equal(complement(u),symmetrization_of(successor_relation))* -> .
% 299.82/300.43  202902[11:MRR:202856.0,160214.0] || equal(complement(unordered_pair(u,successor_relation)),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  202901[11:MRR:202855.0,160214.0] || equal(complement(unordered_pair(successor_relation,u)),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  202889[11:Res:181063.0,168534.1] || equal(complement(ordered_pair(universal_class,u)),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  202870[11:Res:160453.0,168534.1] || equal(complement(successor(successor_relation)),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  202899[13:Rew:160322.0,202873.0] || equal(symmetrization_of(successor_relation),power_class(universal_class))** -> .
% 299.82/300.43  202898[11:Rew:160328.0,202872.0] || equal(symmetrization_of(successor_relation),power_class(successor_relation))** -> .
% 299.82/300.43  202895[20:Res:191039.0,168534.1] || equal(symmetrization_of(successor_relation),complement(omega))** -> .
% 299.82/300.43  3487[0:Res:1476.1,23.0] || subclass(universal_class,intersection(u,v))*+ -> member(unordered_pair(w,x),u)*.
% 299.82/300.43  168534[11:Res:168384.1,26.1] || equal(complement(u),symmetrization_of(successor_relation)) member(successor_relation,u)* -> .
% 299.82/300.43  160827[10:Rew:160202.0,152611.0] ||  -> member(u,image(element_relation,successor_relation)) subclass(singleton(u),power_class(universal_class))*.
% 299.82/300.43  161194[10:Rew:160202.0,148452.0] ||  -> equal(intersection(union(u,successor_relation),universal_class),symmetric_difference(complement(u),universal_class))**.
% 299.82/300.43  3488[0:Res:1476.1,24.0] || subclass(universal_class,intersection(u,v))*+ -> member(unordered_pair(w,x),v)*.
% 299.82/300.43  202480[10:Obv:202479.1] || equal(rest_of(u),successor_relation)** -> equal(cantor(u),successor_relation).
% 299.82/300.43  161423[10:Rew:160202.0,146131.1] inductive(restrict(u,v,w)) ||  -> member(successor_relation,cross_product(v,w))*.
% 299.82/300.43  161360[10:Rew:160202.0,146087.1] || equal(complement(rest_of(u)),universal_class)** -> equal(cantor(u),successor_relation).
% 299.82/300.43  161386[10:Rew:160202.0,147226.1] inductive(complement(domain_of(u))) ||  -> member(successor_relation,complement(cantor(u)))*.
% 299.82/300.43  163217[10:Rew:160202.0,161412.0] ||  -> member(successor_relation,image(element_relation,complement(u)))* member(successor_relation,power_class(u)).
% 299.82/300.43  163225[10:Rew:160202.0,162982.1] ||  -> member(successor_relation,symmetric_difference(universal_class,u))* member(successor_relation,union(u,successor_relation)).
% 299.82/300.43  3486[0:Res:1476.1,26.1] || subclass(universal_class,complement(u)) member(unordered_pair(v,w),u)* -> .
% 299.82/300.43  163032[10:Rew:160202.0,158501.0] ||  -> equal(union(intersection(u,universal_class),successor_relation),complement(symmetric_difference(u,universal_class)))**.
% 299.82/300.43  163107[10:Rew:160202.0,159388.1] || subclass(domain_relation,compose_class(u))* -> equal(compose(u,successor_relation),successor_relation).
% 299.82/300.43  157623[0:Res:9395.0,1322.1] inductive(intersection(u,omega)) ||  -> equal(intersection(u,omega),omega)**.
% 299.82/300.43  157616[0:Res:9509.0,1322.1] inductive(intersection(omega,u)) ||  -> equal(intersection(omega,u),omega)**.
% 299.82/300.43  155765[2:Rew:142543.0,155700.0,142542.0,155700.0] ||  -> equal(symmetric_difference(universal_class,symmetric_difference(universal_class,u)),symmetric_difference(complement(u),universal_class))**.
% 299.82/300.43  202189[10:MRR:202185.2,185111.0] || equal(domain_relation,omega) subclass(universal_class,omega)* -> .
% 299.82/300.43  34085[0:MRR:28322.0,34067.1] || member(u,rest_of(u)) -> member(ordered_pair(u,rest_of(u)),element_relation)*.
% 299.82/300.43  202033[10:Res:161492.2,181220.0] || equal(domain_relation,omega) -> equal(integer_of(singleton(singleton(successor_relation))),successor_relation)**.
% 299.82/300.43  202174[10:MRR:202171.2,185111.0] || equal(rest_relation,omega) subclass(universal_class,omega)* -> .
% 299.82/300.43  202032[10:Res:161492.2,181130.0] || equal(rest_relation,omega) -> equal(integer_of(singleton(singleton(successor_relation))),successor_relation)**.
% 299.82/300.43  202001[10:Res:161492.2,489.0] || equal(omega,ordinal_numbers) -> equal(integer_of(intersection(y__dfg,ordinal_numbers)),successor_relation)**.
% 299.82/300.43  202000[10:Res:161492.2,9563.0] || equal(omega,ordinal_numbers) -> equal(integer_of(y__dfg),successor_relation)**.
% 299.82/300.43  201999[10:Res:161492.2,9449.0] || equal(omega,ordinal_numbers) -> equal(integer_of(ordinal_numbers),successor_relation)**.
% 299.82/300.43  161492[10:Rew:160202.0,158055.1] || equal(u,omega) -> equal(integer_of(v),successor_relation) member(v,u)*.
% 299.82/300.43  201821[10:MRR:201816.1,314.0] || equal(cantor(complement(cross_product(singleton(regular(domain_relation)),universal_class))),universal_class)** -> .
% 299.82/300.43  184006[14:MRR:183985.2,160227.0] || member(u,universal_class) equal(sum_class(range_of(u)),rest_of(u))** -> .
% 299.82/300.43  201648[10:Res:161493.2,201590.0] inductive(domain_relation) ||  -> equal(integer_of(singleton(first(regular(domain_relation)))),successor_relation)**.
% 299.82/300.43  201546[14:MRR:201524.1,201221.0] || equal(sum_class(range_of(first(regular(domain_relation)))),second(regular(domain_relation)))** -> .
% 299.82/300.43  201474[6:Res:8.1,201219.0] || equal(cross_product(universal_class,universal_class),ordinal_numbers) -> member(regular(domain_relation),kind_1_ordinals)*.
% 299.82/300.43  201398[6:Res:201231.1,159.0] || subclass(universal_class,omega) -> equal(integer_of(regular(domain_relation)),regular(domain_relation))**.
% 299.82/300.43  1012[0:SpL:1005.0,21.0] || member(singleton(singleton(singleton(u))),element_relation)*+ -> member(singleton(u),u)*.
% 299.82/300.43  201396[10:Res:201231.1,193819.0] || subclass(universal_class,cantor(complement(cross_product(singleton(regular(domain_relation)),universal_class))))* -> .
% 299.82/300.43  201390[10:Res:201231.1,183723.0] || subclass(universal_class,symmetrization_of(successor_relation)) -> member(regular(domain_relation),inverse(successor_relation))*.
% 299.82/300.43  201374[6:Res:201231.1,141576.1] || subclass(universal_class,complement(kind_1_ordinals))* member(regular(domain_relation),ordinal_numbers) -> .
% 299.82/300.43  160568[10:Rew:160202.0,145991.2] inductive(sum_class(u)) || member(u,ordinal_numbers)* -> member(successor_relation,u)*.
% 299.82/300.43  201788[6:Res:8.1,201583.0] || equal(u,regular(domain_relation)) well_ordering(universal_class,u)* -> .
% 299.82/300.43  201789[6:Res:314.0,201583.0] || well_ordering(universal_class,regular(domain_relation))* -> .
% 299.82/300.43  163228[10:Rew:160202.0,160548.2] inductive(regular(u)) || member(successor_relation,u)* -> equal(u,successor_relation).
% 299.82/300.43  201583[6:Res:201484.0,6045.0] || subclass(regular(domain_relation),u)* well_ordering(universal_class,u) -> .
% 299.82/300.43  201695[10:Res:185430.1,201540.0] || equal(complement(complement(unordered_pair(u,regular(domain_relation)))),successor_relation)** -> .
% 299.82/300.43  201665[10:Res:185430.1,201528.0] || equal(complement(complement(unordered_pair(regular(domain_relation),u))),successor_relation)** -> .
% 299.82/300.43  201545[10:MRR:201525.1,201221.0] || equal(successor(first(regular(domain_relation))),second(regular(domain_relation)))** -> .
% 299.82/300.43  161419[10:Rew:160202.0,146130.1] ||  -> member(regular(complement(complement(u))),u)* equal(complement(complement(u)),successor_relation).
% 299.82/300.43  201540[6:SpL:201355.0,30584.0] || subclass(universal_class,complement(unordered_pair(u,regular(domain_relation))))* -> .
% 299.82/300.43  201539[6:SpL:201355.0,30645.0] || equal(complement(unordered_pair(u,regular(domain_relation))),universal_class)** -> .
% 299.82/300.43  201678[10:Res:201671.0,160435.1] inductive(complement(kind_1_ordinals)) ||  -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.43  201671[3:Obv:201669.0] ||  -> subclass(complement(kind_1_ordinals),complement(ordinal_numbers))*.
% 299.82/300.43  155787[3:Res:4.1,141576.1] || member(not_subclass_element(complement(kind_1_ordinals),u),ordinal_numbers)* -> subclass(complement(kind_1_ordinals),u).
% 299.82/300.43  201528[6:SpL:201355.0,30614.0] || subclass(universal_class,complement(unordered_pair(regular(domain_relation),u)))* -> .
% 299.82/300.43  201527[6:SpL:201355.0,30656.0] || equal(complement(unordered_pair(regular(domain_relation),u)),universal_class)** -> .
% 299.82/300.43  201506[10:SpL:201355.0,185803.0] || equal(complement(complement(singleton(regular(domain_relation)))),successor_relation)** -> .
% 299.82/300.43  201541[10:SpL:201355.0,188646.0] || equal(unordered_pair(u,regular(domain_relation)),successor_relation)** -> .
% 299.82/300.43  155791[3:Res:1476.1,141576.1] || subclass(universal_class,complement(kind_1_ordinals)) member(unordered_pair(u,v),ordinal_numbers)* -> .
% 299.82/300.43  201526[10:SpL:201355.0,188713.0] || equal(unordered_pair(regular(domain_relation),u),successor_relation)** -> .
% 299.82/300.43  201590[10:MRR:201588.1,159406.0] || member(singleton(first(regular(domain_relation))),domain_relation)* -> .
% 299.82/300.43  201505[6:SpL:201355.0,30556.0] || equal(complement(singleton(regular(domain_relation))),universal_class)** -> .
% 299.82/300.43  201504[6:SpL:201355.0,30537.0] || subclass(universal_class,complement(singleton(regular(domain_relation))))* -> .
% 299.82/300.43  201503[10:SpL:201355.0,185804.0] || equal(complement(complement(regular(domain_relation))),successor_relation)** -> .
% 299.82/300.43  201484[6:SpR:201355.0,1004.0] ||  -> member(singleton(first(regular(domain_relation))),regular(domain_relation))*.
% 299.82/300.43  201507[10:SpL:201355.0,185068.0] || subclass(singleton(regular(domain_relation)),successor_relation)* -> .
% 299.82/300.43  201502[6:SpL:201355.0,3898.0] || equal(complement(regular(domain_relation)),universal_class)** -> .
% 299.82/300.43  201501[6:SpL:201355.0,30448.0] || subclass(universal_class,complement(regular(domain_relation)))* -> .
% 299.82/300.43  201520[10:SpL:201355.0,160313.0] || subclass(regular(domain_relation),successor_relation)* -> .
% 299.82/300.43  201519[10:SpL:201355.0,160315.0] || equal(regular(domain_relation),successor_relation)** -> .
% 299.82/300.43  201355[6:Res:201221.0,19.0] ||  -> equal(ordered_pair(first(regular(domain_relation)),second(regular(domain_relation))),regular(domain_relation))**.
% 299.82/300.43  201219[6:Res:159952.1,154493.0] || subclass(cross_product(universal_class,universal_class),ordinal_numbers)* -> member(regular(domain_relation),kind_1_ordinals).
% 299.82/300.43  161261[10:Rew:160202.0,146074.2] function(u) inductive(u) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.43  201231[6:Res:201216.0,3.0] || subclass(universal_class,u) -> member(regular(domain_relation),u)*.
% 299.82/300.43  161414[10:Rew:160202.0,146124.1] inductive(image(element_relation,complement(u))) || member(successor_relation,power_class(u))* -> .
% 299.82/300.43  201233[10:Res:201216.0,163137.0] || equal(rest_of(regular(domain_relation)),successor(regular(domain_relation)))** -> .
% 299.82/300.43  201238[10:Res:201216.0,186157.0] || equal(singleton(regular(domain_relation)),successor_relation)** -> .
% 299.82/300.43  161498[10:Rew:160202.0,148147.0] ||  -> equal(integer_of(not_subclass_element(complement(omega),u)),successor_relation)** subclass(complement(omega),u).
% 299.82/300.43  201235[15:Res:201216.0,189419.0] || equal(successor(regular(domain_relation)),successor_relation)** -> .
% 299.82/300.43  201221[6:Res:314.0,154493.0] ||  -> member(regular(domain_relation),cross_product(universal_class,universal_class))*.
% 299.82/300.43  201234[15:Res:201216.0,193015.0] ||  -> equal(cantor(regular(domain_relation)),successor_relation)**.
% 299.82/300.43  186271[15:MRR:186246.2,160227.0] inductive(application_function) || well_ordering(u,cross_product(universal_class,cross_product(universal_class,universal_class)))* -> .
% 299.82/300.43  201216[6:Res:6.0,154493.0] ||  -> member(regular(domain_relation),universal_class)*.
% 299.82/300.43  154493[6:MRR:148189.1,154490.0] || subclass(cross_product(universal_class,universal_class),u)* -> member(regular(domain_relation),u).
% 299.82/300.43  161403[10:Rew:160202.0,146111.1] inductive(flip(u)) ||  -> member(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class))*.
% 299.82/300.43  201133[10:MRR:201128.1,314.0] || equal(cantor(complement(cross_product(singleton(regular(rest_relation)),universal_class))),universal_class)** -> .
% 299.82/300.43  161402[10:Rew:160202.0,146112.1] inductive(rotate(u)) ||  -> member(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class))*.
% 299.82/300.43  200789[10:Res:161493.2,184528.0] inductive(complement(kind_1_ordinals)) ||  -> equal(integer_of(not_subclass_element(ordinal_numbers,successor_relation)),successor_relation)**.
% 299.82/300.43  200765[10:Res:161493.2,200393.0] inductive(rest_relation) ||  -> equal(integer_of(singleton(first(regular(rest_relation)))),successor_relation)**.
% 299.82/300.43  157982[6:Res:136.1,154494.0] || member(cross_product(universal_class,universal_class),ordinal_numbers)* -> member(least(element_relation,domain_relation),domain_relation).
% 299.82/300.43  200731[10:Res:161493.2,160407.0] inductive(singleton(successor_relation)) ||  -> equal(integer_of(intersection(y__dfg,ordinal_numbers)),successor_relation)**.
% 299.82/300.43  200582[11:Res:183757.0,163137.0] || equal(rest_of(regular(symmetrization_of(successor_relation))),successor(regular(symmetrization_of(successor_relation))))** -> .
% 299.82/300.43  200302[14:MRR:200280.1,199831.0] || equal(sum_class(range_of(first(regular(rest_relation)))),second(regular(rest_relation)))** -> .
% 299.82/300.43  2152[0:Res:4.1,2151.0] ||  -> subclass(singleton(u),v) equal(not_subclass_element(singleton(u),v),u)**.
% 299.82/300.43  200239[6:Res:8.1,199829.0] || equal(cross_product(universal_class,universal_class),ordinal_numbers) -> member(regular(rest_relation),kind_1_ordinals)*.
% 299.82/300.43  200008[6:Res:199848.1,159.0] || subclass(universal_class,omega) -> equal(integer_of(regular(rest_relation)),regular(rest_relation))**.
% 299.82/300.43  200006[10:Res:199848.1,193819.0] || subclass(universal_class,cantor(complement(cross_product(singleton(regular(rest_relation)),universal_class))))* -> .
% 299.82/300.43  51387[0:MRR:33635.0,6.0] ||  -> member(not_subclass_element(u,complement(v)),v)* subclass(u,complement(v)).
% 299.82/300.43  200000[10:Res:199848.1,183723.0] || subclass(universal_class,symmetrization_of(successor_relation)) -> member(regular(rest_relation),inverse(successor_relation))*.
% 299.82/300.43  199984[6:Res:199848.1,141576.1] || subclass(universal_class,complement(kind_1_ordinals))* member(regular(rest_relation),ordinal_numbers) -> .
% 299.82/300.43  200934[10:Res:200802.1,160357.0] || equal(cantor(u),successor_relation) -> subclass(cantor(u),v)*.
% 299.82/300.43  200933[10:Res:200802.1,184766.0] || equal(cantor(u),successor_relation) -> asymmetric(cantor(u),v)*.
% 299.82/300.43  200643[6:Res:8.1,200386.0] || equal(u,regular(rest_relation)) well_ordering(universal_class,u)* -> .
% 299.82/300.43  161247[10:Rew:160202.0,146050.2] inductive(u) || equal(v,u)*+ -> member(successor_relation,v)*.
% 299.82/300.43  200764[10:Res:161493.2,181220.0] inductive(domain_relation) ||  -> equal(integer_of(singleton(singleton(successor_relation))),successor_relation)**.
% 299.82/300.43  200763[10:Res:161493.2,181130.0] inductive(rest_relation) ||  -> equal(integer_of(singleton(singleton(successor_relation))),successor_relation)**.
% 299.82/300.43  200736[10:Res:161493.2,489.0] inductive(ordinal_numbers) ||  -> equal(integer_of(intersection(y__dfg,ordinal_numbers)),successor_relation)**.
% 299.82/300.43  161378[10:Rew:160202.0,146091.1] inductive(symmetric_difference(u,v)) ||  -> member(successor_relation,union(u,v))*.
% 299.82/300.43  200735[10:Res:161493.2,9563.0] inductive(ordinal_numbers) ||  -> equal(integer_of(y__dfg),successor_relation)**.
% 299.82/300.43  200734[10:Res:161493.2,9449.0] inductive(ordinal_numbers) ||  -> equal(integer_of(ordinal_numbers),successor_relation)**.
% 299.82/300.43  200644[6:Res:314.0,200386.0] || well_ordering(universal_class,regular(rest_relation))* -> .
% 299.82/300.43  161493[10:Rew:160202.0,158057.1] inductive(u) ||  -> equal(integer_of(v),successor_relation) member(v,u)*.
% 299.82/300.43  200386[6:Res:200240.0,6045.0] || subclass(regular(rest_relation),u)* well_ordering(universal_class,u) -> .
% 299.82/300.43  200519[10:Res:185430.1,200296.0] || equal(complement(complement(unordered_pair(u,regular(rest_relation)))),successor_relation)** -> .
% 299.82/300.43  200511[10:Res:185430.1,200284.0] || equal(complement(complement(unordered_pair(regular(rest_relation),u))),successor_relation)** -> .
% 299.82/300.43  200550[10:Res:191.0,163137.0] || equal(rest_of(singleton(u)),successor(singleton(u)))** -> .
% 299.82/300.43  200586[10:Res:199826.0,163137.0] || equal(rest_of(regular(rest_relation)),successor(regular(rest_relation)))** -> .
% 299.82/300.43  200556[10:Res:187489.0,163137.0] || equal(rest_of(power_class(successor_relation)),successor(power_class(successor_relation)))** -> .
% 299.82/300.43  200558[10:Res:160214.0,163137.0] || equal(rest_of(successor_relation),successor(successor_relation))** -> .
% 299.82/300.43  200557[10:Res:54.0,163137.0] || equal(rest_of(omega),successor(omega))** -> .
% 299.82/300.43  163137[10:MRR:28323.2,160227.0] || member(u,universal_class)* equal(rest_of(u),successor(u)) -> .
% 299.82/300.43  200301[10:MRR:200281.1,199831.0] || equal(successor(first(regular(rest_relation))),second(regular(rest_relation)))** -> .
% 299.82/300.43  200296[6:SpL:199964.0,30584.0] || subclass(universal_class,complement(unordered_pair(u,regular(rest_relation))))* -> .
% 299.82/300.43  200295[6:SpL:199964.0,30645.0] || equal(complement(unordered_pair(u,regular(rest_relation))),universal_class)** -> .
% 299.82/300.43  200284[6:SpL:199964.0,30614.0] || subclass(universal_class,complement(unordered_pair(regular(rest_relation),u)))* -> .
% 299.82/300.43  200283[6:SpL:199964.0,30656.0] || equal(complement(unordered_pair(regular(rest_relation),u)),universal_class)** -> .
% 299.82/300.43  200262[10:SpL:199964.0,185803.0] || equal(complement(complement(singleton(regular(rest_relation)))),successor_relation)** -> .
% 299.82/300.43  200297[10:SpL:199964.0,188646.0] || equal(unordered_pair(u,regular(rest_relation)),successor_relation)** -> .
% 299.82/300.43  200282[10:SpL:199964.0,188713.0] || equal(unordered_pair(regular(rest_relation),u),successor_relation)** -> .
% 299.82/300.43  160822[10:Rew:160202.0,146036.0] ||  -> equal(singleton(u),successor_relation) equal(apply(choice,singleton(u)),u)**.
% 299.82/300.43  200393[10:MRR:200391.1,160372.0] || member(singleton(first(regular(rest_relation))),rest_relation)* -> .
% 299.82/300.43  200261[6:SpL:199964.0,30556.0] || equal(complement(singleton(regular(rest_relation))),universal_class)** -> .
% 299.82/300.43  200260[6:SpL:199964.0,30537.0] || subclass(universal_class,complement(singleton(regular(rest_relation))))* -> .
% 299.82/300.43  200259[10:SpL:199964.0,185804.0] || equal(complement(complement(regular(rest_relation))),successor_relation)** -> .
% 299.82/300.43  200240[6:SpR:199964.0,1004.0] ||  -> member(singleton(first(regular(rest_relation))),regular(rest_relation))*.
% 299.82/300.43  200263[10:SpL:199964.0,185068.0] || subclass(singleton(regular(rest_relation)),successor_relation)* -> .
% 299.82/300.43  200258[6:SpL:199964.0,3898.0] || equal(complement(regular(rest_relation)),universal_class)** -> .
% 299.82/300.43  200257[6:SpL:199964.0,30448.0] || subclass(universal_class,complement(regular(rest_relation)))* -> .
% 299.82/300.43  200276[10:SpL:199964.0,160313.0] || subclass(regular(rest_relation),successor_relation)* -> .
% 299.82/300.43  200275[10:SpL:199964.0,160315.0] || equal(regular(rest_relation),successor_relation)** -> .
% 299.82/300.43  199964[6:Res:199831.0,19.0] ||  -> equal(ordered_pair(first(regular(rest_relation)),second(regular(rest_relation))),regular(rest_relation))**.
% 299.82/300.43  199829[6:Res:159952.1,153518.0] || subclass(cross_product(universal_class,universal_class),ordinal_numbers)* -> member(regular(rest_relation),kind_1_ordinals).
% 299.82/300.43  163146[10:MRR:34964.2,160227.0] || member(u,universal_class) equal(successor(singleton(u)),u)** -> .
% 299.82/300.43  200028[14:Res:160362.0,199972.0] || member(u,universal_class) -> equal(singleton(range_of(u)),successor_relation)**.
% 299.82/300.43  200027[14:Res:160274.1,199972.0] || member(u,universal_class) -> equal(integer_of(range_of(u)),successor_relation)**.
% 299.82/300.43  189548[15:Rew:189512.0,1014.1] || member(singleton(singleton(singleton(u))),domain_relation)* -> equal(successor_relation,u).
% 299.82/300.43  199972[14:Res:56.1,184789.0] || member(range_of(u),universal_class)* member(u,universal_class) -> .
% 299.82/300.43  199848[6:Res:199826.0,3.0] || subclass(universal_class,u) -> member(regular(rest_relation),u)*.
% 299.82/300.43  189423[15:Rew:189339.1,184883.1] || member(u,universal_class) equal(sum_class(range_of(u)),successor_relation)** -> .
% 299.82/300.43  199854[10:Res:199826.0,186157.0] || equal(singleton(regular(rest_relation)),successor_relation)** -> .
% 299.82/300.43  199851[15:Res:199826.0,189419.0] || equal(successor(regular(rest_relation)),successor_relation)** -> .
% 299.82/300.43  184789[14:EqR:184008.2] || member(sum_class(range_of(u)),universal_class)* member(u,universal_class) -> .
% 299.82/300.43  199831[6:Res:314.0,153518.0] ||  -> member(regular(rest_relation),cross_product(universal_class,universal_class))*.
% 299.82/300.43  199850[15:Res:199826.0,193015.0] ||  -> equal(cantor(regular(rest_relation)),successor_relation)**.
% 299.82/300.43  199826[6:Res:6.0,153518.0] ||  -> member(regular(rest_relation),universal_class)*.
% 299.82/300.43  161328[10:Rew:160202.0,156321.1] single_valued_class(u) ||  -> equal(second(not_subclass_element(successor_relation,successor_relation)),single_valued2(u))*.
% 299.82/300.43  153518[6:MRR:148190.1,153514.0] || subclass(cross_product(universal_class,universal_class),u)* -> member(regular(rest_relation),u).
% 299.82/300.43  100984[2:Res:2457.1,31448.0] inductive(cantor(u)) || equal(complement(rest_of(u)),universal_class)** -> .
% 299.82/300.43  2650[0:Res:1477.1,159.0] || subclass(universal_class,omega) -> equal(integer_of(singleton(u)),singleton(u))**.
% 299.82/300.43  161327[10:Rew:160202.0,156356.1] function(u) ||  -> equal(second(not_subclass_element(successor_relation,successor_relation)),single_valued2(u))*.
% 299.82/300.43  194074[10:Res:1477.1,193819.0] || subclass(universal_class,cantor(complement(cross_product(singleton(singleton(u)),universal_class))))* -> .
% 299.82/300.43  194072[10:Res:114897.1,193819.0] || equal(cantor(complement(cross_product(singleton(singleton(u)),universal_class))),universal_class)** -> .
% 299.82/300.43  161262[10:Rew:160202.0,146075.1] inductive(compose(u,v)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.43  199779[10:Res:107387.1,199761.0] || subclass(universal_class,cantor(complement(cross_product(singleton(successor_relation),universal_class))))* -> .
% 299.82/300.43  185830[10:Res:185430.1,30796.1] || equal(complement(complement(domain_relation)),successor_relation)**+ member(u,universal_class)* -> .
% 299.82/300.43  185805[10:Res:185430.1,30798.1] || equal(complement(complement(rest_relation)),successor_relation)**+ member(u,universal_class)* -> .
% 299.82/300.43  183720[10:SpL:183391.0,2648.0] || subclass(universal_class,symmetrization_of(successor_relation)) -> member(singleton(u),inverse(successor_relation))*.
% 299.82/300.43  199675[10:MRR:199674.1,160227.0] || subclass(universal_class,successor(successor_relation))* -> .
% 299.82/300.43  161843[10:Rew:160202.0,150064.0] ||  -> equal(intersection(power_class(successor_relation),intersection(image(element_relation,universal_class),u)),successor_relation)**.
% 299.82/300.43  161845[10:Rew:160202.0,150069.0] ||  -> equal(intersection(power_class(successor_relation),intersection(u,image(element_relation,universal_class))),successor_relation)**.
% 299.82/300.43  161847[10:Rew:160202.0,150072.0] ||  -> equal(intersection(intersection(image(element_relation,universal_class),u),power_class(successor_relation)),successor_relation)**.
% 299.82/300.43  161852[10:Rew:160202.0,150075.0] ||  -> equal(intersection(intersection(u,image(element_relation,universal_class)),power_class(successor_relation)),successor_relation)**.
% 299.82/300.43  162291[10:Rew:160202.0,150568.0] ||  -> equal(intersection(symmetrization_of(successor_relation),intersection(complement(inverse(successor_relation)),u)),successor_relation)**.
% 299.82/300.43  162292[10:Rew:160202.0,150570.0] ||  -> equal(intersection(symmetrization_of(successor_relation),intersection(u,complement(inverse(successor_relation)))),successor_relation)**.
% 299.82/300.43  199147[11:Res:8.1,199112.0] || equal(intersection(complement(inverse(successor_relation)),u),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  199150[11:Rew:160336.0,199144.0] || subclass(symmetrization_of(successor_relation),complement(symmetrization_of(successor_relation)))* -> .
% 299.82/300.43  199112[11:MRR:199063.1,168458.0] || subclass(symmetrization_of(successor_relation),intersection(complement(inverse(successor_relation)),u))* -> .
% 299.82/300.43  162293[10:Rew:160202.0,150572.0] ||  -> equal(intersection(intersection(complement(inverse(successor_relation)),u),symmetrization_of(successor_relation)),successor_relation)**.
% 299.82/300.43  199013[11:Res:8.1,198982.0] || equal(intersection(u,complement(inverse(successor_relation))),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  198997[11:SpL:160306.0,198982.0] || subclass(symmetrization_of(successor_relation),successor_relation)* -> .
% 299.82/300.43  198982[11:MRR:198939.1,168458.0] || subclass(symmetrization_of(successor_relation),intersection(u,complement(inverse(successor_relation))))* -> .
% 299.82/300.43  162294[10:Rew:160202.0,150574.0] ||  -> equal(intersection(intersection(u,complement(inverse(successor_relation))),symmetrization_of(successor_relation)),successor_relation)**.
% 299.82/300.43  162942[10:Rew:160202.0,150582.0] ||  -> equal(intersection(intersection(u,complement(singleton(successor_relation))),successor(successor_relation)),successor_relation)**.
% 299.82/300.43  198795[10:Res:8.1,198710.0] || equal(intersection(u,complement(singleton(successor_relation))),successor(successor_relation))** -> .
% 299.82/300.43  198728[10:Res:8.1,198694.0] || equal(intersection(complement(singleton(successor_relation)),u),successor(successor_relation))** -> .
% 299.82/300.43  198710[10:SpL:195339.0,198694.0] || subclass(successor(successor_relation),intersection(u,complement(singleton(successor_relation))))* -> .
% 299.82/300.43  198731[10:Rew:160419.0,198725.0] || subclass(successor(successor_relation),complement(successor(successor_relation)))* -> .
% 299.82/300.43  198712[10:SpL:160277.0,198694.0] || subclass(successor(successor_relation),successor_relation)* -> .
% 299.82/300.43  198694[10:MRR:198646.1,160455.0] || subclass(successor(successor_relation),intersection(complement(singleton(successor_relation)),u))* -> .
% 299.82/300.43  162943[10:Rew:160202.0,150580.0] ||  -> equal(intersection(intersection(complement(singleton(successor_relation)),u),successor(successor_relation)),successor_relation)**.
% 299.82/300.43  162944[10:Rew:160202.0,150578.0] ||  -> equal(intersection(successor(successor_relation),intersection(u,complement(singleton(successor_relation)))),successor_relation)**.
% 299.82/300.43  162736[10:Rew:160202.0,146129.2] || member(image(u,image(v,singleton(w))),universal_class) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(universal_class,universal_class)) -> equal(image(u,image(v,singleton(w))),successor_relation) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),compose(u,v))*.
% 299.82/300.43  162945[10:Rew:160202.0,150576.0] ||  -> equal(intersection(successor(successor_relation),intersection(complement(singleton(successor_relation)),u)),successor_relation)**.
% 299.82/300.43  163001[10:Rew:160202.0,156446.0] ||  -> equal(intersection(power_class(universal_class),intersection(image(element_relation,successor_relation),u)),successor_relation)**.
% 299.82/300.43  163003[10:Rew:160202.0,156548.0] ||  -> equal(intersection(power_class(universal_class),intersection(u,image(element_relation,successor_relation))),successor_relation)**.
% 299.82/300.43  163006[10:Rew:160202.0,156621.0] ||  -> equal(intersection(intersection(image(element_relation,successor_relation),u),power_class(universal_class)),successor_relation)**.
% 299.82/300.43  162590[10:Rew:160202.0,146128.2] || transitive(u,v) well_ordering(w,restrict(u,v,v)) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),successor_relation) member(least(w,compose(restrict(u,v,v),restrict(u,v,v))),compose(restrict(u,v,v),restrict(u,v,v)))*.
% 299.82/300.43  163008[10:Rew:160202.0,156726.0] ||  -> equal(intersection(intersection(u,image(element_relation,successor_relation)),power_class(universal_class)),successor_relation)**.
% 299.82/300.43  155790[3:Res:1477.1,141576.1] || subclass(universal_class,complement(kind_1_ordinals))*+ member(singleton(u),ordinal_numbers)* -> .
% 299.82/300.43  197781[10:MRR:197775.1,314.0] || equal(cantor(complement(cross_product(singleton(power_class(successor_relation)),universal_class))),universal_class)** -> .
% 299.82/300.43  197375[10:SpL:186059.1,185724.0] || equal(power_class(successor_relation),successor_relation) subclass(universal_class,power_class(successor_relation))* -> .
% 299.82/300.43  197267[13:SpL:186058.1,185720.0] || equal(power_class(universal_class),successor_relation) subclass(universal_class,power_class(universal_class))* -> .
% 299.82/300.43  196942[13:SoR:183119.0,73.1] one_to_one(image(element_relation,successor_relation)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.43  6187[0:Res:4.1,61.0] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(universal_class,universal_class)) -> subclass(image(v,image(w,singleton(u))),x) member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),compose(v,w))*.
% 299.82/300.43  196916[10:SoR:182364.0,73.1] one_to_one(image(element_relation,universal_class)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.43  162703[10:Rew:160202.0,146127.2] || transitive(u,v) well_ordering(w,restrict(u,v,v)) -> equal(segment(w,compose(restrict(u,v,v),restrict(u,v,v)),least(w,compose(restrict(u,v,v),restrict(u,v,v)))),successor_relation)**.
% 299.82/300.43  195483[0:SpL:194805.1,2.0] || subclass(ordinal_numbers,y__dfg) member(least(element_relation,ordinal_numbers),ordinal_numbers)* -> .
% 299.82/300.43  194098[11:Res:168384.1,193819.0] || equal(cantor(complement(cross_product(singleton(successor_relation),universal_class))),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  194097[10:Res:163169.1,193819.0] || equal(cantor(complement(cross_product(singleton(successor_relation),universal_class))),successor(successor_relation))** -> .
% 299.82/300.43  194096[10:Res:163171.1,193819.0] || equal(cantor(complement(cross_product(singleton(successor_relation),universal_class))),singleton(successor_relation))** -> .
% 299.82/300.43  194095[11:Res:179843.1,193819.0] || equal(cantor(complement(cross_product(singleton(successor_relation),universal_class))),inverse(successor_relation))** -> .
% 299.82/300.43  194094[10:Res:185646.1,193819.0] || equal(complement(cantor(complement(cross_product(singleton(successor_relation),universal_class)))),successor_relation)** -> .
% 299.82/300.43  194078[10:Res:187500.1,193819.0] || subclass(universal_class,cantor(complement(cross_product(singleton(power_class(successor_relation)),universal_class))))* -> .
% 299.82/300.43  194075[10:Res:185647.1,193819.0] || equal(complement(cantor(complement(cross_product(singleton(omega),universal_class)))),successor_relation)** -> .
% 299.82/300.43  162685[10:Rew:160202.0,146126.1] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(universal_class,universal_class)) -> equal(image(v,image(w,singleton(u))),successor_relation) member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),compose(v,w))*.
% 299.82/300.43  5932[0:Res:120.1,9.0] || transitive(u,v) subclass(restrict(u,v,v),compose(restrict(u,v,v),restrict(u,v,v)))* -> equal(compose(restrict(u,v,v),restrict(u,v,v)),restrict(u,v,v)).
% 299.82/300.43  187790[10:Res:187500.1,159.0] || subclass(universal_class,omega) -> equal(integer_of(power_class(successor_relation)),power_class(successor_relation))**.
% 299.82/300.43  187784[10:Res:187500.1,183723.0] || subclass(universal_class,symmetrization_of(successor_relation)) -> member(power_class(successor_relation),inverse(successor_relation))*.
% 299.82/300.43  187769[10:Res:187500.1,141576.1] || subclass(universal_class,complement(kind_1_ordinals))* member(power_class(successor_relation),ordinal_numbers) -> .
% 299.82/300.43  186011[10:Res:185647.1,141576.1] || equal(complement(complement(kind_1_ordinals)),successor_relation)** member(omega,ordinal_numbers) -> .
% 299.82/300.43  161565[10:Rew:160202.0,146081.1] || member(cross_product(u,v),universal_class) -> equal(cross_product(u,v),successor_relation) equal(ordered_pair(first(apply(choice,cross_product(u,v))),second(apply(choice,cross_product(u,v)))),apply(choice,cross_product(u,v)))**.
% 299.82/300.43  185937[10:Res:185646.1,141576.1] || equal(complement(complement(kind_1_ordinals)),successor_relation)** member(successor_relation,ordinal_numbers) -> .
% 299.82/300.43  186059[10:SpL:160328.0,185795.0] || equal(power_class(successor_relation),successor_relation) -> equal(image(element_relation,universal_class),universal_class)**.
% 299.82/300.43  197284[10:SoR:197283.0,73.1] one_to_one(element_relation) || equal(power_class(universal_class),successor_relation)** -> .
% 299.82/300.43  197283[10:MRR:197246.2,197246.3,160214.0,181045.0] function(element_relation) || equal(power_class(universal_class),successor_relation)** -> .
% 299.82/300.43  186058[10:SpL:160322.0,185795.0] || equal(power_class(universal_class),successor_relation) -> equal(image(element_relation,successor_relation),universal_class)**.
% 299.82/300.43  197037[10:MRR:163374.1,197036.0] || member(not_subclass_element(complement(singleton(successor_relation)),successor_relation),successor(successor_relation))* -> .
% 299.82/300.43  197088[10:Res:197071.0,186157.0] || equal(singleton(regular(complement(successor(successor_relation)))),successor_relation)** -> .
% 299.82/300.43  197085[15:Res:197071.0,189419.0] || equal(successor(regular(complement(successor(successor_relation)))),successor_relation)** -> .
% 299.82/300.43  6260[0:Res:18.2,39.1] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,v),u),x) -> member(ordered_pair(ordered_pair(v,w),u),flip(x))*.
% 299.82/300.43  197217[10:Res:8.1,197214.0] || equal(complement(successor(successor_relation)),singleton(successor_relation))** -> .
% 299.82/300.43  197214[10:MRR:197213.1,197033.0] || subclass(complement(successor(successor_relation)),singleton(successor_relation))* -> .
% 299.82/300.43  197074[10:Res:197034.0,26.1] || member(regular(complement(successor(successor_relation))),singleton(successor_relation))* -> .
% 299.82/300.43  6269[0:Res:18.2,36.1] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,u),v),x) -> member(ordered_pair(ordered_pair(v,w),u),rotate(x))*.
% 299.82/300.43  197084[15:Res:197071.0,193015.0] ||  -> equal(cantor(regular(complement(successor(successor_relation)))),successor_relation)**.
% 299.82/300.43  197071[10:Res:197034.0,34067.0] ||  -> member(regular(complement(successor(successor_relation))),universal_class)*.
% 299.82/300.43  197034[10:MRR:163334.1,197033.0] ||  -> member(regular(complement(successor(successor_relation))),complement(singleton(successor_relation)))*.
% 299.82/300.43  197036[10:MRR:184941.1,197033.0] || subclass(complement(singleton(successor_relation)),successor_relation)* -> .
% 299.82/300.43  5536[0:SpL:70.0,139.1] || well_ordering(element_relation,image(u,singleton(v))) subclass(apply(u,v),image(u,singleton(v)))* -> equal(image(u,singleton(v)),ordinal_numbers) member(image(u,singleton(v)),ordinal_numbers).
% 299.82/300.43  197033[10:MRR:197031.1,160217.0] || equal(complement(successor(successor_relation)),successor_relation)** -> .
% 299.82/300.43  186026[10:Res:185647.1,183723.0] || equal(complement(symmetrization_of(successor_relation)),successor_relation) -> member(omega,inverse(successor_relation))*.
% 299.82/300.43  185768[10:SpL:160328.0,185335.0] || equal(image(element_relation,power_class(successor_relation)),power_class(image(element_relation,universal_class)))** -> .
% 299.82/300.43  185767[10:SpL:160322.0,185335.0] || equal(image(element_relation,power_class(universal_class)),power_class(image(element_relation,successor_relation)))** -> .
% 299.82/300.43  185762[10:SpL:160336.0,185335.0] || equal(image(element_relation,symmetrization_of(successor_relation)),power_class(complement(inverse(successor_relation))))** -> .
% 299.82/300.43  185761[10:SpL:160419.0,185335.0] || equal(image(element_relation,successor(successor_relation)),power_class(complement(singleton(successor_relation))))** -> .
% 299.82/300.43  185046[10:SpR:160336.0,184981.1] || subclass(complement(inverse(successor_relation)),successor_relation)* -> subclass(universal_class,symmetrization_of(successor_relation)).
% 299.82/300.43  5565[0:Rew:5536.2,5559.0] || member(ordinal_numbers,universal_class) well_ordering(element_relation,image(u,singleton(v))) subclass(apply(u,v),image(u,singleton(v)))* -> member(image(u,singleton(v)),ordinal_numbers).
% 299.82/300.43  183119[13:Res:64.1,180588.0] function(image(element_relation,successor_relation)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.43  182364[10:Res:64.1,160551.0] function(image(element_relation,universal_class)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.43  162410[10:Rew:160202.0,151067.2] || connected(u,v)* well_ordering(w,complement(complement(symmetrization_of(u))))*+ -> equal(cross_product(v,v),successor_relation) member(least(w,cross_product(v,v)),cross_product(v,v))*.
% 299.82/300.43  157628[0:Res:107233.0,1322.1] inductive(complement(complement(omega))) ||  -> equal(complement(complement(omega)),omega)**.
% 299.82/300.43  162887[10:Rew:160202.0,150635.0] ||  -> equal(symmetric_difference(universal_class,complement(singleton(successor_relation))),intersection(successor(successor_relation),universal_class))**.
% 299.82/300.43  162888[10:Rew:160202.0,152496.0] ||  -> subclass(complement(power_class(complement(singleton(successor_relation)))),image(element_relation,successor(successor_relation)))*.
% 299.82/300.43  162889[10:Rew:160202.0,148216.0] ||  -> equal(complement(image(element_relation,successor(successor_relation))),power_class(complement(singleton(successor_relation))))**.
% 299.82/300.43  2330[0:Res:4.1,19.0] ||  -> subclass(cross_product(u,v),w) equal(ordered_pair(first(not_subclass_element(cross_product(u,v),w)),second(not_subclass_element(cross_product(u,v),w))),not_subclass_element(cross_product(u,v),w))**.
% 299.82/300.43  160971[10:Rew:160202.0,149938.0] ||  -> subclass(complement(power_class(image(element_relation,universal_class))),image(element_relation,power_class(successor_relation)))*.
% 299.82/300.43  161003[10:Rew:160202.0,155723.0] ||  -> equal(symmetric_difference(universal_class,image(element_relation,universal_class)),intersection(power_class(successor_relation),universal_class))**.
% 299.82/300.43  161137[10:Rew:160202.0,148458.0] ||  -> equal(complement(image(element_relation,symmetrization_of(successor_relation))),power_class(complement(inverse(successor_relation))))**.
% 299.82/300.43  161138[10:Rew:160202.0,152747.0] ||  -> subclass(complement(power_class(complement(inverse(successor_relation)))),image(element_relation,symmetrization_of(successor_relation)))*.
% 299.82/300.43  161155[10:Rew:160202.0,150625.0] ||  -> equal(symmetric_difference(universal_class,complement(inverse(successor_relation))),intersection(symmetrization_of(successor_relation),universal_class))**.
% 299.82/300.43  160848[10:Rew:160202.0,152583.0] ||  -> subclass(complement(power_class(image(element_relation,successor_relation))),image(element_relation,power_class(universal_class)))*.
% 299.82/300.43  162444[10:Rew:160202.0,146117.3] || connected(u,v) well_ordering(w,v) -> well_ordering(u,v) equal(segment(w,not_well_ordering(u,v),least(w,not_well_ordering(u,v))),successor_relation)**.
% 299.82/300.43  160889[10:Rew:160202.0,155722.0] ||  -> equal(symmetric_difference(universal_class,image(element_relation,successor_relation)),intersection(power_class(universal_class),universal_class))**.
% 299.82/300.43  161398[10:Rew:160202.0,148124.1] inductive(application_function) ||  -> member(successor_relation,cross_product(universal_class,cross_product(universal_class,universal_class)))*.
% 299.82/300.43  161397[10:Rew:160202.0,148125.1] inductive(composition_function) ||  -> member(successor_relation,cross_product(universal_class,cross_product(universal_class,universal_class)))*.
% 299.82/300.43  162953[10:Rew:160202.0,155794.1] || member(regular(complement(kind_1_ordinals)),ordinal_numbers)* -> equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.43  5841[0:Res:12.1,127.0] || member(u,universal_class) subclass(unordered_pair(v,u),w)*+ well_ordering(x,w)* -> member(least(x,unordered_pair(v,u)),unordered_pair(v,u))*.
% 299.82/300.43  163018[10:Rew:160202.0,157899.1] inductive(complement(compose(element_relation,universal_class))) || member(successor_relation,element_relation)* -> .
% 299.82/300.43  5842[0:Res:11.1,127.0] || member(u,universal_class) subclass(unordered_pair(u,v),w)*+ well_ordering(x,w)* -> member(least(x,unordered_pair(u,v)),unordered_pair(u,v))*.
% 299.82/300.43  195339[0:MRR:195302.0,9395.0] ||  -> equal(intersection(u,intersection(v,u)),intersection(v,u))**.
% 299.82/300.43  195152[0:MRR:195121.0,9395.0] ||  -> equal(intersection(u,intersection(u,v)),intersection(u,v))**.
% 299.82/300.43  5647[0:Res:60.1,5.0] || member(ordered_pair(u,not_subclass_element(v,image(w,image(x,singleton(u))))),compose(w,x))* -> subclass(v,image(w,image(x,singleton(u)))).
% 299.82/300.43  195883[10:MRR:195860.1,160268.1] || equal(sum_class(u),universal_class) -> inductive(sum_class(u))*.
% 299.82/300.43  195720[6:Res:8.1,195543.0] || equal(sum_class(u),universal_class) -> subclass(v,sum_class(u))*.
% 299.82/300.43  195817[10:MRR:195801.1,160268.1] || equal(inverse(u),universal_class) -> inductive(inverse(u))*.
% 299.82/300.43  195710[6:Res:8.1,195539.0] || equal(inverse(u),universal_class) -> subclass(v,inverse(u))*.
% 299.82/300.43  5838[0:Res:27.2,127.0] || member(u,universal_class)* subclass(complement(v),w)*+ well_ordering(x,w)* -> member(u,v)* member(least(x,complement(v)),complement(v))*.
% 299.82/300.43  195543[6:Rew:113504.0,195462.1] || subclass(universal_class,sum_class(u))*+ -> subclass(v,sum_class(u))*.
% 299.82/300.43  195539[6:Rew:113504.0,195456.1] || subclass(universal_class,inverse(u))*+ -> subclass(v,inverse(u))*.
% 299.82/300.43  195540[10:Rew:160278.0,195458.1] || subclass(universal_class,u) -> equal(symmetric_difference(u,universal_class),successor_relation)**.
% 299.82/300.43  162443[10:Rew:160202.0,150894.2] || connected(u,v)* well_ordering(w,complement(complement(symmetrization_of(u))))*+ -> equal(segment(w,cross_product(v,v),least(w,cross_product(v,v))),successor_relation)**.
% 299.82/300.43  195493[10:SpL:194805.1,160407.0] || subclass(ordinal_numbers,y__dfg) member(ordinal_numbers,singleton(successor_relation))* -> .
% 299.82/300.43  195628[10:MRR:195622.1,160217.0] inductive(complement(omega)) ||  -> .
% 299.82/300.43  195436[10:SpR:194805.1,160307.0] || subclass(u,complement(u))* -> equal(u,successor_relation).
% 299.82/300.43  195602[11:Res:8.1,195552.0] || equal(symmetric_difference(universal_class,inverse(successor_relation)),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  195600[10:Res:8.1,195551.0] || equal(symmetric_difference(universal_class,singleton(successor_relation)),successor(successor_relation))** -> .
% 299.82/300.43  195552[11:MRR:195472.1,168458.0] || subclass(symmetrization_of(successor_relation),symmetric_difference(universal_class,inverse(successor_relation)))* -> .
% 299.82/300.43  195551[10:MRR:195471.1,160455.0] || subclass(successor(successor_relation),symmetric_difference(universal_class,singleton(successor_relation)))* -> .
% 299.82/300.43  163662[10:Rew:160202.0,162442.2] inductive(image(u,image(v,singleton(w)))) || member(ordered_pair(w,successor_relation),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,successor_relation),compose(u,v))*.
% 299.82/300.43  195594[12:Res:8.1,195530.0] || equal(complement(compose(element_relation,universal_class)),element_relation)** -> .
% 299.82/300.43  195548[10:MRR:195441.1,185591.0] || subclass(complement(singleton(successor_relation)),successor(successor_relation))* -> .
% 299.82/300.43  195530[12:MRR:195417.1,177130.0] || subclass(element_relation,complement(compose(element_relation,universal_class)))* -> .
% 299.82/300.43  194805[0:MRR:194754.1,9395.0] || subclass(u,v) -> equal(intersection(v,u),u)**.
% 299.82/300.43  193149[15:Res:34189.1,193015.0] ||  -> subclass(u,v) equal(cantor(not_subclass_element(u,v)),successor_relation)**.
% 299.82/300.43  183398[0:SpL:139600.0,23.0] || member(u,complement(complement(v)))* -> member(u,v).
% 299.82/300.43  3537[0:Res:1499.1,17.0] || subclass(universal_class,cross_product(u,v))*+ -> member(w,v)*.
% 299.82/300.43  3536[0:Res:1499.1,16.0] || subclass(universal_class,cross_product(u,v))*+ -> member(w,u)*.
% 299.82/300.43  5540[0:Res:64.1,139.1] function(sum_class(cross_product(universal_class,universal_class))) || well_ordering(element_relation,cross_product(universal_class,universal_class))* -> equal(cross_product(universal_class,universal_class),ordinal_numbers) member(cross_product(universal_class,universal_class),ordinal_numbers).
% 299.82/300.43  5771[0:Res:5760.1,2125.0] || equal(sum_class(u),u) -> subclass(sum_class(u),u)*.
% 299.82/300.43  160569[10:Rew:160202.0,145993.1] inductive(restrict(u,v,w)) ||  -> member(successor_relation,u)*.
% 299.82/300.43  161279[10:Rew:160202.0,146137.0] ||  -> equal(intersection(u,singleton(v)),successor_relation)** member(v,u).
% 299.82/300.43  161286[10:Rew:160202.0,146139.0] ||  -> equal(intersection(singleton(u),v),successor_relation)** member(u,v).
% 299.82/300.43  3886[0:Res:25.2,5.0] || member(not_subclass_element(u,intersection(v,w)),w)*+ member(not_subclass_element(u,intersection(v,w)),v)* -> subclass(u,intersection(v,w)).
% 299.82/300.43  194100[10:Res:160271.1,193819.0] inductive(cantor(complement(cross_product(singleton(successor_relation),universal_class)))) ||  -> .
% 299.82/300.43  193819[10:Res:968.1,193764.0] || member(u,cantor(complement(cross_product(singleton(u),universal_class))))* -> .
% 299.82/300.43  193991[10:Obv:193990.1] || equal(cantor(complement(cross_product(singleton(successor_relation),universal_class))),universal_class)** -> .
% 299.82/300.43  193914[10:Obv:193913.1] || equal(cantor(complement(cross_product(singleton(omega),universal_class))),universal_class)** -> .
% 299.82/300.43  5768[0:Res:99.1,3.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,w) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),w)*.
% 299.82/300.43  193840[20:Res:192287.1,193764.0] || equal(cantor(complement(cross_product(singleton(successor_relation),universal_class))),omega)** -> .
% 299.82/300.43  161592[10:Rew:160202.0,146082.0] ||  -> equal(cross_product(u,v),successor_relation) equal(ordered_pair(first(regular(cross_product(u,v))),second(regular(cross_product(u,v)))),regular(cross_product(u,v)))**.
% 299.82/300.43  193906[10:Res:968.1,193803.0] || member(universal_class,cantor(complement(cross_product(successor_relation,universal_class))))* -> .
% 299.82/300.43  193839[10:Res:160271.1,193764.0] inductive(domain_of(complement(cross_product(singleton(successor_relation),universal_class)))) ||  -> .
% 299.82/300.43  161319[10:Rew:160202.0,147488.0] ||  -> equal(restrict(complement(cross_product(u,v)),u,v),successor_relation)**.
% 299.82/300.43  161320[10:Rew:160202.0,147641.0] ||  -> equal(intersection(complement(u),restrict(u,v,w)),successor_relation)**.
% 299.82/300.43  150815[6:Rew:148462.0,149581.1] || connected(u,v) subclass(complement(complement(symmetrization_of(u))),cross_product(v,v))* -> equal(complement(complement(symmetrization_of(u))),cross_product(v,v)).
% 299.82/300.43  161321[10:Rew:160202.0,147754.0] ||  -> equal(intersection(restrict(u,v,w),complement(u)),successor_relation)**.
% 299.82/300.43  162016[10:Rew:160202.0,153517.0] || equal(cross_product(u,u),successor_relation)**+ -> connected(v,u)*.
% 299.82/300.43  163041[10:Rew:160202.0,158804.0] ||  -> equal(range__dfg(successor_relation,u,v),range__dfg(successor_relation,w,x))*.
% 299.82/300.43  141787[2:Obv:141786.0] ||  -> member(u,inverse(singleton(u)))* asymmetric(singleton(u),v)*.
% 299.82/300.43  193148[15:Res:9089.1,193015.0] function(u) ||  -> equal(cantor(apply(u,v)),successor_relation)**.
% 299.82/300.43  192947[10:Res:160354.1,188851.0] || equal(complement(u),successor_relation) -> member(singleton(v),u)*.
% 299.82/300.43  191101[20:Res:191074.1,24.0] || equal(intersection(u,v),omega)** -> member(successor_relation,v).
% 299.82/300.43  191100[20:Res:191074.1,23.0] || equal(intersection(u,v),omega)** -> member(successor_relation,u).
% 299.82/300.43  5564[0:Rew:5540.2,5563.1] function(sum_class(cross_product(universal_class,universal_class))) || member(ordinal_numbers,universal_class) well_ordering(element_relation,cross_product(universal_class,universal_class))* -> member(cross_product(universal_class,universal_class),ordinal_numbers).
% 299.82/300.43  5714[2:MRR:5693.3,2492.1] || connected(u,v) well_ordering(w,v) -> well_ordering(u,v) member(least(w,not_well_ordering(u,v)),not_well_ordering(u,v))*.
% 299.82/300.43  193048[15:Res:160271.1,189348.0] inductive(cantor(u)) || member(u,universal_class)* -> .
% 299.82/300.43  193015[15:Res:160298.1,189348.0] || member(u,universal_class)* -> equal(cantor(u),successor_relation).
% 299.82/300.43  1348[0:SpR:124.0,102.1] || member(restrict(u,v,singleton(w)),universal_class) -> member(ordered_pair(restrict(u,v,singleton(w)),segment(u,v,w)),domain_relation)*.
% 299.82/300.43  188851[10:MRR:188828.0,191.0] || subclass(complement(u),successor_relation)*+ -> member(singleton(v),u)*.
% 299.82/300.43  188810[10:Res:8.1,181146.0] || equal(u,ordered_pair(universal_class,v))*+ -> member(successor_relation,u)*.
% 299.82/300.43  192343[20:SpL:185605.1,192335.0] || equal(successor_relation,u) equal(power_class(u),omega)** -> .
% 299.82/300.43  192323[20:Res:163162.1,191095.1] || equal(complement(complement(u)),omega)** -> member(successor_relation,u).
% 299.82/300.43  162090[10:Rew:160202.0,146109.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(compose(v,w),successor_relation) member(least(u,compose(v,w)),compose(v,w))*.
% 299.82/300.43  192321[20:Res:160268.1,191095.1] || equal(u,universal_class) equal(complement(u),omega)** -> .
% 299.82/300.43  192315[20:Res:191074.1,191095.1] || equal(u,omega) equal(complement(u),omega)** -> .
% 299.82/300.43  192211[15:MRR:192133.2,160227.0] || member(inverse(u),universal_class)* -> equal(range_of(u),successor_relation).
% 299.82/300.43  191989[15:Rew:160276.0,191970.1] || member(u,universal_class) -> equal(cantor(rest_of(u)),successor_relation)**.
% 299.82/300.43  191934[15:Rew:160276.0,191909.1] || member(u,universal_class) -> equal(cantor(sum_class(u)),successor_relation)**.
% 299.82/300.43  191872[15:Rew:160276.0,191850.1] || member(u,universal_class) -> equal(cantor(power_class(u)),successor_relation)**.
% 299.82/300.43  191629[15:Res:160295.1,189419.0] || equal(successor(regular(u)),successor_relation)** -> equal(u,successor_relation).
% 299.82/300.43  162356[10:Rew:160202.0,148484.3] || member(u,v)+ subclass(v,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(u,least(omega,v))),successor_relation)**.
% 299.82/300.43  191621[15:Res:160362.0,189419.0] || equal(successor(u),successor_relation)** -> equal(singleton(u),successor_relation).
% 299.82/300.43  191620[15:Res:160274.1,189419.0] || equal(successor(u),successor_relation) -> equal(integer_of(u),successor_relation)**.
% 299.82/300.43  191129[20:Res:191074.1,160258.1] || equal(u,omega) equal(complement(u),universal_class)** -> .
% 299.82/300.43  2143[0:Res:4.1,10.0] ||  -> subclass(unordered_pair(u,v),w) equal(not_subclass_element(unordered_pair(u,v),w),v)** equal(not_subclass_element(unordered_pair(u,v),w),u)**.
% 299.82/300.43  192322[20:Res:160271.1,191095.1] inductive(u) || equal(complement(u),omega)** -> .
% 299.82/300.43  192339[20:MRR:192300.0,160214.0] || equal(complement(unordered_pair(u,successor_relation)),omega)** -> .
% 299.82/300.43  192338[20:MRR:192299.0,160214.0] || equal(complement(unordered_pair(successor_relation,u)),omega)** -> .
% 299.82/300.43  192327[20:Res:181063.0,191095.1] || equal(complement(ordered_pair(universal_class,u)),omega)** -> .
% 299.82/300.43  192311[20:Res:160453.0,191095.1] || equal(complement(successor(successor_relation)),omega)** -> .
% 299.82/300.43  192310[20:Res:168372.0,191095.1] || equal(complement(symmetrization_of(successor_relation)),omega)** -> .
% 299.82/300.43  192309[20:Res:168387.0,191095.1] || equal(complement(inverse(successor_relation)),omega)** -> .
% 299.82/300.43  192336[20:Rew:160322.0,192314.0] || equal(power_class(universal_class),omega)** -> .
% 299.82/300.43  161774[10:Rew:160202.0,146098.0] ||  -> equal(unordered_pair(u,v),successor_relation) equal(apply(choice,unordered_pair(u,v)),v)** equal(apply(choice,unordered_pair(u,v)),u)**.
% 299.82/300.43  192335[20:Rew:160328.0,192313.0] || equal(power_class(successor_relation),omega)** -> .
% 299.82/300.43  191095[20:Res:191074.1,26.1] || equal(complement(u),omega) member(successor_relation,u)* -> .
% 299.82/300.43  190721[15:SpR:189515.1,41.0] ||  -> equal(singleton(inverse(u)),successor_relation)** equal(range_of(u),successor_relation).
% 299.82/300.43  190637[15:SpR:189514.1,41.0] ||  -> equal(integer_of(inverse(u)),successor_relation)** equal(range_of(u),successor_relation).
% 299.82/300.43  162026[10:Rew:160202.0,146055.2] || member(u,ordinal_numbers) well_ordering(v,u) -> equal(sum_class(u),successor_relation) member(least(v,sum_class(u)),sum_class(u))*.
% 299.82/300.43  190029[15:SpR:185605.1,189979.0] || equal(successor_relation,u) -> equal(cantor(power_class(u)),successor_relation)**.
% 299.82/300.43  162116[10:Rew:160202.0,146106.1] || well_ordering(u,cross_product(cross_product(universal_class,universal_class),universal_class))*+ -> equal(rotate(v),successor_relation) member(least(u,rotate(v)),rotate(v))*.
% 299.82/300.43  191627[15:Res:13.0,189419.0] || equal(successor(unordered_pair(u,v)),successor_relation)** -> .
% 299.82/300.43  162118[10:Rew:160202.0,146107.1] || well_ordering(u,cross_product(cross_product(universal_class,universal_class),universal_class))*+ -> equal(flip(v),successor_relation) member(least(u,flip(v)),flip(v))*.
% 299.82/300.43  191619[15:Res:999.0,189419.0] || equal(successor(ordered_pair(u,v)),successor_relation)** -> .
% 299.82/300.43  191649[15:Res:183757.0,189419.0] || equal(successor(regular(symmetrization_of(successor_relation))),successor_relation)** -> .
% 299.82/300.43  191618[15:Res:191.0,189419.0] || equal(successor(singleton(u)),successor_relation)** -> .
% 299.82/300.43  191624[15:Res:187489.0,189419.0] || equal(successor(power_class(successor_relation)),successor_relation)** -> .
% 299.82/300.43  162150[10:Rew:160202.0,146104.0] || equal(restrict(restrict(inverse(cross_product(u,v)),u,v),w,w),successor_relation)** -> asymmetric(cross_product(u,v),w).
% 299.82/300.43  191625[15:Res:54.0,189419.0] || equal(successor(omega),successor_relation)** -> .
% 299.82/300.43  189419[15:Rew:189339.1,163138.1] || member(u,universal_class)* equal(successor(u),successor_relation) -> .
% 299.82/300.43  162149[10:Rew:160202.0,146105.1] || asymmetric(cross_product(u,v),w) -> equal(restrict(restrict(inverse(cross_product(u,v)),u,v),w,w),successor_relation)**.
% 299.82/300.43  162148[10:Rew:160202.0,146103.2] || member(u,ordinal_numbers) well_ordering(v,u) -> equal(segment(v,sum_class(u),least(v,sum_class(u))),successor_relation)**.
% 299.82/300.43  191126[20:Res:191074.1,185639.1] || equal(u,omega)* equal(successor_relation,u) -> .
% 299.82/300.43  191125[20:Res:191074.1,2151.0] || equal(singleton(u),omega)** -> equal(successor_relation,u).
% 299.82/300.43  162146[10:Rew:160202.0,146102.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(segment(u,compose(v,w),least(u,compose(v,w))),successor_relation)**.
% 299.82/300.43  191416[20:MRR:191415.0,143555.0] || subclass(omega,successor_relation)* -> .
% 299.82/300.43  191041[20:Res:191039.0,6045.0] || subclass(omega,u) well_ordering(universal_class,u)* -> .
% 299.82/300.43  191410[20:MRR:191403.1,160215.0] || equal(omega,ordinal_numbers) -> section(element_relation,successor_relation,universal_class)*.
% 299.82/300.43  191134[20:Res:191074.1,163173.0] || equal(omega,ordinal_numbers) -> equal(sum_class(successor_relation),successor_relation)**.
% 299.82/300.43  161312[10:Rew:160202.0,146065.1] || member(intersection(u,v),universal_class) -> equal(intersection(u,v),successor_relation) member(apply(choice,intersection(u,v)),v)*.
% 299.82/300.43  191137[20:MRR:191105.1,160315.0] || equal(cross_product(u,v),omega)** -> .
% 299.82/300.43  191131[20:Res:191074.1,183651.0] || equal(complement(singleton(successor_relation)),omega)** -> .
% 299.82/300.43  161311[10:Rew:160202.0,146066.1] || member(intersection(u,v),universal_class) -> equal(intersection(u,v),successor_relation) member(apply(choice,intersection(u,v)),u)*.
% 299.82/300.43  191074[20:Res:8.1,191040.0] || equal(u,omega) -> member(successor_relation,u)*.
% 299.82/300.43  191040[20:MRR:191032.1,160217.0] || subclass(omega,u)* -> member(successor_relation,u).
% 299.82/300.43  161324[10:Rew:160202.0,146027.1] || asymmetric(u,singleton(v)) -> equal(range__dfg(intersection(u,inverse(u)),v,singleton(v)),second(not_subclass_element(successor_relation,successor_relation)))**.
% 299.82/300.43  191048[20:Res:191039.0,160258.1] || equal(complement(omega),universal_class)** -> .
% 299.82/300.43  191039[20:MRR:191029.0,160217.0] ||  -> member(successor_relation,omega)*.
% 299.82/300.43  191021[20:Spt:190857.1] ||  -> equal(regular(omega),successor_relation)**.
% 299.82/300.43  162144[10:Rew:160202.0,146100.1] || well_ordering(u,cross_product(cross_product(universal_class,universal_class),universal_class)) -> equal(segment(u,rotate(v),least(u,rotate(v))),successor_relation)**.
% 299.82/300.43  190816[15:Rew:160276.0,190792.1] ||  -> equal(u,successor_relation) equal(cantor(regular(u)),successor_relation)**.
% 299.82/300.43  162145[10:Rew:160202.0,146101.1] || well_ordering(u,cross_product(cross_product(universal_class,universal_class),universal_class)) -> equal(segment(u,flip(v),least(u,flip(v))),successor_relation)**.
% 299.82/300.43  190749[15:Rew:160276.0,190714.1] ||  -> equal(singleton(u),successor_relation) equal(cantor(u),successor_relation)**.
% 299.82/300.43  190665[15:Rew:160276.0,190631.1] ||  -> equal(integer_of(u),successor_relation)** equal(cantor(u),successor_relation).
% 299.82/300.43  189370[15:Res:160271.1,188793.1] inductive(domain_of(u)) || member(u,universal_class)* -> .
% 299.82/300.43  173[0:Res:27.2,2.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class) -> member(least(element_relation,intersection(y__dfg,ordinal_numbers)),complement(intersection(y__dfg,ordinal_numbers)))*.
% 299.82/300.43  190425[15:Rew:160276.0,190407.0] ||  -> equal(cantor(unordered_pair(u,v)),successor_relation)**.
% 299.82/300.43  190362[15:Rew:160276.0,190344.0] ||  -> equal(cantor(ordered_pair(u,v)),successor_relation)**.
% 299.82/300.43  161779[10:Rew:160202.0,146099.0] ||  -> equal(unordered_pair(u,v),successor_relation) equal(regular(unordered_pair(u,v)),v)** equal(regular(unordered_pair(u,v)),u)**.
% 299.82/300.43  160776[10:Rew:160202.0,146008.2] function(u) || well_ordering(v,cross_product(universal_class,universal_class))*+ -> equal(u,successor_relation) member(least(v,u),u)*.
% 299.82/300.43  190254[15:Rew:160276.0,190238.0] ||  -> equal(cantor(regular(symmetrization_of(successor_relation))),successor_relation)**.
% 299.82/300.43  190089[15:Rew:160276.0,190071.0] ||  -> equal(cantor(singleton(u)),successor_relation)**.
% 299.82/300.43  189374[15:Rew:189339.1,1496.2] || member(u,universal_class) subclass(domain_relation,v) -> member(ordered_pair(u,successor_relation),v)*.
% 299.82/300.43  190006[15:Res:8.1,189624.0] || equal(rotate(domain_relation),rest_relation)** -> .
% 299.82/300.43  189979[15:Rew:160276.0,189961.0] ||  -> equal(cantor(power_class(successor_relation)),successor_relation)**.
% 299.82/300.43  189624[15:AED:1.0,189571.1] || subclass(rest_relation,rotate(domain_relation))* -> .
% 299.82/300.43  189757[15:Res:8.1,189587.0] || equal(rest_relation,element_relation)** -> .
% 299.82/300.43  189730[15:Rew:160276.0,189714.0] ||  -> equal(cantor(omega),successor_relation)**.
% 299.82/300.43  189758[18:Spt:189590.0] ||  -> equal(recursion_equation_functions(u),successor_relation)**.
% 299.82/300.43  189587[15:MRR:189574.1,160227.0] || subclass(rest_relation,element_relation)* -> .
% 299.82/300.43  189478[15:MRR:189470.0,191.0] ||  -> member(singleton(singleton(singleton(successor_relation))),domain_relation)*.
% 299.82/300.43  189373[15:Rew:189339.1,102.1] || member(u,universal_class) -> member(ordered_pair(u,successor_relation),domain_relation)*.
% 299.82/300.43  188436[10:Res:8.1,160549.0] || equal(cross_product(u,v),domain_relation)** -> member(successor_relation,u).
% 299.82/300.43  185660[10:MRR:185535.1,6.0] || equal(complement(symmetrization_of(u)),successor_relation)**+ -> connected(u,v)*.
% 299.82/300.43  185608[10:Rew:113504.0,185396.1] || equal(successor_relation,u) -> equal(intersection(u,v),successor_relation)**.
% 299.82/300.43  161980[10:Rew:160202.0,146097.2] function(u) || well_ordering(v,cross_product(universal_class,universal_class)) -> equal(segment(v,u,least(v,u)),successor_relation)**.
% 299.82/300.43  185607[10:Rew:113504.0,185395.1] || equal(successor_relation,u) -> equal(intersection(v,u),successor_relation)**.
% 299.82/300.43  185228[10:MRR:163389.1,185225.0] inductive(ordered_pair(u,v)) ||  -> equal(singleton(u),successor_relation)**.
% 299.82/300.43  161922[10:Rew:160202.0,146095.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(rest_of(v),successor_relation) member(least(u,rest_of(v)),rest_of(v))*.
% 299.82/300.43  188825[10:Res:114897.1,185065.1] || equal(u,universal_class) subclass(u,successor_relation)* -> .
% 299.82/300.43  188823[10:SpL:181056.0,185065.1] || subclass(u,successor_relation)* member(successor_relation,u) -> .
% 299.82/300.43  185065[10:Res:184981.1,2647.0] || subclass(u,successor_relation) member(singleton(v),u)* -> .
% 299.82/300.43  161927[10:Rew:160202.0,146096.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(compose_class(v),successor_relation) member(least(u,compose_class(v)),compose_class(v))*.
% 299.82/300.43  184279[10:Res:8.1,161234.0] || equal(cross_product(u,v),domain_relation)** -> member(successor_relation,v).
% 299.82/300.43  181146[10:Res:181063.0,3.0] || subclass(ordered_pair(universal_class,u),v)* -> member(successor_relation,v).
% 299.82/300.43  149908[6:MRR:148146.2,146185.0] function(u) inductive(compose(u,inverse(u))) ||  -> .
% 299.82/300.43  149907[6:MRR:148145.2,146185.0] single_valued_class(u) inductive(compose(u,inverse(u))) ||  -> .
% 299.82/300.43  30614[0:SpL:15.0,30460.0] || subclass(universal_class,complement(unordered_pair(ordered_pair(u,v),w)))* -> .
% 299.82/300.43  30656[0:Res:8.1,30614.0] || equal(complement(unordered_pair(ordered_pair(u,v),w)),universal_class)** -> .
% 299.82/300.43  30460[0:MRR:30439.0,13.0] || subclass(universal_class,complement(unordered_pair(unordered_pair(u,v),w)))* -> .
% 299.82/300.43  188737[17:Res:188721.1,34067.0] || well_ordering(u,omega) -> member(least(u,omega),universal_class)*.
% 299.82/300.43  188729[17:Res:188716.1,34067.0] || well_ordering(u,universal_class) -> member(least(u,omega),universal_class)*.
% 299.82/300.43  188721[17:Res:314.0,188715.0] || well_ordering(u,omega) -> member(least(u,omega),omega)*.
% 299.82/300.43  188716[17:Res:6.0,188715.0] || well_ordering(u,universal_class) -> member(least(u,omega),omega)*.
% 299.82/300.43  188713[10:SpL:15.0,188711.0] || equal(unordered_pair(ordered_pair(u,v),w),successor_relation)** -> .
% 299.82/300.43  188715[17:Spt:162139.0,162139.1,162139.3] || subclass(omega,u)+ well_ordering(v,u)* -> member(least(v,omega),omega)*.
% 299.82/300.43  188711[10:Obv:188710.1] || equal(unordered_pair(unordered_pair(u,v),w),successor_relation)** -> .
% 299.82/300.43  30617[0:Res:8.1,30460.0] || equal(complement(unordered_pair(unordered_pair(u,v),w)),universal_class)** -> .
% 299.82/300.43  30459[0:MRR:30438.0,13.0] || subclass(universal_class,complement(unordered_pair(u,unordered_pair(v,w))))* -> .
% 299.82/300.43  188662[10:Obv:188661.1] || equal(unordered_pair(u,unordered_pair(v,w)),successor_relation)** -> .
% 299.82/300.43  3872[0:SpR:30.0,25.2] || member(u,cross_product(v,w)) member(u,x) -> member(u,restrict(x,v,w))*.
% 299.82/300.43  30588[0:Res:8.1,30459.0] || equal(complement(unordered_pair(u,unordered_pair(v,w))),universal_class)** -> .
% 299.82/300.43  30584[0:SpL:15.0,30459.0] || subclass(universal_class,complement(unordered_pair(u,ordered_pair(v,w))))* -> .
% 299.82/300.43  188646[10:Obv:188645.1] || equal(unordered_pair(u,ordered_pair(v,w)),successor_relation)** -> .
% 299.82/300.43  30645[0:Res:8.1,30584.0] || equal(complement(unordered_pair(u,ordered_pair(v,w))),universal_class)** -> .
% 299.82/300.43  2142[0:SpL:15.0,10.0] || member(u,ordered_pair(v,w))* -> equal(u,unordered_pair(v,singleton(w))) equal(u,singleton(v)).
% 299.82/300.43  161439[10:Rew:160202.0,146070.2] || equal(u,v)*+ well_ordering(w,u)* -> equal(v,successor_relation) member(least(w,v),v)*.
% 299.82/300.43  5760[0:Res:8.1,5754.0] || equal(sum_class(u),u) -> section(element_relation,u,universal_class)*.
% 299.82/300.43  160566[10:Rew:160202.0,153208.1] || equal(intersection(u,v),universal_class)** -> member(successor_relation,u).
% 299.82/300.43  160549[10:Rew:160202.0,159383.1] || subclass(domain_relation,cross_product(u,v))* -> member(successor_relation,u).
% 299.82/300.43  161288[10:Rew:160202.0,146145.1] inductive(symmetric_difference(u,u)) ||  -> member(successor_relation,complement(u))*.
% 299.82/300.43  161959[10:Rew:160202.0,146094.2] || equal(u,v)*+ well_ordering(w,u)* -> equal(segment(w,v,least(w,v)),successor_relation)**.
% 299.82/300.43  188187[10:Res:160295.1,186157.0] || equal(singleton(regular(u)),successor_relation)** -> equal(u,successor_relation).
% 299.82/300.43  188178[10:Res:160274.1,186157.0] || equal(singleton(u),successor_relation) -> equal(integer_of(u),successor_relation)**.
% 299.82/300.43  188148[10:Res:8.1,186146.0] || equal(flip(u),rest_relation)** equal(successor_relation,u) -> .
% 299.82/300.43  1032[0:SpR:28.0,27.2] || member(u,universal_class) -> member(u,intersection(complement(v),complement(w)))* member(u,union(v,w)).
% 299.82/300.43  188145[10:Res:8.1,186145.0] || equal(rotate(u),rest_relation)** equal(successor_relation,u) -> .
% 299.82/300.43  184565[10:MRR:161882.1,184560.0] || well_ordering(u,kind_1_ordinals) -> member(least(u,ordinal_numbers),ordinal_numbers)*.
% 299.82/300.43  3595[0:Res:67.2,3.0] function(u) || member(v,universal_class) subclass(universal_class,w) -> member(image(u,v),w)*.
% 299.82/300.43  110370[0:Res:6.0,31922.0] || well_ordering(u,universal_class) -> member(least(u,rest_relation),rest_relation)*.
% 299.82/300.43  110376[0:Res:314.0,31922.0] || well_ordering(u,rest_relation) -> member(least(u,rest_relation),rest_relation)*.
% 299.82/300.43  110388[0:Res:110376.1,34067.0] || well_ordering(u,rest_relation) -> member(least(u,rest_relation),universal_class)*.
% 299.82/300.43  110382[0:Res:110370.1,34067.0] || well_ordering(u,universal_class) -> member(least(u,rest_relation),universal_class)*.
% 299.82/300.43  161957[10:Rew:160202.0,146092.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(segment(u,rest_of(v),least(u,rest_of(v))),successor_relation)**.
% 299.82/300.43  110623[0:Res:6.0,5858.0] || well_ordering(u,universal_class) -> member(least(u,universal_class),universal_class)*.
% 299.82/300.43  184599[10:Res:184565.1,34067.0] || well_ordering(u,kind_1_ordinals) -> member(least(u,ordinal_numbers),universal_class)*.
% 299.82/300.43  186490[10:SpL:185605.1,160334.0] || equal(successor_relation,u) equal(power_class(u),universal_class)** -> .
% 299.82/300.43  186193[11:Res:168384.1,185639.1] || equal(u,symmetrization_of(successor_relation))* equal(successor_relation,u) -> .
% 299.82/300.43  161958[10:Rew:160202.0,146093.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(segment(u,compose_class(v),least(u,compose_class(v))),successor_relation)**.
% 299.82/300.43  186192[10:Res:163169.1,185639.1] || equal(u,successor(successor_relation))* equal(successor_relation,u) -> .
% 299.82/300.43  186191[10:Res:163171.1,185639.1] || equal(u,singleton(successor_relation))* equal(successor_relation,u) -> .
% 299.82/300.43  186190[11:Res:179843.1,185639.1] || equal(u,inverse(successor_relation))* equal(successor_relation,u) -> .
% 299.82/300.43  188199[11:Res:183757.0,186157.0] || equal(singleton(regular(symmetrization_of(successor_relation))),successor_relation)** -> .
% 299.82/300.43  5561[0:Res:8.1,138.2] || equal(sum_class(u),u) member(u,universal_class) well_ordering(element_relation,u)* -> member(u,ordinal_numbers).
% 299.82/300.43  188182[10:Res:187489.0,186157.0] || equal(singleton(power_class(successor_relation)),successor_relation)** -> .
% 299.82/300.43  186157[10:Res:305.1,185639.1] || member(u,universal_class)* equal(singleton(u),successor_relation) -> .
% 299.82/300.43  186146[10:Res:28321.1,185639.1] || subclass(rest_relation,flip(u))* equal(successor_relation,u) -> .
% 299.82/300.43  186145[10:Res:28320.1,185639.1] || subclass(rest_relation,rotate(u))* equal(successor_relation,u) -> .
% 299.82/300.43  185835[10:Res:185430.1,30457.0] || equal(complement(complement(singleton(unordered_pair(u,v)))),successor_relation)** -> .
% 299.82/300.43  161956[10:Rew:160202.0,146089.1] || well_ordering(u,cross_product(universal_class,cross_product(universal_class,universal_class)))*+ -> equal(segment(u,composition_function,least(u,composition_function)),successor_relation)**.
% 299.82/300.43  185833[10:Res:185430.1,30613.0] || equal(complement(complement(unordered_pair(singleton(u),v))),successor_relation)** -> .
% 299.82/300.43  185831[10:Res:185430.1,30583.0] || equal(complement(complement(unordered_pair(u,singleton(v)))),successor_relation)** -> .
% 299.82/300.43  185803[10:Res:185430.1,30537.0] || equal(complement(complement(singleton(ordered_pair(u,v)))),successor_relation)** -> .
% 299.82/300.43  176[0:Res:25.2,2.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),ordinal_numbers)* member(least(element_relation,intersection(y__dfg,ordinal_numbers)),y__dfg) -> .
% 299.82/300.43  303[0:SpR:70.0,137.1] || member(image(u,singleton(v)),ordinal_numbers) -> subclass(apply(u,v),image(u,singleton(v)))*.
% 299.82/300.43  161945[10:Rew:160202.0,148469.2] inductive(u) || well_ordering(v,u)*+ -> equal(segment(v,omega,least(v,omega)),successor_relation)**.
% 299.82/300.43  1314[0:Res:97.0,9.0] || subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)* -> equal(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function).
% 299.82/300.43  180760[11:MRR:180757.1,160215.0] || equal(inverse(successor_relation),ordinal_numbers) -> section(element_relation,successor_relation,universal_class)*.
% 299.82/300.43  163190[10:Rew:160202.0,160400.0] || equal(singleton(successor_relation),ordinal_numbers) -> section(element_relation,successor_relation,universal_class)*.
% 299.82/300.43  160482[10:Rew:160202.0,146071.1] || well_ordering(u,universal_class) -> equal(v,successor_relation) member(least(u,v),v)*.
% 299.82/300.43  163189[10:Rew:160202.0,160399.0] || equal(successor(successor_relation),ordinal_numbers) -> section(element_relation,successor_relation,universal_class)*.
% 299.82/300.43  180020[11:Res:179843.1,163173.0] || equal(inverse(successor_relation),ordinal_numbers) -> equal(sum_class(successor_relation),successor_relation)**.
% 299.82/300.43  168571[11:Res:168384.1,163173.0] || equal(symmetrization_of(successor_relation),ordinal_numbers)** -> equal(sum_class(successor_relation),successor_relation).
% 299.82/300.43  160484[10:Rew:160202.0,146073.1] || well_ordering(u,universal_class) -> equal(segment(u,v,least(u,v)),successor_relation)**.
% 299.82/300.43  163187[10:Rew:160202.0,160318.0] || equal(singleton(successor_relation),ordinal_numbers) -> equal(sum_class(successor_relation),successor_relation)**.
% 299.82/300.43  163186[10:Rew:160202.0,160317.0] || equal(successor(successor_relation),ordinal_numbers) -> equal(sum_class(successor_relation),successor_relation)**.
% 299.82/300.43  185971[10:Res:185646.1,163173.0] || equal(complement(ordinal_numbers),successor_relation)** -> equal(sum_class(successor_relation),successor_relation).
% 299.82/300.43  61[0:Inp] || member(u,image(v,image(w,singleton(x))))* member(ordered_pair(x,u),cross_product(universal_class,universal_class)) -> member(ordered_pair(x,u),compose(v,w)).
% 299.82/300.43  107701[0:Res:13.0,6045.0] || subclass(universal_class,u) well_ordering(universal_class,u)* -> .
% 299.82/300.43  187500[10:Res:187489.0,3.0] || subclass(universal_class,u) -> member(power_class(successor_relation),u)*.
% 299.82/300.43  96[0:Inp] || equal(compose(u,v),w) member(ordered_pair(v,w),cross_product(universal_class,universal_class))*+ -> member(ordered_pair(v,w),compose_class(u))*.
% 299.82/300.43  187563[16:MRR:186268.1,187561.0] || equal(cross_product(universal_class,cross_product(universal_class,universal_class)),successor_relation)** -> .
% 299.82/300.43  22[0:Inp] || member(u,v) member(ordered_pair(u,v),cross_product(universal_class,universal_class))* -> member(ordered_pair(u,v),element_relation).
% 299.82/300.43  99[0:Inp] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),composition_function)*.
% 299.82/300.43  138[0:Inp] || member(u,universal_class) well_ordering(element_relation,u) subclass(sum_class(u),u)* -> member(u,ordinal_numbers).
% 299.82/300.43  160283[10:Rew:160202.0,155793.1] inductive(complement(kind_1_ordinals)) || member(successor_relation,ordinal_numbers)* -> .
% 299.82/300.43  160285[10:Rew:160202.0,153145.1] inductive(sum_class(identity_relation)) || member(successor_relation,ordinal_numbers)* -> .
% 299.82/300.43  184007[14:MRR:183966.2,160227.0] || equal(sum_class(range_of(u)),v) member(ordered_pair(u,v),cross_product(universal_class,universal_class))* -> .
% 299.82/300.43  163173[10:Rew:160202.0,160286.1] || member(successor_relation,ordinal_numbers)* -> equal(sum_class(successor_relation),successor_relation).
% 299.82/300.43  165537[10:Res:137.1,160358.1] inductive(sum_class(successor_relation)) || member(successor_relation,ordinal_numbers)* -> .
% 299.82/300.43  185709[10:Res:185441.1,1312.0] || equal(complement(ordinal_numbers),successor_relation)** -> equal(kind_1_ordinals,universal_class).
% 299.82/300.43  160319[10:Rew:160202.0,153615.1] || equal(universal_class,ordinal_numbers) -> equal(sum_class(successor_relation),successor_relation)**.
% 299.82/300.43  98[0:Inp] || member(ordered_pair(u,ordered_pair(v,w)),composition_function)* -> equal(compose(u,v),w).
% 299.82/300.43  160401[10:Rew:160202.0,154379.1] || equal(universal_class,ordinal_numbers) -> section(element_relation,successor_relation,universal_class)*.
% 299.82/300.43  163134[10:MRR:48.2,160227.0] || equal(successor(u),v) member(ordered_pair(u,v),cross_product(universal_class,universal_class))* -> .
% 299.82/300.43  160320[10:Rew:160202.0,146546.1] inductive(ordinal_numbers) ||  -> equal(sum_class(successor_relation),successor_relation)**.
% 299.82/300.43  160047[3:Res:159952.1,1312.0] || subclass(universal_class,ordinal_numbers)* -> equal(kind_1_ordinals,universal_class).
% 299.82/300.43  160081[3:Res:8.1,160047.0] || equal(universal_class,ordinal_numbers) -> equal(kind_1_ordinals,universal_class)**.
% 299.82/300.43  97[0:Inp] ||  -> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))*.
% 299.82/300.43  160288[10:Rew:160202.0,146025.1] inductive(limit_ordinals) ||  -> member(successor_relation,ordinal_numbers)*.
% 299.82/300.43  185809[10:Res:185430.1,3630.0] || equal(complement(composition_function),successor_relation)** -> .
% 299.82/300.43  160013[3:Res:159951.0,183.1] || well_ordering(element_relation,kind_1_ordinals)* -> .
% 299.82/300.43  159908[7:Res:6.0,155335.0] || well_ordering(universal_class,universal_class)* -> .
% 299.82/300.43  187561[16:Spt:187560.0,161939.1,186523.0] || equal(composition_function,successor_relation)** -> .
% 299.82/300.43  477[0:Res:6.0,183.1] || well_ordering(element_relation,universal_class)* -> .
% 299.82/300.43  3631[0:Res:8.1,3630.0] || equal(composition_function,universal_class)** -> .
% 299.82/300.43  3630[0:AED:1.0,3629.1] || subclass(universal_class,composition_function)* -> .
% 299.82/300.43  187562[16:Spt:187560.0,161939.0,161939.2] || well_ordering(u,cross_product(universal_class,cross_product(universal_class,universal_class)))* -> member(least(u,composition_function),composition_function).
% 299.82/300.43  160784[10:Rew:160202.0,146009.2] || member(u,universal_class) subclass(u,v) -> equal(u,successor_relation) member(apply(choice,u),v)*.
% 299.82/300.43  187489[10:AED:1.0,187488.0] ||  -> member(power_class(successor_relation),universal_class)*.
% 299.82/300.43  186499[10:MRR:186454.1,160214.0] || equal(successor_relation,u) -> member(power_class(u),universal_class)*.
% 299.82/300.43  163042[10:Rew:160202.0,158809.1] || asymmetric(u,singleton(v)) -> equal(domain__dfg(intersection(u,inverse(u)),singleton(v),v),single_valued3(successor_relation))**.
% 299.82/300.43  161299[10:Rew:160202.0,146054.1] || asymmetric(u,v) subclass(compose(successor_relation,successor_relation),successor_relation) -> transitive(intersection(u,inverse(u)),v)*.
% 299.82/300.43  161270[10:Rew:160202.0,146060.2] || member(complement(u),universal_class) member(apply(choice,complement(u)),u)* -> equal(complement(u),successor_relation).
% 299.82/300.43  476[0:SpR:40.0,102.1] || member(flip(cross_product(u,universal_class)),universal_class) -> member(ordered_pair(flip(cross_product(u,universal_class)),inverse(u)),domain_relation)*.
% 299.82/300.43  475[0:SpR:55.0,102.1] || member(restrict(element_relation,universal_class,u),universal_class) -> member(ordered_pair(restrict(element_relation,universal_class,u),sum_class(u)),domain_relation)*.
% 299.82/300.43  185605[10:Rew:160328.0,185383.1] || equal(successor_relation,u) -> equal(power_class(successor_relation),power_class(u))*.
% 299.82/300.43  184982[10:Rew:160370.0,184929.1] || subclass(u,successor_relation) -> equal(union(u,successor_relation),successor_relation)**.
% 299.82/300.43  186233[15:Spt:161941.1] ||  -> equal(application_function,successor_relation)**.
% 299.82/300.43  186226[10:Res:8.1,186152.0] || equal(u,domain_relation)* equal(successor_relation,u) -> .
% 299.82/300.43  186152[10:Res:160251.1,185639.1] || subclass(domain_relation,u)* equal(successor_relation,u) -> .
% 299.82/300.43  185639[10:MRR:185509.2,34067.1] || equal(successor_relation,u) member(v,u)* -> .
% 299.82/300.43  185804[10:Res:185430.1,30448.0] || equal(complement(complement(ordered_pair(u,v))),successor_relation)** -> .
% 299.82/300.43  1487[0:Res:27.2,3.0] || member(u,universal_class)* subclass(complement(v),w)*+ -> member(u,v)* member(u,w)*.
% 299.82/300.43  185795[10:Res:185430.1,1312.0] || equal(complement(u),successor_relation)** -> equal(universal_class,u).
% 299.82/300.43  185647[10:Obv:185533.1] || equal(complement(u),successor_relation) -> member(omega,u)*.
% 299.82/300.43  185978[10:MRR:185945.1,160315.0] || equal(complement(cross_product(u,v)),successor_relation)** -> .
% 299.82/300.43  185646[10:Obv:185532.1] || equal(complement(u),successor_relation) -> member(successor_relation,u)*.
% 299.82/300.43  185508[10:SpL:185302.1,185324.0] || equal(successor_relation,u)* equal(universal_class,u) -> .
% 299.82/300.43  185834[10:Res:185430.1,181112.0] || equal(complement(complement(unordered_pair(successor_relation,u))),successor_relation)** -> .
% 299.82/300.43  185832[10:Res:185430.1,181119.0] || equal(complement(complement(unordered_pair(u,successor_relation))),successor_relation)** -> .
% 299.82/300.43  185802[10:Res:185430.1,30536.0] || equal(complement(complement(singleton(singleton(u)))),successor_relation)** -> .
% 299.82/300.43  185799[10:Res:185430.1,3551.0] || equal(complement(rest_of(u)),successor_relation)** -> .
% 299.82/300.43  185798[10:Res:185430.1,3550.0] || equal(complement(compose_class(u)),successor_relation)** -> .
% 299.82/300.43  185870[10:SoR:185844.0,73.1] one_to_one(complement(cross_product(universal_class,universal_class))) ||  -> .
% 299.82/300.43  185844[10:MRR:161503.1,185826.0] function(complement(cross_product(universal_class,universal_class))) ||  -> .
% 299.82/300.43  161953[10:Rew:160202.0,148531.1] || asymmetric(u,singleton(v)) -> equal(segment(intersection(u,inverse(u)),singleton(v),v),successor_relation)**.
% 299.82/300.43  185430[10:SpR:185302.1,107233.0] || equal(complement(u),successor_relation) -> subclass(universal_class,u)*.
% 299.82/300.43  185343[10:Res:160354.1,185066.0] || equal(successor_relation,u) subclass(universal_class,u)* -> .
% 299.82/300.43  5538[0:Res:8.1,139.1] || equal(sum_class(u),u) well_ordering(element_relation,u)* -> equal(u,ordinal_numbers) member(u,ordinal_numbers).
% 299.82/300.43  185335[10:SpL:57.0,185324.0] || equal(image(element_relation,complement(u)),power_class(u))** -> .
% 299.82/300.43  185332[10:SpL:160367.0,185324.0] || equal(symmetric_difference(universal_class,u),union(u,successor_relation))** -> .
% 299.82/300.43  185724[10:MRR:185723.1,185595.0] || subclass(image(element_relation,universal_class),power_class(successor_relation))* -> .
% 299.82/300.43  185596[10:MRR:163317.1,185595.0] || member(regular(image(element_relation,universal_class)),power_class(successor_relation))* -> .
% 299.82/300.43  185720[13:MRR:185719.1,185593.0] || subclass(image(element_relation,successor_relation),power_class(universal_class))* -> .
% 299.82/300.43  185594[13:MRR:163314.1,185593.0] || member(regular(image(element_relation,successor_relation)),power_class(universal_class))* -> .
% 299.82/300.43  185602[10:Obv:185573.1] || equal(unordered_pair(u,omega),successor_relation)** -> .
% 299.82/300.43  185600[10:Obv:185570.1] || equal(unordered_pair(omega,u),successor_relation)** -> .
% 299.82/300.43  185618[12:MRR:185617.1,177130.0] || equal(compose(element_relation,universal_class),successor_relation)** -> .
% 299.82/300.43  185595[10:MRR:185485.1,160334.0] || equal(image(element_relation,universal_class),successor_relation)** -> .
% 299.82/300.43  160209[10:Rew:160202.0,3925.0] || equal(compose(u,inverse(u)),successor_relation)**+ subclass(u,cross_product(universal_class,universal_class))* -> function(u).
% 299.82/300.43  185593[13:MRR:185484.1,182336.0] || equal(image(element_relation,successor_relation),successor_relation)** -> .
% 299.82/300.43  185586[10:Obv:185539.1] || equal(complement(domain_relation),successor_relation)** -> .
% 299.82/300.43  185585[10:Obv:185538.1] || equal(complement(rest_relation),successor_relation)** -> .
% 299.82/300.43  185584[10:Obv:185537.1] || equal(complement(element_relation),successor_relation)** -> .
% 299.82/300.43  185582[10:Obv:185520.1] || equal(singleton(omega),successor_relation)** -> .
% 299.82/300.43  185302[10:Res:160354.1,185064.0] || equal(successor_relation,u) -> equal(complement(u),universal_class)**.
% 299.82/300.43  185066[10:Res:184981.1,30433.1] || subclass(u,successor_relation)*+ subclass(universal_class,u)* -> .
% 299.82/300.43  185337[10:SpL:160328.0,185324.0] || equal(image(element_relation,universal_class),power_class(successor_relation))** -> .
% 299.82/300.43  185336[10:SpL:160322.0,185324.0] || equal(image(element_relation,successor_relation),power_class(universal_class))** -> .
% 299.82/300.43  185324[10:MRR:185323.1,3567.0] || equal(complement(u),u)** -> .
% 299.82/300.43  185064[10:Res:184981.1,1312.0] || subclass(u,successor_relation)* -> equal(complement(u),universal_class).
% 299.82/300.43  163361[10:Rew:160202.0,161603.1] ||  -> equal(cross_product(u,v),successor_relation) equal(restrict(regular(cross_product(u,v)),u,v),successor_relation)**.
% 299.82/300.43  185246[10:Res:160354.1,185079.0] || equal(singleton(unordered_pair(u,v)),successor_relation)** -> .
% 299.82/300.43  185241[10:Res:160354.1,185077.0] || equal(unordered_pair(singleton(u),v),successor_relation)** -> .
% 299.82/300.43  185225[10:Res:160354.1,185075.0] || equal(unordered_pair(u,singleton(v)),successor_relation)** -> .
% 299.82/300.43  185218[10:Res:160354.1,185068.0] || equal(singleton(ordered_pair(u,v)),successor_relation)** -> .
% 299.82/300.43  185079[10:Res:184981.1,30457.0] || subclass(singleton(unordered_pair(u,v)),successor_relation)* -> .
% 299.82/300.43  185077[10:Res:184981.1,30613.0] || subclass(unordered_pair(singleton(u),v),successor_relation)* -> .
% 299.82/300.43  185075[10:Res:184981.1,30583.0] || subclass(unordered_pair(u,singleton(v)),successor_relation)* -> .
% 299.82/300.43  185068[10:Res:184981.1,30537.0] || subclass(singleton(ordered_pair(u,v)),successor_relation)* -> .
% 299.82/300.43  1495[0:Res:148.1,3.0] || member(u,universal_class) subclass(rest_relation,v) -> member(ordered_pair(u,rest_of(u)),v)*.
% 299.82/300.43  185153[10:Res:160354.1,185078.0] || equal(unordered_pair(successor_relation,u),successor_relation)** -> .
% 299.82/300.43  185116[10:Res:160354.1,185076.0] || equal(unordered_pair(u,successor_relation),successor_relation)** -> .
% 299.82/300.43  185111[10:Res:160354.1,185067.0] || equal(singleton(singleton(u)),successor_relation)** -> .
% 299.82/300.43  185078[10:Res:184981.1,181112.0] || subclass(unordered_pair(successor_relation,u),successor_relation)* -> .
% 299.82/300.43  1028[0:SpR:57.0,27.2] || member(u,universal_class) -> member(u,image(element_relation,complement(v)))* member(u,power_class(v)).
% 299.82/300.43  185076[10:Res:184981.1,181119.0] || subclass(unordered_pair(u,successor_relation),successor_relation)* -> .
% 299.82/300.43  185067[10:Res:184981.1,30536.0] || subclass(singleton(singleton(u)),successor_relation)* -> .
% 299.82/300.43  184793[10:Res:160354.1,184766.0] || equal(successor_relation,u) -> asymmetric(u,v)*.
% 299.82/300.43  184766[10:Obv:184765.1] || subclass(u,successor_relation)*+ -> asymmetric(u,v)*.
% 299.82/300.43  184008[14:MRR:183986.3,160227.0] || member(u,universal_class)* member(v,universal_class) equal(sum_class(range_of(v)),u)*+ -> .
% 299.82/300.43  184745[11:MRR:184704.1,168458.0] || subclass(inverse(successor_relation),successor_relation)* -> .
% 299.82/300.43  184744[10:MRR:184702.1,160455.0] || subclass(singleton(successor_relation),successor_relation)* -> .
% 299.82/300.43  184779[10:Res:160354.1,184743.0] || equal(successor_relation,y__dfg)** -> .
% 299.82/300.43  184743[10:Obv:184717.1] || subclass(y__dfg,successor_relation)* -> .
% 299.82/300.43  163198[10:Rew:160202.0,160501.1] || subclass(u,successor_relation) -> equal(intersection(u,v),successor_relation)**.
% 299.82/300.43  184594[10:Res:160354.1,184544.0] || equal(inverse(u),successor_relation) -> asymmetric(u,v)*.
% 299.82/300.43  184544[10:Obv:184543.1] || subclass(inverse(u),successor_relation)*+ -> asymmetric(u,v)*.
% 299.82/300.43  184589[10:Res:8.1,184584.0] || equal(complement(kind_1_ordinals),ordinal_numbers)** -> .
% 299.82/300.43  184584[10:MRR:184583.1,184527.0] || subclass(ordinal_numbers,complement(kind_1_ordinals))* -> .
% 299.82/300.43  184528[10:MRR:163216.1,184527.0] || member(not_subclass_element(ordinal_numbers,successor_relation),complement(kind_1_ordinals))* -> .
% 299.82/300.43  161754[10:Rew:160202.0,146076.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(segment(u,rest_relation,least(u,rest_relation)),successor_relation)**.
% 299.82/300.43  184563[10:MRR:177132.1,184560.0] || equal(kind_1_ordinals,successor_relation)** -> .
% 299.82/300.43  184560[10:Res:160354.1,184527.0] || equal(successor_relation,ordinal_numbers)** -> .
% 299.82/300.43  184527[10:Obv:184502.1] || subclass(ordinal_numbers,successor_relation)* -> .
% 299.82/300.43  163197[10:Rew:160202.0,160500.1] || subclass(u,successor_relation) -> equal(intersection(v,u),successor_relation)**.
% 299.82/300.43  161755[10:Rew:160202.0,146077.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(segment(u,domain_relation,least(u,domain_relation)),successor_relation)**.
% 299.82/300.43  160511[10:Rew:160202.0,153486.1] single_valued_class(u) || equal(successor_relation,u) -> function(u)*.
% 299.82/300.43  160824[10:Rew:160202.0,146037.0] ||  -> equal(singleton(u),successor_relation) equal(regular(singleton(u)),u)**.
% 299.82/300.43  161757[10:Rew:160202.0,146079.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(segment(u,element_relation,least(u,element_relation)),successor_relation)**.
% 299.82/300.43  161242[10:Rew:160202.0,153209.1] || equal(intersection(u,v),universal_class)** -> member(successor_relation,v).
% 299.82/300.43  161234[10:Rew:160202.0,159384.1] || subclass(domain_relation,cross_product(u,v))* -> member(successor_relation,v).
% 299.82/300.43  184217[10:Res:159952.1,161271.0] || subclass(complement(kind_1_ordinals),ordinal_numbers)* -> equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.43  161271[10:Rew:160202.0,146063.1] || subclass(complement(u),u)* -> equal(complement(u),successor_relation).
% 299.82/300.43  158524[2:SpR:113504.0,144537.1] || asymmetric(universal_class,u) -> section(inverse(universal_class),u,u)*.
% 299.82/300.43  183965[14:Rew:183958.0,157.0] ||  -> equal(apply(recursion(u,successor_relation,successor_relation),v),ordinal_add(u,v))**.
% 299.82/300.43  1510[0:Res:1506.1,23.0] || equal(intersection(u,v),universal_class)** -> member(omega,u).
% 299.82/300.43  1511[0:Res:1506.1,24.0] || equal(intersection(u,v),universal_class)** -> member(omega,v).
% 299.82/300.43  184005[14:MRR:183981.2,160227.0] inductive(union_of_range_map) || well_ordering(u,cross_product(universal_class,universal_class))* -> .
% 299.82/300.43  183964[14:Rew:183958.0,160321.0] ||  -> equal(recursion(successor_relation,apply(add_relation,u),successor_relation),ordinal_multiply(u,v))*.
% 299.82/300.43  183958[14:Spt:161747.1] ||  -> equal(union_of_range_map,successor_relation)**.
% 299.82/300.43  183944[11:Res:183764.1,168466.0] || subclass(universal_class,complement(inverse(successor_relation)))* -> .
% 299.82/300.43  183764[11:Res:183757.0,3.0] || subclass(universal_class,u) -> member(regular(symmetrization_of(successor_relation)),u)*.
% 299.82/300.43  183723[10:SpL:183391.0,23.0] || member(u,symmetrization_of(successor_relation))* -> member(u,inverse(successor_relation)).
% 299.82/300.43  183622[10:SpL:183390.0,23.0] || member(u,successor(successor_relation))* -> member(u,singleton(successor_relation)).
% 299.82/300.43  183458[10:SpR:160328.0,183420.0] ||  -> equal(symmetric_difference(image(element_relation,universal_class),complement(power_class(successor_relation))),successor_relation)**.
% 299.82/300.43  183457[10:SpR:160322.0,183420.0] ||  -> equal(symmetric_difference(image(element_relation,successor_relation),complement(power_class(universal_class))),successor_relation)**.
% 299.82/300.43  1484[0:Res:12.1,3.0] || member(u,universal_class) subclass(unordered_pair(v,u),w)* -> member(u,w).
% 299.82/300.43  183452[10:SpR:160336.0,183420.0] ||  -> equal(symmetric_difference(complement(inverse(successor_relation)),complement(symmetrization_of(successor_relation))),successor_relation)**.
% 299.82/300.43  183451[10:SpR:160419.0,183420.0] ||  -> equal(symmetric_difference(complement(singleton(successor_relation)),complement(successor(successor_relation))),successor_relation)**.
% 299.82/300.43  183757[11:Res:183734.0,34067.0] ||  -> member(regular(symmetrization_of(successor_relation)),universal_class)*.
% 299.82/300.43  183734[11:MRR:183733.0,168458.0] ||  -> member(regular(symmetrization_of(successor_relation)),inverse(successor_relation))*.
% 299.82/300.43  1485[0:Res:11.1,3.0] || member(u,universal_class) subclass(unordered_pair(u,v),w)* -> member(u,w).
% 299.82/300.43  183391[10:SpR:160336.0,139600.0] ||  -> equal(intersection(inverse(successor_relation),symmetrization_of(successor_relation)),symmetrization_of(successor_relation))**.
% 299.82/300.43  183679[11:Res:168384.1,183651.0] || equal(complement(singleton(successor_relation)),symmetrization_of(successor_relation))** -> .
% 299.82/300.43  183676[11:Res:179843.1,183651.0] || equal(complement(singleton(successor_relation)),inverse(successor_relation))** -> .
% 299.82/300.43  1320[0:Res:137.1,9.0] || member(u,ordinal_numbers) subclass(u,sum_class(u))* -> equal(sum_class(u),u).
% 299.82/300.43  183681[10:Res:160271.1,183651.0] inductive(complement(singleton(successor_relation))) ||  -> .
% 299.82/300.43  183651[10:Rew:183650.0,160427.0] || member(successor_relation,complement(singleton(successor_relation)))* -> .
% 299.82/300.43  183655[10:MRR:166946.1,183651.0] inductive(complement(successor(successor_relation))) ||  -> .
% 299.82/300.43  183654[10:MRR:162941.1,183651.0] inductive(complement(successor(identity_relation))) ||  -> .
% 299.82/300.43  34070[0:MRR:5802.1,34067.1] || member(u,universal_class) member(v,u) -> member(ordered_pair(v,u),element_relation)*.
% 299.82/300.43  183650[10:Res:183633.0,2151.0] ||  -> equal(regular(successor(successor_relation)),successor_relation)**.
% 299.82/300.43  183390[10:SpR:160419.0,139600.0] ||  -> equal(intersection(singleton(successor_relation),successor(successor_relation)),successor(successor_relation))**.
% 299.82/300.43  183461[10:SpR:160336.0,183420.0] ||  -> equal(symmetric_difference(inverse(successor_relation),symmetrization_of(successor_relation)),successor_relation)**.
% 299.82/300.43  505[0:SpR:28.0,57.0] ||  -> equal(complement(image(element_relation,union(u,v))),power_class(intersection(complement(u),complement(v))))**.
% 299.82/300.43  183460[10:SpR:160419.0,183420.0] ||  -> equal(symmetric_difference(singleton(successor_relation),successor(successor_relation)),successor_relation)**.
% 299.82/300.43  183420[10:Rew:160306.0,183419.0] ||  -> equal(symmetric_difference(u,complement(complement(u))),successor_relation)**.
% 299.82/300.43  139600[0:MRR:139589.0,9395.0] ||  -> equal(intersection(u,complement(complement(u))),complement(complement(u)))**.
% 299.82/300.43  509[0:SpR:57.0,28.0] ||  -> equal(union(u,image(element_relation,complement(v))),complement(intersection(complement(u),power_class(v))))**.
% 299.82/300.43  183117[13:Res:8.1,180588.0] || equal(u,image(element_relation,successor_relation))*+ -> member(successor_relation,u)*.
% 299.82/300.43  182614[10:Res:8.1,162884.0] || equal(u,successor(successor_relation)) well_ordering(universal_class,u)* -> .
% 299.82/300.43  182465[11:Res:8.1,168391.0] || equal(u,inverse(successor_relation)) well_ordering(universal_class,u)* -> .
% 299.82/300.43  182390[11:Res:8.1,168374.0] || equal(u,symmetrization_of(successor_relation)) well_ordering(universal_class,u)* -> .
% 299.82/300.43  511[0:SpR:57.0,28.0] ||  -> equal(union(image(element_relation,complement(u)),v),complement(intersection(power_class(u),complement(v))))**.
% 299.82/300.43  182362[10:Res:8.1,160551.0] || equal(u,image(element_relation,universal_class))*+ -> member(successor_relation,u)*.
% 299.82/300.43  181044[10:Res:160362.0,168417.0] || member(u,universal_class) -> equal(singleton(successor(u)),successor_relation)**.
% 299.82/300.43  181043[10:Res:160274.1,168417.0] || member(u,universal_class) -> equal(integer_of(successor(u)),successor_relation)**.
% 299.82/300.43  160486[10:Rew:160202.0,146028.0] || member(intersection(y__dfg,ordinal_numbers),unordered_pair(u,successor_relation))* -> equal(intersection(y__dfg,ordinal_numbers),u).
% 299.82/300.43  180588[13:Res:180583.0,3.0] || subclass(image(element_relation,successor_relation),u)* -> member(successor_relation,u).
% 299.82/300.43  180019[11:Res:179843.1,2151.0] || equal(singleton(u),inverse(successor_relation))* -> equal(successor_relation,u).
% 299.82/300.43  160488[10:Rew:160202.0,146029.0] || member(intersection(y__dfg,ordinal_numbers),unordered_pair(successor_relation,u))* -> equal(intersection(y__dfg,ordinal_numbers),u).
% 299.82/300.43  148658[6:Rew:146186.0,142607.0] ||  -> equal(symmetric_difference(complement(compose(element_relation,universal_class)),element_relation),union(complement(compose(element_relation,universal_class)),element_relation))**.
% 299.82/300.43  155823[3:Res:155815.1,5.0] || member(not_subclass_element(u,kind_1_ordinals),ordinal_numbers)* -> subclass(u,kind_1_ordinals).
% 299.82/300.43  142475[2:Rew:142341.0,141896.0] ||  -> equal(symmetric_difference(image(element_relation,complement(u)),power_class(u)),universal_class)**.
% 299.82/300.43  160374[10:Rew:160202.0,148078.1] function(image(successor_relation,cross_product(universal_class,universal_class))) || member(successor_relation,cross_product(universal_class,universal_class))* -> .
% 299.82/300.43  142477[2:Rew:142341.0,141906.0] ||  -> equal(symmetric_difference(power_class(u),image(element_relation,complement(u))),universal_class)**.
% 299.82/300.43  157922[6:MRR:157903.0,34067.1] || member(u,element_relation) -> member(u,compose(element_relation,universal_class))*.
% 299.82/300.43  162871[10:Rew:160202.0,159912.0] || equal(u,singleton(successor_relation)) well_ordering(universal_class,u)* -> .
% 299.82/300.43  160409[10:Rew:160202.0,155335.0] || subclass(singleton(successor_relation),u)* well_ordering(universal_class,u) -> .
% 299.82/300.43  340[0:Res:4.1,23.0] ||  -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),u)*.
% 299.82/300.43  163200[10:Rew:160202.0,160505.0] || equal(singleton(u),singleton(successor_relation))* -> equal(successor_relation,u).
% 299.82/300.43  322[0:Res:4.1,24.0] ||  -> subclass(intersection(u,v),w) member(not_subclass_element(intersection(u,v),w),v)*.
% 299.82/300.43  182615[10:Res:314.0,162884.0] || well_ordering(universal_class,successor(successor_relation))* -> .
% 299.82/300.43  162884[10:Rew:160202.0,157642.0] || subclass(successor(successor_relation),u)* well_ordering(universal_class,u) -> .
% 299.82/300.43  163199[10:Rew:160202.0,160503.0] || equal(singleton(u),successor(successor_relation))* -> equal(successor_relation,u).
% 299.82/300.43  1481[0:Res:4.1,3.0] || subclass(u,v) -> subclass(u,w) member(not_subclass_element(u,w),v)*.
% 299.82/300.43  160289[10:Rew:160202.0,146413.0] ||  -> equal(u,successor_relation) equal(symmetric_difference(u,regular(u)),union(u,regular(u)))**.
% 299.82/300.43  160251[10:Rew:160202.0,148538.1] || subclass(domain_relation,u) -> member(ordered_pair(successor_relation,successor_relation),u)*.
% 299.82/300.43  168391[11:Res:168387.0,6045.0] || subclass(inverse(successor_relation),u)* well_ordering(universal_class,u) -> .
% 299.82/300.43  182393[11:Res:160342.0,168374.0] || well_ordering(universal_class,inverse(successor_relation))* -> .
% 299.82/300.43  182391[11:Res:314.0,168374.0] || well_ordering(universal_class,symmetrization_of(successor_relation))* -> .
% 299.82/300.43  160481[10:Rew:160202.0,146626.2] || member(u,regular(v))* member(u,v) -> equal(v,successor_relation).
% 299.82/300.43  168374[11:Res:168372.0,6045.0] || subclass(symmetrization_of(successor_relation),u)* well_ordering(universal_class,u) -> .
% 299.82/300.43  168569[11:Res:168384.1,2151.0] || equal(singleton(u),symmetrization_of(successor_relation))* -> equal(successor_relation,u).
% 299.82/300.43  160551[10:Rew:160202.0,157929.1] || subclass(image(element_relation,universal_class),u)* -> member(successor_relation,u).
% 299.82/300.43  160544[10:Rew:160202.0,159748.1] || equal(complement(complement(u)),universal_class)** -> member(successor_relation,u).
% 299.82/300.43  302[0:SpR:70.0,56.1] || member(image(u,singleton(v)),universal_class)* -> member(apply(u,v),universal_class).
% 299.82/300.43  182315[11:Res:168387.0,160258.1] || equal(complement(inverse(successor_relation)),universal_class)** -> .
% 299.82/300.43  182336[13:Rew:160322.0,182320.0] || equal(power_class(universal_class),universal_class)** -> .
% 299.82/300.43  160258[10:Rew:160202.0,153205.1] || equal(complement(u),universal_class) member(successor_relation,u)* -> .
% 299.82/300.43  1479[0:Res:56.1,3.0] || member(u,universal_class) subclass(universal_class,v) -> member(sum_class(u),v)*.
% 299.82/300.43  160441[10:Rew:160202.0,146146.1] inductive(symmetric_difference(universal_class,u)) ||  -> member(successor_relation,complement(u))*.
% 299.82/300.43  161203[10:Rew:160202.0,156015.0] ||  -> equal(union(symmetric_difference(universal_class,u),union(u,successor_relation)),universal_class)**.
% 299.82/300.43  161204[10:Rew:160202.0,156016.0] ||  -> equal(union(union(u,successor_relation),symmetric_difference(universal_class,u)),universal_class)**.
% 299.82/300.43  161205[10:Rew:160202.0,156017.0] ||  -> equal(symmetric_difference(symmetric_difference(universal_class,u),union(u,successor_relation)),universal_class)**.
% 299.82/300.43  307[0:SpL:57.0,26.1] || member(u,image(element_relation,complement(v)))* member(u,power_class(v)) -> .
% 299.82/300.43  161206[10:Rew:160202.0,156018.0] ||  -> equal(symmetric_difference(union(u,successor_relation),symmetric_difference(universal_class,u)),universal_class)**.
% 299.82/300.43  160467[10:Rew:160202.0,146056.1] inductive(cantor(inverse(u))) ||  -> member(successor_relation,range_of(u))*.
% 299.82/300.43  160469[10:Rew:160202.0,146171.0] ||  -> equal(intersection(image(element_relation,complement(u)),power_class(u)),successor_relation)**.
% 299.82/300.43  160470[10:Rew:160202.0,146173.0] ||  -> equal(intersection(power_class(u),image(element_relation,complement(u))),successor_relation)**.
% 299.82/300.43  160473[10:Rew:160202.0,148527.0] ||  -> equal(second(not_subclass_element(successor_relation,successor_relation)),range__dfg(successor_relation,u,v))*.
% 299.82/300.43  160489[10:Rew:160202.0,153415.0] || equal(sum_class(u),successor_relation) -> section(element_relation,u,universal_class)*.
% 299.82/300.43  162964[10:Rew:160202.0,156019.0] ||  -> equal(intersection(symmetric_difference(universal_class,u),union(u,successor_relation)),successor_relation)**.
% 299.82/300.43  162965[10:Rew:160202.0,156020.0] ||  -> equal(intersection(union(u,successor_relation),symmetric_difference(universal_class,u)),successor_relation)**.
% 299.82/300.43  309[0:Res:4.1,26.1] || member(not_subclass_element(complement(u),v),u)* -> subclass(complement(u),v).
% 299.82/300.43  181642[10:SpR:160336.0,163000.0] ||  -> equal(intersection(symmetrization_of(successor_relation),symmetric_difference(universal_class,inverse(successor_relation))),successor_relation)**.
% 299.82/300.43  181641[10:SpR:160419.0,163000.0] ||  -> equal(intersection(successor(successor_relation),symmetric_difference(universal_class,singleton(successor_relation))),successor_relation)**.
% 299.82/300.43  163000[10:Rew:160202.0,156405.0] ||  -> equal(intersection(complement(complement(u)),symmetric_difference(universal_class,u)),successor_relation)**.
% 299.82/300.43  181464[10:SpR:160336.0,163005.0] ||  -> equal(intersection(symmetric_difference(universal_class,inverse(successor_relation)),symmetrization_of(successor_relation)),successor_relation)**.
% 299.82/300.43  160290[10:Rew:160202.0,146010.1] || subclass(u,v) -> equal(u,successor_relation) member(regular(u),v)*.
% 299.82/300.43  181463[10:SpR:160419.0,163005.0] ||  -> equal(intersection(symmetric_difference(universal_class,singleton(successor_relation)),successor(successor_relation)),successor_relation)**.
% 299.82/300.43  163005[10:Rew:160202.0,156628.0] ||  -> equal(intersection(symmetric_difference(universal_class,u),complement(complement(u))),successor_relation)**.
% 299.82/300.43  181082[10:SpR:181056.0,70.0] ||  -> equal(sum_class(image(u,successor_relation)),apply(u,universal_class))**.
% 299.82/300.43  160466[10:Rew:160202.0,146067.0] ||  -> equal(intersection(u,v),successor_relation) member(regular(intersection(u,v)),u)*.
% 299.82/300.43  181084[10:SpR:181056.0,1006.0] ||  -> member(unordered_pair(u,successor_relation),ordered_pair(u,universal_class))*.
% 299.82/300.43  181119[10:SpL:181056.0,30583.0] || subclass(universal_class,complement(unordered_pair(u,successor_relation)))* -> .
% 299.82/300.43  181112[10:SpL:181056.0,30613.0] || subclass(universal_class,complement(unordered_pair(successor_relation,u)))* -> .
% 299.82/300.43  181229[10:Res:3907.1,181220.0] || equal(complement(complement(domain_relation)),universal_class)** -> .
% 299.82/300.43  160465[10:Rew:160202.0,146068.0] ||  -> equal(intersection(u,v),successor_relation) member(regular(intersection(u,v)),v)*.
% 299.82/300.43  181220[10:MRR:181219.1,3567.0] || member(singleton(singleton(successor_relation)),domain_relation)* -> .
% 299.82/300.43  181067[10:SpR:181056.0,1005.0] ||  -> equal(ordered_pair(successor_relation,universal_class),singleton(singleton(successor_relation)))**.
% 299.82/300.43  181175[10:Res:3907.1,181130.0] || equal(complement(complement(rest_relation)),universal_class)** -> .
% 299.82/300.43  181130[10:MRR:181129.1,3594.0] || member(singleton(singleton(successor_relation)),rest_relation)* -> .
% 299.82/300.44  181089[10:SpL:181056.0,30536.0] || subclass(universal_class,complement(singleton(successor_relation)))* -> .
% 299.82/300.44  181060[10:SpR:181056.0,1009.0] ||  -> member(singleton(successor_relation),singleton(singleton(successor_relation)))*.
% 299.82/300.44  163227[10:Rew:160202.0,160351.1] inductive(unordered_pair(u,v)) ||  -> equal(successor_relation,v)* equal(successor_relation,u)*.
% 299.82/300.44  181063[10:SpR:181056.0,1004.0] ||  -> member(successor_relation,ordered_pair(universal_class,u))*.
% 299.82/300.44  181056[10:Res:160362.0,181045.0] ||  -> equal(singleton(universal_class),successor_relation)**.
% 299.82/300.44  181055[10:Res:160274.1,181045.0] ||  -> equal(integer_of(universal_class),successor_relation)**.
% 299.82/300.44  181045[10:Obv:181042.0] || member(universal_class,universal_class)* -> .
% 299.82/300.44  160464[10:Rew:160202.0,148144.1] || subclass(omega,u)*+ -> equal(integer_of(v),successor_relation) member(v,u)*.
% 299.82/300.44  168417[10:EqR:163135.2] || member(successor(u),universal_class)* member(u,universal_class) -> .
% 299.82/300.44  231[0:Res:4.1,159.0] ||  -> subclass(omega,u) equal(integer_of(not_subclass_element(omega,u)),not_subclass_element(omega,u))**.
% 299.82/300.44  208[0:SpR:57.0,57.0] ||  -> equal(complement(image(element_relation,power_class(u))),power_class(image(element_relation,complement(u))))**.
% 299.82/300.44  160376[10:Rew:160202.0,148083.1] inductive(compose_class(u)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  160375[10:Rew:160202.0,148084.1] inductive(rest_of(u)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  163194[10:Rew:160202.0,160461.0] || subclass(compose(successor_relation,successor_relation),successor_relation)*+ -> transitive(successor_relation,u)*.
% 299.82/300.44  163196[10:Rew:160202.0,160463.1] || transitive(successor_relation,u)*+ -> equal(compose(successor_relation,successor_relation),successor_relation)**.
% 299.82/300.44  148657[6:Rew:146186.0,141730.1] || member(u,element_relation) member(u,complement(compose(element_relation,universal_class)))* -> .
% 299.82/300.44  163195[10:Rew:160202.0,160462.0] || equal(compose(successor_relation,successor_relation),successor_relation)**+ -> transitive(successor_relation,u)*.
% 299.82/300.44  180748[11:SoR:179845.0,73.1] one_to_one(inverse(successor_relation)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  2418[0:Res:20.0,9.0] || subclass(cross_product(universal_class,universal_class),element_relation)* -> equal(cross_product(universal_class,universal_class),element_relation).
% 299.82/300.44  180608[11:SoR:168386.0,73.1] one_to_one(symmetrization_of(successor_relation)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  160435[10:Rew:160202.0,146051.2] inductive(u) || subclass(u,v)* -> member(successor_relation,v).
% 299.82/300.44  180600[10:SoR:167119.0,73.1] one_to_one(successor(successor_relation)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  160454[10:Rew:160202.0,146061.1] || member(regular(complement(u)),u)* -> equal(complement(u),successor_relation).
% 299.82/300.44  179845[11:Res:64.1,168395.0] function(inverse(successor_relation)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  160051[3:Res:159952.1,5754.0] || subclass(sum_class(kind_1_ordinals),ordinal_numbers) -> section(element_relation,kind_1_ordinals,universal_class)*.
% 299.82/300.44  164227[10:Res:160271.1,47888.0] inductive(rest_of(successor_relation)) || subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.44  164223[10:Res:160271.1,48083.0] inductive(cantor(successor_relation)) || subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.44  164219[10:Res:160271.1,47745.0] inductive(domain_of(successor_relation)) || subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.44  151864[6:Res:145997.1,47888.0] inductive(rest_of(identity_relation)) || subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.44  151860[6:Res:145997.1,48083.0] inductive(cantor(identity_relation)) || subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.44  151856[6:Res:145997.1,47745.0] inductive(domain_of(identity_relation)) || subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.44  81159[2:Res:2457.1,47745.0] inductive(domain_of(singleton_relation)) || subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.44  51731[2:Res:2457.1,47888.0] inductive(rest_of(singleton_relation)) || subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.44  164882[10:MRR:164880.2,145037.0] function(range_of(successor_relation)) || member(successor_relation,cross_product(universal_class,universal_class))* -> .
% 299.82/300.44  51733[2:Res:2457.1,48083.0] inductive(cantor(singleton_relation)) || subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.44  1476[0:Res:13.0,3.0] || subclass(universal_class,u) -> member(unordered_pair(v,w),u)*.
% 299.82/300.44  5754[0:MRR:5748.0,6.0] || subclass(sum_class(u),u)*+ -> section(element_relation,u,universal_class)*.
% 299.82/300.44  168386[11:Res:64.1,168378.0] function(symmetrization_of(successor_relation)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  167119[10:Res:64.1,163170.0] function(successor(successor_relation)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  2125[0:SpR:55.0,134.1] || section(element_relation,u,universal_class)*+ -> subclass(sum_class(u),u)*.
% 299.82/300.44  180583[13:Spt:163193.0] ||  -> member(successor_relation,image(element_relation,successor_relation))*.
% 299.82/300.44  160210[10:Rew:160202.0,2671.0] || equal(compose(u,inverse(u)),successor_relation)** -> single_valued_class(u).
% 299.82/300.44  160252[10:Rew:160202.0,159494.1] || equal(rest_relation,domain_relation) -> member(ordered_pair(successor_relation,successor_relation),rest_relation)*.
% 299.82/300.44  160208[10:Rew:160202.0,148548.1] single_valued_class(u) ||  -> equal(compose(u,inverse(u)),successor_relation)**.
% 299.82/300.44  160207[10:Rew:160202.0,148549.1] function(u) ||  -> equal(compose(u,inverse(u)),successor_relation)**.
% 299.82/300.44  160379[10:Rew:160202.0,157653.1] function(successor(identity_relation)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  160378[10:Rew:160202.0,157988.1] one_to_one(successor(identity_relation)) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  160437[10:Rew:160202.0,148111.0] ||  -> equal(integer_of(not_subclass_element(u,omega)),successor_relation)** subclass(u,omega).
% 299.82/300.44  9418[0:SpR:30.0,9395.0] ||  -> subclass(restrict(u,v,w),cross_product(v,w))*.
% 299.82/300.44  34189[0:Res:4.1,34067.0] ||  -> subclass(u,v) member(not_subclass_element(u,v),universal_class)*.
% 299.82/300.44  1006[0:MRR:1001.0,13.0] ||  -> member(unordered_pair(u,singleton(v)),ordered_pair(u,v))*.
% 299.82/300.44  160447[10:Rew:160202.0,148530.1] || subclass(u,v) -> section(successor_relation,u,v)*.
% 299.82/300.44  305[0:SpR:14.0,12.1] || member(u,universal_class) -> member(u,singleton(u))*.
% 299.82/300.44  9089[0:MRR:9087.1,191.0] function(u) ||  -> member(apply(u,v),universal_class)*.
% 299.82/300.44  160266[10:Rew:160202.0,145994.1] inductive(intersection(u,v)) ||  -> member(successor_relation,u)*.
% 299.82/300.44  160273[10:Rew:160202.0,145999.0] ||  -> equal(integer_of(u),successor_relation)** equal(integer_of(u),u)**.
% 299.82/300.44  160352[10:Rew:160202.0,146031.0] || equal(successor_relation,u) -> equal(integer_of(u),u)**.
% 299.82/300.44  160361[10:Rew:160202.0,146038.0] ||  -> equal(singleton(u),successor_relation) member(u,singleton(u))*.
% 299.82/300.44  160436[10:Rew:160202.0,146052.1] inductive(intersection(u,v)) ||  -> member(successor_relation,v)*.
% 299.82/300.44  160443[10:Rew:160202.0,146160.0] ||  -> equal(intersection(complement(u),intersection(u,v)),successor_relation)**.
% 299.82/300.44  160444[10:Rew:160202.0,146165.0] ||  -> equal(intersection(complement(u),intersection(v,u)),successor_relation)**.
% 299.82/300.44  160445[10:Rew:160202.0,146166.0] ||  -> equal(intersection(intersection(u,v),complement(u)),successor_relation)**.
% 299.82/300.44  36[0:Inp] || member(ordered_pair(ordered_pair(u,v),w),x) member(ordered_pair(ordered_pair(w,u),v),cross_product(cross_product(universal_class,universal_class),universal_class))*+ -> member(ordered_pair(ordered_pair(w,u),v),rotate(x))*.
% 299.82/300.44  160446[10:Rew:160202.0,146168.0] ||  -> equal(intersection(intersection(u,v),complement(v)),successor_relation)**.
% 299.82/300.44  180024[11:MRR:180001.1,160315.0] || equal(cross_product(u,v),inverse(successor_relation))** -> .
% 299.82/300.44  179843[11:Res:8.1,168395.0] || equal(u,inverse(successor_relation)) -> member(successor_relation,u)*.
% 299.82/300.44  39[0:Inp] || member(ordered_pair(ordered_pair(u,v),w),x) member(ordered_pair(ordered_pair(v,u),w),cross_product(cross_product(universal_class,universal_class),universal_class))*+ -> member(ordered_pair(ordered_pair(v,u),w),flip(x))*.
% 299.82/300.44  120366[0:Res:146.0,28300.1] || member(u,universal_class) -> member(rest_of(u),universal_class)*.
% 299.82/300.44  30613[0:SpL:14.0,30460.0] || subclass(universal_class,complement(unordered_pair(singleton(u),v)))* -> .
% 299.82/300.44  3906[0:MRR:3894.0,191.0] || equal(complement(unordered_pair(singleton(u),v)),universal_class)** -> .
% 299.82/300.44  30457[0:MRR:30441.0,13.0] || subclass(universal_class,complement(singleton(unordered_pair(u,v))))* -> .
% 299.82/300.44  30539[0:Res:8.1,30457.0] || equal(complement(singleton(unordered_pair(u,v))),universal_class)** -> .
% 299.82/300.44  30583[0:SpL:14.0,30459.0] || subclass(universal_class,complement(unordered_pair(u,singleton(v))))* -> .
% 299.82/300.44  3905[0:MRR:3893.0,191.0] || equal(complement(unordered_pair(u,singleton(v))),universal_class)** -> .
% 299.82/300.44  5761[0:Res:137.1,5754.0] || member(u,ordinal_numbers) -> section(element_relation,u,universal_class)*.
% 299.82/300.44  1344[0:SpR:124.0,55.0] ||  -> equal(segment(element_relation,universal_class,u),sum_class(singleton(u)))**.
% 299.82/300.44  160396[10:Rew:160202.0,146057.2] || connected(u,v) member(w,not_well_ordering(u,v)) equal(segment(u,not_well_ordering(u,v),w),successor_relation)** -> well_ordering(u,v).
% 299.82/300.44  107289[0:SpR:57.0,107233.0] ||  -> subclass(complement(power_class(u)),image(element_relation,complement(u)))*.
% 299.82/300.44  179890[11:Res:179839.1,160227.0] || equal(inverse(successor_relation),successor_relation)** -> .
% 299.82/300.44  168395[11:Res:168387.0,3.0] || subclass(inverse(successor_relation),u)* -> member(successor_relation,u).
% 299.82/300.44  163171[10:Rew:160202.0,160262.0] || equal(u,singleton(successor_relation)) -> member(successor_relation,u)*.
% 299.82/300.44  163172[10:Rew:160202.0,160264.0] || subclass(singleton(successor_relation),u)* -> member(successor_relation,u).
% 299.82/300.44  163169[10:Rew:160202.0,160260.0] || equal(u,successor(successor_relation)) -> member(successor_relation,u)*.
% 299.82/300.44  163170[10:Rew:160202.0,160261.0] || subclass(successor(successor_relation),u)* -> member(successor_relation,u).
% 299.82/300.44  168384[11:Res:8.1,168378.0] || equal(u,symmetrization_of(successor_relation)) -> member(successor_relation,u)*.
% 299.82/300.44  168378[11:Res:168372.0,3.0] || subclass(symmetrization_of(successor_relation),u)* -> member(successor_relation,u).
% 299.82/300.44  120[0:Inp] || transitive(u,v) -> subclass(compose(restrict(u,v,v),restrict(u,v,v)),restrict(u,v,v))*.
% 299.82/300.44  160265[10:Rew:160202.0,145990.1] inductive(complement(complement(u))) ||  -> member(successor_relation,u)*.
% 299.82/300.44  160257[10:Rew:160202.0,159914.0] || member(successor_relation,u) well_ordering(universal_class,u)* -> .
% 299.82/300.44  160256[10:Rew:160202.0,159916.1] || well_ordering(universal_class,complement(u))* -> member(successor_relation,u).
% 299.82/300.44  160267[10:Rew:160202.0,145995.1] inductive(complement(u)) || member(successor_relation,u)* -> .
% 299.82/300.44  160272[10:Rew:160202.0,155843.0] ||  -> equal(integer_of(u),successor_relation) subclass(singleton(u),omega)*.
% 299.82/300.44  160476[10:Rew:160202.0,158812.1] function(u) ||  -> equal(single_valued3(successor_relation),single_valued1(u))*.
% 299.82/300.44  160475[10:Rew:160202.0,158813.1] single_valued_class(u) ||  -> equal(single_valued3(successor_relation),single_valued1(u))*.
% 299.82/300.44  160367[10:Rew:160202.0,148450.0] ||  -> equal(complement(symmetric_difference(universal_class,u)),union(u,successor_relation))**.
% 299.82/300.44  160368[10:Rew:160202.0,148451.0] ||  -> subclass(symmetric_difference(complement(u),universal_class),union(u,successor_relation))*.
% 299.82/300.44  160369[10:Rew:160202.0,156010.0] ||  -> subclass(complement(union(u,successor_relation)),symmetric_difference(universal_class,u))*.
% 299.82/300.44  160292[10:Rew:160202.0,146011.2] || subclass(u,v)*+ well_ordering(w,v)* -> equal(u,successor_relation) member(least(w,u),u)*.
% 299.82/300.44  160448[10:Rew:160202.0,156837.1] inductive(domain_of(u)) ||  -> member(successor_relation,cantor(u))*.
% 299.82/300.44  160373[10:Rew:160202.0,146053.2] || subclass(u,v)*+ well_ordering(w,v)* -> equal(segment(w,u,least(w,u)),successor_relation)**.
% 299.82/300.44  3587[4:MRR:3584.0,3584.1,54.0,3094.0] ||  -> equal(integer_of(apply(choice,omega)),apply(choice,omega))**.
% 299.82/300.44  139[0:Inp] || well_ordering(element_relation,u) subclass(sum_class(u),u)* -> equal(u,ordinal_numbers) member(u,ordinal_numbers).
% 299.82/300.44  160420[10:Rew:160202.0,152507.0] ||  -> equal(union(successor(successor_relation),complement(singleton(successor_relation))),universal_class)**.
% 299.82/300.44  160421[10:Rew:160202.0,152506.0] ||  -> equal(union(complement(singleton(successor_relation)),successor(successor_relation)),universal_class)**.
% 299.82/300.44  160422[10:Rew:160202.0,150019.0] ||  -> equal(symmetric_difference(successor(successor_relation),complement(singleton(successor_relation))),universal_class)**.
% 299.82/300.44  160423[10:Rew:160202.0,150017.0] ||  -> equal(symmetric_difference(complement(singleton(successor_relation)),successor(successor_relation)),universal_class)**.
% 299.82/300.44  160203[10:Rew:160202.0,66.1] || subclass(u,cross_product(universal_class,universal_class)) subclass(compose(u,inverse(u)),successor_relation)* -> function(u).
% 299.82/300.44  160350[10:Rew:160202.0,146042.0] ||  -> equal(first(not_subclass_element(restrict(u,v,singleton(w)),successor_relation)),domain__dfg(u,v,w))**.
% 299.82/300.44  160330[10:Rew:160202.0,149733.0] ||  -> equal(union(image(element_relation,universal_class),power_class(successor_relation)),universal_class)**.
% 299.82/300.44  160331[10:Rew:160202.0,149734.0] ||  -> equal(union(power_class(successor_relation),image(element_relation,universal_class)),universal_class)**.
% 299.82/300.44  160332[10:Rew:160202.0,149735.0] ||  -> equal(symmetric_difference(image(element_relation,universal_class),power_class(successor_relation)),universal_class)**.
% 299.82/300.44  160333[10:Rew:160202.0,149736.0] ||  -> equal(symmetric_difference(power_class(successor_relation),image(element_relation,universal_class)),universal_class)**.
% 299.82/300.44  160359[10:Rew:160202.0,146043.0] ||  -> equal(second(not_subclass_element(restrict(u,singleton(v),w),successor_relation)),range__dfg(u,v,w))**.
% 299.82/300.44  160338[10:Rew:160202.0,150006.0] ||  -> equal(symmetric_difference(complement(inverse(successor_relation)),symmetrization_of(successor_relation)),universal_class)**.
% 299.82/300.44  160339[10:Rew:160202.0,150008.0] ||  -> equal(symmetric_difference(symmetrization_of(successor_relation),complement(inverse(successor_relation))),universal_class)**.
% 299.82/300.44  160365[10:Rew:160202.0,146044.0] || equal(restrict(intersection(u,inverse(u)),v,v),successor_relation)** -> asymmetric(u,v).
% 299.82/300.44  160340[10:Rew:160202.0,152757.0] ||  -> equal(union(complement(inverse(successor_relation)),symmetrization_of(successor_relation)),universal_class)**.
% 299.82/300.44  160341[10:Rew:160202.0,152758.0] ||  -> equal(union(symmetrization_of(successor_relation),complement(inverse(successor_relation))),universal_class)**.
% 299.82/300.44  160364[10:Rew:160202.0,146045.1] || asymmetric(u,v) -> equal(restrict(intersection(u,inverse(u)),v,v),successor_relation)**.
% 299.82/300.44  168466[11:MRR:163276.1,168458.0] || member(regular(symmetrization_of(successor_relation)),complement(inverse(successor_relation)))* -> .
% 299.82/300.44  160371[10:Rew:160202.0,146046.1] || connected(u,v) equal(not_well_ordering(u,v),successor_relation)** -> well_ordering(u,v).
% 299.82/300.44  160324[10:Rew:160202.0,152593.0] ||  -> equal(union(image(element_relation,successor_relation),power_class(universal_class)),universal_class)**.
% 299.82/300.44  160325[10:Rew:160202.0,152594.0] ||  -> equal(union(power_class(universal_class),image(element_relation,successor_relation)),universal_class)**.
% 299.82/300.44  160326[10:Rew:160202.0,152595.0] ||  -> equal(symmetric_difference(image(element_relation,successor_relation),power_class(universal_class)),universal_class)**.
% 299.82/300.44  160327[10:Rew:160202.0,152596.0] ||  -> equal(symmetric_difference(power_class(universal_class),image(element_relation,successor_relation)),universal_class)**.
% 299.82/300.44  160387[10:Rew:160202.0,148085.1] inductive(element_relation) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  160385[10:Rew:160202.0,148087.1] inductive(domain_relation) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  10[0:Inp] || member(u,unordered_pair(v,w))* -> equal(u,w) equal(u,v).
% 299.82/300.44  160384[10:Rew:160202.0,148088.1] inductive(rest_relation) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  160383[10:Rew:160202.0,148089.1] inductive(union_of_range_map) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  160390[10:Rew:160202.0,148434.0] ||  -> equal(intersection(image(element_relation,successor_relation),power_class(universal_class)),successor_relation)**.
% 299.82/300.44  160391[10:Rew:160202.0,148435.0] ||  -> equal(intersection(power_class(universal_class),image(element_relation,successor_relation)),successor_relation)**.
% 299.82/300.44  67[0:Inp] function(u) || member(v,universal_class) -> member(image(u,v),universal_class)*.
% 299.82/300.44  160392[10:Rew:160202.0,148460.0] ||  -> equal(intersection(image(element_relation,universal_class),power_class(successor_relation)),successor_relation)**.
% 299.82/300.44  160393[10:Rew:160202.0,148461.0] ||  -> equal(intersection(power_class(successor_relation),image(element_relation,universal_class)),successor_relation)**.
% 299.82/300.44  160296[10:Rew:160202.0,146015.1] || member(u,universal_class) -> equal(u,successor_relation) member(apply(choice,u),u)*.
% 299.82/300.44  160397[10:Rew:160202.0,150349.0] ||  -> equal(intersection(complement(inverse(successor_relation)),symmetrization_of(successor_relation)),successor_relation)**.
% 299.82/300.44  160398[10:Rew:160202.0,150351.0] ||  -> equal(intersection(symmetrization_of(successor_relation),complement(inverse(successor_relation))),successor_relation)**.
% 299.82/300.44  27[0:Inp] || member(u,universal_class) -> member(u,v) member(u,complement(v))*.
% 299.82/300.44  160433[10:Rew:160202.0,150357.0] ||  -> equal(intersection(successor(successor_relation),complement(singleton(successor_relation))),successor_relation)**.
% 299.82/300.44  160434[10:Rew:160202.0,150355.0] ||  -> equal(intersection(complement(singleton(successor_relation)),successor(successor_relation)),successor_relation)**.
% 299.82/300.44  160480[10:Rew:160202.0,159380.1] || subclass(domain_relation,rest_relation)* -> equal(rest_of(successor_relation),successor_relation).
% 299.82/300.44  160479[10:Rew:160202.0,159471.1] || equal(rest_relation,domain_relation) -> equal(rest_of(successor_relation),successor_relation)**.
% 299.82/300.44  15[0:Inp] ||  -> equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v))**.
% 299.82/300.44  160357[10:Rew:160202.0,147239.0] || subclass(u,successor_relation)*+ -> subclass(u,v)*.
% 299.82/300.44  160354[10:Rew:160202.0,153302.0] || equal(successor_relation,u) -> subclass(u,v)*.
% 299.82/300.44  160410[10:Rew:160202.0,156316.0] || equal(cross_product(u,v),singleton(successor_relation))** -> .
% 299.82/300.44  160428[10:Rew:160202.0,157871.0] || equal(cross_product(u,v),successor(successor_relation))** -> .
% 299.82/300.44  160269[10:Rew:160202.0,146389.1] || subclass(universal_class,u)* -> member(successor_relation,u).
% 299.82/300.44  160268[10:Rew:160202.0,153020.1] || equal(u,universal_class) -> member(successor_relation,u)*.
% 299.82/300.44  163162[10:Rew:160202.0,160263.1] ||  -> member(successor_relation,u) member(successor_relation,complement(u))*.
% 299.82/300.44  160274[10:Rew:160202.0,148470.0] ||  -> equal(integer_of(u),successor_relation) member(u,universal_class)*.
% 299.82/300.44  168577[11:MRR:168544.1,160315.0] || equal(cross_product(u,v),symmetrization_of(successor_relation))** -> .
% 299.82/300.44  160295[10:Rew:160202.0,146012.0] ||  -> equal(u,successor_relation) member(regular(u),universal_class)*.
% 299.82/300.44  163165[10:Rew:160202.0,160294.0] || equal(successor_relation,u)* -> equal(u,successor_relation).
% 299.82/300.44  163163[10:Rew:160202.0,160293.0] || subclass(u,successor_relation)* -> equal(u,successor_relation).
% 299.82/300.44  160358[10:Rew:160202.0,149704.1] inductive(u) || subclass(u,successor_relation)* -> .
% 299.82/300.44  160356[10:Rew:160202.0,146032.1] inductive(singleton(u)) ||  -> equal(successor_relation,u)*.
% 299.82/300.44  148[0:Inp] || member(u,universal_class) -> member(ordered_pair(u,rest_of(u)),rest_relation)*.
% 299.82/300.44  160355[10:Rew:160202.0,153141.1] inductive(u) || equal(successor_relation,u)* -> .
% 299.82/300.44  163166[10:Rew:160202.0,160360.1] || connected(u,successor_relation) -> well_ordering(u,successor_relation)*.
% 299.82/300.44  160362[10:Rew:160202.0,146039.1] ||  -> member(u,universal_class)* equal(singleton(u),successor_relation).
% 299.82/300.44  160363[10:Rew:160202.0,148462.0] ||  -> equal(union(successor_relation,u),complement(complement(u)))**.
% 299.82/300.44  160205[10:Rew:160202.0,104.0] ||  -> equal(second(not_subclass_element(compose(u,inverse(u)),successor_relation)),single_valued2(u))**.
% 299.82/300.44  160366[10:Rew:160202.0,148488.0] ||  -> equal(symmetric_difference(successor_relation,u),complement(complement(u)))**.
% 299.82/300.44  160370[10:Rew:160202.0,148501.0] ||  -> equal(symmetric_difference(u,successor_relation),union(u,successor_relation))**.
% 299.82/300.44  160477[10:Rew:160202.0,158808.0] ||  -> equal(domain__dfg(successor_relation,u,v),single_valued3(successor_relation))**.
% 299.82/300.44  3419[0:MRR:3416.0,54.0] || equal(complement(unordered_pair(omega,u)),universal_class)** -> .
% 299.82/300.44  160206[10:Rew:160202.0,103.0] ||  -> equal(first(not_subclass_element(compose(u,inverse(u)),successor_relation)),single_valued1(u))**.
% 299.82/300.44  3379[0:MRR:3376.0,54.0] || equal(complement(unordered_pair(u,omega)),universal_class)** -> .
% 299.82/300.44  160485[10:Rew:160202.0,159757.0] || equal(complement(unordered_pair(u,successor_relation)),universal_class)** -> .
% 299.82/300.44  5[0:Inp] || member(not_subclass_element(u,v),v)* -> subclass(u,v).
% 299.82/300.44  160487[10:Rew:160202.0,159758.0] || equal(complement(unordered_pair(successor_relation,u)),universal_class)** -> .
% 299.82/300.44  160407[10:Rew:160202.0,145978.0] || member(intersection(y__dfg,ordinal_numbers),singleton(successor_relation))* -> .
% 299.82/300.44  160417[10:Rew:160202.0,149940.0] ||  -> subclass(complement(successor(successor_relation)),complement(singleton(successor_relation)))*.
% 299.82/300.44  12[0:Inp] || member(u,universal_class) -> member(u,unordered_pair(v,u))*.
% 299.82/300.44  160419[10:Rew:160202.0,148217.0] ||  -> equal(complement(complement(singleton(successor_relation))),successor(successor_relation))**.
% 299.82/300.44  160424[10:Rew:160202.0,157742.0] || subclass(successor(successor_relation),complement(singleton(successor_relation)))* -> .
% 299.82/300.44  160425[10:Rew:160202.0,157743.0] || equal(complement(singleton(successor_relation)),successor(successor_relation))** -> .
% 299.82/300.44  11[0:Inp] || member(u,universal_class) -> member(u,unordered_pair(u,v))*.
% 299.82/300.44  160328[10:Rew:160202.0,148436.0] ||  -> equal(complement(image(element_relation,universal_class)),power_class(successor_relation))**.
% 299.82/300.44  160329[10:Rew:160202.0,148437.0] ||  -> subclass(complement(power_class(successor_relation)),image(element_relation,universal_class))*.
% 299.82/300.44  160336[10:Rew:160202.0,148459.0] ||  -> equal(complement(complement(inverse(successor_relation))),symmetrization_of(successor_relation))**.
% 299.82/300.44  70[0:Inp] ||  -> equal(sum_class(image(u,singleton(v))),apply(u,v))**.
% 299.82/300.44  160337[10:Rew:160202.0,149937.0] ||  -> subclass(complement(symmetrization_of(successor_relation)),complement(inverse(successor_relation)))*.
% 299.82/300.44  168464[11:MRR:163241.1,168458.0] || subclass(symmetrization_of(successor_relation),complement(inverse(successor_relation)))* -> .
% 299.82/300.44  168465[11:MRR:163242.1,168458.0] || equal(complement(inverse(successor_relation)),symmetrization_of(successor_relation))** -> .
% 299.82/300.44  21[0:Inp] || member(ordered_pair(u,v),element_relation)* -> member(u,v).
% 299.82/300.44  160322[10:Rew:160202.0,148320.0] ||  -> equal(complement(image(element_relation,successor_relation)),power_class(universal_class))**.
% 299.82/300.44  160323[10:Rew:160202.0,148321.0] ||  -> subclass(complement(power_class(universal_class)),image(element_relation,successor_relation))*.
% 299.82/300.44  163184[10:Rew:160202.0,160297.1] ||  -> equal(u,successor_relation) equal(intersection(u,regular(u)),successor_relation)**.
% 299.82/300.44  160474[10:Rew:160202.0,158806.0] ||  -> equal(first(not_subclass_element(successor_relation,successor_relation)),single_valued3(successor_relation))**.
% 299.82/300.44  9424[0:SpR:31.0,9395.0] ||  -> subclass(restrict(u,v,w),u)*.
% 299.82/300.44  160204[10:Rew:160202.0,63.0] || subclass(compose(u,inverse(u)),successor_relation)* -> single_valued_class(u).
% 299.82/300.44  159954[3:Obv:159945.0] ||  -> subclass(restrict(ordinal_numbers,u,v),kind_1_ordinals)*.
% 299.82/300.44  160306[10:Rew:160202.0,146149.0] ||  -> equal(intersection(u,complement(u)),successor_relation)**.
% 299.82/300.44  160307[10:Rew:160202.0,146151.0] ||  -> equal(intersection(complement(u),u),successor_relation)**.
% 299.82/300.44  4[0:Inp] ||  -> subclass(u,v) member(not_subclass_element(u,v),u)*.
% 299.82/300.44  160312[10:Rew:160202.0,146201.0] ||  -> equal(restrict(successor_relation,u,v),successor_relation)**.
% 299.82/300.44  160313[10:Rew:160202.0,146207.0] || subclass(ordered_pair(u,v),successor_relation)* -> .
% 299.82/300.44  160314[10:Rew:160202.0,146208.0] ||  -> equal(segment(successor_relation,u,v),successor_relation)**.
% 299.82/300.44  160315[10:Rew:160202.0,146209.0] || equal(ordered_pair(u,v),successor_relation)** -> .
% 299.82/300.44  137[0:Inp] || member(u,ordinal_numbers) -> subclass(sum_class(u),u)*.
% 299.82/300.44  163255[10:AED:1.0,163141.1] || subclass(universal_class,cross_product(universal_class,universal_class))* -> .
% 299.82/300.44  5825[0:Con:5807.1] || equal(complement(complement(element_relation)),universal_class)** -> .
% 299.82/300.44  56[0:Inp] || member(u,universal_class) -> member(sum_class(u),universal_class)*.
% 299.82/300.44  160406[10:Rew:160202.0,159747.0] || equal(complement(singleton(successor_relation)),universal_class)** -> .
% 299.82/300.44  160418[10:Rew:160202.0,159750.0] || equal(complement(successor(successor_relation)),universal_class)** -> .
% 299.82/300.44  168388[11:MRR:163235.0,168387.0] || equal(complement(symmetrization_of(successor_relation)),universal_class)** -> .
% 299.82/300.44  160279[10:Rew:160202.0,146022.0] || subclass(intersection(y__dfg,ordinal_numbers),successor_relation)* -> .
% 299.82/300.44  160299[10:Rew:160202.0,146179.0] ||  -> equal(integer_of(regular(complement(omega))),successor_relation)**.
% 299.82/300.44  160478[10:Rew:160202.0,159402.0] || equal(cross_product(universal_class,universal_class),successor_relation)** -> .
% 299.82/300.44  57[0:Inp] ||  -> equal(complement(image(element_relation,complement(u))),power_class(u))**.
% 299.82/300.44  163161[10:MRR:2417.1,160478.0] || subclass(cross_product(universal_class,universal_class),successor_relation)* -> .
% 299.82/300.44  160278[10:Rew:160202.0,146148.0] ||  -> equal(symmetric_difference(u,u),successor_relation)**.
% 299.82/300.44  160276[10:Rew:160202.0,146193.0] ||  -> equal(intersection(successor_relation,u),successor_relation)**.
% 299.82/300.44  160277[10:Rew:160202.0,146196.0] ||  -> equal(intersection(u,successor_relation),successor_relation)**.
% 299.82/300.44  160308[10:Rew:160202.0,149636.0] ||  -> equal(intersection(complement(compose(element_relation,universal_class)),element_relation),successor_relation)**.
% 299.82/300.44  160298[10:Rew:160202.0,146017.0] ||  -> equal(u,successor_relation) member(regular(u),u)*.
% 299.82/300.44  160275[10:Rew:160202.0,145998.1] ||  -> member(u,omega)* equal(integer_of(u),successor_relation).
% 299.82/300.44  160412[10:Rew:160202.0,159913.0] || well_ordering(universal_class,singleton(successor_relation))* -> .
% 299.82/300.44  160415[10:Rew:160202.0,152527.0] ||  -> subclass(successor(successor_relation),singleton(successor_relation))*.
% 299.82/300.44  160416[10:Rew:160202.0,152557.0] || equal(successor(successor_relation),universal_class)** -> .
% 299.82/300.44  160245[10:Rew:160202.0,146189.0] || subclass(rest_relation,rotate(successor_relation))* -> .
% 299.82/300.44  160246[10:Rew:160202.0,146190.0] || equal(rotate(successor_relation),rest_relation)** -> .
% 299.82/300.44  160248[10:Rew:160202.0,146191.0] || subclass(rest_relation,flip(successor_relation))* -> .
% 299.82/300.44  160249[10:Rew:160202.0,146192.0] || equal(flip(successor_relation),rest_relation)** -> .
% 299.82/300.44  14[0:Inp] ||  -> equal(unordered_pair(u,u),singleton(u))**.
% 299.82/300.44  160250[10:Rew:160202.0,146205.0] ||  -> member(ordered_pair(successor_relation,successor_relation),domain_relation)*.
% 299.82/300.44  160334[10:Rew:160202.0,159755.0] || equal(power_class(successor_relation),universal_class)** -> .
% 299.82/300.44  160342[10:Rew:160202.0,152778.0] ||  -> subclass(symmetrization_of(successor_relation),inverse(successor_relation))*.
% 299.82/300.44  160442[10:Rew:160202.0,156229.0] || equal(singleton(successor_relation),successor_relation)** -> .
% 299.82/300.44  160271[10:Rew:160202.0,145997.1] inductive(u) ||  -> member(successor_relation,u)*.
% 299.82/300.44  160455[10:Rew:160202.0,157738.0] || equal(successor(successor_relation),successor_relation)** -> .
% 299.82/300.44  160460[10:Rew:160202.0,157923.0] ||  -> member(successor_relation,image(element_relation,universal_class))*.
% 299.82/300.44  168458[11:Res:168380.1,160227.0] || equal(symmetrization_of(successor_relation),successor_relation)** -> .
% 299.82/300.44  160468[10:Rew:160202.0,158527.0] ||  -> section(successor_relation,u,u)*.
% 299.82/300.44  160247[10:Rew:160202.0,145985.0] ||  -> equal(intersection(complement(kind_1_ordinals),ordinal_numbers),successor_relation)**.
% 299.82/300.44  160227[10:Rew:160202.0,146185.0] || member(u,successor_relation)* -> .
% 299.82/300.44  5759[0:Res:6.0,5754.0] ||  -> section(element_relation,universal_class,universal_class)*.
% 299.82/300.44  160255[10:Rew:160202.0,145988.0] || equal(intersection(y__dfg,ordinal_numbers),successor_relation)** -> .
% 299.82/300.44  3567[0:Res:8.1,3546.0] || equal(successor_relation,universal_class)** -> .
% 299.82/300.44  3546[0:AED:1.0,3532.1] || subclass(universal_class,successor_relation)* -> .
% 299.82/300.44  159396[7:MRR:159389.1,157738.0] || subclass(domain_relation,successor_relation)* -> .
% 299.82/300.44  159406[7:Res:8.1,159396.0] || equal(domain_relation,successor_relation)** -> .
% 299.82/300.44  13[0:Inp] ||  -> member(unordered_pair(u,v),universal_class)*.
% 299.82/300.44  160220[10:Rew:160202.0,145989.0] ||  -> equal(integer_of(successor_relation),successor_relation)**.
% 299.82/300.44  160221[10:Rew:160202.0,146181.0] ||  -> equal(complement(universal_class),successor_relation)**.
% 299.82/300.44  160222[10:Rew:160202.0,146182.0] ||  -> equal(regular(universal_class),successor_relation)**.
% 299.82/300.44  160223[10:Rew:160202.0,146186.0] ||  -> equal(complement(successor_relation),universal_class)**.
% 299.82/300.44  20[0:Inp] ||  -> subclass(element_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  160225[10:Rew:160202.0,146204.0] ||  -> equal(cantor(successor_relation),successor_relation)**.
% 299.82/300.44  160372[10:Rew:160202.0,153514.0] || equal(rest_relation,successor_relation)** -> .
% 299.82/300.44  160402[10:Rew:160202.0,154416.0] || subclass(rest_relation,successor_relation)* -> .
% 299.82/300.44  160226[10:Rew:160202.0,146183.0] || equal(complement(omega),successor_relation)** -> .
% 299.82/300.44  160414[10:Rew:160202.0,155334.0] ||  -> member(successor_relation,singleton(successor_relation))*.
% 299.82/300.44  160453[10:Rew:160202.0,157641.0] ||  -> member(successor_relation,successor(successor_relation))*.
% 299.82/300.44  168372[11:Spt:163192.1] ||  -> member(successor_relation,symmetrization_of(successor_relation))*.
% 299.82/300.44  168387[11:Res:160342.0,168378.0] ||  -> member(successor_relation,inverse(successor_relation))*.
% 299.82/300.44  177130[12:Spt:176815.0,161679.1,168580.0] || equal(successor_relation,element_relation)** -> .
% 299.82/300.44  160215[10:Rew:160202.0,145984.0] ||  -> subclass(successor_relation,u)*.
% 299.82/300.44  160216[10:Rew:160202.0,146194.0] ||  -> asymmetric(successor_relation,u)*.
% 299.82/300.44  160202[10:Spt:148183.1] ||  -> equal(identity_relation,successor_relation)**.
% 299.82/300.44  160211[10:Rew:160202.0,145975.0] ||  -> equal(singleton_relation,successor_relation)**.
% 299.82/300.44  160217[10:Rew:160202.0,146180.0] || equal(omega,successor_relation)** -> .
% 299.82/300.44  160212[10:Rew:160202.0,145982.0] ||  -> equal(limit_ordinals,successor_relation)**.
% 299.82/300.44  160213[10:Rew:160202.0,145983.0] ||  -> equal(null_class,successor_relation)**.
% 299.82/300.44  160214[10:Rew:160202.0,146184.0] ||  -> member(successor_relation,universal_class)*.
% 299.82/300.44  160449[10:Rew:160202.0,156874.0] ||  -> equal(subset_relation,successor_relation)**.
% 299.82/300.44  177131[12:Spt:176815.0,161679.0,161679.2] || well_ordering(u,cross_product(universal_class,universal_class))* -> member(least(u,element_relation),element_relation).
% 299.82/300.44  163135[10:MRR:5890.3,160227.0] || member(u,universal_class)* member(v,universal_class)* equal(successor(v),u)*+ -> .
% 299.82/300.44  165536[10:Res:9424.0,160358.1] inductive(restrict(successor_relation,u,v)) ||  -> .
% 299.82/300.44  165542[10:Res:9395.0,160358.1] inductive(intersection(u,successor_relation)) ||  -> .
% 299.82/300.44  165535[10:Res:9509.0,160358.1] inductive(intersection(successor_relation,u)) ||  -> .
% 299.82/300.44  165546[10:Res:107233.0,160358.1] inductive(complement(complement(successor_relation))) ||  -> .
% 299.82/300.44  163792[10:MRR:163787.1,160217.0] inductive(successor_relation) ||  -> .
% 299.82/300.44  159953[3:Obv:159937.1] || member(u,ordinal_numbers) -> subclass(singleton(u),kind_1_ordinals)*.
% 299.82/300.44  159952[3:Obv:159947.1] || subclass(u,ordinal_numbers) -> subclass(u,kind_1_ordinals)*.
% 299.82/300.44  159964[3:Res:159948.0,9.0] || subclass(kind_1_ordinals,ordinal_numbers)* -> equal(kind_1_ordinals,ordinal_numbers).
% 299.82/300.44  160019[3:Res:136.1,160013.0] || member(kind_1_ordinals,ordinal_numbers)* -> .
% 299.82/300.44  159951[3:Obv:159946.0] ||  -> subclass(intersection(u,ordinal_numbers),kind_1_ordinals)*.
% 299.82/300.44  159950[3:Obv:159944.0] ||  -> subclass(intersection(ordinal_numbers,u),kind_1_ordinals)*.
% 299.82/300.44  159949[3:Obv:159943.0] ||  -> subclass(complement(complement(ordinal_numbers)),kind_1_ordinals)*.
% 299.82/300.44  159948[3:Obv:159942.0] ||  -> subclass(ordinal_numbers,kind_1_ordinals)*.
% 299.82/300.44  159727[6:Res:145997.1,153205.1] inductive(u) || equal(complement(u),universal_class)** -> .
% 299.82/300.44  149582[6:Rew:148462.0,1848.0] || equal(complement(complement(symmetrization_of(u))),cross_product(v,v))*+ -> connected(u,v)*.
% 299.82/300.44  159401[6:Res:8.1,159395.0] || equal(domain_relation,element_relation)** -> .
% 299.82/300.44  159395[6:MRR:159379.1,146185.0] || subclass(domain_relation,element_relation)* -> .
% 299.82/300.44  144537[2:MRR:5755.1,144535.0] || asymmetric(u,v) -> section(intersection(u,inverse(u)),v,v)*.
% 299.82/300.44  143590[2:Rew:142543.0,143567.0] ||  -> equal(symmetric_difference(universal_class,intersection(u,universal_class)),symmetric_difference(u,universal_class))**.
% 299.82/300.44  3565[0:MRR:3561.0,54.0] || equal(complement(complement(u)),universal_class)** -> member(omega,u).
% 299.82/300.44  1509[0:Res:1506.1,26.1] || equal(complement(u),universal_class) member(omega,u)* -> .
% 299.82/300.44  158164[0:Res:13.0,158046.1] || equal(complement(domain_relation),universal_class)** -> .
% 299.82/300.44  30796[0:Res:102.1,3514.1] || member(u,universal_class)* subclass(universal_class,complement(domain_relation))*+ -> .
% 299.82/300.44  154494[6:MRR:148188.1,154490.0] || well_ordering(u,cross_product(universal_class,universal_class))* -> member(least(u,domain_relation),domain_relation).
% 299.82/300.44  157924[9:MRR:150058.1,157923.0] inductive(power_class(domain_of(intersection(u,identity_relation)))) ||  -> .
% 299.82/300.44  1322[0:Res:53.1,9.0] inductive(u) || subclass(u,omega)* -> equal(u,omega).
% 299.82/300.44  144937[3:Res:144705.0,6045.0] || subclass(domain_relation,u) well_ordering(universal_class,u)* -> .
% 299.82/300.44  155815[3:MRR:155797.0,34067.1] || member(u,ordinal_numbers) -> member(u,kind_1_ordinals)*.
% 299.82/300.44  141576[3:MRR:3875.2,120469.0] || member(u,ordinal_numbers) member(u,complement(kind_1_ordinals))* -> .
% 299.82/300.44  142543[2:Rew:142341.0,142218.0] ||  -> equal(intersection(complement(u),universal_class),symmetric_difference(universal_class,u))**.
% 299.82/300.44  142568[3:Rew:113504.0,142418.0] ||  -> equal(symmetric_difference(complement(kind_1_ordinals),ordinal_numbers),union(complement(kind_1_ordinals),ordinal_numbers))**.
% 299.82/300.44  153242[6:MRR:153213.1,146209.0] || equal(cross_product(u,v),universal_class)** -> .
% 299.82/300.44  153254[6:SoR:153246.0,73.1] one_to_one(complement(singleton_relation)) ||  -> .
% 299.82/300.44  153246[6:MRR:142564.1,153242.0] function(complement(singleton_relation)) ||  -> .
% 299.82/300.44  153244[6:MRR:2615.1,153242.0] one_to_one(universal_class) ||  -> .
% 299.82/300.44  153243[6:MRR:2612.1,153242.0] function(universal_class) ||  -> .
% 299.82/300.44  150062[6:MRR:150061.1,146184.0] inductive(domain_of(restrict(identity_relation,u,v))) ||  -> .
% 299.82/300.44  1506[0:Res:8.1,1475.0] || equal(u,universal_class) -> member(omega,u)*.
% 299.82/300.44  1475[0:Res:54.0,3.0] || subclass(universal_class,u)* -> member(omega,u).
% 299.82/300.44  149580[6:Rew:148462.0,118.1] || connected(u,v) -> subclass(cross_product(v,v),complement(complement(symmetrization_of(u))))*.
% 299.82/300.44  149579[6:Rew:148462.0,119.0] || subclass(cross_product(u,u),complement(complement(symmetrization_of(v))))* -> connected(v,u).
% 299.82/300.44  149673[6:MRR:148051.1,149669.0] inductive(restrict(identity_relation,u,v)) ||  -> .
% 299.82/300.44  149838[6:MRR:149837.1,146184.0] inductive(cantor(intersection(u,identity_relation))) ||  -> .
% 299.82/300.44  149835[6:MRR:149834.1,146184.0] inductive(domain_of(intersection(u,identity_relation))) ||  -> .
% 299.82/300.44  149841[6:MRR:149840.1,146185.0] inductive(complement(diagonalise(u))) ||  -> .
% 299.82/300.44  149672[6:MRR:148056.1,149669.0] inductive(intersection(identity_relation,u)) ||  -> .
% 299.82/300.44  149671[6:MRR:148055.1,149669.0] inductive(intersection(u,identity_relation)) ||  -> .
% 299.82/300.44  149670[6:MRR:148052.1,149669.0] inductive(complement(complement(identity_relation))) ||  -> .
% 299.82/300.44  149379[6:Rew:146186.0,148850.0,146202.0,148850.0] ||  -> equal(diagonalise(u),universal_class)**.
% 299.82/300.44  149715[6:MRR:148581.0,6.0] ||  -> irreflexive(u,v)*.
% 299.82/300.44  142420[2:Rew:142341.0,141603.0] ||  -> equal(symmetric_difference(complement(u),u),universal_class)**.
% 299.82/300.44  142419[2:Rew:142341.0,141595.0] ||  -> equal(symmetric_difference(u,complement(u)),universal_class)**.
% 299.82/300.44  142372[2:Rew:142341.0,120876.0] ||  -> equal(union(complement(u),u),universal_class)**.
% 299.82/300.44  142371[2:Rew:142341.0,120540.0] ||  -> equal(union(u,complement(u)),universal_class)**.
% 299.82/300.44  145037[2:MRR:3640.1,145036.0] inductive(cross_product(u,v)) ||  -> .
% 299.82/300.44  3366[0:MRR:3365.0,54.0] || equal(complement(singleton(omega)),universal_class)** -> .
% 299.82/300.44  159[0:Inp] || member(u,omega)* -> equal(integer_of(u),u).
% 299.82/300.44  142542[2:Rew:142341.0,142223.0] ||  -> equal(union(u,universal_class),universal_class)**.
% 299.82/300.44  143517[2:SpR:142541.0,45.0] ||  -> equal(successor(universal_class),universal_class)**.
% 299.82/300.44  143555[2:MRR:143554.0,6.0] ||  -> connected(universal_class,u)*.
% 299.82/300.44  143504[2:SpR:142541.0,115.0] ||  -> equal(symmetrization_of(universal_class),universal_class)**.
% 299.82/300.44  142541[2:Rew:142341.0,142217.0] ||  -> equal(union(universal_class,u),universal_class)**.
% 299.82/300.44  53[0:Inp] inductive(u) ||  -> subclass(omega,u)*.
% 299.82/300.44  142554[2:Obv:142374.1] inductive(subset_relation) ||  -> .
% 299.82/300.44  142553[2:Obv:142373.1] inductive(identity_relation) ||  -> .
% 299.82/300.44  142268[3:MRR:3589.0,142267.0] ||  -> inductive(universal_class)*.
% 299.82/300.44  54[0:Inp] ||  -> member(omega,universal_class)*.
% 299.82/300.44  52[0:Inp] ||  -> inductive(omega)*.
% 299.82/300.44  9306[0:SpR:31.0,1951.1] || member(u,symmetric_difference(cross_product(v,w),x))* -> member(u,complement(restrict(x,v,w))).
% 299.82/300.44  9300[0:SpR:30.0,1951.1] || member(u,symmetric_difference(v,cross_product(w,x)))* -> member(u,complement(restrict(v,w,x))).
% 299.82/300.44  9156[0:Res:1478.2,595.0] || member(u,universal_class) subclass(universal_class,restrict(v,w,x))*+ -> member(power_class(u),v)*.
% 299.82/300.44  28321[0:MRR:28313.0,999.0] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)*.
% 299.82/300.44  28320[0:MRR:28314.0,999.0] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)*.
% 299.82/300.44  2320[0:SpL:1005.0,144.0] || member(singleton(singleton(singleton(u))),rest_of(v))* -> equal(restrict(v,singleton(u),universal_class),u).
% 299.82/300.44  122532[0:Obv:122494.1] || subclass(u,complement(u))*+ -> subclass(u,v)*.
% 299.82/300.44  9150[0:Res:1478.2,24.0] || member(u,universal_class) subclass(universal_class,intersection(v,w))*+ -> member(power_class(u),w)*.
% 299.82/300.44  9149[0:Res:1478.2,23.0] || member(u,universal_class) subclass(universal_class,intersection(v,w))*+ -> member(power_class(u),v)*.
% 299.82/300.44  119971[0:SpR:114854.0,44.0] ||  -> equal(range_of(cross_product(u,universal_class)),image(universal_class,u))**.
% 299.82/300.44  114854[0:SpR:113504.0,30.0] ||  -> equal(restrict(universal_class,u,v),cross_product(u,v))**.
% 299.82/300.44  114897[0:SpL:113504.0,5909.0] || equal(u,universal_class) -> member(singleton(v),u)*.
% 299.82/300.44  2031[0:SpL:1005.0,95.0] || member(singleton(singleton(singleton(u))),compose_class(v))* -> equal(compose(v,singleton(u)),u).
% 299.82/300.44  9146[0:Res:1478.2,26.1] || member(u,universal_class) subclass(universal_class,complement(v))*+ member(power_class(u),v)* -> .
% 299.82/300.44  18548[0:Res:8.1,2609.1] function(u) || equal(u,cross_product(universal_class,universal_class))* -> equal(cross_product(universal_class,universal_class),u).
% 299.82/300.44  115166[0:SpR:115096.0,28.0] ||  -> equal(union(u,u),complement(complement(u)))**.
% 299.82/300.44  114856[0:SpR:113504.0,9535.0] ||  -> subclass(symmetric_difference(universal_class,u),complement(u))*.
% 299.82/300.44  115096[0:MRR:115025.0,9395.0] ||  -> equal(intersection(u,u),u)**.
% 299.82/300.44  113504[0:MRR:113395.0,9395.0] ||  -> equal(intersection(universal_class,u),u)**.
% 299.82/300.44  10417[0:SpR:955.0,44.0] ||  -> equal(range_of(restrict(cross_product(u,universal_class),v,w)),image(cross_product(v,w),u))**.
% 299.82/300.44  9322[0:SpR:28.0,1951.1] || member(u,symmetric_difference(complement(v),complement(w)))* -> member(u,union(v,w)).
% 299.82/300.44  1705[0:SpL:1005.0,16.0] || member(singleton(singleton(singleton(u))),cross_product(v,w))* -> member(singleton(u),v).
% 299.82/300.44  31922[0:Res:191.0,5850.0] || subclass(rest_relation,u)+ well_ordering(v,u)* -> member(least(v,rest_relation),rest_relation)*.
% 299.82/300.44  9810[0:Res:8.1,2430.0] || equal(compose_class(u),cross_product(universal_class,universal_class))* -> equal(cross_product(universal_class,universal_class),compose_class(u)).
% 299.82/300.44  9687[0:Res:8.1,2429.0] || equal(rest_of(u),cross_product(universal_class,universal_class))* -> equal(cross_product(universal_class,universal_class),rest_of(u)).
% 299.82/300.44  8846[0:SpL:30.0,175.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),restrict(intersection(y__dfg,ordinal_numbers),u,v))* -> .
% 299.82/300.44  31289[0:Res:314.0,5829.0] || well_ordering(u,v)+ -> subclass(v,w)* member(least(u,v),v)*.
% 299.82/300.44  9332[0:Res:1951.1,26.1] || member(u,symmetric_difference(v,w)) member(u,intersection(v,w))* -> .
% 299.82/300.44  6045[0:Res:999.0,129.3] || member(u,v)*+ subclass(v,w)* well_ordering(universal_class,w)* -> .
% 299.82/300.44  107233[0:Obv:107215.0] ||  -> subclass(complement(complement(u)),u)*.
% 299.82/300.44  1522[0:SpL:1005.0,17.0] || member(singleton(singleton(singleton(u))),cross_product(v,w))* -> member(u,w).
% 299.82/300.44  1013[0:SpL:1005.0,147.0] || member(singleton(singleton(singleton(u))),rest_relation)* -> equal(rest_of(singleton(u)),u).
% 299.82/300.44  87694[0:SpR:41.0,31436.1] || equal(complement(rest_of(inverse(u))),universal_class)**+ -> subclass(range_of(u),v)*.
% 299.82/300.44  10254[0:SpL:1934.0,24.0] || member(u,symmetric_difference(v,singleton(v)))* -> member(u,successor(v)).
% 299.82/300.44  5794[0:Res:3907.1,2151.0] || equal(complement(complement(singleton(u))),universal_class)**+ -> equal(singleton(v),u)*.
% 299.82/300.44  5857[0:Res:60.1,127.0] || member(ordered_pair(u,v),compose(w,x))* subclass(image(w,image(x,singleton(u))),y)*+ well_ordering(z,y)* -> member(least(z,image(w,image(x,singleton(u)))),image(w,image(x,singleton(u))))*.
% 299.82/300.44  6036[0:Res:25.2,129.3] || member(ordered_pair(u,least(intersection(v,w),x)),w)*+ member(ordered_pair(u,least(intersection(v,w),x)),v)* member(u,x) subclass(x,y)* well_ordering(intersection(v,w),y)* -> .
% 299.82/300.44  6044[0:Res:60.1,129.3] || member(ordered_pair(u,ordered_pair(v,least(image(w,image(x,singleton(u))),y))),compose(w,x))*+ member(v,y) subclass(y,z)* well_ordering(image(w,image(x,singleton(u))),z)* -> .
% 299.82/300.44  5839[0:Res:25.2,127.0] || member(u,v)* member(u,w)* subclass(intersection(w,v),x)*+ well_ordering(y,x)* -> member(least(y,intersection(w,v)),intersection(w,v))*.
% 299.82/300.44  5853[0:Res:18.2,127.0] || member(u,v)* member(w,x)* subclass(cross_product(x,v),y)*+ well_ordering(z,y)* -> member(least(z,cross_product(x,v)),cross_product(x,v))*.
% 299.82/300.44  6041[0:Res:18.2,129.3] || member(least(cross_product(u,v),w),v)*+ member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,v),y)* -> .
% 299.82/300.44  5554[0:Res:18.2,19.0] || member(u,v)*+ member(w,x)* -> equal(ordered_pair(first(ordered_pair(w,u)),second(ordered_pair(w,u))),ordered_pair(w,u))**.
% 299.82/300.44  6046[0:MRR:6035.0,999.0] || member(u,v) subclass(v,w)* well_ordering(complement(x),w)*+ -> member(ordered_pair(u,least(complement(x),v)),x)*.
% 299.82/300.44  5646[0:Res:60.1,3.0] || member(ordered_pair(u,v),compose(w,x))* subclass(image(w,image(x,singleton(u))),y)*+ -> member(v,y)*.
% 299.82/300.44  6010[0:Res:18.2,96.1] || member(u,universal_class) member(v,universal_class) equal(compose(w,v),u) -> member(ordered_pair(v,u),compose_class(w))*.
% 299.82/300.44  5553[0:Res:18.2,3.0] || member(u,v)* member(w,x)* subclass(cross_product(x,v),y)*+ -> member(ordered_pair(w,u),y)*.
% 299.82/300.44  2078[0:Res:131.2,9.0] || connected(u,v) subclass(v,not_well_ordering(u,v))* -> well_ordering(u,v) equal(not_well_ordering(u,v),v).
% 299.82/300.44  5749[0:SpL:124.0,135.1] || subclass(singleton(u),v) subclass(segment(w,v,u),singleton(u))* -> section(w,singleton(u),v).
% 299.82/300.44  5829[0:Res:4.1,127.0] || subclass(u,v)*+ well_ordering(w,v)* -> subclass(u,x)* member(least(w,u),u)*.
% 299.82/300.44  5832[2:Res:2457.1,127.0] inductive(u) || subclass(u,v)*+ well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.44  6263[0:SoR:2610.0,73.1] one_to_one(intersection(y__dfg,ordinal_numbers)) || well_ordering(element_relation,cross_product(universal_class,universal_class))* -> .
% 299.82/300.44  2610[0:Res:64.1,183.1] function(intersection(y__dfg,ordinal_numbers)) || well_ordering(element_relation,cross_product(universal_class,universal_class))* -> .
% 299.82/300.44  89275[0:Obv:89236.0] ||  -> member(u,v) subclass(singleton(u),complement(v))*.
% 299.82/300.44  6210[0:Res:8.1,1503.0] || equal(u,ordered_pair(v,w))*+ -> member(singleton(v),u)*.
% 299.82/300.44  1503[0:Res:1004.0,3.0] || subclass(ordered_pair(u,v),w)* -> member(singleton(u),w).
% 299.82/300.44  5909[0:Res:8.1,2649.0] || equal(intersection(u,v),universal_class)**+ -> member(singleton(w),v)*.
% 299.82/300.44  5884[0:Res:8.1,2648.0] || equal(intersection(u,v),universal_class)**+ -> member(singleton(w),u)*.
% 299.82/300.44  2648[0:Res:1477.1,23.0] || subclass(universal_class,intersection(u,v))*+ -> member(singleton(w),u)*.
% 299.82/300.44  2649[0:Res:1477.1,24.0] || subclass(universal_class,intersection(u,v))*+ -> member(singleton(w),v)*.
% 299.82/300.44  3907[0:MRR:3889.0,191.0] || equal(complement(complement(u)),universal_class) -> member(singleton(v),u)*.
% 299.82/300.44  3670[0:Res:8.1,2647.0] || equal(complement(u),universal_class) member(singleton(v),u)* -> .
% 299.82/300.44  2647[0:Res:1477.1,26.1] || subclass(universal_class,complement(u))*+ member(singleton(v),u)* -> .
% 299.82/300.44  479[0:Res:8.1,183.1] || equal(u,intersection(y__dfg,ordinal_numbers))*+ well_ordering(element_relation,u)* -> .
% 299.82/300.44  1499[0:Res:999.0,3.0] || subclass(universal_class,u) -> member(ordered_pair(v,w),u)*.
% 299.82/300.44  1478[0:Res:58.1,3.0] || member(u,universal_class) subclass(universal_class,v) -> member(power_class(u),v)*.
% 299.82/300.44  3358[0:Res:1506.1,1509.1] || equal(u,universal_class) equal(complement(u),universal_class)** -> .
% 299.82/300.44  30798[0:Res:148.1,3514.1] || member(u,universal_class)* subclass(universal_class,complement(rest_relation))*+ -> .
% 299.82/300.44  1477[0:Res:191.0,3.0] || subclass(universal_class,u) -> member(singleton(v),u)*.
% 299.82/300.44  30556[0:Res:8.1,30537.0] || equal(complement(singleton(ordered_pair(u,v))),universal_class)** -> .
% 299.82/300.44  1009[0:SpR:1005.0,1004.0] ||  -> member(singleton(singleton(u)),singleton(singleton(singleton(u))))*.
% 299.82/300.44  34067[0:Con:34059.1] || member(u,v)*+ -> member(u,universal_class)*.
% 299.82/300.44  3904[0:MRR:3902.0,191.0] || equal(complement(singleton(singleton(u))),universal_class)** -> .
% 299.82/300.44  58[0:Inp] || member(u,universal_class) -> member(power_class(u),universal_class)*.
% 299.82/300.44  999[0:SpR:15.0,13.0] ||  -> member(ordered_pair(u,v),universal_class)*.
% 299.82/300.44  191[0:SpR:14.0,13.0] ||  -> member(singleton(u),universal_class)*.
% 299.82/300.44  183[0:MRR:181.2,1.0] || well_ordering(element_relation,u) subclass(intersection(y__dfg,ordinal_numbers),u)* -> .
% 299.82/300.44  129[0:Inp] || member(u,v) subclass(v,w)* well_ordering(x,w)* member(ordered_pair(u,least(x,v)),x)*+ -> .
% 299.82/300.44  127[0:Inp] || member(u,v)*+ subclass(v,w)* well_ordering(x,w)* -> member(least(x,v),v)*.
% 299.82/300.44  131[0:Inp] || connected(u,v) -> well_ordering(u,v) subclass(not_well_ordering(u,v),v)*.
% 299.82/300.44  205[0:Res:136.1,125.0] || member(u,ordinal_numbers) -> connected(element_relation,u)*.
% 299.82/300.44  125[0:Inp] || well_ordering(u,v)* -> connected(u,v).
% 299.82/300.44  489[0:Res:136.1,480.0] || member(intersection(y__dfg,ordinal_numbers),ordinal_numbers)* -> .
% 299.82/300.44  480[0:Res:314.0,183.1] || well_ordering(element_relation,intersection(y__dfg,ordinal_numbers))* -> .
% 299.82/300.44  136[0:Inp] || member(u,ordinal_numbers) -> well_ordering(element_relation,u)*.
% 299.82/300.44  9563[0:Res:136.1,9559.0] || member(y__dfg,ordinal_numbers)* -> .
% 299.82/300.44  9449[0:Res:136.1,9445.0] || member(ordinal_numbers,ordinal_numbers)* -> .
% 299.82/300.44  481[0:Res:136.1,477.0] || member(universal_class,ordinal_numbers)* -> .
% 299.82/300.44  9559[0:Res:9509.0,183.1] || well_ordering(element_relation,y__dfg)* -> .
% 299.82/300.44  9445[0:Res:9395.0,183.1] || well_ordering(element_relation,ordinal_numbers)* -> .
% 299.82/300.44  2126[0:SpR:124.0,134.1] || section(u,singleton(v),w) -> subclass(segment(u,w,v),singleton(v))*.
% 299.82/300.44  1934[0:SpR:45.0,161.0] ||  -> equal(intersection(complement(intersection(u,singleton(u))),successor(u)),symmetric_difference(u,singleton(u)))**.
% 299.82/300.44  1005[0:Rew:14.0,1003.0] ||  -> equal(ordered_pair(singleton(u),u),singleton(singleton(singleton(u))))**.
% 299.82/300.44  10293[0:SpR:45.0,9898.0] ||  -> subclass(symmetric_difference(complement(u),complement(singleton(u))),successor(u))*.
% 299.82/300.44  38[0:Inp] || member(ordered_pair(ordered_pair(u,v),w),flip(x))* -> member(ordered_pair(ordered_pair(v,u),w),x).
% 299.82/300.44  35[0:Inp] || member(ordered_pair(ordered_pair(u,v),w),rotate(x))* -> member(ordered_pair(ordered_pair(v,w),u),x).
% 299.82/300.44  60[0:Inp] || member(ordered_pair(u,v),compose(w,x)) -> member(v,image(w,image(x,singleton(u))))*.
% 299.82/300.44  18[0:Inp] || member(u,v) member(w,x) -> member(ordered_pair(w,u),cross_product(x,v))*.
% 299.82/300.44  19[0:Inp] || member(u,cross_product(v,w))*+ -> equal(ordered_pair(first(u),second(u)),u)**.
% 299.82/300.44  144[0:Inp] || member(ordered_pair(u,v),rest_of(w))* -> equal(restrict(w,u,universal_class),v).
% 299.82/300.44  105[0:Inp] ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),single_valued2(u)),single_valued3(u))**.
% 299.82/300.44  95[0:Inp] || member(ordered_pair(u,v),compose_class(w))* -> equal(compose(w,u),v).
% 299.82/300.44  2151[0:Obv:2141.1] || member(u,singleton(v))* -> equal(u,v).
% 299.82/300.44  6219[0:Obv:6215.1] || member(u,v) -> subclass(singleton(u),v)*.
% 299.82/300.44  16[0:Inp] || member(ordered_pair(u,v),cross_product(w,x))* -> member(u,w).
% 299.82/300.44  17[0:Inp] || member(ordered_pair(u,v),cross_product(w,x))* -> member(v,x).
% 299.82/300.44  30537[0:SpL:15.0,30457.0] || subclass(universal_class,complement(singleton(ordered_pair(u,v))))* -> .
% 299.82/300.44  147[0:Inp] || member(ordered_pair(u,v),rest_relation)* -> equal(rest_of(u),v).
% 299.82/300.44  9812[0:SpR:45.0,9421.0] ||  -> subclass(symmetric_difference(u,singleton(u)),successor(u))*.
% 299.82/300.44  3898[0:Res:1004.0,3670.1] || equal(complement(ordered_pair(u,v)),universal_class)** -> .
% 299.82/300.44  30448[0:Res:1006.0,3486.1] || subclass(universal_class,complement(ordered_pair(u,v)))* -> .
% 299.82/300.44  30536[0:SpL:14.0,30457.0] || subclass(universal_class,complement(singleton(singleton(u))))* -> .
% 299.82/300.44  1004[0:MRR:1000.0,191.0] ||  -> member(singleton(u),ordered_pair(u,v))*.
% 299.82/300.44  45[0:Inp] ||  -> equal(union(u,singleton(u)),successor(u))**.
% 299.82/300.44  10191[0:SpL:1933.0,24.0] || member(u,symmetric_difference(v,inverse(v)))* -> member(u,symmetrization_of(v)).
% 299.82/300.44  1931[0:SpR:161.0,161.0] ||  -> equal(intersection(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v))),symmetric_difference(complement(intersection(u,v)),union(u,v)))**.
% 299.82/300.44  5753[0:Res:64.1,135.1] function(domain_of(restrict(u,v,cross_product(universal_class,universal_class)))) || subclass(cross_product(universal_class,universal_class),v) -> section(u,cross_product(universal_class,universal_class),v)*.
% 299.82/300.44  5971[0:Res:8.1,121.0] || equal(compose(restrict(u,v,v),restrict(u,v,v)),restrict(u,v,v))** -> transitive(u,v).
% 299.82/300.44  3874[0:SpR:161.0,25.2] || member(u,union(v,w)) member(u,complement(intersection(v,w)))* -> member(u,symmetric_difference(v,w)).
% 299.82/300.44  3883[0:Res:25.2,3.0] || member(u,v)* member(u,w)* subclass(intersection(w,v),x)*+ -> member(u,x)*.
% 299.82/300.44  1943[0:SpR:31.0,161.0] ||  -> equal(intersection(complement(restrict(u,v,w)),union(cross_product(v,w),u)),symmetric_difference(cross_product(v,w),u))**.
% 299.82/300.44  1938[0:SpR:30.0,161.0] ||  -> equal(intersection(complement(restrict(u,v,w)),union(u,cross_product(v,w))),symmetric_difference(u,cross_product(v,w)))**.
% 299.82/300.44  1315[0:Res:37.0,9.0] || subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(u))* -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),flip(u)).
% 299.82/300.44  1316[0:Res:34.0,9.0] || subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(u))* -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(u)).
% 299.82/300.44  30913[0:Res:191.0,30877.1] || equal(complement(rest_relation),universal_class)** -> .
% 299.82/300.44  30433[0:Res:1476.1,3486.1] || subclass(universal_class,u) subclass(universal_class,complement(u))* -> .
% 299.82/300.44  6317[0:Res:8.1,3926.1] single_valued_class(u) || equal(cross_product(universal_class,universal_class),u)*+ -> function(u)*.
% 299.82/300.44  1948[0:SpR:28.0,161.0] ||  -> equal(intersection(union(u,v),union(complement(u),complement(v))),symmetric_difference(complement(u),complement(v)))**.
% 299.82/300.44  507[0:SpR:28.0,28.0] ||  -> equal(union(u,intersection(complement(v),complement(w))),complement(intersection(complement(u),union(v,w))))**.
% 299.82/300.44  506[0:SpR:28.0,28.0] ||  -> equal(union(intersection(complement(u),complement(v)),w),complement(intersection(union(u,v),complement(w))))**.
% 299.82/300.44  2524[0:Res:59.0,9.0] || subclass(cross_product(universal_class,universal_class),compose(u,v))* -> equal(compose(u,v),cross_product(universal_class,universal_class)).
% 299.82/300.44  513[0:SpL:28.0,26.1] || member(u,intersection(complement(v),complement(w)))* member(u,union(v,w)) -> .
% 299.82/300.44  9927[0:Res:9418.0,3926.1] single_valued_class(restrict(u,universal_class,universal_class)) ||  -> function(restrict(u,universal_class,universal_class))*.
% 299.82/300.44  2609[0:Res:64.1,9.0] function(u) || subclass(cross_product(universal_class,universal_class),u)* -> equal(cross_product(universal_class,universal_class),u).
% 299.82/300.44  2415[0:Res:146.0,9.0] || subclass(cross_product(universal_class,universal_class),rest_relation)* -> equal(cross_product(universal_class,universal_class),rest_relation).
% 299.82/300.44  146[0:Inp] ||  -> subclass(rest_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  6328[0:Res:146.0,3926.1] single_valued_class(rest_relation) ||  -> function(rest_relation)*.
% 299.82/300.44  3544[0:AED:1.0,3530.1] || subclass(universal_class,rest_relation)* -> .
% 299.82/300.44  3553[0:Res:8.1,3544.0] || equal(rest_relation,universal_class)** -> .
% 299.82/300.44  179[0:Res:3.2,2.0] || subclass(u,intersection(y__dfg,ordinal_numbers)) member(least(element_relation,intersection(y__dfg,ordinal_numbers)),u)* -> .
% 299.82/300.44  955[0:SpR:30.0,31.0] ||  -> equal(restrict(cross_product(u,v),w,x),restrict(cross_product(w,x),u,v))*.
% 299.82/300.44  10292[0:SpR:115.0,9898.0] ||  -> subclass(symmetric_difference(complement(u),complement(inverse(u))),symmetrization_of(u))*.
% 299.82/300.44  9898[0:SpR:28.0,9535.0] ||  -> subclass(symmetric_difference(complement(u),complement(v)),union(u,v))*.
% 299.82/300.44  1933[0:SpR:115.0,161.0] ||  -> equal(intersection(complement(intersection(u,inverse(u))),symmetrization_of(u)),symmetric_difference(u,inverse(u)))**.
% 299.82/300.44  9535[0:SpR:161.0,9509.0] ||  -> subclass(symmetric_difference(u,v),complement(intersection(u,v)))*.
% 299.82/300.44  9811[0:SpR:115.0,9421.0] ||  -> subclass(symmetric_difference(u,inverse(u)),symmetrization_of(u))*.
% 299.82/300.44  9421[0:SpR:161.0,9395.0] ||  -> subclass(symmetric_difference(u,v),union(u,v))*.
% 299.82/300.44  2430[0:Res:94.0,9.0] || subclass(cross_product(universal_class,universal_class),compose_class(u))* -> equal(cross_product(universal_class,universal_class),compose_class(u)).
% 299.82/300.44  2429[0:Res:142.0,9.0] || subclass(cross_product(universal_class,universal_class),rest_of(u))* -> equal(cross_product(universal_class,universal_class),rest_of(u)).
% 299.82/300.44  594[0:SpL:31.0,23.0] || member(u,restrict(v,w,x))* -> member(u,cross_product(w,x)).
% 299.82/300.44  9509[0:Obv:9505.0] ||  -> subclass(intersection(u,v),u)*.
% 299.82/300.44  9395[0:Obv:9391.0] ||  -> subclass(intersection(u,v),v)*.
% 299.82/300.44  1951[0:SpL:161.0,23.0] || member(u,symmetric_difference(v,w)) -> member(u,complement(intersection(v,w)))*.
% 299.82/300.44  178[0:Res:24.1,2.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),intersection(u,intersection(y__dfg,ordinal_numbers)))* -> .
% 299.82/300.44  175[0:Res:23.1,2.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),intersection(intersection(y__dfg,ordinal_numbers),u))* -> .
% 299.82/300.44  1952[0:SpL:161.0,24.0] || member(u,symmetric_difference(v,w))* -> member(u,union(v,w)).
% 299.82/300.44  6334[0:Res:59.0,3926.1] single_valued_class(compose(u,v)) ||  -> function(compose(u,v))*.
% 299.82/300.44  6321[0:Res:314.0,3926.1] single_valued_class(cross_product(universal_class,universal_class)) ||  -> function(cross_product(universal_class,universal_class))*.
% 299.82/300.44  6333[0:Res:94.0,3926.1] single_valued_class(compose_class(u)) ||  -> function(compose_class(u))*.
% 299.82/300.44  6332[0:Res:142.0,3926.1] single_valued_class(rest_of(u)) ||  -> function(rest_of(u))*.
% 299.82/300.44  6331[0:Res:20.0,3926.1] single_valued_class(element_relation) ||  -> function(element_relation)*.
% 299.82/300.44  6329[0:Res:100.0,3926.1] single_valued_class(domain_relation) ||  -> function(domain_relation)*.
% 299.82/300.44  3926[0:Res:62.1,66.1] single_valued_class(u) || subclass(u,cross_product(universal_class,universal_class))* -> function(u).
% 299.82/300.44  2416[0:Res:100.0,9.0] || subclass(cross_product(universal_class,universal_class),domain_relation)* -> equal(cross_product(universal_class,universal_class),domain_relation).
% 299.82/300.44  121[0:Inp] || subclass(compose(restrict(u,v,v),restrict(u,v,v)),restrict(u,v,v))* -> transitive(u,v).
% 299.82/300.44  5750[0:Res:6.0,135.1] || subclass(universal_class,u) -> section(v,universal_class,u)*.
% 299.82/300.44  2640[0:Res:73.1,75.1] one_to_one(inverse(u)) function(u) ||  -> one_to_one(u)*.
% 299.82/300.44  3888[0:Res:1477.1,3670.1] || subclass(universal_class,u)* equal(complement(u),universal_class) -> .
% 299.82/300.44  75[0:Inp] function(u) || function(inverse(u))* -> one_to_one(u).
% 299.82/300.44  64[0:Inp] function(u) ||  -> subclass(u,cross_product(universal_class,universal_class))*.
% 299.82/300.44  37[0:Inp] ||  -> subclass(flip(u),cross_product(cross_product(universal_class,universal_class),universal_class))*.
% 299.82/300.44  34[0:Inp] ||  -> subclass(rotate(u),cross_product(cross_product(universal_class,universal_class),universal_class))*.
% 299.82/300.44  84[0:Inp] || compatible(u,v,w)* -> function(u).
% 299.82/300.44  111[0:Inp] || maps(u,v,w)* -> function(u).
% 299.82/300.44  59[0:Inp] ||  -> subclass(compose(u,v),cross_product(universal_class,universal_class))*.
% 299.82/300.44  74[0:Inp] one_to_one(u) ||  -> function(inverse(u))*.
% 299.82/300.44  94[0:Inp] ||  -> subclass(compose_class(u),cross_product(universal_class,universal_class))*.
% 299.82/300.44  142[0:Inp] ||  -> subclass(rest_of(u),cross_product(universal_class,universal_class))*.
% 299.82/300.44  2673[0:Res:65.1,63.0] function(u) ||  -> single_valued_class(u)*.
% 299.82/300.44  203[0:Res:49.1,199.0] inductive(null_class) ||  -> function(u)*.
% 299.82/300.44  73[0:Inp] one_to_one(u) ||  -> function(u)*.
% 299.82/300.44  100[0:Inp] ||  -> subclass(domain_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  71[0:Inp] ||  -> function(choice)*.
% 299.82/300.44  25[0:Inp] || member(u,v) member(u,w) -> member(u,intersection(w,v))*.
% 299.82/300.44  3594[0:Res:8.1,3551.0] || equal(rest_of(u),universal_class)** -> .
% 299.82/300.44  3593[0:Res:8.1,3550.0] || equal(compose_class(u),universal_class)** -> .
% 299.82/300.44  3551[0:AED:1.0,3534.1] || subclass(universal_class,rest_of(u))* -> .
% 299.82/300.44  3550[0:AED:1.0,3538.1] || subclass(universal_class,compose_class(u))* -> .
% 299.82/300.44  3566[0:Res:8.1,3545.0] || equal(domain_relation,universal_class)** -> .
% 299.82/300.44  3545[0:AED:1.0,3531.1] || subclass(universal_class,domain_relation)* -> .
% 299.82/300.44  3541[3:MRR:2688.1,3529.1] || subclass(universal_class,element_relation)* -> .
% 299.82/300.44  3468[2:SpR:2483.0,2483.0] ||  -> equal(ordinal_multiply(u,v),ordinal_multiply(u,w))*.
% 299.82/300.44  3341[2:MRR:3336.0,8.1] || equal(universal_class,element_relation)** -> .
% 299.82/300.44  3096[4:MRR:2572.1,3094.0] inductive(singleton_relation) ||  -> .
% 299.82/300.44  161[0:Rew:28.0,29.0] ||  -> equal(intersection(complement(intersection(u,v)),union(u,v)),symmetric_difference(u,v))**.
% 299.82/300.44  3[0:Inp] || member(u,v)*+ subclass(v,w)* -> member(u,w)*.
% 299.82/300.44  1360[0:Res:8.1,1312.0] || equal(u,universal_class)* -> equal(universal_class,u).
% 299.82/300.44  1312[0:Res:6.0,9.0] || subclass(universal_class,u)* -> equal(universal_class,u).
% 299.82/300.44  9[0:Inp] || subclass(u,v)*+ subclass(v,u)* -> equal(v,u).
% 299.82/300.44  595[0:SpL:31.0,24.0] || member(u,restrict(v,w,x))* -> member(u,v).
% 299.82/300.44  30[0:Inp] ||  -> equal(intersection(u,cross_product(v,w)),restrict(u,v,w))**.
% 299.82/300.44  31[0:Inp] ||  -> equal(intersection(cross_product(u,v),w),restrict(w,u,v))**.
% 299.82/300.44  28[0:Inp] ||  -> equal(complement(intersection(complement(u),complement(v))),union(u,v))**.
% 299.82/300.44  2[0:Inp] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),intersection(y__dfg,ordinal_numbers))* -> .
% 299.82/300.44  23[0:Inp] || member(u,intersection(v,w))* -> member(u,v).
% 299.82/300.44  24[0:Inp] || member(u,intersection(v,w))* -> member(u,w).
% 299.82/300.44  113[0:Inp] || maps(u,v,w)* -> subclass(range_of(u),w).
% 299.82/300.44  314[0:Obv:312.0] ||  -> subclass(u,u)*.
% 299.82/300.44  26[0:Inp] || member(u,v) member(u,complement(v))* -> .
% 299.82/300.44  44[0:Inp] ||  -> equal(range_of(restrict(u,v,universal_class)),image(u,v))**.
% 299.82/300.44  133[0:Inp] || section(u,v,w)* -> subclass(v,w).
% 299.82/300.44  8[0:Inp] || equal(u,v) -> subclass(v,u)*.
% 299.82/300.44  115[0:Inp] ||  -> equal(union(u,inverse(u)),symmetrization_of(u))**.
% 299.82/300.44  6[0:Inp] ||  -> subclass(u,universal_class)*.222494[24:Rew:181085.0,222383.0] ||  -> equal(range__dfg(u,kind_1_ordinals,v),range__dfg(u,universal_class,v))**.
% 299.82/300.44  222496[24:Rew:181087.0,222391.0] ||  -> equal(domain__dfg(u,v,kind_1_ordinals),domain__dfg(u,v,universal_class))**.
% 299.82/300.44  107282[0:SpR:28.0,107233.0] ||  -> subclass(complement(union(u,v)),intersection(complement(u),complement(v)))*.
% 299.82/300.44  107682[0:Res:1004.0,6045.0] || subclass(ordered_pair(u,v),w)* well_ordering(universal_class,w) -> .
% 299.82/300.44  114891[0:SpR:113504.0,1951.1] || member(u,symmetric_difference(universal_class,v))* -> member(u,complement(v)).
% 299.82/300.44  114933[0:SpL:113504.0,9332.1] || member(u,symmetric_difference(universal_class,v))* member(u,v) -> .
% 299.82/300.44  115140[0:SpR:115096.0,30.0] ||  -> equal(restrict(cross_product(u,v),u,v),cross_product(u,v))**.
% 299.82/300.44  122128[0:Obv:122099.1] || member(u,v) -> subclass(intersection(singleton(u),w),v)*.
% 299.82/300.44  122131[0:Obv:122075.0] ||  -> member(u,v) subclass(intersection(singleton(u),w),complement(v))*.
% 299.82/300.44  122337[0:Obv:122308.1] || member(u,v) -> subclass(intersection(w,singleton(u)),v)*.
% 299.82/300.44  122340[0:Obv:122283.0] ||  -> member(u,v) subclass(intersection(w,singleton(u)),complement(v))*.
% 299.82/300.44  125963[0:Res:28320.1,17.0] || subclass(rest_relation,rotate(cross_product(u,v)))* -> member(w,v)*.
% 299.82/300.44  1517[0:Res:1506.1,595.0] || equal(restrict(u,v,w),universal_class)** -> member(omega,u).
% 299.82/300.44  141741[2:MRR:120440.2,120469.0] inductive(symmetric_difference(u,u)) || well_ordering(v,complement(u))* -> .
% 299.82/300.44  142590[2:MRR:142375.0,34067.1] || member(u,complement(v)) -> member(u,symmetric_difference(universal_class,v))*.
% 299.82/300.44  159955[3:Obv:159938.1] || member(u,ordinal_numbers) -> subclass(intersection(singleton(u),v),kind_1_ordinals)*.
% 299.82/300.44  159956[3:Obv:159939.1] || member(u,ordinal_numbers) -> subclass(intersection(v,singleton(u)),kind_1_ordinals)*.
% 299.82/300.44  160063[3:Res:159952.1,1503.0] || subclass(ordered_pair(u,v),ordinal_numbers)* -> member(singleton(u),kind_1_ordinals).
% 299.82/300.44  161396[10:Rew:160202.0,147807.0] ||  -> equal(intersection(symmetric_difference(u,singleton(u)),complement(successor(u))),successor_relation)**.
% 299.82/300.44  161395[10:Rew:160202.0,147806.0] ||  -> equal(intersection(symmetric_difference(u,inverse(u)),complement(symmetrization_of(u))),successor_relation)**.
% 299.82/300.44  161394[10:Rew:160202.0,147805.0] ||  -> equal(intersection(symmetric_difference(u,v),complement(union(u,v))),successor_relation)**.
% 299.82/300.44  161393[10:Rew:160202.0,147743.0] ||  -> equal(intersection(complement(successor(u)),symmetric_difference(u,singleton(u))),successor_relation)**.
% 299.82/300.44  161392[10:Rew:160202.0,147742.0] ||  -> equal(intersection(complement(symmetrization_of(u)),symmetric_difference(u,inverse(u))),successor_relation)**.
% 299.82/300.44  161391[10:Rew:160202.0,147741.0] ||  -> equal(intersection(complement(union(u,v)),symmetric_difference(u,v)),successor_relation)**.
% 299.82/300.44  161390[10:Rew:160202.0,147591.1] || subclass(u,v) -> equal(intersection(complement(v),u),successor_relation)**.
% 299.82/300.44  161389[10:Rew:160202.0,147413.1] inductive(symmetric_difference(u,u)) ||  -> member(successor_relation,complement(complement(u)))*.
% 299.82/300.44  161387[10:Rew:160202.0,147371.0] ||  -> equal(intersection(singleton(u),singleton(v)),successor_relation)** equal(u,v).
% 299.82/300.44  161382[10:Rew:160202.0,146843.1] || subclass(u,v) -> equal(intersection(u,complement(v)),successor_relation)**.
% 299.82/300.44  161347[10:Rew:160202.0,146085.1] inductive(symmetric_difference(u,inverse(u))) ||  -> member(successor_relation,symmetrization_of(u))*.
% 299.82/300.44  161342[10:Rew:160202.0,146084.1] inductive(symmetric_difference(u,singleton(u))) ||  -> member(successor_relation,successor(u))*.
% 299.82/300.44  163209[10:Rew:160202.0,160823.1] ||  -> equal(singleton(u),successor_relation) equal(intersection(singleton(u),u),successor_relation)**.
% 299.82/300.44  163201[10:Rew:160202.0,160499.0] || member(not_subclass_element(u,successor_relation),complement(u))* -> subclass(u,successor_relation).
% 299.82/300.44  162962[10:Rew:160202.0,155845.0] ||  -> equal(integer_of(u),successor_relation) subclass(intersection(v,singleton(u)),omega)*.
% 299.82/300.44  162963[10:Rew:160202.0,155844.0] ||  -> equal(integer_of(u),successor_relation) subclass(intersection(singleton(u),v),omega)*.
% 299.82/300.44  160565[10:Rew:160202.0,153212.1] || equal(restrict(u,v,w),universal_class)** -> member(successor_relation,u).
% 299.82/300.44  168539[11:Res:168384.1,23.0] || equal(intersection(u,v),symmetrization_of(successor_relation))** -> member(successor_relation,u).
% 299.82/300.44  168540[11:Res:168384.1,24.0] || equal(intersection(u,v),symmetrization_of(successor_relation))** -> member(successor_relation,v).
% 299.82/300.44  163204[10:Rew:160202.0,160555.0] || equal(intersection(u,v),successor(successor_relation))** -> member(successor_relation,u).
% 299.82/300.44  163212[10:Rew:160202.0,161237.0] || equal(intersection(u,v),successor(successor_relation))** -> member(successor_relation,v).
% 299.82/300.44  163206[10:Rew:160202.0,160558.0] || equal(intersection(u,v),singleton(successor_relation))** -> member(successor_relation,u).
% 299.82/300.44  163213[10:Rew:160202.0,161240.0] || equal(intersection(u,v),singleton(successor_relation))** -> member(successor_relation,v).
% 299.82/300.44  126777[0:Obv:126734.0] ||  -> subclass(intersection(complement(power_class(u)),v),image(element_relation,complement(u)))*.
% 299.82/300.44  126557[0:Obv:126516.0] ||  -> subclass(intersection(u,complement(power_class(v))),image(element_relation,complement(v)))*.
% 299.82/300.44  179996[11:Res:179843.1,23.0] || equal(intersection(u,v),inverse(successor_relation))** -> member(successor_relation,u).
% 299.82/300.44  179997[11:Res:179843.1,24.0] || equal(intersection(u,v),inverse(successor_relation))** -> member(successor_relation,v).
% 299.82/300.44  181083[10:SpR:181056.0,15.0] ||  -> equal(unordered_pair(singleton(u),unordered_pair(u,successor_relation)),ordered_pair(u,universal_class))**.
% 299.82/300.44  183139[10:SpR:181044.1,1004.0] || member(u,universal_class) -> member(successor_relation,ordered_pair(successor(u),v))*.
% 299.82/300.44  183394[0:SpL:139600.0,2648.0] || subclass(universal_class,complement(complement(u)))* -> member(singleton(v),u)*.
% 299.82/300.44  184441[10:SpR:163197.1,31.0] || subclass(u,successor_relation) -> equal(restrict(u,v,w),successor_relation)**.
% 299.82/300.44  184530[10:Rew:160223.0,184420.1] || subclass(complement(u),successor_relation)* -> equal(union(v,u),universal_class)**.
% 299.82/300.44  184747[10:Rew:160223.0,184635.1] || subclass(complement(u),successor_relation)* -> equal(union(u,v),universal_class)**.
% 299.82/300.44  185329[10:SpL:28.0,185324.0] || equal(intersection(complement(u),complement(v)),union(u,v))** -> .
% 299.82/300.44  185940[10:Res:185646.1,23.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(successor_relation,u).
% 299.82/300.44  185941[10:Res:185646.1,24.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(successor_relation,v).
% 299.82/300.44  186014[10:Res:185647.1,23.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(omega,u).
% 299.82/300.44  186015[10:Res:185647.1,24.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(omega,v).
% 299.82/300.44  186125[10:Res:11.1,185639.1] || member(u,universal_class) equal(unordered_pair(u,v),successor_relation)** -> .
% 299.82/300.44  186126[10:Res:12.1,185639.1] || member(u,universal_class) equal(unordered_pair(v,u),successor_relation)** -> .
% 299.82/300.44  187772[10:Res:187500.1,23.0] || subclass(universal_class,intersection(u,v))* -> member(power_class(successor_relation),u).
% 299.82/300.44  187773[10:Res:187500.1,24.0] || subclass(universal_class,intersection(u,v))* -> member(power_class(successor_relation),v).
% 299.82/300.44  188190[10:Res:9089.1,186157.0] function(u) || equal(singleton(apply(u,v)),successor_relation)** -> .
% 299.82/300.44  188191[10:Res:34189.1,186157.0] || equal(singleton(not_subclass_element(u,v)),successor_relation)** -> subclass(u,v).
% 299.82/300.44  188656[10:Res:185430.1,30584.0] || equal(complement(complement(unordered_pair(u,ordered_pair(v,w)))),successor_relation)** -> .
% 299.82/300.44  188706[10:Res:185430.1,30459.0] || equal(complement(complement(unordered_pair(u,unordered_pair(v,w)))),successor_relation)** -> .
% 299.82/300.44  188769[10:Res:185430.1,30460.0] || equal(complement(complement(unordered_pair(unordered_pair(u,v),w))),successor_relation)** -> .
% 299.82/300.44  188781[10:Res:185430.1,30614.0] || equal(complement(complement(unordered_pair(ordered_pair(u,v),w))),successor_relation)** -> .
% 299.82/300.44  188979[10:SpR:185607.1,31.0] || equal(successor_relation,u) -> equal(restrict(u,v,w),successor_relation)**.
% 299.82/300.44  189079[10:Rew:160223.0,188957.1] || equal(complement(u),successor_relation) -> equal(union(v,u),universal_class)**.
% 299.82/300.44  189281[10:Rew:160223.0,189157.1] || equal(complement(u),successor_relation) -> equal(union(u,v),universal_class)**.
% 299.82/300.44  191104[20:Res:191074.1,595.0] || equal(restrict(u,v,w),omega)** -> member(successor_relation,u).
% 299.82/300.44  191138[20:MRR:191124.1,185225.0] || equal(ordered_pair(u,v),omega)** -> equal(singleton(u),successor_relation).
% 299.82/300.44  191632[15:Res:9089.1,189419.0] function(u) || equal(successor(apply(u,v)),successor_relation)** -> .
% 299.82/300.44  191633[15:Res:34189.1,189419.0] || equal(successor(not_subclass_element(u,v)),successor_relation)** -> subclass(u,v).
% 299.82/300.44  192121[15:SpR:190721.0,1004.0] ||  -> equal(range_of(u),successor_relation) member(successor_relation,ordered_pair(inverse(u),v))*.
% 299.82/300.44  193761[10:Rew:160224.0,193744.0] ||  -> equal(segment(complement(cross_product(u,singleton(v))),u,v),successor_relation)**.
% 299.82/300.44  195368[0:SpR:194805.1,9535.0] || subclass(u,v) -> subclass(symmetric_difference(v,u),complement(u))*.
% 299.82/300.44  195626[10:Res:6219.1,195436.0] || member(u,complement(singleton(u)))* -> equal(singleton(u),successor_relation).
% 299.82/300.44  195711[10:Res:185430.1,195539.0] || equal(complement(inverse(u)),successor_relation) -> subclass(v,inverse(u))*.
% 299.82/300.44  195721[10:Res:185430.1,195543.0] || equal(complement(sum_class(u)),successor_relation) -> subclass(v,sum_class(u))*.
% 299.82/300.44  195901[10:Rew:70.0,195889.0] || equal(apply(u,v),universal_class) -> inductive(apply(u,v))*.
% 299.82/300.44  195930[0:SpR:195152.0,9535.0] ||  -> subclass(symmetric_difference(u,intersection(u,v)),complement(intersection(u,v)))*.
% 299.82/300.44  195972[2:SpR:142543.0,195152.0] ||  -> equal(intersection(complement(u),symmetric_difference(universal_class,u)),symmetric_difference(universal_class,u))**.
% 299.82/300.44  196072[0:SpR:195339.0,9535.0] ||  -> subclass(symmetric_difference(u,intersection(v,u)),complement(intersection(v,u)))*.
% 299.82/300.44  199800[10:SpR:161327.1,160473.0] function(u) ||  -> equal(single_valued2(u),range__dfg(successor_relation,v,w))*.
% 299.82/300.44  199836[10:SpR:161328.1,160473.0] single_valued_class(u) ||  -> equal(single_valued2(u),range__dfg(successor_relation,v,w))*.
% 299.82/300.44  199988[6:Res:199848.1,23.0] || subclass(universal_class,intersection(u,v))* -> member(regular(rest_relation),u).
% 299.82/300.44  199989[6:Res:199848.1,24.0] || subclass(universal_class,intersection(u,v))* -> member(regular(rest_relation),v).
% 299.82/300.44  200061[14:SpR:200028.1,1004.0] || member(u,universal_class) -> member(successor_relation,ordered_pair(range_of(u),v))*.
% 299.82/300.44  200551[10:Res:999.0,163137.0] || equal(rest_of(ordered_pair(u,v)),successor(ordered_pair(u,v)))** -> .
% 299.82/300.44  200552[10:Res:160274.1,163137.0] || equal(rest_of(u),successor(u)) -> equal(integer_of(u),successor_relation)**.
% 299.82/300.44  200553[10:Res:160362.0,163137.0] || equal(rest_of(u),successor(u))** -> equal(singleton(u),successor_relation).
% 299.82/300.44  200559[10:Res:13.0,163137.0] || equal(rest_of(unordered_pair(u,v)),successor(unordered_pair(u,v)))** -> .
% 299.82/300.44  200894[10:MRR:200825.2,160227.0] || equal(cantor(u),successor_relation) member(v,cantor(u))* -> .
% 299.82/300.44  201378[6:Res:201231.1,23.0] || subclass(universal_class,intersection(u,v))* -> member(regular(domain_relation),u).
% 299.82/300.44  201379[6:Res:201231.1,24.0] || subclass(universal_class,intersection(u,v))* -> member(regular(domain_relation),v).
% 299.82/300.44  201902[10:MRR:201871.2,160227.0] || equal(inverse(u),successor_relation) member(v,inverse(u))* -> .
% 299.82/300.44  202298[10:MRR:202267.2,160227.0] || equal(sum_class(u),successor_relation) member(v,sum_class(u))* -> .
% 299.82/300.44  203562[6:Rew:203192.0,119993.0] ||  -> equal(cantor(cross_product(u,singleton(v))),segment(universal_class,u,v))**.
% 299.82/300.44  203933[10:Rew:203192.0,185071.1] || subclass(rest_of(u),successor_relation)* member(v,cantor(u))* -> .
% 299.82/300.44  204010[10:Rew:203192.0,181086.0] ||  -> equal(cantor(restrict(u,v,successor_relation)),segment(u,v,universal_class))**.
% 299.82/300.44  205836[10:SpR:205791.1,9535.0] ||  -> equal(singleton(u),successor_relation) subclass(symmetric_difference(u,universal_class),complement(u))*.
% 299.82/300.44  206683[10:SpR:507.0,206681.0] ||  -> member(successor_relation,complement(intersection(complement(singleton(successor_relation)),union(u,v))))*.
% 299.82/300.44  206696[10:Res:206681.0,3.0] || subclass(union(singleton(successor_relation),u),v)* -> member(successor_relation,v).
% 299.82/300.44  206719[10:Res:206682.0,6045.0] || subclass(symmetrization_of(singleton(successor_relation)),u)* well_ordering(universal_class,u) -> .
% 299.82/300.44  206733[10:Res:206684.0,6045.0] || subclass(successor(singleton(successor_relation)),u)* well_ordering(universal_class,u) -> .
% 299.82/300.44  206968[10:Res:206947.1,595.0] || equal(restrict(u,v,w),kind_1_ordinals)** -> member(successor_relation,u).
% 299.82/300.44  206994[10:Res:206947.1,163205.1] || equal(u,kind_1_ordinals) equal(complement(u),successor(successor_relation))** -> .
% 299.82/300.44  206995[11:Res:206947.1,168534.1] || equal(u,kind_1_ordinals) equal(complement(u),symmetrization_of(successor_relation))* -> .
% 299.82/300.44  207010[10:MRR:206986.1,185225.0] || equal(ordered_pair(u,v),kind_1_ordinals)** -> equal(singleton(u),successor_relation).
% 299.82/300.44  207191[10:SpR:506.0,207189.0] ||  -> member(successor_relation,complement(intersection(union(u,v),complement(singleton(successor_relation)))))*.
% 299.82/300.44  207202[10:Res:207189.0,3.0] || subclass(union(u,singleton(successor_relation)),v)* -> member(successor_relation,v).
% 299.82/300.44  207276[20:SpL:194805.1,206670.0] || subclass(u,complement(singleton(successor_relation)))* equal(u,omega) -> .
% 299.82/300.44  207301[10:SpL:194805.1,206676.0] || subclass(u,complement(singleton(successor_relation)))* equal(u,universal_class) -> .
% 299.82/300.44  207394[10:SpL:194805.1,207006.0] || subclass(u,complement(singleton(successor_relation)))* equal(u,kind_1_ordinals) -> .
% 299.82/300.44  207747[10:SpL:30.0,206671.0] || equal(complement(restrict(complement(singleton(successor_relation)),u,v)),successor_relation)** -> .
% 299.82/300.44  207777[11:SpL:30.0,206672.0] || equal(restrict(complement(singleton(successor_relation)),u,v),inverse(successor_relation))** -> .
% 299.82/300.44  207802[10:SpL:30.0,206673.0] || equal(restrict(complement(singleton(successor_relation)),u,v),singleton(successor_relation))** -> .
% 299.82/300.44  207827[11:SpL:30.0,206675.0] || equal(restrict(complement(singleton(successor_relation)),u,v),symmetrization_of(successor_relation))** -> .
% 299.82/300.44  208253[11:Res:179843.1,206958.1] || equal(u,inverse(successor_relation)) equal(complement(u),kind_1_ordinals)** -> .
% 299.82/300.44  208254[10:Res:163171.1,206958.1] || equal(u,singleton(successor_relation)) equal(complement(u),kind_1_ordinals)** -> .
% 299.82/300.44  208255[10:Res:163169.1,206958.1] || equal(u,successor(successor_relation)) equal(complement(u),kind_1_ordinals)** -> .
% 299.82/300.44  208256[11:Res:168384.1,206958.1] || equal(u,symmetrization_of(successor_relation))* equal(complement(u),kind_1_ordinals)** -> .
% 299.82/300.44  208599[10:SpL:142543.0,206964.0] || equal(symmetric_difference(universal_class,u),kind_1_ordinals) -> member(successor_relation,complement(u))*.
% 299.82/300.44  208937[10:Res:206947.1,163207.1] || equal(u,kind_1_ordinals) equal(complement(u),singleton(successor_relation))** -> .
% 299.82/300.44  208938[20:Res:191074.1,163207.1] || equal(u,omega) equal(complement(u),singleton(successor_relation))** -> .
% 299.82/300.44  208944[10:Res:160268.1,163207.1] || equal(u,universal_class) equal(complement(u),singleton(successor_relation))** -> .
% 299.82/300.44  208972[10:SpL:185605.1,208958.0] || equal(successor_relation,u) equal(power_class(u),singleton(successor_relation))** -> .
% 299.82/300.44  209284[9:Res:8.1,157925.0] || equal(u,image(element_relation,universal_class))* well_ordering(universal_class,u)* -> .
% 299.82/300.44  209312[12:Res:8.1,177133.0] || equal(u,cross_product(universal_class,universal_class)) -> member(regular(element_relation),u)*.
% 299.82/300.44  209315[12:Res:195710.1,177133.0] || equal(inverse(u),universal_class) -> member(regular(element_relation),inverse(u))*.
% 299.82/300.44  209316[12:Res:195720.1,177133.0] || equal(sum_class(u),universal_class) -> member(regular(element_relation),sum_class(u))*.
% 299.82/300.44  209449[12:Res:209377.1,26.1] || subclass(universal_class,complement(u))* member(regular(element_relation),u) -> .
% 299.82/300.44  209453[12:Res:209377.1,183398.0] || subclass(universal_class,complement(complement(u)))* -> member(regular(element_relation),u).
% 299.82/300.44  209455[12:Res:209377.1,23.0] || subclass(universal_class,intersection(u,v))* -> member(regular(element_relation),u).
% 299.82/300.44  209456[12:Res:209377.1,24.0] || subclass(universal_class,intersection(u,v))* -> member(regular(element_relation),v).
% 299.82/300.44  209754[15:Res:999.0,189420.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(ordered_pair(u,v)),successor_relation)**.
% 299.82/300.44  209762[15:Res:13.0,189420.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(unordered_pair(u,v)),successor_relation)**.
% 299.82/300.44  209873[15:Res:999.0,189421.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(ordered_pair(u,v)),successor_relation)**.
% 299.82/300.44  209881[15:Res:13.0,189421.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(unordered_pair(u,v)),successor_relation)**.
% 299.82/300.44  210384[15:Res:189563.1,17.0] || subclass(domain_relation,flip(cross_product(u,v)))* -> member(successor_relation,v).
% 299.82/300.44  210457[15:Res:189564.1,17.0] || subclass(domain_relation,rotate(cross_product(u,v)))* -> member(w,v)*.
% 299.82/300.44  210462[15:Res:189564.1,21.0] || subclass(domain_relation,rotate(element_relation)) -> member(ordered_pair(u,successor_relation),v)*.
% 299.82/300.44  210996[10:Res:1504.1,185639.1] || subclass(ordered_pair(u,v),w)* equal(successor_relation,w) -> .
% 299.82/300.44  211084[11:Res:206947.1,179992.1] || equal(u,kind_1_ordinals) equal(complement(u),inverse(successor_relation))** -> .
% 299.82/300.44  211085[20:Res:191074.1,179992.1] || equal(u,omega) equal(complement(u),inverse(successor_relation))** -> .
% 299.82/300.44  211091[11:Res:160268.1,179992.1] || equal(u,universal_class) equal(complement(u),inverse(successor_relation))** -> .
% 299.82/300.44  211120[11:SpL:185605.1,211105.0] || equal(successor_relation,u) equal(power_class(u),inverse(successor_relation))** -> .
% 299.82/300.44  211274[13:Res:8.1,180584.0] || equal(u,image(element_relation,successor_relation))* well_ordering(universal_class,u)* -> .
% 299.82/300.44  211444[10:Res:8.1,181149.0] || equal(u,singleton(singleton(successor_relation)))* well_ordering(universal_class,u)* -> .
% 299.82/300.44  211486[10:Res:3907.1,211446.0] || equal(complement(complement(u)),universal_class)** well_ordering(universal_class,u) -> .
% 299.82/300.44  211665[10:Res:181213.1,185065.1] || equal(u,singleton(singleton(successor_relation)))* subclass(u,successor_relation)* -> .
% 299.82/300.44  211706[10:Res:181213.1,185639.1] || equal(u,singleton(singleton(successor_relation)))* equal(successor_relation,u) -> .
% 299.82/300.44  212058[2:Res:184090.1,26.1] || equal(symmetric_difference(universal_class,u),universal_class)** member(omega,u) -> .
% 299.82/300.44  212062[2:Res:184090.1,183398.0] || equal(symmetric_difference(universal_class,complement(u)),universal_class)** -> member(omega,u).
% 299.82/300.44  212302[10:MRR:212230.1,314.0] || equal(complement(u),successor_relation) -> member(unordered_pair(v,w),u)*.
% 299.82/300.44  212464[10:Rew:57.0,212453.1] || equal(power_class(u),successor_relation)** equal(power_class(u),universal_class) -> .
% 299.82/300.44  212537[10:SpL:185605.1,212517.0] || equal(successor_relation,u) equal(complement(power_class(u)),successor_relation)** -> .
% 299.82/300.44  212559[13:Res:212548.0,3.0] || subclass(universal_class,u) -> member(regular(complement(power_class(universal_class))),u)*.
% 299.82/300.44  212659[10:SpR:185605.1,212652.0] || equal(successor_relation,u) -> member(regular(complement(power_class(u))),universal_class)*.
% 299.82/300.44  212666[10:Res:212652.0,3.0] || subclass(universal_class,u) -> member(regular(complement(power_class(successor_relation))),u)*.
% 299.82/300.44  212986[10:Res:8.1,187767.0] || equal(complement(u),universal_class) member(power_class(successor_relation),u)* -> .
% 299.82/300.44  213115[10:Res:188444.1,26.1] || equal(symmetric_difference(universal_class,u),universal_class)** member(successor_relation,u) -> .
% 299.82/300.44  213119[10:Res:188444.1,183398.0] || equal(symmetric_difference(universal_class,complement(u)),universal_class)** -> member(successor_relation,u).
% 299.82/300.44  213244[15:Res:189485.1,1705.0] || subclass(domain_relation,cross_product(u,v))* -> member(singleton(successor_relation),u).
% 299.82/300.44  213784[15:Rew:160223.0,213751.1] || equal(successor(u),successor_relation) -> subclass(universal_class,symmetric_difference(universal_class,u))*.
% 299.82/300.44  214149[20:Res:193270.1,26.1] || equal(symmetric_difference(universal_class,u),omega)** member(successor_relation,u) -> .
% 299.82/300.44  214153[20:Res:193270.1,183398.0] || equal(symmetric_difference(universal_class,complement(u)),omega)** -> member(successor_relation,u).
% 299.82/300.44  214273[10:Res:8.1,194520.0] || equal(complement(complement(u)),universal_class) -> member(power_class(successor_relation),u)*.
% 299.82/300.44  214726[2:Res:8.1,195403.0] || equal(complement(u),universal_class) -> equal(symmetric_difference(universal_class,u),universal_class)**.
% 299.82/300.44  214808[10:Res:195538.1,163163.0] || subclass(universal_class,inverse(u))* -> equal(complement(inverse(u)),successor_relation).
% 299.82/300.44  214809[10:Res:195538.1,160358.1] inductive(complement(inverse(u))) || subclass(universal_class,inverse(u))* -> .
% 299.82/300.44  215054[10:Res:195541.1,163163.0] || subclass(universal_class,sum_class(u))* -> equal(complement(sum_class(u)),successor_relation).
% 299.82/300.44  215055[10:Res:195541.1,160358.1] inductive(complement(sum_class(u))) || subclass(universal_class,sum_class(u))* -> .
% 299.82/300.44  215073[6:Res:136.1,195776.1] || member(inverse(u),ordinal_numbers)* equal(inverse(u),universal_class) -> .
% 299.82/300.44  215514[10:MRR:215513.1,314.0] || equal(inverse(u),universal_class) -> member(power_class(successor_relation),inverse(u))*.
% 299.82/300.44  215563[6:Res:136.1,195835.1] || member(sum_class(u),ordinal_numbers)* equal(sum_class(u),universal_class) -> .
% 299.82/300.44  215790[10:MRR:215789.1,314.0] || equal(sum_class(u),universal_class) -> member(power_class(successor_relation),sum_class(u))*.
% 299.82/300.44  215834[10:Res:8.1,197069.0] || equal(u,complement(singleton(successor_relation)))* well_ordering(universal_class,u)* -> .
% 299.82/300.44  216139[10:Res:199830.1,185639.1] || equal(u,cross_product(universal_class,universal_class))* equal(successor_relation,u) -> .
% 299.82/300.44  216183[6:Res:8.1,199959.0] || equal(u,cross_product(universal_class,universal_class))* well_ordering(universal_class,u)* -> .
% 299.82/300.44  216439[6:Res:8.1,199982.0] || equal(complement(u),universal_class) member(regular(rest_relation),u)* -> .
% 299.82/300.44  216461[6:Res:8.1,199986.0] || equal(complement(complement(u)),universal_class) -> member(regular(rest_relation),u)*.
% 299.82/300.44  216821[6:Res:8.1,201372.0] || equal(complement(u),universal_class) member(regular(domain_relation),u)* -> .
% 299.82/300.44  216843[6:Res:8.1,201376.0] || equal(complement(complement(u)),universal_class) -> member(regular(domain_relation),u)*.
% 299.82/300.44  217181[10:Res:8.1,206542.0] || equal(u,complement(complement(successor(successor_relation))))* -> member(successor_relation,u)*.
% 299.82/300.44  217189[10:Res:8.1,206660.0] || equal(complement(singleton(successor_relation)),u)* member(successor_relation,u)* -> .
% 299.82/300.44  217228[11:Res:179843.1,217209.0] || equal(singleton(u),inverse(successor_relation)) -> member(u,singleton(successor_relation))*.
% 299.82/300.44  217229[10:Res:163171.1,217209.0] || equal(singleton(u),singleton(successor_relation)) -> member(u,singleton(successor_relation))*.
% 299.82/300.44  217230[10:Res:163169.1,217209.0] || equal(singleton(u),successor(successor_relation)) -> member(u,singleton(successor_relation))*.
% 299.82/300.44  217231[11:Res:168384.1,217209.0] || equal(singleton(u),symmetrization_of(successor_relation)) -> member(u,singleton(successor_relation))*.
% 299.82/300.44  218374[10:MRR:218332.2,195777.1] || equal(inverse(u),universal_class) -> subclass(regular(inverse(u)),successor_relation)*.
% 299.82/300.44  218375[10:MRR:218343.2,195836.1] || equal(sum_class(u),universal_class) -> subclass(regular(sum_class(u)),successor_relation)*.
% 299.82/300.44  218429[13:Res:218371.0,160435.1] inductive(regular(image(element_relation,successor_relation))) ||  -> member(successor_relation,power_class(universal_class))*.
% 299.82/300.44  218440[10:Res:218372.0,160435.1] inductive(regular(image(element_relation,universal_class))) ||  -> member(successor_relation,power_class(successor_relation))*.
% 299.82/300.44  218476[10:Res:185430.1,217932.0] || equal(complement(complement(kind_1_ordinals)),successor_relation) -> subclass(universal_class,complement(ordinal_numbers))*.
% 299.82/300.44  218482[10:Res:206224.1,217932.0] || member(successor_relation,complement(kind_1_ordinals)) -> subclass(successor(successor_relation),complement(ordinal_numbers))*.
% 299.82/300.44  218486[3:Res:6219.1,217932.0] || member(u,complement(kind_1_ordinals)) -> subclass(singleton(u),complement(ordinal_numbers))*.
% 299.82/300.44  218527[10:Res:218494.0,160435.1] inductive(complement(complement(complement(kind_1_ordinals)))) ||  -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  218617[10:Res:218475.0,160435.1] inductive(intersection(complement(kind_1_ordinals),u)) ||  -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  218651[10:Res:218485.0,160435.1] inductive(intersection(u,complement(kind_1_ordinals))) ||  -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  218879[22:Res:218867.1,26.1] || subclass(kind_1_ordinals,complement(u))* member(singleton(successor_relation),u) -> .
% 299.82/300.44  218881[22:Res:218867.1,141576.1] || subclass(kind_1_ordinals,complement(kind_1_ordinals))* member(singleton(successor_relation),ordinal_numbers) -> .
% 299.82/300.44  218883[22:Res:218867.1,183398.0] || subclass(kind_1_ordinals,complement(complement(u)))* -> member(singleton(successor_relation),u).
% 299.82/300.44  218885[22:Res:218867.1,23.0] || subclass(kind_1_ordinals,intersection(u,v))* -> member(singleton(successor_relation),u).
% 299.82/300.44  218886[22:Res:218867.1,24.0] || subclass(kind_1_ordinals,intersection(u,v))* -> member(singleton(successor_relation),v).
% 299.82/300.44  218898[22:Res:218867.1,183723.0] || subclass(kind_1_ordinals,symmetrization_of(successor_relation)) -> member(singleton(successor_relation),inverse(successor_relation))*.
% 299.82/300.44  218899[22:Res:218867.1,193819.0] || subclass(kind_1_ordinals,cantor(complement(cross_product(singleton(singleton(successor_relation)),universal_class))))* -> .
% 299.82/300.44  218902[22:Res:218867.1,183622.0] || subclass(kind_1_ordinals,successor(successor_relation)) -> member(singleton(successor_relation),singleton(successor_relation))*.
% 299.82/300.44  218903[22:Res:218867.1,159.0] || subclass(kind_1_ordinals,omega) -> equal(integer_of(singleton(successor_relation)),singleton(successor_relation))**.
% 299.82/300.44  219102[15:Res:218473.1,213194.0] || equal(complement(kind_1_ordinals),domain_relation) subclass(complement(ordinal_numbers),successor_relation)* -> .
% 299.82/300.44  219174[3:Res:1477.1,218628.0] || subclass(universal_class,complement(kind_1_ordinals)) -> member(singleton(u),complement(ordinal_numbers))*.
% 299.82/300.44  219175[10:Res:160298.1,218628.0] ||  -> equal(complement(kind_1_ordinals),successor_relation) member(regular(complement(kind_1_ordinals)),complement(ordinal_numbers))*.
% 299.82/300.44  219177[10:Res:185647.1,218628.0] || equal(complement(complement(kind_1_ordinals)),successor_relation) -> member(omega,complement(ordinal_numbers))*.
% 299.82/300.44  219186[10:Res:187500.1,218628.0] || subclass(universal_class,complement(kind_1_ordinals)) -> member(power_class(successor_relation),complement(ordinal_numbers))*.
% 299.82/300.44  219213[22:Res:218867.1,218628.0] || subclass(kind_1_ordinals,complement(kind_1_ordinals)) -> member(singleton(successor_relation),complement(ordinal_numbers))*.
% 299.82/300.44  219221[10:Res:185646.1,218628.0] || equal(complement(complement(kind_1_ordinals)),successor_relation) -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  219228[20:Res:193270.1,218628.0] || equal(symmetric_difference(universal_class,kind_1_ordinals),omega) -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  219229[10:Res:188444.1,218628.0] || equal(symmetric_difference(universal_class,kind_1_ordinals),universal_class) -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  219237[6:Res:199848.1,218628.0] || subclass(universal_class,complement(kind_1_ordinals)) -> member(regular(rest_relation),complement(ordinal_numbers))*.
% 299.82/300.44  219240[6:Res:201231.1,218628.0] || subclass(universal_class,complement(kind_1_ordinals)) -> member(regular(domain_relation),complement(ordinal_numbers))*.
% 299.82/300.44  219241[12:Res:209377.1,218628.0] || subclass(universal_class,complement(kind_1_ordinals)) -> member(regular(element_relation),complement(ordinal_numbers))*.
% 299.82/300.44  219243[3:Res:184090.1,218628.0] || equal(symmetric_difference(universal_class,kind_1_ordinals),universal_class) -> member(omega,complement(ordinal_numbers))*.
% 299.82/300.44  219397[10:Res:185430.1,217589.0] || equal(complement(regular(unordered_pair(u,unordered_pair(v,w)))),successor_relation)** -> .
% 299.82/300.44  219555[10:MRR:219550.1,185116.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(u,successor_relation)),successor_relation)**.
% 299.82/300.44  219656[10:MRR:219654.1,185116.0] || equal(u,universal_class) -> equal(regular(unordered_pair(u,successor_relation)),successor_relation)**.
% 299.82/300.44  163251[10:Rew:160305.0,162946.0] ||  -> equal(intersection(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),complement(kind_1_ordinals)),successor_relation)**.
% 299.82/300.44  163252[10:Rew:160305.0,162947.0] ||  -> equal(intersection(complement(kind_1_ordinals),symmetric_difference(singleton(successor_relation),range_of(successor_relation))),successor_relation)**.
% 299.82/300.44  180612[11:SoR:164295.0,168572.1] || equal(range_of(successor_relation),symmetrization_of(successor_relation))** -> equal(range_of(successor_relation),omega).
% 299.82/300.44  180629[10:SoR:164295.0,167062.1] || equal(range_of(successor_relation),successor(successor_relation))** -> equal(range_of(successor_relation),omega).
% 299.82/300.44  180633[10:SoR:164295.0,167163.1] || equal(range_of(successor_relation),singleton(successor_relation))** -> equal(range_of(successor_relation),omega).
% 299.82/300.44  180790[11:SoR:164295.0,180021.1] || equal(range_of(successor_relation),inverse(successor_relation))** -> equal(range_of(successor_relation),omega).
% 299.82/300.44  206509[20:SoR:206272.0,166976.1] || equal(range_of(successor_relation),successor(successor_relation))** -> equal(successor(successor_relation),omega).
% 299.82/300.44  193779[10:SpR:193730.0,181082.0] ||  -> equal(apply(complement(cross_product(successor_relation,universal_class)),universal_class),sum_class(range_of(successor_relation)))**.
% 299.82/300.44  220884[23:Res:220417.0,189419.0] || equal(successor(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),successor_relation)** -> .
% 299.82/300.44  220886[23:Res:220417.0,186157.0] || equal(singleton(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),successor_relation)** -> .
% 299.82/300.44  221328[10:Res:185430.1,217590.0] || equal(complement(regular(unordered_pair(unordered_pair(u,v),w))),successor_relation)** -> .
% 299.82/300.44  221351[10:MRR:221347.1,185153.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(successor_relation,u)),successor_relation)**.
% 299.82/300.44  221359[10:MRR:221358.1,185153.0] || equal(u,universal_class) -> equal(regular(unordered_pair(successor_relation,u)),successor_relation)**.
% 299.82/300.44  221455[15:Res:218373.0,213194.0] || subclass(complement(singleton(domain_relation)),successor_relation)* -> equal(singleton(domain_relation),successor_relation).
% 299.82/300.44  221527[10:MRR:221485.1,185111.0] || member(u,universal_class) -> member(u,complement(singleton(singleton(u))))*.
% 299.82/300.44  221534[20:Res:221515.0,6045.0] || subclass(complement(singleton(omega)),u)* well_ordering(universal_class,u) -> .
% 299.82/300.44  221574[10:Res:221516.0,3.0] || subclass(complement(singleton(singleton(successor_relation))),u)* -> member(successor_relation,u).
% 299.82/300.44  221689[15:MRR:221681.1,999.0] || subclass(domain_relation,rotate(ordinal_numbers)) subclass(domain_relation,complement(kind_1_ordinals))* -> .
% 299.82/300.44  221690[15:MRR:221684.1,999.0] || subclass(domain_relation,flip(ordinal_numbers)) subclass(domain_relation,complement(kind_1_ordinals))* -> .
% 299.82/300.44  221692[15:MRR:221680.1,999.0] || subclass(rest_relation,rotate(ordinal_numbers))* subclass(domain_relation,complement(kind_1_ordinals)) -> .
% 299.82/300.44  221722[10:Obv:221718.0] ||  -> equal(intersection(singleton(u),omega),successor_relation)** equal(integer_of(u),u).
% 299.82/300.44  221732[10:Res:221565.0,160435.1] inductive(complement(compose(element_relation,universal_class))) ||  -> member(successor_relation,complement(element_relation))*.
% 299.82/300.44  221771[10:Obv:221767.0] ||  -> equal(intersection(omega,singleton(u)),successor_relation)** equal(integer_of(u),u).
% 299.82/300.44  221786[11:Res:221522.0,179992.1] || equal(complement(complement(singleton(ordered_pair(universal_class,u)))),inverse(successor_relation))** -> .
% 299.82/300.44  221787[10:Res:221522.0,163207.1] || equal(complement(complement(singleton(ordered_pair(universal_class,u)))),singleton(successor_relation))** -> .
% 299.82/300.44  221789[10:Res:221522.0,163205.1] || equal(complement(complement(singleton(ordered_pair(universal_class,u)))),successor(successor_relation))** -> .
% 299.82/300.44  221790[11:Res:221522.0,168534.1] || equal(complement(complement(singleton(ordered_pair(universal_class,u)))),symmetrization_of(successor_relation))** -> .
% 299.82/300.44  222131[10:SpR:1005.0,221525.0] ||  -> member(singleton(singleton(u)),complement(singleton(singleton(singleton(singleton(u))))))*.
% 299.82/300.44  222228[10:SpL:1005.0,222147.0] || member(singleton(singleton(u)),singleton(singleton(singleton(singleton(u)))))* -> .
% 299.82/300.44  222300[15:MRR:222263.1,999.0] || subclass(domain_relation,rotate(u)) subclass(domain_relation,complement(u))* -> .
% 299.82/300.44  222301[15:MRR:222279.1,999.0] || subclass(domain_relation,flip(u)) subclass(domain_relation,complement(u))* -> .
% 299.82/300.44  222307[15:MRR:222262.1,999.0] || subclass(rest_relation,rotate(u))* subclass(domain_relation,complement(u)) -> .
% 299.82/300.44  222346[24:SpR:222326.0,15.0] ||  -> equal(unordered_pair(successor_relation,unordered_pair(kind_1_ordinals,singleton(u))),ordered_pair(kind_1_ordinals,u))**.
% 299.82/300.44  222490[24:Rew:142543.0,222336.0,160223.0,222336.0] ||  -> equal(complement(image(element_relation,successor(kind_1_ordinals))),power_class(symmetric_difference(universal_class,kind_1_ordinals)))**.
% 299.82/300.44  222502[24:Rew:181135.1,222501.1] || member(singleton(singleton(successor_relation)),compose_class(u))* -> equal(kind_1_ordinals,universal_class).
% 299.82/300.44  222508[24:Rew:181136.1,222507.1] || member(singleton(singleton(successor_relation)),rest_of(u))* -> equal(kind_1_ordinals,universal_class).
% 299.82/300.44  222753[25:MRR:160538.2,222730.0] single_valued_class(domain_of(u)) || equal(complement(rest_of(u)),universal_class)** -> .
% 299.82/300.44  222759[25:MRR:6326.2,222758.0] single_valued_class(singleton(u)) || member(u,cross_product(universal_class,universal_class))* -> .
% 299.82/300.44  223128[24:Res:222474.0,160435.1] inductive(symmetric_difference(complement(kind_1_ordinals),universal_class)) ||  -> member(successor_relation,successor(kind_1_ordinals))*.
% 299.82/300.44  223138[24:SpR:185628.1,223096.0] || equal(complement(kind_1_ordinals),successor_relation) -> subclass(complement(successor(kind_1_ordinals)),successor_relation)*.
% 299.82/300.44  223141[24:Res:223096.0,160435.1] inductive(complement(successor(kind_1_ordinals))) ||  -> member(successor_relation,symmetric_difference(universal_class,kind_1_ordinals))*.
% 299.82/300.44  223163[24:Res:222372.0,179992.1] || equal(complement(complement(singleton(ordered_pair(kind_1_ordinals,u)))),inverse(successor_relation))** -> .
% 299.82/300.44  223164[24:Res:222372.0,163207.1] || equal(complement(complement(singleton(ordered_pair(kind_1_ordinals,u)))),singleton(successor_relation))** -> .
% 299.82/300.44  223166[24:Res:222372.0,163205.1] || equal(complement(complement(singleton(ordered_pair(kind_1_ordinals,u)))),successor(successor_relation))** -> .
% 299.82/300.44  223167[24:Res:222372.0,168534.1] || equal(complement(complement(singleton(ordered_pair(kind_1_ordinals,u)))),symmetrization_of(successor_relation))** -> .
% 299.82/300.44  223246[24:SpR:222476.0,183964.0] ||  -> equal(recursion(successor_relation,apply(add_relation,universal_class),successor_relation),ordinal_multiply(kind_1_ordinals,u))*.
% 299.82/300.44  223298[24:SpL:222479.0,147.0] || member(ordered_pair(u,universal_class),rest_relation)* -> equal(rest_of(u),kind_1_ordinals).
% 299.82/300.44  223320[24:SpL:222479.0,203286.0] || member(ordered_pair(u,universal_class),domain_relation)* -> equal(cantor(u),kind_1_ordinals).
% 299.82/300.44  224661[25:SpR:224236.1,204209.0] function(flip(cross_product(u,universal_class))) ||  -> equal(inverse(u),universal_class)**.
% 299.82/300.44  224662[25:SpR:224236.1,204281.0] function(restrict(element_relation,universal_class,u)) ||  -> equal(sum_class(u),universal_class)**.
% 299.82/300.44  224919[25:SpR:224739.1,1005.0] function(u) ||  -> equal(ordered_pair(successor_relation,u),singleton(singleton(successor_relation)))**.
% 299.82/300.44  224954[25:SpR:224739.1,221525.0] function(u) ||  -> member(successor_relation,complement(singleton(ordered_pair(u,v))))*.
% 299.82/300.44  224963[25:SpR:224739.1,1006.0] function(u) ||  -> member(unordered_pair(v,successor_relation),ordered_pair(v,u))*.
% 299.82/300.44  225113[25:SpL:224739.1,222147.0] function(u) || member(successor_relation,singleton(ordered_pair(u,v)))* -> .
% 299.82/300.44  225448[25:Rew:160223.0,224916.1] function(u) ||  -> subclass(symmetric_difference(complement(u),universal_class),successor(u))*.
% 299.82/300.44  225450[25:Rew:181082.0,224960.1] function(u) ||  -> equal(apply(v,universal_class),apply(v,u))*.
% 299.82/300.44  225461[25:Rew:181083.0,224962.1] function(u) ||  -> equal(ordered_pair(v,universal_class),ordered_pair(v,u))*.
% 299.82/300.44  225630[25:SpR:225544.1,3587.0] function(apply(choice,omega)) ||  -> equal(apply(choice,omega),successor_relation)**.
% 299.82/300.44  226384[25:SpR:226350.1,119971.0] one_to_one(cross_product(u,universal_class)) ||  -> equal(image(universal_class,u),universal_class)**.
% 299.82/300.44  226763[10:SpR:194805.1,226634.0] || subclass(u,ordinal_numbers) -> equal(intersection(u,complement(kind_1_ordinals)),successor_relation)**.
% 299.82/300.44  227335[25:Res:224913.1,206958.1] function(u) || equal(complement(ordered_pair(u,v)),kind_1_ordinals)** -> .
% 299.82/300.44  227338[25:Res:224913.1,191095.1] function(u) || equal(complement(ordered_pair(u,v)),omega)** -> .
% 299.82/300.44  227652[10:SpR:194805.1,227524.0] || subclass(u,ordinal_numbers) -> equal(intersection(complement(kind_1_ordinals),u),successor_relation)**.
% 299.82/300.44  228738[10:MRR:228722.2,185225.0] || equal(singleton(u),v)* equal(complement(v),successor_relation)** -> .
% 299.82/300.44  228740[10:MRR:228719.2,188662.0] || equal(unordered_pair(u,v),w)* subclass(universal_class,w)* -> .
% 299.82/300.44  228785[24:SpR:223107.0,9535.0] ||  -> subclass(symmetric_difference(successor(kind_1_ordinals),universal_class),complement(symmetric_difference(complement(kind_1_ordinals),universal_class)))*.
% 299.82/300.44  228791[24:SpR:223107.0,160445.0] ||  -> equal(intersection(symmetric_difference(complement(kind_1_ordinals),universal_class),complement(successor(kind_1_ordinals))),successor_relation)**.
% 299.82/300.44  228792[24:SpR:223107.0,160443.0] ||  -> equal(intersection(complement(successor(kind_1_ordinals)),symmetric_difference(complement(kind_1_ordinals),universal_class)),successor_relation)**.
% 299.82/300.44  229015[10:Res:228991.1,26.1] || subclass(kind_1_ordinals,complement(u))* member(regular(ordinal_numbers),u) -> .
% 299.82/300.44  229017[10:Res:228991.1,218628.0] || subclass(kind_1_ordinals,complement(kind_1_ordinals)) -> member(regular(ordinal_numbers),complement(ordinal_numbers))*.
% 299.82/300.44  229018[10:Res:228991.1,141576.1] || subclass(kind_1_ordinals,complement(kind_1_ordinals))* member(regular(ordinal_numbers),ordinal_numbers) -> .
% 299.82/300.44  229020[10:Res:228991.1,183398.0] || subclass(kind_1_ordinals,complement(complement(u)))* -> member(regular(ordinal_numbers),u).
% 299.82/300.44  229022[10:Res:228991.1,23.0] || subclass(kind_1_ordinals,intersection(u,v))* -> member(regular(ordinal_numbers),u).
% 299.82/300.44  229023[10:Res:228991.1,24.0] || subclass(kind_1_ordinals,intersection(u,v))* -> member(regular(ordinal_numbers),v).
% 299.82/300.44  229035[10:Res:228991.1,183723.0] || subclass(kind_1_ordinals,symmetrization_of(successor_relation)) -> member(regular(ordinal_numbers),inverse(successor_relation))*.
% 299.82/300.44  229036[10:Res:228991.1,193819.0] || subclass(kind_1_ordinals,cantor(complement(cross_product(singleton(regular(ordinal_numbers)),universal_class))))* -> .
% 299.82/300.44  229039[10:Res:228991.1,183622.0] || subclass(kind_1_ordinals,successor(successor_relation)) -> member(regular(ordinal_numbers),singleton(successor_relation))*.
% 299.82/300.44  229040[10:Res:228991.1,159.0] || subclass(kind_1_ordinals,omega) -> equal(integer_of(regular(ordinal_numbers)),regular(ordinal_numbers))**.
% 299.82/300.44  229243[10:Res:229228.1,26.1] || subclass(universal_class,complement(u))* member(regular(ordinal_numbers),u) -> .
% 299.82/300.44  229245[10:Res:229228.1,218628.0] || subclass(universal_class,complement(kind_1_ordinals)) -> member(regular(ordinal_numbers),complement(ordinal_numbers))*.
% 299.82/300.44  229246[10:Res:229228.1,141576.1] || subclass(universal_class,complement(kind_1_ordinals))* member(regular(ordinal_numbers),ordinal_numbers) -> .
% 299.82/300.44  229248[10:Res:229228.1,183398.0] || subclass(universal_class,complement(complement(u)))* -> member(regular(ordinal_numbers),u).
% 299.82/300.44  229250[10:Res:229228.1,23.0] || subclass(universal_class,intersection(u,v))* -> member(regular(ordinal_numbers),u).
% 299.82/300.44  229251[10:Res:229228.1,24.0] || subclass(universal_class,intersection(u,v))* -> member(regular(ordinal_numbers),v).
% 299.82/300.44  229263[10:Res:229228.1,183723.0] || subclass(universal_class,symmetrization_of(successor_relation)) -> member(regular(ordinal_numbers),inverse(successor_relation))*.
% 299.82/300.44  229264[10:Res:229228.1,193819.0] || subclass(universal_class,cantor(complement(cross_product(singleton(regular(ordinal_numbers)),universal_class))))* -> .
% 299.82/300.44  229268[10:Res:229228.1,159.0] || subclass(universal_class,omega) -> equal(integer_of(regular(ordinal_numbers)),regular(ordinal_numbers))**.
% 299.82/300.44  229501[15:MRR:229471.1,229170.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(regular(ordinal_numbers),successor_relation),rest_relation)*.
% 299.82/300.44  229851[20:Res:64.1,221538.0] function(complement(singleton(omega))) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  230149[10:SpL:1005.0,222140.0] || equal(complement(complement(singleton(singleton(singleton(singleton(u)))))),universal_class)** -> .
% 299.82/300.44  230543[22:Res:218867.1,229800.0] || subclass(kind_1_ordinals,singleton(omega))* -> equal(integer_of(singleton(successor_relation)),successor_relation).
% 299.82/300.44  230570[10:Res:228991.1,229800.0] || subclass(kind_1_ordinals,singleton(omega))* -> equal(integer_of(regular(ordinal_numbers)),successor_relation).
% 299.82/300.44  230663[10:Res:185430.1,219386.0] || equal(complement(regular(unordered_pair(u,ordered_pair(v,w)))),successor_relation)** -> .
% 299.82/300.44  230664[10:MRR:230660.2,188646.0] || equal(ordered_pair(u,v),w)* subclass(universal_class,w)* -> .
% 299.82/300.44  230732[10:MRR:230730.2,200297.0] || equal(regular(rest_relation),u) equal(complement(u),successor_relation)** -> .
% 299.82/300.44  230739[10:MRR:230737.2,201541.0] || equal(regular(domain_relation),u) equal(complement(u),successor_relation)** -> .
% 299.82/300.44  230765[12:MRR:230763.2,209559.0] || equal(regular(element_relation),u) equal(complement(u),successor_relation)** -> .
% 299.82/300.44  230897[10:MRR:230896.2,188662.0] || equal(unordered_pair(u,v),w)* equal(w,universal_class) -> .
% 299.82/300.44  231195[10:Res:185430.1,221320.0] || equal(complement(regular(unordered_pair(ordered_pair(u,v),w))),successor_relation)** -> .
% 299.82/300.44  231553[15:MRR:231547.1,999.0] || subclass(domain_relation,rotate(ordinal_numbers)) subclass(rest_relation,complement(kind_1_ordinals))* -> .
% 299.82/300.44  231554[3:MRR:231548.1,999.0] || subclass(rest_relation,flip(ordinal_numbers)) subclass(rest_relation,complement(kind_1_ordinals))* -> .
% 299.82/300.44  231640[25:SpR:224912.1,160369.0] function(u) ||  -> subclass(complement(successor(u)),symmetric_difference(universal_class,u))*.
% 299.82/300.44  231726[10:MRR:231725.2,188646.0] || equal(ordered_pair(u,v),w)* equal(w,universal_class) -> .
% 299.82/300.44  9444[0:Res:9395.0,9.0] || subclass(u,intersection(v,u))* -> equal(intersection(v,u),u).
% 299.82/300.44  9558[0:Res:9509.0,9.0] || subclass(u,intersection(u,v))* -> equal(intersection(u,v),u).
% 299.82/300.44  9876[0:SpR:30.0,9535.0] ||  -> subclass(symmetric_difference(u,cross_product(v,w)),complement(restrict(u,v,w)))*.
% 299.82/300.44  9882[0:SpR:31.0,9535.0] ||  -> subclass(symmetric_difference(cross_product(u,v),w),complement(restrict(w,u,v)))*.
% 299.82/300.44  2654[0:Res:1477.1,595.0] || subclass(universal_class,restrict(u,v,w))* -> member(singleton(x),u)*.
% 299.82/300.44  3514[0:Res:1499.1,26.1] || subclass(universal_class,complement(u)) member(ordered_pair(v,w),u)* -> .
% 299.82/300.44  30825[0:MRR:30782.0,999.0] || subclass(universal_class,complement(complement(u)))* -> member(ordered_pair(v,w),u)*.
% 299.82/300.44  3516[0:Res:1499.1,24.0] || subclass(universal_class,intersection(u,v))* -> member(ordered_pair(w,x),v)*.
% 299.82/300.44  3515[0:Res:1499.1,23.0] || subclass(universal_class,intersection(u,v))* -> member(ordered_pair(w,x),u)*.
% 299.82/300.44  34256[0:Res:60.1,34067.0] || member(ordered_pair(u,v),compose(w,x))* -> member(v,universal_class).
% 299.82/300.44  6140[0:SpL:30.0,5884.0] || equal(restrict(u,v,w),universal_class)** -> member(singleton(x),u)*.
% 299.82/300.44  107102[0:Res:3907.1,1522.0] || equal(complement(complement(cross_product(u,v))),universal_class)** -> member(w,v)*.
% 299.82/300.44  107305[0:Res:107233.0,9.0] || subclass(u,complement(complement(u)))* -> equal(complement(complement(u)),u).
% 299.82/300.44  107556[0:Res:4.1,6045.0] || subclass(u,v)* well_ordering(universal_class,v)* -> subclass(u,w)*.
% 299.82/300.44  107564[2:Res:2457.1,6045.0] inductive(u) || subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  107688[0:Res:1009.0,6045.0] || subclass(singleton(singleton(singleton(u))),v)* well_ordering(universal_class,v) -> .
% 299.82/300.44  108429[0:Res:1504.1,3486.1] || subclass(ordered_pair(u,v),w)* subclass(universal_class,complement(w)) -> .
% 299.82/300.44  111900[0:SpR:10417.0,44.0] ||  -> equal(image(cross_product(u,universal_class),v),image(cross_product(v,universal_class),u))*.
% 299.82/300.44  113241[0:Obv:113185.1] || member(u,v) -> subclass(singleton(u),intersection(v,singleton(u)))*.
% 299.82/300.44  3447[0:SpL:161.0,1511.0] || equal(symmetric_difference(u,v),universal_class) -> member(omega,union(u,v))*.
% 299.82/300.44  1508[0:Res:1506.1,3.0] || equal(u,universal_class) subclass(u,v)* -> member(omega,v).
% 299.82/300.44  110378[0:Res:146.0,31922.0] || well_ordering(u,cross_product(universal_class,universal_class))* -> member(least(u,rest_relation),rest_relation).
% 299.82/300.44  141706[2:MRR:127344.2,120469.0] || member(u,intersection(v,w))* member(u,complement(v)) -> .
% 299.82/300.44  141716[2:MRR:128689.2,120469.0] || member(u,intersection(v,w))* member(u,complement(w)) -> .
% 299.82/300.44  141791[2:MRR:120439.2,120469.0] inductive(symmetric_difference(u,u)) || well_ordering(v,complement(complement(u)))* -> .
% 299.82/300.44  142241[2:Rew:142218.0,142224.0] ||  -> equal(symmetric_difference(cross_product(u,v),universal_class),symmetric_difference(universal_class,cross_product(u,v)))**.
% 299.82/300.44  145198[2:SpR:28.0,142419.0] ||  -> equal(symmetric_difference(intersection(complement(u),complement(v)),union(u,v)),universal_class)**.
% 299.82/300.44  145330[2:SpR:28.0,142420.0] ||  -> equal(symmetric_difference(union(u,v),intersection(complement(u),complement(v))),universal_class)**.
% 299.82/300.44  150077[6:MRR:148045.1,149669.0] inductive(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) ||  -> .
% 299.82/300.44  152923[0:Res:1506.1,10191.0] || equal(symmetric_difference(u,inverse(u)),universal_class)** -> member(omega,symmetrization_of(u)).
% 299.82/300.44  152924[0:Res:1506.1,10254.0] || equal(symmetric_difference(u,singleton(u)),universal_class)** -> member(omega,successor(u)).
% 299.82/300.44  155727[2:SpL:142543.0,5884.0] || equal(symmetric_difference(universal_class,u),universal_class) -> member(singleton(v),complement(u))*.
% 299.82/300.44  155730[2:SpL:142543.0,2648.0] || subclass(universal_class,symmetric_difference(universal_class,u))* -> member(singleton(v),complement(u))*.
% 299.82/300.44  155806[3:Res:1499.1,141576.1] || subclass(universal_class,complement(kind_1_ordinals)) member(ordered_pair(u,v),ordinal_numbers)* -> .
% 299.82/300.44  155822[3:Res:155815.1,3.0] || member(u,ordinal_numbers)* subclass(kind_1_ordinals,v)* -> member(u,v)*.
% 299.82/300.44  158211[0:MRR:158194.0,54.0] || equal(complement(union(u,v)),universal_class)** -> member(omega,complement(u)).
% 299.82/300.44  158212[0:MRR:158195.0,54.0] || equal(complement(union(u,v)),universal_class)** -> member(omega,complement(v)).
% 299.82/300.44  159260[6:SpR:158812.1,158812.1] function(u) function(v) ||  -> equal(single_valued1(u),single_valued1(v))*.
% 299.82/300.44  159263[6:SpR:158813.1,158813.1] single_valued_class(u) single_valued_class(v) ||  -> equal(single_valued1(u),single_valued1(v))*.
% 299.82/300.44  159264[6:SpR:158813.1,158812.1] single_valued_class(u) function(v) ||  -> equal(single_valued1(u),single_valued1(v))*.
% 299.82/300.44  159970[3:Res:159949.0,9.0] || subclass(kind_1_ordinals,complement(complement(ordinal_numbers)))* -> equal(complement(complement(ordinal_numbers)),kind_1_ordinals).
% 299.82/300.44  159995[3:Res:159950.0,9.0] || subclass(kind_1_ordinals,intersection(ordinal_numbers,u))* -> equal(intersection(ordinal_numbers,u),kind_1_ordinals).
% 299.82/300.44  160012[3:Res:159951.0,9.0] || subclass(kind_1_ordinals,intersection(u,ordinal_numbers))* -> equal(intersection(u,ordinal_numbers),kind_1_ordinals).
% 299.82/300.44  160040[3:Res:159952.1,9.0] || subclass(u,ordinal_numbers)* subclass(kind_1_ordinals,u)* -> equal(kind_1_ordinals,u).
% 299.82/300.44  163039[10:Rew:160202.0,158627.0] ||  -> equal(intersection(power_class(image(element_relation,successor_relation)),image(element_relation,power_class(universal_class))),successor_relation)**.
% 299.82/300.44  163038[10:Rew:160202.0,158622.0] ||  -> equal(intersection(power_class(complement(inverse(successor_relation))),image(element_relation,symmetrization_of(successor_relation))),successor_relation)**.
% 299.82/300.44  163037[10:Rew:160202.0,158621.0] ||  -> equal(intersection(power_class(complement(singleton(successor_relation))),image(element_relation,successor(successor_relation))),successor_relation)**.
% 299.82/300.44  163035[10:Rew:160202.0,158559.0] ||  -> equal(intersection(image(element_relation,power_class(universal_class)),power_class(image(element_relation,successor_relation))),successor_relation)**.
% 299.82/300.44  163034[10:Rew:160202.0,158554.0] ||  -> equal(intersection(image(element_relation,symmetrization_of(successor_relation)),power_class(complement(inverse(successor_relation)))),successor_relation)**.
% 299.82/300.44  163033[10:Rew:160202.0,158553.0] ||  -> equal(intersection(image(element_relation,successor(successor_relation)),power_class(complement(singleton(successor_relation)))),successor_relation)**.
% 299.82/300.44  163016[10:Rew:160202.0,157441.0] ||  -> equal(restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),successor_relation)**.
% 299.82/300.44  163009[10:Rew:160202.0,156722.0] ||  -> equal(intersection(intersection(u,symmetric_difference(universal_class,v)),union(v,successor_relation)),successor_relation)**.
% 299.82/300.44  163007[10:Rew:160202.0,156617.0] ||  -> equal(intersection(intersection(symmetric_difference(universal_class,u),v),union(u,successor_relation)),successor_relation)**.
% 299.82/300.44  163004[10:Rew:160202.0,156544.0] ||  -> equal(intersection(union(u,successor_relation),intersection(v,symmetric_difference(universal_class,u))),successor_relation)**.
% 299.82/300.44  163002[10:Rew:160202.0,156442.0] ||  -> equal(intersection(union(u,successor_relation),intersection(symmetric_difference(universal_class,u),v)),successor_relation)**.
% 299.82/300.44  162704[10:Rew:160202.0,156148.1] || equal(cantor(u),universal_class) -> equal(symmetric_difference(universal_class,cantor(u)),successor_relation)**.
% 299.82/300.44  161944[10:Rew:160202.0,150148.0] ||  -> equal(union(image(element_relation,universal_class),successor_relation),complement(intersection(power_class(successor_relation),universal_class)))**.
% 299.82/300.44  161936[10:Rew:160202.0,150140.0] ||  -> equal(intersection(power_class(image(element_relation,universal_class)),image(element_relation,power_class(successor_relation))),successor_relation)**.
% 299.82/300.44  161934[10:Rew:160202.0,150137.0] ||  -> equal(intersection(image(element_relation,power_class(successor_relation)),power_class(image(element_relation,universal_class))),successor_relation)**.
% 299.82/300.44  161652[10:Rew:160202.0,156034.1] ||  -> member(u,symmetric_difference(universal_class,v)) subclass(singleton(u),union(v,successor_relation))*.
% 299.82/300.44  161501[10:Rew:160202.0,148480.0] ||  -> equal(integer_of(singleton(omega)),successor_relation) member(singleton(singleton(singleton(omega))),element_relation)*.
% 299.82/300.44  161499[10:Rew:160202.0,148471.1] || subclass(universal_class,complement(omega)) -> equal(integer_of(unordered_pair(u,v)),successor_relation)**.
% 299.82/300.44  161483[10:Rew:160202.0,147809.0] ||  -> equal(intersection(intersection(u,image(element_relation,complement(v))),power_class(v)),successor_relation)**.
% 299.82/300.44  161482[10:Rew:160202.0,147758.0] ||  -> equal(intersection(restrict(u,v,w),complement(cross_product(v,w))),successor_relation)**.
% 299.82/300.44  161481[10:Rew:160202.0,147757.0] ||  -> equal(intersection(symmetric_difference(u,v),complement(complement(intersection(u,v)))),successor_relation)**.
% 299.82/300.44  161480[10:Rew:160202.0,147756.0] ||  -> equal(intersection(intersection(image(element_relation,complement(u)),v),power_class(u)),successor_relation)**.
% 299.82/300.44  161479[10:Rew:160202.0,147747.0] ||  -> equal(intersection(power_class(u),intersection(v,image(element_relation,complement(u)))),successor_relation)**.
% 299.82/300.44  161477[10:Rew:160202.0,147704.0] ||  -> equal(intersection(intersection(u,v),singleton(w)),successor_relation)** member(w,u).
% 299.82/300.44  161478[10:Rew:160202.0,147703.0] ||  -> equal(intersection(intersection(u,v),singleton(w)),successor_relation)** member(w,v).
% 299.82/300.44  161476[10:Rew:160202.0,147647.0] ||  -> equal(intersection(power_class(u),intersection(image(element_relation,complement(u)),v)),successor_relation)**.
% 299.82/300.44  161475[10:Rew:160202.0,147643.0] ||  -> equal(intersection(complement(cross_product(u,v)),restrict(w,u,v)),successor_relation)**.
% 299.82/300.44  161474[10:Rew:160202.0,147642.0] ||  -> equal(intersection(complement(complement(intersection(u,v))),symmetric_difference(u,v)),successor_relation)**.
% 299.82/300.44  161472[10:Rew:160202.0,147606.0] ||  -> equal(intersection(singleton(u),intersection(v,w)),successor_relation)** member(u,v).
% 299.82/300.44  161473[10:Rew:160202.0,147605.0] ||  -> equal(intersection(singleton(u),intersection(v,w)),successor_relation)** member(u,w).
% 299.82/300.44  161471[10:Rew:160202.0,147515.0] ||  -> equal(intersection(union(u,v),intersection(complement(u),complement(v))),successor_relation)**.
% 299.82/300.44  161470[10:Rew:160202.0,147496.1] || member(u,v) -> equal(intersection(complement(v),singleton(u)),successor_relation)**.
% 299.82/300.44  161469[10:Rew:160202.0,147489.0] ||  -> equal(intersection(intersection(complement(u),complement(v)),union(u,v)),successor_relation)**.
% 299.82/300.44  161468[10:Rew:160202.0,147469.1] || member(u,v) -> equal(intersection(singleton(u),complement(v)),successor_relation)**.
% 299.82/300.44  161464[10:Rew:160202.0,147415.1] || asymmetric(universal_class,u) -> equal(restrict(inverse(universal_class),u,u),successor_relation)**.
% 299.82/300.44  161465[10:Rew:160202.0,147414.0] || equal(restrict(inverse(universal_class),u,u),successor_relation)** -> asymmetric(universal_class,u).
% 299.82/300.44  161463[10:Rew:160202.0,147342.1] inductive(intersection(u,cantor(inverse(v)))) ||  -> member(successor_relation,range_of(v))*.
% 299.82/300.44  161461[10:Rew:160202.0,159762.1] || equal(complement(union(u,v)),universal_class)** -> member(successor_relation,complement(v)).
% 299.82/300.44  161462[10:Rew:160202.0,147189.2] inductive(singleton(u)) ||  -> member(u,v)* member(successor_relation,complement(v))*.
% 299.82/300.44  161460[10:Rew:160202.0,146850.1] inductive(intersection(u,v)) || member(successor_relation,symmetric_difference(u,v))* -> .
% 299.82/300.44  161453[10:Rew:160202.0,146646.1] || subclass(universal_class,u)* -> equal(singleton(v),successor_relation) member(v,u)*.
% 299.82/300.44  161447[10:Rew:160202.0,146638.1] inductive(symmetric_difference(u,v)) ||  -> member(successor_relation,complement(intersection(u,v)))*.
% 299.82/300.44  161446[10:Rew:160202.0,146637.1] || subclass(universal_class,u) -> equal(v,successor_relation) member(regular(v),u)*.
% 299.82/300.44  161409[10:Rew:160202.0,146121.1] inductive(cantor(flip(cross_product(u,universal_class)))) ||  -> member(successor_relation,inverse(u))*.
% 299.82/300.44  161406[10:Rew:160202.0,146120.1] inductive(cantor(restrict(element_relation,universal_class,u))) ||  -> member(successor_relation,sum_class(u))*.
% 299.82/300.44  163017[10:Rew:160202.0,157898.1] || equal(complement(compose(element_relation,universal_class)),universal_class)** member(successor_relation,element_relation) -> .
% 299.82/300.44  162983[10:Rew:160202.0,157794.1] inductive(symmetric_difference(complement(u),universal_class)) ||  -> member(successor_relation,union(u,successor_relation))*.
% 299.82/300.44  162981[10:Rew:160202.0,157819.1] inductive(complement(union(u,identity_relation))) ||  -> member(successor_relation,symmetric_difference(universal_class,u))*.
% 299.82/300.44  167517[10:Res:160369.0,160435.1] inductive(complement(union(u,successor_relation))) ||  -> member(successor_relation,symmetric_difference(universal_class,u))*.
% 299.82/300.44  161496[10:Rew:160202.0,153069.1] || subclass(universal_class,u)* -> equal(integer_of(v),successor_relation) member(v,u)*.
% 299.82/300.44  161454[10:Rew:160202.0,159930.1] || well_ordering(universal_class,power_class(u)) -> member(successor_relation,image(element_relation,complement(u)))*.
% 299.82/300.44  161455[10:Rew:160202.0,146667.1] inductive(complement(power_class(u))) ||  -> member(successor_relation,image(element_relation,complement(u)))*.
% 299.82/300.44  161373[10:Rew:160202.0,153214.1] || equal(symmetric_difference(u,v),universal_class) -> member(successor_relation,union(u,v))*.
% 299.82/300.44  161377[10:Rew:160202.0,146588.1] || subclass(universal_class,symmetric_difference(u,v))* -> member(successor_relation,union(u,v)).
% 299.82/300.44  161345[10:Rew:160202.0,153215.1] || equal(symmetric_difference(u,inverse(u)),universal_class)** -> member(successor_relation,symmetrization_of(u)).
% 299.82/300.44  161340[10:Rew:160202.0,153216.1] || equal(symmetric_difference(u,singleton(u)),universal_class)** -> member(successor_relation,successor(u)).
% 299.82/300.44  161267[10:Rew:160202.0,147262.1] inductive(complement(complement(cantor(inverse(u))))) ||  -> member(successor_relation,range_of(u))*.
% 299.82/300.44  161268[10:Rew:160202.0,147261.1] inductive(intersection(cantor(inverse(u)),v)) ||  -> member(successor_relation,range_of(u))*.
% 299.82/300.44  168561[11:Res:168384.1,47888.0] || equal(rest_of(successor_relation),symmetrization_of(successor_relation)) subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.44  162870[10:Rew:160202.0,156302.0] || equal(rest_of(successor_relation),singleton(successor_relation)) subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.44  161241[10:Rew:160202.0,153204.2] || equal(u,universal_class) subclass(u,v)* -> member(successor_relation,v).
% 299.82/300.44  161246[10:Rew:160202.0,146545.2] inductive(singleton(u)) || member(u,v)* -> member(successor_relation,v)*.
% 299.82/300.44  163245[10:Rew:160202.0,161233.1] || well_ordering(universal_class,union(u,successor_relation))* -> member(successor_relation,symmetric_difference(universal_class,u)).
% 299.82/300.44  161217[10:Rew:160202.0,159776.1] inductive(symmetric_difference(universal_class,u)) || equal(union(u,successor_relation),universal_class)** -> .
% 299.82/300.44  161207[10:Rew:160202.0,156005.0] ||  -> subclass(complement(power_class(symmetric_difference(universal_class,u))),image(element_relation,union(u,successor_relation)))*.
% 299.82/300.44  160892[10:Rew:160202.0,158315.1] || equal(complement(power_class(universal_class)),universal_class) -> member(omega,image(element_relation,successor_relation))*.
% 299.82/300.44  160839[10:Rew:160202.0,152617.0] || subclass(universal_class,image(element_relation,successor_relation))* subclass(universal_class,power_class(universal_class)) -> .
% 299.82/300.44  160835[10:Rew:160202.0,152602.0] ||  -> subclass(symmetric_difference(complement(u),power_class(universal_class)),union(u,image(element_relation,successor_relation)))*.
% 299.82/300.44  160831[10:Rew:160202.0,152577.0] ||  -> subclass(symmetric_difference(power_class(universal_class),complement(u)),union(image(element_relation,successor_relation),u))*.
% 299.82/300.44  160856[10:Rew:160202.0,158384.0] ||  -> equal(symmetric_difference(power_class(image(element_relation,successor_relation)),image(element_relation,power_class(universal_class))),universal_class)**.
% 299.82/300.44  160855[10:Rew:160202.0,158347.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(universal_class)),power_class(image(element_relation,successor_relation))),universal_class)**.
% 299.82/300.44  160829[10:Rew:160202.0,148323.0] || member(u,image(element_relation,successor_relation))* member(u,power_class(universal_class)) -> .
% 299.82/300.44  160510[10:Rew:160202.0,153398.0] || equal(successor_relation,u) subclass(v,u)* -> equal(v,u).
% 299.82/300.44  160805[10:Rew:160202.0,146494.2] || subclass(u,v)* well_ordering(universal_class,v)* -> equal(u,successor_relation).
% 299.82/300.44  162954[10:Rew:160202.0,160053.1] || subclass(omega,ordinal_numbers)* -> equal(integer_of(u),successor_relation) member(u,kind_1_ordinals)*.
% 299.82/300.44  161287[10:Rew:160202.0,159761.1] || equal(complement(union(u,v)),universal_class)** -> member(successor_relation,complement(u)).
% 299.82/300.44  163231[10:Rew:160202.0,160562.2] || subclass(complement(u),v)* -> member(successor_relation,u) member(successor_relation,v).
% 299.82/300.44  168543[11:Res:168384.1,595.0] || equal(restrict(u,v,w),symmetrization_of(successor_relation))** -> member(successor_relation,u).
% 299.82/300.44  163243[10:Rew:160202.0,161178.1] || subclass(inverse(successor_relation),symmetrization_of(successor_relation))* -> equal(symmetrization_of(successor_relation),inverse(successor_relation)).
% 299.82/300.44  161151[10:Rew:160202.0,152741.0] ||  -> subclass(symmetric_difference(symmetrization_of(successor_relation),complement(u)),union(complement(inverse(successor_relation)),u))*.
% 299.82/300.44  161147[10:Rew:160202.0,152766.0] ||  -> subclass(symmetric_difference(complement(u),symmetrization_of(successor_relation)),union(u,complement(inverse(successor_relation))))*.
% 299.82/300.44  163240[10:Rew:160202.0,161119.0] ||  -> member(not_subclass_element(symmetrization_of(successor_relation),u),inverse(successor_relation))* subclass(symmetrization_of(successor_relation),u).
% 299.82/300.44  161145[10:Rew:160202.0,158379.0] ||  -> equal(symmetric_difference(power_class(complement(inverse(successor_relation))),image(element_relation,symmetrization_of(successor_relation))),universal_class)**.
% 299.82/300.44  161144[10:Rew:160202.0,158342.0] ||  -> equal(symmetric_difference(image(element_relation,symmetrization_of(successor_relation)),power_class(complement(inverse(successor_relation)))),universal_class)**.
% 299.82/300.44  163244[10:Rew:160202.0,161180.0] || subclass(sum_class(inverse(successor_relation)),successor_relation) -> section(element_relation,inverse(successor_relation),universal_class)*.
% 299.82/300.44  163237[10:Rew:160202.0,161106.0] || member(u,complement(inverse(successor_relation)))* member(u,symmetrization_of(successor_relation)) -> .
% 299.82/300.44  163234[10:Rew:160202.0,161057.1] || subclass(power_class(successor_relation),image(element_relation,universal_class))* -> equal(power_class(successor_relation),successor_relation).
% 299.82/300.44  161000[10:Rew:160202.0,150011.0] ||  -> subclass(symmetric_difference(power_class(successor_relation),complement(u)),union(image(element_relation,universal_class),u))*.
% 299.82/300.44  160999[10:Rew:160202.0,150010.1] || subclass(universal_class,image(element_relation,universal_class))* subclass(universal_class,power_class(successor_relation)) -> .
% 299.82/300.44  160990[10:Rew:160202.0,150002.0] ||  -> subclass(symmetric_difference(complement(u),power_class(successor_relation)),union(u,image(element_relation,universal_class)))*.
% 299.82/300.44  160906[10:Rew:160202.0,148439.1] || member(u,image(element_relation,universal_class))* member(u,power_class(successor_relation)) -> .
% 299.82/300.44  160985[10:Rew:160202.0,158385.0] ||  -> equal(symmetric_difference(power_class(image(element_relation,universal_class)),image(element_relation,power_class(successor_relation))),universal_class)**.
% 299.82/300.44  160984[10:Rew:160202.0,158348.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(successor_relation)),power_class(image(element_relation,universal_class))),universal_class)**.
% 299.82/300.44  160893[10:Rew:160202.0,150013.0] || equal(complement(power_class(successor_relation)),universal_class) -> member(omega,image(element_relation,universal_class))*.
% 299.82/300.44  163079[10:Rew:160202.0,159351.1] || subclass(domain_relation,intersection(u,v))* -> member(ordered_pair(successor_relation,successor_relation),v).
% 299.82/300.44  163076[10:Rew:160202.0,159347.1] || subclass(domain_relation,complement(kind_1_ordinals)) member(ordered_pair(successor_relation,successor_relation),ordinal_numbers)* -> .
% 299.82/300.44  163074[10:Rew:160202.0,159350.1] || subclass(domain_relation,intersection(u,v))* -> member(ordered_pair(successor_relation,successor_relation),u).
% 299.82/300.44  163075[10:Rew:160202.0,159345.1] || subclass(domain_relation,complement(u)) member(ordered_pair(successor_relation,successor_relation),u)* -> .
% 299.82/300.44  162899[10:Rew:160202.0,152490.0] ||  -> subclass(symmetric_difference(successor(successor_relation),complement(u)),union(complement(singleton(successor_relation)),u))*.
% 299.82/300.44  162898[10:Rew:160202.0,152515.0] ||  -> subclass(symmetric_difference(complement(u),successor(successor_relation)),union(u,complement(singleton(successor_relation))))*.
% 299.82/300.44  163250[10:Rew:160202.0,162897.1] || subclass(singleton(successor_relation),successor(successor_relation))* -> equal(successor(successor_relation),singleton(successor_relation)).
% 299.82/300.44  163229[10:Rew:160202.0,160554.0] || equal(restrict(u,v,w),successor(successor_relation))** -> member(successor_relation,u).
% 299.82/300.44  162896[10:Rew:160202.0,158378.0] ||  -> equal(symmetric_difference(power_class(complement(singleton(successor_relation))),image(element_relation,successor(successor_relation))),universal_class)**.
% 299.82/300.44  162895[10:Rew:160202.0,158341.0] ||  -> equal(symmetric_difference(image(element_relation,successor(successor_relation)),power_class(complement(singleton(successor_relation)))),universal_class)**.
% 299.82/300.44  163230[10:Rew:160202.0,160557.0] || equal(restrict(u,v,w),singleton(successor_relation))** -> member(successor_relation,u).
% 299.82/300.44  163248[10:Rew:160202.0,162773.1] || member(u,complement(singleton(successor_relation)))* member(u,successor(successor_relation)) -> .
% 299.82/300.44  48051[0:SpL:41.0,47745.0] || member(inverse(u),range_of(u))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.44  157902[6:Res:1506.1,148657.1] || equal(complement(compose(element_relation,universal_class)),universal_class)** member(omega,element_relation) -> .
% 299.82/300.44  155719[2:SpR:57.0,142543.0] ||  -> equal(symmetric_difference(universal_class,image(element_relation,complement(u))),intersection(power_class(u),universal_class))**.
% 299.82/300.44  125132[0:Obv:125114.0] ||  -> member(u,power_class(v)) subclass(singleton(u),image(element_relation,complement(v)))*.
% 299.82/300.44  89295[0:SpR:57.0,89275.1] ||  -> member(u,image(element_relation,complement(v)))* subclass(singleton(u),power_class(v)).
% 299.82/300.44  107290[0:SpR:208.0,107233.0] ||  -> subclass(complement(power_class(image(element_relation,complement(u)))),image(element_relation,power_class(u)))*.
% 299.82/300.44  9090[0:SpR:157.0,9089.1] function(recursion(u,successor_relation,union_of_range_map)) ||  -> member(ordinal_add(u,v),universal_class)*.
% 299.82/300.44  30101[0:SoR:9090.0,73.1] one_to_one(recursion(u,successor_relation,union_of_range_map)) ||  -> member(ordinal_add(u,v),universal_class)*.
% 299.82/300.44  159777[6:SpL:57.0,159727.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),universal_class)** -> .
% 299.82/300.44  30461[0:MRR:30434.0,13.0] || subclass(universal_class,complement(complement(u)))* -> member(unordered_pair(v,w),u)*.
% 299.82/300.44  48188[0:Res:8.1,3488.0] || equal(intersection(u,v),universal_class)** -> member(unordered_pair(w,x),v)*.
% 299.82/300.44  48050[0:Res:8.1,3487.0] || equal(intersection(u,v),universal_class)** -> member(unordered_pair(w,x),u)*.
% 299.82/300.44  122542[0:MRR:122515.0,34189.1] || subclass(u,complement(singleton(not_subclass_element(u,v))))* -> subclass(u,v).
% 299.82/300.44  159972[3:Res:159949.0,1487.1] || member(u,universal_class) -> member(u,complement(ordinal_numbers))* member(u,kind_1_ordinals).
% 299.82/300.44  142788[2:MRR:142751.2,120469.0] || equal(u,universal_class) member(v,universal_class)* -> member(v,u)*.
% 299.82/300.44  177134[12:Res:136.1,177131.0] || member(cross_product(universal_class,universal_class),ordinal_numbers)* -> member(least(element_relation,element_relation),element_relation).
% 299.82/300.44  180000[11:Res:179843.1,595.0] || equal(restrict(u,v,w),inverse(successor_relation))** -> member(successor_relation,u).
% 299.82/300.44  181093[10:SpL:181056.0,1522.0] || member(singleton(singleton(successor_relation)),cross_product(u,v))* -> member(universal_class,v).
% 299.82/300.44  181125[10:Rew:181086.0,163290.1] || section(u,successor_relation,v) -> equal(segment(u,v,universal_class),successor_relation)**.
% 299.82/300.44  181133[10:Rew:181056.0,181092.1] || member(singleton(singleton(successor_relation)),cross_product(u,v))* -> member(successor_relation,u).
% 299.82/300.44  181139[10:MRR:181138.0,160215.0] || subclass(segment(u,v,universal_class),successor_relation)* -> section(u,successor_relation,v).
% 299.82/300.44  181338[10:Res:181084.0,3.0] || subclass(ordered_pair(u,universal_class),v)* -> member(unordered_pair(u,successor_relation),v).
% 299.82/300.44  181431[10:SpR:181082.0,56.1] || member(image(u,successor_relation),universal_class) -> member(apply(u,universal_class),universal_class)*.
% 299.82/300.44  181491[10:Rew:155765.0,181456.0] ||  -> equal(intersection(symmetric_difference(complement(u),universal_class),complement(union(u,successor_relation))),successor_relation)**.
% 299.82/300.44  181665[10:Rew:155765.0,181634.0] ||  -> equal(intersection(complement(union(u,successor_relation)),symmetric_difference(complement(u),universal_class)),successor_relation)**.
% 299.82/300.44  183367[0:SpR:139600.0,28.0] ||  -> equal(union(u,complement(complement(u))),complement(complement(complement(complement(u)))))**.
% 299.82/300.44  183381[10:SpR:160419.0,139600.0] ||  -> equal(intersection(complement(singleton(successor_relation)),complement(successor(successor_relation))),complement(successor(successor_relation)))**.
% 299.82/300.44  183382[10:SpR:160336.0,139600.0] ||  -> equal(intersection(complement(inverse(successor_relation)),complement(symmetrization_of(successor_relation))),complement(symmetrization_of(successor_relation)))**.
% 299.82/300.44  183387[10:SpR:160322.0,139600.0] ||  -> equal(intersection(image(element_relation,successor_relation),complement(power_class(universal_class))),complement(power_class(universal_class)))**.
% 299.82/300.44  183388[10:SpR:160328.0,139600.0] ||  -> equal(intersection(image(element_relation,universal_class),complement(power_class(successor_relation))),complement(power_class(successor_relation)))**.
% 299.82/300.44  183639[10:Rew:183460.0,183601.0] ||  -> equal(intersection(complement(successor(successor_relation)),union(singleton(successor_relation),successor(successor_relation))),successor_relation)**.
% 299.82/300.44  183739[10:Rew:183461.0,183702.0] ||  -> equal(intersection(complement(symmetrization_of(successor_relation)),union(inverse(successor_relation),symmetrization_of(successor_relation))),successor_relation)**.
% 299.82/300.44  183825[10:Res:160251.1,183622.0] || subclass(domain_relation,successor(successor_relation)) -> member(ordered_pair(successor_relation,successor_relation),singleton(successor_relation))*.
% 299.82/300.44  183847[10:Res:1476.1,183723.0] || subclass(universal_class,symmetrization_of(successor_relation)) -> member(unordered_pair(u,v),inverse(successor_relation))*.
% 299.82/300.44  183857[10:Res:1499.1,183723.0] || subclass(universal_class,symmetrization_of(successor_relation)) -> member(ordered_pair(u,v),inverse(successor_relation))*.
% 299.82/300.44  183858[10:Res:160251.1,183723.0] || subclass(domain_relation,symmetrization_of(successor_relation)) -> member(ordered_pair(successor_relation,successor_relation),inverse(successor_relation))*.
% 299.82/300.44  183911[11:Res:183764.1,26.1] || subclass(universal_class,complement(u)) member(regular(symmetrization_of(successor_relation)),u)* -> .
% 299.82/300.44  183913[11:Res:183764.1,141576.1] || subclass(universal_class,complement(kind_1_ordinals)) member(regular(symmetrization_of(successor_relation)),ordinal_numbers)* -> .
% 299.82/300.44  183916[11:Res:183764.1,23.0] || subclass(universal_class,intersection(u,v))* -> member(regular(symmetrization_of(successor_relation)),u).
% 299.82/300.44  183917[11:Res:183764.1,24.0] || subclass(universal_class,intersection(u,v))* -> member(regular(symmetrization_of(successor_relation)),v).
% 299.82/300.44  184146[14:SpR:183965.0,9089.1] function(recursion(u,successor_relation,successor_relation)) ||  -> member(ordinal_add(u,v),universal_class)*.
% 299.82/300.44  184220[10:Rew:160322.0,184209.1] || subclass(power_class(universal_class),image(element_relation,successor_relation))* -> equal(power_class(universal_class),successor_relation).
% 299.82/300.44  184425[10:SpR:163197.1,161.0] || subclass(union(u,v),successor_relation)* -> equal(symmetric_difference(u,v),successor_relation).
% 299.82/300.44  184426[10:SpR:163197.1,1933.0] || subclass(symmetrization_of(u),successor_relation) -> equal(symmetric_difference(u,inverse(u)),successor_relation)**.
% 299.82/300.44  184427[10:SpR:163197.1,1934.0] || subclass(successor(u),successor_relation) -> equal(symmetric_difference(u,singleton(u)),successor_relation)**.
% 299.82/300.44  184532[10:Rew:113504.0,184396.1,160223.0,184396.1] || subclass(u,successor_relation) -> equal(symmetric_difference(v,u),union(v,u))**.
% 299.82/300.44  184552[10:MRR:184551.2,160215.0] || subclass(u,successor_relation)* member(v,u)* -> member(v,w)*.
% 299.82/300.44  184582[10:Res:27.2,184528.0] || member(not_subclass_element(ordinal_numbers,successor_relation),universal_class) -> member(not_subclass_element(ordinal_numbers,successor_relation),kind_1_ordinals)*.
% 299.82/300.44  184756[10:Rew:113504.0,184610.1,160223.0,184610.1] || subclass(u,successor_relation) -> equal(symmetric_difference(u,v),union(u,v))**.
% 299.82/300.44  184942[10:SpR:160336.0,184676.1] || subclass(complement(inverse(successor_relation)),successor_relation)* -> equal(complement(symmetrization_of(successor_relation)),successor_relation).
% 299.82/300.44  185047[10:SpR:160367.0,184981.1] || subclass(symmetric_difference(universal_class,u),successor_relation)* -> subclass(universal_class,union(u,successor_relation)).
% 299.82/300.44  185050[10:SpR:57.0,184981.1] || subclass(image(element_relation,complement(u)),successor_relation)* -> subclass(universal_class,power_class(u)).
% 299.82/300.44  185230[11:MRR:168562.1,185225.0] || equal(ordered_pair(u,v),symmetrization_of(successor_relation))** -> equal(singleton(u),successor_relation).
% 299.82/300.44  185231[10:MRR:163473.1,185225.0] || equal(ordered_pair(u,v),successor(successor_relation))** -> equal(singleton(u),successor_relation).
% 299.82/300.44  185232[10:MRR:163474.1,185225.0] || equal(ordered_pair(u,v),singleton(successor_relation))** -> equal(singleton(u),successor_relation).
% 299.82/300.44  185338[10:SpL:208.0,185324.0] || equal(power_class(image(element_relation,complement(u))),image(element_relation,power_class(u)))** -> .
% 299.82/300.44  185384[10:SpR:185302.1,107289.0] || equal(successor_relation,u) -> subclass(complement(power_class(u)),image(element_relation,universal_class))*.
% 299.82/300.44  185455[10:SpR:185302.1,160367.0] || equal(symmetric_difference(universal_class,u),successor_relation)** -> equal(union(u,successor_relation),universal_class).
% 299.82/300.44  185483[10:SpR:185302.1,57.0] || equal(image(element_relation,complement(u)),successor_relation)** -> equal(power_class(u),universal_class).
% 299.82/300.44  185648[10:Rew:113504.0,185365.1] || equal(successor_relation,u) -> equal(union(u,v),complement(complement(v)))**.
% 299.82/300.44  185654[10:Rew:160367.0,185398.1,142543.0,185398.1] || equal(successor_relation,u) -> equal(union(v,successor_relation),union(v,u))*.
% 299.82/300.44  185759[10:SpL:185302.1,185335.0] || equal(successor_relation,u) equal(image(element_relation,universal_class),power_class(u))* -> .
% 299.82/300.44  185763[10:SpL:160367.0,185335.0] || equal(image(element_relation,union(u,successor_relation)),power_class(symmetric_difference(universal_class,u)))** -> .
% 299.82/300.44  185800[10:Res:185430.1,2647.0] || equal(complement(complement(u)),successor_relation) member(singleton(v),u)* -> .
% 299.82/300.44  185815[10:Res:185430.1,2648.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(singleton(w),u)*.
% 299.82/300.44  185816[10:Res:185430.1,2649.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(singleton(w),v)*.
% 299.82/300.44  185944[10:Res:185646.1,595.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(successor_relation,u).
% 299.82/300.44  186018[10:Res:185647.1,595.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(omega,u).
% 299.82/300.44  186054[10:SpL:160367.0,185795.0] || equal(union(u,successor_relation),successor_relation) -> equal(symmetric_difference(universal_class,u),universal_class)**.
% 299.82/300.44  186057[10:SpL:57.0,185795.0] || equal(power_class(u),successor_relation) -> equal(image(element_relation,complement(u)),universal_class)**.
% 299.82/300.44  186130[10:Res:1481.2,185639.1] || subclass(u,v)* equal(successor_relation,v) -> subclass(u,w)*.
% 299.82/300.44  186133[10:Res:160290.2,185639.1] || subclass(u,v)* equal(successor_relation,v) -> equal(u,successor_relation).
% 299.82/300.44  186492[10:SpL:185605.1,185724.0] || equal(successor_relation,u) subclass(image(element_relation,universal_class),power_class(u))* -> .
% 299.82/300.44  141778[2:MRR:52472.3,120469.0] inductive(singleton(u)) || well_ordering(v,w)* -> member(u,universal_class)*.
% 299.82/300.44  161500[10:Rew:160202.0,148477.1] || well_ordering(u,universal_class) -> equal(integer_of(least(u,complement(omega))),successor_relation)**.
% 299.82/300.44  183836[10:MRR:183821.1,160455.0] || well_ordering(u,universal_class) -> member(least(u,successor(successor_relation)),singleton(successor_relation))*.
% 299.82/300.44  183867[11:MRR:183854.1,168458.0] || well_ordering(u,universal_class) -> member(least(u,symmetrization_of(successor_relation)),inverse(successor_relation))*.
% 299.82/300.44  184566[10:MRR:163337.2,184560.0] || equal(universal_class,ordinal_numbers) well_ordering(element_relation,successor_relation)* -> member(successor_relation,ordinal_numbers).
% 299.82/300.44  187776[10:Res:187500.1,595.0] || subclass(universal_class,restrict(u,v,w))* -> member(power_class(successor_relation),u).
% 299.82/300.44  188205[10:MRR:188169.2,3567.0] || well_ordering(u,universal_class) equal(singleton(least(u,universal_class)),successor_relation)** -> .
% 299.82/300.44  188235[10:Res:184599.1,186157.0] || well_ordering(u,kind_1_ordinals) equal(singleton(least(u,ordinal_numbers)),successor_relation)** -> .
% 299.82/300.44  188260[10:Res:110382.1,186157.0] || well_ordering(u,universal_class) equal(singleton(least(u,rest_relation)),successor_relation)** -> .
% 299.82/300.44  188268[10:Res:110388.1,186157.0] || well_ordering(u,rest_relation) equal(singleton(least(u,rest_relation)),successor_relation)** -> .
% 299.82/300.44  188640[11:MRR:188628.1,185225.0] || equal(ordered_pair(u,v),inverse(successor_relation))** -> equal(singleton(u),successor_relation).
% 299.82/300.44  188750[17:Res:188729.1,186157.0] || well_ordering(u,universal_class) equal(singleton(least(u,omega)),successor_relation)** -> .
% 299.82/300.44  188762[17:Res:188737.1,186157.0] || well_ordering(u,omega) equal(singleton(least(u,omega)),successor_relation)** -> .
% 299.82/300.44  188839[10:Res:157922.1,185065.1] || member(singleton(u),element_relation)* subclass(compose(element_relation,universal_class),successor_relation)* -> .
% 299.82/300.44  188962[10:SpR:185607.1,161.0] || equal(union(u,v),successor_relation) -> equal(symmetric_difference(u,v),successor_relation)**.
% 299.82/300.44  188963[10:SpR:185607.1,1933.0] || equal(symmetrization_of(u),successor_relation) -> equal(symmetric_difference(u,inverse(u)),successor_relation)**.
% 299.82/300.44  189086[10:Rew:113504.0,188928.1,160223.0,188928.1] || equal(successor_relation,u) -> equal(symmetric_difference(v,u),union(v,u))**.
% 299.82/300.44  189093[10:Rew:185654.1,189092.1,189086.1,189092.1] || equal(inverse(u),successor_relation) -> equal(union(u,successor_relation),symmetrization_of(u))**.
% 299.82/300.44  189095[10:Rew:185654.1,189094.1,189086.1,189094.1] || equal(singleton(u),successor_relation) -> equal(union(u,successor_relation),successor(u))**.
% 299.82/300.44  189300[10:Rew:185648.1,189299.1] || equal(successor_relation,u) -> equal(symmetric_difference(u,v),complement(complement(v)))**.
% 299.82/300.44  189307[10:Rew:189300.1,189306.1] || equal(successor_relation,u) -> equal(complement(complement(inverse(u))),symmetrization_of(u))**.
% 299.82/300.44  189309[10:Rew:189300.1,189308.1] || equal(successor_relation,u) -> equal(complement(complement(singleton(u))),successor(u))**.
% 299.82/300.44  189572[15:Rew:189513.0,126103.1] || subclass(rest_relation,flip(domain_relation)) -> equal(rest_of(ordered_pair(u,v)),successor_relation)**.
% 299.82/300.44  190619[15:SpR:189514.1,55.0] ||  -> equal(integer_of(restrict(element_relation,universal_class,u)),successor_relation)** equal(sum_class(u),successor_relation).
% 299.82/300.44  190638[15:SpR:189514.1,40.0] ||  -> equal(integer_of(flip(cross_product(u,universal_class))),successor_relation)** equal(inverse(u),successor_relation).
% 299.82/300.44  190702[15:SpR:189515.1,55.0] ||  -> equal(singleton(restrict(element_relation,universal_class,u)),successor_relation)** equal(sum_class(u),successor_relation).
% 299.82/300.44  190722[15:SpR:189515.1,40.0] ||  -> equal(singleton(flip(cross_product(u,universal_class))),successor_relation)** equal(inverse(u),successor_relation).
% 299.82/300.44  190862[15:SpR:190665.0,3587.0] ||  -> equal(cantor(apply(choice,omega)),successor_relation)** equal(apply(choice,omega),successor_relation).
% 299.82/300.44  191094[20:Res:191074.1,3.0] || equal(u,omega) subclass(u,v)* -> member(successor_relation,v).
% 299.82/300.44  191098[20:Res:191074.1,148657.1] || equal(complement(compose(element_relation,universal_class)),omega)** member(successor_relation,element_relation) -> .
% 299.82/300.44  191106[20:Res:191074.1,1952.0] || equal(symmetric_difference(u,v),omega) -> member(successor_relation,union(u,v))*.
% 299.82/300.44  191107[20:Res:191074.1,10191.0] || equal(symmetric_difference(u,inverse(u)),omega)** -> member(successor_relation,symmetrization_of(u)).
% 299.82/300.44  191108[20:Res:191074.1,10254.0] || equal(symmetric_difference(u,singleton(u)),omega)** -> member(successor_relation,successor(u)).
% 299.82/300.44  191411[20:MRR:191404.2,191404.3,160215.0,184560.0] || equal(omega,ordinal_numbers) well_ordering(element_relation,successor_relation)* -> member(successor_relation,ordinal_numbers).
% 299.82/300.44  191634[15:Res:184599.1,189419.0] || well_ordering(u,kind_1_ordinals) equal(successor(least(u,ordinal_numbers)),successor_relation)** -> .
% 299.82/300.44  191635[15:Res:110623.1,189419.0] || well_ordering(u,universal_class) equal(successor(least(u,universal_class)),successor_relation)** -> .
% 299.82/300.44  191636[15:Res:110388.1,189419.0] || well_ordering(u,rest_relation) equal(successor(least(u,rest_relation)),successor_relation)** -> .
% 299.82/300.44  191637[15:Res:110382.1,189419.0] || well_ordering(u,universal_class) equal(successor(least(u,rest_relation)),successor_relation)** -> .
% 299.82/300.44  191638[17:Res:188737.1,189419.0] || well_ordering(u,omega) equal(successor(least(u,omega)),successor_relation)** -> .
% 299.82/300.44  191639[17:Res:188729.1,189419.0] || well_ordering(u,universal_class) equal(successor(least(u,omega)),successor_relation)** -> .
% 299.82/300.44  192382[20:SpL:160367.0,192322.1] inductive(symmetric_difference(universal_class,u)) || equal(union(u,successor_relation),omega)** -> .
% 299.82/300.44  192385[20:SpL:57.0,192322.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),omega)** -> .
% 299.82/300.44  192943[10:SpL:160322.0,188851.0] || subclass(power_class(universal_class),successor_relation) -> member(singleton(u),image(element_relation,successor_relation))*.
% 299.82/300.44  192944[10:SpL:160328.0,188851.0] || subclass(power_class(successor_relation),successor_relation) -> member(singleton(u),image(element_relation,universal_class))*.
% 299.82/300.44  193398[10:Res:192947.1,141576.1] || equal(complement(complement(kind_1_ordinals)),successor_relation) member(singleton(u),ordinal_numbers)* -> .
% 299.82/300.44  193413[10:Res:192947.1,183723.0] || equal(complement(symmetrization_of(successor_relation)),successor_relation) -> member(singleton(u),inverse(successor_relation))*.
% 299.82/300.44  193447[10:Rew:57.0,193422.0] || equal(power_class(u),successor_relation) member(singleton(v),power_class(u))* -> .
% 299.82/300.44  193540[2:Res:141787.0,1509.1] || equal(complement(inverse(singleton(omega))),universal_class)** -> asymmetric(singleton(omega),u)*.
% 299.82/300.44  193549[20:Res:141787.0,191095.1] || equal(complement(inverse(singleton(successor_relation))),omega)** -> asymmetric(singleton(successor_relation),u)*.
% 299.82/300.44  193550[10:Res:141787.0,160258.1] || equal(complement(inverse(singleton(successor_relation))),universal_class)** -> asymmetric(singleton(successor_relation),u)*.
% 299.82/300.44  193590[10:SpR:160419.0,161321.0] ||  -> equal(intersection(restrict(complement(singleton(successor_relation)),u,v),successor(successor_relation)),successor_relation)**.
% 299.82/300.44  193591[10:SpR:160336.0,161321.0] ||  -> equal(intersection(restrict(complement(inverse(successor_relation)),u,v),symmetrization_of(successor_relation)),successor_relation)**.
% 299.82/300.44  193596[10:SpR:160322.0,161321.0] ||  -> equal(intersection(restrict(image(element_relation,successor_relation),u,v),power_class(universal_class)),successor_relation)**.
% 299.82/300.44  193597[10:SpR:160328.0,161321.0] ||  -> equal(intersection(restrict(image(element_relation,universal_class),u,v),power_class(successor_relation)),successor_relation)**.
% 299.82/300.44  193688[10:SpR:160419.0,161320.0] ||  -> equal(intersection(successor(successor_relation),restrict(complement(singleton(successor_relation)),u,v)),successor_relation)**.
% 299.82/300.44  193689[10:SpR:160336.0,161320.0] ||  -> equal(intersection(symmetrization_of(successor_relation),restrict(complement(inverse(successor_relation)),u,v)),successor_relation)**.
% 299.82/300.44  193694[10:SpR:160322.0,161320.0] ||  -> equal(intersection(power_class(universal_class),restrict(image(element_relation,successor_relation),u,v)),successor_relation)**.
% 299.82/300.44  193695[10:SpR:160328.0,161320.0] ||  -> equal(intersection(power_class(successor_relation),restrict(image(element_relation,universal_class),u,v)),successor_relation)**.
% 299.82/300.44  193763[10:Rew:160474.0,193745.0] ||  -> equal(domain__dfg(complement(cross_product(u,singleton(v))),u,v),single_valued3(successor_relation))**.
% 299.82/300.44  193769[10:MRR:193768.1,160354.1] || equal(successor_relation,u) -> section(complement(cross_product(v,u)),u,v)*.
% 299.82/300.44  193771[10:MRR:193770.1,160215.0] || subclass(u,v) -> section(complement(cross_product(v,u)),u,v)*.
% 299.82/300.44  193907[10:SpL:185302.1,193906.0] || equal(cross_product(successor_relation,universal_class),successor_relation) member(universal_class,cantor(universal_class))* -> .
% 299.82/300.44  194071[10:Res:192947.1,193819.0] || equal(complement(cantor(complement(cross_product(singleton(singleton(u)),universal_class)))),successor_relation)** -> .
% 299.82/300.44  194077[10:Res:1476.1,193819.0] || subclass(universal_class,cantor(complement(cross_product(singleton(unordered_pair(u,v)),universal_class))))* -> .
% 299.82/300.44  194088[10:Res:1499.1,193819.0] || subclass(universal_class,cantor(complement(cross_product(singleton(ordered_pair(u,v)),universal_class))))* -> .
% 299.82/300.44  194089[10:Res:160251.1,193819.0] || subclass(domain_relation,cantor(complement(cross_product(singleton(ordered_pair(successor_relation,successor_relation)),universal_class))))* -> .
% 299.82/300.44  194104[11:Res:183764.1,193819.0] || subclass(universal_class,cantor(complement(cross_product(singleton(regular(symmetrization_of(successor_relation))),universal_class))))* -> .
% 299.82/300.44  194494[10:SpL:160419.0,183398.0] || member(u,complement(successor(successor_relation)))* -> member(u,complement(singleton(successor_relation))).
% 299.82/300.44  194495[10:SpL:160336.0,183398.0] || member(u,complement(symmetrization_of(successor_relation)))* -> member(u,complement(inverse(successor_relation))).
% 299.82/300.44  194500[10:SpL:160322.0,183398.0] || member(u,complement(power_class(universal_class))) -> member(u,image(element_relation,successor_relation))*.
% 299.82/300.44  194501[10:SpL:160328.0,183398.0] || member(u,complement(power_class(successor_relation))) -> member(u,image(element_relation,universal_class))*.
% 299.82/300.44  194507[10:Res:192947.1,183398.0] || equal(complement(complement(complement(u))),successor_relation)** -> member(singleton(v),u)*.
% 299.82/300.44  194536[10:Res:160251.1,183398.0] || subclass(domain_relation,complement(complement(u)))* -> member(ordered_pair(successor_relation,successor_relation),u).
% 299.82/300.44  194548[11:Res:183764.1,183398.0] || subclass(universal_class,complement(complement(u)))* -> member(regular(symmetrization_of(successor_relation)),u).
% 299.82/300.44  194688[10:SpR:163198.1,113227.1] || subclass(u,successor_relation)* subclass(v,u)* -> subclass(v,successor_relation)*.
% 299.82/300.44  194713[10:SpR:161286.0,113227.1] || subclass(u,singleton(v))* -> member(v,u) subclass(u,successor_relation).
% 299.82/300.44  195051[10:SpR:185607.1,113243.0] || equal(intersection(u,v),successor_relation) -> subclass(intersection(u,v),successor_relation)*.
% 299.82/300.44  195376[10:SpR:194805.1,163198.1] || subclass(u,v)* subclass(v,successor_relation)* -> equal(u,successor_relation).
% 299.82/300.44  195431[10:SpR:194805.1,161286.0] || subclass(u,singleton(v))* -> equal(u,successor_relation) member(v,u).
% 299.82/300.44  195445[10:SpR:194805.1,160446.0] || subclass(complement(u),intersection(v,u))* -> equal(complement(u),successor_relation).
% 299.82/300.44  195446[10:SpR:194805.1,160445.0] || subclass(complement(u),intersection(u,v))* -> equal(complement(u),successor_relation).
% 299.82/300.44  195723[6:Rew:70.0,195712.1] || subclass(universal_class,apply(u,v))* -> subclass(w,apply(u,v))*.
% 299.82/300.44  195879[6:Rew:70.0,195821.0] || equal(apply(u,v),universal_class) -> subclass(w,apply(u,v))*.
% 299.82/300.44  195965[0:SpR:30.0,195152.0] ||  -> equal(intersection(u,restrict(u,v,w)),restrict(u,v,w))**.
% 299.82/300.44  196121[0:SpR:161.0,195339.0] ||  -> equal(intersection(union(u,v),symmetric_difference(u,v)),symmetric_difference(u,v))**.
% 299.82/300.44  196396[10:SpR:160889.0,160367.0] ||  -> equal(union(image(element_relation,successor_relation),successor_relation),complement(intersection(power_class(universal_class),universal_class)))**.
% 299.82/300.44  196456[10:SpR:161155.0,160367.0] ||  -> equal(union(complement(inverse(successor_relation)),successor_relation),complement(intersection(symmetrization_of(successor_relation),universal_class)))**.
% 299.82/300.44  196516[10:SpR:161137.0,114856.0] ||  -> subclass(symmetric_difference(universal_class,image(element_relation,symmetrization_of(successor_relation))),power_class(complement(inverse(successor_relation))))*.
% 299.82/300.44  196517[10:SpR:161137.0,142371.0] ||  -> equal(union(image(element_relation,symmetrization_of(successor_relation)),power_class(complement(inverse(successor_relation)))),universal_class)**.
% 299.82/300.44  196518[10:SpR:161137.0,142372.0] ||  -> equal(union(power_class(complement(inverse(successor_relation))),image(element_relation,symmetrization_of(successor_relation))),universal_class)**.
% 299.82/300.44  196722[10:SpR:162889.0,114856.0] ||  -> subclass(symmetric_difference(universal_class,image(element_relation,successor(successor_relation))),power_class(complement(singleton(successor_relation))))*.
% 299.82/300.44  196723[10:SpR:162889.0,142371.0] ||  -> equal(union(image(element_relation,successor(successor_relation)),power_class(complement(singleton(successor_relation)))),universal_class)**.
% 299.82/300.44  196724[10:SpR:162889.0,142372.0] ||  -> equal(union(power_class(complement(singleton(successor_relation))),image(element_relation,successor(successor_relation))),universal_class)**.
% 299.82/300.44  196817[10:SpR:162887.0,160367.0] ||  -> equal(union(complement(singleton(successor_relation)),successor_relation),complement(intersection(successor(successor_relation),universal_class)))**.
% 299.82/300.44  197248[10:SpR:186058.1,181082.0] || equal(power_class(universal_class),successor_relation) -> equal(apply(element_relation,universal_class),sum_class(universal_class))**.
% 299.82/300.44  197282[10:Rew:185302.1,197260.1] || equal(power_class(universal_class),successor_relation) -> subclass(universal_class,image(element_relation,power_class(universal_class)))*.
% 299.82/300.44  197567[10:Res:185430.1,187769.0] || equal(complement(complement(kind_1_ordinals)),successor_relation) member(power_class(successor_relation),ordinal_numbers)* -> .
% 299.82/300.44  197679[11:Res:168384.1,188862.1] || equal(symmetrization_of(successor_relation),sum_class(successor_relation))** equal(sum_class(successor_relation),successor_relation) -> .
% 299.82/300.44  197844[10:Res:185430.1,194078.0] || equal(complement(cantor(complement(cross_product(singleton(power_class(successor_relation)),universal_class)))),successor_relation)** -> .
% 299.82/300.44  198722[10:SpL:194805.1,198694.0] || subclass(u,complement(singleton(successor_relation)))* subclass(successor(successor_relation),u) -> .
% 299.82/300.44  198815[10:SpL:194805.1,198728.0] || subclass(u,complement(singleton(successor_relation)))* equal(u,successor(successor_relation)) -> .
% 299.82/300.44  199141[11:SpL:194805.1,199112.0] || subclass(u,complement(inverse(successor_relation)))* subclass(symmetrization_of(successor_relation),u) -> .
% 299.82/300.44  199171[11:SpL:194805.1,199147.0] || subclass(u,complement(inverse(successor_relation)))* equal(u,symmetrization_of(successor_relation)) -> .
% 299.82/300.44  199802[10:SpR:161327.1,161327.1] function(u) function(v) ||  -> equal(single_valued2(u),single_valued2(v))*.
% 299.82/300.44  199835[6:Res:149580.1,153518.0] || connected(u,universal_class) -> member(regular(rest_relation),complement(complement(symmetrization_of(u))))*.
% 299.82/300.44  199838[10:SpR:161328.1,161328.1] single_valued_class(u) single_valued_class(v) ||  -> equal(single_valued2(u),single_valued2(v))*.
% 299.82/300.44  199839[10:SpR:161328.1,161327.1] single_valued_class(u) function(v) ||  -> equal(single_valued2(u),single_valued2(v))*.
% 299.82/300.44  199992[6:Res:199848.1,595.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(rest_relation),u).
% 299.82/300.44  200242[6:SpR:199964.0,1006.0] ||  -> member(unordered_pair(first(regular(rest_relation)),singleton(second(regular(rest_relation)))),regular(rest_relation))*.
% 299.82/300.44  200274[6:SpL:199964.0,1503.0] || subclass(regular(rest_relation),u) -> member(singleton(first(regular(rest_relation))),u)*.
% 299.82/300.44  200289[6:SpL:199964.0,6210.0] || equal(u,regular(rest_relation)) -> member(singleton(first(regular(rest_relation))),u)*.
% 299.82/300.44  200561[10:Res:160295.1,163137.0] || equal(rest_of(regular(u)),successor(regular(u)))** -> equal(u,successor_relation).
% 299.82/300.44  200730[10:Res:161493.2,2151.0] inductive(singleton(u)) ||  -> equal(integer_of(v),successor_relation)** equal(v,u)*.
% 299.82/300.44  200782[13:Res:161493.2,185594.0] inductive(power_class(universal_class)) ||  -> equal(integer_of(regular(image(element_relation,successor_relation))),successor_relation)**.
% 299.82/300.44  200783[10:Res:161493.2,185596.0] inductive(power_class(successor_relation)) ||  -> equal(integer_of(regular(image(element_relation,universal_class))),successor_relation)**.
% 299.82/300.44  200785[10:Res:161493.2,197074.0] inductive(singleton(successor_relation)) ||  -> equal(integer_of(regular(complement(successor(successor_relation)))),successor_relation)**.
% 299.82/300.44  201031[10:Res:185430.1,199984.0] || equal(complement(complement(kind_1_ordinals)),successor_relation) member(regular(rest_relation),ordinal_numbers)* -> .
% 299.82/300.44  201138[10:Res:185430.1,200006.0] || equal(complement(cantor(complement(cross_product(singleton(regular(rest_relation)),universal_class)))),successor_relation)** -> .
% 299.82/300.44  201225[6:Res:149580.1,154493.0] || connected(u,universal_class) -> member(regular(domain_relation),complement(complement(symmetrization_of(u))))*.
% 299.82/300.44  201382[6:Res:201231.1,595.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(domain_relation),u).
% 299.82/300.44  201486[6:SpR:201355.0,1006.0] ||  -> member(unordered_pair(first(regular(domain_relation)),singleton(second(regular(domain_relation)))),regular(domain_relation))*.
% 299.82/300.44  201518[6:SpL:201355.0,1503.0] || subclass(regular(domain_relation),u) -> member(singleton(first(regular(domain_relation))),u)*.
% 299.82/300.44  201533[6:SpL:201355.0,6210.0] || equal(u,regular(domain_relation)) -> member(singleton(first(regular(domain_relation))),u)*.
% 299.82/300.44  201683[3:Res:201671.0,9.0] || subclass(complement(ordinal_numbers),complement(kind_1_ordinals))* -> equal(complement(kind_1_ordinals),complement(ordinal_numbers)).
% 299.82/300.44  201802[10:Res:185430.1,201374.0] || equal(complement(complement(kind_1_ordinals)),successor_relation) member(regular(domain_relation),ordinal_numbers)* -> .
% 299.82/300.44  201826[10:Res:185430.1,201396.0] || equal(complement(cantor(complement(cross_product(singleton(regular(domain_relation)),universal_class)))),successor_relation)** -> .
% 299.82/300.44  201996[10:Res:161492.2,160407.0] || equal(singleton(successor_relation),omega) -> equal(integer_of(intersection(y__dfg,ordinal_numbers)),successor_relation)**.
% 299.82/300.44  202208[10:SpR:155765.0,160367.0] ||  -> equal(union(symmetric_difference(universal_class,u),successor_relation),complement(symmetric_difference(complement(u),universal_class)))**.
% 299.82/300.44  202240[10:Rew:202208.0,162975.0] ||  -> subclass(symmetric_difference(union(u,successor_relation),universal_class),complement(symmetric_difference(complement(u),universal_class)))*.
% 299.82/300.44  202877[11:Res:179843.1,168534.1] || equal(u,inverse(successor_relation)) equal(complement(u),symmetrization_of(successor_relation))* -> .
% 299.82/300.44  202878[11:Res:163171.1,168534.1] || equal(u,singleton(successor_relation)) equal(complement(u),symmetrization_of(successor_relation))* -> .
% 299.82/300.44  202879[11:Res:163169.1,168534.1] || equal(u,successor(successor_relation)) equal(complement(u),symmetrization_of(successor_relation))* -> .
% 299.82/300.44  202880[11:Res:168384.1,168534.1] || equal(u,symmetrization_of(successor_relation)) equal(complement(u),symmetrization_of(successor_relation))* -> .
% 299.82/300.44  203274[6:Rew:203192.0,30826.0] || member(u,cantor(v))* subclass(universal_class,complement(rest_of(v)))* -> .
% 299.82/300.44  203565[6:Rew:203192.0,119988.1] || section(universal_class,u,v) -> subclass(cantor(cross_product(v,u)),u)*.
% 299.82/300.44  203896[10:Rew:203192.0,181134.1] || member(singleton(singleton(successor_relation)),rest_of(u))* -> member(successor_relation,cantor(u)).
% 299.82/300.44  204143[10:Rew:203285.0,161466.1] inductive(symmetric_difference(range_of(u),universal_class)) ||  -> member(successor_relation,complement(range_of(u)))*.
% 299.82/300.44  205445[10:SpR:203302.0,195540.1] || subclass(universal_class,cantor(u)) -> equal(symmetric_difference(universal_class,cantor(u)),successor_relation)**.
% 299.82/300.44  205499[10:SpR:204042.0,195540.1] || subclass(universal_class,range_of(u)) -> equal(symmetric_difference(universal_class,range_of(u)),successor_relation)**.
% 299.82/300.44  205501[6:SpR:44.0,204042.0] ||  -> equal(symmetric_difference(image(u,v),universal_class),symmetric_difference(universal_class,image(u,v)))**.
% 299.82/300.44  205513[10:SpR:205150.0,195540.1] || subclass(universal_class,inverse(u)) -> equal(symmetric_difference(universal_class,inverse(u)),successor_relation)**.
% 299.82/300.44  205523[10:SpR:205288.0,195540.1] || subclass(universal_class,sum_class(u)) -> equal(symmetric_difference(universal_class,sum_class(u)),successor_relation)**.
% 299.82/300.44  205525[6:SpR:70.0,205288.0] ||  -> equal(symmetric_difference(apply(u,v),universal_class),symmetric_difference(universal_class,apply(u,v)))**.
% 299.82/300.44  205546[10:Rew:44.0,205542.0] || equal(image(u,v),successor_relation) -> asymmetric(image(u,v),w)*.
% 299.82/300.44  205576[10:Rew:44.0,205548.0] || equal(image(u,v),successor_relation) -> subclass(image(u,v),w)*.
% 299.82/300.44  205646[10:Rew:70.0,205638.0] || equal(apply(u,v),successor_relation) -> asymmetric(apply(u,v),w)*.
% 299.82/300.44  205680[10:Rew:70.0,205647.0] || equal(apply(u,v),successor_relation) -> subclass(apply(u,v),w)*.
% 299.82/300.44  205852[10:SpR:205791.1,142543.0] ||  -> equal(singleton(complement(u)),successor_relation) equal(symmetric_difference(universal_class,u),complement(u))**.
% 299.82/300.44  205876[10:SpR:205791.1,143590.0] ||  -> equal(singleton(u),successor_relation) equal(symmetric_difference(universal_class,u),symmetric_difference(u,universal_class))*.
% 299.82/300.44  205950[14:SpR:205787.0,143590.0] ||  -> equal(symmetric_difference(ordinal_add(u,v),universal_class),symmetric_difference(universal_class,ordinal_add(u,v)))**.
% 299.82/300.44  206077[11:Res:179843.1,163205.1] || equal(u,inverse(successor_relation)) equal(complement(u),successor(successor_relation))** -> .
% 299.82/300.44  206078[10:Res:163171.1,163205.1] || equal(u,singleton(successor_relation)) equal(complement(u),successor(successor_relation))** -> .
% 299.82/300.44  206079[10:Res:163169.1,163205.1] || equal(u,successor(successor_relation)) equal(complement(u),successor(successor_relation))** -> .
% 299.82/300.44  206080[11:Res:168384.1,163205.1] || equal(u,symmetrization_of(successor_relation))* equal(complement(u),successor(successor_relation))** -> .
% 299.82/300.44  206580[10:Res:206541.0,6045.0] || subclass(complement(complement(successor(successor_relation))),u)* well_ordering(universal_class,u) -> .
% 299.82/300.44  206692[10:Res:206681.0,6045.0] || subclass(union(singleton(successor_relation),u),v)* well_ordering(universal_class,v) -> .
% 299.82/300.44  206957[10:Res:206947.1,3.0] || equal(u,kind_1_ordinals) subclass(u,v)* -> member(successor_relation,v).
% 299.82/300.44  206961[10:Res:206947.1,148657.1] || equal(complement(compose(element_relation,universal_class)),kind_1_ordinals)** member(successor_relation,element_relation) -> .
% 299.82/300.44  206970[10:Res:206947.1,1952.0] || equal(symmetric_difference(u,v),kind_1_ordinals) -> member(successor_relation,union(u,v))*.
% 299.82/300.44  206971[10:Res:206947.1,10191.0] || equal(symmetric_difference(u,inverse(u)),kind_1_ordinals)** -> member(successor_relation,symmetrization_of(u)).
% 299.82/300.44  206972[10:Res:206947.1,10254.0] || equal(symmetric_difference(u,singleton(u)),kind_1_ordinals)** -> member(successor_relation,successor(u)).
% 299.82/300.44  207152[10:MRR:207145.2,207145.3,160215.0,184560.0] || equal(kind_1_ordinals,ordinal_numbers) well_ordering(element_relation,successor_relation)* -> member(successor_relation,ordinal_numbers).
% 299.82/300.44  207198[10:Res:207189.0,6045.0] || subclass(union(u,singleton(successor_relation)),v)* well_ordering(universal_class,v) -> .
% 299.82/300.44  207315[20:SpL:509.0,206700.0] || equal(complement(complement(intersection(complement(singleton(successor_relation)),power_class(u)))),omega)** -> .
% 299.82/300.44  207371[10:SpL:509.0,206701.0] || equal(complement(complement(intersection(complement(singleton(successor_relation)),power_class(u)))),universal_class)** -> .
% 299.82/300.44  207508[20:SpL:511.0,207206.0] || equal(complement(complement(intersection(power_class(u),complement(singleton(successor_relation))))),omega)** -> .
% 299.82/300.44  207520[10:SpL:511.0,207207.0] || equal(complement(complement(intersection(power_class(u),complement(singleton(successor_relation))))),universal_class)** -> .
% 299.82/300.44  207529[10:SpR:160367.0,206226.1] ||  -> member(successor_relation,symmetric_difference(universal_class,u)) subclass(successor(successor_relation),union(u,successor_relation))*.
% 299.82/300.44  207532[10:SpR:57.0,206226.1] ||  -> member(successor_relation,image(element_relation,complement(u)))* subclass(successor(successor_relation),power_class(u)).
% 299.82/300.44  207763[10:SpL:194805.1,206671.0] || subclass(u,complement(singleton(successor_relation)))* equal(complement(u),successor_relation) -> .
% 299.82/300.44  207793[11:SpL:194805.1,206672.0] || subclass(u,complement(singleton(successor_relation)))* equal(u,inverse(successor_relation)) -> .
% 299.82/300.44  207818[10:SpL:194805.1,206673.0] || subclass(u,complement(singleton(successor_relation)))* equal(u,singleton(successor_relation)) -> .
% 299.82/300.44  207843[11:SpL:194805.1,206675.0] || subclass(u,complement(singleton(successor_relation)))* equal(u,symmetrization_of(successor_relation)) -> .
% 299.82/300.44  208232[10:Res:141787.0,206958.1] || equal(complement(inverse(singleton(successor_relation))),kind_1_ordinals)** -> asymmetric(singleton(successor_relation),u)*.
% 299.82/300.44  208261[10:Res:206688.0,206958.1] || equal(complement(complement(intersection(complement(singleton(successor_relation)),power_class(u)))),kind_1_ordinals)** -> .
% 299.82/300.44  208262[10:Res:207196.0,206958.1] || equal(complement(complement(intersection(power_class(u),complement(singleton(successor_relation))))),kind_1_ordinals)** -> .
% 299.82/300.44  208340[10:SpL:160367.0,208258.1] inductive(symmetric_difference(universal_class,u)) || equal(union(u,successor_relation),kind_1_ordinals)** -> .
% 299.82/300.44  208343[10:SpL:57.0,208258.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),kind_1_ordinals)** -> .
% 299.82/300.44  208813[21:Res:208805.0,9.0] || subclass(symmetrization_of(successor_relation),successor(successor_relation))* -> equal(symmetrization_of(successor_relation),successor(successor_relation)).
% 299.82/300.44  208940[11:Res:179843.1,163207.1] || equal(u,inverse(successor_relation)) equal(complement(u),singleton(successor_relation))** -> .
% 299.82/300.44  208941[10:Res:163171.1,163207.1] || equal(u,singleton(successor_relation)) equal(complement(u),singleton(successor_relation))** -> .
% 299.82/300.44  208942[10:Res:163169.1,163207.1] || equal(u,successor(successor_relation)) equal(complement(u),singleton(successor_relation))** -> .
% 299.82/300.44  208943[11:Res:168384.1,163207.1] || equal(u,symmetrization_of(successor_relation))* equal(complement(u),singleton(successor_relation))** -> .
% 299.82/300.44  209137[11:Res:179843.1,47888.0] || equal(rest_of(successor_relation),inverse(successor_relation)) subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.44  209150[10:Res:185430.1,209134.1] || equal(complement(complement(element_relation)),successor_relation)** equal(rest_of(successor_relation),kind_1_ordinals) -> .
% 299.82/300.44  209154[20:Res:185430.1,209135.1] || equal(complement(complement(element_relation)),successor_relation)** equal(rest_of(successor_relation),omega) -> .
% 299.82/300.44  209317[12:Res:149580.1,177133.0] || connected(u,universal_class) -> member(regular(element_relation),complement(complement(symmetrization_of(u))))*.
% 299.82/300.44  209459[12:Res:209377.1,595.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(element_relation),u).
% 299.82/300.44  209508[12:SpR:209433.0,1006.0] ||  -> member(unordered_pair(first(regular(element_relation)),singleton(second(regular(element_relation)))),regular(element_relation))*.
% 299.82/300.44  209538[12:SpL:209433.0,1503.0] || subclass(regular(element_relation),u) -> member(singleton(first(regular(element_relation))),u)*.
% 299.82/300.44  209553[12:SpL:209433.0,6210.0] || equal(u,regular(element_relation)) -> member(singleton(first(regular(element_relation))),u)*.
% 299.82/300.44  209679[12:Res:161492.2,209662.0] || equal(omega,element_relation) -> equal(integer_of(singleton(first(regular(element_relation)))),successor_relation)**.
% 299.82/300.44  209788[15:Res:197071.0,189420.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(complement(successor(successor_relation)))),successor_relation)**.
% 299.82/300.44  209907[15:Res:197071.0,189421.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(complement(successor(successor_relation)))),successor_relation)**.
% 299.82/300.44  210304[12:Res:185430.1,209451.0] || equal(complement(complement(kind_1_ordinals)),successor_relation) member(regular(element_relation),ordinal_numbers)* -> .
% 299.82/300.44  210319[12:Res:185430.1,209469.0] || equal(complement(cantor(complement(cross_product(singleton(regular(element_relation)),universal_class)))),successor_relation)** -> .
% 299.82/300.44  210336[15:SpR:199964.0,189563.1] || subclass(domain_relation,flip(u)) -> member(ordered_pair(regular(rest_relation),successor_relation),u)*.
% 299.82/300.44  210337[15:SpR:201355.0,189563.1] || subclass(domain_relation,flip(u)) -> member(ordered_pair(regular(domain_relation),successor_relation),u)*.
% 299.82/300.44  210338[15:SpR:209433.0,189563.1] || subclass(domain_relation,flip(u)) -> member(ordered_pair(regular(element_relation),successor_relation),u)*.
% 299.82/300.44  210380[15:Res:189563.1,147.0] || subclass(domain_relation,flip(rest_relation)) -> equal(rest_of(ordered_pair(u,v)),successor_relation)**.
% 299.82/300.44  210883[15:MRR:210852.1,183757.0] || subclass(rest_relation,domain_relation) -> member(ordered_pair(regular(symmetrization_of(successor_relation)),successor_relation),rest_relation)*.
% 299.82/300.44  210997[3:Res:1504.1,155791.1] || subclass(ordered_pair(u,v),ordinal_numbers)* subclass(universal_class,complement(kind_1_ordinals)) -> .
% 299.82/300.44  211087[11:Res:179843.1,179992.1] || equal(u,inverse(successor_relation)) equal(complement(u),inverse(successor_relation))** -> .
% 299.82/300.44  211088[11:Res:163171.1,179992.1] || equal(u,singleton(successor_relation)) equal(complement(u),inverse(successor_relation))** -> .
% 299.82/300.44  211089[11:Res:163169.1,179992.1] || equal(u,successor(successor_relation)) equal(complement(u),inverse(successor_relation))** -> .
% 299.82/300.44  211090[11:Res:168384.1,179992.1] || equal(u,symmetrization_of(successor_relation))* equal(complement(u),inverse(successor_relation))** -> .
% 299.82/300.44  211451[10:Res:160827.1,181149.0] || well_ordering(universal_class,power_class(universal_class)) -> member(singleton(successor_relation),image(element_relation,successor_relation))*.
% 299.82/300.44  211452[10:Res:160970.1,181149.0] || well_ordering(universal_class,power_class(successor_relation)) -> member(singleton(successor_relation),image(element_relation,universal_class))*.
% 299.82/300.44  211498[10:Res:157922.1,211446.0] || member(singleton(successor_relation),element_relation) well_ordering(universal_class,compose(element_relation,universal_class))* -> .
% 299.82/300.44  211582[10:Res:160827.1,181153.0] ||  -> member(singleton(successor_relation),image(element_relation,successor_relation))* member(singleton(successor_relation),power_class(universal_class)).
% 299.82/300.44  211583[10:Res:160970.1,181153.0] ||  -> member(singleton(successor_relation),image(element_relation,universal_class))* member(singleton(successor_relation),power_class(successor_relation)).
% 299.82/300.44  211584[10:Res:163210.1,181153.0] ||  -> member(singleton(successor_relation),complement(inverse(successor_relation)))* member(singleton(successor_relation),symmetrization_of(successor_relation)).
% 299.82/300.44  211585[10:Res:163218.1,181153.0] ||  -> member(singleton(successor_relation),complement(singleton(successor_relation)))* member(singleton(successor_relation),successor(successor_relation)).
% 299.82/300.44  211666[10:Res:181213.1,3670.1] || equal(u,singleton(singleton(successor_relation)))* equal(complement(u),universal_class)** -> .
% 299.82/300.44  211705[10:Res:181213.1,2151.0] || equal(singleton(u),singleton(singleton(successor_relation)))* -> equal(singleton(successor_relation),u).
% 299.82/300.44  212003[11:Res:183759.1,2151.0] || subclass(inverse(successor_relation),singleton(u))* -> equal(regular(symmetrization_of(successor_relation)),u).
% 299.82/300.44  212187[10:SpR:185433.1,142543.0] || equal(complement(complement(u)),successor_relation) -> equal(symmetric_difference(universal_class,u),universal_class)**.
% 299.82/300.44  212561[15:Res:212548.0,189421.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(complement(power_class(universal_class)))),successor_relation)**.
% 299.82/300.44  212562[15:Res:212548.0,189420.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(complement(power_class(universal_class)))),successor_relation)**.
% 299.82/300.44  212668[15:Res:212652.0,189421.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(complement(power_class(successor_relation)))),successor_relation)**.
% 299.82/300.44  212669[15:Res:212652.0,189420.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(complement(power_class(successor_relation)))),successor_relation)**.
% 299.82/300.44  212694[15:SpR:185605.1,212671.0] || equal(successor_relation,u) -> equal(cantor(regular(complement(power_class(u)))),successor_relation)**.
% 299.82/300.44  212987[10:Res:185430.1,187767.0] || equal(complement(complement(u)),successor_relation) member(power_class(successor_relation),u)* -> .
% 299.82/300.44  213234[15:Res:189485.1,2151.0] || subclass(domain_relation,singleton(u))* -> equal(singleton(singleton(singleton(successor_relation))),u)*.
% 299.82/300.44  213248[15:Res:189485.1,2031.0] || subclass(domain_relation,compose_class(u)) -> equal(compose(u,singleton(successor_relation)),successor_relation)**.
% 299.82/300.44  213312[15:SpL:160336.0,213296.1] || equal(complement(inverse(successor_relation)),domain_relation)** equal(symmetrization_of(successor_relation),universal_class) -> .
% 299.82/300.44  213792[15:Rew:160276.0,213762.1] || equal(successor(u),successor_relation) -> equal(symmetric_difference(complement(u),universal_class),successor_relation)**.
% 299.82/300.44  213850[10:MRR:213849.1,13.0] || equal(u,ordered_pair(universal_class,universal_class)) -> member(unordered_pair(universal_class,successor_relation),u)*.
% 299.82/300.44  214274[10:Res:185430.1,194520.0] || equal(complement(complement(complement(u))),successor_relation)** -> member(power_class(successor_relation),u).
% 299.82/300.44  214292[10:Res:214277.1,23.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(power_class(successor_relation),u).
% 299.82/300.44  214293[10:Res:214277.1,24.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(power_class(successor_relation),v).
% 299.82/300.44  214305[10:Res:214277.1,183723.0] || equal(complement(symmetrization_of(successor_relation)),successor_relation) -> member(power_class(successor_relation),inverse(successor_relation))*.
% 299.82/300.44  214332[10:Rew:57.0,214313.0] || equal(power_class(u),successor_relation) member(power_class(successor_relation),power_class(u))* -> .
% 299.82/300.44  214417[10:MRR:214409.0,160214.0] || equal(complement(union(u,v)),kind_1_ordinals)** -> member(successor_relation,complement(v)).
% 299.82/300.44  214418[20:MRR:214412.0,160214.0] || equal(complement(union(u,v)),omega)** -> member(successor_relation,complement(v)).
% 299.82/300.44  214419[10:MRR:214386.0,191.0] || subclass(union(u,v),successor_relation)* -> member(singleton(w),complement(v))*.
% 299.82/300.44  214420[10:MRR:214404.0,191.0] || well_ordering(universal_class,union(u,v))* -> member(singleton(successor_relation),complement(v)).
% 299.82/300.44  214445[21:Res:214433.0,3.0] || subclass(universal_class,u) -> member(regular(complement(complement(symmetrization_of(successor_relation)))),u)*.
% 299.82/300.44  214565[10:MRR:214556.0,160214.0] || equal(complement(union(u,v)),kind_1_ordinals)** -> member(successor_relation,complement(u)).
% 299.82/300.44  214566[20:MRR:214559.0,160214.0] || equal(complement(union(u,v)),omega)** -> member(successor_relation,complement(u)).
% 299.82/300.44  214568[10:MRR:214533.0,191.0] || subclass(union(u,v),successor_relation)* -> member(singleton(w),complement(u))*.
% 299.82/300.44  214569[10:MRR:214551.0,191.0] || well_ordering(universal_class,union(u,v))* -> member(singleton(successor_relation),complement(u)).
% 299.82/300.44  215228[10:Obv:215162.1] || member(successor_relation,u) -> subclass(successor(successor_relation),intersection(u,successor(successor_relation)))*.
% 299.82/300.44  215256[11:MRR:215255.1,198997.0] || member(not_subclass_element(symmetrization_of(successor_relation),successor_relation),intersection(complement(inverse(successor_relation)),u))* -> .
% 299.82/300.44  215258[11:MRR:215257.1,198997.0] || member(not_subclass_element(symmetrization_of(successor_relation),successor_relation),intersection(u,complement(inverse(successor_relation))))* -> .
% 299.82/300.44  215468[10:Rew:205150.0,215308.1,160223.0,215308.1] || equal(inverse(u),universal_class) -> equal(symmetric_difference(universal_class,inverse(u)),successor_relation)**.
% 299.82/300.44  215478[10:Rew:160322.0,215317.1] || equal(inverse(u),universal_class) -> equal(power_class(inverse(u)),power_class(universal_class))**.
% 299.82/300.44  215503[10:Rew:160223.0,215297.1,160276.0,215297.1] || equal(inverse(u),universal_class) -> equal(union(inverse(u),v),universal_class)**.
% 299.82/300.44  215511[10:Rew:160223.0,215343.1,160277.0,215343.1] || equal(inverse(u),universal_class) -> equal(union(v,inverse(u)),universal_class)**.
% 299.82/300.44  215750[10:Rew:205288.0,215622.1,160223.0,215622.1] || equal(sum_class(u),universal_class) -> equal(symmetric_difference(universal_class,sum_class(u)),successor_relation)**.
% 299.82/300.44  215754[10:Rew:160322.0,215631.1] || equal(sum_class(u),universal_class) -> equal(power_class(sum_class(u)),power_class(universal_class))**.
% 299.82/300.44  215779[10:Rew:160223.0,215611.1,160276.0,215611.1] || equal(sum_class(u),universal_class) -> equal(union(sum_class(u),v),universal_class)**.
% 299.82/300.44  215787[10:Rew:160223.0,215657.1,160277.0,215657.1] || equal(sum_class(u),universal_class) -> equal(union(v,sum_class(u)),universal_class)**.
% 299.82/300.44  215957[10:Obv:215945.1] || member(u,ordinal_numbers) -> equal(intersection(singleton(u),complement(kind_1_ordinals)),successor_relation)**.
% 299.82/300.44  216096[10:MRR:216095.1,160442.0] || member(regular(complement(kind_1_ordinals)),ordinal_numbers)* -> equal(symmetric_difference(universal_class,kind_1_ordinals),successor_relation).
% 299.82/300.44  216098[10:Obv:216080.1] || member(u,ordinal_numbers) -> equal(intersection(complement(kind_1_ordinals),singleton(u)),successor_relation)**.
% 299.82/300.44  216138[6:Res:199830.1,2151.0] || equal(singleton(u),cross_product(universal_class,universal_class))* -> equal(regular(rest_relation),u).
% 299.82/300.44  216188[6:Res:149580.1,199959.0] || connected(u,universal_class) well_ordering(universal_class,complement(complement(symmetrization_of(u))))* -> .
% 299.82/300.44  216223[14:SpR:199971.1,1004.0] || member(u,universal_class) -> member(successor_relation,ordered_pair(sum_class(range_of(u)),v))*.
% 299.82/300.44  216440[10:Res:185430.1,199982.0] || equal(complement(complement(u)),successor_relation) member(regular(rest_relation),u)* -> .
% 299.82/300.44  216462[10:Res:185430.1,199986.0] || equal(complement(complement(complement(u))),successor_relation)** -> member(regular(rest_relation),u).
% 299.82/300.44  216478[10:Res:216465.1,23.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(regular(rest_relation),u).
% 299.82/300.44  216479[10:Res:216465.1,24.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(regular(rest_relation),v).
% 299.82/300.44  216491[10:Res:216465.1,183723.0] || equal(complement(symmetrization_of(successor_relation)),successor_relation) -> member(regular(rest_relation),inverse(successor_relation))*.
% 299.82/300.44  216517[10:Rew:57.0,216499.0] || equal(power_class(u),successor_relation) member(regular(rest_relation),power_class(u))* -> .
% 299.82/300.44  216746[6:Res:201220.1,2151.0] || equal(singleton(u),cross_product(universal_class,universal_class))* -> equal(regular(domain_relation),u).
% 299.82/300.44  216822[10:Res:185430.1,201372.0] || equal(complement(complement(u)),successor_relation) member(regular(domain_relation),u)* -> .
% 299.82/300.44  216844[10:Res:185430.1,201376.0] || equal(complement(complement(complement(u))),successor_relation)** -> member(regular(domain_relation),u).
% 299.82/300.44  216875[10:MRR:216865.2,184563.0] || member(apply(choice,regular(kind_1_ordinals)),ordinal_numbers)* -> equal(regular(kind_1_ordinals),successor_relation).
% 299.82/300.44  216906[10:Res:216847.1,23.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(regular(domain_relation),u).
% 299.82/300.44  216907[10:Res:216847.1,24.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(regular(domain_relation),v).
% 299.82/300.44  216919[10:Res:216847.1,183723.0] || equal(complement(symmetrization_of(successor_relation)),successor_relation) -> member(regular(domain_relation),inverse(successor_relation))*.
% 299.82/300.44  216945[10:Rew:57.0,216927.0] || equal(power_class(u),successor_relation) member(regular(domain_relation),power_class(u))* -> .
% 299.82/300.44  217183[10:Res:64.1,206542.0] function(complement(complement(successor(successor_relation)))) ||  -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.44  217202[10:Res:6219.1,206660.0] || member(u,complement(singleton(successor_relation)))* member(successor_relation,singleton(u)) -> .
% 299.82/300.44  217372[10:MRR:217371.1,160442.0] || member(regular(complement(u)),u)* -> equal(symmetric_difference(universal_class,u),successor_relation).
% 299.82/300.44  217576[10:MRR:217553.2,184563.0] || member(unordered_pair(u,v),ordinal_numbers)* subclass(universal_class,regular(kind_1_ordinals)) -> .
% 299.82/300.44  217587[10:MRR:217586.2,212302.0] || subclass(universal_class,regular(complement(u)))* -> member(unordered_pair(v,w),u)*.
% 299.82/300.44  218300[10:MRR:218281.2,184563.0] || member(not_subclass_element(regular(kind_1_ordinals),u),ordinal_numbers)* -> subclass(regular(kind_1_ordinals),u).
% 299.82/300.44  218353[10:Res:218298.0,160435.1] inductive(regular(u)) ||  -> equal(u,successor_relation) member(successor_relation,complement(u))*.
% 299.82/300.44  218438[10:SpR:185605.1,218372.0] || equal(successor_relation,u) -> subclass(regular(image(element_relation,universal_class)),power_class(u))*.
% 299.82/300.44  218480[3:Res:137.1,217932.0] || member(complement(kind_1_ordinals),ordinal_numbers) -> subclass(sum_class(complement(kind_1_ordinals)),complement(ordinal_numbers))*.
% 299.82/300.44  218506[10:Res:218497.0,9.0] || subclass(complement(ordinal_numbers),regular(kind_1_ordinals))* -> equal(complement(ordinal_numbers),regular(kind_1_ordinals)).
% 299.82/300.44  218753[10:Res:218481.0,160435.1] inductive(restrict(complement(kind_1_ordinals),u,v)) ||  -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  218768[10:Res:218493.1,160435.1] inductive(singleton(u)) ||  -> member(u,kind_1_ordinals)* member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  218889[22:Res:218867.1,595.0] || subclass(kind_1_ordinals,restrict(u,v,w))* -> member(singleton(successor_relation),u).
% 299.82/300.44  218910[22:Res:218867.1,47888.0] || subclass(kind_1_ordinals,rest_of(singleton(successor_relation)))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.44  219101[15:Res:218473.1,213195.0] || equal(complement(kind_1_ordinals),domain_relation) equal(complement(complement(ordinal_numbers)),universal_class)** -> .
% 299.82/300.44  219109[10:Res:218473.1,206737.0] || equal(successor(singleton(successor_relation)),complement(kind_1_ordinals)) -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  219118[10:Res:218473.1,160551.0] || equal(image(element_relation,universal_class),complement(kind_1_ordinals)) -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  219120[13:Res:218473.1,180588.0] || equal(image(element_relation,successor_relation),complement(kind_1_ordinals)) -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  219121[6:Res:218473.1,200386.0] || equal(complement(kind_1_ordinals),regular(rest_relation)) well_ordering(universal_class,complement(ordinal_numbers))* -> .
% 299.82/300.44  219122[6:Res:218473.1,201583.0] || equal(complement(kind_1_ordinals),regular(domain_relation)) well_ordering(universal_class,complement(ordinal_numbers))* -> .
% 299.82/300.44  219123[12:Res:218473.1,209655.0] || equal(complement(kind_1_ordinals),regular(element_relation)) well_ordering(universal_class,complement(ordinal_numbers))* -> .
% 299.82/300.44  219127[10:Res:218473.1,206723.0] || equal(symmetrization_of(singleton(successor_relation)),complement(kind_1_ordinals)) -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  219135[10:Res:218473.1,181146.0] || equal(ordered_pair(universal_class,u),complement(kind_1_ordinals))** -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  219171[10:Res:192947.1,218628.0] || equal(complement(complement(kind_1_ordinals)),successor_relation) -> member(singleton(u),complement(ordinal_numbers))*.
% 299.82/300.44  219179[3:Res:4.1,218628.0] ||  -> subclass(complement(kind_1_ordinals),u) member(not_subclass_element(complement(kind_1_ordinals),u),complement(ordinal_numbers))*.
% 299.82/300.44  219184[3:Res:1476.1,218628.0] || subclass(universal_class,complement(kind_1_ordinals)) -> member(unordered_pair(u,v),complement(ordinal_numbers))*.
% 299.82/300.44  219185[10:Res:214277.1,218628.0] || equal(complement(complement(kind_1_ordinals)),successor_relation) -> member(power_class(successor_relation),complement(ordinal_numbers))*.
% 299.82/300.44  219206[3:Res:1499.1,218628.0] || subclass(universal_class,complement(kind_1_ordinals)) -> member(ordered_pair(u,v),complement(ordinal_numbers))*.
% 299.82/300.44  219207[10:Res:160251.1,218628.0] || subclass(domain_relation,complement(kind_1_ordinals)) -> member(ordered_pair(successor_relation,successor_relation),complement(ordinal_numbers))*.
% 299.82/300.44  219232[11:Res:183764.1,218628.0] || subclass(universal_class,complement(kind_1_ordinals)) -> member(regular(symmetrization_of(successor_relation)),complement(ordinal_numbers))*.
% 299.82/300.44  219235[10:Res:216465.1,218628.0] || equal(complement(complement(kind_1_ordinals)),successor_relation) -> member(regular(rest_relation),complement(ordinal_numbers))*.
% 299.82/300.44  219238[10:Res:216847.1,218628.0] || equal(complement(complement(kind_1_ordinals)),successor_relation) -> member(regular(domain_relation),complement(ordinal_numbers))*.
% 299.82/300.44  219804[10:MRR:219801.1,185116.0] || equal(complement(u),successor_relation) -> equal(regular(unordered_pair(u,successor_relation)),successor_relation)**.
% 299.82/300.44  184041[10:SpL:163458.0,1511.0] || equal(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),universal_class)** -> member(omega,kind_1_ordinals).
% 299.82/300.44  206743[10:Res:206684.0,163256.1] || equal(successor(singleton(successor_relation)),range_of(successor_relation)) -> inductive(successor(singleton(successor_relation)))*.
% 299.82/300.44  206729[10:Res:206682.0,163256.1] || equal(symmetrization_of(singleton(successor_relation)),range_of(successor_relation)) -> inductive(symmetrization_of(singleton(successor_relation)))*.
% 299.82/300.44  181147[10:Res:181063.0,163256.1] || equal(ordered_pair(universal_class,u),range_of(successor_relation)) -> inductive(ordered_pair(universal_class,u))*.
% 299.82/300.44  180999[13:Res:180583.0,163256.1] || equal(image(element_relation,successor_relation),range_of(successor_relation)) -> inductive(image(element_relation,successor_relation))*.
% 299.82/300.44  160610[10:Rew:160202.0,146370.1] || asymmetric(universal_class,universal_class) -> equal(image(inverse(universal_class),universal_class),range_of(successor_relation))**.
% 299.82/300.44  166977[10:Res:160460.0,163256.1] || equal(image(element_relation,universal_class),range_of(successor_relation)) -> inductive(image(element_relation,universal_class))*.
% 299.82/300.44  166955[10:Res:160268.1,163256.1] || equal(u,universal_class) equal(range_of(successor_relation),u)* -> inductive(u)*.
% 299.82/300.44  191130[20:Res:191074.1,163256.1] || equal(u,omega) equal(range_of(successor_relation),u)* -> inductive(u)*.
% 299.82/300.44  206998[10:Res:206947.1,163256.1] || equal(u,kind_1_ordinals) equal(range_of(successor_relation),u)* -> inductive(u)*.
% 299.82/300.44  163262[10:Rew:160305.0,160564.0,160202.0,160564.0] || equal(range_of(successor_relation),successor_relation) member(successor_relation,u)* -> inductive(u).
% 299.82/300.44  189098[10:Rew:185654.1,189097.1,189086.1,189097.1] || equal(range_of(successor_relation),successor_relation) -> equal(union(singleton(successor_relation),successor_relation),kind_1_ordinals)**.
% 299.82/300.44  197700[10:SpR:193779.0,9089.1] function(complement(cross_product(successor_relation,universal_class))) ||  -> member(sum_class(range_of(successor_relation)),universal_class)*.
% 299.82/300.44  193782[10:SpR:193730.0,70.0] ||  -> equal(apply(complement(cross_product(singleton(u),universal_class)),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.44  202035[10:Res:161492.2,201590.0] || equal(domain_relation,omega) -> equal(integer_of(singleton(first(regular(domain_relation)))),successor_relation)**.
% 299.82/300.44  202034[10:Res:161492.2,200393.0] || equal(rest_relation,omega) -> equal(integer_of(singleton(first(regular(rest_relation)))),successor_relation)**.
% 299.82/300.44  221366[10:MRR:221364.1,185153.0] || equal(complement(u),successor_relation) -> equal(regular(unordered_pair(successor_relation,u)),successor_relation)**.
% 299.82/300.44  221454[15:Res:218373.0,213195.0] || equal(complement(complement(singleton(domain_relation))),universal_class)** -> equal(singleton(domain_relation),successor_relation).
% 299.82/300.44  221458[10:Res:218373.0,163170.0] ||  -> equal(singleton(successor(successor_relation)),successor_relation) member(successor_relation,complement(singleton(successor(successor_relation))))*.
% 299.82/300.44  221466[11:Res:218373.0,168395.0] ||  -> equal(singleton(inverse(successor_relation)),successor_relation) member(successor_relation,complement(singleton(inverse(successor_relation))))*.
% 299.82/300.44  221514[11:Res:218373.0,168378.0] ||  -> equal(singleton(symmetrization_of(successor_relation)),successor_relation) member(successor_relation,complement(singleton(symmetrization_of(successor_relation))))*.
% 299.82/300.44  221526[17:MRR:221452.1,185582.0] || well_ordering(u,complement(singleton(omega)))* -> member(least(u,omega),omega).
% 299.82/300.44  221528[10:MRR:221481.1,185246.0] || member(u,universal_class) -> member(u,complement(singleton(unordered_pair(u,v))))*.
% 299.82/300.44  221529[10:MRR:221483.1,185246.0] || member(u,universal_class) -> member(u,complement(singleton(unordered_pair(v,u))))*.
% 299.82/300.44  221541[20:Res:221515.0,163256.1] || equal(complement(singleton(omega)),range_of(successor_relation)) -> inductive(complement(singleton(omega)))*.
% 299.82/300.44  221570[10:Res:221516.0,6045.0] || subclass(complement(singleton(singleton(successor_relation))),u)* well_ordering(universal_class,u) -> .
% 299.82/300.44  221782[10:Res:221522.0,3.0] || subclass(complement(singleton(ordered_pair(universal_class,u))),v)* -> member(successor_relation,v).
% 299.82/300.44  221971[10:Res:161493.2,221891.0] inductive(singleton(singleton(singleton(successor_relation)))) ||  -> equal(integer_of(singleton(successor_relation)),successor_relation)**.
% 299.82/300.44  222240[10:Res:161493.2,222147.0] inductive(singleton(ordered_pair(u,v))) ||  -> equal(integer_of(singleton(u)),successor_relation)**.
% 299.82/300.44  222403[24:SpL:222326.0,1522.0] || member(singleton(singleton(successor_relation)),cross_product(u,v))* -> member(kind_1_ordinals,v).
% 299.82/300.44  222622[24:Res:222332.0,163256.1] || equal(ordered_pair(kind_1_ordinals,u),range_of(successor_relation)) -> inductive(ordered_pair(kind_1_ordinals,u))*.
% 299.82/300.44  222696[25:Res:222646.2,193819.0] function(complement(cross_product(singleton(u),universal_class))) || member(u,universal_class)* -> .
% 299.82/300.44  222726[25:Res:222646.2,212820.0] function(first(regular(rest_relation))) || member(second(regular(rest_relation)),universal_class)* -> .
% 299.82/300.44  222727[25:Res:222646.2,212821.0] function(first(regular(domain_relation))) || member(second(regular(domain_relation)),universal_class)* -> .
% 299.82/300.44  222728[25:Res:222646.2,212822.0] function(first(regular(element_relation))) || member(second(regular(element_relation)),universal_class)* -> .
% 299.82/300.44  223070[25:SoR:222758.0,6317.2] single_valued_class(singleton(u)) || equal(cross_product(universal_class,universal_class),singleton(u))* -> .
% 299.82/300.44  223159[24:Res:222372.0,3.0] || subclass(complement(singleton(ordered_pair(kind_1_ordinals,u))),v)* -> member(successor_relation,v).
% 299.82/300.44  223302[24:SpL:222479.0,17.0] || member(ordered_pair(u,universal_class),cross_product(v,w))* -> member(kind_1_ordinals,w).
% 299.82/300.44  224016[10:Obv:223994.0] ||  -> member(successor_relation,power_class(u)) subclass(successor(successor_relation),image(element_relation,complement(u)))*.
% 299.82/300.44  224809[25:SoR:224725.0,6317.2] single_valued_class(power_class(successor_relation)) || equal(cross_product(universal_class,universal_class),power_class(successor_relation))** -> .
% 299.82/300.44  224812[25:SoR:224726.0,6317.2] single_valued_class(regular(rest_relation)) || equal(cross_product(universal_class,universal_class),regular(rest_relation))** -> .
% 299.82/300.44  224819[25:SoR:224727.0,6317.2] single_valued_class(regular(domain_relation)) || equal(cross_product(universal_class,universal_class),regular(domain_relation))** -> .
% 299.82/300.44  224822[25:SoR:224728.0,6317.2] single_valued_class(regular(element_relation)) || equal(cross_product(universal_class,universal_class),regular(element_relation))** -> .
% 299.82/300.44  224838[25:SoR:224733.0,160511.2] single_valued_class(regular(symmetrization_of(successor_relation))) || equal(regular(symmetrization_of(successor_relation)),successor_relation)** -> .
% 299.82/300.44  224849[25:SoR:224735.0,160511.2] single_valued_class(unordered_pair(u,v)) || equal(unordered_pair(u,v),successor_relation)** -> .
% 299.82/300.44  225103[25:SpL:224739.1,193819.0] function(u) || member(u,cantor(complement(cross_product(successor_relation,universal_class))))* -> .
% 299.82/300.44  225655[24:SpL:185302.1,222440.0] || equal(cross_product(successor_relation,universal_class),successor_relation) member(kind_1_ordinals,cantor(universal_class))* -> .
% 299.82/300.44  225726[24:MRR:225680.2,160227.0] || member(u,symmetric_difference(universal_class,kind_1_ordinals))* member(u,successor(kind_1_ordinals)) -> .
% 299.82/300.44  225761[24:SpR:223100.0,194805.1] || subclass(successor(kind_1_ordinals),symmetric_difference(universal_class,kind_1_ordinals))* -> equal(successor(kind_1_ordinals),successor_relation).
% 299.82/300.44  225831[24:Rew:181137.1,225830.1] || member(ordered_pair(u,singleton(singleton(successor_relation))),composition_function)* -> equal(kind_1_ordinals,universal_class).
% 299.82/300.44  225855[24:Rew:160370.0,225850.1] || equal(complement(kind_1_ordinals),successor_relation) -> equal(union(successor(kind_1_ordinals),successor_relation),universal_class)**.
% 299.82/300.44  225879[24:Rew:160366.0,225875.1] || equal(complement(kind_1_ordinals),successor_relation) -> equal(complement(complement(successor(kind_1_ordinals))),universal_class)**.
% 299.82/300.44  226267[15:MRR:226188.1,160227.0] || member(u,universal_class) -> equal(apply(omega,u),sum_class(range_of(successor_relation)))**.
% 299.82/300.44  226382[25:SpR:226350.1,44.0] one_to_one(restrict(u,v,universal_class)) ||  -> equal(image(u,v),universal_class)**.
% 299.82/300.44  226745[10:SpR:226634.0,194805.1] || subclass(complement(kind_1_ordinals),intersection(ordinal_numbers,u))* -> equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.44  226812[10:MRR:226741.2,160227.0] || member(u,complement(kind_1_ordinals)) member(u,intersection(ordinal_numbers,v))* -> .
% 299.82/300.44  226853[10:SpR:226766.0,194805.1] || subclass(complement(kind_1_ordinals),complement(complement(ordinal_numbers)))* -> equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.44  226911[10:MRR:226849.2,160227.0] || member(u,complement(kind_1_ordinals)) member(u,complement(complement(ordinal_numbers)))* -> .
% 299.82/300.44  226938[10:Rew:142543.0,226924.0] ||  -> equal(symmetric_difference(universal_class,intersection(complement(ordinal_numbers),kind_1_ordinals)),symmetric_difference(complement(ordinal_numbers),kind_1_ordinals))**.
% 299.82/300.44  226966[10:SpR:226757.0,194805.1] || subclass(complement(kind_1_ordinals),intersection(u,ordinal_numbers))* -> equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.44  227029[10:MRR:226962.2,160227.0] || member(u,complement(kind_1_ordinals)) member(u,intersection(v,ordinal_numbers))* -> .
% 299.82/300.44  227333[25:Res:224913.1,179992.1] function(u) || equal(complement(ordered_pair(u,v)),inverse(successor_relation))** -> .
% 299.82/300.44  227334[25:Res:224913.1,163207.1] function(u) || equal(complement(ordered_pair(u,v)),singleton(successor_relation))** -> .
% 299.82/300.44  227336[25:Res:224913.1,163205.1] function(u) || equal(complement(ordered_pair(u,v)),successor(successor_relation))** -> .
% 299.82/300.44  227337[25:Res:224913.1,168534.1] function(u) || equal(complement(ordered_pair(u,v)),symmetrization_of(successor_relation))** -> .
% 299.82/300.44  227835[10:Rew:142543.0,227821.0] ||  -> equal(symmetric_difference(universal_class,intersection(kind_1_ordinals,complement(ordinal_numbers))),symmetric_difference(kind_1_ordinals,complement(ordinal_numbers)))**.
% 299.82/300.44  228250[25:SpR:224739.1,222126.0] function(first(regular(rest_relation))) ||  -> member(successor_relation,complement(singleton(regular(rest_relation))))*.
% 299.82/300.44  228254[10:Res:222126.0,6045.0] || subclass(complement(singleton(regular(rest_relation))),u)* well_ordering(universal_class,u) -> .
% 299.82/300.44  228454[25:SpR:224739.1,222127.0] function(first(regular(domain_relation))) ||  -> member(successor_relation,complement(singleton(regular(domain_relation))))*.
% 299.82/300.44  228458[10:Res:222127.0,6045.0] || subclass(complement(singleton(regular(domain_relation))),u)* well_ordering(universal_class,u) -> .
% 299.82/300.44  228471[25:SpR:224739.1,222128.0] function(first(regular(element_relation))) ||  -> member(successor_relation,complement(singleton(regular(element_relation))))*.
% 299.82/300.44  228475[12:Res:222128.0,6045.0] || subclass(complement(singleton(regular(element_relation))),u)* well_ordering(universal_class,u) -> .
% 299.82/300.44  228675[25:SpL:224739.1,222223.0] function(first(regular(rest_relation))) || member(successor_relation,singleton(regular(rest_relation)))* -> .
% 299.82/300.44  228683[25:SpL:224739.1,222224.0] function(first(regular(domain_relation))) || member(successor_relation,singleton(regular(domain_relation)))* -> .
% 299.82/300.44  228691[25:SpL:224739.1,222225.0] function(first(regular(element_relation))) || member(successor_relation,singleton(regular(element_relation)))* -> .
% 299.82/300.44  228794[24:SpR:223107.0,163198.1] || subclass(successor(kind_1_ordinals),successor_relation) -> equal(symmetric_difference(complement(kind_1_ordinals),universal_class),successor_relation)**.
% 299.82/300.44  228812[24:SpR:223107.0,194805.1] || subclass(universal_class,successor(kind_1_ordinals)) -> equal(symmetric_difference(complement(kind_1_ordinals),universal_class),universal_class)**.
% 299.82/300.44  228821[24:SpL:223107.0,160566.0] || equal(symmetric_difference(complement(kind_1_ordinals),universal_class),universal_class)** -> member(successor_relation,successor(kind_1_ordinals)).
% 299.82/300.44  228823[24:SpL:223107.0,1510.0] || equal(symmetric_difference(complement(kind_1_ordinals),universal_class),universal_class)** -> member(omega,successor(kind_1_ordinals)).
% 299.82/300.44  228832[24:SpL:223107.0,191100.0] || equal(symmetric_difference(complement(kind_1_ordinals),universal_class),omega)** -> member(successor_relation,successor(kind_1_ordinals)).
% 299.82/300.44  228834[24:SpL:223107.0,206964.0] || equal(symmetric_difference(complement(kind_1_ordinals),universal_class),kind_1_ordinals)** -> member(successor_relation,successor(kind_1_ordinals)).
% 299.82/300.44  228836[24:SpL:223107.0,23.0] || member(u,symmetric_difference(complement(kind_1_ordinals),universal_class))* -> member(u,successor(kind_1_ordinals)).
% 299.82/300.44  228868[24:MRR:228808.0,34067.1] || member(u,successor(kind_1_ordinals)) -> member(u,symmetric_difference(complement(kind_1_ordinals),universal_class))*.
% 299.82/300.44  229026[10:Res:228991.1,595.0] || subclass(kind_1_ordinals,restrict(u,v,w))* -> member(regular(ordinal_numbers),u).
% 299.82/300.44  229048[10:Res:228991.1,47888.0] || subclass(kind_1_ordinals,rest_of(regular(ordinal_numbers)))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.44  229068[25:SoR:229059.0,6317.2] single_valued_class(regular(ordinal_numbers)) || equal(cross_product(universal_class,universal_class),regular(ordinal_numbers))** -> .
% 299.82/300.44  229145[20:MRR:229132.1,160217.0] || subclass(omega,symmetric_difference(u,v))* -> member(successor_relation,union(u,v)).
% 299.82/300.44  229254[10:Res:229228.1,595.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(ordinal_numbers),u).
% 299.82/300.44  229784[10:Res:221521.1,185065.1] || subclass(complement(singleton(omega)),successor_relation)* -> equal(integer_of(singleton(u)),successor_relation)**.
% 299.82/300.44  229811[10:Res:221521.1,211446.0] || well_ordering(universal_class,complement(singleton(omega)))* -> equal(integer_of(singleton(successor_relation)),successor_relation).
% 299.82/300.44  229854[20:Res:218473.1,221538.0] || equal(complement(singleton(omega)),complement(kind_1_ordinals)) -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  230157[15:SpL:160419.0,222296.1] || subclass(domain_relation,complement(singleton(successor_relation)))* subclass(domain_relation,successor(successor_relation)) -> .
% 299.82/300.44  230158[15:SpL:160336.0,222296.1] || subclass(domain_relation,complement(inverse(successor_relation)))* subclass(domain_relation,symmetrization_of(successor_relation)) -> .
% 299.82/300.44  230164[15:SpL:160322.0,222296.1] || subclass(domain_relation,image(element_relation,successor_relation))* subclass(domain_relation,power_class(universal_class)) -> .
% 299.82/300.44  230165[15:SpL:160328.0,222296.1] || subclass(domain_relation,image(element_relation,universal_class))* subclass(domain_relation,power_class(successor_relation)) -> .
% 299.82/300.44  230536[10:Res:160251.1,229800.0] || subclass(domain_relation,singleton(omega)) -> equal(integer_of(ordered_pair(successor_relation,successor_relation)),successor_relation)**.
% 299.82/300.44  230614[15:Res:218473.1,230172.1] || equal(complement(kind_1_ordinals),domain_relation) equal(complement(complement(ordinal_numbers)),domain_relation)** -> .
% 299.82/300.44  230615[15:Res:218373.0,230172.1] || equal(complement(complement(singleton(domain_relation))),domain_relation)** -> equal(singleton(domain_relation),successor_relation).
% 299.82/300.44  230634[15:SpL:160419.0,230608.1] || equal(complement(singleton(successor_relation)),domain_relation)** equal(successor(successor_relation),domain_relation) -> .
% 299.82/300.44  230635[15:SpL:160336.0,230608.1] || equal(complement(inverse(successor_relation)),domain_relation)** equal(symmetrization_of(successor_relation),domain_relation) -> .
% 299.82/300.44  230641[15:SpL:160322.0,230608.1] || equal(image(element_relation,successor_relation),domain_relation)** equal(power_class(universal_class),domain_relation) -> .
% 299.82/300.44  230642[15:SpL:160328.0,230608.1] || equal(image(element_relation,universal_class),domain_relation)** equal(power_class(successor_relation),domain_relation) -> .
% 299.82/300.44  231603[24:Res:218473.1,222619.0] || equal(ordered_pair(kind_1_ordinals,u),complement(kind_1_ordinals))** -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  231643[25:SpR:224912.1,162965.0] function(u) ||  -> equal(intersection(successor(u),symmetric_difference(universal_class,u)),successor_relation)**.
% 299.82/300.44  231644[25:SpR:224912.1,162964.0] function(u) ||  -> equal(intersection(symmetric_difference(universal_class,u),successor(u)),successor_relation)**.
% 299.82/300.44  231645[25:SpR:224912.1,161206.0] function(u) ||  -> equal(symmetric_difference(successor(u),symmetric_difference(universal_class,u)),universal_class)**.
% 299.82/300.44  231646[25:SpR:224912.1,161205.0] function(u) ||  -> equal(symmetric_difference(symmetric_difference(universal_class,u),successor(u)),universal_class)**.
% 299.82/300.44  231647[25:SpR:224912.1,161204.0] function(u) ||  -> equal(union(successor(u),symmetric_difference(universal_class,u)),universal_class)**.
% 299.82/300.44  231648[25:SpR:224912.1,161203.0] function(u) ||  -> equal(union(symmetric_difference(universal_class,u),successor(u)),universal_class)**.
% 299.82/300.44  231650[25:SpR:224912.1,184982.1] function(u) || subclass(u,successor_relation)* -> equal(successor(u),successor_relation).
% 299.82/300.44  9448[0:Rew:30.0,9447.1] single_valued_class(intersection(u,cross_product(universal_class,universal_class))) ||  -> function(restrict(u,universal_class,universal_class))*.
% 299.82/300.44  9562[0:Rew:31.0,9561.1] single_valued_class(intersection(cross_product(universal_class,universal_class),u)) ||  -> function(restrict(u,universal_class,universal_class))*.
% 299.82/300.44  31431[0:SpL:41.0,31279.1] || equal(complement(rest_of(inverse(u))),universal_class)** member(v,range_of(u))* -> .
% 299.82/300.44  10251[0:SpL:1934.0,2649.0] || subclass(universal_class,symmetric_difference(u,singleton(u)))* -> member(singleton(v),successor(u))*.
% 299.82/300.44  10188[0:SpL:1933.0,2649.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(singleton(v),symmetrization_of(u))*.
% 299.82/300.44  5784[0:Res:3907.1,26.1] || equal(complement(complement(complement(u))),universal_class)** member(singleton(v),u)* -> .
% 299.82/300.44  5903[0:SpL:161.0,2649.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(singleton(w),union(u,v))*.
% 299.82/300.44  2646[0:Res:1477.1,3.0] || subclass(universal_class,u)* subclass(u,v)* -> member(singleton(w),v)*.
% 299.82/300.44  5787[0:Res:3907.1,24.0] || equal(complement(complement(intersection(u,v))),universal_class)** -> member(singleton(w),v)*.
% 299.82/300.44  5786[0:Res:3907.1,23.0] || equal(complement(complement(intersection(u,v))),universal_class)** -> member(singleton(w),u)*.
% 299.82/300.44  5632[0:Res:1499.1,38.0] || subclass(universal_class,flip(u)) -> member(ordered_pair(ordered_pair(v,w),x),u)*.
% 299.82/300.44  5642[0:Res:1499.1,35.0] || subclass(universal_class,rotate(u)) -> member(ordered_pair(ordered_pair(v,w),x),u)*.
% 299.82/300.44  3520[0:Res:1499.1,595.0] || subclass(universal_class,restrict(u,v,w))* -> member(ordered_pair(x,y),u)*.
% 299.82/300.44  1502[0:Res:1009.0,3.0] || subclass(singleton(singleton(singleton(u))),v)* -> member(singleton(singleton(u)),v).
% 299.82/300.44  6178[0:SpL:161.0,5909.0] || equal(symmetric_difference(u,v),universal_class) -> member(singleton(w),union(u,v))*.
% 299.82/300.44  10184[0:SpL:1933.0,5909.0] || equal(symmetric_difference(u,inverse(u)),universal_class)** -> member(singleton(v),symmetrization_of(u))*.
% 299.82/300.44  6240[0:SpL:1005.0,6210.0] || equal(u,singleton(singleton(singleton(v)))) -> member(singleton(singleton(v)),u)*.
% 299.82/300.44  10247[0:SpL:1934.0,5909.0] || equal(symmetric_difference(u,singleton(u)),universal_class)** -> member(singleton(v),successor(u))*.
% 299.82/300.44  107559[0:Res:1477.1,6045.0] || subclass(universal_class,u)* subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  107696[0:Res:51387.0,6045.0] || subclass(u,v)* well_ordering(universal_class,v)* -> subclass(w,complement(u))*.
% 299.82/300.44  108978[0:Res:136.1,31289.0] || member(u,ordinal_numbers) -> subclass(u,v)* member(least(element_relation,u),u)*.
% 299.82/300.44  110678[0:Res:3907.1,1705.0] || equal(complement(complement(cross_product(u,v))),universal_class)** -> member(singleton(w),u)*.
% 299.82/300.44  112479[0:MRR:112439.0,191.0] || equal(complement(union(u,v)),universal_class)** -> member(singleton(w),complement(v))*.
% 299.82/300.44  112640[0:MRR:112606.0,191.0] || equal(complement(union(u,v)),universal_class)** -> member(singleton(w),complement(u))*.
% 299.82/300.44  119667[0:Res:114897.1,3.0] || equal(u,universal_class) subclass(u,v)* -> member(singleton(w),v)*.
% 299.82/300.44  122540[0:Obv:122521.2] || subclass(u,v) subclass(u,complement(v))* -> subclass(u,w)*.
% 299.82/300.44  126092[0:Res:28321.1,16.0] || subclass(rest_relation,flip(cross_product(u,v)))* -> member(ordered_pair(w,x),u)*.
% 299.82/300.44  3527[0:Res:1499.1,159.0] || subclass(universal_class,omega) -> equal(integer_of(ordered_pair(u,v)),ordered_pair(u,v))**.
% 299.82/300.44  3430[0:SpL:161.0,1510.0] || equal(symmetric_difference(u,v),universal_class) -> member(omega,complement(intersection(u,v)))*.
% 299.82/300.44  3433[0:SpL:31.0,1510.0] || equal(restrict(u,v,w),universal_class)** -> member(omega,cross_product(v,w))*.
% 299.82/300.44  119663[0:Res:114897.1,6045.0] || equal(u,universal_class) subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  141737[2:MRR:110957.3,120469.0] || member(u,singleton(v))* member(u,w)* -> member(v,w)*.
% 299.82/300.44  142592[2:Rew:113504.0,142437.1] ||  -> member(u,v) equal(symmetric_difference(v,singleton(u)),union(v,singleton(u)))**.
% 299.82/300.44  142594[2:Rew:113504.0,142438.1] ||  -> member(u,v) equal(symmetric_difference(singleton(u),v),union(singleton(u),v))**.
% 299.82/300.44  143596[2:Rew:142543.0,143595.0] ||  -> equal(symmetric_difference(complement(intersection(u,universal_class)),universal_class),symmetric_difference(universal_class,symmetric_difference(u,universal_class)))**.
% 299.82/300.44  152915[0:Res:1506.1,9332.1] || equal(intersection(u,v),universal_class) member(omega,symmetric_difference(u,v))* -> .
% 299.82/300.44  155789[3:Res:3907.1,141576.1] || equal(complement(complement(complement(kind_1_ordinals))),universal_class)** member(singleton(u),ordinal_numbers)* -> .
% 299.82/300.44  157617[0:Res:9424.0,1322.1] inductive(restrict(omega,u,v)) ||  -> equal(restrict(omega,u,v),omega)**.
% 299.82/300.44  157625[0:Res:6219.1,1322.1] inductive(singleton(u)) || member(u,omega)* -> equal(singleton(u),omega).
% 299.82/300.44  159340[6:Res:148538.1,6045.0] || subclass(domain_relation,u)* subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  160016[3:Rew:160012.1,155824.0] || member(least(element_relation,kind_1_ordinals),ordinal_numbers) subclass(kind_1_ordinals,intersection(y__dfg,ordinal_numbers))* -> .
% 299.82/300.44  163040[10:Rew:160202.0,158623.0] ||  -> equal(intersection(power_class(symmetric_difference(universal_class,u)),image(element_relation,union(u,successor_relation))),successor_relation)**.
% 299.82/300.44  163036[10:Rew:160202.0,158555.0] ||  -> equal(intersection(image(element_relation,union(u,successor_relation)),power_class(symmetric_difference(universal_class,u))),successor_relation)**.
% 299.82/300.44  162758[10:Rew:160202.0,153080.0] ||  -> equal(integer_of(image(u,singleton(v))),successor_relation)** member(apply(u,v),universal_class).
% 299.82/300.44  163291[10:Rew:160202.0,161746.1] || member(not_subclass_element(element_relation,successor_relation),complement(compose(element_relation,universal_class)))* -> subclass(element_relation,successor_relation).
% 299.82/300.44  161633[10:Rew:160202.0,153151.1] inductive(domain_of(restrict(u,v,identity_relation))) || section(u,successor_relation,v)* -> .
% 299.82/300.44  165543[10:Res:134.1,160358.1] inductive(domain_of(restrict(u,v,successor_relation))) || section(u,successor_relation,v)* -> .
% 299.82/300.44  161628[10:Rew:160202.0,147761.0] ||  -> equal(intersection(symmetric_difference(complement(u),complement(v)),complement(union(u,v))),successor_relation)**.
% 299.82/300.44  161627[10:Rew:160202.0,147648.0] ||  -> equal(intersection(complement(union(u,v)),symmetric_difference(complement(u),complement(v))),successor_relation)**.
% 299.82/300.44  161626[10:Rew:160202.0,147588.1] inductive(cantor(inverse(cross_product(u,universal_class)))) ||  -> member(successor_relation,image(universal_class,u))*.
% 299.82/300.44  161625[10:Rew:160202.0,147517.0] ||  -> equal(intersection(power_class(image(element_relation,complement(u))),image(element_relation,power_class(u))),successor_relation)**.
% 299.82/300.44  161624[10:Rew:160202.0,147491.0] ||  -> equal(intersection(image(element_relation,power_class(u)),power_class(image(element_relation,complement(u)))),successor_relation)**.
% 299.82/300.44  161623[10:Rew:160202.0,147462.0] ||  -> equal(first(not_subclass_element(cross_product(u,singleton(v)),successor_relation)),domain__dfg(universal_class,u,v))**.
% 299.82/300.44  161622[10:Rew:160202.0,147461.0] ||  -> equal(second(not_subclass_element(cross_product(singleton(u),v),successor_relation)),range__dfg(universal_class,u,v))**.
% 299.82/300.44  161617[10:Rew:160202.0,147418.1] || member(regular(symmetric_difference(universal_class,u)),u)* -> equal(symmetric_difference(universal_class,u),successor_relation).
% 299.82/300.44  161618[10:Rew:160202.0,147417.0] ||  -> equal(symmetric_difference(universal_class,u),successor_relation) member(regular(symmetric_difference(universal_class,u)),complement(u))*.
% 299.82/300.44  161615[10:Rew:160202.0,147328.1] ||  -> member(u,cross_product(v,w)) equal(restrict(singleton(u),v,w),successor_relation)**.
% 299.82/300.44  161613[10:Rew:160202.0,147215.1] || equal(u,v) -> equal(unordered_pair(v,u),successor_relation)** member(v,universal_class).
% 299.82/300.44  163289[10:Rew:160202.0,161606.0] || subclass(regular(cross_product(u,v)),successor_relation)* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.44  163288[10:Rew:160202.0,161517.1] || equal(regular(cross_product(u,v)),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.44  161512[10:Rew:160202.0,146665.0] ||  -> equal(singleton(image(u,singleton(v))),successor_relation)** member(apply(u,v),universal_class).
% 299.82/300.44  161511[10:Rew:160202.0,146664.1] || well_ordering(u,v)* -> equal(segment(u,successor_relation,least(u,successor_relation)),successor_relation)**.
% 299.82/300.44  161506[10:Rew:160202.0,146654.1] || subclass(power_class(u),image(element_relation,complement(u)))* -> equal(power_class(u),successor_relation).
% 299.82/300.44  161653[10:Rew:160202.0,156025.0] ||  -> subclass(symmetric_difference(complement(u),union(v,successor_relation)),union(u,symmetric_difference(universal_class,v)))*.
% 299.82/300.44  161646[10:Rew:160202.0,155780.0] || member(u,union(v,successor_relation)) -> member(u,symmetric_difference(complement(v),universal_class))*.
% 299.82/300.44  161648[10:Rew:160202.0,148465.1] || member(u,symmetric_difference(complement(v),universal_class))* -> member(u,union(v,successor_relation)).
% 299.82/300.44  161649[10:Rew:160202.0,148464.1] || member(u,symmetric_difference(universal_class,v))* member(u,union(v,successor_relation)) -> .
% 299.82/300.44  161459[10:Rew:160202.0,153207.1] || equal(intersection(u,v),universal_class) member(successor_relation,symmetric_difference(u,v))* -> .
% 299.82/300.44  161443[10:Rew:160202.0,146633.1] || equal(singleton(u),v)* -> equal(v,successor_relation) equal(regular(v),u)*.
% 299.82/300.44  161422[10:Rew:160202.0,153211.1] || equal(restrict(u,v,w),universal_class)** -> member(successor_relation,cross_product(v,w))*.
% 299.82/300.44  161407[10:Rew:160202.0,159616.1] inductive(complement(complement(intersection(inverse(u),universal_class)))) ||  -> member(successor_relation,inverse(u))*.
% 299.82/300.44  161404[10:Rew:160202.0,159644.1] inductive(complement(complement(intersection(sum_class(u),universal_class)))) ||  -> member(successor_relation,sum_class(u))*.
% 299.82/300.44  161413[10:Rew:160202.0,153222.1] || equal(image(element_relation,complement(u)),universal_class)** member(successor_relation,power_class(u)) -> .
% 299.82/300.44  161385[10:Rew:160202.0,147225.1] inductive(symmetric_difference(domain_of(u),cantor(u))) ||  -> member(successor_relation,complement(cantor(u)))*.
% 299.82/300.44  163286[10:Rew:160202.0,161369.0] ||  -> member(successor_relation,intersection(complement(u),complement(v)))* member(successor_relation,union(u,v)).
% 299.82/300.44  161376[10:Rew:160202.0,146590.1] inductive(symmetric_difference(complement(u),complement(v))) ||  -> member(successor_relation,union(u,v))*.
% 299.82/300.44  161346[10:Rew:160202.0,146579.1] inductive(symmetric_difference(complement(u),complement(inverse(u)))) ||  -> member(successor_relation,symmetrization_of(u))*.
% 299.82/300.44  161341[10:Rew:160202.0,146578.1] inductive(symmetric_difference(complement(u),complement(singleton(u)))) ||  -> member(successor_relation,successor(u))*.
% 299.82/300.44  161285[10:Rew:160202.0,146735.0] ||  -> equal(intersection(singleton(u),v),successor_relation) member(u,intersection(singleton(u),v))*.
% 299.82/300.44  161278[10:Rew:160202.0,146721.0] ||  -> equal(intersection(u,singleton(v)),successor_relation) member(v,intersection(u,singleton(v)))*.
% 299.82/300.44  161269[10:Rew:160202.0,153537.0] || equal(complement(u),successor_relation) member(v,universal_class)* -> member(v,u)*.
% 299.82/300.44  161266[10:Rew:160202.0,147260.1] inductive(restrict(cantor(inverse(u)),v,w)) ||  -> member(successor_relation,range_of(u))*.
% 299.82/300.44  161216[10:Rew:160202.0,156044.1] || subclass(universal_class,symmetric_difference(universal_class,u))* subclass(universal_class,union(u,successor_relation)) -> .
% 299.82/300.44  161214[10:Rew:160202.0,155999.0] ||  -> subclass(symmetric_difference(union(u,successor_relation),complement(v)),union(symmetric_difference(universal_class,u),v))*.
% 299.82/300.44  161198[10:Rew:160202.0,155784.0] ||  -> equal(symmetric_difference(universal_class,symmetric_difference(complement(u),universal_class)),symmetric_difference(union(u,successor_relation),universal_class))**.
% 299.82/300.44  161218[10:Rew:160202.0,156045.1] || equal(symmetric_difference(universal_class,u),universal_class)** equal(union(u,successor_relation),universal_class) -> .
% 299.82/300.44  161213[10:Rew:160202.0,158380.0] ||  -> equal(symmetric_difference(power_class(symmetric_difference(universal_class,u)),image(element_relation,union(u,successor_relation))),universal_class)**.
% 299.82/300.44  161212[10:Rew:160202.0,158343.0] ||  -> equal(symmetric_difference(image(element_relation,union(u,successor_relation)),power_class(symmetric_difference(universal_class,u))),universal_class)**.
% 299.82/300.44  161202[10:Rew:160202.0,158311.0] || equal(complement(union(u,successor_relation)),universal_class) -> member(omega,symmetric_difference(universal_class,u))*.
% 299.82/300.44  160821[10:Rew:160202.0,146401.1] || subclass(singleton(u),v)* -> equal(singleton(u),successor_relation) member(u,v).
% 299.82/300.44  160866[10:Rew:160202.0,152639.0] ||  -> member(not_subclass_element(u,power_class(universal_class)),image(element_relation,successor_relation))* subclass(u,power_class(universal_class)).
% 299.82/300.44  160858[10:Rew:160202.0,152616.1] || subclass(universal_class,power_class(universal_class)) member(singleton(u),image(element_relation,successor_relation))* -> .
% 299.82/300.44  163266[10:Rew:160202.0,160838.1] || member(regular(power_class(universal_class)),image(element_relation,successor_relation))* -> equal(power_class(universal_class),successor_relation).
% 299.82/300.44  160834[10:Rew:160202.0,148325.0] ||  -> equal(complement(intersection(complement(u),power_class(universal_class))),union(u,image(element_relation,successor_relation)))**.
% 299.82/300.44  160830[10:Rew:160202.0,148324.0] ||  -> equal(complement(intersection(power_class(universal_class),complement(u))),union(image(element_relation,successor_relation),u))**.
% 299.82/300.44  160509[10:Rew:160202.0,153401.0] || equal(successor_relation,u) member(u,ordinal_numbers)* -> equal(sum_class(u),u).
% 299.82/300.44  160702[10:Rew:160202.0,159701.2] || equal(regular(u),universal_class) member(omega,u)* -> equal(u,successor_relation).
% 299.82/300.44  160803[10:Rew:160202.0,146541.1] || member(u,universal_class) -> equal(u,successor_relation) member(apply(choice,u),universal_class)*.
% 299.82/300.44  162959[10:Rew:160202.0,157627.1] inductive(singleton(u)) ||  -> equal(integer_of(u),successor_relation)** equal(singleton(u),omega).
% 299.82/300.44  163261[10:Rew:160202.0,160547.2] || equal(regular(u),universal_class) member(successor_relation,u)* -> equal(u,successor_relation).
% 299.82/300.44  160561[10:Rew:160202.0,156185.2] || subclass(complement(u),v)* well_ordering(universal_class,v) -> member(successor_relation,u).
% 299.82/300.44  168547[11:Res:168384.1,10254.0] || equal(symmetric_difference(u,singleton(u)),symmetrization_of(successor_relation))** -> member(successor_relation,successor(u)).
% 299.82/300.44  168546[11:Res:168384.1,10191.0] || equal(symmetric_difference(u,inverse(u)),symmetrization_of(successor_relation))** -> member(successor_relation,symmetrization_of(u)).
% 299.82/300.44  168545[11:Res:168384.1,1952.0] || equal(symmetric_difference(u,v),symmetrization_of(successor_relation)) -> member(successor_relation,union(u,v))*.
% 299.82/300.44  168537[11:Res:168384.1,148657.1] || equal(complement(compose(element_relation,universal_class)),symmetrization_of(successor_relation))** member(successor_relation,element_relation) -> .
% 299.82/300.44  168533[11:Res:168384.1,3.0] || equal(u,symmetrization_of(successor_relation)) subclass(u,v)* -> member(successor_relation,v).
% 299.82/300.44  161150[10:Rew:160202.0,150399.0] ||  -> equal(complement(intersection(symmetrization_of(successor_relation),complement(u))),union(complement(inverse(successor_relation)),u))**.
% 299.82/300.44  161146[10:Rew:160202.0,150389.0] ||  -> equal(complement(intersection(complement(u),symmetrization_of(successor_relation))),union(u,complement(inverse(successor_relation))))**.
% 299.82/300.44  163273[10:Rew:160202.0,161116.0] ||  -> member(not_subclass_element(u,symmetrization_of(successor_relation)),complement(inverse(successor_relation)))* subclass(u,symmetrization_of(successor_relation)).
% 299.82/300.44  168467[11:MRR:163435.1,168458.0] || well_ordering(u,inverse(successor_relation)) -> member(least(u,symmetrization_of(successor_relation)),symmetrization_of(successor_relation))*.
% 299.82/300.44  163272[10:Rew:160202.0,161114.1] || subclass(universal_class,symmetrization_of(successor_relation)) member(singleton(u),complement(inverse(successor_relation)))* -> .
% 299.82/300.44  163271[10:Rew:160202.0,161051.1] ||  -> member(not_subclass_element(u,power_class(successor_relation)),image(element_relation,universal_class))* subclass(u,power_class(successor_relation)).
% 299.82/300.44  163269[10:Rew:160202.0,160969.1] || member(regular(power_class(successor_relation)),image(element_relation,universal_class))* -> equal(power_class(successor_relation),successor_relation).
% 299.82/300.44  160939[10:Rew:160202.0,150100.0] ||  -> subclass(complement(union(u,image(element_relation,universal_class))),intersection(complement(u),power_class(successor_relation)))*.
% 299.82/300.44  160938[10:Rew:160202.0,148441.0] ||  -> equal(complement(intersection(complement(u),power_class(successor_relation))),union(u,image(element_relation,universal_class)))**.
% 299.82/300.44  160908[10:Rew:160202.0,150102.0] ||  -> subclass(complement(union(image(element_relation,universal_class),u)),intersection(power_class(successor_relation),complement(u)))*.
% 299.82/300.44  160907[10:Rew:160202.0,148440.0] ||  -> equal(complement(intersection(power_class(successor_relation),complement(u))),union(image(element_relation,universal_class),u))**.
% 299.82/300.44  160998[10:Rew:160202.0,150101.0] || subclass(universal_class,power_class(successor_relation)) member(singleton(u),image(element_relation,universal_class))* -> .
% 299.82/300.44  163300[10:Rew:160202.0,163103.0] || equal(compose(u,successor_relation),successor_relation) -> member(ordered_pair(successor_relation,successor_relation),compose_class(u))*.
% 299.82/300.44  163086[10:Rew:160202.0,159374.1] || subclass(domain_relation,omega) -> equal(integer_of(ordered_pair(successor_relation,successor_relation)),ordered_pair(successor_relation,successor_relation))**.
% 299.82/300.44  163073[10:Rew:160202.0,159354.1] || subclass(domain_relation,restrict(u,v,w))* -> member(ordered_pair(successor_relation,successor_relation),u).
% 299.82/300.44  163299[10:Rew:160202.0,162932.1] || equal(complement(compose(element_relation,universal_class)),successor(successor_relation))** member(successor_relation,element_relation) -> .
% 299.82/300.44  162903[10:Rew:160202.0,150394.0] ||  -> equal(complement(intersection(complement(u),successor(successor_relation))),union(u,complement(singleton(successor_relation))))**.
% 299.82/300.44  162901[10:Rew:160202.0,150409.0] ||  -> equal(complement(intersection(successor(successor_relation),complement(u))),union(complement(singleton(successor_relation)),u))**.
% 299.82/300.44  163297[10:Rew:160202.0,162900.1] ||  -> member(not_subclass_element(u,successor(successor_relation)),complement(singleton(successor_relation)))* subclass(u,successor(successor_relation)).
% 299.82/300.44  163284[10:Rew:160202.0,161364.0] || equal(symmetric_difference(u,v),successor(successor_relation)) -> member(successor_relation,union(u,v))*.
% 299.82/300.44  163282[10:Rew:160202.0,161343.0] || equal(symmetric_difference(u,inverse(u)),successor(successor_relation))** -> member(successor_relation,symmetrization_of(u)).
% 299.82/300.44  163280[10:Rew:160202.0,161338.0] || equal(symmetric_difference(u,singleton(u)),successor(successor_relation))** -> member(successor_relation,successor(u)).
% 299.82/300.44  163277[10:Rew:160202.0,161236.0] || equal(u,successor(successor_relation)) subclass(u,v)* -> member(successor_relation,v).
% 299.82/300.44  163296[10:Rew:160202.0,162877.1] || equal(complement(compose(element_relation,universal_class)),singleton(successor_relation))** member(successor_relation,element_relation) -> .
% 299.82/300.44  163295[10:Rew:160202.0,162856.1] || well_ordering(u,singleton(successor_relation)) -> member(least(u,successor(successor_relation)),successor(successor_relation))*.
% 299.82/300.44  163285[10:Rew:160202.0,161368.0] || equal(symmetric_difference(u,v),singleton(successor_relation)) -> member(successor_relation,union(u,v))*.
% 299.82/300.44  163283[10:Rew:160202.0,161344.0] || equal(symmetric_difference(u,inverse(u)),singleton(successor_relation))** -> member(successor_relation,symmetrization_of(u)).
% 299.82/300.44  163281[10:Rew:160202.0,161339.0] || equal(symmetric_difference(u,singleton(u)),singleton(successor_relation))** -> member(successor_relation,successor(u)).
% 299.82/300.44  163278[10:Rew:160202.0,161239.0] || equal(u,singleton(successor_relation)) subclass(u,v)* -> member(successor_relation,v).
% 299.82/300.44  162772[10:Rew:160202.0,146222.2] || member(u,universal_class) -> member(u,kind_1_ordinals) member(u,complement(singleton(successor_relation)))*.
% 299.82/300.44  157892[6:Res:114897.1,148657.1] || equal(complement(compose(element_relation,universal_class)),universal_class)** member(singleton(u),element_relation)* -> .
% 299.82/300.44  157894[6:Res:1477.1,148657.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(singleton(u),element_relation)* -> .
% 299.82/300.44  3600[0:SpL:57.0,3565.0] || equal(complement(power_class(u)),universal_class) -> member(omega,image(element_relation,complement(u)))*.
% 299.82/300.44  3421[0:SpL:57.0,3358.1] || equal(image(element_relation,complement(u)),universal_class)** equal(power_class(u),universal_class) -> .
% 299.82/300.44  152930[0:Res:1506.1,307.0] || equal(image(element_relation,complement(u)),universal_class)** member(omega,power_class(u)) -> .
% 299.82/300.44  30574[0:SpL:57.0,30433.1] || subclass(universal_class,image(element_relation,complement(u)))* subclass(universal_class,power_class(u)) -> .
% 299.82/300.44  125133[0:Obv:125127.1] || subclass(u,complement(power_class(v))) -> subclass(u,image(element_relation,complement(v)))*.
% 299.82/300.44  145343[2:SpR:208.0,142420.0] ||  -> equal(symmetric_difference(power_class(image(element_relation,complement(u))),image(element_relation,power_class(u))),universal_class)**.
% 299.82/300.44  145211[2:SpR:208.0,142419.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(u)),power_class(image(element_relation,complement(u)))),universal_class)**.
% 299.82/300.44  142425[2:Rew:142341.0,140212.0] ||  -> equal(union(power_class(image(element_relation,complement(u))),image(element_relation,power_class(u))),universal_class)**.
% 299.82/300.44  142424[2:Rew:142341.0,139750.0] ||  -> equal(union(image(element_relation,power_class(u)),power_class(image(element_relation,complement(u)))),universal_class)**.
% 299.82/300.44  115608[0:SpR:208.0,114856.0] ||  -> subclass(symmetric_difference(universal_class,image(element_relation,power_class(u))),power_class(image(element_relation,complement(u))))*.
% 299.82/300.44  9094[0:Res:9089.1,3.0] function(u) || subclass(universal_class,v) -> member(apply(u,w),v)*.
% 299.82/300.44  101894[0:SoR:5762.0,73.1] one_to_one(sum_class(cross_product(universal_class,universal_class))) ||  -> section(element_relation,cross_product(universal_class,universal_class),universal_class)*.
% 299.82/300.44  143757[0:Res:3907.1,159.0] || equal(complement(complement(omega)),universal_class) -> equal(integer_of(singleton(u)),singleton(u))**.
% 299.82/300.44  155728[2:SpL:142543.0,3487.0] || subclass(universal_class,symmetric_difference(universal_class,u)) -> member(unordered_pair(v,w),complement(u))*.
% 299.82/300.44  122550[0:MRR:122504.0,34189.1] || subclass(u,complement(unordered_pair(not_subclass_element(u,v),w)))* -> subclass(u,v).
% 299.82/300.44  112359[0:MRR:112358.1,13.0] || equal(u,ordered_pair(v,w)) -> member(unordered_pair(v,singleton(w)),u)*.
% 299.82/300.44  108559[0:Res:8.1,3492.0] || equal(restrict(u,v,w),universal_class)** -> member(unordered_pair(x,y),u)*.
% 299.82/300.44  122549[0:MRR:122503.0,34189.1] || subclass(u,complement(unordered_pair(v,not_subclass_element(u,w))))* -> subclass(u,w).
% 299.82/300.44  89267[0:Res:51387.0,2151.0] ||  -> subclass(u,complement(singleton(v))) equal(not_subclass_element(u,complement(singleton(v))),v)**.
% 299.82/300.44  143080[0:Res:53.1,9649.0] inductive(singleton(u)) ||  -> subclass(omega,v) equal(not_subclass_element(omega,v),u)*.
% 299.82/300.44  35387[0:Res:34189.1,3.0] || subclass(universal_class,u) -> subclass(v,w) member(not_subclass_element(v,w),u)*.
% 299.82/300.44  122749[0:Res:120366.1,3.0] || member(u,universal_class) subclass(universal_class,v) -> member(rest_of(u),v)*.
% 299.82/300.44  112582[0:SpR:115.0,30984.1] || member(u,universal_class) -> member(u,symmetrization_of(v))* member(u,complement(v)).
% 299.82/300.44  112586[0:SpR:45.0,30984.1] || member(u,universal_class) -> member(u,successor(v)) member(u,complement(v))*.
% 299.82/300.44  160064[3:Res:159952.1,1486.1] || subclass(singleton(u),ordinal_numbers)* member(u,universal_class) -> member(u,kind_1_ordinals).
% 299.82/300.44  108023[0:Res:8.1,1486.1] || equal(u,singleton(v)) member(v,universal_class)* -> member(v,u)*.
% 299.82/300.44  179991[11:Res:179843.1,3.0] || equal(u,inverse(successor_relation)) subclass(u,v)* -> member(successor_relation,v).
% 299.82/300.44  180002[11:Res:179843.1,1952.0] || equal(symmetric_difference(u,v),inverse(successor_relation)) -> member(successor_relation,union(u,v))*.
% 299.82/300.44  180003[11:Res:179843.1,10191.0] || equal(symmetric_difference(u,inverse(u)),inverse(successor_relation))** -> member(successor_relation,symmetrization_of(u)).
% 299.82/300.44  180004[11:Res:179843.1,10254.0] || equal(symmetric_difference(u,singleton(u)),inverse(successor_relation))** -> member(successor_relation,successor(u)).
% 299.82/300.44  180891[11:Res:179843.1,148657.1] || equal(complement(compose(element_relation,universal_class)),inverse(successor_relation))** member(successor_relation,element_relation) -> .
% 299.82/300.44  181085[10:SpR:181056.0,160359.0] ||  -> equal(second(not_subclass_element(restrict(u,successor_relation,v),successor_relation)),range__dfg(u,universal_class,v))**.
% 299.82/300.44  181087[10:SpR:181056.0,160350.0] ||  -> equal(first(not_subclass_element(restrict(u,v,successor_relation),successor_relation)),domain__dfg(u,v,universal_class))**.
% 299.82/300.44  181135[10:Rew:181056.0,181096.1] || member(singleton(singleton(successor_relation)),compose_class(u))* -> equal(compose(u,successor_relation),universal_class).
% 299.82/300.44  181495[10:MRR:181450.2,160227.0] || member(u,complement(complement(v))) member(u,symmetric_difference(universal_class,v))* -> .
% 299.82/300.44  181531[10:MRR:181513.2,160227.0] || member(u,successor(successor_relation)) member(u,symmetric_difference(universal_class,singleton(successor_relation)))* -> .
% 299.82/300.44  181606[10:MRR:181588.2,160227.0] || member(u,symmetrization_of(successor_relation)) member(u,symmetric_difference(universal_class,inverse(successor_relation)))* -> .
% 299.82/300.44  182347[10:SpL:160367.0,160544.0] || equal(complement(union(u,successor_relation)),universal_class) -> member(successor_relation,symmetric_difference(universal_class,u))*.
% 299.82/300.44  182350[10:SpL:57.0,160544.0] || equal(complement(power_class(u)),universal_class) -> member(successor_relation,image(element_relation,complement(u)))*.
% 299.82/300.44  183138[10:SpR:181044.1,45.0] || member(u,universal_class) -> equal(union(successor(u),successor_relation),successor(successor(u)))**.
% 299.82/300.44  183206[10:Rew:181082.0,183158.1] || member(u,universal_class) -> equal(apply(v,successor(u)),apply(v,universal_class))**.
% 299.82/300.44  183208[10:Rew:181083.0,183159.1] || member(u,universal_class) -> equal(ordered_pair(v,successor(u)),ordered_pair(v,universal_class))**.
% 299.82/300.44  183386[0:SpR:57.0,139600.0] ||  -> equal(intersection(image(element_relation,complement(u)),complement(power_class(u))),complement(power_class(u)))**.
% 299.82/300.44  183406[0:SpL:139600.0,175.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),complement(complement(intersection(y__dfg,ordinal_numbers))))* -> .
% 299.82/300.44  183450[10:SpR:28.0,183420.0] ||  -> equal(symmetric_difference(intersection(complement(u),complement(v)),complement(union(u,v))),successor_relation)**.
% 299.82/300.44  183806[10:Res:3907.1,183622.0] || equal(complement(complement(successor(successor_relation))),universal_class) -> member(singleton(u),singleton(successor_relation))*.
% 299.82/300.44  183837[10:MRR:183813.1,160455.0] || member(successor(successor_relation),universal_class) -> member(apply(choice,successor(successor_relation)),singleton(successor_relation))*.
% 299.82/300.44  183839[10:Res:3907.1,183723.0] || equal(complement(complement(symmetrization_of(successor_relation))),universal_class) -> member(singleton(u),inverse(successor_relation))*.
% 299.82/300.44  183868[11:MRR:183846.1,168458.0] || member(symmetrization_of(successor_relation),universal_class) -> member(apply(choice,symmetrization_of(successor_relation)),inverse(successor_relation))*.
% 299.82/300.44  183920[11:Res:183764.1,595.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(symmetrization_of(successor_relation)),u).
% 299.82/300.44  183934[11:Res:183764.1,159.0] || subclass(universal_class,omega) -> equal(integer_of(regular(symmetrization_of(successor_relation))),regular(symmetrization_of(successor_relation)))**.
% 299.82/300.44  184164[10:Res:149759.0,160435.1] inductive(intersection(u,intersection(inverse(v),universal_class))) ||  -> member(successor_relation,inverse(v))*.
% 299.82/300.44  184183[10:Res:149775.0,160435.1] inductive(intersection(intersection(inverse(u),universal_class),v)) ||  -> member(successor_relation,inverse(u))*.
% 299.82/300.44  184395[10:SpR:163197.1,30.0] || subclass(cross_product(u,v),successor_relation)* -> equal(restrict(w,u,v),successor_relation)**.
% 299.82/300.44  184559[10:MRR:184558.2,184558.4,160215.0,160227.0] || subclass(u,successor_relation)* member(v,u)* well_ordering(w,x)* -> .
% 299.82/300.44  184640[10:SpR:163198.1,161.0] || subclass(complement(intersection(u,v)),successor_relation)* -> equal(symmetric_difference(u,v),successor_relation).
% 299.82/300.44  184943[10:SpR:160367.0,184676.1] || subclass(symmetric_difference(universal_class,u),successor_relation)* -> equal(complement(union(u,successor_relation)),successor_relation).
% 299.82/300.44  184946[10:SpR:57.0,184676.1] || subclass(image(element_relation,complement(u)),successor_relation)* -> equal(complement(power_class(u)),successor_relation).
% 299.82/300.44  185369[10:SpR:185302.1,10292.0] || equal(successor_relation,u) -> subclass(symmetric_difference(universal_class,complement(inverse(u))),symmetrization_of(u))*.
% 299.82/300.44  185371[10:SpR:185302.1,10293.0] || equal(successor_relation,u) -> subclass(symmetric_difference(universal_class,complement(singleton(u))),successor(u))*.
% 299.82/300.44  185385[10:SpR:185302.1,160470.0] || equal(successor_relation,u) -> equal(intersection(power_class(u),image(element_relation,universal_class)),successor_relation)**.
% 299.82/300.44  185386[10:SpR:185302.1,160469.0] || equal(successor_relation,u) -> equal(intersection(image(element_relation,universal_class),power_class(u)),successor_relation)**.
% 299.82/300.44  185387[10:SpR:185302.1,142477.0] || equal(successor_relation,u) -> equal(symmetric_difference(power_class(u),image(element_relation,universal_class)),universal_class)**.
% 299.82/300.44  185388[10:SpR:185302.1,142475.0] || equal(successor_relation,u) -> equal(symmetric_difference(image(element_relation,universal_class),power_class(u)),universal_class)**.
% 299.82/300.44  185400[10:SpR:185302.1,9898.0] || equal(successor_relation,u) -> subclass(symmetric_difference(complement(v),universal_class),union(v,u))*.
% 299.82/300.44  185419[10:SpR:185302.1,10293.0] || equal(singleton(u),successor_relation) -> subclass(symmetric_difference(complement(u),universal_class),successor(u))*.
% 299.82/300.44  185443[10:SpR:185302.1,10292.0] || equal(inverse(u),successor_relation) -> subclass(symmetric_difference(complement(u),universal_class),symmetrization_of(u))*.
% 299.82/300.44  185934[10:Res:185646.1,3.0] || equal(complement(u),successor_relation) subclass(u,v)* -> member(successor_relation,v).
% 299.82/300.44  185938[10:Res:185646.1,148657.1] || equal(complement(complement(compose(element_relation,universal_class))),successor_relation)** member(successor_relation,element_relation) -> .
% 299.82/300.44  185946[10:Res:185646.1,1952.0] || equal(complement(symmetric_difference(u,v)),successor_relation) -> member(successor_relation,union(u,v))*.
% 299.82/300.44  185947[10:Res:185646.1,10191.0] || equal(complement(symmetric_difference(u,inverse(u))),successor_relation)** -> member(successor_relation,symmetrization_of(u)).
% 299.82/300.44  185948[10:Res:185646.1,10254.0] || equal(complement(symmetric_difference(u,singleton(u))),successor_relation)** -> member(successor_relation,successor(u)).
% 299.82/300.44  185980[10:Rew:28.0,185942.0] || equal(union(u,v),successor_relation) member(successor_relation,union(u,v))* -> .
% 299.82/300.44  186008[10:Res:185647.1,3.0] || equal(complement(u),successor_relation) subclass(u,v)* -> member(omega,v).
% 299.82/300.44  186012[10:Res:185647.1,148657.1] || equal(complement(complement(compose(element_relation,universal_class))),successor_relation)** member(omega,element_relation) -> .
% 299.82/300.44  186020[10:Res:185647.1,1952.0] || equal(complement(symmetric_difference(u,v)),successor_relation) -> member(omega,union(u,v))*.
% 299.82/300.44  186021[10:Res:185647.1,10191.0] || equal(complement(symmetric_difference(u,inverse(u))),successor_relation)** -> member(omega,symmetrization_of(u)).
% 299.82/300.44  186022[10:Res:185647.1,10254.0] || equal(complement(symmetric_difference(u,singleton(u))),successor_relation)** -> member(omega,successor(u)).
% 299.82/300.44  186046[10:Rew:28.0,186016.0] || equal(union(u,v),successor_relation) member(omega,union(u,v))* -> .
% 299.82/300.44  186143[10:Res:1495.2,185639.1] || member(u,universal_class)* subclass(rest_relation,v)* equal(successor_relation,v) -> .
% 299.82/300.44  186469[10:SpR:185605.1,160331.0] || equal(successor_relation,u) -> equal(union(power_class(u),image(element_relation,universal_class)),universal_class)**.
% 299.82/300.44  186470[10:SpR:185605.1,160330.0] || equal(successor_relation,u) -> equal(union(image(element_relation,universal_class),power_class(u)),universal_class)**.
% 299.82/300.44  186491[10:SpL:185605.1,185596.0] || equal(successor_relation,u) member(regular(image(element_relation,universal_class)),power_class(u))* -> .
% 299.82/300.44  186522[10:MRR:186455.1,160214.0] || equal(successor_relation,u) subclass(universal_class,v) -> member(power_class(u),v)*.
% 299.82/300.44  161645[10:Rew:160202.0,148456.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,successor_relation) -> .
% 299.82/300.44  108792[2:Res:31076.2,34067.0] inductive(u) || well_ordering(v,u) -> member(least(v,u),universal_class)*.
% 299.82/300.44  108239[2:Res:31069.2,34067.0] inductive(u) || well_ordering(v,universal_class) -> member(least(v,u),universal_class)*.
% 299.82/300.44  161444[10:Rew:160202.0,146632.1] || well_ordering(u,v) -> equal(v,successor_relation) member(least(u,v),universal_class)*.
% 299.82/300.44  161442[10:Rew:160202.0,146636.1] || well_ordering(u,universal_class) -> equal(v,successor_relation) member(least(u,v),universal_class)*.
% 299.82/300.44  163119[10:Rew:160202.0,159960.1] || well_ordering(u,kind_1_ordinals) -> equal(segment(u,ordinal_numbers,least(u,ordinal_numbers)),successor_relation)**.
% 299.82/300.44  184597[10:Res:184565.1,6045.0] || well_ordering(u,kind_1_ordinals)* subclass(ordinal_numbers,v) well_ordering(universal_class,v)* -> .
% 299.82/300.44  143797[4:MRR:143772.1,3094.0] || well_ordering(u,omega) -> equal(integer_of(least(u,omega)),least(u,omega))**.
% 299.82/300.44  184567[10:MRR:163381.2,184560.0] || connected(element_relation,successor_relation)* equal(sum_class(successor_relation),successor_relation) -> member(successor_relation,ordinal_numbers).
% 299.82/300.44  184568[10:MRR:163378.2,184560.0] || equal(successor(successor_relation),ordinal_numbers) well_ordering(element_relation,successor_relation)* -> member(successor_relation,ordinal_numbers).
% 299.82/300.44  184569[10:MRR:163379.2,184560.0] || equal(singleton(successor_relation),ordinal_numbers) well_ordering(element_relation,successor_relation)* -> member(successor_relation,ordinal_numbers).
% 299.82/300.44  184570[11:MRR:180761.2,184560.0] || equal(inverse(successor_relation),ordinal_numbers) well_ordering(element_relation,successor_relation)* -> member(successor_relation,ordinal_numbers).
% 299.82/300.44  187564[16:MRR:161940.1,187561.0] || subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),u)* -> member(regular(composition_function),u).
% 299.82/300.44  187766[10:Res:187500.1,3.0] || subclass(universal_class,u)* subclass(u,v)* -> member(power_class(successor_relation),v)*.
% 299.82/300.44  187770[10:Res:187500.1,148657.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(power_class(successor_relation),element_relation) -> .
% 299.82/300.44  187778[10:Res:187500.1,1952.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(power_class(successor_relation),union(u,v))*.
% 299.82/300.44  187779[10:Res:187500.1,10191.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(power_class(successor_relation),symmetrization_of(u)).
% 299.82/300.44  187780[10:Res:187500.1,10254.0] || subclass(universal_class,symmetric_difference(u,singleton(u)))* -> member(power_class(successor_relation),successor(u)).
% 299.82/300.44  188423[10:SpR:188178.1,3587.0] || equal(singleton(apply(choice,omega)),successor_relation)** -> equal(apply(choice,omega),successor_relation).
% 299.82/300.44  188447[10:SpL:161.0,160566.0] || equal(symmetric_difference(u,v),universal_class) -> member(successor_relation,complement(intersection(u,v)))*.
% 299.82/300.44  188529[10:Res:149820.0,160435.1] inductive(intersection(intersection(sum_class(u),universal_class),v)) ||  -> member(successor_relation,sum_class(u))*.
% 299.82/300.44  188572[10:Res:149802.0,160435.1] inductive(intersection(u,intersection(sum_class(v),universal_class))) ||  -> member(successor_relation,sum_class(v))*.
% 299.82/300.44  188853[10:MRR:188838.0,191.0] || subclass(image(element_relation,complement(u)),successor_relation)* -> member(singleton(v),power_class(u))*.
% 299.82/300.44  188927[10:SpR:185607.1,30.0] || equal(cross_product(u,v),successor_relation) -> equal(restrict(w,u,v),successor_relation)**.
% 299.82/300.44  189162[10:SpR:185608.1,161.0] || equal(complement(intersection(u,v)),successor_relation)** -> equal(symmetric_difference(u,v),successor_relation).
% 299.82/300.44  189329[15:SpL:55.0,188793.1] || member(restrict(element_relation,universal_class,u),universal_class)* member(v,sum_class(u))* -> .
% 299.82/300.44  189334[15:SpL:40.0,188793.1] || member(flip(cross_product(u,universal_class)),universal_class)* member(v,inverse(u))* -> .
% 299.82/300.44  191090[20:Res:191074.1,6045.0] || equal(u,omega) subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  191099[20:Res:191074.1,9332.1] || equal(intersection(u,v),omega) member(successor_relation,symmetric_difference(u,v))* -> .
% 299.82/300.44  191103[20:Res:191074.1,594.0] || equal(restrict(u,v,w),omega)** -> member(successor_relation,cross_product(v,w))*.
% 299.82/300.44  191120[20:Res:191074.1,10.0] || equal(unordered_pair(u,v),omega)** -> equal(successor_relation,v) equal(successor_relation,u).
% 299.82/300.44  191121[20:Res:191074.1,307.0] || equal(image(element_relation,complement(u)),omega)** member(successor_relation,power_class(u)) -> .
% 299.82/300.44  191123[20:Res:191074.1,160481.0] || equal(regular(u),omega) member(successor_relation,u)* -> equal(u,successor_relation).
% 299.82/300.44  192120[15:SpR:190721.0,45.0] ||  -> equal(range_of(u),successor_relation) equal(union(inverse(u),successor_relation),successor(inverse(u)))**.
% 299.82/300.44  192215[15:Rew:181082.0,192144.1] ||  -> equal(range_of(u),successor_relation) equal(apply(v,inverse(u)),apply(v,universal_class))**.
% 299.82/300.44  192217[15:Rew:181083.0,192146.1] ||  -> equal(range_of(u),successor_relation) equal(ordered_pair(v,inverse(u)),ordered_pair(v,universal_class))**.
% 299.82/300.44  192469[20:SpL:160367.0,191129.1] || equal(symmetric_difference(universal_class,u),omega)** equal(union(u,successor_relation),universal_class) -> .
% 299.82/300.44  192472[20:SpL:57.0,191129.1] || equal(image(element_relation,complement(u)),omega)** equal(power_class(u),universal_class) -> .
% 299.82/300.44  192489[15:SpR:191620.1,3587.0] || equal(successor(apply(choice,omega)),successor_relation)** -> equal(apply(choice,omega),successor_relation).
% 299.82/300.44  192708[15:SpR:181082.0,191934.1] || member(image(u,successor_relation),universal_class)* -> equal(cantor(apply(u,universal_class)),successor_relation).
% 299.82/300.44  192879[20:SpL:160367.0,192315.1] || equal(symmetric_difference(universal_class,u),omega)** equal(union(u,successor_relation),omega) -> .
% 299.82/300.44  192882[20:SpL:57.0,192315.1] || equal(image(element_relation,complement(u)),omega)** equal(power_class(u),omega) -> .
% 299.82/300.44  192891[20:SpL:160367.0,192321.1] || equal(symmetric_difference(universal_class,u),universal_class)** equal(union(u,successor_relation),omega) -> .
% 299.82/300.44  192894[20:SpL:57.0,192321.1] || equal(image(element_relation,complement(u)),universal_class)** equal(power_class(u),omega) -> .
% 299.82/300.44  192916[20:SpL:160367.0,192323.0] || equal(complement(union(u,successor_relation)),omega) -> member(successor_relation,symmetric_difference(universal_class,u))*.
% 299.82/300.44  192919[20:SpL:57.0,192323.0] || equal(complement(power_class(u)),omega) -> member(successor_relation,image(element_relation,complement(u)))*.
% 299.82/300.44  192939[10:SpL:160367.0,188851.0] || subclass(union(u,successor_relation),successor_relation) -> member(singleton(v),symmetric_difference(universal_class,u))*.
% 299.82/300.44  192942[10:SpL:57.0,188851.0] || subclass(power_class(u),successor_relation) -> member(singleton(v),image(element_relation,complement(u)))*.
% 299.82/300.44  193273[20:SpL:161.0,191100.0] || equal(symmetric_difference(u,v),omega) -> member(successor_relation,complement(intersection(u,v)))*.
% 299.82/300.44  193405[10:Res:192947.1,595.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(singleton(x),u)*.
% 299.82/300.44  193472[15:SpR:183965.0,193148.1] function(recursion(u,successor_relation,successor_relation)) ||  -> equal(cantor(ordinal_add(u,v)),successor_relation)**.
% 299.82/300.44  193592[10:SpR:160367.0,161321.0] ||  -> equal(intersection(restrict(symmetric_difference(universal_class,u),v,w),union(u,successor_relation)),successor_relation)**.
% 299.82/300.44  193595[10:SpR:57.0,161321.0] ||  -> equal(intersection(restrict(image(element_relation,complement(u)),v,w),power_class(u)),successor_relation)**.
% 299.82/300.44  193634[10:MRR:193583.2,160227.0] || member(u,complement(v)) member(u,restrict(v,w,x))* -> .
% 299.82/300.44  193690[10:SpR:160367.0,161320.0] ||  -> equal(intersection(union(u,successor_relation),restrict(symmetric_difference(universal_class,u),v,w)),successor_relation)**.
% 299.82/300.44  193693[10:SpR:57.0,161320.0] ||  -> equal(intersection(power_class(u),restrict(image(element_relation,complement(u)),v,w)),successor_relation)**.
% 299.82/300.44  193750[10:SpL:161319.0,121.0] || subclass(compose(successor_relation,successor_relation),successor_relation) -> transitive(complement(cross_product(u,u)),u)*.
% 299.82/300.44  193751[10:SpL:161319.0,5971.0] || equal(compose(successor_relation,successor_relation),successor_relation) -> transitive(complement(cross_product(u,u)),u)*.
% 299.82/300.44  193992[20:SpL:185302.1,193840.0] || equal(cross_product(singleton(successor_relation),universal_class),successor_relation)** equal(cantor(universal_class),omega) -> .
% 299.82/300.44  194062[10:SpL:185302.1,193914.0] || equal(cross_product(singleton(omega),universal_class),successor_relation)** equal(cantor(universal_class),universal_class) -> .
% 299.82/300.44  194064[10:SpL:185302.1,193991.0] || equal(cross_product(singleton(successor_relation),universal_class),successor_relation)** equal(cantor(universal_class),universal_class) -> .
% 299.82/300.44  194069[10:SpL:185302.1,193819.0] || equal(cross_product(singleton(u),universal_class),successor_relation)** member(u,cantor(universal_class)) -> .
% 299.82/300.44  194073[10:Res:3907.1,193819.0] || equal(complement(complement(cantor(complement(cross_product(singleton(singleton(u)),universal_class))))),universal_class)** -> .
% 299.82/300.44  194291[10:SpR:161286.0,139600.0] ||  -> member(u,complement(complement(singleton(u))))* equal(complement(complement(singleton(u))),successor_relation).
% 299.82/300.44  194496[10:SpL:160367.0,183398.0] || member(u,complement(union(v,successor_relation)))* -> member(u,symmetric_difference(universal_class,v)).
% 299.82/300.44  194499[0:SpL:57.0,183398.0] || member(u,complement(power_class(v))) -> member(u,image(element_relation,complement(v)))*.
% 299.82/300.44  194509[0:Res:3907.1,183398.0] || equal(complement(complement(complement(complement(u)))),universal_class)** -> member(singleton(v),u)*.
% 299.82/300.44  195400[10:SpR:194805.1,163184.1] || subclass(regular(u),u)* -> equal(u,successor_relation) equal(regular(u),successor_relation).
% 299.82/300.44  195404[10:SpR:194805.1,160444.0] || subclass(intersection(u,v),complement(v))* -> equal(intersection(u,v),successor_relation).
% 299.82/300.44  195405[10:SpR:194805.1,160443.0] || subclass(intersection(u,v),complement(u))* -> equal(intersection(u,v),successor_relation).
% 299.82/300.44  195424[0:SpR:194805.1,31.0] || subclass(u,cross_product(v,w))* -> equal(restrict(u,v,w),u).
% 299.82/300.44  195449[10:SpR:194805.1,161321.0] || subclass(complement(u),restrict(u,v,w))* -> equal(complement(u),successor_relation).
% 299.82/300.44  195484[0:SpL:194805.1,175.0] || subclass(ordinal_numbers,y__dfg) member(least(element_relation,ordinal_numbers),intersection(ordinal_numbers,u))* -> .
% 299.82/300.44  195485[0:SpL:194805.1,178.0] || subclass(ordinal_numbers,y__dfg) member(least(element_relation,ordinal_numbers),intersection(u,ordinal_numbers))* -> .
% 299.82/300.44  195488[0:SpL:194805.1,183.1] || subclass(ordinal_numbers,y__dfg) well_ordering(element_relation,u)* subclass(ordinal_numbers,u) -> .
% 299.82/300.44  195489[0:SpL:194805.1,479.0] || subclass(ordinal_numbers,y__dfg) equal(u,ordinal_numbers) well_ordering(element_relation,u)* -> .
% 299.82/300.44  195976[0:SpR:161.0,195152.0] ||  -> equal(intersection(complement(intersection(u,v)),symmetric_difference(u,v)),symmetric_difference(u,v))**.
% 299.82/300.44  196056[0:Rew:31.0,195990.0] ||  -> equal(restrict(restrict(u,v,w),v,w),restrict(u,v,w))**.
% 299.82/300.44  196122[0:SpR:1933.0,195339.0] ||  -> equal(intersection(symmetrization_of(u),symmetric_difference(u,inverse(u))),symmetric_difference(u,inverse(u)))**.
% 299.82/300.44  196123[0:SpR:1934.0,195339.0] ||  -> equal(intersection(successor(u),symmetric_difference(u,singleton(u))),symmetric_difference(u,singleton(u)))**.
% 299.82/300.44  196354[10:SpR:184982.1,162973.0] || subclass(complement(inverse(successor_relation)),successor_relation) -> subclass(symmetric_difference(symmetrization_of(successor_relation),universal_class),successor_relation)*.
% 299.82/300.44  196515[10:SpR:161137.0,183420.0] ||  -> equal(symmetric_difference(image(element_relation,symmetrization_of(successor_relation)),complement(power_class(complement(inverse(successor_relation))))),successor_relation)**.
% 299.82/300.44  196531[10:SpR:161137.0,163162.1] ||  -> member(successor_relation,image(element_relation,symmetrization_of(successor_relation)))* member(successor_relation,power_class(complement(inverse(successor_relation)))).
% 299.82/300.44  196721[10:SpR:162889.0,183420.0] ||  -> equal(symmetric_difference(image(element_relation,successor(successor_relation)),complement(power_class(complement(singleton(successor_relation))))),successor_relation)**.
% 299.82/300.44  196737[10:SpR:162889.0,163162.1] ||  -> member(successor_relation,image(element_relation,successor(successor_relation)))* member(successor_relation,power_class(complement(singleton(successor_relation)))).
% 299.82/300.44  197073[10:Res:197034.0,3.0] || subclass(complement(singleton(successor_relation)),u) -> member(regular(complement(successor(successor_relation))),u)*.
% 299.82/300.44  197747[10:MRR:197746.1,160215.0] || transitive(complement(cross_product(u,u)),u)* -> equal(compose(successor_relation,successor_relation),successor_relation).
% 299.82/300.44  198245[10:SpR:194805.1,163006.0] || subclass(u,image(element_relation,successor_relation))* -> equal(intersection(u,power_class(universal_class)),successor_relation).
% 299.82/300.44  198397[10:SpR:194805.1,163001.0] || subclass(u,image(element_relation,successor_relation))* -> equal(intersection(power_class(universal_class),u),successor_relation).
% 299.82/300.44  198480[10:SpR:194805.1,162945.0] || subclass(u,complement(singleton(successor_relation)))* -> equal(intersection(successor(successor_relation),u),successor_relation).
% 299.82/300.44  198666[10:SpR:194805.1,162943.0] || subclass(u,complement(singleton(successor_relation)))* -> equal(intersection(u,successor(successor_relation)),successor_relation).
% 299.82/300.44  199084[10:SpR:194805.1,162293.0] || subclass(u,complement(inverse(successor_relation)))* -> equal(intersection(u,symmetrization_of(successor_relation)),successor_relation).
% 299.82/300.44  199298[10:SpR:194805.1,162291.0] || subclass(u,complement(inverse(successor_relation)))* -> equal(intersection(symmetrization_of(successor_relation),u),successor_relation).
% 299.82/300.44  199451[10:SpR:194805.1,161847.0] || subclass(u,image(element_relation,universal_class))* -> equal(intersection(u,power_class(successor_relation)),successor_relation).
% 299.82/300.44  199607[10:SpR:194805.1,161843.0] || subclass(u,image(element_relation,universal_class))* -> equal(intersection(power_class(successor_relation),u),successor_relation).
% 299.82/300.44  199782[10:SpL:185302.1,199779.0] || equal(cross_product(singleton(successor_relation),universal_class),successor_relation)** subclass(universal_class,cantor(universal_class)) -> .
% 299.82/300.44  199981[6:Res:199848.1,3.0] || subclass(universal_class,u)* subclass(u,v)* -> member(regular(rest_relation),v)*.
% 299.82/300.44  199985[6:Res:199848.1,148657.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(regular(rest_relation),element_relation) -> .
% 299.82/300.44  199994[6:Res:199848.1,1952.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(regular(rest_relation),union(u,v))*.
% 299.82/300.44  199995[6:Res:199848.1,10191.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(regular(rest_relation),symmetrization_of(u)).
% 299.82/300.44  199996[6:Res:199848.1,10254.0] || subclass(universal_class,symmetric_difference(u,singleton(u)))* -> member(regular(rest_relation),successor(u)).
% 299.82/300.44  200026[14:SpL:119971.0,199972.0] || member(image(universal_class,u),universal_class)* member(cross_product(u,universal_class),universal_class) -> .
% 299.82/300.44  200057[14:SpR:119971.0,200027.1] || member(cross_product(u,universal_class),universal_class)* -> equal(integer_of(image(universal_class,u)),successor_relation).
% 299.82/300.44  200060[14:SpR:200028.1,45.0] || member(u,universal_class) -> equal(union(range_of(u),successor_relation),successor(range_of(u)))**.
% 299.82/300.44  200111[14:SpR:119971.0,200028.1] || member(cross_product(u,universal_class),universal_class)* -> equal(singleton(image(universal_class,u)),successor_relation).
% 299.82/300.44  200180[14:Rew:181082.0,200094.1] || member(u,universal_class) -> equal(apply(v,range_of(u)),apply(v,universal_class))**.
% 299.82/300.44  200183[14:Rew:181083.0,200096.1] || member(u,universal_class) -> equal(ordered_pair(v,range_of(u)),ordered_pair(v,universal_class))**.
% 299.82/300.44  200269[6:SpL:199964.0,16.0] || member(regular(rest_relation),cross_product(u,v))* -> member(first(regular(rest_relation)),u).
% 299.82/300.44  200270[6:SpL:199964.0,17.0] || member(regular(rest_relation),cross_product(u,v))* -> member(second(regular(rest_relation)),v).
% 299.82/300.44  200277[6:SpL:199964.0,21.0] || member(regular(rest_relation),element_relation) -> member(first(regular(rest_relation)),second(regular(rest_relation)))*.
% 299.82/300.44  200304[6:MRR:200303.1,199831.0] || member(first(regular(rest_relation)),second(regular(rest_relation)))* -> member(regular(rest_relation),element_relation).
% 299.82/300.44  200554[10:Res:186499.1,163137.0] || equal(successor_relation,u) equal(rest_of(power_class(u)),successor(power_class(u)))** -> .
% 299.82/300.44  200555[10:Res:58.1,163137.0] || member(u,universal_class) equal(rest_of(power_class(u)),successor(power_class(u)))** -> .
% 299.82/300.44  200560[10:Res:56.1,163137.0] || member(u,universal_class) equal(rest_of(sum_class(u)),successor(sum_class(u)))** -> .
% 299.82/300.44  200563[10:Res:120366.1,163137.0] || member(u,universal_class) equal(rest_of(rest_of(u)),successor(rest_of(u)))** -> .
% 299.82/300.44  200584[10:Res:197071.0,163137.0] || equal(rest_of(regular(complement(successor(successor_relation)))),successor(regular(complement(successor(successor_relation)))))** -> .
% 299.82/300.44  200660[10:Res:161493.2,26.1] inductive(complement(u)) || member(v,u)* -> equal(integer_of(v),successor_relation).
% 299.82/300.44  200662[10:Res:161493.2,141576.1] inductive(complement(kind_1_ordinals)) || member(u,ordinal_numbers)* -> equal(integer_of(u),successor_relation).
% 299.82/300.44  200664[10:Res:161493.2,183398.0] inductive(complement(complement(u))) ||  -> equal(integer_of(v),successor_relation) member(v,u)*.
% 299.82/300.44  200666[10:Res:161493.2,23.0] inductive(intersection(u,v)) ||  -> equal(integer_of(w),successor_relation) member(w,u)*.
% 299.82/300.44  200667[10:Res:161493.2,24.0] inductive(intersection(u,v)) ||  -> equal(integer_of(w),successor_relation) member(w,v)*.
% 299.82/300.44  200678[10:Res:161493.2,183723.0] inductive(symmetrization_of(successor_relation)) ||  -> equal(integer_of(u),successor_relation) member(u,inverse(successor_relation))*.
% 299.82/300.44  200679[10:Res:161493.2,150034.0] inductive(domain_of(u)) ||  -> equal(integer_of(v),successor_relation) member(v,cantor(u))*.
% 299.82/300.44  200680[10:Res:161493.2,193764.0] inductive(domain_of(complement(cross_product(singleton(u),universal_class)))) ||  -> equal(integer_of(u),successor_relation)**.
% 299.82/300.44  200684[10:Res:161493.2,193819.0] inductive(cantor(complement(cross_product(singleton(u),universal_class)))) ||  -> equal(integer_of(u),successor_relation)**.
% 299.82/300.44  200685[10:Res:161493.2,183622.0] inductive(successor(successor_relation)) ||  -> equal(integer_of(u),successor_relation) member(u,singleton(successor_relation))*.
% 299.82/300.44  200693[10:Res:161493.2,5.0] inductive(u) ||  -> equal(integer_of(not_subclass_element(v,u)),successor_relation)** subclass(v,u).
% 299.82/300.44  200713[10:Res:161493.2,21.0] inductive(element_relation) ||  -> equal(integer_of(ordered_pair(u,v)),successor_relation)** member(u,v).
% 299.82/300.44  200732[10:Res:161493.2,195493.1] inductive(singleton(successor_relation)) || subclass(ordinal_numbers,y__dfg)* -> equal(integer_of(ordinal_numbers),successor_relation).
% 299.82/300.44  200738[10:Res:161493.2,155823.0] inductive(ordinal_numbers) ||  -> equal(integer_of(not_subclass_element(u,kind_1_ordinals)),successor_relation)** subclass(u,kind_1_ordinals).
% 299.82/300.44  200790[10:Res:161493.2,197037.0] inductive(successor(successor_relation)) ||  -> equal(integer_of(not_subclass_element(complement(singleton(successor_relation)),successor_relation)),successor_relation)**.
% 299.82/300.44  201371[6:Res:201231.1,3.0] || subclass(universal_class,u)* subclass(u,v)* -> member(regular(domain_relation),v)*.
% 299.82/300.44  201375[6:Res:201231.1,148657.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(regular(domain_relation),element_relation) -> .
% 299.82/300.44  201384[6:Res:201231.1,1952.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(regular(domain_relation),union(u,v))*.
% 299.82/300.44  201385[6:Res:201231.1,10191.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(regular(domain_relation),symmetrization_of(u)).
% 299.82/300.44  201386[6:Res:201231.1,10254.0] || subclass(universal_class,symmetric_difference(u,singleton(u)))* -> member(regular(domain_relation),successor(u)).
% 299.82/300.44  201513[6:SpL:201355.0,16.0] || member(regular(domain_relation),cross_product(u,v))* -> member(first(regular(domain_relation)),u).
% 299.82/300.44  201514[6:SpL:201355.0,17.0] || member(regular(domain_relation),cross_product(u,v))* -> member(second(regular(domain_relation)),v).
% 299.82/300.44  201521[6:SpL:201355.0,21.0] || member(regular(domain_relation),element_relation) -> member(first(regular(domain_relation)),second(regular(domain_relation)))*.
% 299.82/300.44  201548[6:MRR:201547.1,201221.0] || member(first(regular(domain_relation)),second(regular(domain_relation)))* -> member(regular(domain_relation),element_relation).
% 299.82/300.44  201797[10:SoR:160568.0,195883.1] || member(u,ordinal_numbers)* equal(sum_class(u),universal_class) -> member(successor_relation,u)*.
% 299.82/300.44  201995[10:Res:161492.2,2151.0] || equal(singleton(u),omega)** -> equal(integer_of(v),successor_relation)** equal(v,u)*.
% 299.82/300.44  202055[10:Res:161492.2,197074.0] || equal(singleton(successor_relation),omega) -> equal(integer_of(regular(complement(successor(successor_relation)))),successor_relation)**.
% 299.82/300.44  202322[10:SpR:163032.0,184982.1] || subclass(intersection(u,universal_class),successor_relation)* -> equal(complement(symmetric_difference(u,universal_class)),successor_relation).
% 299.82/300.44  202458[10:SpR:160322.0,163217.0] ||  -> member(successor_relation,image(element_relation,power_class(universal_class)))* member(successor_relation,power_class(image(element_relation,successor_relation))).
% 299.82/300.44  202459[10:SpR:160328.0,163217.0] ||  -> member(successor_relation,image(element_relation,power_class(successor_relation)))* member(successor_relation,power_class(image(element_relation,universal_class))).
% 299.82/300.44  202491[10:SpR:202485.1,55.0] || equal(rest_of(restrict(element_relation,universal_class,u)),successor_relation)** -> equal(sum_class(u),successor_relation).
% 299.82/300.44  202517[10:SpR:202485.1,40.0] || equal(rest_of(flip(cross_product(u,universal_class))),successor_relation)** -> equal(inverse(u),successor_relation).
% 299.82/300.44  202689[10:Res:185430.1,3488.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(unordered_pair(w,x),v)*.
% 299.82/300.44  202701[10:SpR:161194.0,185608.1] || equal(union(u,successor_relation),successor_relation) -> equal(symmetric_difference(complement(u),universal_class),successor_relation)**.
% 299.82/300.44  202702[10:SpR:161194.0,163198.1] || subclass(union(u,successor_relation),successor_relation)* -> equal(symmetric_difference(complement(u),universal_class),successor_relation).
% 299.82/300.44  202715[10:SpR:161194.0,194805.1] || subclass(universal_class,union(u,successor_relation))* -> equal(symmetric_difference(complement(u),universal_class),universal_class).
% 299.82/300.44  202728[10:SpL:161194.0,160566.0] || equal(symmetric_difference(complement(u),universal_class),universal_class) -> member(successor_relation,union(u,successor_relation))*.
% 299.82/300.44  202730[10:SpL:161194.0,1510.0] || equal(symmetric_difference(complement(u),universal_class),universal_class) -> member(omega,union(u,successor_relation))*.
% 299.82/300.44  202738[20:SpL:161194.0,191100.0] || equal(symmetric_difference(complement(u),universal_class),omega) -> member(successor_relation,union(u,successor_relation))*.
% 299.82/300.44  202859[11:Res:141787.0,168534.1] || equal(complement(inverse(singleton(successor_relation))),symmetrization_of(successor_relation))** -> asymmetric(singleton(successor_relation),u)*.
% 299.82/300.44  202994[10:Res:185430.1,3487.0] || equal(complement(intersection(u,v)),successor_relation)** -> member(unordered_pair(w,x),u)*.
% 299.82/300.44  203117[11:SpL:160367.0,202882.1] inductive(symmetric_difference(universal_class,u)) || equal(union(u,successor_relation),symmetrization_of(successor_relation))** -> .
% 299.82/300.44  203118[11:SpL:57.0,202882.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),symmetrization_of(successor_relation))* -> .
% 299.82/300.44  203862[6:Rew:203192.0,110310.1] || equal(complement(complement(rest_of(u))),universal_class) -> member(singleton(v),cantor(u))*.
% 299.82/300.44  203863[6:Rew:203192.0,126091.1] || subclass(rest_relation,flip(rest_of(u))) -> member(ordered_pair(v,w),cantor(u))*.
% 299.82/300.44  203932[10:Rew:203192.0,185806.1] || equal(complement(complement(rest_of(u))),successor_relation)** member(v,cantor(u))* -> .
% 299.82/300.44  203958[10:Rew:203192.0,181109.0] || member(universal_class,cantor(u)) equal(restrict(u,successor_relation,universal_class),successor_relation)** -> .
% 299.82/300.44  203977[6:Rew:203192.0,200268.1] || member(regular(rest_relation),rest_of(u)) -> member(first(regular(rest_relation)),cantor(u))*.
% 299.82/300.44  203984[6:Rew:203192.0,201512.1] || member(regular(domain_relation),rest_of(u)) -> member(first(regular(domain_relation)),cantor(u))*.
% 299.82/300.44  205877[10:SpR:205791.1,163032.0] ||  -> equal(singleton(u),successor_relation) equal(complement(symmetric_difference(u,universal_class)),union(u,successor_relation))**.
% 299.82/300.44  206059[10:Res:141787.0,163205.1] || equal(complement(inverse(singleton(successor_relation))),successor(successor_relation))** -> asymmetric(singleton(successor_relation),u)*.
% 299.82/300.44  206180[10:Res:203330.1,160358.1] inductive(cantor(restrict(u,v,successor_relation))) || section(u,successor_relation,v)* -> .
% 299.82/300.44  206198[10:SpL:160367.0,206082.1] inductive(symmetric_difference(universal_class,u)) || equal(union(u,successor_relation),successor(successor_relation))** -> .
% 299.82/300.44  206201[10:SpL:57.0,206082.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),successor(successor_relation))** -> .
% 299.82/300.44  206953[10:Res:206947.1,6045.0] || equal(u,kind_1_ordinals) subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  206963[10:Res:206947.1,9332.1] || equal(intersection(u,v),kind_1_ordinals) member(successor_relation,symmetric_difference(u,v))* -> .
% 299.82/300.44  206967[10:Res:206947.1,594.0] || equal(restrict(u,v,w),kind_1_ordinals)** -> member(successor_relation,cross_product(v,w))*.
% 299.82/300.44  206982[10:Res:206947.1,10.0] || equal(unordered_pair(u,v),kind_1_ordinals)** -> equal(successor_relation,v) equal(successor_relation,u).
% 299.82/300.44  206983[10:Res:206947.1,307.0] || equal(image(element_relation,complement(u)),kind_1_ordinals)** member(successor_relation,power_class(u)) -> .
% 299.82/300.44  206985[10:Res:206947.1,160481.0] || equal(regular(u),kind_1_ordinals) member(successor_relation,u)* -> equal(u,successor_relation).
% 299.82/300.44  207310[20:SpL:507.0,206700.0] || equal(complement(complement(intersection(complement(singleton(successor_relation)),union(u,v)))),omega)** -> .
% 299.82/300.44  207366[10:SpL:507.0,206701.0] || equal(complement(complement(intersection(complement(singleton(successor_relation)),union(u,v)))),universal_class)** -> .
% 299.82/300.44  207503[20:SpL:506.0,207206.0] || equal(complement(complement(intersection(union(u,v),complement(singleton(successor_relation))))),omega)** -> .
% 299.82/300.44  207515[10:SpL:506.0,207207.0] || equal(complement(complement(intersection(union(u,v),complement(singleton(successor_relation))))),universal_class)** -> .
% 299.82/300.44  207648[10:SpL:185302.1,206978.0] || equal(cross_product(singleton(successor_relation),universal_class),successor_relation)** equal(cantor(universal_class),kind_1_ordinals) -> .
% 299.82/300.44  207856[10:SpR:194805.1,206688.0] || subclass(power_class(u),complement(singleton(successor_relation)))* -> member(successor_relation,complement(power_class(u))).
% 299.82/300.44  207869[10:Res:206688.0,163205.1] || equal(complement(complement(intersection(complement(singleton(successor_relation)),power_class(u)))),successor(successor_relation))** -> .
% 299.82/300.44  207870[11:Res:206688.0,168534.1] || equal(complement(complement(intersection(complement(singleton(successor_relation)),power_class(u)))),symmetrization_of(successor_relation))** -> .
% 299.82/300.44  208149[10:Res:207196.0,163205.1] || equal(complement(complement(intersection(power_class(u),complement(singleton(successor_relation))))),successor(successor_relation))** -> .
% 299.82/300.44  208150[11:Res:207196.0,168534.1] || equal(complement(complement(intersection(power_class(u),complement(singleton(successor_relation))))),symmetrization_of(successor_relation))** -> .
% 299.82/300.44  208312[10:SpL:506.0,208266.0] || equal(complement(complement(intersection(union(u,v),complement(singleton(successor_relation))))),kind_1_ordinals)** -> .
% 299.82/300.44  208324[10:SpL:507.0,208267.0] || equal(complement(complement(intersection(complement(singleton(successor_relation)),union(u,v)))),kind_1_ordinals)** -> .
% 299.82/300.44  208354[10:SpL:160367.0,206962.0] || equal(complement(union(u,successor_relation)),kind_1_ordinals) -> member(successor_relation,symmetric_difference(universal_class,u))*.
% 299.82/300.44  208357[10:SpL:57.0,206962.0] || equal(complement(power_class(u)),kind_1_ordinals) -> member(successor_relation,image(element_relation,complement(u)))*.
% 299.82/300.44  208393[20:SpL:160367.0,206996.1] || equal(symmetric_difference(universal_class,u),kind_1_ordinals)** equal(union(u,successor_relation),omega) -> .
% 299.82/300.44  208396[20:SpL:57.0,206996.1] || equal(image(element_relation,complement(u)),kind_1_ordinals)** equal(power_class(u),omega) -> .
% 299.82/300.44  208407[10:SpL:160367.0,206997.1] || equal(symmetric_difference(universal_class,u),kind_1_ordinals)** equal(union(u,successor_relation),universal_class) -> .
% 299.82/300.44  208410[10:SpL:57.0,206997.1] || equal(image(element_relation,complement(u)),kind_1_ordinals)** equal(power_class(u),universal_class) -> .
% 299.82/300.44  208480[10:SpL:160367.0,208250.1] || equal(symmetric_difference(universal_class,u),kind_1_ordinals)** equal(union(u,successor_relation),kind_1_ordinals) -> .
% 299.82/300.44  208483[10:SpL:57.0,208250.1] || equal(image(element_relation,complement(u)),kind_1_ordinals)** equal(power_class(u),kind_1_ordinals) -> .
% 299.82/300.44  208494[20:SpL:160367.0,208251.1] || equal(symmetric_difference(universal_class,u),omega)** equal(union(u,successor_relation),kind_1_ordinals) -> .
% 299.82/300.44  208497[20:SpL:57.0,208251.1] || equal(image(element_relation,complement(u)),omega)** equal(power_class(u),kind_1_ordinals) -> .
% 299.82/300.44  208508[10:SpL:160367.0,208257.1] || equal(symmetric_difference(universal_class,u),universal_class)** equal(union(u,successor_relation),kind_1_ordinals) -> .
% 299.82/300.44  208511[10:SpL:57.0,208257.1] || equal(image(element_relation,complement(u)),universal_class)** equal(power_class(u),kind_1_ordinals) -> .
% 299.82/300.44  208603[10:SpL:161.0,206964.0] || equal(symmetric_difference(u,v),kind_1_ordinals) -> member(successor_relation,complement(intersection(u,v)))*.
% 299.82/300.44  208636[10:SpL:161194.0,206964.0] || equal(symmetric_difference(complement(u),universal_class),kind_1_ordinals) -> member(successor_relation,union(u,successor_relation))*.
% 299.82/300.44  195442[10:SpR:194805.1,160398.0] || subclass(complement(inverse(successor_relation)),symmetrization_of(successor_relation))* -> equal(complement(inverse(successor_relation)),successor_relation).
% 299.82/300.44  208816[21:MRR:208809.1,160455.0] || well_ordering(u,symmetrization_of(successor_relation)) -> member(least(u,successor(successor_relation)),successor(successor_relation))*.
% 299.82/300.44  208919[10:Res:141787.0,163207.1] || equal(complement(inverse(singleton(successor_relation))),singleton(successor_relation))** -> asymmetric(singleton(successor_relation),u)*.
% 299.82/300.44  208948[10:Res:206688.0,163207.1] || equal(complement(complement(intersection(complement(singleton(successor_relation)),power_class(u)))),singleton(successor_relation))** -> .
% 299.82/300.44  208949[10:Res:207196.0,163207.1] || equal(complement(complement(intersection(power_class(u),complement(singleton(successor_relation))))),singleton(successor_relation))** -> .
% 299.82/300.44  209064[10:SpL:160367.0,208945.1] inductive(symmetric_difference(universal_class,u)) || equal(union(u,successor_relation),singleton(successor_relation))** -> .
% 299.82/300.44  209067[10:SpL:57.0,208945.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),singleton(successor_relation))** -> .
% 299.82/300.44  209448[12:Res:209377.1,3.0] || subclass(universal_class,u)* subclass(u,v)* -> member(regular(element_relation),v)*.
% 299.82/300.44  209452[12:Res:209377.1,148657.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(regular(element_relation),element_relation) -> .
% 299.82/300.44  209461[12:Res:209377.1,1952.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(regular(element_relation),union(u,v))*.
% 299.82/300.44  209462[12:Res:209377.1,10191.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(regular(element_relation),symmetrization_of(u)).
% 299.82/300.44  209463[12:Res:209377.1,10254.0] || subclass(universal_class,symmetric_difference(u,singleton(u)))* -> member(regular(element_relation),successor(u)).
% 299.82/300.44  209531[12:SpL:209433.0,203263.0] || member(regular(element_relation),rest_of(u)) -> member(first(regular(element_relation)),cantor(u))*.
% 299.82/300.44  209533[12:SpL:209433.0,16.0] || member(regular(element_relation),cross_product(u,v))* -> member(first(regular(element_relation)),u).
% 299.82/300.44  209534[12:SpL:209433.0,17.0] || member(regular(element_relation),cross_product(u,v))* -> member(second(regular(element_relation)),v).
% 299.82/300.44  209541[12:SpL:209433.0,21.0] || member(regular(element_relation),element_relation) -> member(first(regular(element_relation)),second(regular(element_relation)))*.
% 299.82/300.44  209568[12:MRR:209567.1,209313.0] || member(first(regular(element_relation)),second(regular(element_relation)))* -> member(regular(element_relation),element_relation).
% 299.82/300.44  209755[15:Res:160274.1,189420.0] || subclass(domain_relation,rest_relation)* -> equal(integer_of(u),successor_relation)** equal(rest_of(u),successor_relation).
% 299.82/300.44  209756[15:Res:160362.0,189420.0] || subclass(domain_relation,rest_relation)* -> equal(singleton(u),successor_relation) equal(rest_of(u),successor_relation)**.
% 299.82/300.44  209764[15:Res:160295.1,189420.0] || subclass(domain_relation,rest_relation) -> equal(u,successor_relation) equal(rest_of(regular(u)),successor_relation)**.
% 299.82/300.44  209874[15:Res:160274.1,189421.0] || subclass(rest_relation,domain_relation)* -> equal(integer_of(u),successor_relation)** equal(rest_of(u),successor_relation).
% 299.82/300.44  209875[15:Res:160362.0,189421.0] || subclass(rest_relation,domain_relation)* -> equal(singleton(u),successor_relation) equal(rest_of(u),successor_relation)**.
% 299.82/300.44  209883[15:Res:160295.1,189421.0] || subclass(rest_relation,domain_relation) -> equal(u,successor_relation) equal(rest_of(regular(u)),successor_relation)**.
% 299.82/300.44  210307[2:Res:136.1,143095.1] inductive(u) || member(u,ordinal_numbers)* -> member(least(element_relation,omega),omega)*.
% 299.82/300.44  210342[15:SpR:181067.0,189563.1] || subclass(domain_relation,flip(u)) -> member(ordered_pair(singleton(singleton(successor_relation)),successor_relation),u)*.
% 299.82/300.44  210381[15:Res:189563.1,203263.0] || subclass(domain_relation,flip(rest_of(u))) -> member(ordered_pair(v,w),cantor(u))*.
% 299.82/300.44  210383[15:Res:189563.1,16.0] || subclass(domain_relation,flip(cross_product(u,v)))* -> member(ordered_pair(w,x),u)*.
% 299.82/300.44  210456[15:Res:189564.1,16.0] || subclass(domain_relation,rotate(cross_product(u,v)))* -> member(ordered_pair(w,successor_relation),u)*.
% 299.82/300.44  210506[6:SpL:203285.0,149475.0] || member(u,range_of(v))* subclass(universal_class,w)* -> member(u,w)*.
% 299.82/300.44  210525[6:SpL:204209.0,149475.0] || member(u,inverse(v))* subclass(universal_class,w)* -> member(u,w)*.
% 299.82/300.44  210526[6:SpL:204281.0,149475.0] || member(u,sum_class(v))* subclass(universal_class,w)* -> member(u,w)*.
% 299.82/300.44  211066[11:Res:141787.0,179992.1] || equal(complement(inverse(singleton(successor_relation))),inverse(successor_relation))** -> asymmetric(singleton(successor_relation),u)*.
% 299.82/300.44  211095[11:Res:206688.0,179992.1] || equal(complement(complement(intersection(complement(singleton(successor_relation)),power_class(u)))),inverse(successor_relation))** -> .
% 299.82/300.44  211096[11:Res:207196.0,179992.1] || equal(complement(complement(intersection(power_class(u),complement(singleton(successor_relation))))),inverse(successor_relation))** -> .
% 299.82/300.44  211170[11:MRR:211147.1,168458.0] || well_ordering(u,symmetrization_of(successor_relation)) -> member(least(u,symmetrization_of(successor_relation)),inverse(successor_relation))*.
% 299.82/300.44  211171[10:MRR:211149.1,160455.0] || well_ordering(u,successor(successor_relation)) -> member(least(u,successor(successor_relation)),singleton(successor_relation))*.
% 299.82/300.44  211260[11:SpL:160367.0,211092.1] inductive(symmetric_difference(universal_class,u)) || equal(union(u,successor_relation),inverse(successor_relation))** -> .
% 299.82/300.44  211263[11:SpL:57.0,211092.1] inductive(image(element_relation,complement(u))) || equal(power_class(u),inverse(successor_relation))** -> .
% 299.82/300.44  211499[10:Res:141787.0,211446.0] || well_ordering(universal_class,inverse(singleton(singleton(successor_relation))))* -> asymmetric(singleton(singleton(successor_relation)),u)*.
% 299.82/300.44  211505[10:Res:161493.2,211446.0] inductive(u) || well_ordering(universal_class,u)* -> equal(integer_of(singleton(successor_relation)),successor_relation)**.
% 299.82/300.44  211514[10:MRR:211497.0,191.0] || well_ordering(universal_class,image(element_relation,complement(u)))* -> member(singleton(successor_relation),power_class(u)).
% 299.82/300.44  211529[10:SpL:160367.0,211448.0] || well_ordering(universal_class,union(u,successor_relation)) -> member(singleton(successor_relation),symmetric_difference(universal_class,u))*.
% 299.82/300.44  211532[10:SpL:57.0,211448.0] || well_ordering(universal_class,power_class(u)) -> member(singleton(successor_relation),image(element_relation,complement(u)))*.
% 299.82/300.44  211608[10:Res:114856.0,160705.0] || member(regular(symmetric_difference(universal_class,kind_1_ordinals)),ordinal_numbers)* -> equal(symmetric_difference(universal_class,kind_1_ordinals),successor_relation).
% 299.82/300.44  211625[10:SpR:160367.0,211579.1] ||  -> member(singleton(successor_relation),symmetric_difference(universal_class,u))* member(singleton(successor_relation),union(u,successor_relation)).
% 299.82/300.44  211628[10:SpR:57.0,211579.1] ||  -> member(singleton(successor_relation),image(element_relation,complement(u)))* member(singleton(successor_relation),power_class(u)).
% 299.82/300.44  211673[10:Res:181213.1,26.1] || equal(complement(u),singleton(singleton(successor_relation))) member(singleton(successor_relation),u)* -> .
% 299.82/300.44  211675[10:Res:181213.1,141576.1] || equal(singleton(singleton(successor_relation)),complement(kind_1_ordinals)) member(singleton(successor_relation),ordinal_numbers)* -> .
% 299.82/300.44  211677[10:Res:181213.1,183398.0] || equal(complement(complement(u)),singleton(singleton(successor_relation))) -> member(singleton(successor_relation),u)*.
% 299.82/300.44  211679[10:Res:181213.1,23.0] || equal(intersection(u,v),singleton(singleton(successor_relation)))** -> member(singleton(successor_relation),u)*.
% 299.82/300.44  211680[10:Res:181213.1,24.0] || equal(intersection(u,v),singleton(singleton(successor_relation)))** -> member(singleton(successor_relation),v)*.
% 299.82/300.44  211693[10:Res:181213.1,193819.0] || equal(cantor(complement(cross_product(singleton(singleton(successor_relation)),universal_class))),singleton(singleton(successor_relation)))** -> .
% 299.82/300.44  211948[10:SpR:160322.0,183456.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(universal_class)),complement(power_class(image(element_relation,successor_relation)))),successor_relation)**.
% 299.82/300.44  211949[10:SpR:160328.0,183456.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(successor_relation)),complement(power_class(image(element_relation,universal_class)))),successor_relation)**.
% 299.82/300.44  211971[11:Res:183759.1,26.1] || subclass(inverse(successor_relation),complement(u))* member(regular(symmetrization_of(successor_relation)),u) -> .
% 299.82/300.44  211973[11:Res:183759.1,141576.1] || subclass(inverse(successor_relation),complement(kind_1_ordinals))* member(regular(symmetrization_of(successor_relation)),ordinal_numbers) -> .
% 299.82/300.44  211975[11:Res:183759.1,183398.0] || subclass(inverse(successor_relation),complement(complement(u)))* -> member(regular(symmetrization_of(successor_relation)),u).
% 299.82/300.44  211977[11:Res:183759.1,23.0] || subclass(inverse(successor_relation),intersection(u,v))* -> member(regular(symmetrization_of(successor_relation)),u).
% 299.82/300.44  211978[11:Res:183759.1,24.0] || subclass(inverse(successor_relation),intersection(u,v))* -> member(regular(symmetrization_of(successor_relation)),v).
% 299.82/300.44  211991[11:Res:183759.1,193819.0] || subclass(inverse(successor_relation),cantor(complement(cross_product(singleton(regular(symmetrization_of(successor_relation))),universal_class))))* -> .
% 299.82/300.44  211994[11:Res:183759.1,183622.0] || subclass(inverse(successor_relation),successor(successor_relation)) -> member(regular(symmetrization_of(successor_relation)),singleton(successor_relation))*.
% 299.82/300.44  212051[2:Res:184090.1,1509.1] || equal(symmetric_difference(universal_class,u),universal_class)** equal(complement(complement(u)),universal_class) -> .
% 299.82/300.44  212061[6:Res:184090.1,148657.1] || equal(symmetric_difference(universal_class,compose(element_relation,universal_class)),universal_class)** member(omega,element_relation) -> .
% 299.82/300.44  212465[10:Rew:28.0,212447.1] || equal(union(u,v),successor_relation)** equal(union(u,v),universal_class) -> .
% 299.82/300.44  212550[13:Res:212515.0,3.0] || subclass(image(element_relation,successor_relation),u) -> member(regular(complement(power_class(universal_class))),u)*.
% 299.82/300.44  212563[13:Res:212548.0,163137.0] || equal(rest_of(regular(complement(power_class(universal_class)))),successor(regular(complement(power_class(universal_class)))))** -> .
% 299.82/300.44  212647[10:SpR:185605.1,212518.0] || equal(successor_relation,u) -> member(regular(complement(power_class(u))),image(element_relation,universal_class))*.
% 299.82/300.44  212654[10:Res:212518.0,3.0] || subclass(image(element_relation,universal_class),u) -> member(regular(complement(power_class(successor_relation))),u)*.
% 299.82/300.44  212670[10:Res:212652.0,163137.0] || equal(rest_of(regular(complement(power_class(successor_relation)))),successor(regular(complement(power_class(successor_relation)))))** -> .
% 299.82/300.44  212751[15:SpL:185605.1,212672.0] || equal(successor_relation,u) equal(successor(regular(complement(power_class(u)))),successor_relation)** -> .
% 299.82/300.44  212777[10:SpL:185605.1,212674.0] || equal(successor_relation,u) equal(singleton(regular(complement(power_class(u)))),successor_relation)** -> .
% 299.82/300.44  212781[13:SpL:186058.1,212516.0] || equal(power_class(universal_class),successor_relation) member(not_subclass_element(universal_class,successor_relation),power_class(universal_class))* -> .
% 299.82/300.44  212784[13:Res:161493.2,212516.0] inductive(power_class(universal_class)) ||  -> equal(integer_of(not_subclass_element(image(element_relation,successor_relation),successor_relation)),successor_relation)**.
% 299.82/300.44  212787[10:SpL:186059.1,212521.0] || equal(power_class(successor_relation),successor_relation) member(not_subclass_element(universal_class,successor_relation),power_class(successor_relation))* -> .
% 299.82/300.44  212790[10:Res:161493.2,212521.0] inductive(power_class(successor_relation)) ||  -> equal(integer_of(not_subclass_element(image(element_relation,universal_class),successor_relation)),successor_relation)**.
% 299.82/300.44  212828[15:Res:161493.2,212820.0] inductive(cantor(first(regular(rest_relation)))) ||  -> equal(integer_of(second(regular(rest_relation))),successor_relation)**.
% 299.82/300.44  212831[15:Res:161493.2,212821.0] inductive(cantor(first(regular(domain_relation)))) ||  -> equal(integer_of(second(regular(domain_relation))),successor_relation)**.
% 299.82/300.44  212834[15:Res:161493.2,212822.0] inductive(cantor(first(regular(element_relation)))) ||  -> equal(integer_of(second(regular(element_relation))),successor_relation)**.
% 299.82/300.44  212858[10:SpL:160336.0,186009.0] || equal(complement(symmetrization_of(successor_relation)),successor_relation) member(omega,complement(inverse(successor_relation)))* -> .
% 299.82/300.44  212974[10:SpL:160336.0,187767.0] || subclass(universal_class,symmetrization_of(successor_relation)) member(power_class(successor_relation),complement(inverse(successor_relation)))* -> .
% 299.82/300.44  212979[10:SpL:160322.0,187767.0] || subclass(universal_class,power_class(universal_class)) member(power_class(successor_relation),image(element_relation,successor_relation))* -> .
% 299.82/300.44  212980[10:SpL:160328.0,187767.0] || subclass(universal_class,power_class(successor_relation)) member(power_class(successor_relation),image(element_relation,universal_class))* -> .
% 299.82/300.44  213118[10:Res:188444.1,148657.1] || equal(symmetric_difference(universal_class,compose(element_relation,universal_class)),universal_class)** member(successor_relation,element_relation) -> .
% 299.82/300.44  213123[10:Res:188444.1,206958.1] || equal(symmetric_difference(universal_class,u),universal_class)** equal(complement(complement(u)),kind_1_ordinals) -> .
% 299.82/300.44  213126[20:Res:188444.1,191095.1] || equal(symmetric_difference(universal_class,u),universal_class)** equal(complement(complement(u)),omega) -> .
% 299.82/300.44  213202[15:Res:189485.1,26.1] || subclass(domain_relation,complement(u)) member(singleton(singleton(singleton(successor_relation))),u)* -> .
% 299.82/300.44  213204[15:Res:189485.1,141576.1] || subclass(domain_relation,complement(kind_1_ordinals)) member(singleton(singleton(singleton(successor_relation))),ordinal_numbers)* -> .
% 299.82/300.44  213206[15:Res:189485.1,183398.0] || subclass(domain_relation,complement(complement(u))) -> member(singleton(singleton(singleton(successor_relation))),u)*.
% 299.82/300.44  213208[15:Res:189485.1,23.0] || subclass(domain_relation,intersection(u,v))* -> member(singleton(singleton(singleton(successor_relation))),u)*.
% 299.82/300.44  213209[15:Res:189485.1,24.0] || subclass(domain_relation,intersection(u,v))* -> member(singleton(singleton(singleton(successor_relation))),v)*.
% 299.82/300.44  213221[15:Res:189485.1,183723.0] || subclass(domain_relation,symmetrization_of(successor_relation)) -> member(singleton(singleton(singleton(successor_relation))),inverse(successor_relation))*.
% 299.82/300.44  213222[15:Res:189485.1,193819.0] || subclass(domain_relation,cantor(complement(cross_product(singleton(singleton(singleton(singleton(successor_relation)))),universal_class))))* -> .
% 299.82/300.44  213225[15:Res:189485.1,183622.0] || subclass(domain_relation,successor(successor_relation)) -> member(singleton(singleton(singleton(successor_relation))),singleton(successor_relation))*.
% 299.82/300.44  213313[15:SpL:160367.0,213296.1] || equal(symmetric_difference(universal_class,u),domain_relation)** equal(union(u,successor_relation),universal_class) -> .
% 299.82/300.44  213316[15:SpL:57.0,213296.1] || equal(image(element_relation,complement(u)),domain_relation)** equal(power_class(u),universal_class) -> .
% 299.82/300.44  213590[10:MRR:213520.1,6.0] || equal(complement(u),successor_relation) -> equal(v,successor_relation) member(regular(v),u)*.
% 299.82/300.44  213791[15:Rew:160223.0,213752.1] || equal(successor(u),successor_relation) -> equal(symmetric_difference(symmetric_difference(universal_class,u),universal_class),successor_relation)**.
% 299.82/300.44  213796[15:Rew:142543.0,213749.1,160223.0,213749.1,160322.0,213749.1] || equal(successor(u),successor_relation) -> equal(power_class(symmetric_difference(universal_class,u)),power_class(universal_class))**.
% 299.82/300.44  214152[20:Res:193270.1,148657.1] || equal(symmetric_difference(universal_class,compose(element_relation,universal_class)),omega)** member(successor_relation,element_relation) -> .
% 299.82/300.44  214157[20:Res:193270.1,206958.1] || equal(symmetric_difference(universal_class,u),omega)** equal(complement(complement(u)),kind_1_ordinals) -> .
% 299.82/300.44  214160[20:Res:193270.1,191095.1] || equal(symmetric_difference(universal_class,u),omega)** equal(complement(complement(u)),omega) -> .
% 299.82/300.44  214161[20:Res:193270.1,160258.1] || equal(symmetric_difference(universal_class,u),omega)** equal(complement(complement(u)),universal_class) -> .
% 299.82/300.44  214233[10:SpL:160322.0,194513.0] || equal(complement(complement(power_class(universal_class))),successor_relation) -> member(omega,image(element_relation,successor_relation))*.
% 299.82/300.44  214234[10:SpL:160328.0,194513.0] || equal(complement(complement(power_class(successor_relation))),successor_relation) -> member(omega,image(element_relation,universal_class))*.
% 299.82/300.44  214257[10:SpL:160419.0,194520.0] || subclass(universal_class,complement(successor(successor_relation))) -> member(power_class(successor_relation),complement(singleton(successor_relation)))*.
% 299.82/300.44  214258[10:SpL:160336.0,194520.0] || subclass(universal_class,complement(symmetrization_of(successor_relation))) -> member(power_class(successor_relation),complement(inverse(successor_relation)))*.
% 299.82/300.44  214263[10:SpL:160322.0,194520.0] || subclass(universal_class,complement(power_class(universal_class))) -> member(power_class(successor_relation),image(element_relation,successor_relation))*.
% 299.82/300.44  214264[10:SpL:160328.0,194520.0] || subclass(universal_class,complement(power_class(successor_relation))) -> member(power_class(successor_relation),image(element_relation,universal_class))*.
% 299.82/300.44  214296[10:Res:214277.1,595.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(power_class(successor_relation),u).
% 299.82/300.44  214421[11:MRR:214407.0,160214.0] || equal(complement(union(u,v)),inverse(successor_relation))** -> member(successor_relation,complement(v)).
% 299.82/300.44  214422[10:MRR:214408.0,160214.0] || equal(complement(union(u,v)),singleton(successor_relation))** -> member(successor_relation,complement(v)).
% 299.82/300.44  214423[10:MRR:214410.0,160214.0] || equal(complement(union(u,v)),successor(successor_relation))** -> member(successor_relation,complement(v)).
% 299.82/300.44  214424[11:MRR:214411.0,160214.0] || equal(complement(union(u,v)),symmetrization_of(successor_relation))** -> member(successor_relation,complement(v)).
% 299.82/300.44  214435[21:Res:214356.0,3.0] || subclass(inverse(successor_relation),u) -> member(regular(complement(complement(symmetrization_of(successor_relation)))),u)*.
% 299.82/300.44  214447[21:Res:214433.0,189421.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(complement(complement(symmetrization_of(successor_relation))))),successor_relation)**.
% 299.82/300.44  214448[21:Res:214433.0,189420.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(complement(complement(symmetrization_of(successor_relation))))),successor_relation)**.
% 299.82/300.44  214570[11:MRR:214554.0,160214.0] || equal(complement(union(u,v)),inverse(successor_relation))** -> member(successor_relation,complement(u)).
% 299.82/300.44  214571[10:MRR:214555.0,160214.0] || equal(complement(union(u,v)),singleton(successor_relation))** -> member(successor_relation,complement(u)).
% 299.82/300.44  214572[10:MRR:214557.0,160214.0] || equal(complement(union(u,v)),successor(successor_relation))** -> member(successor_relation,complement(u)).
% 299.82/300.44  214573[11:MRR:214558.0,160214.0] || equal(complement(union(u,v)),symmetrization_of(successor_relation))** -> member(successor_relation,complement(u)).
% 299.82/300.44  215067[10:Rew:70.0,215030.0] || subclass(universal_class,apply(u,v)) -> subclass(complement(apply(u,v)),successor_relation)*.
% 299.82/300.44  215470[10:Rew:160370.0,215354.1] || equal(inverse(u),universal_class) -> subclass(union(complement(u),successor_relation),symmetrization_of(u))*.
% 299.82/300.44  215568[6:Rew:70.0,215555.0] || equal(apply(u,v),universal_class) well_ordering(element_relation,apply(u,v))* -> .
% 299.82/300.44  215592[10:Rew:70.0,215577.0] || equal(apply(u,v),universal_class) equal(apply(u,v),successor_relation)** -> .
% 299.82/300.44  215610[6:Rew:70.0,215599.0] || equal(apply(u,v),universal_class) -> section(element_relation,apply(u,v),universal_class)*.
% 299.82/300.44  215772[10:Rew:70.0,215671.0] || equal(apply(u,v),universal_class) -> equal(complement(apply(u,v)),successor_relation)**.
% 299.82/300.44  215865[10:Res:197082.1,26.1] || subclass(universal_class,complement(u)) member(regular(complement(successor(successor_relation))),u)* -> .
% 299.82/300.44  215867[10:Res:197082.1,141576.1] || subclass(universal_class,complement(kind_1_ordinals)) member(regular(complement(successor(successor_relation))),ordinal_numbers)* -> .
% 299.82/300.44  215869[10:Res:197082.1,183398.0] || subclass(universal_class,complement(complement(u))) -> member(regular(complement(successor(successor_relation))),u)*.
% 299.82/300.44  215871[10:Res:197082.1,23.0] || subclass(universal_class,intersection(u,v))* -> member(regular(complement(successor(successor_relation))),u)*.
% 299.82/300.44  215872[10:Res:197082.1,24.0] || subclass(universal_class,intersection(u,v))* -> member(regular(complement(successor(successor_relation))),v)*.
% 299.82/300.44  215884[10:Res:197082.1,183723.0] || subclass(universal_class,symmetrization_of(successor_relation)) -> member(regular(complement(successor(successor_relation))),inverse(successor_relation))*.
% 299.82/300.44  215885[10:Res:197082.1,193819.0] || subclass(universal_class,cantor(complement(cross_product(singleton(regular(complement(successor(successor_relation)))),universal_class))))* -> .
% 299.82/300.44  216106[6:Res:199830.1,26.1] || equal(complement(u),cross_product(universal_class,universal_class)) member(regular(rest_relation),u)* -> .
% 299.82/300.44  216108[6:Res:199830.1,141576.1] || equal(cross_product(universal_class,universal_class),complement(kind_1_ordinals)) member(regular(rest_relation),ordinal_numbers)* -> .
% 299.82/300.44  216110[6:Res:199830.1,183398.0] || equal(complement(complement(u)),cross_product(universal_class,universal_class)) -> member(regular(rest_relation),u)*.
% 299.82/300.44  216112[6:Res:199830.1,23.0] || equal(intersection(u,v),cross_product(universal_class,universal_class))** -> member(regular(rest_relation),u)*.
% 299.82/300.44  216113[6:Res:199830.1,24.0] || equal(intersection(u,v),cross_product(universal_class,universal_class))** -> member(regular(rest_relation),v)*.
% 299.82/300.44  216126[10:Res:199830.1,193819.0] || equal(cantor(complement(cross_product(singleton(regular(rest_relation)),universal_class))),cross_product(universal_class,universal_class))** -> .
% 299.82/300.44  216176[6:Rew:70.0,216157.0] || equal(apply(u,v),universal_class) -> member(regular(rest_relation),apply(u,v))*.
% 299.82/300.44  216425[10:SpL:160336.0,199982.0] || subclass(universal_class,symmetrization_of(successor_relation)) member(regular(rest_relation),complement(inverse(successor_relation)))* -> .
% 299.82/300.44  216431[10:SpL:160322.0,199982.0] || subclass(universal_class,power_class(universal_class)) member(regular(rest_relation),image(element_relation,successor_relation))* -> .
% 299.82/300.44  216432[10:SpL:160328.0,199982.0] || subclass(universal_class,power_class(successor_relation)) member(regular(rest_relation),image(element_relation,universal_class))* -> .
% 299.82/300.44  216443[10:SpL:160419.0,199986.0] || subclass(universal_class,complement(successor(successor_relation))) -> member(regular(rest_relation),complement(singleton(successor_relation)))*.
% 299.82/300.44  216444[10:SpL:160336.0,199986.0] || subclass(universal_class,complement(symmetrization_of(successor_relation))) -> member(regular(rest_relation),complement(inverse(successor_relation)))*.
% 299.82/300.44  216450[10:SpL:160322.0,199986.0] || subclass(universal_class,complement(power_class(universal_class))) -> member(regular(rest_relation),image(element_relation,successor_relation))*.
% 299.82/300.44  216451[10:SpL:160328.0,199986.0] || subclass(universal_class,complement(power_class(successor_relation))) -> member(regular(rest_relation),image(element_relation,universal_class))*.
% 299.82/300.44  216482[10:Res:216465.1,595.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(regular(rest_relation),u).
% 299.82/300.44  216714[6:Res:201220.1,26.1] || equal(complement(u),cross_product(universal_class,universal_class)) member(regular(domain_relation),u)* -> .
% 299.82/300.44  216716[6:Res:201220.1,141576.1] || equal(cross_product(universal_class,universal_class),complement(kind_1_ordinals)) member(regular(domain_relation),ordinal_numbers)* -> .
% 299.82/300.44  216718[6:Res:201220.1,183398.0] || equal(complement(complement(u)),cross_product(universal_class,universal_class)) -> member(regular(domain_relation),u)*.
% 299.82/300.44  216720[6:Res:201220.1,23.0] || equal(intersection(u,v),cross_product(universal_class,universal_class))** -> member(regular(domain_relation),u)*.
% 299.82/300.44  216721[6:Res:201220.1,24.0] || equal(intersection(u,v),cross_product(universal_class,universal_class))** -> member(regular(domain_relation),v)*.
% 299.82/300.44  216734[10:Res:201220.1,193819.0] || equal(cantor(complement(cross_product(singleton(regular(domain_relation)),universal_class))),cross_product(universal_class,universal_class))** -> .
% 299.82/300.44  216800[6:Rew:70.0,216781.0] || equal(apply(u,v),universal_class) -> member(regular(domain_relation),apply(u,v))*.
% 299.82/300.44  216807[10:SpL:160336.0,201372.0] || subclass(universal_class,symmetrization_of(successor_relation)) member(regular(domain_relation),complement(inverse(successor_relation)))* -> .
% 299.82/300.44  216813[10:SpL:160322.0,201372.0] || subclass(universal_class,power_class(universal_class)) member(regular(domain_relation),image(element_relation,successor_relation))* -> .
% 299.82/300.44  216814[10:SpL:160328.0,201372.0] || subclass(universal_class,power_class(successor_relation)) member(regular(domain_relation),image(element_relation,universal_class))* -> .
% 299.82/300.44  216825[10:SpL:160419.0,201376.0] || subclass(universal_class,complement(successor(successor_relation))) -> member(regular(domain_relation),complement(singleton(successor_relation)))*.
% 299.82/300.44  216826[10:SpL:160336.0,201376.0] || subclass(universal_class,complement(symmetrization_of(successor_relation))) -> member(regular(domain_relation),complement(inverse(successor_relation)))*.
% 299.82/300.44  216832[10:SpL:160322.0,201376.0] || subclass(universal_class,complement(power_class(universal_class))) -> member(regular(domain_relation),image(element_relation,successor_relation))*.
% 299.82/300.44  216833[10:SpL:160328.0,201376.0] || subclass(universal_class,complement(power_class(successor_relation))) -> member(regular(domain_relation),image(element_relation,universal_class))*.
% 299.82/300.44  216910[10:Res:216847.1,595.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(regular(domain_relation),u).
% 299.82/300.44  216996[10:Rew:57.0,216995.0] || equal(power_class(u),successor_relation) member(unordered_pair(v,w),power_class(u))* -> .
% 299.82/300.44  217060[10:Rew:44.0,217056.1] || equal(image(u,v),successor_relation)** equal(image(u,v),universal_class) -> .
% 299.82/300.44  217079[10:Rew:44.0,217062.0] || equal(image(u,v),successor_relation) member(successor_relation,image(u,v))* -> .
% 299.82/300.44  217089[10:Rew:44.0,217081.0] || equal(image(u,v),successor_relation) subclass(universal_class,image(u,v))* -> .
% 299.82/300.44  217114[10:Rew:70.0,217100.0] || equal(apply(u,v),successor_relation) subclass(universal_class,apply(u,v))* -> .
% 299.82/300.44  217251[10:Res:217225.1,5.0] || equal(singleton(not_subclass_element(u,singleton(successor_relation))),kind_1_ordinals)** -> subclass(u,singleton(successor_relation)).
% 299.82/300.44  217414[20:Res:217226.1,5.0] || equal(singleton(not_subclass_element(u,singleton(successor_relation))),omega)** -> subclass(u,singleton(successor_relation)).
% 299.82/300.44  217544[10:Res:1476.1,160697.1] || subclass(universal_class,u) subclass(universal_class,regular(u))* -> equal(u,successor_relation).
% 299.82/300.44  217661[10:SpL:161592.1,217599.0] || subclass(universal_class,regular(cross_product(u,v)))* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.44  217877[10:SpL:161592.1,217670.0] || equal(regular(cross_product(u,v)),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.44  217933[3:Obv:217926.2] || subclass(u,ordinal_numbers) subclass(u,complement(kind_1_ordinals))* -> subclass(u,v)*.
% 299.82/300.44  218331[10:SpR:160336.0,218298.0] ||  -> subclass(regular(complement(inverse(successor_relation))),symmetrization_of(successor_relation))* equal(complement(inverse(successor_relation)),successor_relation).
% 299.82/300.44  218874[22:Res:218867.1,6045.0] || subclass(kind_1_ordinals,u)* subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  218878[22:Res:218867.1,3.0] || subclass(kind_1_ordinals,u)* subclass(u,v)* -> member(singleton(successor_relation),v)*.
% 299.82/300.44  218882[22:Res:218867.1,148657.1] || subclass(kind_1_ordinals,complement(compose(element_relation,universal_class)))* member(singleton(successor_relation),element_relation) -> .
% 299.82/300.44  218891[22:Res:218867.1,1952.0] || subclass(kind_1_ordinals,symmetric_difference(u,v)) -> member(singleton(successor_relation),union(u,v))*.
% 299.82/300.44  218892[22:Res:218867.1,10191.0] || subclass(kind_1_ordinals,symmetric_difference(u,inverse(u)))* -> member(singleton(successor_relation),symmetrization_of(u)).
% 299.82/300.44  218893[22:Res:218867.1,10254.0] || subclass(kind_1_ordinals,symmetric_difference(u,singleton(u)))* -> member(singleton(successor_relation),successor(u)).
% 299.82/300.44  219084[10:Res:218473.1,160435.1] inductive(u) || equal(complement(kind_1_ordinals),u)* -> member(successor_relation,complement(ordinal_numbers))*.
% 299.82/300.44  219090[3:Res:218473.1,183.1] || equal(intersection(y__dfg,ordinal_numbers),complement(kind_1_ordinals)) well_ordering(element_relation,complement(ordinal_numbers))* -> .
% 299.82/300.44  219105[3:Res:218473.1,5754.0] || equal(sum_class(complement(ordinal_numbers)),complement(kind_1_ordinals)) -> section(element_relation,complement(ordinal_numbers),universal_class)*.
% 299.82/300.44  219112[10:Res:218473.1,181153.0] || equal(singleton(singleton(successor_relation)),complement(kind_1_ordinals)) -> member(singleton(successor_relation),complement(ordinal_numbers))*.
% 299.82/300.44  219113[10:Res:218473.1,181149.0] || equal(singleton(singleton(successor_relation)),complement(kind_1_ordinals)) well_ordering(universal_class,complement(ordinal_numbers))* -> .
% 299.82/300.44  219117[9:Res:218473.1,157925.0] || equal(image(element_relation,universal_class),complement(kind_1_ordinals)) well_ordering(universal_class,complement(ordinal_numbers))* -> .
% 299.82/300.44  219119[13:Res:218473.1,180584.0] || equal(image(element_relation,successor_relation),complement(kind_1_ordinals)) well_ordering(universal_class,complement(ordinal_numbers))* -> .
% 299.82/300.44  219128[3:Res:218473.1,1503.0] || equal(ordered_pair(u,v),complement(kind_1_ordinals))** -> member(singleton(u),complement(ordinal_numbers))*.
% 299.82/300.44  219136[6:Res:218473.1,199959.0] || equal(cross_product(universal_class,universal_class),complement(kind_1_ordinals)) well_ordering(universal_class,complement(ordinal_numbers))* -> .
% 299.82/300.44  219137[12:Res:218473.1,177133.0] || equal(cross_product(universal_class,universal_class),complement(kind_1_ordinals)) -> member(regular(element_relation),complement(ordinal_numbers))*.
% 299.82/300.44  219138[6:Res:218473.1,154493.0] || equal(cross_product(universal_class,universal_class),complement(kind_1_ordinals)) -> member(regular(domain_relation),complement(ordinal_numbers))*.
% 299.82/300.44  219139[6:Res:218473.1,153518.0] || equal(cross_product(universal_class,universal_class),complement(kind_1_ordinals)) -> member(regular(rest_relation),complement(ordinal_numbers))*.
% 299.82/300.44  219156[10:Res:218473.1,161271.0] || equal(complement(complement(ordinal_numbers)),complement(kind_1_ordinals))** -> equal(complement(complement(ordinal_numbers)),successor_relation).
% 299.82/300.44  219159[10:Res:218473.1,197069.0] || equal(complement(singleton(successor_relation)),complement(kind_1_ordinals)) well_ordering(universal_class,complement(ordinal_numbers))* -> .
% 299.82/300.44  219160[10:Res:218473.1,206542.0] || equal(complement(complement(successor(successor_relation))),complement(kind_1_ordinals))** -> member(successor_relation,complement(ordinal_numbers)).
% 299.82/300.44  219173[3:Res:3907.1,218628.0] || equal(complement(complement(complement(kind_1_ordinals))),universal_class) -> member(singleton(u),complement(ordinal_numbers))*.
% 299.82/300.44  219211[10:Res:161493.2,218628.0] inductive(complement(kind_1_ordinals)) ||  -> equal(integer_of(u),successor_relation) member(u,complement(ordinal_numbers))*.
% 299.82/300.44  219212[15:Res:189485.1,218628.0] || subclass(domain_relation,complement(kind_1_ordinals)) -> member(singleton(singleton(singleton(successor_relation))),complement(ordinal_numbers))*.
% 299.82/300.44  219231[11:Res:183759.1,218628.0] || subclass(inverse(successor_relation),complement(kind_1_ordinals)) -> member(regular(symmetrization_of(successor_relation)),complement(ordinal_numbers))*.
% 299.82/300.44  219233[10:Res:197082.1,218628.0] || subclass(universal_class,complement(kind_1_ordinals)) -> member(regular(complement(successor(successor_relation))),complement(ordinal_numbers))*.
% 299.82/300.44  219548[10:MRR:219543.1,185225.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(u,singleton(v))),singleton(v))**.
% 299.82/300.44  219828[10:MRR:219826.1,185225.0] || equal(u,universal_class) -> equal(regular(unordered_pair(u,singleton(v))),singleton(v))**.
% 299.82/300.44  201599[10:Res:185647.1,163294.0] || equal(complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),successor_relation)** -> member(omega,kind_1_ordinals).
% 299.82/300.44  163332[10:Rew:160305.0,162812.0] || subclass(universal_class,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(singleton(u),kind_1_ordinals)*.
% 299.82/300.44  201606[10:Res:187500.1,163294.0] || subclass(universal_class,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(power_class(successor_relation),kind_1_ordinals).
% 299.82/300.44  201636[10:Res:199848.1,163294.0] || subclass(universal_class,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(regular(rest_relation),kind_1_ordinals).
% 299.82/300.44  201637[10:Res:201231.1,163294.0] || subclass(universal_class,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(regular(domain_relation),kind_1_ordinals).
% 299.82/300.44  209467[12:Res:209377.1,163294.0] || subclass(universal_class,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(regular(element_relation),kind_1_ordinals).
% 299.82/300.44  163333[10:Rew:160305.0,162813.0] || equal(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),universal_class)** -> member(singleton(u),kind_1_ordinals)*.
% 299.82/300.44  201195[10:SoR:200731.0,166971.1] || equal(range_of(successor_relation),singleton(successor_relation)) -> equal(integer_of(intersection(y__dfg,ordinal_numbers)),successor_relation)**.
% 299.82/300.44  193786[10:SpR:185302.1,193730.0] || equal(cross_product(u,universal_class),successor_relation) -> equal(image(universal_class,u),range_of(successor_relation))**.
% 299.82/300.44  166980[10:Res:163162.1,163256.1] || equal(range_of(successor_relation),complement(u)) -> member(successor_relation,u) inductive(complement(u))*.
% 299.82/300.44  163263[10:Rew:160202.0,160620.0] || member(ordered_pair(u,v),compose(successor_relation,w))* -> member(v,range_of(successor_relation)).
% 299.82/300.44  168528[11:Res:168384.1,163256.1] || equal(u,symmetrization_of(successor_relation)) equal(range_of(successor_relation),u)* -> inductive(u)*.
% 299.82/300.44  167020[10:Res:163169.1,163256.1] || equal(u,successor(successor_relation)) equal(range_of(successor_relation),u)* -> inductive(u)*.
% 299.82/300.44  167121[10:Res:163171.1,163256.1] || equal(u,singleton(successor_relation)) equal(range_of(successor_relation),u)* -> inductive(u)*.
% 299.82/300.44  181000[11:Res:179843.1,163256.1] || equal(u,inverse(successor_relation)) equal(range_of(successor_relation),u)* -> inductive(u)*.
% 299.82/300.44  185969[10:Res:185646.1,163256.1] || equal(complement(u),successor_relation)** equal(range_of(successor_relation),u)* -> inductive(u).
% 299.82/300.44  163158[10:Rew:160305.0,112434.2] || member(u,universal_class) -> member(u,kind_1_ordinals) member(u,complement(range_of(successor_relation)))*.
% 299.82/300.44  185471[10:SpR:185302.1,163219.0] || equal(range_of(successor_relation),successor_relation) -> subclass(symmetric_difference(complement(singleton(successor_relation)),universal_class),kind_1_ordinals)*.
% 299.82/300.44  197703[15:SpR:193779.0,193148.1] function(complement(cross_product(successor_relation,universal_class))) ||  -> equal(cantor(sum_class(range_of(successor_relation))),successor_relation)**.
% 299.82/300.44  220408[23:MRR:163630.1,220405.0] || subclass(kind_1_ordinals,u) -> member(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),u)*.
% 299.82/300.44  220878[23:Res:220417.0,3.0] || subclass(universal_class,u) -> member(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),u)*.
% 299.82/300.44  221066[23:Rew:160221.0,221062.1] || equal(universal_class,ordinal_numbers) subclass(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),successor_relation)* -> .
% 299.82/300.44  221342[10:MRR:221338.1,185241.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(singleton(v),u)),singleton(v))**.
% 299.82/300.44  221376[10:MRR:221375.1,185241.0] || equal(u,universal_class) -> equal(regular(unordered_pair(singleton(v),u)),singleton(v))**.
% 299.82/300.44  221437[10:Res:218373.0,160435.1] inductive(u) ||  -> equal(singleton(u),successor_relation) member(successor_relation,complement(singleton(u)))*.
% 299.82/300.44  221457[10:Res:218373.0,162884.0] || well_ordering(universal_class,complement(singleton(successor(successor_relation))))* -> equal(singleton(successor(successor_relation)),successor_relation).
% 299.82/300.44  221465[11:Res:218373.0,168391.0] || well_ordering(universal_class,complement(singleton(inverse(successor_relation))))* -> equal(singleton(inverse(successor_relation)),successor_relation).
% 299.82/300.44  221513[11:Res:218373.0,168374.0] || well_ordering(universal_class,complement(singleton(symmetrization_of(successor_relation))))* -> equal(singleton(symmetrization_of(successor_relation)),successor_relation).
% 299.82/300.44  221671[10:MRR:221606.1,184560.0] inductive(regular(ordinal_numbers)) ||  -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.44  221672[10:SSi:221609.0,52.0] || equal(universal_class,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.44  221886[10:Res:221523.0,6045.0] || subclass(complement(singleton(singleton(singleton(successor_relation)))),u)* well_ordering(universal_class,u) -> .
% 299.82/300.44  221890[10:Res:221523.0,3.0] || subclass(complement(singleton(singleton(singleton(successor_relation)))),u)* -> member(singleton(successor_relation),u).
% 299.82/300.44  221970[10:Res:161492.2,221891.0] || equal(singleton(singleton(singleton(successor_relation))),omega)** -> equal(integer_of(singleton(successor_relation)),successor_relation).
% 299.82/300.44  222135[10:SpR:181044.1,221525.0] || member(u,universal_class) -> member(successor_relation,complement(singleton(ordered_pair(successor(u),v))))*.
% 299.82/300.44  222136[15:SpR:190721.0,221525.0] ||  -> equal(range_of(u),successor_relation) member(successor_relation,complement(singleton(ordered_pair(inverse(u),v))))*.
% 299.82/300.44  222137[14:SpR:200028.1,221525.0] || member(u,universal_class) -> member(successor_relation,complement(singleton(ordered_pair(range_of(u),v))))*.
% 299.82/300.44  222142[10:Res:221525.0,6045.0] || subclass(complement(singleton(ordered_pair(u,v))),w)* well_ordering(universal_class,w) -> .
% 299.82/300.44  222146[10:Res:221525.0,3.0] || subclass(complement(singleton(ordered_pair(u,v))),w)* -> member(singleton(u),w).
% 299.82/300.44  222231[10:SpL:181044.1,222147.0] || member(u,universal_class) member(successor_relation,singleton(ordered_pair(successor(u),v)))* -> .
% 299.82/300.44  222232[15:SpL:190721.0,222147.0] || member(successor_relation,singleton(ordered_pair(inverse(u),v)))* -> equal(range_of(u),successor_relation).
% 299.82/300.44  222233[14:SpL:200028.1,222147.0] || member(u,universal_class) member(successor_relation,singleton(ordered_pair(range_of(u),v)))* -> .
% 299.82/300.44  222239[10:Res:161492.2,222147.0] || equal(singleton(ordered_pair(u,v)),omega)** -> equal(integer_of(singleton(u)),successor_relation).
% 299.82/300.44  222303[15:MRR:222282.0,999.0] || member(u,universal_class) subclass(domain_relation,complement(singleton(ordered_pair(u,successor_relation))))* -> .
% 299.82/300.44  222424[24:SpL:222326.0,203272.1] || member(kind_1_ordinals,cantor(u)) equal(restrict(u,successor_relation,universal_class),successor_relation)** -> .
% 299.82/300.44  223303[24:SpL:222479.0,95.0] || member(ordered_pair(u,universal_class),compose_class(v))* -> equal(compose(v,u),kind_1_ordinals).
% 299.82/300.44  224024[10:Obv:224000.0] ||  -> subclass(regular(power_class(u)),image(element_relation,complement(u)))* equal(power_class(u),successor_relation).
% 299.82/300.44  225462[25:Rew:204010.0,224992.1] function(u) ||  -> equal(segment(v,w,universal_class),segment(v,w,u))*.
% 299.82/300.44  225463[25:Rew:224739.1,225069.2] function(u) || member(singleton(singleton(successor_relation)),element_relation)* -> member(successor_relation,u)*.
% 299.82/300.44  225471[25:Rew:181085.0,224965.1] function(u) ||  -> equal(range__dfg(v,universal_class,w),range__dfg(v,u,w))*.
% 299.82/300.44  225473[25:Rew:181087.0,224990.1] function(u) ||  -> equal(domain__dfg(v,w,universal_class),domain__dfg(v,w,u))*.
% 299.82/300.44  225502[25:SoR:224740.0,160511.2] single_valued_class(regular(u)) || equal(regular(u),successor_relation)** -> equal(u,successor_relation).
% 299.82/300.44  225554[25:Res:67.2,225443.1] function(u) function(image(u,v)) || member(v,universal_class)* -> .
% 299.82/300.44  225604[25:MRR:225526.2,6.0] function(apply(choice,u)) || member(u,universal_class)* -> equal(u,successor_relation).
% 299.82/300.44  225684[24:SpR:223099.0,194805.1] || subclass(symmetric_difference(universal_class,kind_1_ordinals),successor(kind_1_ordinals))* -> equal(symmetric_difference(universal_class,kind_1_ordinals),successor_relation).
% 299.82/300.44  226268[15:MRR:226189.1,160227.0] || member(u,universal_class) -> equal(apply(power_class(successor_relation),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.44  226269[15:MRR:226192.1,160227.0] || member(u,universal_class) -> equal(apply(singleton(v),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.44  226270[15:MRR:226199.1,160227.0] || member(u,universal_class) -> equal(apply(regular(rest_relation),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.44  226271[15:MRR:226200.1,160227.0] || member(u,universal_class) -> equal(apply(regular(domain_relation),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.44  226272[15:MRR:226201.1,160227.0] || member(u,universal_class) -> equal(apply(regular(element_relation),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.44  226375[25:SpR:226350.1,199970.1] one_to_one(u) || member(u,universal_class)* -> equal(integer_of(sum_class(universal_class)),successor_relation)**.
% 299.82/300.44  226376[25:SpR:226350.1,199971.1] one_to_one(u) || member(u,universal_class)* -> equal(singleton(sum_class(universal_class)),successor_relation)**.
% 299.82/300.44  226396[25:SpL:226350.1,184789.0] one_to_one(u) || member(sum_class(universal_class),universal_class)* member(u,universal_class)* -> .
% 299.82/300.44  226397[25:SpL:226350.1,189423.1] one_to_one(u) || member(u,universal_class)* equal(sum_class(universal_class),successor_relation) -> .
% 299.82/300.44  226422[25:SpL:226350.1,200302.0] one_to_one(first(regular(rest_relation))) || equal(second(regular(rest_relation)),sum_class(universal_class))** -> .
% 299.82/300.44  226423[25:SpL:226350.1,201546.0] one_to_one(first(regular(domain_relation))) || equal(second(regular(domain_relation)),sum_class(universal_class))** -> .
% 299.82/300.44  226424[25:SpL:226350.1,209566.0] one_to_one(first(regular(element_relation))) || equal(second(regular(element_relation)),sum_class(universal_class))** -> .
% 299.82/300.44  227329[25:Res:224913.1,3.0] function(u) || subclass(ordered_pair(u,v),w)* -> member(successor_relation,w).
% 299.82/300.44  227638[10:SpR:227524.0,194805.1] || subclass(intersection(ordinal_numbers,u),complement(kind_1_ordinals))* -> equal(intersection(ordinal_numbers,u),successor_relation).
% 299.82/300.44  227749[10:SpR:227655.0,194805.1] || subclass(complement(complement(ordinal_numbers)),complement(kind_1_ordinals))* -> equal(complement(complement(ordinal_numbers)),successor_relation).
% 299.82/300.44  227868[10:SpR:227646.0,194805.1] || subclass(intersection(u,ordinal_numbers),complement(kind_1_ordinals))* -> equal(intersection(u,ordinal_numbers),successor_relation).
% 299.82/300.44  228681[10:Res:161493.2,222223.0] inductive(singleton(regular(rest_relation))) ||  -> equal(integer_of(singleton(first(regular(rest_relation)))),successor_relation)**.
% 299.82/300.44  228689[10:Res:161493.2,222224.0] inductive(singleton(regular(domain_relation))) ||  -> equal(integer_of(singleton(first(regular(domain_relation)))),successor_relation)**.
% 299.82/300.44  228697[12:Res:161493.2,222225.0] inductive(singleton(regular(element_relation))) ||  -> equal(integer_of(singleton(first(regular(element_relation)))),successor_relation)**.
% 299.82/300.44  228801[24:SpR:223107.0,195152.0] ||  -> equal(intersection(successor(kind_1_ordinals),symmetric_difference(complement(kind_1_ordinals),universal_class)),symmetric_difference(complement(kind_1_ordinals),universal_class))**.
% 299.82/300.44  228817[24:SpR:223107.0,205791.1] ||  -> equal(singleton(successor(kind_1_ordinals)),successor_relation) equal(symmetric_difference(complement(kind_1_ordinals),universal_class),successor(kind_1_ordinals))**.
% 299.82/300.44  228818[24:SpR:223107.0,185433.1] || equal(complement(successor(kind_1_ordinals)),successor_relation) -> equal(symmetric_difference(complement(kind_1_ordinals),universal_class),universal_class)**.
% 299.82/300.44  228826[24:SpL:223107.0,5884.0] || equal(symmetric_difference(complement(kind_1_ordinals),universal_class),universal_class) -> member(singleton(u),successor(kind_1_ordinals))*.
% 299.82/300.44  228829[24:SpL:223107.0,2648.0] || subclass(universal_class,symmetric_difference(complement(kind_1_ordinals),universal_class))* -> member(singleton(u),successor(kind_1_ordinals))*.
% 299.82/300.44  229014[10:Res:228991.1,3.0] || subclass(kind_1_ordinals,u)* subclass(u,v)* -> member(regular(ordinal_numbers),v)*.
% 299.82/300.44  229019[10:Res:228991.1,148657.1] || subclass(kind_1_ordinals,complement(compose(element_relation,universal_class)))* member(regular(ordinal_numbers),element_relation) -> .
% 299.82/300.44  229028[10:Res:228991.1,1952.0] || subclass(kind_1_ordinals,symmetric_difference(u,v)) -> member(regular(ordinal_numbers),union(u,v))*.
% 299.82/300.44  229029[10:Res:228991.1,10191.0] || subclass(kind_1_ordinals,symmetric_difference(u,inverse(u)))* -> member(regular(ordinal_numbers),symmetrization_of(u)).
% 299.82/300.44  229030[10:Res:228991.1,10254.0] || subclass(kind_1_ordinals,symmetric_difference(u,singleton(u)))* -> member(regular(ordinal_numbers),successor(u)).
% 299.82/300.44  229034[10:Res:228991.1,163294.0] || subclass(kind_1_ordinals,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(regular(ordinal_numbers),kind_1_ordinals).
% 299.82/300.44  229090[15:MRR:229077.1,160227.0] || member(u,universal_class) -> equal(apply(regular(ordinal_numbers),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.44  229149[10:MRR:229127.1,160455.0] || subclass(successor(successor_relation),symmetric_difference(u,v))* -> member(successor_relation,union(u,v)).
% 299.82/300.44  229242[10:Res:229228.1,3.0] || subclass(universal_class,u)* subclass(u,v)* -> member(regular(ordinal_numbers),v)*.
% 299.82/300.44  229247[10:Res:229228.1,148657.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(regular(ordinal_numbers),element_relation) -> .
% 299.82/300.44  229256[10:Res:229228.1,1952.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(regular(ordinal_numbers),union(u,v))*.
% 299.82/300.44  229257[10:Res:229228.1,10191.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(regular(ordinal_numbers),symmetrization_of(u)).
% 299.82/300.44  229258[10:Res:229228.1,10254.0] || subclass(universal_class,symmetric_difference(u,singleton(u)))* -> member(regular(ordinal_numbers),successor(u)).
% 299.82/300.44  229262[10:Res:229228.1,163294.0] || subclass(universal_class,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(regular(ordinal_numbers),kind_1_ordinals).
% 299.82/300.44  230160[15:SpL:160367.0,222296.1] || subclass(domain_relation,symmetric_difference(universal_class,u))* subclass(domain_relation,union(u,successor_relation)) -> .
% 299.82/300.44  230163[15:SpL:57.0,222296.1] || subclass(domain_relation,image(element_relation,complement(u)))* subclass(domain_relation,power_class(u)) -> .
% 299.82/300.44  230237[24:Res:161493.2,223309.0] inductive(element_relation) ||  -> equal(integer_of(ordered_pair(u,universal_class)),successor_relation)** member(u,kind_1_ordinals).
% 299.82/300.44  230326[10:SpR:226753.0,194805.1] || subclass(complement(kind_1_ordinals),restrict(ordinal_numbers,u,v))* -> equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.44  230375[10:MRR:230322.2,160227.0] || member(u,complement(kind_1_ordinals)) member(u,restrict(ordinal_numbers,v,w))* -> .
% 299.82/300.44  230542[15:Res:189485.1,229800.0] || subclass(domain_relation,singleton(omega)) -> equal(integer_of(singleton(singleton(singleton(successor_relation)))),successor_relation)**.
% 299.82/300.44  230544[10:Res:181213.1,229800.0] || equal(singleton(singleton(successor_relation)),singleton(omega)) -> equal(integer_of(singleton(successor_relation)),successor_relation)**.
% 299.82/300.44  230557[11:Res:183759.1,229800.0] || subclass(inverse(successor_relation),singleton(omega))* -> equal(integer_of(regular(symmetrization_of(successor_relation))),successor_relation).
% 299.82/300.44  230562[10:Res:199830.1,229800.0] || equal(cross_product(universal_class,universal_class),singleton(omega))** -> equal(integer_of(regular(rest_relation)),successor_relation).
% 299.82/300.44  230565[10:Res:201220.1,229800.0] || equal(cross_product(universal_class,universal_class),singleton(omega))** -> equal(integer_of(regular(domain_relation)),successor_relation).
% 299.82/300.44  230637[15:SpL:160367.0,230608.1] || equal(symmetric_difference(universal_class,u),domain_relation)** equal(union(u,successor_relation),domain_relation) -> .
% 299.82/300.44  230640[15:SpL:57.0,230608.1] || equal(image(element_relation,complement(u)),domain_relation)** equal(power_class(u),domain_relation) -> .
% 299.82/300.44  230678[10:MRR:230671.1,200297.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(u,regular(rest_relation))),regular(rest_relation))**.
% 299.82/300.44  230687[10:MRR:230680.1,201541.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(u,regular(domain_relation))),regular(domain_relation))**.
% 299.82/300.44  230696[12:MRR:230689.1,209559.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(u,regular(element_relation))),regular(element_relation))**.
% 299.82/300.44  230702[10:MRR:230698.1,200297.0] || equal(u,universal_class) -> equal(regular(unordered_pair(u,regular(rest_relation))),regular(rest_relation))**.
% 299.82/300.44  230703[10:Res:6.0,192570.0] || well_ordering(omega,universal_class) -> equal(integer_of(ordered_pair(omega,least(omega,universal_class))),successor_relation)**.
% 299.82/300.44  230720[10:MRR:230716.1,201541.0] || equal(u,universal_class) -> equal(regular(unordered_pair(u,regular(domain_relation))),regular(domain_relation))**.
% 299.82/300.44  230726[12:MRR:230722.1,209559.0] || equal(u,universal_class) -> equal(regular(unordered_pair(u,regular(element_relation))),regular(element_relation))**.
% 299.82/300.44  231088[10:Rew:160223.0,230992.1] || subclass(power_class(u),successor_relation) -> equal(symmetrization_of(image(element_relation,complement(u))),universal_class)**.
% 299.82/300.44  231204[10:MRR:231199.1,200282.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(regular(rest_relation),u)),regular(rest_relation))**.
% 299.82/300.44  231212[10:MRR:231207.1,201526.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(regular(domain_relation),u)),regular(domain_relation))**.
% 299.82/300.44  231220[12:MRR:231215.1,209545.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(regular(element_relation),u)),regular(element_relation))**.
% 299.82/300.44  231412[10:Rew:160223.0,231316.1] || subclass(power_class(u),successor_relation) -> equal(successor(image(element_relation,complement(u))),universal_class)**.
% 299.82/300.44  231513[10:MRR:231511.1,200282.0] || equal(u,universal_class) -> equal(regular(unordered_pair(regular(rest_relation),u)),regular(rest_relation))**.
% 299.82/300.44  231518[10:MRR:231516.1,201526.0] || equal(u,universal_class) -> equal(regular(unordered_pair(regular(domain_relation),u)),regular(domain_relation))**.
% 299.82/300.44  231523[12:MRR:231521.1,209545.0] || equal(u,universal_class) -> equal(regular(unordered_pair(regular(element_relation),u)),regular(element_relation))**.
% 299.82/300.44  231641[25:SpR:224912.1,183453.0] function(u) ||  -> equal(symmetric_difference(symmetric_difference(universal_class,u),complement(successor(u))),successor_relation)**.
% 299.82/300.44  231651[25:SpR:224912.1,161194.0] function(u) ||  -> equal(intersection(successor(u),universal_class),symmetric_difference(complement(u),universal_class))**.
% 299.82/300.44  9628[0:Res:9424.0,9.0] || subclass(u,restrict(u,v,w))* -> equal(restrict(u,v,w),u).
% 299.82/300.44  9879[0:SpR:161.0,9535.0] ||  -> subclass(symmetric_difference(complement(intersection(u,v)),union(u,v)),complement(symmetric_difference(u,v)))*.
% 299.82/300.44  6236[0:Res:6219.1,9.0] || member(u,v) subclass(v,singleton(u))* -> equal(v,singleton(u)).
% 299.82/300.44  48619[0:Res:1499.1,10254.0] || subclass(universal_class,symmetric_difference(u,singleton(u)))* -> member(ordered_pair(v,w),successor(u))*.
% 299.82/300.44  5878[0:SpL:161.0,2648.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(singleton(w),complement(intersection(u,v)))*.
% 299.82/300.44  5881[0:SpL:31.0,2648.0] || subclass(universal_class,restrict(u,v,w))* -> member(singleton(x),cross_product(v,w))*.
% 299.82/300.44  5792[0:Res:3907.1,595.0] || equal(complement(complement(restrict(u,v,w))),universal_class)** -> member(singleton(x),u)*.
% 299.82/300.44  48517[0:Res:1499.1,10191.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(ordered_pair(v,w),symmetrization_of(u))*.
% 299.82/300.44  6845[0:Res:1499.1,1952.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(ordered_pair(w,x),union(u,v))*.
% 299.82/300.44  3513[0:Res:1499.1,3.0] || subclass(universal_class,u)* subclass(u,v)* -> member(ordered_pair(w,x),v)*.
% 299.82/300.44  30800[0:Res:1495.2,3514.1] || member(u,universal_class)* subclass(rest_relation,v) subclass(universal_class,complement(v))* -> .
% 299.82/300.44  6145[0:SpL:31.0,5884.0] || equal(restrict(u,v,w),universal_class)** -> member(singleton(x),cross_product(v,w))*.
% 299.82/300.44  6142[0:SpL:161.0,5884.0] || equal(symmetric_difference(u,v),universal_class) -> member(singleton(w),complement(intersection(u,v)))*.
% 299.82/300.44  87695[0:SpR:40.0,31436.1] || equal(complement(rest_of(flip(cross_product(u,universal_class)))),universal_class)** -> subclass(inverse(u),v)*.
% 299.82/300.44  89290[0:SpR:28.0,89275.1] ||  -> member(u,intersection(complement(v),complement(w)))* subclass(singleton(u),union(v,w)).
% 299.82/300.44  107312[0:Res:107233.0,3926.1] single_valued_class(complement(complement(cross_product(universal_class,universal_class)))) ||  -> function(complement(complement(cross_product(universal_class,universal_class))))*.
% 299.82/300.44  108360[0:Res:1477.1,9332.1] || subclass(universal_class,intersection(u,v)) member(singleton(w),symmetric_difference(u,v))* -> .
% 299.82/300.44  110375[0:Res:8.1,31922.0] || equal(u,rest_relation) well_ordering(v,u)* -> member(least(v,rest_relation),rest_relation)*.
% 299.82/300.44  111980[0:Res:6842.1,3486.1] || subclass(universal_class,symmetric_difference(u,v)) subclass(universal_class,complement(union(u,v)))* -> .
% 299.82/300.44  115627[0:Res:114856.0,9.0] || subclass(complement(u),symmetric_difference(universal_class,u))* -> equal(symmetric_difference(universal_class,u),complement(u)).
% 299.82/300.44  118990[0:Res:3907.1,2031.0] || equal(complement(complement(compose_class(u))),universal_class) -> equal(compose(u,singleton(v)),v)**.
% 299.82/300.44  119672[0:Res:114897.1,9332.1] || equal(intersection(u,v),universal_class) member(singleton(w),symmetric_difference(u,v))* -> .
% 299.82/300.44  125905[0:Res:28320.1,6045.0] || subclass(rest_relation,rotate(u))* subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  126035[0:Res:28321.1,6045.0] || subclass(rest_relation,flip(u))* subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  126093[0:Res:28321.1,17.0] || subclass(rest_relation,flip(cross_product(u,v)))* -> member(rest_of(ordered_pair(w,x)),v)*.
% 299.82/300.44  30799[0:Res:1496.2,3514.1] || member(u,universal_class)* subclass(domain_relation,v) subclass(universal_class,complement(v))* -> .
% 299.82/300.44  142598[2:Rew:113504.0,142448.0] ||  -> equal(symmetric_difference(complement(u),intersection(u,v)),union(complement(u),intersection(u,v)))**.
% 299.82/300.44  142600[2:Rew:113504.0,142451.0] ||  -> equal(symmetric_difference(complement(u),intersection(v,u)),union(complement(u),intersection(v,u)))**.
% 299.82/300.44  142601[2:Rew:113504.0,142452.0] ||  -> equal(symmetric_difference(intersection(u,v),complement(u)),union(intersection(u,v),complement(u)))**.
% 299.82/300.44  142603[2:Rew:113504.0,142455.0] ||  -> equal(symmetric_difference(intersection(u,v),complement(v)),union(intersection(u,v),complement(v)))**.
% 299.82/300.44  144940[3:Res:144705.0,127.0] || subclass(domain_relation,u) well_ordering(v,u)* -> member(least(v,domain_relation),domain_relation)*.
% 299.82/300.44  152926[0:Res:1506.1,9322.0] || equal(symmetric_difference(complement(u),complement(v)),universal_class)** -> member(omega,union(u,v)).
% 299.82/300.44  155712[2:SpR:28.0,142543.0] ||  -> equal(symmetric_difference(universal_class,intersection(complement(u),complement(v))),intersection(union(u,v),universal_class))**.
% 299.82/300.44  155732[2:SpL:142543.0,9332.1] || member(u,symmetric_difference(complement(v),universal_class))* member(u,symmetric_difference(universal_class,v)) -> .
% 299.82/300.44  159769[6:SpL:28.0,159727.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),universal_class)** -> .
% 299.82/300.44  160028[3:Res:159954.0,9.0] || subclass(kind_1_ordinals,restrict(ordinal_numbers,u,v))* -> equal(restrict(ordinal_numbers,u,v),kind_1_ordinals).
% 299.82/300.44  160197[3:Res:159953.1,9.0] || member(u,ordinal_numbers) subclass(kind_1_ordinals,singleton(u))* -> equal(singleton(u),kind_1_ordinals).
% 299.82/300.44  162133[10:Rew:160202.0,150361.0] ||  -> equal(intersection(union(u,image(element_relation,universal_class)),intersection(complement(u),power_class(successor_relation))),successor_relation)**.
% 299.82/300.44  162132[10:Rew:160202.0,150360.0] ||  -> equal(intersection(intersection(complement(u),power_class(successor_relation)),union(u,image(element_relation,universal_class))),successor_relation)**.
% 299.82/300.44  162131[10:Rew:160202.0,150359.0] ||  -> equal(intersection(union(image(element_relation,universal_class),u),intersection(power_class(successor_relation),complement(u))),successor_relation)**.
% 299.82/300.44  162130[10:Rew:160202.0,150358.0] ||  -> equal(intersection(intersection(power_class(successor_relation),complement(u)),union(image(element_relation,universal_class),u)),successor_relation)**.
% 299.82/300.44  163331[10:Rew:160202.0,161801.1] ||  -> member(successor_relation,image(element_relation,power_class(u))) member(successor_relation,power_class(image(element_relation,complement(u))))*.
% 299.82/300.44  161752[10:Rew:160202.0,148545.0] || equal(not_subclass_element(cross_product(u,v),w),successor_relation)** -> subclass(cross_product(u,v),w).
% 299.82/300.44  163330[10:Rew:160202.0,161751.2,160202.0,161751.1] || connected(successor_relation,u) member(v,not_well_ordering(successor_relation,u))* -> well_ordering(successor_relation,u).
% 299.82/300.44  161750[10:Rew:160202.0,148541.0] || subclass(not_subclass_element(cross_product(u,v),w),successor_relation)* -> subclass(cross_product(u,v),w).
% 299.82/300.44  161749[10:Rew:160202.0,148472.0] ||  -> equal(integer_of(not_subclass_element(u,intersection(omega,u))),successor_relation)** subclass(u,intersection(omega,u)).
% 299.82/300.44  161737[10:Rew:160202.0,147812.0] ||  -> equal(intersection(intersection(u,intersection(complement(v),complement(w))),union(v,w)),successor_relation)**.
% 299.82/300.44  161736[10:Rew:160202.0,147762.0] ||  -> equal(intersection(intersection(intersection(complement(u),complement(v)),w),union(u,v)),successor_relation)**.
% 299.82/300.44  161735[10:Rew:160202.0,147748.0] ||  -> equal(intersection(union(u,v),intersection(w,intersection(complement(u),complement(v)))),successor_relation)**.
% 299.82/300.44  161733[10:Rew:160202.0,147698.1] || subclass(u,v)* -> equal(intersection(u,singleton(w)),successor_relation)** member(w,v)*.
% 299.82/300.44  161732[10:Rew:160202.0,147649.0] ||  -> equal(intersection(union(u,v),intersection(intersection(complement(u),complement(v)),w)),successor_relation)**.
% 299.82/300.44  161731[10:Rew:160202.0,147599.1] || subclass(u,v)* -> equal(intersection(singleton(w),u),successor_relation)** member(w,v)*.
% 299.82/300.44  161730[10:Rew:160202.0,147263.0] ||  -> equal(complement(complement(singleton(u))),successor_relation) equal(regular(complement(complement(singleton(u)))),u)**.
% 299.82/300.44  161728[10:Rew:160202.0,147073.1] || equal(intersection(u,v),w)* -> equal(w,successor_relation) member(regular(w),u)*.
% 299.82/300.44  161729[10:Rew:160202.0,147072.1] || equal(intersection(u,v),w)* -> equal(w,successor_relation) member(regular(w),v)*.
% 299.82/300.44  161723[10:Rew:160202.0,146904.2] || subclass(u,v)* well_ordering(universal_class,v)* -> equal(intersection(u,w),successor_relation)**.
% 299.82/300.44  161712[10:Rew:160202.0,146883.2] || subclass(u,v)* well_ordering(universal_class,v)* -> equal(intersection(w,u),successor_relation)**.
% 299.82/300.44  161701[10:Rew:160202.0,146846.1] || subclass(intersection(complement(u),v),u)* -> equal(intersection(complement(u),v),successor_relation).
% 299.82/300.44  161698[10:Rew:160202.0,146842.1] inductive(cantor(inverse(restrict(u,v,universal_class)))) ||  -> member(successor_relation,image(u,v))*.
% 299.82/300.44  163306[10:Rew:160202.0,160532.0] || member(not_subclass_element(complement(u),successor_relation),intersection(u,v))* -> subclass(complement(u),successor_relation).
% 299.82/300.44  163305[10:Rew:160202.0,160531.0] || member(not_subclass_element(complement(u),successor_relation),intersection(v,u))* -> subclass(complement(u),successor_relation).
% 299.82/300.44  161604[10:Rew:160202.0,146833.1] || subclass(universal_class,complement(regular(cross_product(u,v))))* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.44  161605[10:Rew:160202.0,146832.1] || equal(complement(regular(cross_product(u,v))),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.44  162984[10:Rew:160202.0,159922.1] || well_ordering(universal_class,union(u,v)) -> member(successor_relation,intersection(complement(u),complement(v)))*.
% 299.82/300.44  161650[10:Rew:160202.0,148466.0] ||  -> equal(complement(intersection(complement(u),union(v,successor_relation))),union(u,symmetric_difference(universal_class,v)))**.
% 299.82/300.44  161452[10:Rew:160202.0,146642.2] || member(u,v) member(u,singleton(v))* -> equal(singleton(v),successor_relation).
% 299.82/300.44  161441[10:Rew:160202.0,146628.2] || equal(complement(u),v) member(regular(v),u)* -> equal(v,successor_relation).
% 299.82/300.44  161418[10:Rew:160202.0,146619.2] || subclass(u,v)* well_ordering(universal_class,v)* -> equal(complement(complement(u)),successor_relation)**.
% 299.82/300.44  161408[10:Rew:160202.0,146640.1] inductive(complement(complement(cantor(flip(cross_product(u,universal_class)))))) ||  -> member(successor_relation,inverse(u))*.
% 299.82/300.44  161405[10:Rew:160202.0,146639.1] inductive(complement(complement(cantor(restrict(element_relation,universal_class,u))))) ||  -> member(successor_relation,sum_class(u))*.
% 299.82/300.44  161381[10:Rew:160202.0,146844.1] || subclass(intersection(u,complement(v)),v)* -> equal(intersection(u,complement(v)),successor_relation).
% 299.82/300.44  161372[10:Rew:160202.0,153218.1] || equal(symmetric_difference(complement(u),complement(v)),universal_class)** -> member(successor_relation,union(u,v)).
% 299.82/300.44  161195[10:Rew:160202.0,148453.0] ||  -> equal(complement(intersection(union(u,successor_relation),complement(v))),union(symmetric_difference(universal_class,u),v))**.
% 299.82/300.44  161215[10:Rew:160202.0,156043.0] || subclass(universal_class,union(u,successor_relation)) member(singleton(v),symmetric_difference(universal_class,u))* -> .
% 299.82/300.44  160820[10:Rew:160202.0,146391.0] ||  -> equal(singleton(u),successor_relation) equal(symmetric_difference(singleton(u),u),union(singleton(u),u))**.
% 299.82/300.44  160864[10:Rew:160202.0,152586.0] ||  -> subclass(symmetric_difference(power_class(universal_class),complement(singleton(image(element_relation,successor_relation)))),successor(image(element_relation,successor_relation)))*.
% 299.82/300.44  160862[10:Rew:160202.0,152578.0] ||  -> subclass(symmetric_difference(power_class(universal_class),complement(inverse(image(element_relation,successor_relation)))),symmetrization_of(image(element_relation,successor_relation)))*.
% 299.82/300.44  163313[10:Rew:160202.0,160842.1] ||  -> member(not_subclass_element(u,image(element_relation,successor_relation)),power_class(universal_class))* subclass(u,image(element_relation,successor_relation)).
% 299.82/300.44  160841[10:Rew:160202.0,148328.0] || member(not_subclass_element(power_class(universal_class),u),image(element_relation,successor_relation))* -> subclass(power_class(universal_class),u).
% 299.82/300.44  160840[10:Rew:160202.0,148327.0] || subclass(universal_class,image(element_relation,successor_relation)) member(unordered_pair(u,v),power_class(universal_class))* -> .
% 299.82/300.44  160828[10:Rew:160202.0,148322.1] || member(u,universal_class) -> member(u,image(element_relation,successor_relation))* member(u,power_class(universal_class)).
% 299.82/300.44  160700[10:Rew:160202.0,159692.2] || subclass(universal_class,regular(u))* member(singleton(v),u)* -> equal(u,successor_relation).
% 299.82/300.44  160701[10:Rew:160202.0,159690.2] || equal(regular(u),universal_class) member(singleton(v),u)* -> equal(u,successor_relation).
% 299.82/300.44  163302[10:Rew:160202.0,160498.0] || member(not_subclass_element(u,successor_relation),singleton(v))* -> member(v,u) subclass(u,successor_relation).
% 299.82/300.44  162960[10:Rew:160202.0,156241.1] || subclass(omega,singleton(u))* -> equal(integer_of(u),successor_relation) equal(singleton(u),omega).
% 299.82/300.44  168568[11:Res:168384.1,160481.0] || equal(regular(u),symmetrization_of(successor_relation)) member(successor_relation,u)* -> equal(u,successor_relation).
% 299.82/300.44  168554[11:Res:168384.1,307.0] || equal(image(element_relation,complement(u)),symmetrization_of(successor_relation))** member(successor_relation,power_class(u)) -> .
% 299.82/300.44  168551[11:Res:168384.1,10.0] || equal(unordered_pair(u,v),symmetrization_of(successor_relation))** -> equal(successor_relation,v) equal(successor_relation,u).
% 299.82/300.44  168542[11:Res:168384.1,594.0] || equal(restrict(u,v,w),symmetrization_of(successor_relation))** -> member(successor_relation,cross_product(v,w))*.
% 299.82/300.44  168538[11:Res:168384.1,9332.1] || equal(intersection(u,v),symmetrization_of(successor_relation)) member(successor_relation,symmetric_difference(u,v))* -> .
% 299.82/300.44  168529[11:Res:168384.1,6045.0] || equal(u,symmetrization_of(successor_relation)) subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  161158[10:Rew:160202.0,150864.0] ||  -> subclass(symmetric_difference(symmetrization_of(successor_relation),complement(inverse(complement(inverse(successor_relation))))),symmetrization_of(complement(inverse(successor_relation))))*.
% 299.82/300.44  161156[10:Rew:160202.0,150862.0] ||  -> subclass(symmetric_difference(symmetrization_of(successor_relation),complement(singleton(complement(inverse(successor_relation))))),successor(complement(inverse(successor_relation))))*.
% 299.82/300.44  163319[10:Rew:160202.0,161120.0] || member(not_subclass_element(symmetrization_of(successor_relation),u),complement(inverse(successor_relation)))* -> subclass(symmetrization_of(successor_relation),u).
% 299.82/300.44  163320[10:Rew:160202.0,161168.1] ||  -> member(regular(complement(symmetrization_of(successor_relation))),complement(inverse(successor_relation)))* equal(complement(symmetrization_of(successor_relation)),successor_relation).
% 299.82/300.44  163321[10:Rew:160202.0,161182.0] || subclass(singleton(u),successor_relation)* member(u,universal_class) -> member(u,inverse(successor_relation)).
% 299.82/300.44  161007[10:Rew:160202.0,150282.0] ||  -> subclass(symmetric_difference(power_class(successor_relation),complement(inverse(image(element_relation,universal_class)))),symmetrization_of(image(element_relation,universal_class)))*.
% 299.82/300.44  161006[10:Rew:160202.0,150281.0] ||  -> subclass(symmetric_difference(power_class(successor_relation),complement(singleton(image(element_relation,universal_class)))),successor(image(element_relation,universal_class)))*.
% 299.82/300.44  160988[10:Rew:160202.0,148445.0] ||  -> member(not_subclass_element(u,image(element_relation,universal_class)),power_class(successor_relation))* subclass(u,image(element_relation,universal_class)).
% 299.82/300.44  163316[10:Rew:160202.0,160987.1] || member(not_subclass_element(power_class(successor_relation),u),image(element_relation,universal_class))* -> subclass(power_class(successor_relation),u).
% 299.82/300.44  160986[10:Rew:160202.0,148443.1] || subclass(universal_class,image(element_relation,universal_class)) member(unordered_pair(u,v),power_class(successor_relation))* -> .
% 299.82/300.44  160942[10:Rew:160202.0,150177.0] ||  -> equal(symmetric_difference(union(u,image(element_relation,universal_class)),intersection(complement(u),power_class(successor_relation))),universal_class)**.
% 299.82/300.44  160941[10:Rew:160202.0,150176.0] ||  -> equal(symmetric_difference(intersection(complement(u),power_class(successor_relation)),union(u,image(element_relation,universal_class))),universal_class)**.
% 299.82/300.44  160940[10:Rew:160202.0,150175.0] ||  -> subclass(symmetric_difference(universal_class,intersection(complement(u),power_class(successor_relation))),union(u,image(element_relation,universal_class)))*.
% 299.82/300.44  160911[10:Rew:160202.0,150192.0] ||  -> equal(symmetric_difference(union(image(element_relation,universal_class),u),intersection(power_class(successor_relation),complement(u))),universal_class)**.
% 299.82/300.44  160910[10:Rew:160202.0,150191.0] ||  -> equal(symmetric_difference(intersection(power_class(successor_relation),complement(u)),union(image(element_relation,universal_class),u)),universal_class)**.
% 299.82/300.44  160909[10:Rew:160202.0,150190.0] ||  -> subclass(symmetric_difference(universal_class,intersection(power_class(successor_relation),complement(u))),union(image(element_relation,universal_class),u))*.
% 299.82/300.44  160996[10:Rew:160202.0,150189.0] || subclass(universal_class,power_class(successor_relation)) member(unordered_pair(u,v),image(element_relation,universal_class))* -> .
% 299.82/300.44  160997[10:Rew:160202.0,150188.0] || subclass(universal_class,power_class(successor_relation)) member(ordered_pair(u,v),image(element_relation,universal_class))* -> .
% 299.82/300.44  160905[10:Rew:160202.0,148438.2] || member(u,universal_class) -> member(u,image(element_relation,universal_class))* member(u,power_class(successor_relation)).
% 299.82/300.44  163094[10:Rew:160202.0,159358.1] || subclass(domain_relation,symmetric_difference(u,singleton(u)))* -> member(ordered_pair(successor_relation,successor_relation),successor(u)).
% 299.82/300.44  163093[10:Rew:160202.0,159357.1] || subclass(domain_relation,symmetric_difference(u,inverse(u)))* -> member(ordered_pair(successor_relation,successor_relation),symmetrization_of(u)).
% 299.82/300.44  163092[10:Rew:160202.0,159356.1] || subclass(domain_relation,symmetric_difference(u,v)) -> member(ordered_pair(successor_relation,successor_relation),union(u,v))*.
% 299.82/300.44  163088[10:Rew:160202.0,159348.1] || subclass(domain_relation,complement(compose(element_relation,universal_class)))* member(ordered_pair(successor_relation,successor_relation),element_relation) -> .
% 299.82/300.44  163078[10:Rew:160202.0,159344.2] || subclass(domain_relation,u)* subclass(u,v)* -> member(ordered_pair(successor_relation,successor_relation),v)*.
% 299.82/300.44  163072[10:Rew:160202.0,159498.2] || equal(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(successor_relation,successor_relation),u)*.
% 299.82/300.44  162906[10:Rew:160202.0,150874.0] ||  -> subclass(symmetric_difference(successor(successor_relation),complement(singleton(complement(singleton(successor_relation))))),successor(complement(singleton(successor_relation))))*.
% 299.82/300.44  162905[10:Rew:160202.0,150876.0] ||  -> subclass(symmetric_difference(successor(successor_relation),complement(inverse(complement(singleton(successor_relation))))),symmetrization_of(complement(singleton(successor_relation))))*.
% 299.82/300.44  163323[10:Rew:160202.0,161410.0] || equal(image(element_relation,complement(u)),successor(successor_relation))** member(successor_relation,power_class(u)) -> .
% 299.82/300.44  163308[10:Rew:160202.0,160546.2,160202.0,160546.0] || equal(regular(u),successor(successor_relation)) member(successor_relation,u)* -> equal(u,successor_relation).
% 299.82/300.44  163303[10:Rew:160202.0,160502.1,160202.0,160502.0] || equal(unordered_pair(u,v),successor(successor_relation))** -> equal(successor_relation,v) equal(successor_relation,u).
% 299.82/300.44  163325[10:Rew:160202.0,161420.0] || equal(restrict(u,v,w),successor(successor_relation))** -> member(successor_relation,cross_product(v,w))*.
% 299.82/300.44  163327[10:Rew:160202.0,161457.0] || equal(intersection(u,v),successor(successor_relation)) member(successor_relation,symmetric_difference(u,v))* -> .
% 299.82/300.44  162920[10:Rew:160202.0,157826.0] || equal(u,successor(successor_relation)) subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  163324[10:Rew:160202.0,161411.0] || equal(image(element_relation,complement(u)),singleton(successor_relation))** member(successor_relation,power_class(u)) -> .
% 299.82/300.44  163307[10:Rew:160202.0,160545.2,160202.0,160545.0] || equal(regular(u),singleton(successor_relation)) member(successor_relation,u)* -> equal(u,successor_relation).
% 299.82/300.44  163304[10:Rew:160202.0,160504.1,160202.0,160504.0] || equal(unordered_pair(u,v),singleton(successor_relation))** -> equal(successor_relation,v) equal(successor_relation,u).
% 299.82/300.44  163326[10:Rew:160202.0,161421.0] || equal(restrict(u,v,w),singleton(successor_relation))** -> member(successor_relation,cross_product(v,w))*.
% 299.82/300.44  163328[10:Rew:160202.0,161458.0] || equal(intersection(u,v),singleton(successor_relation)) member(successor_relation,symmetric_difference(u,v))* -> .
% 299.82/300.44  162874[10:Rew:160202.0,156272.0] || equal(u,singleton(successor_relation)) subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  107650[0:Res:34085.1,6045.0] || member(u,rest_of(u))* subclass(element_relation,v) well_ordering(universal_class,v)* -> .
% 299.82/300.44  48342[0:Res:3907.1,47888.0] || equal(complement(complement(rest_of(singleton(u)))),universal_class)** subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.44  34091[0:MRR:33512.1,34067.1] || member(u,universal_class)* member(v,u)* subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.44  48052[0:SpL:55.0,47745.0] || member(restrict(element_relation,universal_class,u),sum_class(u))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.44  48054[0:SpL:40.0,47745.0] || member(flip(cross_product(u,universal_class)),inverse(u))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.44  157912[6:Res:1499.1,148657.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(ordered_pair(u,v),element_relation)* -> .
% 299.82/300.44  47751[0:Rew:41.0,47719.0] || member(inverse(u),range_of(u)) -> member(ordered_pair(inverse(u),range_of(u)),element_relation)*.
% 299.82/300.44  125958[0:Res:28320.1,21.0] || subclass(rest_relation,rotate(element_relation)) -> member(ordered_pair(u,rest_of(ordered_pair(v,u))),v)*.
% 299.82/300.44  126088[0:Res:28321.1,21.0] || subclass(rest_relation,flip(element_relation)) -> member(ordered_pair(u,v),rest_of(ordered_pair(v,u)))*.
% 299.82/300.44  119698[0:Res:114897.1,307.0] || equal(image(element_relation,complement(u)),universal_class) member(singleton(v),power_class(u))* -> .
% 299.82/300.44  3664[0:SpL:57.0,2647.0] || subclass(universal_class,power_class(u)) member(singleton(v),image(element_relation,complement(u)))* -> .
% 299.82/300.44  10031[0:SpR:511.0,9421.0] ||  -> subclass(symmetric_difference(image(element_relation,complement(u)),v),complement(intersection(power_class(u),complement(v))))*.
% 299.82/300.44  9066[0:Res:1477.1,307.0] || subclass(universal_class,image(element_relation,complement(u)))* member(singleton(v),power_class(u))* -> .
% 299.82/300.44  125144[0:Obv:125115.0] ||  -> member(u,power_class(v)) subclass(intersection(singleton(u),w),image(element_relation,complement(v)))*.
% 299.82/300.44  125143[0:Obv:125116.0] ||  -> member(u,power_class(v)) subclass(intersection(w,singleton(u)),image(element_relation,complement(v)))*.
% 299.82/300.44  89279[0:Rew:57.0,89228.1] ||  -> member(not_subclass_element(u,power_class(v)),image(element_relation,complement(v)))* subclass(u,power_class(v)).
% 299.82/300.44  9991[0:SpR:509.0,9421.0] ||  -> subclass(symmetric_difference(u,image(element_relation,complement(v))),complement(intersection(complement(u),power_class(v))))*.
% 299.82/300.44  107292[0:SpR:505.0,107233.0] ||  -> subclass(complement(power_class(intersection(complement(u),complement(v)))),image(element_relation,union(u,v)))*.
% 299.82/300.44  87692[0:SpR:55.0,31436.1] || equal(complement(rest_of(restrict(element_relation,universal_class,u))),universal_class)** -> subclass(sum_class(u),v)*.
% 299.82/300.44  160058[3:Res:159952.1,1484.1] || subclass(unordered_pair(u,v),ordinal_numbers)* member(v,universal_class) -> member(v,kind_1_ordinals).
% 299.82/300.44  160060[3:Res:159952.1,1485.1] || subclass(unordered_pair(u,v),ordinal_numbers)* member(u,universal_class) -> member(u,kind_1_ordinals).
% 299.82/300.44  108480[0:Res:1504.1,2151.0] || subclass(ordered_pair(u,v),singleton(w))* -> equal(unordered_pair(u,singleton(v)),w).
% 299.82/300.44  48154[0:SpL:1933.0,3488.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(unordered_pair(v,w),symmetrization_of(u))*.
% 299.82/300.44  48155[0:SpL:1934.0,3488.0] || subclass(universal_class,symmetric_difference(u,singleton(u)))* -> member(unordered_pair(v,w),successor(u))*.
% 299.82/300.44  112647[0:MRR:112608.0,13.0] || subclass(universal_class,complement(union(u,v)))* -> member(unordered_pair(w,x),complement(u))*.
% 299.82/300.44  112486[0:MRR:112441.0,13.0] || subclass(universal_class,complement(union(u,v)))* -> member(unordered_pair(w,x),complement(v))*.
% 299.82/300.44  112054[0:Res:8.1,3485.0] || equal(u,universal_class) subclass(u,v)* -> member(unordered_pair(w,x),v)*.
% 299.82/300.44  89240[0:Res:51387.0,26.1] || member(not_subclass_element(u,complement(complement(v))),v)* -> subclass(u,complement(complement(v))).
% 299.82/300.44  155812[3:Res:51387.0,141576.1] || member(not_subclass_element(u,complement(complement(kind_1_ordinals))),ordinal_numbers)* -> subclass(u,complement(complement(kind_1_ordinals))).
% 299.82/300.44  40235[0:Obv:40233.1] || member(not_subclass_element(u,intersection(v,universal_class)),v)* -> subclass(u,intersection(v,universal_class)).
% 299.82/300.44  112649[0:MRR:112617.0,34189.1] ||  -> member(not_subclass_element(u,union(v,w)),complement(v))* subclass(u,union(v,w)).
% 299.82/300.44  112488[0:MRR:112450.0,34189.1] ||  -> member(not_subclass_element(u,union(v,w)),complement(w))* subclass(u,union(v,w)).
% 299.82/300.44  155768[2:Rew:142543.0,155746.1] || member(not_subclass_element(symmetric_difference(universal_class,u),v),u)* -> subclass(symmetric_difference(universal_class,u),v).
% 299.82/300.44  131789[0:SpR:113504.0,9529.1] ||  -> subclass(symmetric_difference(universal_class,u),v) member(not_subclass_element(symmetric_difference(universal_class,u),v),complement(u))*.
% 299.82/300.44  113107[0:Res:8.1,9649.0] || equal(singleton(u),v)* -> subclass(v,w) equal(not_subclass_element(v,w),u)*.
% 299.82/300.44  143074[0:Res:53.1,9640.0] inductive(intersection(u,v)) ||  -> subclass(omega,w) member(not_subclass_element(omega,w),v)*.
% 299.82/300.44  143073[0:Res:53.1,9639.0] inductive(intersection(u,v)) ||  -> subclass(omega,w) member(not_subclass_element(omega,w),u)*.
% 299.82/300.44  155832[3:Res:155815.1,40234.0] || member(not_subclass_element(u,intersection(kind_1_ordinals,u)),ordinal_numbers)* -> subclass(u,intersection(kind_1_ordinals,u)).
% 299.82/300.44  112415[0:SpR:115.0,30985.1] || member(u,universal_class) -> member(u,symmetrization_of(v)) member(u,complement(inverse(v)))*.
% 299.82/300.44  112419[0:SpR:45.0,30985.1] || member(u,universal_class) -> member(u,successor(v)) member(u,complement(singleton(v)))*.
% 299.82/300.44  110820[0:Res:8.1,28299.1] || equal(cross_product(u,v),rest_relation)** member(w,universal_class)* -> member(w,u)*.
% 299.82/300.44  110845[0:Res:8.1,28123.1] || equal(cross_product(u,v),domain_relation)** member(w,universal_class)* -> member(w,u)*.
% 299.82/300.44  179987[11:Res:179843.1,6045.0] || equal(u,inverse(successor_relation)) subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  179995[11:Res:179843.1,9332.1] || equal(intersection(u,v),inverse(successor_relation)) member(successor_relation,symmetric_difference(u,v))* -> .
% 299.82/300.44  179999[11:Res:179843.1,594.0] || equal(restrict(u,v,w),inverse(successor_relation))** -> member(successor_relation,cross_product(v,w))*.
% 299.82/300.44  180017[11:Res:179843.1,10.0] || equal(unordered_pair(u,v),inverse(successor_relation))** -> equal(successor_relation,v) equal(successor_relation,u).
% 299.82/300.44  181136[10:Rew:181056.0,181094.1] || member(singleton(singleton(successor_relation)),rest_of(u))* -> equal(restrict(u,successor_relation,universal_class),universal_class).
% 299.82/300.44  182172[11:Res:179843.1,307.0] || equal(image(element_relation,complement(u)),inverse(successor_relation))** member(successor_relation,power_class(u)) -> .
% 299.82/300.44  182411[11:Res:179843.1,160481.0] || equal(regular(u),inverse(successor_relation)) member(successor_relation,u)* -> equal(u,successor_relation).
% 299.82/300.44  182935[6:Res:157922.1,3.0] || member(u,element_relation)* subclass(compose(element_relation,universal_class),v)* -> member(u,v)*.
% 299.82/300.44  182936[6:Res:157922.1,5.0] || member(not_subclass_element(u,compose(element_relation,universal_class)),element_relation)* -> subclass(u,compose(element_relation,universal_class)).
% 299.82/300.44  183207[10:Rew:160223.0,183142.1] || member(u,universal_class) -> subclass(symmetric_difference(complement(successor(u)),universal_class),successor(successor(u)))*.
% 299.82/300.44  183383[10:SpR:160367.0,139600.0] ||  -> equal(intersection(symmetric_difference(universal_class,u),complement(union(u,successor_relation))),complement(union(u,successor_relation)))**.
% 299.82/300.44  183459[10:SpR:208.0,183420.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(u)),complement(power_class(image(element_relation,complement(u))))),successor_relation)**.
% 299.82/300.44  183819[10:Res:160290.2,183622.0] || subclass(u,successor(successor_relation)) -> equal(u,successor_relation) member(regular(u),singleton(successor_relation))*.
% 299.82/300.44  183852[10:Res:160290.2,183723.0] || subclass(u,symmetrization_of(successor_relation)) -> equal(u,successor_relation) member(regular(u),inverse(successor_relation))*.
% 299.82/300.44  183910[11:Res:183764.1,3.0] || subclass(universal_class,u)* subclass(u,v)* -> member(regular(symmetrization_of(successor_relation)),v)*.
% 299.82/300.44  183914[11:Res:183764.1,148657.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(regular(symmetrization_of(successor_relation)),element_relation) -> .
% 299.82/300.44  183922[11:Res:183764.1,1952.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(regular(symmetrization_of(successor_relation)),union(u,v))*.
% 299.82/300.44  183923[11:Res:183764.1,10191.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(regular(symmetrization_of(successor_relation)),symmetrization_of(u)).
% 299.82/300.44  183924[11:Res:183764.1,10254.0] || subclass(universal_class,symmetric_difference(u,singleton(u)))* -> member(regular(symmetrization_of(successor_relation)),successor(u)).
% 299.82/300.44  184222[10:Rew:160367.0,184205.1] || subclass(union(u,successor_relation),symmetric_difference(universal_class,u))* -> equal(union(u,successor_relation),successor_relation).
% 299.82/300.44  184677[10:SpR:163198.1,1948.0] || subclass(union(u,v),successor_relation) -> equal(symmetric_difference(complement(u),complement(v)),successor_relation)**.
% 299.82/300.44  185043[10:SpR:28.0,184981.1] || subclass(intersection(complement(u),complement(v)),successor_relation)* -> subclass(universal_class,union(u,v)).
% 299.82/300.44  185072[10:Res:184981.1,9146.1] || subclass(u,successor_relation) member(v,universal_class) member(power_class(v),u)* -> .
% 299.82/300.44  185339[10:SpL:505.0,185324.0] || equal(power_class(intersection(complement(u),complement(v))),image(element_relation,union(u,v)))** -> .
% 299.82/300.44  185407[10:SpR:185302.1,28.0] || equal(intersection(complement(u),complement(v)),successor_relation)** -> equal(union(u,v),universal_class).
% 299.82/300.44  185658[10:Rew:113504.0,185408.1] || equal(intersection(u,v),successor_relation)** -> equal(symmetric_difference(u,v),union(u,v)).
% 299.82/300.44  185862[10:SpR:113504.0,161953.1] || asymmetric(universal_class,singleton(u)) -> equal(segment(inverse(universal_class),singleton(u),u),successor_relation)**.
% 299.82/300.44  185866[10:Rew:181056.0,185858.0] || asymmetric(u,successor_relation) -> equal(segment(intersection(u,inverse(u)),successor_relation,universal_class),successor_relation)**.
% 299.82/300.44  185930[10:Res:185646.1,6045.0] || equal(complement(u),successor_relation) subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.44  185943[10:Res:185646.1,594.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(successor_relation,cross_product(v,w)).
% 299.82/300.44  185966[10:Res:185646.1,160481.0] || equal(complement(regular(u)),successor_relation)** member(successor_relation,u) -> equal(u,successor_relation).
% 299.82/300.44  186017[10:Res:185647.1,594.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(omega,cross_product(v,w)).
% 299.82/300.44  186040[10:Res:185647.1,160481.0] || equal(complement(regular(u)),successor_relation)** member(omega,u) -> equal(u,successor_relation).
% 299.82/300.44  186051[10:SpL:28.0,185795.0] || equal(union(u,v),successor_relation) -> equal(intersection(complement(u),complement(v)),universal_class)**.
% 299.82/300.44  186464[10:SpR:185605.1,183458.0] || equal(successor_relation,u) -> equal(symmetric_difference(image(element_relation,universal_class),complement(power_class(u))),successor_relation)**.
% 299.82/300.44  186471[10:SpR:185605.1,185605.1] || equal(successor_relation,u) equal(successor_relation,v) -> equal(power_class(u),power_class(v))*.
% 299.82/300.44  181137[10:Rew:181056.0,181117.1] || member(ordered_pair(u,singleton(singleton(successor_relation))),composition_function)* -> equal(compose(u,successor_relation),universal_class).
% 299.82/300.44  30797[0:Res:99.1,3514.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(universal_class,complement(composition_function)) -> .
% 299.82/300.44  107687[0:Res:305.1,6045.0] || member(u,universal_class) subclass(singleton(u),v)* well_ordering(universal_class,v) -> .
% 299.82/300.44  110628[0:Res:8.1,5858.0] || equal(u,universal_class) well_ordering(v,u)* -> member(least(v,universal_class),universal_class)*.
% 299.82/300.44  110390[0:Res:110376.1,3.0] || well_ordering(u,rest_relation) subclass(rest_relation,v) -> member(least(u,rest_relation),v)*.
% 299.82/300.44  110410[0:Res:110388.1,3.0] || well_ordering(u,rest_relation) subclass(universal_class,v) -> member(least(u,rest_relation),v)*.
% 299.82/300.44  168468[11:MRR:163488.2,168458.0] || well_ordering(u,universal_class) member(least(u,symmetrization_of(successor_relation)),complement(inverse(successor_relation)))* -> .
% 299.82/300.44  162907[10:Rew:160202.0,157746.1] || well_ordering(u,universal_class) member(least(u,successor(successor_relation)),complement(singleton(successor_relation)))* -> .
% 299.82/300.44  110384[0:Res:110370.1,3.0] || well_ordering(u,universal_class) subclass(rest_relation,v) -> member(least(u,rest_relation),v)*.
% 299.82/300.44  110396[0:Res:110382.1,3.0] || well_ordering(u,universal_class) subclass(universal_class,v) -> member(least(u,rest_relation),v)*.
% 299.82/300.44  110639[0:Res:110623.1,3.0] || well_ordering(u,universal_class) subclass(universal_class,v) -> member(least(u,universal_class),v)*.
% 299.82/300.44  160072[3:Res:159952.1,31922.0] || subclass(rest_relation,ordinal_numbers) well_ordering(u,kind_1_ordinals) -> member(least(u,rest_relation),rest_relation)*.
% 299.82/300.44  184601[10:Res:184565.1,3.0] || well_ordering(u,kind_1_ordinals) subclass(ordinal_numbers,v) -> member(least(u,ordinal_numbers),v)*.
% 299.82/300.44  184607[10:Res:184599.1,3.0] || well_ordering(u,kind_1_ordinals) subclass(universal_class,v) -> member(least(u,ordinal_numbers),v)*.
% 299.82/300.44  181432[10:SpR:181082.0,137.1] || member(image(u,successor_relation),ordinal_numbers) -> subclass(apply(u,universal_class),image(u,successor_relation))*.
% 299.82/300.44  181222[10:MRR:181221.0,160214.0] || member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> member(singleton(singleton(successor_relation)),element_relation).
% 299.82/300.44  187565[16:Res:136.1,187562.0] || member(cross_product(universal_class,cross_product(universal_class,universal_class)),ordinal_numbers)* -> member(least(element_relation,composition_function),composition_function).
% 299.82/300.44  187771[10:Res:187500.1,9332.1] || subclass(universal_class,intersection(u,v)) member(power_class(successor_relation),symmetric_difference(u,v))* -> .
% 299.82/300.44  187775[10:Res:187500.1,594.0] || subclass(universal_class,restrict(u,v,w))* -> member(power_class(successor_relation),cross_product(v,w)).
% 299.82/300.44  187796[10:Res:187500.1,307.0] || subclass(universal_class,image(element_relation,complement(u)))* member(power_class(successor_relation),power_class(u)) -> .
% 299.82/300.44  187797[10:Res:187500.1,160481.0] || subclass(universal_class,regular(u))* member(power_class(successor_relation),u) -> equal(u,successor_relation).
% 299.82/300.44  188719[17:Res:159952.1,188715.0] || subclass(omega,ordinal_numbers) well_ordering(u,kind_1_ordinals) -> member(least(u,omega),omega)*.
% 299.82/300.44  188720[17:Res:8.1,188715.0] || equal(u,omega) well_ordering(v,u)* -> member(least(v,omega),omega)*.
% 299.82/300.44  188731[17:Res:188716.1,3.0] || well_ordering(u,universal_class) subclass(omega,v) -> member(least(u,omega),v)*.
% 299.82/300.44  188739[17:Res:188721.1,3.0] || well_ordering(u,omega) subclass(omega,v) -> member(least(u,omega),v)*.
% 299.82/300.44  188747[17:Res:188729.1,3.0] || well_ordering(u,universal_class) subclass(universal_class,v) -> member(least(u,omega),v)*.
% 299.82/300.44  188759[17:Res:188737.1,3.0] || well_ordering(u,omega) subclass(universal_class,v) -> member(least(u,omega),v)*.
% 299.82/300.44  189202[10:SpR:185608.1,1948.0] || equal(union(u,v),successor_relation) -> equal(symmetric_difference(complement(u),complement(v)),successor_relation)**.
% 299.82/300.44  191110[20:Res:191074.1,9322.0] || equal(symmetric_difference(complement(u),complement(v)),omega)** -> member(successor_relation,union(u,v)).
% 299.82/300.44  192216[15:Rew:160223.0,192124.1] ||  -> equal(range_of(u),successor_relation) subclass(symmetric_difference(complement(inverse(u)),universal_class),successor(inverse(u)))*.
% 299.82/300.44  192379[20:SpL:28.0,192322.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),omega)** -> .
% 299.82/300.44  192707[15:SpR:70.0,191934.1] || member(image(u,singleton(v)),universal_class)* -> equal(cantor(apply(u,v)),successor_relation).
% 299.82/300.44  193146[15:Res:67.2,193015.0] function(u) || member(v,universal_class) -> equal(cantor(image(u,v)),successor_relation)**.
% 299.82/300.44  193182[15:MRR:193125.1,6.0] || member(u,universal_class) -> equal(u,successor_relation) equal(cantor(apply(choice,u)),successor_relation)**.
% 299.82/300.44  193395[10:Res:192947.1,3.0] || equal(complement(u),successor_relation) subclass(u,v)* -> member(singleton(w),v)*.
% 299.82/300.44  193399[10:Res:192947.1,148657.1] || equal(complement(complement(compose(element_relation,universal_class))),successor_relation)** member(singleton(u),element_relation)* -> .
% 299.82/300.44  193407[10:Res:192947.1,1952.0] || equal(complement(symmetric_difference(u,v)),successor_relation) -> member(singleton(w),union(u,v))*.
% 299.82/300.44  193408[10:Res:192947.1,10191.0] || equal(complement(symmetric_difference(u,inverse(u))),successor_relation)** -> member(singleton(v),symmetrization_of(u))*.
% 299.82/300.44  193409[10:Res:192947.1,10254.0] || equal(complement(symmetric_difference(u,singleton(u))),successor_relation)** -> member(singleton(v),successor(u))*.
% 299.82/300.44  193449[10:Rew:28.0,193403.0] || equal(union(u,v),successor_relation) member(singleton(w),union(u,v))* -> .
% 299.82/300.44  193520[10:MRR:193519.0,100.0] || subclass(composition_function,u) well_ordering(v,u)* -> member(least(v,composition_function),composition_function)*.
% 299.82/300.44  193539[2:Res:141787.0,3670.1] || equal(complement(inverse(singleton(singleton(u)))),universal_class)** -> asymmetric(singleton(singleton(u)),v)*.
% 299.82/300.44  193546[2:Res:141787.0,3.0] || subclass(inverse(singleton(u)),v)* -> asymmetric(singleton(u),w)* member(u,v).
% 299.82/300.44  193738[10:SpR:161319.0,160359.0] ||  -> equal(range__dfg(complement(cross_product(singleton(u),v)),u,v),second(not_subclass_element(successor_relation,successor_relation)))**.
% 299.82/300.44  193810[10:SpL:109924.1,193764.0] || equal(cantor(complement(cross_product(singleton(u),universal_class))),universal_class)** member(u,universal_class) -> .
% 299.82/300.44  193938[10:SpL:161592.1,185068.0] || subclass(singleton(regular(cross_product(u,v))),successor_relation)* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.44  194067[10:SpL:181044.1,193819.0] || member(u,universal_class) member(successor(u),cantor(complement(cross_product(successor_relation,universal_class))))* -> .
% 299.82/300.44  194068[15:SpL:190721.0,193819.0] || member(inverse(u),cantor(complement(cross_product(successor_relation,universal_class))))* -> equal(range_of(u),successor_relation).
% 299.82/300.44  194081[10:Res:160290.2,193819.0] || subclass(u,cantor(complement(cross_product(singleton(regular(u)),universal_class))))* -> equal(u,successor_relation).
% 299.82/300.44  194197[10:Con:194196.2] || subclass(u,successor_relation) member(not_subclass_element(v,successor_relation),u)* -> subclass(v,successor_relation).
% 299.82/300.44  194526[10:Res:160290.2,183398.0] || subclass(u,complement(complement(v)))* -> equal(u,successor_relation) member(regular(u),v).
% 299.82/300.44  195401[0:SpR:194805.1,28.0] || subclass(complement(u),complement(v))* -> equal(union(v,u),complement(complement(u))).
% 299.82/300.44  195422[10:SpR:194805.1,163000.0] || subclass(symmetric_difference(universal_class,u),complement(complement(u)))* -> equal(symmetric_difference(universal_class,u),successor_relation).
% 299.82/300.44  195447[10:SpR:194805.1,163005.0] || subclass(complement(complement(u)),symmetric_difference(universal_class,u))* -> equal(complement(complement(u)),successor_relation).
% 299.82/300.44  195476[10:SpR:194805.1,162965.0] || subclass(symmetric_difference(universal_class,u),union(u,successor_relation))* -> equal(symmetric_difference(universal_class,u),successor_relation).
% 299.82/300.44  195490[0:SpL:194805.1,8846.0] || subclass(ordinal_numbers,y__dfg) member(least(element_relation,ordinal_numbers),restrict(ordinal_numbers,u,v))* -> .
% 299.82/300.44  195571[10:Rew:194805.1,195494.2] || subclass(ordinal_numbers,y__dfg) member(ordinal_numbers,unordered_pair(successor_relation,u))* -> equal(ordinal_numbers,u).
% 299.82/300.44  195572[10:Rew:194805.1,195495.2] || subclass(ordinal_numbers,y__dfg) member(ordinal_numbers,unordered_pair(u,successor_relation))* -> equal(ordinal_numbers,u).
% 299.82/300.44  195785[10:Res:195710.1,160464.0] || equal(inverse(u),universal_class) -> equal(integer_of(v),successor_relation) member(v,inverse(u))*.
% 299.82/300.44  195819[6:Con:195808.2] || equal(inverse(u),universal_class) member(v,w)* -> member(v,inverse(u))*.
% 299.82/300.44  195834[6:Res:195720.1,1320.1] || equal(sum_class(u),universal_class) member(u,ordinal_numbers)* -> equal(sum_class(u),u).
% 299.82/300.44  195844[10:Res:195720.1,160464.0] || equal(sum_class(u),universal_class) -> equal(integer_of(v),successor_relation) member(v,sum_class(u))*.
% 299.82/300.44  195885[6:Con:195867.2] || equal(sum_class(u),universal_class) member(v,w)* -> member(v,sum_class(u))*.
% 299.82/300.44  196441[10:SpR:185302.1,160848.0] || equal(power_class(image(element_relation,successor_relation)),successor_relation) -> subclass(universal_class,image(element_relation,power_class(universal_class)))*.
% 299.82/300.44  196442[10:Res:160848.0,160435.1] inductive(complement(power_class(image(element_relation,successor_relation)))) ||  -> member(successor_relation,image(element_relation,power_class(universal_class)))*.
% 299.82/300.44  196494[10:Res:161138.0,160435.1] inductive(complement(power_class(complement(inverse(successor_relation))))) ||  -> member(successor_relation,image(element_relation,symmetrization_of(successor_relation)))*.
% 299.82/300.44  196506[10:SpR:161137.0,185302.1] || equal(image(element_relation,symmetrization_of(successor_relation)),successor_relation)** -> equal(power_class(complement(inverse(successor_relation))),universal_class).
% 299.82/300.44  196521[10:SpR:161137.0,142543.0] ||  -> equal(intersection(power_class(complement(inverse(successor_relation))),universal_class),symmetric_difference(universal_class,image(element_relation,symmetrization_of(successor_relation))))**.
% 299.82/300.44  196523[10:SpR:161137.0,107289.0] ||  -> subclass(complement(power_class(image(element_relation,symmetrization_of(successor_relation)))),image(element_relation,power_class(complement(inverse(successor_relation)))))*.
% 299.82/300.44  196532[10:SpR:161137.0,160368.0] ||  -> subclass(symmetric_difference(power_class(complement(inverse(successor_relation))),universal_class),union(image(element_relation,symmetrization_of(successor_relation)),successor_relation))*.
% 299.82/300.44  196533[10:SpR:161137.0,160445.0] ||  -> equal(intersection(intersection(image(element_relation,symmetrization_of(successor_relation)),u),power_class(complement(inverse(successor_relation)))),successor_relation)**.
% 299.82/300.44  196534[10:SpR:161137.0,160444.0] ||  -> equal(intersection(power_class(complement(inverse(successor_relation))),intersection(u,image(element_relation,symmetrization_of(successor_relation)))),successor_relation)**.
% 299.82/300.44  196535[10:SpR:161137.0,160443.0] ||  -> equal(intersection(power_class(complement(inverse(successor_relation))),intersection(image(element_relation,symmetrization_of(successor_relation)),u)),successor_relation)**.
% 299.82/300.44  196545[10:SpR:161137.0,89275.1] ||  -> member(u,image(element_relation,symmetrization_of(successor_relation))) subclass(singleton(u),power_class(complement(inverse(successor_relation))))*.
% 299.82/300.44  196546[10:SpR:161137.0,160446.0] ||  -> equal(intersection(intersection(u,image(element_relation,symmetrization_of(successor_relation))),power_class(complement(inverse(successor_relation)))),successor_relation)**.
% 299.82/300.44  196555[10:SpL:161137.0,159727.1] inductive(image(element_relation,symmetrization_of(successor_relation))) || equal(power_class(complement(inverse(successor_relation))),universal_class)** -> .
% 299.82/300.44  196562[10:SpL:161137.0,185335.0] || equal(image(element_relation,power_class(complement(inverse(successor_relation)))),power_class(image(element_relation,symmetrization_of(successor_relation))))** -> .
% 299.82/300.44  196563[10:SpL:161137.0,160256.0] || well_ordering(universal_class,power_class(complement(inverse(successor_relation))))* -> member(successor_relation,image(element_relation,symmetrization_of(successor_relation))).
% 299.82/300.44  196565[10:SpL:161137.0,185795.0] || equal(power_class(complement(inverse(successor_relation))),successor_relation) -> equal(image(element_relation,symmetrization_of(successor_relation)),universal_class)**.
% 299.82/300.44  196572[20:SpL:161137.0,192322.1] inductive(image(element_relation,symmetrization_of(successor_relation))) || equal(power_class(complement(inverse(successor_relation))),omega)** -> .
% 299.82/300.44  196633[10:SpR:185302.1,160971.0] || equal(power_class(image(element_relation,universal_class)),successor_relation) -> subclass(universal_class,image(element_relation,power_class(successor_relation)))*.
% 299.82/300.44  196634[10:Res:160971.0,160435.1] inductive(complement(power_class(image(element_relation,universal_class)))) ||  -> member(successor_relation,image(element_relation,power_class(successor_relation)))*.
% 299.82/300.44  196712[10:SpR:162889.0,185302.1] || equal(image(element_relation,successor(successor_relation)),successor_relation)** -> equal(power_class(complement(singleton(successor_relation))),universal_class).
% 299.82/300.44  196727[10:SpR:162889.0,142543.0] ||  -> equal(intersection(power_class(complement(singleton(successor_relation))),universal_class),symmetric_difference(universal_class,image(element_relation,successor(successor_relation))))**.
% 299.82/300.44  196729[10:SpR:162889.0,107289.0] ||  -> subclass(complement(power_class(image(element_relation,successor(successor_relation)))),image(element_relation,power_class(complement(singleton(successor_relation)))))*.
% 299.82/300.44  196738[10:SpR:162889.0,160368.0] ||  -> subclass(symmetric_difference(power_class(complement(singleton(successor_relation))),universal_class),union(image(element_relation,successor(successor_relation)),successor_relation))*.
% 299.82/300.44  196739[10:SpR:162889.0,160445.0] ||  -> equal(intersection(intersection(image(element_relation,successor(successor_relation)),u),power_class(complement(singleton(successor_relation)))),successor_relation)**.
% 299.82/300.44  196740[10:SpR:162889.0,160444.0] ||  -> equal(intersection(power_class(complement(singleton(successor_relation))),intersection(u,image(element_relation,successor(successor_relation)))),successor_relation)**.
% 299.82/300.44  196741[10:SpR:162889.0,160443.0] ||  -> equal(intersection(power_class(complement(singleton(successor_relation))),intersection(image(element_relation,successor(successor_relation)),u)),successor_relation)**.
% 299.82/300.44  196751[10:SpR:162889.0,89275.1] ||  -> member(u,image(element_relation,successor(successor_relation))) subclass(singleton(u),power_class(complement(singleton(successor_relation))))*.
% 299.82/300.44  196752[10:SpR:162889.0,160446.0] ||  -> equal(intersection(intersection(u,image(element_relation,successor(successor_relation))),power_class(complement(singleton(successor_relation)))),successor_relation)**.
% 299.82/300.44  196761[10:SpL:162889.0,159727.1] inductive(image(element_relation,successor(successor_relation))) || equal(power_class(complement(singleton(successor_relation))),universal_class)** -> .
% 299.82/300.44  196768[10:SpL:162889.0,185335.0] || equal(image(element_relation,power_class(complement(singleton(successor_relation)))),power_class(image(element_relation,successor(successor_relation))))** -> .
% 299.82/300.44  196769[10:SpL:162889.0,160256.0] || well_ordering(universal_class,power_class(complement(singleton(successor_relation))))* -> member(successor_relation,image(element_relation,successor(successor_relation))).
% 299.82/300.44  196771[10:SpL:162889.0,185795.0] || equal(power_class(complement(singleton(successor_relation))),successor_relation) -> equal(image(element_relation,successor(successor_relation)),universal_class)**.
% 299.82/300.44  196778[20:SpL:162889.0,192322.1] inductive(image(element_relation,successor(successor_relation))) || equal(power_class(complement(singleton(successor_relation))),omega)** -> .
% 299.82/300.44  196802[10:Res:162888.0,160435.1] inductive(complement(power_class(complement(singleton(successor_relation))))) ||  -> member(successor_relation,image(element_relation,successor(successor_relation)))*.
% 299.82/300.44  197368[10:SpR:186059.1,160971.0] || equal(power_class(successor_relation),successor_relation) -> subclass(complement(power_class(universal_class)),image(element_relation,power_class(successor_relation)))*.
% 299.82/300.44  197835[10:SpL:185302.1,194075.0] || equal(cross_product(singleton(omega),universal_class),successor_relation)** equal(complement(cantor(universal_class)),successor_relation) -> .
% 299.82/300.44  197840[10:SpL:185302.1,194078.0] || equal(cross_product(singleton(power_class(successor_relation)),universal_class),successor_relation)** subclass(universal_class,cantor(universal_class)) -> .
% 299.82/300.44  197846[10:SpL:185302.1,194094.0] || equal(cross_product(singleton(successor_relation),universal_class),successor_relation)** equal(complement(cantor(universal_class)),successor_relation) -> .
% 299.82/300.44  197849[11:SpL:185302.1,194095.0] || equal(cross_product(singleton(successor_relation),universal_class),successor_relation)** equal(cantor(universal_class),inverse(successor_relation)) -> .
% 299.82/300.44  197851[10:SpL:185302.1,194096.0] || equal(cross_product(singleton(successor_relation),universal_class),successor_relation)** equal(cantor(universal_class),singleton(successor_relation)) -> .
% 299.82/300.44  197853[10:SpL:185302.1,194097.0] || equal(cross_product(singleton(successor_relation),universal_class),successor_relation)** equal(cantor(universal_class),successor(successor_relation)) -> .
% 299.82/300.44  197855[11:SpL:185302.1,194098.0] || equal(cross_product(singleton(successor_relation),universal_class),successor_relation)** equal(symmetrization_of(successor_relation),cantor(universal_class)) -> .
% 299.82/300.45  198054[10:SpL:185302.1,197781.0] || equal(cross_product(singleton(power_class(successor_relation)),universal_class),successor_relation)** equal(cantor(universal_class),universal_class) -> .
% 299.82/300.45  198085[10:SpR:163008.0,194805.1] || subclass(power_class(universal_class),intersection(u,image(element_relation,successor_relation)))* -> equal(power_class(universal_class),successor_relation).
% 299.82/300.45  198127[10:MRR:198081.2,160227.0] || member(u,power_class(universal_class)) member(u,intersection(v,image(element_relation,successor_relation)))* -> .
% 299.82/300.45  198230[10:SpR:163006.0,194805.1] || subclass(power_class(universal_class),intersection(image(element_relation,successor_relation),u))* -> equal(power_class(universal_class),successor_relation).
% 299.82/300.45  198277[10:MRR:198226.2,160227.0] || member(u,power_class(universal_class)) member(u,intersection(image(element_relation,successor_relation),v))* -> .
% 299.82/300.45  198510[10:MRR:198456.2,160227.0] || member(u,intersection(complement(singleton(successor_relation)),v))* member(u,successor(successor_relation)) -> .
% 299.82/300.45  198615[10:MRR:198565.2,160227.0] || member(u,intersection(v,complement(singleton(successor_relation))))* member(u,successor(successor_relation)) -> .
% 299.82/300.45  198985[10:MRR:198935.2,160227.0] || member(u,symmetrization_of(successor_relation)) member(u,intersection(v,complement(inverse(successor_relation))))* -> .
% 299.82/300.45  199115[10:MRR:199059.2,160227.0] || member(u,symmetrization_of(successor_relation)) member(u,intersection(complement(inverse(successor_relation)),v))* -> .
% 299.82/300.45  199358[10:SpR:161852.0,194805.1] || subclass(power_class(successor_relation),intersection(u,image(element_relation,universal_class)))* -> equal(power_class(successor_relation),successor_relation).
% 299.82/300.45  199403[10:MRR:199354.2,160227.0] || member(u,power_class(successor_relation)) member(u,intersection(v,image(element_relation,universal_class)))* -> .
% 299.82/300.45  199434[10:SpR:161847.0,194805.1] || subclass(power_class(successor_relation),intersection(image(element_relation,universal_class),u))* -> equal(power_class(successor_relation),successor_relation).
% 299.82/300.45  199484[10:MRR:199430.2,160227.0] || member(u,power_class(successor_relation)) member(u,intersection(image(element_relation,universal_class),v))* -> .
% 299.82/300.45  199790[10:SpL:185302.1,194072.0] || equal(cross_product(singleton(singleton(u)),universal_class),successor_relation)** equal(cantor(universal_class),universal_class) -> .
% 299.82/300.45  199795[10:SpL:185302.1,194074.0] || equal(cross_product(singleton(singleton(u)),universal_class),successor_relation)** subclass(universal_class,cantor(universal_class)) -> .
% 299.82/300.45  199968[14:SpL:119971.0,184789.0] || member(sum_class(image(universal_class,u)),universal_class)* member(cross_product(u,universal_class),universal_class) -> .
% 299.82/300.45  199975[15:SpL:119971.0,189423.1] || member(cross_product(u,universal_class),universal_class)* equal(sum_class(image(universal_class,u)),successor_relation) -> .
% 299.82/300.45  199987[6:Res:199848.1,9332.1] || subclass(universal_class,intersection(u,v)) member(regular(rest_relation),symmetric_difference(u,v))* -> .
% 299.82/300.45  199991[6:Res:199848.1,594.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(rest_relation),cross_product(v,w)).
% 299.82/300.45  200011[6:Res:199848.1,307.0] || subclass(universal_class,image(element_relation,complement(u)))* member(regular(rest_relation),power_class(u)) -> .
% 299.82/300.45  200013[10:Res:199848.1,160481.0] || subclass(universal_class,regular(u))* member(regular(rest_relation),u) -> equal(u,successor_relation).
% 299.82/300.45  200024[14:SpL:44.0,199972.0] || member(image(u,v),universal_class) member(restrict(u,v,universal_class),universal_class)* -> .
% 299.82/300.45  200055[14:SpR:44.0,200027.1] || member(restrict(u,v,universal_class),universal_class)* -> equal(integer_of(image(u,v)),successor_relation).
% 299.82/300.45  200109[14:SpR:44.0,200028.1] || member(restrict(u,v,universal_class),universal_class)* -> equal(singleton(image(u,v)),successor_relation).
% 299.82/300.45  200161[14:SpL:200028.1,193819.0] || member(u,universal_class) member(range_of(u),cantor(complement(cross_product(successor_relation,universal_class))))* -> .
% 299.82/300.45  200181[14:Rew:160223.0,200064.1] || member(u,universal_class) -> subclass(symmetric_difference(complement(range_of(u)),universal_class),successor(range_of(u)))*.
% 299.82/300.45  200266[6:SpL:199964.0,147.0] || member(regular(rest_relation),rest_relation) -> equal(rest_of(first(regular(rest_relation))),second(regular(rest_relation)))**.
% 299.82/300.45  200564[10:Res:9089.1,163137.0] function(u) || equal(rest_of(apply(u,v)),successor(apply(u,v)))** -> .
% 299.82/300.45  200565[10:Res:34189.1,163137.0] || equal(rest_of(not_subclass_element(u,v)),successor(not_subclass_element(u,v)))** -> subclass(u,v).
% 299.82/300.45  200650[10:Res:161493.2,160454.0] inductive(u) ||  -> equal(integer_of(regular(complement(u))),successor_relation)** equal(complement(u),successor_relation).
% 299.82/300.45  200670[10:Res:161493.2,595.0] inductive(restrict(u,v,w)) ||  -> equal(integer_of(x),successor_relation) member(x,u)*.
% 299.82/300.45  200682[10:Res:161493.2,970.0] inductive(cantor(inverse(u))) ||  -> equal(integer_of(v),successor_relation) member(v,range_of(u))*.
% 299.82/300.45  200694[10:Res:161493.2,2.0] inductive(intersection(y__dfg,ordinal_numbers)) ||  -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation)**.
% 299.82/300.45  200704[10:Res:161493.2,147.0] inductive(rest_relation) ||  -> equal(integer_of(ordered_pair(u,v)),successor_relation)** equal(rest_of(u),v).
% 299.82/300.45  200740[10:Res:161493.2,195483.1] inductive(ordinal_numbers) || subclass(ordinal_numbers,y__dfg) -> equal(integer_of(least(element_relation,ordinal_numbers)),successor_relation)**.
% 299.82/300.45  200762[15:Res:161493.2,189548.0] inductive(domain_relation) ||  -> equal(integer_of(singleton(singleton(singleton(u)))),successor_relation)** equal(successor_relation,u).
% 299.82/300.45  200784[10:Res:161493.2,162953.0] inductive(ordinal_numbers) ||  -> equal(integer_of(regular(complement(kind_1_ordinals))),successor_relation)** equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.45  201081[10:Res:51387.0,183723.0] ||  -> subclass(u,complement(symmetrization_of(successor_relation))) member(not_subclass_element(u,complement(symmetrization_of(successor_relation))),inverse(successor_relation))*.
% 299.82/300.45  201086[10:Res:51387.0,183622.0] ||  -> subclass(u,complement(successor(successor_relation))) member(not_subclass_element(u,complement(successor(successor_relation))),singleton(successor_relation))*.
% 299.82/300.45  201134[10:SpL:185302.1,200006.0] || equal(cross_product(singleton(regular(rest_relation)),universal_class),successor_relation)** subclass(universal_class,cantor(universal_class)) -> .
% 299.82/300.45  201214[10:SpL:185302.1,201133.0] || equal(cross_product(singleton(regular(rest_relation)),universal_class),successor_relation)** equal(cantor(universal_class),universal_class) -> .
% 299.82/300.45  201377[6:Res:201231.1,9332.1] || subclass(universal_class,intersection(u,v)) member(regular(domain_relation),symmetric_difference(u,v))* -> .
% 299.82/300.45  201381[6:Res:201231.1,594.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(domain_relation),cross_product(v,w)).
% 299.82/300.45  201401[6:Res:201231.1,307.0] || subclass(universal_class,image(element_relation,complement(u)))* member(regular(domain_relation),power_class(u)) -> .
% 299.82/300.45  201403[10:Res:201231.1,160481.0] || subclass(universal_class,regular(u))* member(regular(domain_relation),u) -> equal(u,successor_relation).
% 299.82/300.45  201439[10:EmS:161261.0,161261.1,74.1,195817.1] one_to_one(u) || equal(inverse(u),universal_class)** -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.45  201510[6:SpL:201355.0,147.0] || member(regular(domain_relation),rest_relation) -> equal(rest_of(first(regular(domain_relation))),second(regular(domain_relation)))**.
% 299.82/300.45  201822[10:SpL:185302.1,201396.0] || equal(cross_product(singleton(regular(domain_relation)),universal_class),successor_relation)** subclass(universal_class,cantor(universal_class)) -> .
% 299.82/300.45  201910[10:SpL:185302.1,201821.0] || equal(cross_product(singleton(regular(domain_relation)),universal_class),successor_relation)** equal(cantor(universal_class),universal_class) -> .
% 299.82/300.45  201912[10:Res:161492.2,185065.1] || equal(u,omega) subclass(u,successor_relation)* -> equal(integer_of(singleton(v)),successor_relation)**.
% 299.82/300.45  201924[10:Res:161492.2,26.1] || equal(complement(u),omega) member(v,u)* -> equal(integer_of(v),successor_relation).
% 299.82/300.45  201928[10:Res:161492.2,183398.0] || equal(complement(complement(u)),omega)** -> equal(integer_of(v),successor_relation) member(v,u)*.
% 299.82/300.45  201930[10:Res:161492.2,23.0] || equal(intersection(u,v),omega)** -> equal(integer_of(w),successor_relation) member(w,u)*.
% 299.82/300.45  201931[10:Res:161492.2,24.0] || equal(intersection(u,v),omega)** -> equal(integer_of(w),successor_relation) member(w,v)*.
% 299.82/300.45  201949[10:Res:161492.2,193819.0] || equal(cantor(complement(cross_product(singleton(u),universal_class))),omega)** -> equal(integer_of(u),successor_relation).
% 299.82/300.45  201950[10:Res:161492.2,183622.0] || equal(successor(successor_relation),omega) -> equal(integer_of(u),successor_relation) member(u,singleton(successor_relation))*.
% 299.82/300.45  201958[10:Res:161492.2,5.0] || equal(u,omega) -> equal(integer_of(not_subclass_element(v,u)),successor_relation)** subclass(v,u).
% 299.82/300.45  201978[10:Res:161492.2,21.0] || equal(omega,element_relation) -> equal(integer_of(ordered_pair(u,v)),successor_relation)** member(u,v).
% 299.82/300.45  201997[10:Res:161492.2,195493.1] || equal(singleton(successor_relation),omega) subclass(ordinal_numbers,y__dfg)* -> equal(integer_of(ordinal_numbers),successor_relation).
% 299.82/300.45  202003[10:Res:161492.2,155823.0] || equal(omega,ordinal_numbers) -> equal(integer_of(not_subclass_element(u,kind_1_ordinals)),successor_relation)** subclass(u,kind_1_ordinals).
% 299.82/300.45  202062[10:Res:161492.2,197037.0] || equal(successor(successor_relation),omega) -> equal(integer_of(not_subclass_element(complement(singleton(successor_relation)),successor_relation)),successor_relation)**.
% 299.82/300.45  202448[10:Rew:114854.0,202426.1] ||  -> member(successor_relation,union(cross_product(u,v),successor_relation))* member(successor_relation,complement(cross_product(u,v))).
% 299.82/300.45  202454[10:SpR:160367.0,163217.0] ||  -> member(successor_relation,image(element_relation,union(u,successor_relation)))* member(successor_relation,power_class(symmetric_difference(universal_class,u))).
% 299.82/300.45  202709[10:SpR:161194.0,195152.0] ||  -> equal(intersection(union(u,successor_relation),symmetric_difference(complement(u),universal_class)),symmetric_difference(complement(u),universal_class))**.
% 299.82/300.45  202718[10:SpR:161194.0,163032.0] ||  -> equal(union(symmetric_difference(complement(u),universal_class),successor_relation),complement(symmetric_difference(union(u,successor_relation),universal_class)))**.
% 299.82/300.45  202733[10:SpL:161194.0,5884.0] || equal(symmetric_difference(complement(u),universal_class),universal_class) -> member(singleton(v),union(u,successor_relation))*.
% 299.82/300.45  202735[10:SpL:161194.0,2648.0] || subclass(universal_class,symmetric_difference(complement(u),universal_class))* -> member(singleton(v),union(u,successor_relation))*.
% 299.82/300.45  202776[10:Res:160827.1,160435.1] inductive(singleton(u)) ||  -> member(u,image(element_relation,successor_relation))* member(successor_relation,power_class(universal_class)).
% 299.82/300.45  203377[6:Rew:203192.0,201509.1] || member(regular(domain_relation),domain_relation) -> equal(cantor(first(regular(domain_relation))),second(regular(domain_relation)))**.
% 299.82/300.45  203378[6:Rew:203192.0,200265.1] || member(regular(rest_relation),domain_relation) -> equal(cantor(first(regular(rest_relation))),second(regular(rest_relation)))**.
% 299.82/300.45  203654[15:Rew:203192.0,186273.1] || subclass(universal_class,cross_product(universal_class,cross_product(universal_class,universal_class)))* member(u,cantor(v))* -> .
% 299.82/300.45  203917[6:Rew:203192.0,107657.0] || member(u,cantor(u))* subclass(element_relation,v) well_ordering(universal_class,v)* -> .
% 299.82/300.45  203937[6:Rew:203192.0,110435.2] || equal(rest_of(u),rest_relation) member(v,universal_class) -> member(v,cantor(u))*.
% 299.82/300.45  203979[10:Rew:203192.0,200717.2] inductive(domain_relation) ||  -> equal(integer_of(ordered_pair(u,v)),successor_relation)** equal(cantor(u),v).
% 299.82/300.45  204908[10:MRR:204907.2,160227.0] inductive(symmetric_difference(domain_of(u),cantor(u))) || well_ordering(v,complement(cantor(u)))* -> .
% 299.82/300.45  206031[10:Res:160970.1,160435.1] inductive(singleton(u)) ||  -> member(u,image(element_relation,universal_class))* member(successor_relation,power_class(successor_relation)).
% 299.82/300.45  206139[10:Rew:203335.0,206111.0] || equal(segment(u,v,w),successor_relation) -> asymmetric(segment(u,v,w),x)*.
% 299.82/300.45  206140[10:Rew:203335.0,206112.0] || equal(segment(u,v,w),successor_relation) -> subclass(segment(u,v,w),x)*.
% 299.82/300.45  206237[10:Res:206225.1,9.0] || member(successor_relation,ordinal_numbers) subclass(kind_1_ordinals,successor(successor_relation))* -> equal(successor(successor_relation),kind_1_ordinals).
% 299.82/300.45  206246[10:Res:206224.1,9.0] || member(successor_relation,u) subclass(u,successor(successor_relation))* -> equal(u,successor(successor_relation)).
% 299.82/300.45  206252[10:Res:206224.1,3926.1] single_valued_class(successor(successor_relation)) || member(successor_relation,cross_product(universal_class,universal_class))* -> function(successor(successor_relation)).
% 299.82/300.45  206710[10:Res:206690.0,127.0] || subclass(kind_1_ordinals,u) well_ordering(v,u)* -> member(least(v,kind_1_ordinals),kind_1_ordinals)*.
% 299.82/300.45  206974[10:Res:206947.1,9322.0] || equal(symmetric_difference(complement(u),complement(v)),kind_1_ordinals)** -> member(successor_relation,union(u,v)).
% 299.82/300.45  207526[10:SpR:28.0,206226.1] ||  -> member(successor_relation,intersection(complement(u),complement(v)))* subclass(successor(successor_relation),union(u,v)).
% 299.82/300.45  207537[10:SpR:161137.0,206226.1] ||  -> member(successor_relation,image(element_relation,symmetrization_of(successor_relation))) subclass(successor(successor_relation),power_class(complement(inverse(successor_relation))))*.
% 299.82/300.45  207538[10:SpR:162889.0,206226.1] ||  -> member(successor_relation,image(element_relation,successor(successor_relation))) subclass(successor(successor_relation),power_class(complement(singleton(successor_relation))))*.
% 299.82/300.45  207865[10:Res:206688.0,3.0] || subclass(complement(intersection(complement(singleton(successor_relation)),power_class(u))),v)* -> member(successor_relation,v).
% 299.82/300.45  207878[10:SpL:507.0,206698.0] || equal(complement(complement(intersection(complement(singleton(successor_relation)),union(u,v)))),successor(successor_relation))** -> .
% 299.82/300.45  208025[11:SpL:507.0,206699.0] || equal(complement(complement(intersection(complement(singleton(successor_relation)),union(u,v)))),symmetrization_of(successor_relation))** -> .
% 299.82/300.45  208145[10:Res:207196.0,3.0] || subclass(complement(intersection(power_class(u),complement(singleton(successor_relation)))),v)* -> member(successor_relation,v).
% 299.82/300.45  208159[10:SpL:506.0,207204.0] || equal(complement(complement(intersection(union(u,v),complement(singleton(successor_relation))))),successor(successor_relation))** -> .
% 299.82/300.45  208171[11:SpL:506.0,207205.0] || equal(complement(complement(intersection(union(u,v),complement(singleton(successor_relation))))),symmetrization_of(successor_relation))** -> .
% 299.82/300.45  208337[10:SpL:28.0,208258.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),kind_1_ordinals)** -> .
% 299.82/300.45  208348[10:SpL:161137.0,208258.1] inductive(image(element_relation,symmetrization_of(successor_relation))) || equal(power_class(complement(inverse(successor_relation))),kind_1_ordinals)** -> .
% 299.82/300.45  208349[10:SpL:162889.0,208258.1] inductive(image(element_relation,successor(successor_relation))) || equal(power_class(complement(singleton(successor_relation))),kind_1_ordinals)** -> .
% 299.82/300.45  201943[10:Res:161492.2,183723.0] || equal(symmetrization_of(successor_relation),omega) -> equal(integer_of(u),successor_relation) member(u,inverse(successor_relation))*.
% 299.82/300.45  163318[10:Rew:160202.0,161110.1] || equal(symmetrization_of(successor_relation),universal_class) subclass(inverse(successor_relation),u)* -> member(omega,u).
% 299.82/300.45  208891[10:SpL:160367.0,162918.1] || equal(symmetric_difference(universal_class,u),successor(successor_relation))** equal(union(u,successor_relation),universal_class) -> .
% 299.82/300.45  208894[10:SpL:57.0,162918.1] || equal(image(element_relation,complement(u)),successor(successor_relation))** equal(power_class(u),universal_class) -> .
% 299.82/300.45  209036[10:SpL:506.0,208953.0] || equal(complement(complement(intersection(union(u,v),complement(singleton(successor_relation))))),singleton(successor_relation))** -> .
% 299.82/300.45  209048[10:SpL:507.0,208954.0] || equal(complement(complement(intersection(complement(singleton(successor_relation)),union(u,v)))),singleton(successor_relation))** -> .
% 299.82/300.45  209078[10:SpL:160367.0,162872.1] || equal(symmetric_difference(universal_class,u),singleton(successor_relation))** equal(union(u,successor_relation),universal_class) -> .
% 299.82/300.45  209081[10:SpL:57.0,162872.1] || equal(image(element_relation,complement(u)),singleton(successor_relation))** equal(power_class(u),universal_class) -> .
% 299.82/300.45  209131[10:Res:161493.2,47888.0] inductive(rest_of(u)) || subclass(universal_class,complement(element_relation))* -> equal(integer_of(u),successor_relation)**.
% 299.82/300.45  209229[10:Res:161493.2,48083.0] inductive(cantor(u)) || subclass(universal_class,complement(element_relation))* -> equal(integer_of(u),successor_relation)**.
% 299.82/300.45  209454[12:Res:209377.1,9332.1] || subclass(universal_class,intersection(u,v)) member(regular(element_relation),symmetric_difference(u,v))* -> .
% 299.82/300.45  209458[12:Res:209377.1,594.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(element_relation),cross_product(v,w)).
% 299.82/300.45  209475[12:Res:209377.1,307.0] || subclass(universal_class,image(element_relation,complement(u)))* member(regular(element_relation),power_class(u)) -> .
% 299.82/300.45  209477[12:Res:209377.1,160481.0] || subclass(universal_class,regular(u))* member(regular(element_relation),u) -> equal(u,successor_relation).
% 299.82/300.45  209530[12:SpL:209433.0,147.0] || member(regular(element_relation),rest_relation) -> equal(rest_of(first(regular(element_relation))),second(regular(element_relation)))**.
% 299.82/300.45  209552[12:SpL:209433.0,203286.0] || member(regular(element_relation),domain_relation) -> equal(cantor(first(regular(element_relation))),second(regular(element_relation)))**.
% 299.82/300.45  209757[15:Res:186499.1,189420.0] || equal(successor_relation,u) subclass(domain_relation,rest_relation) -> equal(rest_of(power_class(u)),successor_relation)**.
% 299.82/300.45  209758[15:Res:58.1,189420.0] || member(u,universal_class) subclass(domain_relation,rest_relation) -> equal(rest_of(power_class(u)),successor_relation)**.
% 299.82/300.45  209763[15:Res:56.1,189420.0] || member(u,universal_class) subclass(domain_relation,rest_relation) -> equal(rest_of(sum_class(u)),successor_relation)**.
% 299.82/300.45  209767[15:Res:9089.1,189420.0] function(u) || subclass(domain_relation,rest_relation) -> equal(rest_of(apply(u,v)),successor_relation)**.
% 299.82/300.45  209768[15:Res:34189.1,189420.0] || subclass(domain_relation,rest_relation) -> subclass(u,v) equal(rest_of(not_subclass_element(u,v)),successor_relation)**.
% 299.82/300.45  209833[15:MRR:209806.1,54.0] || equal(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(omega,successor_relation),u)*.
% 299.82/300.45  209876[15:Res:186499.1,189421.0] || equal(successor_relation,u) subclass(rest_relation,domain_relation) -> equal(rest_of(power_class(u)),successor_relation)**.
% 299.82/300.45  209877[15:Res:58.1,189421.0] || member(u,universal_class) subclass(rest_relation,domain_relation) -> equal(rest_of(power_class(u)),successor_relation)**.
% 299.82/300.45  209882[15:Res:56.1,189421.0] || member(u,universal_class) subclass(rest_relation,domain_relation) -> equal(rest_of(sum_class(u)),successor_relation)**.
% 299.82/300.45  209886[15:Res:9089.1,189421.0] function(u) || subclass(rest_relation,domain_relation) -> equal(rest_of(apply(u,v)),successor_relation)**.
% 299.82/300.45  209887[15:Res:34189.1,189421.0] || subclass(rest_relation,domain_relation) -> subclass(u,v) equal(rest_of(not_subclass_element(u,v)),successor_relation)**.
% 299.82/300.45  210315[12:SpL:185302.1,209469.0] || equal(cross_product(singleton(regular(element_relation)),universal_class),successor_relation)** subclass(universal_class,cantor(universal_class)) -> .
% 299.82/300.45  210341[15:SpR:1005.0,189563.1] || subclass(domain_relation,flip(u)) -> member(ordered_pair(singleton(singleton(singleton(v))),successor_relation),u)*.
% 299.82/300.45  210344[15:Res:189563.1,6045.0] || subclass(domain_relation,flip(u))* subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.45  210388[15:Res:189563.1,95.0] || subclass(domain_relation,flip(compose_class(u))) -> equal(compose(u,ordered_pair(v,w)),successor_relation)**.
% 299.82/300.45  210392[15:Res:189563.1,35.0] || subclass(domain_relation,flip(rotate(u))) -> member(ordered_pair(ordered_pair(v,successor_relation),w),u)*.
% 299.82/300.45  210393[15:Res:189563.1,38.0] || subclass(domain_relation,flip(flip(u))) -> member(ordered_pair(ordered_pair(v,w),successor_relation),u)*.
% 299.82/300.45  210400[15:Res:189563.1,2151.0] || subclass(domain_relation,flip(singleton(u)))* -> equal(ordered_pair(ordered_pair(v,w),successor_relation),u)*.
% 299.82/300.45  210415[15:SpR:1005.0,189564.1] || subclass(domain_relation,rotate(u)) -> member(ordered_pair(singleton(singleton(singleton(successor_relation))),v),u)*.
% 299.82/300.45  210417[15:Res:189564.1,6045.0] || subclass(domain_relation,rotate(u))* subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.45  210469[15:Res:189564.1,35.0] || subclass(domain_relation,rotate(rotate(u))) -> member(ordered_pair(ordered_pair(successor_relation,v),w),u)*.
% 299.82/300.45  210470[15:Res:189564.1,38.0] || subclass(domain_relation,rotate(flip(u))) -> member(ordered_pair(ordered_pair(successor_relation,v),w),u)*.
% 299.82/300.45  210478[15:Res:189564.1,2151.0] || subclass(domain_relation,rotate(singleton(u)))* -> equal(ordered_pair(ordered_pair(v,successor_relation),w),u)*.
% 299.82/300.45  211009[12:SpL:185302.1,210318.0] || equal(cross_product(singleton(regular(element_relation)),universal_class),successor_relation)** equal(cantor(universal_class),universal_class) -> .
% 299.82/300.45  211023[10:Res:185430.1,3492.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(unordered_pair(x,y),u)*.
% 299.82/300.45  211042[15:Res:211024.1,3.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(successor_relation,successor_relation),u)*.
% 299.82/300.45  211232[11:SpL:506.0,211100.0] || equal(complement(complement(intersection(union(u,v),complement(singleton(successor_relation))))),inverse(successor_relation))** -> .
% 299.82/300.45  211244[11:SpL:507.0,211101.0] || equal(complement(complement(intersection(complement(singleton(successor_relation)),union(u,v)))),inverse(successor_relation))** -> .
% 299.82/300.45  211504[10:Res:161492.2,211446.0] || equal(u,omega) well_ordering(universal_class,u)* -> equal(integer_of(singleton(successor_relation)),successor_relation)**.
% 299.82/300.45  211521[6:Res:8.1,157895.0] || equal(complement(compose(element_relation,universal_class)),universal_class) member(unordered_pair(u,v),element_relation)* -> .
% 299.82/300.45  211591[10:Res:8.1,160705.0] || equal(complement(kind_1_ordinals),u) member(regular(u),ordinal_numbers)* -> equal(u,successor_relation).
% 299.82/300.45  211638[10:Res:211579.1,6045.0] || subclass(complement(u),v)* well_ordering(universal_class,v) -> member(singleton(successor_relation),u).
% 299.82/300.45  211642[10:Res:211579.1,3.0] || subclass(complement(u),v)* -> member(singleton(successor_relation),u) member(singleton(successor_relation),v).
% 299.82/300.45  211683[10:Res:181213.1,595.0] || equal(restrict(u,v,w),singleton(singleton(successor_relation)))** -> member(singleton(successor_relation),u).
% 299.82/300.45  211704[10:Res:181213.1,47888.0] || equal(rest_of(singleton(successor_relation)),singleton(singleton(successor_relation))) subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.45  211753[10:SpR:185608.1,9949.0] || equal(complement(u),successor_relation) -> equal(complement(image(element_relation,successor(u))),power_class(successor_relation))**.
% 299.82/300.45  211754[10:SpR:163198.1,9949.0] || subclass(complement(u),successor_relation) -> equal(complement(image(element_relation,successor(u))),power_class(successor_relation))**.
% 299.82/300.45  211788[11:SpL:160367.0,182321.1] || equal(symmetric_difference(universal_class,u),inverse(successor_relation))** equal(union(u,successor_relation),universal_class) -> .
% 299.82/300.45  211791[11:SpL:57.0,182321.1] || equal(image(element_relation,complement(u)),inverse(successor_relation))** equal(power_class(u),universal_class) -> .
% 299.82/300.45  211850[10:SpR:185608.1,9948.0] || equal(complement(u),successor_relation) -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(successor_relation))**.
% 299.82/300.45  211851[10:SpR:163198.1,9948.0] || subclass(complement(u),successor_relation) -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(successor_relation))**.
% 299.82/300.45  211944[10:SpR:160367.0,183456.0] ||  -> equal(symmetric_difference(image(element_relation,union(u,successor_relation)),complement(power_class(symmetric_difference(universal_class,u)))),successor_relation)**.
% 299.82/300.45  211966[11:Res:183759.1,6045.0] || subclass(inverse(successor_relation),u)* subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.45  211981[11:Res:183759.1,595.0] || subclass(inverse(successor_relation),restrict(u,v,w))* -> member(regular(symmetrization_of(successor_relation)),u).
% 299.82/300.45  211995[11:Res:183759.1,159.0] || subclass(inverse(successor_relation),omega) -> equal(integer_of(regular(symmetrization_of(successor_relation))),regular(symmetrization_of(successor_relation)))**.
% 299.82/300.45  212002[11:Res:183759.1,47888.0] || subclass(inverse(successor_relation),rest_of(regular(symmetrization_of(successor_relation))))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.45  212102[10:Rew:160824.1,212101.1] || member(regular(u),singleton(u))* -> equal(u,successor_relation) equal(singleton(u),successor_relation).
% 299.82/300.45  212117[10:Res:161493.2,212099.0] inductive(ordinal_numbers) ||  -> equal(integer_of(regular(regular(kind_1_ordinals))),successor_relation)** equal(regular(kind_1_ordinals),successor_relation).
% 299.82/300.45  212167[10:Obv:212163.1] || subclass(singleton(u),omega)* -> equal(singleton(u),successor_relation) equal(integer_of(u),u).
% 299.82/300.45  212215[10:SpR:185433.1,161194.0] || equal(complement(union(u,successor_relation)),successor_relation) -> equal(symmetric_difference(complement(u),universal_class),universal_class)**.
% 299.82/300.45  212309[10:MRR:212244.2,314.0] || equal(complement(u),successor_relation) member(v,universal_class) -> member(power_class(v),u)*.
% 299.82/300.45  212482[10:SpL:160367.0,185801.0] || equal(complement(union(u,successor_relation)),successor_relation) subclass(universal_class,symmetric_difference(universal_class,u))* -> .
% 299.82/300.45  212485[10:SpL:57.0,185801.0] || equal(complement(power_class(u)),successor_relation) subclass(universal_class,image(element_relation,complement(u)))* -> .
% 299.82/300.45  212499[10:SpL:160367.0,185935.0] || equal(complement(union(u,successor_relation)),successor_relation) member(successor_relation,symmetric_difference(universal_class,u))* -> .
% 299.82/300.45  212502[10:SpL:57.0,185935.0] || equal(complement(power_class(u)),successor_relation) member(successor_relation,image(element_relation,complement(u)))* -> .
% 299.82/300.45  212786[10:SpL:185605.1,212521.0] || equal(successor_relation,u) member(not_subclass_element(image(element_relation,universal_class),successor_relation),power_class(u))* -> .
% 299.82/300.45  212827[15:Res:161492.2,212820.0] || equal(cantor(first(regular(rest_relation))),omega) -> equal(integer_of(second(regular(rest_relation))),successor_relation)**.
% 299.82/300.45  212830[15:Res:161492.2,212821.0] || equal(cantor(first(regular(domain_relation))),omega) -> equal(integer_of(second(regular(domain_relation))),successor_relation)**.
% 299.82/300.45  212833[15:Res:161492.2,212822.0] || equal(cantor(first(regular(element_relation))),omega) -> equal(integer_of(second(regular(element_relation))),successor_relation)**.
% 299.82/300.45  212859[10:SpL:160367.0,186009.0] || equal(complement(union(u,successor_relation)),successor_relation) member(omega,symmetric_difference(universal_class,u))* -> .
% 299.82/300.45  212862[10:SpL:57.0,186009.0] || equal(complement(power_class(u)),successor_relation) member(omega,image(element_relation,complement(u)))* -> .
% 299.82/300.45  212975[10:SpL:160367.0,187767.0] || subclass(universal_class,union(u,successor_relation)) member(power_class(successor_relation),symmetric_difference(universal_class,u))* -> .
% 299.82/300.45  212978[10:SpL:57.0,187767.0] || subclass(universal_class,power_class(u)) member(power_class(successor_relation),image(element_relation,complement(u)))* -> .
% 299.82/300.45  213069[10:SpL:181082.0,188186.1] || member(image(u,successor_relation),universal_class)* equal(singleton(apply(u,universal_class)),successor_relation) -> .
% 299.82/300.45  213121[11:Res:188444.1,179992.1] || equal(symmetric_difference(universal_class,u),universal_class)** equal(complement(complement(u)),inverse(successor_relation)) -> .
% 299.82/300.45  213122[10:Res:188444.1,163207.1] || equal(symmetric_difference(universal_class,u),universal_class)** equal(complement(complement(u)),singleton(successor_relation)) -> .
% 299.82/300.45  213124[10:Res:188444.1,163205.1] || equal(symmetric_difference(universal_class,u),universal_class)** equal(complement(complement(u)),successor(successor_relation)) -> .
% 299.82/300.45  213125[11:Res:188444.1,168534.1] || equal(symmetric_difference(universal_class,u),universal_class)** equal(complement(complement(u)),symmetrization_of(successor_relation)) -> .
% 299.82/300.45  213180[10:Res:160337.0,160800.0] || member(regular(complement(symmetrization_of(successor_relation))),inverse(successor_relation))* -> equal(complement(symmetrization_of(successor_relation)),successor_relation).
% 299.82/300.45  213212[15:Res:189485.1,595.0] || subclass(domain_relation,restrict(u,v,w))* -> member(singleton(singleton(singleton(successor_relation))),u).
% 299.82/300.45  213608[15:SpL:181082.0,191628.1] || member(image(u,successor_relation),universal_class)* equal(successor(apply(u,universal_class)),successor_relation) -> .
% 299.82/300.45  213771[15:SpR:191656.1,163032.0] || equal(successor(intersection(u,universal_class)),successor_relation) -> equal(complement(symmetric_difference(u,universal_class)),successor_relation)**.
% 299.82/300.45  213807[20:SpL:160367.0,192317.1] || equal(symmetric_difference(universal_class,u),inverse(successor_relation))** equal(union(u,successor_relation),omega) -> .
% 299.82/300.45  213810[20:SpL:57.0,192317.1] || equal(image(element_relation,complement(u)),inverse(successor_relation))** equal(power_class(u),omega) -> .
% 299.82/300.45  213821[20:SpL:160367.0,192318.1] || equal(symmetric_difference(universal_class,u),singleton(successor_relation))** equal(union(u,successor_relation),omega) -> .
% 299.82/300.45  213824[20:SpL:57.0,192318.1] || equal(image(element_relation,complement(u)),singleton(successor_relation))** equal(power_class(u),omega) -> .
% 299.82/300.45  213835[20:SpL:160367.0,192319.1] || equal(symmetric_difference(universal_class,u),successor(successor_relation))** equal(union(u,successor_relation),omega) -> .
% 299.82/300.45  213838[20:SpL:57.0,192319.1] || equal(image(element_relation,complement(u)),successor(successor_relation))** equal(power_class(u),omega) -> .
% 299.82/300.45  214155[20:Res:193270.1,179992.1] || equal(symmetric_difference(universal_class,u),omega)** equal(complement(complement(u)),inverse(successor_relation)) -> .
% 299.82/300.45  214156[20:Res:193270.1,163207.1] || equal(symmetric_difference(universal_class,u),omega)** equal(complement(complement(u)),singleton(successor_relation)) -> .
% 299.82/300.45  214158[20:Res:193270.1,163205.1] || equal(symmetric_difference(universal_class,u),omega)** equal(complement(complement(u)),successor(successor_relation)) -> .
% 299.82/300.45  214159[20:Res:193270.1,168534.1] || equal(symmetric_difference(universal_class,u),omega)** equal(complement(complement(u)),symmetrization_of(successor_relation)) -> .
% 299.82/300.45  214229[10:SpL:160367.0,194513.0] || equal(complement(complement(union(u,successor_relation))),successor_relation)** -> member(omega,symmetric_difference(universal_class,u)).
% 299.82/300.45  214232[10:SpL:57.0,194513.0] || equal(complement(complement(power_class(u))),successor_relation) -> member(omega,image(element_relation,complement(u)))*.
% 299.82/300.45  214259[10:SpL:160367.0,194520.0] || subclass(universal_class,complement(union(u,successor_relation)))* -> member(power_class(successor_relation),symmetric_difference(universal_class,u)).
% 299.82/300.45  214262[10:SpL:57.0,194520.0] || subclass(universal_class,complement(power_class(u))) -> member(power_class(successor_relation),image(element_relation,complement(u)))*.
% 299.82/300.45  214279[10:SpR:185605.1,214277.1] || equal(successor_relation,u) equal(complement(v),successor_relation) -> member(power_class(u),v)*.
% 299.82/300.45  214285[10:Res:214277.1,3.0] || equal(complement(u),successor_relation) subclass(u,v)* -> member(power_class(successor_relation),v)*.
% 299.82/300.45  214289[10:Res:214277.1,148657.1] || equal(complement(complement(compose(element_relation,universal_class))),successor_relation)** member(power_class(successor_relation),element_relation) -> .
% 299.82/300.45  214298[10:Res:214277.1,1952.0] || equal(complement(symmetric_difference(u,v)),successor_relation) -> member(power_class(successor_relation),union(u,v))*.
% 299.82/300.45  214299[10:Res:214277.1,10191.0] || equal(complement(symmetric_difference(u,inverse(u))),successor_relation)** -> member(power_class(successor_relation),symmetrization_of(u)).
% 299.82/300.45  214300[10:Res:214277.1,10254.0] || equal(complement(symmetric_difference(u,singleton(u))),successor_relation)** -> member(power_class(successor_relation),successor(u)).
% 299.82/300.45  214333[10:Rew:28.0,214294.0] || equal(union(u,v),successor_relation) member(power_class(successor_relation),union(u,v))* -> .
% 299.82/300.45  214340[10:SpL:160367.0,194540.0] || equal(complement(complement(union(u,successor_relation))),successor_relation)** -> member(successor_relation,symmetric_difference(universal_class,u)).
% 299.82/300.45  214343[10:SpL:57.0,194540.0] || equal(complement(complement(power_class(u))),successor_relation) -> member(successor_relation,image(element_relation,complement(u)))*.
% 299.82/300.45  214567[15:MRR:214512.2,160227.0] || equal(successor(u),successor_relation) member(v,universal_class) -> member(v,complement(u))*.
% 299.82/300.45  214587[11:SpL:160367.0,194541.0] || equal(complement(union(u,successor_relation)),inverse(successor_relation)) -> member(successor_relation,symmetric_difference(universal_class,u))*.
% 299.82/300.45  214590[11:SpL:57.0,194541.0] || equal(complement(power_class(u)),inverse(successor_relation)) -> member(successor_relation,image(element_relation,complement(u)))*.
% 299.82/300.45  214656[10:SpL:160367.0,194542.0] || equal(complement(union(u,successor_relation)),singleton(successor_relation)) -> member(successor_relation,symmetric_difference(universal_class,u))*.
% 299.82/300.45  214659[10:SpL:57.0,194542.0] || equal(complement(power_class(u)),singleton(successor_relation)) -> member(successor_relation,image(element_relation,complement(u)))*.
% 299.82/300.45  214675[10:SpL:160367.0,194543.0] || equal(complement(union(u,successor_relation)),successor(successor_relation)) -> member(successor_relation,symmetric_difference(universal_class,u))*.
% 299.82/300.45  214678[10:SpL:57.0,194543.0] || equal(complement(power_class(u)),successor(successor_relation)) -> member(successor_relation,image(element_relation,complement(u)))*.
% 299.82/300.45  214695[11:SpL:160367.0,194544.0] || equal(complement(union(u,successor_relation)),symmetrization_of(successor_relation)) -> member(successor_relation,symmetric_difference(universal_class,u))*.
% 299.82/300.45  214698[11:SpL:57.0,194544.0] || equal(complement(power_class(u)),symmetrization_of(successor_relation)) -> member(successor_relation,image(element_relation,complement(u)))*.
% 299.82/300.45  215293[11:Res:161493.2,215242.0] inductive(symmetric_difference(universal_class,inverse(successor_relation))) ||  -> equal(integer_of(not_subclass_element(symmetrization_of(successor_relation),successor_relation)),successor_relation)**.
% 299.82/300.45  215349[10:SpR:195811.1,89275.1] || equal(inverse(u),universal_class) -> member(v,inverse(u))* subclass(singleton(v),successor_relation)*.
% 299.82/300.45  215517[10:Rew:160277.0,215355.1] || equal(inverse(u),universal_class) -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(successor_relation))**.
% 299.82/300.45  215576[10:Obv:215573.1] || subclass(complement(compose(element_relation,universal_class)),element_relation)* -> equal(complement(compose(element_relation,universal_class)),successor_relation).
% 299.82/300.45  215663[10:SpR:195870.1,89275.1] || equal(sum_class(u),universal_class) -> member(v,sum_class(u))* subclass(singleton(v),successor_relation)*.
% 299.82/300.45  215875[10:Res:197082.1,595.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(complement(successor(successor_relation))),u).
% 299.82/300.45  215959[10:Obv:215947.1] || subclass(intersection(u,complement(kind_1_ordinals)),ordinal_numbers)* -> equal(intersection(u,complement(kind_1_ordinals)),successor_relation).
% 299.82/300.45  216099[10:Obv:216082.1] || subclass(intersection(complement(kind_1_ordinals),u),ordinal_numbers)* -> equal(intersection(complement(kind_1_ordinals),u),successor_relation).
% 299.82/300.45  216116[6:Res:199830.1,595.0] || equal(restrict(u,v,w),cross_product(universal_class,universal_class))** -> member(regular(rest_relation),u).
% 299.82/300.45  216137[6:Res:199830.1,47888.0] || equal(cross_product(universal_class,universal_class),rest_of(regular(rest_relation))) subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.45  216206[14:SpR:119971.0,199970.1] || member(cross_product(u,universal_class),universal_class) -> equal(integer_of(sum_class(image(universal_class,u))),successor_relation)**.
% 299.82/300.45  216285[14:SpR:119971.0,199971.1] || member(cross_product(u,universal_class),universal_class) -> equal(singleton(sum_class(image(universal_class,u))),successor_relation)**.
% 299.82/300.45  216367[14:Rew:181082.0,216266.1] || member(u,universal_class) -> equal(apply(v,sum_class(range_of(u))),apply(v,universal_class))**.
% 299.82/300.45  216371[14:Rew:181083.0,216268.1] || member(u,universal_class) -> equal(ordered_pair(v,sum_class(range_of(u))),ordered_pair(v,universal_class))**.
% 299.82/300.45  216427[10:SpL:160367.0,199982.0] || subclass(universal_class,union(u,successor_relation)) member(regular(rest_relation),symmetric_difference(universal_class,u))* -> .
% 299.82/300.45  216430[6:SpL:57.0,199982.0] || subclass(universal_class,power_class(u)) member(regular(rest_relation),image(element_relation,complement(u)))* -> .
% 299.82/300.45  216446[10:SpL:160367.0,199986.0] || subclass(universal_class,complement(union(u,successor_relation)))* -> member(regular(rest_relation),symmetric_difference(universal_class,u)).
% 299.82/300.45  216449[6:SpL:57.0,199986.0] || subclass(universal_class,complement(power_class(u))) -> member(regular(rest_relation),image(element_relation,complement(u)))*.
% 299.82/300.45  216471[10:Res:216465.1,3.0] || equal(complement(u),successor_relation) subclass(u,v)* -> member(regular(rest_relation),v)*.
% 299.82/300.45  216475[10:Res:216465.1,148657.1] || equal(complement(complement(compose(element_relation,universal_class))),successor_relation)** member(regular(rest_relation),element_relation) -> .
% 299.82/300.45  216484[10:Res:216465.1,1952.0] || equal(complement(symmetric_difference(u,v)),successor_relation) -> member(regular(rest_relation),union(u,v))*.
% 299.82/300.45  216485[10:Res:216465.1,10191.0] || equal(complement(symmetric_difference(u,inverse(u))),successor_relation)** -> member(regular(rest_relation),symmetrization_of(u)).
% 299.82/300.45  216486[10:Res:216465.1,10254.0] || equal(complement(symmetric_difference(u,singleton(u))),successor_relation)** -> member(regular(rest_relation),successor(u)).
% 299.82/300.45  216518[10:Rew:28.0,216480.0] || equal(union(u,v),successor_relation) member(regular(rest_relation),union(u,v))* -> .
% 299.82/300.45  216724[6:Res:201220.1,595.0] || equal(restrict(u,v,w),cross_product(universal_class,universal_class))** -> member(regular(domain_relation),u).
% 299.82/300.45  216745[6:Res:201220.1,47888.0] || equal(cross_product(universal_class,universal_class),rest_of(regular(domain_relation))) subclass(universal_class,complement(element_relation))* -> .
% 299.82/300.45  216809[10:SpL:160367.0,201372.0] || subclass(universal_class,union(u,successor_relation)) member(regular(domain_relation),symmetric_difference(universal_class,u))* -> .
% 299.82/300.45  216812[6:SpL:57.0,201372.0] || subclass(universal_class,power_class(u)) member(regular(domain_relation),image(element_relation,complement(u)))* -> .
% 299.82/300.45  216828[10:SpL:160367.0,201376.0] || subclass(universal_class,complement(union(u,successor_relation)))* -> member(regular(domain_relation),symmetric_difference(universal_class,u)).
% 299.82/300.45  216831[6:SpL:57.0,201376.0] || subclass(universal_class,complement(power_class(u))) -> member(regular(domain_relation),image(element_relation,complement(u)))*.
% 299.82/300.45  216899[10:Res:216847.1,3.0] || equal(complement(u),successor_relation) subclass(u,v)* -> member(regular(domain_relation),v)*.
% 299.82/300.45  216903[10:Res:216847.1,148657.1] || equal(complement(complement(compose(element_relation,universal_class))),successor_relation)** member(regular(domain_relation),element_relation) -> .
% 299.82/300.45  216912[10:Res:216847.1,1952.0] || equal(complement(symmetric_difference(u,v)),successor_relation) -> member(regular(domain_relation),union(u,v))*.
% 299.82/300.45  216913[10:Res:216847.1,10191.0] || equal(complement(symmetric_difference(u,inverse(u))),successor_relation)** -> member(regular(domain_relation),symmetrization_of(u)).
% 299.82/300.45  216914[10:Res:216847.1,10254.0] || equal(complement(symmetric_difference(u,singleton(u))),successor_relation)** -> member(regular(domain_relation),successor(u)).
% 299.82/300.45  216946[10:Rew:28.0,216908.0] || equal(union(u,v),successor_relation) member(regular(domain_relation),union(u,v))* -> .
% 299.82/300.45  217004[20:SpL:160367.0,202875.1] || equal(symmetric_difference(universal_class,u),omega)** equal(union(u,successor_relation),symmetrization_of(successor_relation)) -> .
% 299.82/300.45  217005[20:SpL:57.0,202875.1] || equal(image(element_relation,complement(u)),omega)** equal(power_class(u),symmetrization_of(successor_relation)) -> .
% 299.82/300.45  217020[11:SpL:160367.0,202881.1] || equal(symmetric_difference(universal_class,u),universal_class)** equal(union(u,successor_relation),symmetrization_of(successor_relation)) -> .
% 299.82/300.45  217021[11:SpL:57.0,202881.1] || equal(image(element_relation,complement(u)),universal_class)** equal(power_class(u),symmetrization_of(successor_relation)) -> .
% 299.82/300.45  217125[20:SpL:160367.0,206075.1] || equal(symmetric_difference(universal_class,u),omega)** equal(union(u,successor_relation),successor(successor_relation)) -> .
% 299.82/300.45  217128[20:SpL:57.0,206075.1] || equal(image(element_relation,complement(u)),omega)** equal(power_class(u),successor(successor_relation)) -> .
% 299.82/300.45  217142[10:SpL:160367.0,206081.1] || equal(symmetric_difference(universal_class,u),universal_class)** equal(union(u,successor_relation),successor(successor_relation)) -> .
% 299.82/300.45  217145[10:SpL:57.0,206081.1] || equal(image(element_relation,complement(u)),universal_class)** equal(power_class(u),successor(successor_relation)) -> .
% 299.82/300.45  217196[10:Res:137.1,206660.0] || member(complement(singleton(successor_relation)),ordinal_numbers) member(successor_relation,sum_class(complement(singleton(successor_relation))))* -> .
% 299.82/300.45  217250[10:Res:217225.1,3.0] || equal(singleton(u),kind_1_ordinals) subclass(singleton(successor_relation),v)* -> member(u,v)*.
% 299.82/300.45  217413[20:Res:217226.1,3.0] || equal(singleton(u),omega) subclass(singleton(successor_relation),v)* -> member(u,v)*.
% 299.82/300.45  217581[12:MRR:217557.2,185618.0] || member(unordered_pair(u,v),element_relation)* subclass(universal_class,regular(compose(element_relation,universal_class)))* -> .
% 299.82/300.45  217665[10:SpL:2330.1,217599.0] || subclass(universal_class,not_subclass_element(cross_product(u,v),w))* -> subclass(cross_product(u,v),w).
% 299.82/300.45  217870[10:MRR:217822.2,314.0] || equal(complement(u),successor_relation) member(v,universal_class) -> member(sum_class(v),u)*.
% 299.82/300.45  217881[10:SpL:2330.1,217670.0] || equal(not_subclass_element(cross_product(u,v),w),universal_class)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  217899[10:SpL:161592.1,217574.0] || subclass(universal_class,regular(regular(cross_product(u,v))))* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  217982[10:SpL:161592.1,217671.0] || equal(complement(regular(cross_product(u,v))),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  217991[10:SpL:161592.1,217908.0] || equal(regular(regular(cross_product(u,v))),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  218333[10:SpR:160367.0,218298.0] ||  -> subclass(regular(symmetric_difference(universal_class,u)),union(u,successor_relation))* equal(symmetric_difference(universal_class,u),successor_relation).
% 299.82/300.45  218376[10:Obv:218346.0] ||  -> subclass(u,complement(intersection(singleton(u),v)))* equal(intersection(singleton(u),v),successor_relation).
% 299.82/300.45  218377[10:Obv:218347.0] ||  -> subclass(u,complement(intersection(v,singleton(u))))* equal(intersection(v,singleton(u)),successor_relation).
% 299.82/300.45  218479[3:Res:5771.1,217932.0] || equal(sum_class(complement(kind_1_ordinals)),complement(kind_1_ordinals)) -> subclass(sum_class(complement(kind_1_ordinals)),complement(ordinal_numbers))*.
% 299.82/300.45  218518[3:Res:218490.0,9.0] || subclass(complement(ordinal_numbers),symmetric_difference(universal_class,kind_1_ordinals))* -> equal(symmetric_difference(universal_class,kind_1_ordinals),complement(ordinal_numbers)).
% 299.82/300.45  218534[3:Res:218494.0,1487.1] || member(u,universal_class) -> member(u,complement(complement(kind_1_ordinals)))* member(u,complement(ordinal_numbers)).
% 299.82/300.45  218884[22:Res:218867.1,9332.1] || subclass(kind_1_ordinals,intersection(u,v)) member(singleton(successor_relation),symmetric_difference(u,v))* -> .
% 299.82/300.45  218888[22:Res:218867.1,594.0] || subclass(kind_1_ordinals,restrict(u,v,w))* -> member(singleton(successor_relation),cross_product(v,w)).
% 299.82/300.45  218906[22:Res:218867.1,307.0] || subclass(kind_1_ordinals,image(element_relation,complement(u)))* member(singleton(successor_relation),power_class(u)) -> .
% 299.82/300.45  218908[22:Res:218867.1,160481.0] || subclass(kind_1_ordinals,regular(u))* member(singleton(successor_relation),u) -> equal(u,successor_relation).
% 299.82/300.45  219045[10:MRR:218977.1,6.0] || equal(complement(u),successor_relation) -> subclass(v,w) member(not_subclass_element(v,w),u)*.
% 299.82/300.45  219190[3:Res:51387.0,218628.0] ||  -> subclass(u,complement(complement(kind_1_ordinals))) member(not_subclass_element(u,complement(complement(kind_1_ordinals))),complement(ordinal_numbers))*.
% 299.82/300.45  219193[10:Res:160290.2,218628.0] || subclass(u,complement(kind_1_ordinals)) -> equal(u,successor_relation) member(regular(u),complement(ordinal_numbers))*.
% 299.82/300.45  201622[10:Res:160251.1,163294.0] || subclass(domain_relation,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(ordered_pair(successor_relation,successor_relation),kind_1_ordinals).
% 299.82/300.45  196294[10:SpR:163251.0,194805.1] || subclass(complement(kind_1_ordinals),symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.45  196124[10:SpR:163458.0,195339.0] ||  -> equal(intersection(kind_1_ordinals,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),symmetric_difference(singleton(successor_relation),range_of(successor_relation)))**.
% 299.82/300.45  201593[10:Res:192947.1,163294.0] || equal(complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),successor_relation)** -> member(singleton(u),kind_1_ordinals)*.
% 299.82/300.45  214304[10:Res:214277.1,163294.0] || equal(complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),successor_relation)** -> member(power_class(successor_relation),kind_1_ordinals).
% 299.82/300.45  216490[10:Res:216465.1,163294.0] || equal(complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),successor_relation)** -> member(regular(rest_relation),kind_1_ordinals).
% 299.82/300.45  216918[10:Res:216847.1,163294.0] || equal(complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),successor_relation)** -> member(regular(domain_relation),kind_1_ordinals).
% 299.82/300.45  163370[10:Rew:160305.0,162810.0] || subclass(universal_class,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(unordered_pair(u,v),kind_1_ordinals)*.
% 299.82/300.45  163371[10:Rew:160305.0,162811.0] || subclass(universal_class,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(ordered_pair(u,v),kind_1_ordinals)*.
% 299.82/300.45  201635[11:Res:183764.1,163294.0] || subclass(universal_class,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(regular(symmetrization_of(successor_relation)),kind_1_ordinals).
% 299.82/300.45  196263[10:MRR:196231.2,160227.0] || member(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* member(u,complement(kind_1_ordinals)) -> .
% 299.82/300.45  206273[20:Rew:206272.1,206248.2] inductive(successor(successor_relation)) || member(successor_relation,range_of(successor_relation))* -> equal(range_of(successor_relation),omega).
% 299.82/300.45  207208[10:Res:207189.0,163256.1] || equal(union(u,singleton(successor_relation)),range_of(successor_relation)) -> inductive(union(u,singleton(successor_relation)))*.
% 299.82/300.45  206702[10:Res:206681.0,163256.1] || equal(union(singleton(successor_relation),u),range_of(successor_relation)) -> inductive(union(singleton(successor_relation),u))*.
% 299.82/300.45  206592[10:Res:206541.0,163256.1] || equal(complement(complement(successor(successor_relation))),range_of(successor_relation)) -> inductive(complement(complement(successor(successor_relation))))*.
% 299.82/300.45  167678[10:Res:9509.0,163335.1] inductive(intersection(range_of(successor_relation),u)) ||  -> equal(intersection(range_of(successor_relation),u),range_of(successor_relation))**.
% 299.82/300.45  167685[10:Res:9395.0,163335.1] inductive(intersection(u,range_of(successor_relation))) ||  -> equal(intersection(u,range_of(successor_relation)),range_of(successor_relation))**.
% 299.82/300.45  167693[10:Res:107233.0,163335.1] inductive(complement(complement(range_of(successor_relation)))) ||  -> equal(complement(complement(range_of(successor_relation))),range_of(successor_relation))**.
% 299.82/300.45  211423[10:SpR:163197.1,163369.0] || subclass(complement(range_of(successor_relation)),successor_relation)* -> equal(complement(image(element_relation,kind_1_ordinals)),power_class(successor_relation)).
% 299.82/300.45  211422[10:SpR:185607.1,163369.0] || equal(complement(range_of(successor_relation)),successor_relation) -> equal(complement(image(element_relation,kind_1_ordinals)),power_class(successor_relation))**.
% 299.82/300.45  163497[10:Rew:160305.0,162096.2,160305.0,162096.1] inductive(singleton(u)) ||  -> equal(range_of(successor_relation),successor_relation) equal(regular(range_of(successor_relation)),u)*.
% 299.82/300.45  197705[10:SpR:185302.1,193779.0] || equal(cross_product(successor_relation,universal_class),successor_relation) -> equal(apply(universal_class,universal_class),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  161244[10:Rew:160202.0,146542.2] inductive(domain_of(u)) || equal(complement(rest_of(u)),universal_class)** -> member(successor_relation,v)*.
% 299.82/300.45  220409[23:MRR:163644.1,220405.0] || well_ordering(u,universal_class) -> member(least(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals)*.
% 299.82/300.45  220880[23:Res:220417.0,189421.0] || subclass(rest_relation,domain_relation) -> equal(rest_of(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),successor_relation)**.
% 299.82/300.45  220881[23:Res:220417.0,189420.0] || subclass(domain_relation,rest_relation) -> equal(rest_of(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),successor_relation)**.
% 299.82/300.45  221139[10:MRR:221136.1,185225.0] || equal(complement(u),successor_relation) -> equal(regular(unordered_pair(u,singleton(v))),singleton(v))**.
% 299.82/300.45  221387[10:MRR:221385.1,185241.0] || equal(complement(u),successor_relation) -> equal(regular(unordered_pair(singleton(v),u)),singleton(v))**.
% 299.82/300.45  221459[10:Res:218373.0,206737.0] ||  -> equal(singleton(successor(singleton(successor_relation))),successor_relation) member(successor_relation,complement(singleton(successor(singleton(successor_relation)))))*.
% 299.82/300.45  221468[10:Res:218373.0,160551.0] ||  -> equal(singleton(image(element_relation,universal_class)),successor_relation) member(successor_relation,complement(singleton(image(element_relation,universal_class))))*.
% 299.82/300.45  221470[13:Res:218373.0,180588.0] ||  -> equal(singleton(image(element_relation,successor_relation)),successor_relation) member(successor_relation,complement(singleton(image(element_relation,successor_relation))))*.
% 299.82/300.45  221478[10:Res:218373.0,206723.0] ||  -> equal(singleton(symmetrization_of(singleton(successor_relation))),successor_relation) member(successor_relation,complement(singleton(symmetrization_of(singleton(successor_relation)))))*.
% 299.82/300.45  221577[10:Res:221516.0,163256.1] || equal(complement(singleton(singleton(successor_relation))),range_of(successor_relation)) -> inductive(complement(singleton(singleton(successor_relation))))*.
% 299.82/300.45  221673[10:SSi:221608.0,52.0] || equal(complement(ordinal_numbers),successor_relation) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.45  221739[6:Res:221565.0,1487.1] || member(u,universal_class) -> member(u,compose(element_relation,universal_class))* member(u,complement(element_relation)).
% 299.82/300.45  222101[3:Rew:142543.0,222076.1] || member(not_subclass_element(symmetric_difference(universal_class,kind_1_ordinals),u),ordinal_numbers)* -> subclass(symmetric_difference(universal_class,kind_1_ordinals),u).
% 299.82/300.45  222138[14:SpR:199971.1,221525.0] || member(u,universal_class) -> member(successor_relation,complement(singleton(ordered_pair(sum_class(range_of(u)),v))))*.
% 299.82/300.45  222234[14:SpL:199971.1,222147.0] || member(u,universal_class) member(successor_relation,singleton(ordered_pair(sum_class(range_of(u)),v)))* -> .
% 299.82/300.45  222266[15:Res:1499.1,189380.2] || subclass(universal_class,u) member(v,universal_class)* subclass(domain_relation,complement(u))* -> .
% 299.82/300.45  222304[15:MRR:222254.0,999.0] || member(u,universal_class) subclass(domain_relation,complement(unordered_pair(ordered_pair(u,successor_relation),v)))* -> .
% 299.82/300.45  222305[15:MRR:222255.0,999.0] || member(u,universal_class) subclass(domain_relation,complement(unordered_pair(v,ordered_pair(u,successor_relation))))* -> .
% 299.82/300.45  222509[24:Rew:222326.0,222409.0] || equal(successor(successor_relation),kind_1_ordinals) member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> .
% 299.82/300.45  223148[24:Res:223096.0,1487.1] || member(u,universal_class) -> member(u,successor(kind_1_ordinals)) member(u,symmetric_difference(universal_class,kind_1_ordinals))*.
% 299.82/300.45  223300[24:SpL:222479.0,144.0] || member(ordered_pair(u,universal_class),rest_of(v))* -> equal(restrict(v,u,universal_class),kind_1_ordinals).
% 299.82/300.45  223310[24:SpL:222479.0,203931.0] || member(ordered_pair(u,universal_class),cross_product(universal_class,universal_class))* member(kind_1_ordinals,cantor(u)) -> .
% 299.82/300.45  223313[24:SpL:222479.0,163134.1] || equal(successor(u),kind_1_ordinals) member(ordered_pair(u,universal_class),cross_product(universal_class,universal_class))* -> .
% 299.82/300.45  223327[24:SpL:222479.0,98.0] || member(ordered_pair(u,ordered_pair(v,universal_class)),composition_function)* -> equal(compose(u,v),kind_1_ordinals).
% 299.82/300.45  224663[25:SpR:224236.1,203335.0] function(restrict(u,v,singleton(w))) ||  -> equal(segment(u,v,w),universal_class)**.
% 299.82/300.45  224837[25:SoR:224733.0,6317.2] single_valued_class(regular(symmetrization_of(successor_relation))) || equal(cross_product(universal_class,universal_class),regular(symmetrization_of(successor_relation)))** -> .
% 299.82/300.45  224845[25:SoR:224734.0,6317.2] single_valued_class(ordered_pair(u,v)) || equal(cross_product(universal_class,universal_class),ordered_pair(u,v))* -> .
% 299.82/300.45  224848[25:SoR:224735.0,6317.2] single_valued_class(unordered_pair(u,v)) || equal(cross_product(universal_class,universal_class),unordered_pair(u,v))* -> .
% 299.82/300.45  224857[25:SoR:224736.0,160511.2] single_valued_class(regular(complement(successor(successor_relation)))) || equal(regular(complement(successor(successor_relation))),successor_relation)** -> .
% 299.82/300.45  224860[25:SoR:224737.0,160511.2] single_valued_class(regular(complement(power_class(universal_class)))) || equal(regular(complement(power_class(universal_class))),successor_relation)** -> .
% 299.82/300.45  224863[25:SoR:224738.0,160511.2] single_valued_class(regular(complement(power_class(successor_relation)))) || equal(regular(complement(power_class(successor_relation))),successor_relation)** -> .
% 299.82/300.45  224928[25:SpR:224739.1,15.0] function(u) ||  -> equal(unordered_pair(successor_relation,unordered_pair(u,singleton(v))),ordered_pair(u,v))**.
% 299.82/300.45  225468[25:Rew:142543.0,224917.1,160223.0,224917.1] function(u) ||  -> equal(complement(image(element_relation,successor(u))),power_class(symmetric_difference(universal_class,u)))**.
% 299.82/300.45  225479[25:Rew:181135.1,225478.2] function(u) || member(singleton(singleton(successor_relation)),compose_class(v))* -> equal(universal_class,u)*.
% 299.82/300.45  225483[25:Rew:181136.1,225482.2] function(u) || member(singleton(singleton(successor_relation)),rest_of(v))* -> equal(universal_class,u)*.
% 299.82/300.45  225807[24:Rew:223100.0,225797.1] || member(not_subclass_element(successor(kind_1_ordinals),successor_relation),symmetric_difference(universal_class,kind_1_ordinals))* -> subclass(successor(kind_1_ordinals),successor_relation).
% 299.82/300.45  225967[20:MRR:225960.2,217612.0] || equal(singleton(least(u,complement(singleton(successor_relation)))),omega)** well_ordering(u,universal_class) -> .
% 299.82/300.45  225968[10:MRR:225961.2,217612.0] || equal(singleton(least(u,complement(singleton(successor_relation)))),kind_1_ordinals)** well_ordering(u,universal_class) -> .
% 299.82/300.45  226273[15:MRR:226193.1,160227.0] || member(u,universal_class) -> equal(apply(regular(symmetrization_of(successor_relation)),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226274[15:MRR:226203.1,160227.0] || member(u,universal_class) -> equal(apply(ordered_pair(v,w),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226275[15:MRR:226204.1,160227.0] || member(u,universal_class) -> equal(apply(unordered_pair(v,w),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226279[10:MRR:226221.0,54.0] || equal(complement(cantor(u)),universal_class) -> equal(apply(u,omega),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226280[10:MRR:226255.0,160214.0] || equal(complement(cantor(u)),kind_1_ordinals) -> equal(apply(u,successor_relation),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226281[20:MRR:226258.0,160214.0] || equal(complement(cantor(u)),omega) -> equal(apply(u,successor_relation),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226282[10:MRR:226259.0,160214.0] || equal(complement(cantor(u)),universal_class) -> equal(apply(u,successor_relation),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226286[10:MRR:226218.0,191.0] || subclass(cantor(u),successor_relation) -> equal(apply(u,singleton(v)),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226287[10:MRR:226249.0,191.0] || well_ordering(universal_class,cantor(u)) -> equal(apply(u,singleton(successor_relation)),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226353[25:SoR:224638.0,160511.2] single_valued_class(inverse(u)) || equal(inverse(u),successor_relation) -> equal(range_of(u),universal_class)**.
% 299.82/300.45  226398[25:SpL:226350.1,184006.1] one_to_one(u) || member(u,universal_class)* equal(rest_of(u),sum_class(universal_class)) -> .
% 299.82/300.45  226439[25:SoR:224774.0,160511.2] single_valued_class(power_class(u)) || member(u,universal_class)* equal(power_class(u),successor_relation) -> .
% 299.82/300.45  226442[25:SoR:224775.0,160511.2] single_valued_class(power_class(u)) || equal(successor_relation,u) equal(power_class(u),successor_relation)** -> .
% 299.82/300.45  226445[25:SoR:224777.0,160511.2] single_valued_class(sum_class(u)) || member(u,universal_class)* equal(sum_class(u),successor_relation) -> .
% 299.82/300.45  226448[25:SoR:224778.0,160511.2] single_valued_class(rest_of(u)) || member(u,universal_class)* equal(rest_of(u),successor_relation) -> .
% 299.82/300.45  226815[10:Rew:113504.0,226721.0,160223.0,226721.0] ||  -> equal(symmetric_difference(intersection(ordinal_numbers,u),complement(kind_1_ordinals)),union(intersection(ordinal_numbers,u),complement(kind_1_ordinals)))**.
% 299.82/300.45  226818[10:Rew:226634.0,226802.1] || member(not_subclass_element(complement(kind_1_ordinals),successor_relation),intersection(ordinal_numbers,u))* -> subclass(complement(kind_1_ordinals),successor_relation).
% 299.82/300.45  226914[10:Rew:113504.0,226825.0,160223.0,226825.0] ||  -> equal(symmetric_difference(complement(complement(ordinal_numbers)),complement(kind_1_ordinals)),union(complement(complement(ordinal_numbers)),complement(kind_1_ordinals)))**.
% 299.82/300.45  226917[10:Rew:226766.0,226895.1] || member(not_subclass_element(complement(kind_1_ordinals),successor_relation),complement(complement(ordinal_numbers)))* -> subclass(complement(kind_1_ordinals),successor_relation).
% 299.82/300.45  227032[10:Rew:113504.0,226942.0,160223.0,226942.0] ||  -> equal(symmetric_difference(intersection(u,ordinal_numbers),complement(kind_1_ordinals)),union(intersection(u,ordinal_numbers),complement(kind_1_ordinals)))**.
% 299.82/300.45  227035[10:Rew:226757.0,227020.1] || member(not_subclass_element(complement(kind_1_ordinals),successor_relation),intersection(u,ordinal_numbers))* -> subclass(complement(kind_1_ordinals),successor_relation).
% 299.82/300.45  227706[10:Rew:113504.0,227609.0,160223.0,227609.0] ||  -> equal(symmetric_difference(complement(kind_1_ordinals),intersection(ordinal_numbers,u)),union(complement(kind_1_ordinals),intersection(ordinal_numbers,u)))**.
% 299.82/300.45  227809[10:Rew:113504.0,227718.0,160223.0,227718.0] ||  -> equal(symmetric_difference(complement(kind_1_ordinals),complement(complement(ordinal_numbers))),union(complement(kind_1_ordinals),complement(complement(ordinal_numbers))))**.
% 299.82/300.45  227932[10:Rew:113504.0,227839.0,160223.0,227839.0] ||  -> equal(symmetric_difference(complement(kind_1_ordinals),intersection(u,ordinal_numbers)),union(complement(kind_1_ordinals),intersection(u,ordinal_numbers)))**.
% 299.82/300.45  228258[10:Res:222126.0,3.0] || subclass(complement(singleton(regular(rest_relation))),u)* -> member(singleton(first(regular(rest_relation))),u).
% 299.82/300.45  228396[10:Res:161722.2,185639.1] || subclass(u,v)* equal(successor_relation,v) -> equal(intersection(u,w),successor_relation)**.
% 299.82/300.45  228462[10:Res:222127.0,3.0] || subclass(complement(singleton(regular(domain_relation))),u)* -> member(singleton(first(regular(domain_relation))),u).
% 299.82/300.45  228479[12:Res:222128.0,3.0] || subclass(complement(singleton(regular(element_relation))),u)* -> member(singleton(first(regular(element_relation))),u).
% 299.82/300.45  228617[10:Res:161711.2,185639.1] || subclass(u,v)* equal(successor_relation,v) -> equal(intersection(w,u),successor_relation)**.
% 299.82/300.45  228680[10:Res:161492.2,222223.0] || equal(singleton(regular(rest_relation)),omega) -> equal(integer_of(singleton(first(regular(rest_relation)))),successor_relation)**.
% 299.82/300.45  228688[10:Res:161492.2,222224.0] || equal(singleton(regular(domain_relation)),omega) -> equal(integer_of(singleton(first(regular(domain_relation)))),successor_relation)**.
% 299.82/300.45  228696[12:Res:161492.2,222225.0] || equal(singleton(regular(element_relation)),omega) -> equal(integer_of(singleton(first(regular(element_relation)))),successor_relation)**.
% 299.82/300.45  228741[15:Obv:228703.1] || equal(u,v) -> equal(unordered_pair(v,u),successor_relation)** equal(cantor(v),successor_relation).
% 299.82/300.45  228827[24:SpL:223107.0,3487.0] || subclass(universal_class,symmetric_difference(complement(kind_1_ordinals),universal_class))* -> member(unordered_pair(u,v),successor(kind_1_ordinals))*.
% 299.82/300.45  229021[10:Res:228991.1,9332.1] || subclass(kind_1_ordinals,intersection(u,v)) member(regular(ordinal_numbers),symmetric_difference(u,v))* -> .
% 299.82/300.45  229025[10:Res:228991.1,594.0] || subclass(kind_1_ordinals,restrict(u,v,w))* -> member(regular(ordinal_numbers),cross_product(v,w)).
% 299.82/300.45  229043[10:Res:228991.1,307.0] || subclass(kind_1_ordinals,image(element_relation,complement(u)))* member(regular(ordinal_numbers),power_class(u)) -> .
% 299.82/300.45  229046[10:Res:228991.1,160481.0] || subclass(kind_1_ordinals,regular(u))* member(regular(ordinal_numbers),u) -> equal(u,successor_relation).
% 299.82/300.45  229249[10:Res:229228.1,9332.1] || subclass(universal_class,intersection(u,v)) member(regular(ordinal_numbers),symmetric_difference(u,v))* -> .
% 299.82/300.45  229253[10:Res:229228.1,594.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(ordinal_numbers),cross_product(v,w)).
% 299.82/300.45  229271[10:Res:229228.1,307.0] || subclass(universal_class,image(element_relation,complement(u)))* member(regular(ordinal_numbers),power_class(u)) -> .
% 299.82/300.45  229274[10:Res:229228.1,160481.0] || subclass(universal_class,regular(u))* member(regular(ordinal_numbers),u) -> equal(u,successor_relation).
% 299.82/300.45  229793[10:Res:221521.1,3486.1] || subclass(universal_class,complement(complement(singleton(omega))))* -> equal(integer_of(unordered_pair(u,v)),successor_relation)**.
% 299.82/300.45  229799[10:Res:221521.1,3.0] || subclass(complement(singleton(omega)),u)* -> equal(integer_of(v),successor_relation) member(v,u)*.
% 299.82/300.45  229830[10:MRR:229792.2,217612.0] || subclass(universal_class,regular(complement(singleton(omega))))* -> equal(integer_of(unordered_pair(u,v)),successor_relation)**.
% 299.82/300.45  229855[20:Res:218373.0,221538.0] ||  -> equal(singleton(complement(singleton(omega))),successor_relation) member(successor_relation,complement(singleton(complement(singleton(omega)))))*.
% 299.82/300.45  230232[24:Res:28320.1,223309.0] || subclass(rest_relation,rotate(element_relation)) -> member(ordered_pair(u,rest_of(ordered_pair(universal_class,u))),kind_1_ordinals)*.
% 299.82/300.45  230236[24:Res:161492.2,223309.0] || equal(omega,element_relation) -> equal(integer_of(ordered_pair(u,universal_class)),successor_relation)** member(u,kind_1_ordinals).
% 299.82/300.45  230522[10:Res:160290.2,229800.0] || subclass(u,singleton(omega))* -> equal(u,successor_relation) equal(integer_of(regular(u)),successor_relation).
% 299.82/300.45  230733[10:MRR:230728.1,200297.0] || equal(complement(u),successor_relation) -> equal(regular(unordered_pair(u,regular(rest_relation))),regular(rest_relation))**.
% 299.82/300.45  230740[10:MRR:230735.1,201541.0] || equal(complement(u),successor_relation) -> equal(regular(unordered_pair(u,regular(domain_relation))),regular(domain_relation))**.
% 299.82/300.45  230766[12:MRR:230761.1,209559.0] || equal(complement(u),successor_relation) -> equal(regular(unordered_pair(u,regular(element_relation))),regular(element_relation))**.
% 299.82/300.45  231529[10:MRR:231526.1,200282.0] || equal(complement(u),successor_relation) -> equal(regular(unordered_pair(regular(rest_relation),u)),regular(rest_relation))**.
% 299.82/300.45  231555[3:Obv:231546.0] || subclass(rest_relation,ordinal_numbers) member(u,universal_class)* subclass(rest_relation,complement(kind_1_ordinals))* -> .
% 299.82/300.45  231577[10:MRR:231574.1,201526.0] || equal(complement(u),successor_relation) -> equal(regular(unordered_pair(regular(domain_relation),u)),regular(domain_relation))**.
% 299.82/300.45  231583[12:MRR:231580.1,209545.0] || equal(complement(u),successor_relation) -> equal(regular(unordered_pair(regular(element_relation),u)),regular(element_relation))**.
% 299.82/300.45  10169[0:SpR:1933.0,9535.0] ||  -> subclass(symmetric_difference(complement(intersection(u,inverse(u))),symmetrization_of(u)),complement(symmetric_difference(u,inverse(u))))*.
% 299.82/300.45  30567[0:SpL:28.0,30433.1] || subclass(universal_class,intersection(complement(u),complement(v)))* subclass(universal_class,union(u,v)) -> .
% 299.82/300.45  31434[0:SpL:40.0,31279.1] || equal(complement(rest_of(flip(cross_product(u,universal_class)))),universal_class)** member(v,inverse(u))* -> .
% 299.82/300.45  40243[0:Rew:2152.1,40242.1] || member(u,v) member(u,w) -> subclass(singleton(u),intersection(w,v))*.
% 299.82/300.45  10231[0:SpR:1934.0,9535.0] ||  -> subclass(symmetric_difference(complement(intersection(u,singleton(u))),successor(u)),complement(symmetric_difference(u,singleton(u))))*.
% 299.82/300.45  48589[0:Res:3907.1,10254.0] || equal(complement(complement(symmetric_difference(u,singleton(u)))),universal_class)** -> member(singleton(v),successor(u))*.
% 299.82/300.45  48487[0:Res:3907.1,10191.0] || equal(complement(complement(symmetric_difference(u,inverse(u)))),universal_class)** -> member(singleton(v),symmetrization_of(u))*.
% 299.82/300.45  6833[0:Res:3907.1,1952.0] || equal(complement(complement(symmetric_difference(u,v))),universal_class) -> member(singleton(w),union(u,v))*.
% 299.82/300.45  29399[0:SpL:1948.0,2648.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v)))* -> member(singleton(w),union(u,v))*.
% 299.82/300.45  5783[0:Res:3907.1,3.0] || equal(complement(complement(u)),universal_class)** subclass(u,v)* -> member(singleton(w),v)*.
% 299.82/300.45  41264[0:Res:1499.1,5647.0] || subclass(universal_class,compose(u,v)) -> subclass(w,image(u,image(v,singleton(x))))*.
% 299.82/300.45  9599[0:Res:1499.1,594.0] || subclass(universal_class,restrict(u,v,w))* -> member(ordered_pair(x,y),cross_product(v,w))*.
% 299.82/300.45  3426[0:SpL:28.0,3358.1] || equal(intersection(complement(u),complement(v)),universal_class)** equal(union(u,v),universal_class) -> .
% 299.82/300.45  29395[0:SpL:1948.0,5884.0] || equal(symmetric_difference(complement(u),complement(v)),universal_class) -> member(singleton(w),union(u,v))*.
% 299.82/300.45  89309[0:Res:89275.1,9.0] || subclass(complement(u),singleton(v))* -> member(v,u) equal(complement(u),singleton(v)).
% 299.82/300.45  108371[0:Res:25.2,9332.1] || member(u,v) member(u,w) member(u,symmetric_difference(w,v))* -> .
% 299.82/300.45  108398[0:Res:1499.1,9332.1] || subclass(universal_class,intersection(u,v)) member(ordered_pair(w,x),symmetric_difference(u,v))* -> .
% 299.82/300.45  108430[0:Res:1504.1,6045.0] || subclass(ordered_pair(u,v),w)* subclass(w,x)* well_ordering(universal_class,x)* -> .
% 299.82/300.45  118404[0:Res:8.1,9146.1] || equal(complement(u),universal_class) member(v,universal_class) member(power_class(v),u)* -> .
% 299.82/300.45  120178[0:Res:8.1,9149.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> member(power_class(w),u)*.
% 299.82/300.45  120231[0:Res:8.1,9150.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> member(power_class(w),v)*.
% 299.82/300.45  122548[0:Obv:122489.2] || subclass(singleton(u),complement(v))* member(u,v) -> subclass(singleton(u),w)*.
% 299.82/300.45  122722[0:Obv:122693.1] || subclass(symmetric_difference(u,v),complement(union(u,v)))* -> subclass(symmetric_difference(u,v),w)*.
% 299.82/300.45  125198[0:Res:3907.1,2320.0] || equal(complement(complement(rest_of(u))),universal_class) -> equal(restrict(u,singleton(v),universal_class),v)**.
% 299.82/300.45  125959[0:Res:28320.1,147.0] || subclass(rest_relation,rotate(rest_relation)) -> equal(rest_of(ordered_pair(u,rest_of(ordered_pair(v,u)))),v)**.
% 299.82/300.45  126089[0:Res:28321.1,147.0] || subclass(rest_relation,flip(rest_relation)) -> equal(rest_of(ordered_pair(u,v)),rest_of(ordered_pair(v,u)))*.
% 299.82/300.45  3605[0:SpL:28.0,3565.0] || equal(complement(union(u,v)),universal_class) -> member(omega,intersection(complement(u),complement(v)))*.
% 299.82/300.45  152918[0:Res:1506.1,513.0] || equal(intersection(complement(u),complement(v)),universal_class)** member(omega,union(u,v)) -> .
% 299.82/300.45  155773[2:MRR:155745.0,34067.1] || member(u,complement(v))* subclass(symmetric_difference(universal_class,v),w)* -> member(u,w)*.
% 299.82/300.45  158190[0:Res:1951.1,1509.1] || member(omega,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),universal_class)** -> .
% 299.82/300.45  162976[10:Rew:160202.0,156097.0] ||  -> subclass(symmetric_difference(power_class(image(element_relation,complement(u))),universal_class),union(image(element_relation,power_class(u)),successor_relation))*.
% 299.82/300.45  163367[10:Rew:160202.0,162768.1] || member(not_subclass_element(complement(inverse(successor_relation)),successor_relation),symmetrization_of(successor_relation))* -> subclass(complement(inverse(successor_relation)),successor_relation).
% 299.82/300.45  161863[10:Rew:160202.0,148476.1] || subclass(u,complement(omega)) -> equal(integer_of(not_subclass_element(u,v)),successor_relation)** subclass(u,v).
% 299.82/300.45  163364[10:Rew:160202.0,161862.1] ||  -> equal(integer_of(regular(intersection(u,complement(omega)))),successor_relation)** equal(intersection(u,complement(omega)),successor_relation).
% 299.82/300.45  163363[10:Rew:160202.0,161861.1] ||  -> equal(integer_of(regular(intersection(complement(omega),u))),successor_relation)** equal(intersection(complement(omega),u),successor_relation).
% 299.82/300.45  161859[10:Rew:160202.0,153071.1] || subclass(universal_class,intersection(y__dfg,ordinal_numbers)) -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation)**.
% 299.82/300.45  161855[10:Rew:160202.0,147857.1] inductive(cantor(restrict(u,v,singleton(w)))) ||  -> member(successor_relation,segment(u,v,w))*.
% 299.82/300.45  161851[10:Rew:160202.0,147814.0] ||  -> equal(intersection(intersection(u,image(element_relation,power_class(v))),power_class(image(element_relation,complement(v)))),successor_relation)**.
% 299.82/300.45  161849[10:Rew:160202.0,147768.0] ||  -> equal(intersection(symmetric_difference(cross_product(u,v),w),complement(complement(restrict(w,u,v)))),successor_relation)**.
% 299.82/300.45  161848[10:Rew:160202.0,147767.0] ||  -> equal(intersection(symmetric_difference(u,cross_product(v,w)),complement(complement(restrict(u,v,w)))),successor_relation)**.
% 299.82/300.45  161846[10:Rew:160202.0,147764.0] ||  -> equal(intersection(intersection(image(element_relation,power_class(u)),v),power_class(image(element_relation,complement(u)))),successor_relation)**.
% 299.82/300.45  161844[10:Rew:160202.0,147750.0] ||  -> equal(intersection(power_class(image(element_relation,complement(u))),intersection(v,image(element_relation,power_class(u)))),successor_relation)**.
% 299.82/300.45  161842[10:Rew:160202.0,147654.0] ||  -> equal(intersection(power_class(image(element_relation,complement(u))),intersection(image(element_relation,power_class(u)),v)),successor_relation)**.
% 299.82/300.45  161840[10:Rew:160202.0,147651.0] ||  -> equal(intersection(complement(complement(restrict(u,v,w))),symmetric_difference(cross_product(v,w),u)),successor_relation)**.
% 299.82/300.45  161839[10:Rew:160202.0,147650.0] ||  -> equal(intersection(complement(complement(restrict(u,v,w))),symmetric_difference(u,cross_product(v,w))),successor_relation)**.
% 299.82/300.45  161838[10:Rew:160202.0,147520.0] ||  -> equal(intersection(power_class(intersection(complement(u),complement(v))),image(element_relation,union(u,v))),successor_relation)**.
% 299.82/300.45  161837[10:Rew:160202.0,147494.0] ||  -> equal(intersection(image(element_relation,union(u,v)),power_class(intersection(complement(u),complement(v)))),successor_relation)**.
% 299.82/300.45  161836[10:Rew:160202.0,147422.2] || subclass(u,v)* well_ordering(universal_class,v)* -> equal(restrict(u,w,x),successor_relation)**.
% 299.82/300.45  161821[10:Rew:160202.0,147281.1] ||  -> member(regular(complement(union(u,v))),complement(v))* equal(complement(union(u,v)),successor_relation).
% 299.82/300.45  161822[10:Rew:160202.0,147279.1] ||  -> member(regular(complement(union(u,v))),complement(u))* equal(complement(union(u,v)),successor_relation).
% 299.82/300.45  161816[10:Rew:160202.0,147270.1] ||  -> member(regular(complement(power_class(u))),image(element_relation,complement(u)))* equal(complement(power_class(u)),successor_relation).
% 299.82/300.45  161814[10:Rew:160202.0,147264.1] || member(regular(complement(complement(complement(u)))),u)* -> equal(complement(complement(complement(u))),successor_relation).
% 299.82/300.45  161813[10:Rew:160202.0,147160.1] || equal(restrict(u,v,w),x)* -> equal(x,successor_relation) member(regular(x),u)*.
% 299.82/300.45  161811[10:Rew:160202.0,146916.1] inductive(symmetric_difference(cross_product(u,v),w)) ||  -> member(successor_relation,complement(restrict(w,u,v)))*.
% 299.82/300.45  161807[10:Rew:160202.0,146915.1] inductive(symmetric_difference(u,cross_product(v,w))) ||  -> member(successor_relation,complement(restrict(u,v,w)))*.
% 299.82/300.45  161797[10:Rew:160202.0,146854.1] || subclass(image(element_relation,complement(u)),power_class(u))* -> equal(image(element_relation,complement(u)),successor_relation).
% 299.82/300.45  161793[10:Rew:160202.0,146849.1] || subclass(universal_class,intersection(y__dfg,ordinal_numbers)) -> equal(singleton(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation)**.
% 299.82/300.45  161791[10:Rew:160202.0,146841.0] ||  -> equal(symmetric_difference(u,inverse(u)),successor_relation) member(regular(symmetric_difference(u,inverse(u))),symmetrization_of(u))*.
% 299.82/300.45  161788[10:Rew:160202.0,146838.0] ||  -> equal(symmetric_difference(u,singleton(u)),successor_relation) member(regular(symmetric_difference(u,singleton(u))),successor(u))*.
% 299.82/300.45  163340[10:Rew:160202.0,160537.0] || member(not_subclass_element(intersection(u,v),successor_relation),complement(u))* -> subclass(intersection(u,v),successor_relation).
% 299.82/300.45  163339[10:Rew:160202.0,160536.0] || member(not_subclass_element(intersection(u,v),successor_relation),complement(v))* -> subclass(intersection(u,v),successor_relation).
% 299.82/300.45  161798[10:Rew:160202.0,159931.1] || well_ordering(universal_class,power_class(image(element_relation,complement(u))))* -> member(successor_relation,image(element_relation,power_class(u))).
% 299.82/300.45  161803[10:Rew:160202.0,146913.1] inductive(power_class(image(element_relation,complement(u)))) || member(successor_relation,image(element_relation,power_class(u)))* -> .
% 299.82/300.45  161784[10:Rew:160202.0,146710.1] ||  -> equal(regular(unordered_pair(u,v)),u)** equal(unordered_pair(u,v),successor_relation) member(v,universal_class).
% 299.82/300.45  161785[10:Rew:160202.0,146709.1] ||  -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),successor_relation) member(u,universal_class).
% 299.82/300.45  161689[10:Rew:160202.0,146729.1] || member(regular(symmetric_difference(u,v)),intersection(u,v))* -> equal(symmetric_difference(u,v),successor_relation).
% 299.82/300.45  161612[10:Rew:160202.0,147214.1] || equal(u,v) -> equal(unordered_pair(v,u),successor_relation) member(v,unordered_pair(v,u))*.
% 299.82/300.45  161601[10:Rew:160202.0,146831.1] || subclass(universal_class,complement(singleton(regular(cross_product(u,v)))))* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  161602[10:Rew:160202.0,146830.1] || equal(complement(singleton(regular(cross_product(u,v)))),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  163362[10:Rew:160202.0,161654.1] ||  -> member(not_subclass_element(u,union(v,successor_relation)),symmetric_difference(universal_class,v))* subclass(u,union(v,successor_relation)).
% 299.82/300.45  161647[10:Rew:160202.0,148463.2] || member(u,universal_class) -> member(u,symmetric_difference(universal_class,v))* member(u,union(v,successor_relation)).
% 299.82/300.45  161456[10:Rew:160202.0,159729.0] || member(successor_relation,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),universal_class)** -> .
% 299.82/300.45  161371[10:Rew:160202.0,153210.1] || equal(intersection(complement(u),complement(v)),universal_class)** member(successor_relation,union(u,v)) -> .
% 299.82/300.45  163358[10:Rew:160202.0,161283.1] ||  -> equal(intersection(singleton(u),v),successor_relation) equal(intersection(intersection(singleton(u),v),u),successor_relation)**.
% 299.82/300.45  163357[10:Rew:160202.0,161276.1] ||  -> equal(intersection(u,singleton(v)),successor_relation) equal(intersection(intersection(u,singleton(v)),v),successor_relation)**.
% 299.82/300.45  161313[10:Rew:160202.0,146614.1] || member(regular(intersection(u,v)),symmetric_difference(u,v))* -> equal(intersection(u,v),successor_relation).
% 299.82/300.45  161300[10:Rew:160202.0,146576.1] || asymmetric(universal_class,u) subclass(compose(successor_relation,successor_relation),successor_relation)* -> transitive(inverse(universal_class),u)*.
% 299.82/300.45  163354[10:Rew:160202.0,161232.1] || member(regular(union(u,successor_relation)),symmetric_difference(universal_class,u))* -> equal(union(u,successor_relation),successor_relation).
% 299.82/300.45  161221[10:Rew:160202.0,156008.0] ||  -> subclass(symmetric_difference(union(u,successor_relation),complement(singleton(symmetric_difference(universal_class,u)))),successor(symmetric_difference(universal_class,u)))*.
% 299.82/300.45  161220[10:Rew:160202.0,156000.0] ||  -> subclass(symmetric_difference(union(u,successor_relation),complement(inverse(symmetric_difference(universal_class,u)))),symmetrization_of(symmetric_difference(universal_class,u)))*.
% 299.82/300.45  160875[10:Rew:160202.0,152641.0] ||  -> member(not_subclass_element(complement(power_class(universal_class)),u),image(element_relation,successor_relation))* subclass(complement(power_class(universal_class)),u).
% 299.82/300.45  160845[10:Rew:160202.0,148331.1] || member(u,image(element_relation,power_class(universal_class)))* member(u,power_class(image(element_relation,successor_relation))) -> .
% 299.82/300.45  160696[10:Rew:160202.0,159713.2] || subclass(universal_class,regular(u)) member(ordered_pair(v,w),u)* -> equal(u,successor_relation).
% 299.82/300.45  160791[10:Rew:160202.0,146538.2] || subclass(u,rest_of(regular(u)))* subclass(universal_class,complement(element_relation)) -> equal(u,successor_relation).
% 299.82/300.45  168549[11:Res:168384.1,9322.0] || equal(symmetric_difference(complement(u),complement(v)),symmetrization_of(successor_relation))** -> member(successor_relation,union(u,v)).
% 299.82/300.45  168469[11:MRR:163521.2,168458.0] || member(symmetrization_of(successor_relation),universal_class) member(apply(choice,symmetrization_of(successor_relation)),complement(inverse(successor_relation)))* -> .
% 299.82/300.45  163348[10:Rew:160202.0,161099.0] ||  -> member(not_subclass_element(complement(symmetrization_of(successor_relation)),u),complement(inverse(successor_relation)))* subclass(complement(symmetrization_of(successor_relation)),u).
% 299.82/300.45  163353[10:Rew:160202.0,161183.0] || subclass(unordered_pair(u,v),successor_relation)* member(v,universal_class) -> member(v,inverse(successor_relation)).
% 299.82/300.45  163352[10:Rew:160202.0,161181.0] || subclass(unordered_pair(u,v),successor_relation)* member(u,universal_class) -> member(u,inverse(successor_relation)).
% 299.82/300.45  163347[10:Rew:160202.0,161096.1] || member(u,image(element_relation,symmetrization_of(successor_relation)))* member(u,power_class(complement(inverse(successor_relation)))) -> .
% 299.82/300.45  160973[10:Rew:160202.0,148447.0] || member(u,image(element_relation,power_class(successor_relation)))* member(u,power_class(image(element_relation,universal_class))) -> .
% 299.82/300.45  163346[10:Rew:160202.0,160898.1] ||  -> member(not_subclass_element(complement(power_class(successor_relation)),u),image(element_relation,universal_class))* subclass(complement(power_class(successor_relation)),u).
% 299.82/300.45  160895[10:Rew:160202.0,150283.0] || equal(complement(complement(power_class(successor_relation))),universal_class) member(singleton(u),image(element_relation,universal_class))* -> .
% 299.82/300.45  163097[10:Rew:160202.0,159365.1] || subclass(domain_relation,image(element_relation,complement(u)))* member(ordered_pair(successor_relation,successor_relation),power_class(u)) -> .
% 299.82/300.45  163096[10:Rew:160202.0,159353.1] || subclass(domain_relation,restrict(u,v,w))* -> member(ordered_pair(successor_relation,successor_relation),cross_product(v,w))*.
% 299.82/300.45  163095[10:Rew:160202.0,159349.1] || subclass(domain_relation,intersection(u,v)) member(ordered_pair(successor_relation,successor_relation),symmetric_difference(u,v))* -> .
% 299.82/300.45  163344[10:Rew:160202.0,160695.1] || subclass(domain_relation,regular(u)) member(ordered_pair(successor_relation,successor_relation),u)* -> equal(u,successor_relation).
% 299.82/300.45  163373[10:Rew:160202.0,162925.1] || member(successor(successor_relation),universal_class) member(apply(choice,successor(successor_relation)),complement(singleton(successor_relation)))* -> .
% 299.82/300.45  163359[10:Rew:160202.0,161363.0] || equal(symmetric_difference(complement(u),complement(v)),successor(successor_relation))** -> member(successor_relation,union(u,v)).
% 299.82/300.45  163372[10:Rew:160202.0,162881.1] ||  -> member(not_subclass_element(complement(successor(successor_relation)),u),complement(singleton(successor_relation)))* subclass(complement(successor(successor_relation)),u).
% 299.82/300.45  163360[10:Rew:160202.0,161367.0] || equal(symmetric_difference(complement(u),complement(v)),singleton(successor_relation))** -> member(successor_relation,union(u,v)).
% 299.82/300.45  163368[10:Rew:160202.0,162776.0] || member(u,image(element_relation,successor(successor_relation)))* member(u,power_class(complement(singleton(successor_relation)))) -> .
% 299.82/300.45  120067[0:SpL:119971.0,48051.0] || member(inverse(cross_product(u,universal_class)),image(universal_class,u))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.45  157893[6:Res:3907.1,148657.1] || equal(complement(complement(complement(compose(element_relation,universal_class)))),universal_class)** member(singleton(u),element_relation)* -> .
% 299.82/300.45  124614[0:Res:1477.1,33515.1] || subclass(universal_class,u) member(u,universal_class) -> member(singleton(singleton(singleton(u))),element_relation)*.
% 299.82/300.45  124612[0:Res:114897.1,33515.1] || equal(u,universal_class) member(u,universal_class) -> member(singleton(singleton(singleton(u))),element_relation)*.
% 299.82/300.45  118053[0:Res:8.1,9069.0] || equal(image(element_relation,complement(u)),universal_class) member(unordered_pair(v,w),power_class(u))* -> .
% 299.82/300.45  9077[0:Res:1499.1,307.0] || subclass(universal_class,image(element_relation,complement(u)))* member(ordered_pair(v,w),power_class(u))* -> .
% 299.82/300.45  159778[6:SpL:208.0,159727.1] inductive(image(element_relation,power_class(u))) || equal(power_class(image(element_relation,complement(u))),universal_class)** -> .
% 299.82/300.45  155720[2:SpR:208.0,142543.0] ||  -> equal(intersection(power_class(image(element_relation,complement(u))),universal_class),symmetric_difference(universal_class,image(element_relation,power_class(u))))**.
% 299.82/300.45  89296[0:SpR:208.0,89275.1] ||  -> member(u,image(element_relation,power_class(v))) subclass(singleton(u),power_class(image(element_relation,complement(v))))*.
% 299.82/300.45  108217[0:SpR:208.0,107289.0] ||  -> subclass(complement(power_class(image(element_relation,power_class(u)))),image(element_relation,power_class(image(element_relation,complement(u)))))*.
% 299.82/300.45  145345[2:SpR:505.0,142420.0] ||  -> equal(symmetric_difference(power_class(intersection(complement(u),complement(v))),image(element_relation,union(u,v))),universal_class)**.
% 299.82/300.45  145213[2:SpR:505.0,142419.0] ||  -> equal(symmetric_difference(image(element_relation,union(u,v)),power_class(intersection(complement(u),complement(v)))),universal_class)**.
% 299.82/300.45  145155[2:SpR:505.0,142372.0] ||  -> equal(union(power_class(intersection(complement(u),complement(v))),image(element_relation,union(u,v))),universal_class)**.
% 299.82/300.45  145088[2:SpR:505.0,142371.0] ||  -> equal(union(image(element_relation,union(u,v)),power_class(intersection(complement(u),complement(v)))),universal_class)**.
% 299.82/300.45  115610[0:SpR:505.0,114856.0] ||  -> subclass(symmetric_difference(universal_class,image(element_relation,union(u,v))),power_class(intersection(complement(u),complement(v))))*.
% 299.82/300.45  31432[0:SpL:55.0,31279.1] || equal(complement(rest_of(restrict(element_relation,universal_class,u))),universal_class)** member(v,sum_class(u))* -> .
% 299.82/300.45  118688[0:Res:8.1,9118.1] || equal(complement(u),universal_class) member(v,universal_class) member(sum_class(v),u)* -> .
% 299.82/300.45  120340[0:Res:8.1,9122.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> member(sum_class(w),v)*.
% 299.82/300.45  120299[0:Res:8.1,9121.1] || equal(intersection(u,v),universal_class)** member(w,universal_class) -> member(sum_class(w),u)*.
% 299.82/300.45  155814[3:Res:1504.1,141576.1] || subclass(ordered_pair(u,v),complement(kind_1_ordinals))* member(unordered_pair(u,singleton(v)),ordinal_numbers) -> .
% 299.82/300.45  108441[0:Res:1504.1,24.0] || subclass(ordered_pair(u,v),intersection(w,x))* -> member(unordered_pair(u,singleton(v)),x).
% 299.82/300.45  108435[0:Res:1504.1,26.1] || subclass(ordered_pair(u,v),complement(w))* member(unordered_pair(u,singleton(v)),w) -> .
% 299.82/300.45  108440[0:Res:1504.1,23.0] || subclass(ordered_pair(u,v),intersection(w,x))* -> member(unordered_pair(u,singleton(v)),w).
% 299.82/300.45  108363[0:Res:1476.1,9332.1] || subclass(universal_class,intersection(u,v)) member(unordered_pair(w,x),symmetric_difference(u,v))* -> .
% 299.82/300.45  48015[0:SpL:161.0,3487.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(unordered_pair(w,x),complement(intersection(u,v)))*.
% 299.82/300.45  122437[0:Res:8.1,9587.0] || equal(restrict(u,v,w),universal_class)** -> member(unordered_pair(x,y),cross_product(v,w))*.
% 299.82/300.45  155769[2:Rew:142543.0,155747.1] || member(not_subclass_element(universal_class,symmetric_difference(universal_class,u)),complement(u))* -> subclass(universal_class,symmetric_difference(universal_class,u)).
% 299.82/300.45  89245[0:Res:51387.0,24.0] ||  -> subclass(u,complement(intersection(v,w))) member(not_subclass_element(u,complement(intersection(v,w))),w)*.
% 299.82/300.45  89244[0:Res:51387.0,23.0] ||  -> subclass(u,complement(intersection(v,w))) member(not_subclass_element(u,complement(intersection(v,w))),v)*.
% 299.82/300.45  143793[0:Res:51387.0,159.0] ||  -> subclass(u,complement(omega)) equal(integer_of(not_subclass_element(u,complement(omega))),not_subclass_element(u,complement(omega)))**.
% 299.82/300.45  122553[0:MRR:122495.0,34189.1] || subclass(u,complement(complement(v)))* -> member(not_subclass_element(u,w),v)* subclass(u,w).
% 299.82/300.45  107216[0:Res:34429.0,2151.0] ||  -> subclass(complement(complement(singleton(u))),v) equal(not_subclass_element(complement(complement(singleton(u))),v),u)**.
% 299.82/300.45  41915[0:SpL:2330.1,3898.0] || equal(complement(not_subclass_element(cross_product(u,v),w)),universal_class)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  41916[0:SpL:2330.1,30448.0] || subclass(universal_class,complement(not_subclass_element(cross_product(u,v),w)))* -> subclass(cross_product(u,v),w).
% 299.82/300.45  113249[0:MRR:113189.0,34189.1] ||  -> member(not_subclass_element(u,intersection(complement(v),u)),v)* subclass(u,intersection(complement(v),u)).
% 299.82/300.45  123440[0:Res:8.1,9639.0] || equal(intersection(u,v),w)* -> subclass(w,x) member(not_subclass_element(w,x),u)*.
% 299.82/300.45  122849[0:Res:8.1,9640.0] || equal(intersection(u,v),w)* -> subclass(w,x) member(not_subclass_element(w,x),v)*.
% 299.82/300.45  143082[0:Res:53.1,9647.0] inductive(restrict(u,v,w)) ||  -> subclass(omega,x) member(not_subclass_element(omega,x),u)*.
% 299.82/300.45  89239[0:Res:51387.0,3.0] || subclass(u,v) -> subclass(w,complement(u)) member(not_subclass_element(w,complement(u)),v)*.
% 299.82/300.45  120364[0:Res:8.1,28300.1] || equal(cross_product(u,v),rest_relation)** member(w,universal_class) -> member(rest_of(w),v)*.
% 299.82/300.45  180006[11:Res:179843.1,9322.0] || equal(symmetric_difference(complement(u),complement(v)),inverse(successor_relation))** -> member(successor_relation,union(u,v)).
% 299.82/300.45  181435[10:SpL:181082.0,5754.0] || subclass(apply(u,universal_class),image(u,successor_relation))* -> section(element_relation,image(u,successor_relation),universal_class).
% 299.82/300.45  182344[10:SpL:28.0,160544.0] || equal(complement(union(u,v)),universal_class) -> member(successor_relation,intersection(complement(u),complement(v)))*.
% 299.82/300.45  182931[6:Res:157922.1,6045.0] || member(u,element_relation)* subclass(compose(element_relation,universal_class),v)* well_ordering(universal_class,v) -> .
% 299.82/300.45  183211[10:Rew:181086.0,183162.1] || member(u,universal_class) -> equal(segment(v,w,successor(u)),segment(v,w,universal_class))**.
% 299.82/300.45  183217[10:Rew:181085.0,183161.1] || member(u,universal_class) -> equal(range__dfg(v,successor(u),w),range__dfg(v,universal_class,w))**.
% 299.82/300.45  183218[10:Rew:181087.0,183163.1] || member(u,universal_class) -> equal(domain__dfg(v,w,successor(u)),domain__dfg(v,w,universal_class))**.
% 299.82/300.45  183371[0:SpR:139600.0,31.0] ||  -> equal(restrict(complement(complement(cross_product(u,v))),u,v),complement(complement(cross_product(u,v))))**.
% 299.82/300.45  183403[0:SpL:139600.0,9149.1] || member(u,universal_class) subclass(universal_class,complement(complement(v)))* -> member(power_class(u),v)*.
% 299.82/300.45  183641[10:MRR:183640.2,160227.0] || member(u,union(singleton(successor_relation),successor(successor_relation)))* member(u,complement(successor(successor_relation))) -> .
% 299.82/300.45  183728[10:SpL:183391.0,9149.1] || member(u,universal_class) subclass(universal_class,symmetrization_of(successor_relation)) -> member(power_class(u),inverse(successor_relation))*.
% 299.82/300.45  183741[10:MRR:183740.2,160227.0] || member(u,union(inverse(successor_relation),symmetrization_of(successor_relation)))* member(u,complement(symmetrization_of(successor_relation))) -> .
% 299.82/300.45  183809[10:Res:160466.1,183622.0] ||  -> equal(intersection(successor(successor_relation),u),successor_relation) member(regular(intersection(successor(successor_relation),u)),singleton(successor_relation))*.
% 299.82/300.45  183816[10:Res:1481.2,183622.0] || subclass(u,successor(successor_relation)) -> subclass(u,v) member(not_subclass_element(u,v),singleton(successor_relation))*.
% 299.82/300.45  183818[10:Res:160465.1,183622.0] ||  -> equal(intersection(u,successor(successor_relation)),successor_relation) member(regular(intersection(u,successor(successor_relation))),singleton(successor_relation))*.
% 299.82/300.45  183842[10:Res:160466.1,183723.0] ||  -> equal(intersection(symmetrization_of(successor_relation),u),successor_relation) member(regular(intersection(symmetrization_of(successor_relation),u)),inverse(successor_relation))*.
% 299.82/300.45  183849[10:Res:1481.2,183723.0] || subclass(u,symmetrization_of(successor_relation)) -> subclass(u,v) member(not_subclass_element(u,v),inverse(successor_relation))*.
% 299.82/300.45  183851[10:Res:160465.1,183723.0] ||  -> equal(intersection(u,symmetrization_of(successor_relation)),successor_relation) member(regular(intersection(u,symmetrization_of(successor_relation))),inverse(successor_relation))*.
% 299.82/300.45  183853[10:Res:1479.2,183723.0] || member(u,universal_class) subclass(universal_class,symmetrization_of(successor_relation)) -> member(sum_class(u),inverse(successor_relation))*.
% 299.82/300.45  183915[11:Res:183764.1,9332.1] || subclass(universal_class,intersection(u,v)) member(regular(symmetrization_of(successor_relation)),symmetric_difference(u,v))* -> .
% 299.82/300.45  183919[11:Res:183764.1,594.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(symmetrization_of(successor_relation)),cross_product(v,w))*.
% 299.82/300.45  183941[11:Res:183764.1,307.0] || subclass(universal_class,image(element_relation,complement(u)))* member(regular(symmetrization_of(successor_relation)),power_class(u)) -> .
% 299.82/300.45  183942[11:Res:183764.1,160481.0] || subclass(universal_class,regular(u)) member(regular(symmetrization_of(successor_relation)),u)* -> equal(u,successor_relation).
% 299.82/300.45  184378[10:Res:160511.2,75.1] single_valued_class(inverse(u)) function(u) || equal(inverse(u),successor_relation)** -> one_to_one(u).
% 299.82/300.45  184934[10:SpR:184676.1,149580.1] || subclass(symmetrization_of(u),successor_relation)* connected(u,v)* -> subclass(cross_product(v,v),successor_relation)*.
% 299.82/300.45  184940[10:SpR:28.0,184676.1] || subclass(intersection(complement(u),complement(v)),successor_relation)* -> equal(complement(union(u,v)),successor_relation).
% 299.82/300.45  184973[10:SpL:184676.1,149579.0] || subclass(symmetrization_of(u),successor_relation)* subclass(cross_product(v,v),successor_relation)* -> connected(u,v)*.
% 299.82/300.45  185053[10:SpR:208.0,184981.1] || subclass(image(element_relation,power_class(u)),successor_relation) -> subclass(universal_class,power_class(image(element_relation,complement(u))))*.
% 299.82/300.45  185486[10:SpR:185302.1,208.0] || equal(image(element_relation,power_class(u)),successor_relation) -> equal(power_class(image(element_relation,complement(u))),universal_class)**.
% 299.82/300.45  185661[10:Rew:160221.0,185559.1] || equal(symmetrization_of(u),successor_relation) subclass(cross_product(v,v),successor_relation)* -> connected(u,v)*.
% 299.82/300.45  185670[10:Rew:142542.0,185402.1] || equal(successor_relation,u) -> equal(intersection(union(v,u),universal_class),symmetric_difference(complement(v),universal_class))**.
% 299.82/300.45  185769[10:SpL:208.0,185335.0] || equal(image(element_relation,power_class(image(element_relation,complement(u)))),power_class(image(element_relation,power_class(u))))** -> .
% 299.82/300.45  185950[10:Res:185646.1,9322.0] || equal(complement(symmetric_difference(complement(u),complement(v))),successor_relation)** -> member(successor_relation,union(u,v)).
% 299.82/300.45  186024[10:Res:185647.1,9322.0] || equal(complement(symmetric_difference(complement(u),complement(v))),successor_relation)** -> member(omega,union(u,v)).
% 299.82/300.45  186060[10:SpL:208.0,185795.0] || equal(power_class(image(element_relation,complement(u))),successor_relation)** -> equal(image(element_relation,power_class(u)),universal_class).
% 299.82/300.45  186121[10:Res:25.2,185639.1] || member(u,v)* member(u,w)* equal(intersection(w,v),successor_relation)** -> .
% 299.82/300.45  186144[10:Res:18.2,185639.1] || member(u,v)* member(w,x)* equal(cross_product(x,v),successor_relation)** -> .
% 299.82/300.45  186347[10:Rew:160223.0,186326.1] || subclass(image(element_relation,complement(u)),successor_relation)* -> equal(complement(intersection(power_class(u),universal_class)),successor_relation).
% 299.82/300.45  187471[10:SpR:113504.0,163042.1] || asymmetric(universal_class,singleton(u)) -> equal(domain__dfg(inverse(universal_class),singleton(u),u),single_valued3(successor_relation))**.
% 299.82/300.45  187474[10:Rew:181056.0,187467.0] || asymmetric(u,successor_relation) -> equal(domain__dfg(intersection(u,inverse(u)),successor_relation,universal_class),single_valued3(successor_relation))**.
% 299.82/300.45  163376[10:Rew:160202.0,163013.2] || subclass(unordered_pair(u,v),successor_relation)* member(u,universal_class) well_ordering(w,successor_relation)* -> .
% 299.82/300.45  107579[0:Res:11.1,6045.0] || member(u,universal_class) subclass(unordered_pair(u,v),w)* well_ordering(universal_class,w) -> .
% 299.82/300.45  107578[0:Res:12.1,6045.0] || member(u,universal_class) subclass(unordered_pair(v,u),w)* well_ordering(universal_class,w) -> .
% 299.82/300.45  163375[10:Rew:160202.0,163012.2] || subclass(unordered_pair(u,v),successor_relation)* member(v,universal_class) well_ordering(w,successor_relation)* -> .
% 299.82/300.45  185852[10:MRR:185783.2,3567.0] || equal(complement(u),successor_relation) well_ordering(v,u)* -> member(least(v,universal_class),universal_class)*.
% 299.82/300.45  108286[2:Res:31069.2,2151.0] inductive(singleton(u)) || well_ordering(v,universal_class) -> equal(least(v,singleton(u)),u)**.
% 299.82/300.45  187782[10:Res:187500.1,9322.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v)))* -> member(power_class(successor_relation),union(u,v)).
% 299.82/300.45  188188[10:Res:67.2,186157.0] function(u) || member(v,universal_class) equal(singleton(image(u,v)),successor_relation)** -> .
% 299.82/300.45  188206[10:MRR:188168.1,6.0] || member(u,universal_class) equal(singleton(apply(choice,u)),successor_relation)** -> equal(u,successor_relation).
% 299.82/300.45  188854[10:MRR:188831.0,191.0] || subclass(intersection(complement(u),complement(v)),successor_relation)* -> member(singleton(w),union(u,v))*.
% 299.82/300.45  190617[15:SpR:189514.1,124.0] ||  -> equal(integer_of(restrict(u,v,singleton(w))),successor_relation)** equal(segment(u,v,w),successor_relation).
% 299.82/300.45  190700[15:SpR:189515.1,124.0] ||  -> equal(singleton(restrict(u,v,singleton(w))),successor_relation)** equal(segment(u,v,w),successor_relation).
% 299.82/300.45  191102[20:Res:191074.1,513.0] || equal(intersection(complement(u),complement(v)),omega)** member(successor_relation,union(u,v)) -> .
% 299.82/300.45  191630[15:Res:67.2,189419.0] function(u) || member(v,universal_class) equal(successor(image(u,v)),successor_relation)** -> .
% 299.82/300.45  191657[15:MRR:191609.1,6.0] || member(u,universal_class) equal(successor(apply(choice,u)),successor_relation)** -> equal(u,successor_relation).
% 299.82/300.45  192220[15:Rew:181086.0,192152.1] ||  -> equal(range_of(u),successor_relation) equal(segment(v,w,inverse(u)),segment(v,w,universal_class))**.
% 299.82/300.45  192225[15:Rew:181085.0,192148.1] ||  -> equal(range_of(u),successor_relation) equal(range__dfg(v,inverse(u),w),range__dfg(v,universal_class,w))**.
% 299.82/300.45  192226[15:Rew:181087.0,192153.1] ||  -> equal(range_of(u),successor_relation) equal(domain__dfg(v,w,inverse(u)),domain__dfg(v,w,universal_class))**.
% 299.82/300.45  192292[20:Res:1951.1,191095.1] || member(successor_relation,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),omega)** -> .
% 299.82/300.45  192388[20:SpL:208.0,192322.1] inductive(image(element_relation,power_class(u))) || equal(power_class(image(element_relation,complement(u))),omega)** -> .
% 299.82/300.45  192466[20:SpL:28.0,191129.1] || equal(intersection(complement(u),complement(v)),omega)** equal(union(u,v),universal_class) -> .
% 299.82/300.45  192876[20:SpL:28.0,192315.1] || equal(intersection(complement(u),complement(v)),omega)** equal(union(u,v),omega) -> .
% 299.82/300.45  192888[20:SpL:28.0,192321.1] || equal(intersection(complement(u),complement(v)),universal_class)** equal(union(u,v),omega) -> .
% 299.82/300.45  192913[20:SpL:28.0,192323.0] || equal(complement(union(u,v)),omega) -> member(successor_relation,intersection(complement(u),complement(v)))*.
% 299.82/300.45  192936[10:SpL:28.0,188851.0] || subclass(union(u,v),successor_relation) -> member(singleton(w),intersection(complement(u),complement(v)))*.
% 299.82/300.45  193404[10:Res:192947.1,594.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(singleton(x),cross_product(v,w))*.
% 299.82/300.45  193424[10:Res:192947.1,160481.0] || equal(complement(regular(u)),successor_relation) member(singleton(v),u)* -> equal(u,successor_relation).
% 299.82/300.45  193542[2:Res:141787.0,6045.0] || subclass(inverse(singleton(u)),v)* well_ordering(universal_class,v) -> asymmetric(singleton(u),w)*.
% 299.82/300.45  193589[10:SpR:28.0,161321.0] ||  -> equal(intersection(restrict(intersection(complement(u),complement(v)),w,x),union(u,v)),successor_relation)**.
% 299.82/300.45  193652[10:MRR:193651.2,160215.0] || equal(symmetrization_of(u),successor_relation) connected(u,v)* -> equal(cross_product(v,v),successor_relation)**.
% 299.82/300.45  193687[10:SpR:28.0,161320.0] ||  -> equal(intersection(union(u,v),restrict(intersection(complement(u),complement(v)),w,x)),successor_relation)**.
% 299.82/300.45  193934[10:SpL:161592.1,185804.0] || equal(complement(complement(regular(cross_product(u,v)))),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  193957[10:SpL:161592.1,188713.0] || equal(unordered_pair(regular(cross_product(u,v)),w),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  193970[10:SpL:161592.1,188646.0] || equal(unordered_pair(u,regular(cross_product(v,w))),successor_relation)** -> equal(cross_product(v,w),successor_relation).
% 299.82/300.45  194079[10:Res:1478.2,193819.0] || member(u,universal_class) subclass(universal_class,cantor(complement(cross_product(singleton(power_class(u)),universal_class))))* -> .
% 299.82/300.45  194080[10:Res:1481.2,193819.0] || subclass(u,cantor(complement(cross_product(singleton(not_subclass_element(u,v)),universal_class))))* -> subclass(u,v).
% 299.82/300.45  194082[10:Res:1479.2,193819.0] || member(u,universal_class) subclass(universal_class,cantor(complement(cross_product(singleton(sum_class(u)),universal_class))))* -> .
% 299.82/300.45  194493[0:SpL:28.0,183398.0] || member(u,complement(union(v,w))) -> member(u,intersection(complement(v),complement(w)))*.
% 299.82/300.45  194527[0:Res:1479.2,183398.0] || member(u,universal_class) subclass(universal_class,complement(complement(v)))* -> member(sum_class(u),v)*.
% 299.82/300.45  195366[0:SpR:194805.1,30.0] || subclass(cross_product(u,v),w)* -> equal(restrict(w,u,v),cross_product(u,v)).
% 299.82/300.45  195367[0:SpR:194805.1,161.0] || subclass(u,v) -> equal(intersection(complement(u),union(v,u)),symmetric_difference(v,u))**.
% 299.82/300.45  195384[2:SpR:194805.1,144537.1] || subclass(inverse(u),u)* asymmetric(u,v) -> section(inverse(u),v,v)*.
% 299.82/300.45  195406[10:SpR:194805.1,161320.0] || subclass(restrict(u,v,w),complement(u))* -> equal(restrict(u,v,w),successor_relation).
% 299.82/300.45  195423[0:SpR:194805.1,1951.1] || subclass(u,v) member(w,symmetric_difference(v,u))* -> member(w,complement(u)).
% 299.82/300.45  195474[10:SpR:194805.1,181641.0] || subclass(symmetric_difference(universal_class,singleton(successor_relation)),successor(successor_relation))* -> equal(symmetric_difference(universal_class,singleton(successor_relation)),successor_relation).
% 299.82/300.45  195475[10:SpR:194805.1,181642.0] || subclass(symmetric_difference(universal_class,inverse(successor_relation)),symmetrization_of(successor_relation))* -> equal(symmetric_difference(universal_class,inverse(successor_relation)),successor_relation).
% 299.82/300.45  195509[0:SpL:194805.1,9332.1] || subclass(u,v) member(w,symmetric_difference(v,u))* member(w,u) -> .
% 299.82/300.45  195577[0:Rew:194805.1,195480.1] || subclass(ordinal_numbers,y__dfg) subclass(u,ordinal_numbers) member(least(element_relation,ordinal_numbers),u)* -> .
% 299.82/300.45  195775[6:Res:195710.1,9.0] || equal(inverse(u),universal_class) subclass(inverse(u),v)* -> equal(inverse(u),v).
% 299.82/300.45  195833[6:Res:195720.1,9.0] || equal(sum_class(u),universal_class) subclass(sum_class(u),v)* -> equal(sum_class(u),v).
% 299.82/300.45  195950[0:SpR:195152.0,1951.1] || member(u,symmetric_difference(v,intersection(v,w)))* -> member(u,complement(intersection(v,w))).
% 299.82/300.45  196040[0:SpL:195152.0,9332.1] || member(u,symmetric_difference(v,intersection(v,w)))* member(u,intersection(v,w)) -> .
% 299.82/300.45  196093[0:SpR:195339.0,1951.1] || member(u,symmetric_difference(v,intersection(w,v)))* -> member(u,complement(intersection(w,v))).
% 299.82/300.45  196185[0:SpL:195339.0,9332.1] || member(u,symmetric_difference(v,intersection(w,v)))* member(u,intersection(w,v)) -> .
% 299.82/300.45  196507[10:SpR:161137.0,9898.0] ||  -> subclass(symmetric_difference(power_class(complement(inverse(successor_relation))),complement(u)),union(image(element_relation,symmetrization_of(successor_relation)),u))*.
% 299.82/300.45  196512[10:SpR:161137.0,163005.0] ||  -> equal(intersection(symmetric_difference(universal_class,image(element_relation,symmetrization_of(successor_relation))),complement(power_class(complement(inverse(successor_relation))))),successor_relation)**.
% 299.82/300.45  196513[10:SpR:161137.0,163000.0] ||  -> equal(intersection(complement(power_class(complement(inverse(successor_relation)))),symmetric_difference(universal_class,image(element_relation,symmetrization_of(successor_relation)))),successor_relation)**.
% 299.82/300.45  196524[10:SpR:161137.0,160470.0] ||  -> equal(intersection(power_class(image(element_relation,symmetrization_of(successor_relation))),image(element_relation,power_class(complement(inverse(successor_relation))))),successor_relation)**.
% 299.82/300.45  196525[10:SpR:161137.0,160469.0] ||  -> equal(intersection(image(element_relation,power_class(complement(inverse(successor_relation)))),power_class(image(element_relation,symmetrization_of(successor_relation)))),successor_relation)**.
% 299.82/300.45  196526[10:SpR:161137.0,142477.0] ||  -> equal(symmetric_difference(power_class(image(element_relation,symmetrization_of(successor_relation))),image(element_relation,power_class(complement(inverse(successor_relation))))),universal_class)**.
% 299.82/300.45  196527[10:SpR:161137.0,142475.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(complement(inverse(successor_relation)))),power_class(image(element_relation,symmetrization_of(successor_relation)))),universal_class)**.
% 299.82/300.45  196536[10:SpR:161137.0,161321.0] ||  -> equal(intersection(restrict(image(element_relation,symmetrization_of(successor_relation)),u,v),power_class(complement(inverse(successor_relation)))),successor_relation)**.
% 299.82/300.45  196537[10:SpR:161137.0,161320.0] ||  -> equal(intersection(power_class(complement(inverse(successor_relation))),restrict(image(element_relation,symmetrization_of(successor_relation)),u,v)),successor_relation)**.
% 299.82/300.45  196541[10:SpR:161137.0,9898.0] ||  -> subclass(symmetric_difference(complement(u),power_class(complement(inverse(successor_relation)))),union(u,image(element_relation,symmetrization_of(successor_relation))))*.
% 299.82/300.45  196553[10:SpL:161137.0,30433.1] || subclass(universal_class,image(element_relation,symmetrization_of(successor_relation)))* subclass(universal_class,power_class(complement(inverse(successor_relation)))) -> .
% 299.82/300.45  196554[20:SpL:161137.0,191129.1] || equal(image(element_relation,symmetrization_of(successor_relation)),omega)** equal(power_class(complement(inverse(successor_relation))),universal_class) -> .
% 299.82/300.45  196556[10:SpL:161137.0,3358.1] || equal(image(element_relation,symmetrization_of(successor_relation)),universal_class)** equal(power_class(complement(inverse(successor_relation))),universal_class) -> .
% 299.82/300.45  196557[10:SpL:161137.0,160544.0] || equal(complement(power_class(complement(inverse(successor_relation)))),universal_class) -> member(successor_relation,image(element_relation,symmetrization_of(successor_relation)))*.
% 299.82/300.45  196558[10:SpL:161137.0,3565.0] || equal(complement(power_class(complement(inverse(successor_relation)))),universal_class) -> member(omega,image(element_relation,symmetrization_of(successor_relation)))*.
% 299.82/300.45  196559[20:SpL:161137.0,192323.0] || equal(complement(power_class(complement(inverse(successor_relation)))),omega) -> member(successor_relation,image(element_relation,symmetrization_of(successor_relation)))*.
% 299.82/300.45  196570[20:SpL:161137.0,192321.1] || equal(image(element_relation,symmetrization_of(successor_relation)),universal_class)** equal(power_class(complement(inverse(successor_relation))),omega) -> .
% 299.82/300.45  196571[20:SpL:161137.0,192315.1] || equal(image(element_relation,symmetrization_of(successor_relation)),omega)** equal(power_class(complement(inverse(successor_relation))),omega) -> .
% 299.82/300.45  196573[10:SpL:161137.0,188851.0] || subclass(power_class(complement(inverse(successor_relation))),successor_relation) -> member(singleton(u),image(element_relation,symmetrization_of(successor_relation)))*.
% 299.82/300.45  196581[10:SpL:161137.0,183398.0] || member(u,complement(power_class(complement(inverse(successor_relation)))))* -> member(u,image(element_relation,symmetrization_of(successor_relation))).
% 299.82/300.45  196631[10:SpR:185605.1,160971.0] || equal(successor_relation,u) -> subclass(complement(power_class(image(element_relation,universal_class))),image(element_relation,power_class(u)))*.
% 299.82/300.45  196667[10:SpL:2330.1,185068.0] || subclass(singleton(not_subclass_element(cross_product(u,v),w)),successor_relation)* -> subclass(cross_product(u,v),w).
% 299.82/300.45  196713[10:SpR:162889.0,9898.0] ||  -> subclass(symmetric_difference(power_class(complement(singleton(successor_relation))),complement(u)),union(image(element_relation,successor(successor_relation)),u))*.
% 299.82/300.45  196718[10:SpR:162889.0,163005.0] ||  -> equal(intersection(symmetric_difference(universal_class,image(element_relation,successor(successor_relation))),complement(power_class(complement(singleton(successor_relation))))),successor_relation)**.
% 299.82/300.45  196719[10:SpR:162889.0,163000.0] ||  -> equal(intersection(complement(power_class(complement(singleton(successor_relation)))),symmetric_difference(universal_class,image(element_relation,successor(successor_relation)))),successor_relation)**.
% 299.82/300.45  196730[10:SpR:162889.0,160470.0] ||  -> equal(intersection(power_class(image(element_relation,successor(successor_relation))),image(element_relation,power_class(complement(singleton(successor_relation))))),successor_relation)**.
% 299.82/300.45  196731[10:SpR:162889.0,160469.0] ||  -> equal(intersection(image(element_relation,power_class(complement(singleton(successor_relation)))),power_class(image(element_relation,successor(successor_relation)))),successor_relation)**.
% 299.82/300.45  196732[10:SpR:162889.0,142477.0] ||  -> equal(symmetric_difference(power_class(image(element_relation,successor(successor_relation))),image(element_relation,power_class(complement(singleton(successor_relation))))),universal_class)**.
% 299.82/300.45  196733[10:SpR:162889.0,142475.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(complement(singleton(successor_relation)))),power_class(image(element_relation,successor(successor_relation)))),universal_class)**.
% 299.82/300.45  196742[10:SpR:162889.0,161321.0] ||  -> equal(intersection(restrict(image(element_relation,successor(successor_relation)),u,v),power_class(complement(singleton(successor_relation)))),successor_relation)**.
% 299.82/300.45  196743[10:SpR:162889.0,161320.0] ||  -> equal(intersection(power_class(complement(singleton(successor_relation))),restrict(image(element_relation,successor(successor_relation)),u,v)),successor_relation)**.
% 299.82/300.45  196747[10:SpR:162889.0,9898.0] ||  -> subclass(symmetric_difference(complement(u),power_class(complement(singleton(successor_relation)))),union(u,image(element_relation,successor(successor_relation))))*.
% 299.82/300.45  196759[10:SpL:162889.0,30433.1] || subclass(universal_class,image(element_relation,successor(successor_relation)))* subclass(universal_class,power_class(complement(singleton(successor_relation)))) -> .
% 299.82/300.45  196760[20:SpL:162889.0,191129.1] || equal(image(element_relation,successor(successor_relation)),omega)** equal(power_class(complement(singleton(successor_relation))),universal_class) -> .
% 299.82/300.45  196762[10:SpL:162889.0,3358.1] || equal(image(element_relation,successor(successor_relation)),universal_class)** equal(power_class(complement(singleton(successor_relation))),universal_class) -> .
% 299.82/300.45  196763[10:SpL:162889.0,160544.0] || equal(complement(power_class(complement(singleton(successor_relation)))),universal_class) -> member(successor_relation,image(element_relation,successor(successor_relation)))*.
% 299.82/300.45  196764[10:SpL:162889.0,3565.0] || equal(complement(power_class(complement(singleton(successor_relation)))),universal_class) -> member(omega,image(element_relation,successor(successor_relation)))*.
% 299.82/300.45  196765[20:SpL:162889.0,192323.0] || equal(complement(power_class(complement(singleton(successor_relation)))),omega) -> member(successor_relation,image(element_relation,successor(successor_relation)))*.
% 299.82/300.45  196776[20:SpL:162889.0,192321.1] || equal(image(element_relation,successor(successor_relation)),universal_class)** equal(power_class(complement(singleton(successor_relation))),omega) -> .
% 299.82/300.45  196777[20:SpL:162889.0,192315.1] || equal(image(element_relation,successor(successor_relation)),omega)** equal(power_class(complement(singleton(successor_relation))),omega) -> .
% 299.82/300.45  196779[10:SpL:162889.0,188851.0] || subclass(power_class(complement(singleton(successor_relation))),successor_relation) -> member(singleton(u),image(element_relation,successor(successor_relation)))*.
% 299.82/300.45  196787[10:SpL:162889.0,183398.0] || member(u,complement(power_class(complement(singleton(successor_relation)))))* -> member(u,image(element_relation,successor(successor_relation))).
% 299.82/300.45  197014[10:SpL:185605.1,185768.0] || equal(successor_relation,u) equal(image(element_relation,power_class(u)),power_class(image(element_relation,universal_class)))** -> .
% 299.82/300.45  197022[10:Res:186026.1,3.0] || equal(complement(symmetrization_of(successor_relation)),successor_relation) subclass(inverse(successor_relation),u)* -> member(omega,u).
% 299.82/300.45  197285[10:SoR:197283.0,6317.2] single_valued_class(element_relation) || equal(power_class(universal_class),successor_relation) equal(cross_product(universal_class,universal_class),element_relation)** -> .
% 299.82/300.45  197570[10:SpR:185605.1,187784.1] || equal(successor_relation,u) subclass(universal_class,symmetrization_of(successor_relation)) -> member(power_class(u),inverse(successor_relation))*.
% 299.82/300.45  197576[10:Res:187784.1,3.0] || subclass(universal_class,symmetrization_of(successor_relation)) subclass(inverse(successor_relation),u)* -> member(power_class(successor_relation),u).
% 299.82/300.45  197667[10:SpR:185605.1,187790.1] || equal(successor_relation,u) subclass(universal_class,omega) -> equal(integer_of(power_class(u)),power_class(u))**.
% 299.82/300.45  197839[10:SpL:185605.1,194078.0] || equal(successor_relation,u) subclass(universal_class,cantor(complement(cross_product(singleton(power_class(u)),universal_class))))* -> .
% 299.82/300.45  198017[10:SpL:185605.1,197375.1] || equal(successor_relation,u) equal(power_class(successor_relation),successor_relation) subclass(universal_class,power_class(u))* -> .
% 299.82/300.45  198053[10:SpL:185605.1,197781.0] || equal(successor_relation,u) equal(cantor(complement(cross_product(singleton(power_class(u)),universal_class))),universal_class)** -> .
% 299.82/300.45  199362[10:SpR:185605.1,161852.0] || equal(successor_relation,u) -> equal(intersection(intersection(v,image(element_relation,universal_class)),power_class(u)),successor_relation)**.
% 299.82/300.45  199439[10:SpR:185605.1,161847.0] || equal(successor_relation,u) -> equal(intersection(intersection(image(element_relation,universal_class),v),power_class(u)),successor_relation)**.
% 299.82/300.45  199534[10:SpR:185605.1,161845.0] || equal(successor_relation,u) -> equal(intersection(power_class(u),intersection(v,image(element_relation,universal_class))),successor_relation)**.
% 299.82/300.45  199614[10:SpR:185605.1,161843.0] || equal(successor_relation,u) -> equal(intersection(power_class(u),intersection(image(element_relation,universal_class),v)),successor_relation)**.
% 299.82/300.45  199701[10:Res:183720.1,3.0] || subclass(universal_class,symmetrization_of(successor_relation)) subclass(inverse(successor_relation),u)* -> member(singleton(v),u)*.
% 299.82/300.45  199966[14:SpL:44.0,184789.0] || member(sum_class(image(u,v)),universal_class) member(restrict(u,v,universal_class),universal_class)* -> .
% 299.82/300.45  199973[15:SpL:44.0,189423.1] || member(restrict(u,v,universal_class),universal_class)* equal(sum_class(image(u,v)),successor_relation) -> .
% 299.82/300.45  199998[6:Res:199848.1,9322.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v)))* -> member(regular(rest_relation),union(u,v)).
% 299.82/300.45  200186[14:Rew:181086.0,200103.1] || member(u,universal_class) -> equal(segment(v,w,range_of(u)),segment(v,w,universal_class))**.
% 299.82/300.45  200192[14:Rew:181085.0,200098.1] || member(u,universal_class) -> equal(range__dfg(v,range_of(u),w),range__dfg(v,universal_class,w))**.
% 299.82/300.45  200193[14:Rew:181087.0,200104.1] || member(u,universal_class) -> equal(domain__dfg(v,w,range_of(u)),domain__dfg(v,w,universal_class))**.
% 299.82/300.45  200566[10:Res:184599.1,163137.0] || well_ordering(u,kind_1_ordinals) equal(rest_of(least(u,ordinal_numbers)),successor(least(u,ordinal_numbers)))** -> .
% 299.82/300.45  200567[10:Res:110623.1,163137.0] || well_ordering(u,universal_class) equal(rest_of(least(u,universal_class)),successor(least(u,universal_class)))** -> .
% 299.82/300.45  200568[10:Res:110388.1,163137.0] || well_ordering(u,rest_relation) equal(rest_of(least(u,rest_relation)),successor(least(u,rest_relation)))** -> .
% 299.82/300.45  200569[10:Res:110382.1,163137.0] || well_ordering(u,universal_class) equal(rest_of(least(u,rest_relation)),successor(least(u,rest_relation)))** -> .
% 299.82/300.45  200570[17:Res:188737.1,163137.0] || well_ordering(u,omega) equal(rest_of(least(u,omega)),successor(least(u,omega)))** -> .
% 299.82/300.45  200571[17:Res:188729.1,163137.0] || well_ordering(u,universal_class) equal(rest_of(least(u,omega)),successor(least(u,omega)))** -> .
% 299.82/300.45  200652[10:Res:161493.2,309.0] inductive(u) ||  -> equal(integer_of(not_subclass_element(complement(u),v)),successor_relation)** subclass(complement(u),v).
% 299.82/300.45  200659[10:Res:161493.2,3.0] inductive(u) || subclass(u,v)* -> equal(integer_of(w),successor_relation) member(w,v)*.
% 299.82/300.45  200663[10:Res:161493.2,148657.1] inductive(complement(compose(element_relation,universal_class))) || member(u,element_relation)* -> equal(integer_of(u),successor_relation).
% 299.82/300.45  200672[10:Res:161493.2,1952.0] inductive(symmetric_difference(u,v)) ||  -> equal(integer_of(w),successor_relation) member(w,union(u,v))*.
% 299.82/300.45  200673[10:Res:161493.2,10191.0] inductive(symmetric_difference(u,inverse(u))) ||  -> equal(integer_of(v),successor_relation) member(v,symmetrization_of(u))*.
% 299.82/300.45  200674[10:Res:161493.2,10254.0] inductive(symmetric_difference(u,singleton(u))) ||  -> equal(integer_of(v),successor_relation) member(v,successor(u))*.
% 299.82/300.45  200998[10:Res:200934.1,9.0] || equal(cantor(u),successor_relation) subclass(v,cantor(u))* -> equal(v,cantor(u)).
% 299.82/300.45  201038[10:Res:200000.1,3.0] || subclass(universal_class,symmetrization_of(successor_relation)) subclass(inverse(successor_relation),u)* -> member(regular(rest_relation),u).
% 299.82/300.45  201067[0:Res:51387.0,183398.0] ||  -> subclass(u,complement(complement(complement(v)))) member(not_subclass_element(u,complement(complement(complement(v)))),v)*.
% 299.82/300.45  201152[6:Res:200239.1,3.0] || equal(cross_product(universal_class,universal_class),ordinal_numbers) subclass(kind_1_ordinals,u) -> member(regular(rest_relation),u)*.
% 299.82/300.45  201196[10:Res:161493.2,157982.0] inductive(ordinal_numbers) ||  -> equal(integer_of(cross_product(universal_class,universal_class)),successor_relation) member(least(element_relation,domain_relation),domain_relation)*.
% 299.82/300.45  201388[6:Res:201231.1,9322.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v)))* -> member(regular(domain_relation),union(u,v)).
% 299.82/300.45  201423[10:EmS:161261.0,161261.1,73.1,195883.1] one_to_one(sum_class(u)) || equal(sum_class(u),universal_class)** -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.45  201440[10:EmS:161261.0,161261.1,73.1,195817.1] one_to_one(inverse(u)) || equal(inverse(u),universal_class)** -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.45  201624[10:Res:161493.2,163294.0] inductive(symmetric_difference(singleton(successor_relation),range_of(successor_relation))) ||  -> equal(integer_of(u),successor_relation) member(u,kind_1_ordinals)*.
% 299.82/300.45  201653[10:Res:161493.2,155791.1] inductive(ordinal_numbers) || subclass(universal_class,complement(kind_1_ordinals)) -> equal(integer_of(unordered_pair(u,v)),successor_relation)**.
% 299.82/300.45  201670[10:Res:161493.2,155787.0] inductive(ordinal_numbers) ||  -> equal(integer_of(not_subclass_element(complement(kind_1_ordinals),u)),successor_relation)** subclass(complement(kind_1_ordinals),u).
% 299.82/300.45  201721[10:Res:161419.0,141576.1] || member(regular(complement(complement(complement(kind_1_ordinals)))),ordinal_numbers)* -> equal(complement(complement(complement(kind_1_ordinals))),successor_relation).
% 299.82/300.45  201809[10:Res:201390.1,3.0] || subclass(universal_class,symmetrization_of(successor_relation)) subclass(inverse(successor_relation),u)* -> member(regular(domain_relation),u).
% 299.82/300.45  201835[10:Res:161493.2,1012.0] inductive(element_relation) ||  -> equal(integer_of(singleton(singleton(singleton(u)))),successor_relation)** member(singleton(u),u)*.
% 299.82/300.45  201836[10:Rew:181044.1,201828.2] || member(u,universal_class) member(singleton(singleton(successor_relation)),element_relation)* -> member(successor_relation,successor(u))*.
% 299.82/300.45  201837[15:Rew:190721.0,201829.2] || member(singleton(singleton(successor_relation)),element_relation)* -> equal(range_of(u),successor_relation) member(successor_relation,inverse(u))*.
% 299.82/300.45  201838[14:Rew:200028.1,201830.2] || member(u,universal_class) member(singleton(singleton(successor_relation)),element_relation)* -> member(successor_relation,range_of(u))*.
% 299.82/300.45  201852[6:Res:201474.1,3.0] || equal(cross_product(universal_class,universal_class),ordinal_numbers) subclass(kind_1_ordinals,u) -> member(regular(domain_relation),u)*.
% 299.82/300.45  201914[10:Res:161492.2,160454.0] || equal(u,omega) -> equal(integer_of(regular(complement(u))),successor_relation)** equal(complement(u),successor_relation).
% 299.82/300.45  201934[10:Res:161492.2,595.0] || equal(restrict(u,v,w),omega)** -> equal(integer_of(x),successor_relation) member(x,u)*.
% 299.82/300.45  201969[10:Res:161492.2,147.0] || equal(rest_relation,omega) -> equal(integer_of(ordered_pair(u,v)),successor_relation)** equal(rest_of(u),v).
% 299.82/300.45  202006[10:Res:161492.2,195483.1] || equal(omega,ordinal_numbers) subclass(ordinal_numbers,y__dfg) -> equal(integer_of(least(element_relation,ordinal_numbers)),successor_relation)**.
% 299.82/300.45  202030[15:Res:161492.2,189548.0] || equal(domain_relation,omega) -> equal(integer_of(singleton(singleton(singleton(u)))),successor_relation)** equal(successor_relation,u).
% 299.82/300.45  202054[10:Res:161492.2,162953.0] || equal(omega,ordinal_numbers) -> equal(integer_of(regular(complement(kind_1_ordinals))),successor_relation)** equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.45  202395[10:Res:161493.2,3486.1] inductive(u) || subclass(universal_class,complement(u))* -> equal(integer_of(unordered_pair(v,w)),successor_relation)**.
% 299.82/300.45  202422[10:Res:163225.0,3.0] || subclass(symmetric_difference(universal_class,u),v)* -> member(successor_relation,union(u,successor_relation)) member(successor_relation,v).
% 299.82/300.45  202469[10:Res:163217.0,3.0] || subclass(image(element_relation,complement(u)),v)* -> member(successor_relation,power_class(u)) member(successor_relation,v).
% 299.82/300.45  202960[10:SpL:161194.0,3487.0] || subclass(universal_class,symmetric_difference(complement(u),universal_class)) -> member(unordered_pair(v,w),union(u,successor_relation))*.
% 299.82/300.45  203114[11:SpL:28.0,202882.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),symmetrization_of(successor_relation))** -> .
% 299.82/300.45  203123[11:SpL:161137.0,202882.1] inductive(image(element_relation,symmetrization_of(successor_relation))) || equal(power_class(complement(inverse(successor_relation))),symmetrization_of(successor_relation))** -> .
% 299.82/300.45  203124[11:SpL:162889.0,202882.1] inductive(image(element_relation,successor(successor_relation))) || equal(power_class(complement(singleton(successor_relation))),symmetrization_of(successor_relation))** -> .
% 299.82/300.45  203519[10:Rew:203192.0,161620.1] || member(u,universal_class) -> member(u,cantor(universal_class)) equal(cross_product(singleton(u),universal_class),successor_relation)**.
% 299.82/300.45  203664[6:Rew:203192.0,107786.0] || member(u,cantor(v))* subclass(rest_of(v),w)* well_ordering(universal_class,w) -> .
% 299.82/300.45  203929[10:Rew:203192.0,200706.2] inductive(rest_of(u)) ||  -> equal(integer_of(ordered_pair(v,w)),successor_relation)** member(v,cantor(u))*.
% 299.82/300.45  203978[10:Rew:203192.0,201982.2] || equal(domain_relation,omega) -> equal(integer_of(ordered_pair(u,v)),successor_relation)** equal(cantor(u),v).
% 299.82/300.45  204015[10:Rew:203192.0,181081.0] ||  -> equal(cantor(restrict(cross_product(u,successor_relation),v,w)),segment(cross_product(v,w),u,universal_class))**.
% 299.82/300.45  205556[10:Res:205036.1,9.0] || equal(range_of(u),successor_relation) subclass(v,range_of(u))* -> equal(v,range_of(u)).
% 299.82/300.45  205612[10:Res:205359.1,9.0] || equal(inverse(u),successor_relation) subclass(v,inverse(u))* -> equal(v,inverse(u)).
% 299.82/300.45  205659[10:Res:205375.1,9.0] || equal(sum_class(u),successor_relation) subclass(v,sum_class(u))* -> equal(v,sum_class(u)).
% 299.82/300.45  205853[10:SpR:205791.1,1951.1] || member(u,symmetric_difference(v,universal_class))* -> equal(singleton(v),successor_relation) member(u,complement(v)).
% 299.82/300.45  205879[10:SpR:205791.1,161194.0] ||  -> equal(singleton(union(u,successor_relation)),successor_relation) equal(symmetric_difference(complement(u),universal_class),union(u,successor_relation))**.
% 299.82/300.45  205898[10:SpL:205791.1,9332.1] || member(u,symmetric_difference(v,universal_class))* member(u,v) -> equal(singleton(v),successor_relation).
% 299.82/300.45  205921[10:MRR:205920.0,34067.1] || member(u,complement(v)) -> equal(singleton(v),successor_relation) member(u,symmetric_difference(v,universal_class))*.
% 299.82/300.45  205924[10:Rew:142543.0,205837.1,142542.0,205837.1,142542.0,205837.1] ||  -> equal(singleton(u),successor_relation) equal(symmetric_difference(universal_class,symmetric_difference(u,universal_class)),symmetric_difference(complement(u),universal_class))**.
% 299.82/300.45  206026[10:SpR:185605.1,160970.1] || equal(successor_relation,u) -> member(v,image(element_relation,universal_class)) subclass(singleton(v),power_class(u))*.
% 299.82/300.45  206195[10:SpL:28.0,206082.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),successor(successor_relation))** -> .
% 299.82/300.45  206206[10:SpL:161137.0,206082.1] inductive(image(element_relation,symmetrization_of(successor_relation))) || equal(power_class(complement(inverse(successor_relation))),successor(successor_relation))** -> .
% 299.82/300.45  206207[10:SpL:162889.0,206082.1] inductive(image(element_relation,successor(successor_relation))) || equal(power_class(complement(singleton(successor_relation))),successor(successor_relation))** -> .
% 299.82/300.45  206229[10:Rew:163222.1,206228.1] || member(successor_relation,u) member(successor_relation,v) -> subclass(successor(successor_relation),intersection(v,u))*.
% 299.82/300.45  206966[10:Res:206947.1,513.0] || equal(intersection(complement(u),complement(v)),kind_1_ordinals)** member(successor_relation,union(u,v)) -> .
% 299.82/300.45  207535[10:SpR:208.0,206226.1] ||  -> member(successor_relation,image(element_relation,power_class(u))) subclass(successor(successor_relation),power_class(image(element_relation,complement(u))))*.
% 299.82/300.45  207544[10:Res:206226.1,9.0] || subclass(complement(u),successor(successor_relation))* -> member(successor_relation,u) equal(complement(u),successor(successor_relation)).
% 299.82/300.45  207861[10:Res:206688.0,6045.0] || subclass(complement(intersection(complement(singleton(successor_relation)),power_class(u))),v)* well_ordering(universal_class,v) -> .
% 299.82/300.45  208141[10:Res:207196.0,6045.0] || subclass(complement(intersection(power_class(u),complement(singleton(successor_relation)))),v)* well_ordering(universal_class,v) -> .
% 299.82/300.45  208222[10:Res:1951.1,206958.1] || member(successor_relation,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),kind_1_ordinals)** -> .
% 299.82/300.45  208346[10:SpL:208.0,208258.1] inductive(image(element_relation,power_class(u))) || equal(power_class(image(element_relation,complement(u))),kind_1_ordinals)** -> .
% 299.82/300.45  208351[10:SpL:28.0,206962.0] || equal(complement(union(u,v)),kind_1_ordinals) -> member(successor_relation,intersection(complement(u),complement(v)))*.
% 299.82/300.45  208362[10:SpL:161137.0,206962.0] || equal(complement(power_class(complement(inverse(successor_relation)))),kind_1_ordinals) -> member(successor_relation,image(element_relation,symmetrization_of(successor_relation)))*.
% 299.82/300.45  208363[10:SpL:162889.0,206962.0] || equal(complement(power_class(complement(singleton(successor_relation)))),kind_1_ordinals) -> member(successor_relation,image(element_relation,successor(successor_relation)))*.
% 299.82/300.45  208390[20:SpL:28.0,206996.1] || equal(intersection(complement(u),complement(v)),kind_1_ordinals)** equal(union(u,v),omega) -> .
% 299.82/300.45  208401[20:SpL:161137.0,206996.1] || equal(image(element_relation,symmetrization_of(successor_relation)),kind_1_ordinals)** equal(power_class(complement(inverse(successor_relation))),omega) -> .
% 299.82/300.45  208402[20:SpL:162889.0,206996.1] || equal(image(element_relation,successor(successor_relation)),kind_1_ordinals)** equal(power_class(complement(singleton(successor_relation))),omega) -> .
% 299.82/300.45  208404[10:SpL:28.0,206997.1] || equal(intersection(complement(u),complement(v)),kind_1_ordinals)** equal(union(u,v),universal_class) -> .
% 299.82/300.45  208415[10:SpL:161137.0,206997.1] || equal(image(element_relation,symmetrization_of(successor_relation)),kind_1_ordinals)** equal(power_class(complement(inverse(successor_relation))),universal_class) -> .
% 299.82/300.45  208416[10:SpL:162889.0,206997.1] || equal(image(element_relation,successor(successor_relation)),kind_1_ordinals)** equal(power_class(complement(singleton(successor_relation))),universal_class) -> .
% 299.82/300.45  208477[10:SpL:28.0,208250.1] || equal(intersection(complement(u),complement(v)),kind_1_ordinals)** equal(union(u,v),kind_1_ordinals) -> .
% 299.82/300.45  208488[10:SpL:161137.0,208250.1] || equal(image(element_relation,symmetrization_of(successor_relation)),kind_1_ordinals)** equal(power_class(complement(inverse(successor_relation))),kind_1_ordinals) -> .
% 299.82/300.45  208489[10:SpL:162889.0,208250.1] || equal(image(element_relation,successor(successor_relation)),kind_1_ordinals)** equal(power_class(complement(singleton(successor_relation))),kind_1_ordinals) -> .
% 299.82/300.45  208491[20:SpL:28.0,208251.1] || equal(intersection(complement(u),complement(v)),omega)** equal(union(u,v),kind_1_ordinals) -> .
% 299.82/300.45  208502[20:SpL:161137.0,208251.1] || equal(image(element_relation,symmetrization_of(successor_relation)),omega)** equal(power_class(complement(inverse(successor_relation))),kind_1_ordinals) -> .
% 299.82/300.45  208503[20:SpL:162889.0,208251.1] || equal(image(element_relation,successor(successor_relation)),omega)** equal(power_class(complement(singleton(successor_relation))),kind_1_ordinals) -> .
% 299.82/300.45  208505[10:SpL:28.0,208257.1] || equal(intersection(complement(u),complement(v)),universal_class)** equal(union(u,v),kind_1_ordinals) -> .
% 299.82/300.45  208516[10:SpL:161137.0,208257.1] || equal(image(element_relation,symmetrization_of(successor_relation)),universal_class)** equal(power_class(complement(inverse(successor_relation))),kind_1_ordinals) -> .
% 299.82/300.45  208517[10:SpL:162889.0,208257.1] || equal(image(element_relation,successor(successor_relation)),universal_class)** equal(power_class(complement(singleton(successor_relation))),kind_1_ordinals) -> .
% 299.82/300.45  199689[10:Res:183719.1,3.0] || equal(symmetrization_of(successor_relation),universal_class) subclass(inverse(successor_relation),u)* -> member(singleton(v),u)*.
% 299.82/300.45  209061[10:SpL:28.0,208945.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),singleton(successor_relation))** -> .
% 299.82/300.45  209072[10:SpL:161137.0,208945.1] inductive(image(element_relation,symmetrization_of(successor_relation))) || equal(power_class(complement(inverse(successor_relation))),singleton(successor_relation))** -> .
% 299.82/300.45  209073[10:SpL:162889.0,208945.1] inductive(image(element_relation,successor(successor_relation))) || equal(power_class(complement(singleton(successor_relation))),singleton(successor_relation))** -> .
% 299.82/300.45  209130[10:Res:161492.2,47888.0] || equal(rest_of(u),omega) subclass(universal_class,complement(element_relation))* -> equal(integer_of(u),successor_relation)**.
% 299.82/300.45  209465[12:Res:209377.1,9322.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v)))* -> member(regular(element_relation),union(u,v)).
% 299.82/300.45  209769[15:Res:184599.1,189420.0] || well_ordering(u,kind_1_ordinals) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,ordinal_numbers)),successor_relation)**.
% 299.82/300.45  209770[15:Res:110623.1,189420.0] || well_ordering(u,universal_class) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,universal_class)),successor_relation)**.
% 299.82/300.45  209771[15:Res:110388.1,189420.0] || well_ordering(u,rest_relation) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,rest_relation)),successor_relation)**.
% 299.82/300.45  209772[15:Res:110382.1,189420.0] || well_ordering(u,universal_class) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,rest_relation)),successor_relation)**.
% 299.82/300.45  209773[17:Res:188737.1,189420.0] || well_ordering(u,omega) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,omega)),successor_relation)**.
% 299.82/300.45  209774[17:Res:188729.1,189420.0] || well_ordering(u,universal_class) subclass(domain_relation,rest_relation) -> equal(rest_of(least(u,omega)),successor_relation)**.
% 299.82/300.45  209888[15:Res:184599.1,189421.0] || well_ordering(u,kind_1_ordinals) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,ordinal_numbers)),successor_relation)**.
% 299.82/300.45  209889[15:Res:110623.1,189421.0] || well_ordering(u,universal_class) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,universal_class)),successor_relation)**.
% 299.82/300.45  209890[15:Res:110388.1,189421.0] || well_ordering(u,rest_relation) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,rest_relation)),successor_relation)**.
% 299.82/300.45  209891[15:Res:110382.1,189421.0] || well_ordering(u,universal_class) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,rest_relation)),successor_relation)**.
% 299.82/300.45  209892[17:Res:188737.1,189421.0] || well_ordering(u,omega) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,omega)),successor_relation)**.
% 299.82/300.45  209893[17:Res:188729.1,189421.0] || well_ordering(u,universal_class) subclass(rest_relation,domain_relation) -> equal(rest_of(least(u,omega)),successor_relation)**.
% 299.82/300.45  210106[15:MRR:210075.1,187489.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(power_class(successor_relation),successor_relation),u)*.
% 299.82/300.45  210141[15:MRR:210112.1,199826.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(regular(rest_relation),successor_relation),u)*.
% 299.82/300.45  210176[15:MRR:210147.1,201216.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(regular(domain_relation),successor_relation),u)*.
% 299.82/300.45  210211[15:MRR:210182.1,209309.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(regular(element_relation),successor_relation),u)*.
% 299.82/300.45  210295[15:MRR:210262.1,191.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(singleton(v),successor_relation),u)*.
% 299.82/300.45  210313[12:Res:209468.1,3.0] || subclass(universal_class,symmetrization_of(successor_relation)) subclass(inverse(successor_relation),u)* -> member(regular(element_relation),u).
% 299.82/300.45  210333[12:Res:209505.1,3.0] || equal(cross_product(universal_class,universal_class),ordinal_numbers) subclass(kind_1_ordinals,u) -> member(regular(element_relation),u)*.
% 299.82/300.45  210349[15:Res:189563.1,26.1] || subclass(domain_relation,flip(complement(u))) member(ordered_pair(ordered_pair(v,w),successor_relation),u)* -> .
% 299.82/300.45  210351[15:Res:189563.1,141576.1] || subclass(domain_relation,flip(complement(kind_1_ordinals))) member(ordered_pair(ordered_pair(u,v),successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  210353[15:Res:189563.1,183398.0] || subclass(domain_relation,flip(complement(complement(u)))) -> member(ordered_pair(ordered_pair(v,w),successor_relation),u)*.
% 299.82/300.45  210355[15:Res:189563.1,23.0] || subclass(domain_relation,flip(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,x),successor_relation),u)*.
% 299.82/300.45  210356[15:Res:189563.1,24.0] || subclass(domain_relation,flip(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,x),successor_relation),v)*.
% 299.82/300.45  210368[15:Res:189563.1,183723.0] || subclass(domain_relation,flip(symmetrization_of(successor_relation))) -> member(ordered_pair(ordered_pair(u,v),successor_relation),inverse(successor_relation))*.
% 299.82/300.45  210369[15:Res:189563.1,193819.0] || subclass(domain_relation,flip(cantor(complement(cross_product(singleton(ordered_pair(ordered_pair(u,v),successor_relation)),universal_class)))))* -> .
% 299.82/300.45  210371[15:Res:189563.1,183622.0] || subclass(domain_relation,flip(successor(successor_relation))) -> member(ordered_pair(ordered_pair(u,v),successor_relation),singleton(successor_relation))*.
% 299.82/300.45  210382[15:Res:189563.1,144.0] || subclass(domain_relation,flip(rest_of(u))) -> equal(restrict(u,ordered_pair(v,w),universal_class),successor_relation)**.
% 299.82/300.45  210422[15:Res:189564.1,26.1] || subclass(domain_relation,rotate(complement(u))) member(ordered_pair(ordered_pair(v,successor_relation),w),u)* -> .
% 299.82/300.45  210424[15:Res:189564.1,141576.1] || subclass(domain_relation,rotate(complement(kind_1_ordinals))) member(ordered_pair(ordered_pair(u,successor_relation),v),ordinal_numbers)* -> .
% 299.82/300.45  210426[15:Res:189564.1,183398.0] || subclass(domain_relation,rotate(complement(complement(u)))) -> member(ordered_pair(ordered_pair(v,successor_relation),w),u)*.
% 299.82/300.45  210428[15:Res:189564.1,23.0] || subclass(domain_relation,rotate(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,successor_relation),x),u)*.
% 299.82/300.45  210429[15:Res:189564.1,24.0] || subclass(domain_relation,rotate(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,successor_relation),x),v)*.
% 299.82/300.45  210441[15:Res:189564.1,183723.0] || subclass(domain_relation,rotate(symmetrization_of(successor_relation))) -> member(ordered_pair(ordered_pair(u,successor_relation),v),inverse(successor_relation))*.
% 299.82/300.45  210442[15:Res:189564.1,193819.0] || subclass(domain_relation,rotate(cantor(complement(cross_product(singleton(ordered_pair(ordered_pair(u,successor_relation),v)),universal_class)))))* -> .
% 299.82/300.45  210444[15:Res:189564.1,183622.0] || subclass(domain_relation,rotate(successor(successor_relation))) -> member(ordered_pair(ordered_pair(u,successor_relation),v),singleton(successor_relation))*.
% 299.82/300.45  210527[6:SpL:203335.0,149475.0] || member(u,segment(v,w,x))* subclass(universal_class,y)* -> member(u,y)*.
% 299.82/300.45  210890[15:SpR:185605.1,210104.1] || equal(successor_relation,u) subclass(rest_relation,domain_relation) -> member(ordered_pair(power_class(u),successor_relation),rest_relation)*.
% 299.82/300.45  210967[0:Res:1504.1,183398.0] || subclass(ordered_pair(u,v),complement(complement(w)))* -> member(unordered_pair(u,singleton(v)),w).
% 299.82/300.45  210982[10:Res:1504.1,183723.0] || subclass(ordered_pair(u,v),symmetrization_of(successor_relation)) -> member(unordered_pair(u,singleton(v)),inverse(successor_relation))*.
% 299.82/300.45  210983[10:Res:1504.1,193819.0] || subclass(ordered_pair(u,v),cantor(complement(cross_product(singleton(unordered_pair(u,singleton(v))),universal_class))))* -> .
% 299.82/300.45  210986[10:Res:1504.1,183622.0] || subclass(ordered_pair(u,v),successor(successor_relation)) -> member(unordered_pair(u,singleton(v)),singleton(successor_relation))*.
% 299.82/300.45  211052[15:Res:211028.1,3.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(singleton(singleton(singleton(successor_relation))),u)*.
% 299.82/300.45  211257[11:SpL:28.0,211092.1] inductive(intersection(complement(u),complement(v))) || equal(union(u,v),inverse(successor_relation))** -> .
% 299.82/300.45  211268[11:SpL:161137.0,211092.1] inductive(image(element_relation,symmetrization_of(successor_relation))) || equal(power_class(complement(inverse(successor_relation))),inverse(successor_relation))** -> .
% 299.82/300.45  211269[11:SpL:162889.0,211092.1] inductive(image(element_relation,successor(successor_relation))) || equal(power_class(complement(singleton(successor_relation))),inverse(successor_relation))** -> .
% 299.82/300.45  211389[10:SpL:211297.0,10.0] || member(u,ordered_pair(universal_class,universal_class))* -> equal(u,unordered_pair(universal_class,successor_relation)) equal(u,successor_relation).
% 299.82/300.45  211396[10:MRR:211395.0,160315.0] ||  -> equal(regular(ordered_pair(universal_class,universal_class)),unordered_pair(universal_class,successor_relation))** equal(regular(ordered_pair(universal_class,universal_class)),successor_relation).
% 299.82/300.45  211489[10:Res:1951.1,211446.0] || member(singleton(successor_relation),symmetric_difference(u,v)) well_ordering(universal_class,complement(intersection(u,v)))* -> .
% 299.82/300.45  211515[10:MRR:211491.0,191.0] || well_ordering(universal_class,intersection(complement(u),complement(v)))* -> member(singleton(successor_relation),union(u,v)).
% 299.82/300.45  211522[10:Res:185430.1,157895.0] || equal(complement(complement(compose(element_relation,universal_class))),successor_relation)** member(unordered_pair(u,v),element_relation)* -> .
% 299.82/300.45  211526[10:SpL:28.0,211448.0] || well_ordering(universal_class,union(u,v)) -> member(singleton(successor_relation),intersection(complement(u),complement(v)))*.
% 299.82/300.45  211537[10:SpL:161137.0,211448.0] || well_ordering(universal_class,power_class(complement(inverse(successor_relation)))) -> member(singleton(successor_relation),image(element_relation,symmetrization_of(successor_relation)))*.
% 299.82/300.45  211538[10:SpL:162889.0,211448.0] || well_ordering(universal_class,power_class(complement(singleton(successor_relation)))) -> member(singleton(successor_relation),image(element_relation,successor(successor_relation)))*.
% 299.82/300.45  211622[10:SpR:28.0,211579.1] ||  -> member(singleton(successor_relation),intersection(complement(u),complement(v)))* member(singleton(successor_relation),union(u,v)).
% 299.82/300.45  211633[10:SpR:161137.0,211579.1] ||  -> member(singleton(successor_relation),image(element_relation,symmetrization_of(successor_relation)))* member(singleton(successor_relation),power_class(complement(inverse(successor_relation)))).
% 299.82/300.45  211634[10:SpR:162889.0,211579.1] ||  -> member(singleton(successor_relation),image(element_relation,successor(successor_relation)))* member(singleton(successor_relation),power_class(complement(singleton(successor_relation)))).
% 299.82/300.45  211668[10:Res:181213.1,6045.0] || equal(u,singleton(singleton(successor_relation)))* subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.45  211672[10:Res:181213.1,3.0] || equal(u,singleton(singleton(successor_relation)))* subclass(u,v)* -> member(singleton(successor_relation),v)*.
% 299.82/300.45  211676[10:Res:181213.1,148657.1] || equal(complement(compose(element_relation,universal_class)),singleton(singleton(successor_relation)))** member(singleton(successor_relation),element_relation) -> .
% 299.82/300.45  211685[10:Res:181213.1,1952.0] || equal(symmetric_difference(u,v),singleton(singleton(successor_relation))) -> member(singleton(successor_relation),union(u,v))*.
% 299.82/300.45  211686[10:Res:181213.1,10191.0] || equal(symmetric_difference(u,inverse(u)),singleton(singleton(successor_relation)))** -> member(singleton(successor_relation),symmetrization_of(u))*.
% 299.82/300.45  211687[10:Res:181213.1,10254.0] || equal(symmetric_difference(u,singleton(u)),singleton(singleton(successor_relation)))** -> member(singleton(successor_relation),successor(u))*.
% 299.82/300.45  211757[10:SpR:163197.1,9949.0] || subclass(complement(singleton(u)),successor_relation) -> equal(complement(image(element_relation,successor(u))),power_class(successor_relation))**.
% 299.82/300.45  211769[10:Rew:113504.0,211739.1] || equal(successor_relation,u) -> equal(complement(image(element_relation,successor(u))),power_class(complement(singleton(u))))**.
% 299.82/300.45  211853[10:SpR:185607.1,9948.0] || equal(complement(inverse(u)),successor_relation) -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(successor_relation))**.
% 299.82/300.45  211854[10:SpR:163197.1,9948.0] || subclass(complement(inverse(u)),successor_relation) -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(successor_relation))**.
% 299.82/300.45  211865[10:Rew:113504.0,211836.1] || equal(successor_relation,u) -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(complement(inverse(u))))**.
% 299.82/300.45  211970[11:Res:183759.1,3.0] || subclass(inverse(successor_relation),u)* subclass(u,v)* -> member(regular(symmetrization_of(successor_relation)),v)*.
% 299.82/300.45  211974[11:Res:183759.1,148657.1] || subclass(inverse(successor_relation),complement(compose(element_relation,universal_class)))* member(regular(symmetrization_of(successor_relation)),element_relation) -> .
% 299.82/300.45  211983[11:Res:183759.1,1952.0] || subclass(inverse(successor_relation),symmetric_difference(u,v)) -> member(regular(symmetrization_of(successor_relation)),union(u,v))*.
% 299.82/300.45  211984[11:Res:183759.1,10191.0] || subclass(inverse(successor_relation),symmetric_difference(u,inverse(u)))* -> member(regular(symmetrization_of(successor_relation)),symmetrization_of(u)).
% 299.82/300.45  211985[11:Res:183759.1,10254.0] || subclass(inverse(successor_relation),symmetric_difference(u,singleton(u)))* -> member(regular(symmetrization_of(successor_relation)),successor(u)).
% 299.82/300.45  212057[2:Res:184090.1,3.0] || equal(symmetric_difference(universal_class,u),universal_class) subclass(complement(u),v)* -> member(omega,v).
% 299.82/300.45  212103[12:MRR:212090.2,185618.0] || member(regular(regular(compose(element_relation,universal_class))),element_relation)* -> equal(regular(compose(element_relation,universal_class)),successor_relation).
% 299.82/300.45  212116[10:Res:161492.2,212099.0] || equal(omega,ordinal_numbers) -> equal(integer_of(regular(regular(kind_1_ordinals))),successor_relation)** equal(regular(kind_1_ordinals),successor_relation).
% 299.82/300.45  212835[10:SpL:185605.1,185977.1] || equal(successor_relation,u) equal(power_class(u),successor_relation)** member(successor_relation,power_class(successor_relation))* -> .
% 299.82/300.45  212836[10:SpL:185605.1,185977.1] || equal(successor_relation,u) equal(power_class(successor_relation),successor_relation) member(successor_relation,power_class(u))* -> .
% 299.82/300.45  212854[10:Rew:163369.0,212839.0] || equal(complement(image(element_relation,kind_1_ordinals)),successor_relation) member(successor_relation,complement(image(element_relation,kind_1_ordinals)))* -> .
% 299.82/300.45  212872[10:SpL:185605.1,186044.1] || equal(successor_relation,u) equal(power_class(u),successor_relation)** member(omega,power_class(successor_relation))* -> .
% 299.82/300.45  212873[10:SpL:185605.1,186044.1] || equal(successor_relation,u) equal(power_class(successor_relation),successor_relation) member(omega,power_class(u))* -> .
% 299.82/300.45  212884[10:Rew:163369.0,212876.0] || equal(complement(image(element_relation,kind_1_ordinals)),successor_relation) member(omega,complement(image(element_relation,kind_1_ordinals)))* -> .
% 299.82/300.45  213068[10:SpL:70.0,188186.1] || member(image(u,singleton(v)),universal_class)* equal(singleton(apply(u,v)),successor_relation) -> .
% 299.82/300.45  213114[10:Res:188444.1,3.0] || equal(symmetric_difference(universal_class,u),universal_class) subclass(complement(u),v)* -> member(successor_relation,v).
% 299.82/300.45  213201[15:Res:189485.1,3.0] || subclass(domain_relation,u)* subclass(u,v)* -> member(singleton(singleton(singleton(successor_relation))),v)*.
% 299.82/300.45  213205[15:Res:189485.1,148657.1] || subclass(domain_relation,complement(compose(element_relation,universal_class)))* member(singleton(singleton(singleton(successor_relation))),element_relation) -> .
% 299.82/300.45  213214[15:Res:189485.1,1952.0] || subclass(domain_relation,symmetric_difference(u,v)) -> member(singleton(singleton(singleton(successor_relation))),union(u,v))*.
% 299.82/300.45  213215[15:Res:189485.1,10191.0] || subclass(domain_relation,symmetric_difference(u,inverse(u)))* -> member(singleton(singleton(singleton(successor_relation))),symmetrization_of(u))*.
% 299.82/300.45  213216[15:Res:189485.1,10254.0] || subclass(domain_relation,symmetric_difference(u,singleton(u)))* -> member(singleton(singleton(singleton(successor_relation))),successor(u))*.
% 299.82/300.45  213226[15:Res:189485.1,159.0] || subclass(domain_relation,omega) -> equal(integer_of(singleton(singleton(singleton(successor_relation)))),singleton(singleton(singleton(successor_relation))))**.
% 299.82/300.45  213310[15:SpL:28.0,213296.1] || equal(intersection(complement(u),complement(v)),domain_relation)** equal(union(u,v),universal_class) -> .
% 299.82/300.45  213321[15:SpL:161137.0,213296.1] || equal(image(element_relation,symmetrization_of(successor_relation)),domain_relation)** equal(power_class(complement(inverse(successor_relation))),universal_class) -> .
% 299.82/300.45  213322[15:SpL:162889.0,213296.1] || equal(image(element_relation,successor(successor_relation)),domain_relation)** equal(power_class(complement(singleton(successor_relation))),universal_class) -> .
% 299.82/300.45  213484[10:SpL:142543.0,160801.0] || subclass(u,symmetric_difference(universal_class,v))* -> equal(u,successor_relation) member(regular(u),complement(v)).
% 299.82/300.45  213607[15:SpL:70.0,191628.1] || member(image(u,singleton(v)),universal_class)* equal(successor(apply(u,v)),successor_relation) -> .
% 299.82/300.45  214148[20:Res:193270.1,3.0] || equal(symmetric_difference(universal_class,u),omega) subclass(complement(u),v)* -> member(successor_relation,v).
% 299.82/300.45  214250[10:Res:185430.1,3485.0] || equal(complement(u),successor_relation) subclass(u,v)* -> member(unordered_pair(w,x),v)*.
% 299.82/300.45  214295[10:Res:214277.1,594.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(power_class(successor_relation),cross_product(v,w))*.
% 299.82/300.45  214315[10:Res:214277.1,160481.0] || equal(complement(regular(u)),successor_relation) member(power_class(successor_relation),u)* -> equal(u,successor_relation).
% 299.82/300.45  214403[10:Res:30985.1,185639.1] || member(u,universal_class) equal(union(v,w),successor_relation)** -> member(u,complement(w))*.
% 299.82/300.45  214449[21:Res:214433.0,163137.0] || equal(rest_of(regular(complement(complement(symmetrization_of(successor_relation))))),successor(regular(complement(complement(symmetrization_of(successor_relation))))))** -> .
% 299.82/300.45  214550[10:Res:30984.1,185639.1] || member(u,universal_class) equal(union(v,w),successor_relation)** -> member(u,complement(v))*.
% 299.82/300.45  215247[10:Rew:161321.0,215116.1] || member(not_subclass_element(complement(u),successor_relation),restrict(u,v,w))* -> subclass(complement(u),successor_relation).
% 299.82/300.45  215516[10:Rew:195811.1,215353.2] || equal(inverse(u),universal_class) -> member(not_subclass_element(v,successor_relation),inverse(u))* subclass(v,successor_relation).
% 299.82/300.45  215521[10:Rew:160223.0,215310.2,195811.1,215310.2,160223.0,215310.1] || equal(inverse(u),universal_class) -> member(not_subclass_element(universal_class,v),inverse(u))* subclass(universal_class,v).
% 299.82/300.45  215530[10:Rew:160276.0,215339.1] || equal(inverse(u),universal_class) -> equal(complement(image(element_relation,successor(inverse(u)))),power_class(successor_relation))**.
% 299.82/300.45  215531[10:Rew:160276.0,215340.1] || equal(inverse(u),universal_class) -> equal(complement(image(element_relation,symmetrization_of(inverse(u)))),power_class(successor_relation))**.
% 299.82/300.45  215792[10:Rew:195870.1,215667.2] || equal(sum_class(u),universal_class) -> member(not_subclass_element(v,successor_relation),sum_class(u))* subclass(v,successor_relation).
% 299.82/300.45  215796[10:Rew:160223.0,215624.2,195870.1,215624.2,160223.0,215624.1] || equal(sum_class(u),universal_class) -> member(not_subclass_element(universal_class,v),sum_class(u))* subclass(universal_class,v).
% 299.82/300.45  215805[10:Rew:160276.0,215653.1] || equal(sum_class(u),universal_class) -> equal(complement(image(element_relation,successor(sum_class(u)))),power_class(successor_relation))**.
% 299.82/300.45  215806[10:Rew:160276.0,215654.1] || equal(sum_class(u),universal_class) -> equal(complement(image(element_relation,symmetrization_of(sum_class(u)))),power_class(successor_relation))**.
% 299.82/300.45  215851[10:Rew:194805.1,215848.1] || subclass(ordinal_numbers,y__dfg) subclass(omega,ordinal_numbers) -> equal(integer_of(least(element_relation,ordinal_numbers)),successor_relation)**.
% 299.82/300.45  215864[10:Res:197082.1,3.0] || subclass(universal_class,u)* subclass(u,v)* -> member(regular(complement(successor(successor_relation))),v)*.
% 299.82/300.45  215868[10:Res:197082.1,148657.1] || subclass(universal_class,complement(compose(element_relation,universal_class)))* member(regular(complement(successor(successor_relation))),element_relation) -> .
% 299.82/300.45  215877[10:Res:197082.1,1952.0] || subclass(universal_class,symmetric_difference(u,v)) -> member(regular(complement(successor(successor_relation))),union(u,v))*.
% 299.82/300.45  215878[10:Res:197082.1,10191.0] || subclass(universal_class,symmetric_difference(u,inverse(u)))* -> member(regular(complement(successor(successor_relation))),symmetrization_of(u))*.
% 299.82/300.45  215879[10:Res:197082.1,10254.0] || subclass(universal_class,symmetric_difference(u,singleton(u)))* -> member(regular(complement(successor(successor_relation))),successor(u))*.
% 299.82/300.45  215889[10:Res:197082.1,159.0] || subclass(universal_class,omega) -> equal(integer_of(regular(complement(successor(successor_relation)))),regular(complement(successor(successor_relation))))**.
% 299.82/300.45  216101[6:Res:199830.1,6045.0] || equal(u,cross_product(universal_class,universal_class))* subclass(u,v)* well_ordering(universal_class,v)* -> .
% 299.82/300.45  216105[6:Res:199830.1,3.0] || equal(u,cross_product(universal_class,universal_class))* subclass(u,v)* -> member(regular(rest_relation),v)*.
% 299.82/300.45  216109[6:Res:199830.1,148657.1] || equal(complement(compose(element_relation,universal_class)),cross_product(universal_class,universal_class))** member(regular(rest_relation),element_relation) -> .
% 299.82/300.45  216118[6:Res:199830.1,1952.0] || equal(symmetric_difference(u,v),cross_product(universal_class,universal_class)) -> member(regular(rest_relation),union(u,v))*.
% 299.82/300.45  216119[6:Res:199830.1,10191.0] || equal(symmetric_difference(u,inverse(u)),cross_product(universal_class,universal_class))** -> member(regular(rest_relation),symmetrization_of(u))*.
% 299.82/300.45  216120[6:Res:199830.1,10254.0] || equal(symmetric_difference(u,singleton(u)),cross_product(universal_class,universal_class))** -> member(regular(rest_relation),successor(u))*.
% 299.82/300.45  216155[6:Res:199833.1,3.0] || equal(inverse(u),universal_class) subclass(inverse(u),v)* -> member(regular(rest_relation),v).
% 299.82/300.45  216170[6:Res:199834.1,3.0] || equal(sum_class(u),universal_class) subclass(sum_class(u),v)* -> member(regular(rest_relation),v).
% 299.82/300.45  216204[14:SpR:44.0,199970.1] || member(restrict(u,v,universal_class),universal_class)* -> equal(integer_of(sum_class(image(u,v))),successor_relation).
% 299.82/300.45  216222[14:SpR:199971.1,45.0] || member(u,universal_class) -> equal(union(sum_class(range_of(u)),successor_relation),successor(sum_class(range_of(u))))**.
% 299.82/300.45  216283[14:SpR:44.0,199971.1] || member(restrict(u,v,universal_class),universal_class)* -> equal(singleton(sum_class(image(u,v))),successor_relation).
% 299.82/300.45  216342[14:SpL:199971.1,193819.0] || member(u,universal_class) member(sum_class(range_of(u)),cantor(complement(cross_product(successor_relation,universal_class))))* -> .
% 299.82/300.45  216481[10:Res:216465.1,594.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(regular(rest_relation),cross_product(v,w))*.
% 299.82/300.45  216501[10:Res:216465.1,160481.0] || equal(complement(regular(u)),successor_relation) member(regular(rest_relation),u)* -> equal(u,successor_relation).
% 299.82/300.45  216667[10:Rew:203335.0,216600.1] || equal(segment(u,v,w),successor_relation)** equal(segment(u,v,w),universal_class) -> .
% 299.82/300.45  216707[10:Rew:203335.0,216693.0] || equal(segment(u,v,w),successor_relation) subclass(universal_class,segment(u,v,w))* -> .
% 299.82/300.45  216713[6:Res:201220.1,3.0] || equal(u,cross_product(universal_class,universal_class))* subclass(u,v)* -> member(regular(domain_relation),v)*.
% 299.82/300.45  216717[6:Res:201220.1,148657.1] || equal(complement(compose(element_relation,universal_class)),cross_product(universal_class,universal_class))** member(regular(domain_relation),element_relation) -> .
% 299.82/300.45  216726[6:Res:201220.1,1952.0] || equal(symmetric_difference(u,v),cross_product(universal_class,universal_class)) -> member(regular(domain_relation),union(u,v))*.
% 299.82/300.45  216727[6:Res:201220.1,10191.0] || equal(symmetric_difference(u,inverse(u)),cross_product(universal_class,universal_class))** -> member(regular(domain_relation),symmetrization_of(u))*.
% 299.82/300.45  216728[6:Res:201220.1,10254.0] || equal(symmetric_difference(u,singleton(u)),cross_product(universal_class,universal_class))** -> member(regular(domain_relation),successor(u))*.
% 299.82/300.45  216779[6:Res:201223.1,3.0] || equal(inverse(u),universal_class) subclass(inverse(u),v)* -> member(regular(domain_relation),v).
% 299.82/300.45  216794[6:Res:201224.1,3.0] || equal(sum_class(u),universal_class) subclass(sum_class(u),v)* -> member(regular(domain_relation),v).
% 299.82/300.45  216878[10:Rew:160824.1,216877.1] || member(apply(choice,u),singleton(u))* -> equal(u,successor_relation) equal(singleton(u),successor_relation).
% 299.82/300.45  216909[10:Res:216847.1,594.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(regular(domain_relation),cross_product(v,w))*.
% 299.82/300.45  216929[10:Res:216847.1,160481.0] || equal(complement(regular(u)),successor_relation) member(regular(domain_relation),u)* -> equal(u,successor_relation).
% 299.82/300.45  217163[15:Res:8.1,189383.1] || equal(singleton(u),domain_relation)** member(v,universal_class) -> equal(ordered_pair(v,successor_relation),u)*.
% 299.82/300.45  217235[15:Res:8.1,189417.1] || equal(compose_class(u),domain_relation) member(v,universal_class) -> equal(compose(u,v),successor_relation)**.
% 299.82/300.45  217241[10:Res:217225.1,309.0] || equal(singleton(not_subclass_element(complement(singleton(successor_relation)),u)),kind_1_ordinals)** -> subclass(complement(singleton(successor_relation)),u).
% 299.82/300.45  217404[20:Res:217226.1,309.0] || equal(singleton(not_subclass_element(complement(singleton(successor_relation)),u)),omega)** -> subclass(complement(singleton(successor_relation)),u).
% 299.82/300.45  217571[10:Res:1504.1,160697.1] || subclass(ordered_pair(u,v),w)* subclass(universal_class,regular(w)) -> equal(w,successor_relation).
% 299.82/300.45  217903[10:SpL:2330.1,217574.0] || subclass(universal_class,regular(not_subclass_element(cross_product(u,v),w)))* -> subclass(cross_product(u,v),w).
% 299.82/300.45  217937[3:Obv:217919.2] || subclass(singleton(u),complement(kind_1_ordinals))* member(u,ordinal_numbers) -> subclass(singleton(u),v)*.
% 299.82/300.45  217938[10:Obv:217920.2] || subclass(successor(successor_relation),complement(kind_1_ordinals))* member(successor_relation,ordinal_numbers) -> subclass(successor(successor_relation),u)*.
% 299.82/300.45  217986[10:SpL:2330.1,217671.0] || equal(complement(not_subclass_element(cross_product(u,v),w)),successor_relation)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  217995[10:SpL:2330.1,217908.0] || equal(regular(not_subclass_element(cross_product(u,v),w)),universal_class)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  218255[10:SpL:161592.1,217909.0] || equal(complement(regular(regular(cross_product(u,v)))),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  218310[10:Rew:160824.1,218309.1] || member(not_subclass_element(u,v),singleton(u))* -> subclass(u,v) equal(singleton(u),successor_relation).
% 299.82/300.45  218336[10:SpR:57.0,218298.0] ||  -> subclass(regular(image(element_relation,complement(u))),power_class(u))* equal(image(element_relation,complement(u)),successor_relation).
% 299.82/300.45  218358[10:Res:218298.0,9.0] || subclass(complement(u),regular(u))* -> equal(u,successor_relation) equal(complement(u),regular(u)).
% 299.82/300.45  218586[10:Obv:218540.2] || subclass(successor(successor_relation),complement(u))* member(successor_relation,u) -> subclass(successor(successor_relation),v)*.
% 299.82/300.45  218773[3:Res:218493.1,9.0] || subclass(complement(ordinal_numbers),singleton(u))* -> member(u,kind_1_ordinals) equal(complement(ordinal_numbers),singleton(u)).
% 299.82/300.45  218895[22:Res:218867.1,9322.0] || subclass(kind_1_ordinals,symmetric_difference(complement(u),complement(v)))* -> member(singleton(successor_relation),union(u,v)).
% 299.82/300.45  218905[22:Res:218867.1,10.0] || subclass(kind_1_ordinals,unordered_pair(u,v))* -> equal(singleton(successor_relation),v) equal(singleton(successor_relation),u).
% 299.82/300.45  219089[3:Res:218473.1,9.0] || equal(complement(kind_1_ordinals),u) subclass(complement(ordinal_numbers),u)* -> equal(complement(ordinal_numbers),u).
% 299.82/300.45  219134[3:Res:218473.1,1486.1] || equal(complement(kind_1_ordinals),singleton(u)) member(u,universal_class) -> member(u,complement(ordinal_numbers))*.
% 299.82/300.45  219176[10:Res:160466.1,218628.0] ||  -> equal(intersection(complement(kind_1_ordinals),u),successor_relation) member(regular(intersection(complement(kind_1_ordinals),u)),complement(ordinal_numbers))*.
% 299.82/300.45  219188[3:Res:1478.2,218628.0] || member(u,universal_class) subclass(universal_class,complement(kind_1_ordinals)) -> member(power_class(u),complement(ordinal_numbers))*.
% 299.82/300.45  219189[3:Res:1481.2,218628.0] || subclass(u,complement(kind_1_ordinals)) -> subclass(u,v) member(not_subclass_element(u,v),complement(ordinal_numbers))*.
% 299.82/300.45  219192[10:Res:160465.1,218628.0] ||  -> equal(intersection(u,complement(kind_1_ordinals)),successor_relation) member(regular(intersection(u,complement(kind_1_ordinals))),complement(ordinal_numbers))*.
% 299.82/300.45  219194[3:Res:1479.2,218628.0] || member(u,universal_class) subclass(universal_class,complement(kind_1_ordinals)) -> member(sum_class(u),complement(ordinal_numbers))*.
% 299.82/300.45  219204[15:Res:189564.1,218628.0] || subclass(domain_relation,rotate(complement(kind_1_ordinals))) -> member(ordered_pair(ordered_pair(u,successor_relation),v),complement(ordinal_numbers))*.
% 299.82/300.45  219208[15:Res:189563.1,218628.0] || subclass(domain_relation,flip(complement(kind_1_ordinals))) -> member(ordered_pair(ordered_pair(u,v),successor_relation),complement(ordinal_numbers))*.
% 299.82/300.45  219218[3:Res:1504.1,218628.0] || subclass(ordered_pair(u,v),complement(kind_1_ordinals)) -> member(unordered_pair(u,singleton(v)),complement(ordinal_numbers))*.
% 299.82/300.45  219234[10:Res:161419.0,218628.0] ||  -> equal(complement(complement(complement(kind_1_ordinals))),successor_relation) member(regular(complement(complement(complement(kind_1_ordinals)))),complement(ordinal_numbers))*.
% 299.82/300.45  219398[10:MRR:219393.1,188662.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(u,unordered_pair(v,w))),unordered_pair(v,w))**.
% 299.82/300.45  216124[10:Res:199830.1,163294.0] || equal(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),cross_product(universal_class,universal_class))** -> member(regular(rest_relation),kind_1_ordinals).
% 299.82/300.45  216732[10:Res:201220.1,163294.0] || equal(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),cross_product(universal_class,universal_class))** -> member(regular(domain_relation),kind_1_ordinals).
% 299.82/300.45  211989[11:Res:183759.1,163294.0] || subclass(inverse(successor_relation),symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(regular(symmetrization_of(successor_relation)),kind_1_ordinals).
% 299.82/300.45  213220[15:Res:189485.1,163294.0] || subclass(domain_relation,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(singleton(singleton(singleton(successor_relation))),kind_1_ordinals).
% 299.82/300.45  163410[10:Rew:160305.0,162814.0] || equal(complement(complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),universal_class)** -> member(singleton(u),kind_1_ordinals)*.
% 299.82/300.45  215883[10:Res:197082.1,163294.0] || subclass(universal_class,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(regular(complement(successor(successor_relation))),kind_1_ordinals).
% 299.82/300.45  219133[10:Res:218473.1,163257.1] || equal(range_of(successor_relation),complement(kind_1_ordinals)) member(successor_relation,complement(ordinal_numbers))* -> inductive(complement(ordinal_numbers)).
% 299.82/300.45  190699[19:Res:136.1,190697.1] inductive(u) || member(u,ordinal_numbers)* -> member(least(element_relation,range_of(successor_relation)),range_of(successor_relation))*.
% 299.82/300.45  163342[10:Rew:160202.0,160626.0] || member(ordered_pair(u,v),compose(w,successor_relation))* -> member(v,image(w,range_of(successor_relation))).
% 299.82/300.45  163465[10:Rew:160305.0,163151.2] inductive(singleton(u)) || member(u,range_of(successor_relation))* -> equal(range_of(successor_relation),singleton(u)).
% 299.82/300.45  163466[10:Rew:160305.0,163152.2] inductive(singleton(u)) ||  -> subclass(range_of(successor_relation),v) equal(not_subclass_element(range_of(successor_relation),v),u)*.
% 299.82/300.45  204046[10:Rew:203285.0,167689.1] inductive(intersection(cantor(inverse(successor_relation)),u)) ||  -> equal(intersection(range_of(successor_relation),u),range_of(successor_relation))**.
% 299.82/300.45  204045[10:Rew:203285.0,167690.1] inductive(intersection(u,cantor(inverse(successor_relation)))) ||  -> equal(intersection(u,range_of(successor_relation)),range_of(successor_relation))**.
% 299.82/300.45  204044[10:Rew:203285.0,167694.1] inductive(complement(complement(cantor(inverse(successor_relation))))) ||  -> equal(complement(complement(range_of(successor_relation))),range_of(successor_relation))**.
% 299.82/300.45  193777[10:SpR:193730.0,67.2] function(complement(cross_product(u,universal_class))) || member(u,universal_class)* -> member(range_of(successor_relation),universal_class)*.
% 299.82/300.45  163406[10:Rew:160305.0,161943.2] inductive(domain_of(u)) || equal(complement(rest_of(u)),universal_class)** -> equal(range_of(successor_relation),successor_relation).
% 299.82/300.45  163533[10:Rew:160305.0,162187.2,160305.0,162187.1] inductive(complement(u)) || member(regular(range_of(successor_relation)),u)* -> equal(range_of(successor_relation),successor_relation).
% 299.82/300.45  163606[10:Rew:160305.0,162329.2,160305.0,162329.1] inductive(intersection(u,v)) ||  -> equal(range_of(successor_relation),successor_relation) member(regular(range_of(successor_relation)),u)*.
% 299.82/300.45  163607[10:Rew:160305.0,162330.2,160305.0,162330.1] inductive(intersection(u,v)) ||  -> equal(range_of(successor_relation),successor_relation) member(regular(range_of(successor_relation)),v)*.
% 299.82/300.45  211601[10:Res:163149.1,160705.0] inductive(complement(kind_1_ordinals)) || member(regular(range_of(successor_relation)),ordinal_numbers)* -> equal(range_of(successor_relation),successor_relation).
% 299.82/300.45  204570[10:Rew:203192.0,203944.1] ||  -> equal(apply(u,not_subclass_element(v,cantor(u))),sum_class(range_of(successor_relation)))** subclass(v,cantor(u)).
% 299.82/300.45  203778[10:Rew:203192.0,160579.0] || equal(complement(cantor(u)),universal_class) -> equal(apply(u,singleton(v)),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  184009[14:MRR:184002.2,160227.0] || equal(sum_class(range_of(successor_relation)),universal_class) member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> .
% 299.82/300.45  201959[10:Res:161492.2,2.0] || equal(intersection(y__dfg,ordinal_numbers),omega) -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation)**.
% 299.82/300.45  220887[10:SpL:161592.1,219813.0] || subclass(universal_class,regular(singleton(regular(cross_product(u,v)))))* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  220925[10:SpL:161592.1,220897.0] || equal(regular(singleton(regular(cross_product(u,v)))),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  221329[10:MRR:221325.1,188711.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(unordered_pair(v,w),u)),unordered_pair(v,w))**.
% 299.82/300.45  221443[10:Res:218373.0,183.1] || well_ordering(element_relation,complement(singleton(intersection(y__dfg,ordinal_numbers))))* -> equal(singleton(intersection(y__dfg,ordinal_numbers)),successor_relation).
% 299.82/300.45  221467[10:Res:218373.0,157925.0] || well_ordering(universal_class,complement(singleton(image(element_relation,universal_class))))* -> equal(singleton(image(element_relation,universal_class)),successor_relation).
% 299.82/300.45  221469[13:Res:218373.0,180584.0] || well_ordering(universal_class,complement(singleton(image(element_relation,successor_relation))))* -> equal(singleton(image(element_relation,successor_relation)),successor_relation).
% 299.82/300.45  221487[10:Res:218373.0,199959.0] || well_ordering(universal_class,complement(singleton(cross_product(universal_class,universal_class))))* -> equal(singleton(cross_product(universal_class,universal_class)),successor_relation).
% 299.82/300.45  221488[12:Res:218373.0,177133.0] ||  -> equal(singleton(cross_product(universal_class,universal_class)),successor_relation) member(regular(element_relation),complement(singleton(cross_product(universal_class,universal_class))))*.
% 299.82/300.45  221489[10:Res:218373.0,154493.0] ||  -> equal(singleton(cross_product(universal_class,universal_class)),successor_relation) member(regular(domain_relation),complement(singleton(cross_product(universal_class,universal_class))))*.
% 299.82/300.45  221490[10:Res:218373.0,153518.0] ||  -> equal(singleton(cross_product(universal_class,universal_class)),successor_relation) member(regular(rest_relation),complement(singleton(cross_product(universal_class,universal_class))))*.
% 299.82/300.45  221508[10:Res:218373.0,197069.0] || well_ordering(universal_class,complement(singleton(complement(singleton(successor_relation)))))* -> equal(singleton(complement(singleton(successor_relation))),successor_relation).
% 299.82/300.45  221906[10:Res:3907.1,163147.1] || equal(complement(complement(cross_product(universal_class,universal_class))),universal_class)** equal(successor(singleton(u)),u)** -> .
% 299.82/300.45  221957[20:MRR:221944.1,191.0] || equal(singleton(singleton(singleton(successor_relation))),omega) -> member(singleton(singleton(singleton(singleton(successor_relation)))),element_relation)*.
% 299.82/300.45  221959[15:MRR:221954.1,191.0] || subclass(domain_relation,singleton(singleton(successor_relation))) -> member(singleton(singleton(singleton(singleton(singleton(successor_relation))))),element_relation)*.
% 299.82/300.45  222152[10:SpL:161592.1,222139.0] || subclass(complement(singleton(regular(cross_product(u,v)))),successor_relation)* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  223312[24:SpL:222479.0,184007.1] || equal(sum_class(range_of(u)),kind_1_ordinals) member(ordered_pair(u,universal_class),cross_product(universal_class,universal_class))* -> .
% 299.82/300.45  224507[25:Rew:224236.1,224298.2] function(restrict(u,v,w)) || section(u,w,v)* -> equal(universal_class,w).
% 299.82/300.45  224664[25:SpR:224236.1,203330.1] function(restrict(u,v,w)) || section(u,w,v)* -> subclass(universal_class,w).
% 299.82/300.45  224964[25:SpR:224739.1,1504.1] function(u) || subclass(ordered_pair(v,u),w)* -> member(unordered_pair(v,successor_relation),w).
% 299.82/300.45  225064[25:SpL:224739.1,1522.0] function(u) || member(singleton(singleton(successor_relation)),cross_product(v,w))* -> member(u,w)*.
% 299.82/300.45  225118[25:SpL:224739.1,302.0] function(u) || member(image(v,successor_relation),universal_class) -> member(apply(v,u),universal_class)*.
% 299.82/300.45  225470[25:Rew:224739.1,224955.1] function(u) || section(v,successor_relation,w) -> subclass(segment(v,w,u),successor_relation)*.
% 299.82/300.45  225487[25:MRR:225486.1,160215.0] function(u) || subclass(segment(v,w,u),successor_relation)* -> section(v,successor_relation,w).
% 299.82/300.45  225501[25:SoR:224740.0,6317.2] single_valued_class(regular(u)) || equal(cross_product(universal_class,universal_class),regular(u))* -> equal(u,successor_relation).
% 299.82/300.45  225731[24:Rew:223099.0,225720.1] || member(not_subclass_element(symmetric_difference(universal_class,kind_1_ordinals),successor_relation),successor(kind_1_ordinals))* -> subclass(symmetric_difference(universal_class,kind_1_ordinals),successor_relation).
% 299.82/300.45  225833[25:Rew:181137.1,225832.2] function(u) || member(ordered_pair(v,singleton(singleton(successor_relation))),composition_function)* -> equal(universal_class,u)*.
% 299.82/300.45  226083[15:MRR:226035.2,6.0] || equal(complement(u),successor_relation) member(v,universal_class) -> member(ordered_pair(v,successor_relation),u)*.
% 299.82/300.45  226276[15:MRR:226195.1,160227.0] || member(u,universal_class) -> equal(apply(regular(complement(successor(successor_relation))),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226277[15:MRR:226196.1,160227.0] || member(u,universal_class) -> equal(apply(regular(complement(power_class(universal_class))),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226278[15:MRR:226197.1,160227.0] || member(u,universal_class) -> equal(apply(regular(complement(power_class(successor_relation))),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226288[11:MRR:226253.0,160214.0] || equal(complement(cantor(u)),inverse(successor_relation)) -> equal(apply(u,successor_relation),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226289[10:MRR:226254.0,160214.0] || equal(complement(cantor(u)),singleton(successor_relation)) -> equal(apply(u,successor_relation),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226290[10:MRR:226256.0,160214.0] || equal(complement(cantor(u)),successor(successor_relation)) -> equal(apply(u,successor_relation),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226291[11:MRR:226257.0,160214.0] || equal(complement(cantor(u)),symmetrization_of(successor_relation)) -> equal(apply(u,successor_relation),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226455[25:SoR:224779.0,160511.2] function(u) single_valued_class(apply(u,v)) || equal(apply(u,v),successor_relation)** -> .
% 299.82/300.45  226941[10:Rew:142543.0,226928.0,142542.0,226928.0] ||  -> equal(symmetric_difference(complement(intersection(complement(ordinal_numbers),kind_1_ordinals)),universal_class),symmetric_difference(universal_class,symmetric_difference(complement(ordinal_numbers),kind_1_ordinals)))**.
% 299.82/300.45  227332[25:Res:224913.1,163256.1] function(u) || equal(ordered_pair(u,v),range_of(successor_relation)) -> inductive(ordered_pair(u,v))*.
% 299.82/300.45  227342[25:SoR:224780.0,160511.2] single_valued_class(not_subclass_element(u,v)) || equal(not_subclass_element(u,v),successor_relation)** -> subclass(u,v).
% 299.82/300.45  227711[10:Rew:227524.0,227696.1] || member(not_subclass_element(intersection(ordinal_numbers,u),successor_relation),complement(kind_1_ordinals))* -> subclass(intersection(ordinal_numbers,u),successor_relation).
% 299.82/300.45  227814[10:Rew:227655.0,227792.1] || member(not_subclass_element(complement(complement(ordinal_numbers)),successor_relation),complement(kind_1_ordinals))* -> subclass(complement(complement(ordinal_numbers)),successor_relation).
% 299.82/300.45  227838[10:Rew:142543.0,227825.0,142542.0,227825.0] ||  -> equal(symmetric_difference(complement(intersection(kind_1_ordinals,complement(ordinal_numbers))),universal_class),symmetric_difference(universal_class,symmetric_difference(kind_1_ordinals,complement(ordinal_numbers))))**.
% 299.82/300.45  227937[10:Rew:227646.0,227923.1] || member(not_subclass_element(intersection(u,ordinal_numbers),successor_relation),complement(kind_1_ordinals))* -> subclass(intersection(u,ordinal_numbers),successor_relation).
% 299.82/300.45  228743[10:Obv:228713.2] || equal(u,v) equal(singleton(v),successor_relation) -> equal(unordered_pair(v,u),successor_relation)**.
% 299.82/300.45  228744[15:Obv:228714.2] || equal(u,v) equal(successor(v),successor_relation) -> equal(unordered_pair(v,u),successor_relation)**.
% 299.82/300.45  228862[24:Rew:223107.0,228796.0] ||  -> equal(symmetric_difference(complement(kind_1_ordinals),universal_class),successor_relation) member(regular(symmetric_difference(complement(kind_1_ordinals),universal_class)),successor(kind_1_ordinals))*.
% 299.82/300.45  228804[24:SpR:223107.0,1951.1] || member(u,symmetric_difference(successor(kind_1_ordinals),universal_class)) -> member(u,complement(symmetric_difference(complement(kind_1_ordinals),universal_class)))*.
% 299.82/300.45  228835[24:SpL:223107.0,9332.1] || member(u,symmetric_difference(successor(kind_1_ordinals),universal_class)) member(u,symmetric_difference(complement(kind_1_ordinals),universal_class))* -> .
% 299.82/300.45  228878[24:MRR:228877.0,34067.1] || member(u,complement(symmetric_difference(complement(kind_1_ordinals),universal_class)))* -> member(u,symmetric_difference(successor(kind_1_ordinals),universal_class)).
% 299.82/300.45  228967[10:Res:201671.0,160788.0] || subclass(complement(ordinal_numbers),u) -> equal(complement(kind_1_ordinals),successor_relation) member(regular(complement(kind_1_ordinals)),u)*.
% 299.82/300.45  228990[10:Res:218497.0,160788.0] || subclass(complement(ordinal_numbers),u) -> equal(regular(kind_1_ordinals),successor_relation) member(regular(regular(kind_1_ordinals)),u)*.
% 299.82/300.45  229032[10:Res:228991.1,9322.0] || subclass(kind_1_ordinals,symmetric_difference(complement(u),complement(v)))* -> member(regular(ordinal_numbers),union(u,v)).
% 299.82/300.45  229042[10:Res:228991.1,10.0] || subclass(kind_1_ordinals,unordered_pair(u,v))* -> equal(regular(ordinal_numbers),v) equal(regular(ordinal_numbers),u).
% 299.82/300.45  229156[10:MRR:229124.1,206430.0] || subclass(complement(complement(successor(successor_relation))),symmetric_difference(u,v))* -> member(successor_relation,union(u,v)).
% 299.82/300.45  229260[10:Res:229228.1,9322.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v)))* -> member(regular(ordinal_numbers),union(u,v)).
% 299.82/300.45  229503[15:MRR:229472.1,229170.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(regular(ordinal_numbers),successor_relation),u)*.
% 299.82/300.45  229831[10:MRR:229822.2,217612.0] ||  -> equal(integer_of(regular(regular(complement(singleton(omega))))),successor_relation)** equal(regular(complement(singleton(omega))),successor_relation).
% 299.82/300.45  230156[15:SpL:28.0,222296.1] || subclass(domain_relation,intersection(complement(u),complement(v)))* subclass(domain_relation,union(u,v)) -> .
% 299.82/300.45  230168[15:SpL:161137.0,222296.1] || subclass(domain_relation,image(element_relation,symmetrization_of(successor_relation)))* subclass(domain_relation,power_class(complement(inverse(successor_relation)))) -> .
% 299.82/300.45  230169[15:SpL:162889.0,222296.1] || subclass(domain_relation,image(element_relation,successor(successor_relation)))* subclass(domain_relation,power_class(complement(singleton(successor_relation)))) -> .
% 299.82/300.45  230382[10:Rew:226753.0,230366.1] || member(not_subclass_element(complement(kind_1_ordinals),successor_relation),restrict(ordinal_numbers,u,v))* -> subclass(complement(kind_1_ordinals),successor_relation).
% 299.82/300.45  230424[10:SpR:227642.0,194805.1] || subclass(restrict(ordinal_numbers,u,v),complement(kind_1_ordinals))* -> equal(restrict(ordinal_numbers,u,v),successor_relation).
% 299.82/300.45  230518[10:Res:1481.2,229800.0] || subclass(u,singleton(omega)) -> subclass(u,v) equal(integer_of(not_subclass_element(u,v)),successor_relation)**.
% 299.82/300.45  230533[15:Res:189564.1,229800.0] || subclass(domain_relation,rotate(singleton(omega))) -> equal(integer_of(ordered_pair(ordered_pair(u,successor_relation),v)),successor_relation)**.
% 299.82/300.45  230537[15:Res:189563.1,229800.0] || subclass(domain_relation,flip(singleton(omega))) -> equal(integer_of(ordered_pair(ordered_pair(u,v),successor_relation)),successor_relation)**.
% 299.82/300.45  230547[10:Res:1504.1,229800.0] || subclass(ordered_pair(u,v),singleton(omega))* -> equal(integer_of(unordered_pair(u,singleton(v))),successor_relation).
% 299.82/300.45  230633[15:SpL:28.0,230608.1] || equal(intersection(complement(u),complement(v)),domain_relation)** equal(union(u,v),domain_relation) -> .
% 299.82/300.45  230645[15:SpL:161137.0,230608.1] || equal(image(element_relation,symmetrization_of(successor_relation)),domain_relation)** equal(power_class(complement(inverse(successor_relation))),domain_relation) -> .
% 299.82/300.45  230646[15:SpL:162889.0,230608.1] || equal(image(element_relation,successor(successor_relation)),domain_relation)** equal(power_class(complement(singleton(successor_relation))),domain_relation) -> .
% 299.82/300.45  230665[10:MRR:230658.1,188646.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(u,ordered_pair(v,w))),ordered_pair(v,w))**.
% 299.82/300.45  230854[10:MRR:230808.0,191.0] || subclass(image(element_relation,power_class(successor_relation)),successor_relation) -> member(singleton(u),power_class(image(element_relation,universal_class)))*.
% 299.82/300.45  230855[10:MRR:230834.0,191.0] || well_ordering(universal_class,image(element_relation,power_class(successor_relation))) -> member(singleton(successor_relation),power_class(image(element_relation,universal_class)))*.
% 299.82/300.45  230898[10:MRR:230894.1,188662.0] || equal(u,universal_class) -> equal(regular(unordered_pair(u,unordered_pair(v,w))),unordered_pair(v,w))**.
% 299.82/300.45  231196[10:MRR:231191.1,188713.0] || subclass(universal_class,u) -> equal(regular(unordered_pair(ordered_pair(v,w),u)),ordered_pair(v,w))**.
% 299.82/300.45  231432[15:Rew:160223.0,231361.1,191621.1,231361.1] || equal(successor(image(element_relation,complement(u))),successor_relation)** -> equal(intersection(power_class(u),universal_class),universal_class).
% 299.82/300.45  231592[10:MRR:231590.1,188711.0] || equal(u,universal_class) -> equal(regular(unordered_pair(unordered_pair(v,w),u)),unordered_pair(v,w))**.
% 299.82/300.45  231623[24:Rew:222326.0,231611.0] || equal(sum_class(range_of(successor_relation)),kind_1_ordinals) member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> .
% 299.82/300.45  231664[25:SpR:224912.1,163032.0] function(intersection(u,universal_class)) ||  -> equal(complement(symmetric_difference(u,universal_class)),successor(intersection(u,universal_class)))**.
% 299.82/300.45  231727[10:MRR:231723.1,188646.0] || equal(u,universal_class) -> equal(regular(unordered_pair(u,ordered_pair(v,w))),ordered_pair(v,w))**.
% 299.82/300.45  231741[10:MRR:231739.1,188713.0] || equal(u,universal_class) -> equal(regular(unordered_pair(ordered_pair(v,w),u)),ordered_pair(v,w))**.
% 299.82/300.45  9630[0:Res:9424.0,3926.1] single_valued_class(restrict(cross_product(universal_class,universal_class),u,v)) ||  -> function(restrict(cross_product(universal_class,universal_class),u,v))*.
% 299.82/300.45  9823[0:Res:9421.0,9.0] || subclass(union(u,v),symmetric_difference(u,v))* -> equal(symmetric_difference(u,v),union(u,v)).
% 299.82/300.45  9841[0:Res:9811.0,9.0] || subclass(symmetrization_of(u),symmetric_difference(u,inverse(u)))* -> equal(symmetric_difference(u,inverse(u)),symmetrization_of(u)).
% 299.82/300.45  29193[0:SpR:506.0,9421.0] ||  -> subclass(symmetric_difference(intersection(complement(u),complement(v)),w),complement(intersection(union(u,v),complement(w))))*.
% 299.82/300.45  29277[0:SpR:507.0,9421.0] ||  -> subclass(symmetric_difference(u,intersection(complement(v),complement(w))),complement(intersection(complement(u),union(v,w))))*.
% 299.82/300.45  9851[0:Res:9812.0,9.0] || subclass(successor(u),symmetric_difference(u,singleton(u)))* -> equal(symmetric_difference(u,singleton(u)),successor(u)).
% 299.82/300.45  28578[0:Res:1477.1,513.0] || subclass(universal_class,intersection(complement(u),complement(v)))* member(singleton(w),union(u,v))* -> .
% 299.82/300.45  3669[0:SpL:28.0,2647.0] || subclass(universal_class,union(u,v)) member(singleton(w),intersection(complement(u),complement(v)))* -> .
% 299.82/300.45  9583[0:Res:3907.1,594.0] || equal(complement(complement(restrict(u,v,w))),universal_class)** -> member(singleton(x),cross_product(v,w))*.
% 299.82/300.45  9326[0:Res:1951.1,3670.1] || member(singleton(u),symmetric_difference(v,w))* equal(complement(complement(intersection(v,w))),universal_class) -> .
% 299.82/300.45  107695[0:Res:1481.2,6045.0] || subclass(u,v)* subclass(v,w)* well_ordering(universal_class,w)* -> subclass(u,x)*.
% 299.82/300.45  108317[0:SpL:30.0,9332.1] || member(u,symmetric_difference(v,cross_product(w,x)))* member(u,restrict(v,w,x)) -> .
% 299.82/300.45  108332[0:SpL:31.0,9332.1] || member(u,symmetric_difference(cross_product(v,w),x))* member(u,restrict(x,v,w)) -> .
% 299.82/300.45  111836[0:Res:1499.1,9322.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v)))* -> member(ordered_pair(w,x),union(u,v))*.
% 299.82/300.45  119675[0:Res:114897.1,513.0] || equal(intersection(complement(u),complement(v)),universal_class) member(singleton(w),union(u,v))* -> .
% 299.82/300.45  119980[0:SpR:114854.0,120.1] || transitive(universal_class,u) -> subclass(compose(cross_product(u,u),cross_product(u,u)),cross_product(u,u))*.
% 299.82/300.45  120001[0:SpL:114854.0,121.0] || subclass(compose(cross_product(u,u),cross_product(u,u)),cross_product(u,u))* -> transitive(universal_class,u).
% 299.82/300.45  120002[0:SpL:114854.0,5971.0] || equal(compose(cross_product(u,u),cross_product(u,u)),cross_product(u,u))** -> transitive(universal_class,u).
% 299.82/300.45  122152[0:Obv:122105.1] || member(u,v) -> subclass(intersection(singleton(u),w),intersection(v,intersection(singleton(u),w)))*.
% 299.82/300.45  122363[0:Obv:122314.1] || member(u,v) -> subclass(intersection(w,singleton(u)),intersection(v,intersection(w,singleton(u))))*.
% 299.82/300.45  125962[0:Res:28320.1,16.0] || subclass(rest_relation,rotate(cross_product(u,v)))* -> member(ordered_pair(w,rest_of(ordered_pair(x,w))),u)*.
% 299.82/300.45  126259[0:Res:8.1,9156.1] || equal(restrict(u,v,w),universal_class)** member(x,universal_class) -> member(power_class(x),u)*.
% 299.82/300.45  126370[0:Res:10258.1,6045.0] || subclass(successor(u),v)* well_ordering(universal_class,v) -> subclass(symmetric_difference(u,singleton(u)),w)*.
% 299.82/300.45  126384[0:Obv:126377.1] || subclass(symmetric_difference(u,singleton(u)),complement(successor(u)))* -> subclass(symmetric_difference(u,singleton(u)),v)*.
% 299.82/300.45  126438[0:Res:10194.1,6045.0] || subclass(symmetrization_of(u),v)* well_ordering(universal_class,v) -> subclass(symmetric_difference(u,inverse(u)),w)*.
% 299.82/300.45  126449[0:Obv:126445.1] || subclass(symmetric_difference(u,inverse(u)),complement(symmetrization_of(u)))* -> subclass(symmetric_difference(u,inverse(u)),v)*.
% 299.82/300.45  130937[0:SpR:10422.0,124.0] ||  -> equal(segment(cross_product(u,singleton(v)),w,x),segment(cross_product(w,singleton(x)),u,v))*.
% 299.82/300.45  131924[0:Obv:131866.1] || subclass(symmetric_difference(u,v),complement(complement(intersection(u,v))))* -> subclass(symmetric_difference(u,v),w)*.
% 299.82/300.45  3881[0:Res:25.2,1509.1] || member(omega,u) member(omega,v) equal(complement(intersection(v,u)),universal_class)** -> .
% 299.82/300.45  152925[0:Res:1506.1,9300.0] || equal(symmetric_difference(u,cross_product(v,w)),universal_class) -> member(omega,complement(restrict(u,v,w)))*.
% 299.82/300.45  152927[0:Res:1506.1,9306.0] || equal(symmetric_difference(cross_product(u,v),w),universal_class) -> member(omega,complement(restrict(w,u,v)))*.
% 299.82/300.45  155743[2:SpL:142543.0,9149.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(universal_class,v))* -> member(power_class(u),complement(v))*.
% 299.82/300.45  163413[10:Rew:160202.0,162986.1] ||  -> member(successor_relation,image(element_relation,union(u,v))) member(successor_relation,power_class(intersection(complement(u),complement(v))))*.
% 299.82/300.45  162586[10:Rew:160202.0,153487.0] || equal(compose(restrict(u,v,v),restrict(u,v,v)),successor_relation)** -> transitive(u,v).
% 299.82/300.45  162318[10:Rew:160202.0,150590.0] ||  -> equal(intersection(intersection(u,intersection(complement(v),power_class(successor_relation))),union(v,image(element_relation,universal_class))),successor_relation)**.
% 299.82/300.45  162317[10:Rew:160202.0,150589.0] ||  -> equal(intersection(intersection(intersection(complement(u),power_class(successor_relation)),v),union(u,image(element_relation,universal_class))),successor_relation)**.
% 299.82/300.45  162316[10:Rew:160202.0,150588.0] ||  -> equal(intersection(union(u,image(element_relation,universal_class)),intersection(v,intersection(complement(u),power_class(successor_relation)))),successor_relation)**.
% 299.82/300.45  162315[10:Rew:160202.0,150587.0] ||  -> equal(intersection(union(u,image(element_relation,universal_class)),intersection(intersection(complement(u),power_class(successor_relation)),v)),successor_relation)**.
% 299.82/300.45  162314[10:Rew:160202.0,150586.0] ||  -> equal(intersection(intersection(u,intersection(power_class(successor_relation),complement(v))),union(image(element_relation,universal_class),v)),successor_relation)**.
% 299.82/300.45  162313[10:Rew:160202.0,150585.0] ||  -> equal(intersection(intersection(intersection(power_class(successor_relation),complement(u)),v),union(image(element_relation,universal_class),u)),successor_relation)**.
% 299.82/300.45  162312[10:Rew:160202.0,150584.0] ||  -> equal(intersection(union(image(element_relation,universal_class),u),intersection(v,intersection(power_class(successor_relation),complement(u)))),successor_relation)**.
% 299.82/300.45  162311[10:Rew:160202.0,150583.0] ||  -> equal(intersection(union(image(element_relation,universal_class),u),intersection(intersection(power_class(successor_relation),complement(u)),v)),successor_relation)**.
% 299.82/300.45  161952[10:Rew:160202.0,148517.0] ||  -> equal(complement(complement(omega)),successor_relation) equal(integer_of(regular(complement(complement(omega)))),regular(complement(complement(omega))))**.
% 299.82/300.45  161947[10:Rew:160202.0,148479.0] ||  -> equal(integer_of(not_subclass_element(intersection(u,complement(omega)),v)),successor_relation)** subclass(intersection(u,complement(omega)),v).
% 299.82/300.45  161946[10:Rew:160202.0,148478.0] ||  -> equal(integer_of(not_subclass_element(intersection(complement(omega),u),v)),successor_relation)** subclass(intersection(complement(omega),u),v).
% 299.82/300.45  161935[10:Rew:160202.0,147867.0] ||  -> equal(intersection(power_class(image(element_relation,power_class(u))),image(element_relation,power_class(image(element_relation,complement(u))))),successor_relation)**.
% 299.82/300.45  161933[10:Rew:160202.0,147847.0] ||  -> equal(intersection(image(element_relation,power_class(image(element_relation,complement(u)))),power_class(image(element_relation,power_class(u)))),successor_relation)**.
% 299.82/300.45  161932[10:Rew:160202.0,147559.1] || member(regular(image(element_relation,kind_1_ordinals)),complement(image(element_relation,kind_1_ordinals)))* -> equal(image(element_relation,kind_1_ordinals),successor_relation).
% 299.82/300.45  161931[10:Rew:160202.0,147507.1] ||  -> member(regular(intersection(complement(complement(u)),v)),u)* equal(intersection(complement(complement(u)),v),successor_relation).
% 299.82/300.45  161930[10:Rew:160202.0,147480.1] ||  -> member(regular(intersection(u,complement(complement(v)))),v)* equal(intersection(u,complement(complement(v))),successor_relation).
% 299.82/300.45  161929[10:Rew:160202.0,147195.1] || subclass(cross_product(universal_class,universal_class),u)* -> equal(compose_class(v),successor_relation) member(regular(compose_class(v)),u)*.
% 299.82/300.45  161924[10:Rew:160202.0,147191.1] || subclass(cross_product(universal_class,universal_class),u)* -> equal(rest_of(v),successor_relation) member(regular(rest_of(v)),u)*.
% 299.82/300.45  161918[10:Rew:160202.0,147158.1] || subclass(universal_class,complement(unordered_pair(u,regular(cross_product(v,w)))))* -> equal(cross_product(v,w),successor_relation).
% 299.82/300.45  161919[10:Rew:160202.0,147157.1] || equal(complement(unordered_pair(u,regular(cross_product(v,w)))),universal_class)** -> equal(cross_product(v,w),successor_relation).
% 299.82/300.45  161898[10:Rew:160202.0,147082.2] || subclass(complement(u),v)* -> member(w,u)* equal(singleton(w),successor_relation) member(w,v)*.
% 299.82/300.45  161891[10:Rew:160202.0,146977.0] ||  -> equal(complement(complement(intersection(u,v))),successor_relation) member(regular(complement(complement(intersection(u,v)))),u)*.
% 299.82/300.45  161892[10:Rew:160202.0,146976.0] ||  -> equal(complement(complement(intersection(u,v))),successor_relation) member(regular(complement(complement(intersection(u,v)))),v)*.
% 299.82/300.45  163404[10:Rew:160202.0,161888.1] ||  -> equal(singleton(cross_product(u,v)),successor_relation) equal(restrict(singleton(cross_product(u,v)),u,v),successor_relation)**.
% 299.82/300.45  161885[10:Rew:160202.0,146866.1] || subclass(union(u,v),intersection(complement(u),complement(v)))* -> equal(union(u,v),successor_relation).
% 299.82/300.45  161820[10:Rew:160202.0,147277.1] || subclass(complement(union(u,v)),symmetric_difference(u,v))* -> equal(complement(union(u,v)),successor_relation).
% 299.82/300.45  161810[10:Rew:160202.0,153219.1] || equal(symmetric_difference(cross_product(u,v),w),universal_class) -> member(successor_relation,complement(restrict(w,u,v)))*.
% 299.82/300.45  161806[10:Rew:160202.0,153217.1] || equal(symmetric_difference(u,cross_product(v,w)),universal_class) -> member(successor_relation,complement(restrict(u,v,w)))*.
% 299.82/300.45  161802[10:Rew:160202.0,153228.1] || equal(power_class(image(element_relation,complement(u))),universal_class) member(successor_relation,image(element_relation,power_class(u)))* -> .
% 299.82/300.45  161782[10:Rew:160202.0,146702.0] ||  -> equal(unordered_pair(u,v),successor_relation) equal(apply(choice,unordered_pair(u,v)),u)** member(v,universal_class).
% 299.82/300.45  161783[10:Rew:160202.0,146701.0] ||  -> equal(unordered_pair(u,v),successor_relation) equal(apply(choice,unordered_pair(u,v)),v)** member(u,universal_class).
% 299.82/300.45  161688[10:Rew:160202.0,146728.2] || subclass(union(u,v),w)* well_ordering(universal_class,w) -> equal(symmetric_difference(u,v),successor_relation).
% 299.82/300.45  161614[10:Rew:160202.0,147329.0] ||  -> equal(restrict(singleton(u),v,w),successor_relation) equal(regular(restrict(singleton(u),v,w)),u)**.
% 299.82/300.45  161599[10:Rew:160202.0,146829.1] || subclass(universal_class,complement(unordered_pair(regular(cross_product(u,v)),w)))* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  161600[10:Rew:160202.0,146828.1] || equal(complement(unordered_pair(regular(cross_product(u,v)),w)),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  161656[10:Rew:160202.0,156053.0] || member(u,image(element_relation,union(v,successor_relation)))* member(u,power_class(symmetric_difference(universal_class,v))) -> .
% 299.82/300.45  161440[10:Rew:160202.0,146627.2] || equal(u,v)* subclass(u,w)* -> equal(v,successor_relation) member(regular(v),w)*.
% 299.82/300.45  161417[10:Rew:160202.0,146621.1] || subclass(u,v) -> equal(complement(complement(u)),successor_relation) member(regular(complement(complement(u))),v)*.
% 299.82/300.45  162020[10:Rew:160202.0,153414.0] || equal(sum_class(u),successor_relation) well_ordering(element_relation,u)* -> equal(u,ordinal_numbers) member(u,ordinal_numbers).
% 299.82/300.45  163400[10:Rew:160202.0,161222.1] || member(not_subclass_element(union(u,successor_relation),v),symmetric_difference(universal_class,u))* -> subclass(union(u,successor_relation),v).
% 299.82/300.45  163390[10:Rew:160202.0,160884.1] || subclass(image(element_relation,successor_relation),complement(power_class(universal_class)))* -> equal(image(element_relation,successor_relation),complement(power_class(universal_class))).
% 299.82/300.45  160873[10:Rew:160202.0,152636.1] || member(u,symmetric_difference(complement(v),power_class(universal_class)))* -> member(u,union(v,image(element_relation,successor_relation))).
% 299.82/300.45  160869[10:Rew:160202.0,152630.1] || member(u,symmetric_difference(power_class(universal_class),complement(v)))* -> member(u,union(image(element_relation,successor_relation),v)).
% 299.82/300.45  160847[10:Rew:160202.0,148333.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,successor_relation)))),union(u,image(element_relation,power_class(universal_class))))**.
% 299.82/300.45  160846[10:Rew:160202.0,148332.0] ||  -> equal(complement(intersection(power_class(image(element_relation,successor_relation)),complement(u))),union(image(element_relation,power_class(universal_class)),u))**.
% 299.82/300.45  160694[10:Rew:160202.0,159691.2] || equal(complement(complement(regular(u))),universal_class)** member(singleton(v),u)* -> equal(u,successor_relation).
% 299.82/300.45  160785[10:Rew:160202.0,146537.1] || subclass(u,symmetric_difference(v,inverse(v)))* -> equal(u,successor_relation) member(regular(u),symmetrization_of(v)).
% 299.82/300.45  160786[10:Rew:160202.0,146536.1] || subclass(u,symmetric_difference(v,singleton(v)))* -> equal(u,successor_relation) member(regular(u),successor(v)).
% 299.82/300.45  160787[10:Rew:160202.0,146493.3] || subclass(u,v)* subclass(v,w)* well_ordering(universal_class,w)* -> equal(u,successor_relation).
% 299.82/300.45  163382[10:Rew:160202.0,160543.1] || member(successor_relation,u) member(successor_relation,v) equal(complement(intersection(v,u)),universal_class)** -> .
% 299.82/300.45  168541[11:Res:168384.1,513.0] || equal(intersection(complement(u),complement(v)),symmetrization_of(successor_relation))** member(successor_relation,union(u,v)) -> .
% 299.82/300.45  161140[10:Rew:160202.0,152771.0] ||  -> equal(complement(intersection(complement(u),power_class(complement(inverse(successor_relation))))),union(u,image(element_relation,symmetrization_of(successor_relation))))**.
% 299.82/300.45  161139[10:Rew:160202.0,152746.0] ||  -> equal(complement(intersection(power_class(complement(inverse(successor_relation))),complement(u))),union(image(element_relation,symmetrization_of(successor_relation)),u))**.
% 299.82/300.45  163395[10:Rew:160202.0,161176.1] || subclass(complement(inverse(successor_relation)),complement(symmetrization_of(successor_relation)))* -> equal(complement(symmetrization_of(successor_relation)),complement(inverse(successor_relation))).
% 299.82/300.45  163396[10:Rew:160202.0,161179.1] || well_ordering(u,inverse(successor_relation)) -> equal(segment(u,symmetrization_of(successor_relation),least(u,symmetrization_of(successor_relation))),successor_relation)**.
% 299.82/300.45  163394[10:Rew:160202.0,161129.1] || member(u,symmetric_difference(complement(v),symmetrization_of(successor_relation)))* -> member(u,union(v,complement(inverse(successor_relation)))).
% 299.82/300.45  163393[10:Rew:160202.0,161128.1] || member(u,symmetric_difference(symmetrization_of(successor_relation),complement(v)))* -> member(u,union(complement(inverse(successor_relation)),v)).
% 299.82/300.45  163387[10:Rew:160202.0,160720.1,160202.0,160720.0] || subclass(u,symmetrization_of(successor_relation)) member(regular(u),complement(inverse(successor_relation)))* -> equal(u,successor_relation).
% 299.82/300.45  161056[10:Rew:160202.0,150381.0] || member(u,symmetric_difference(power_class(successor_relation),complement(v)))* -> member(u,union(image(element_relation,universal_class),v)).
% 299.82/300.45  161036[10:Rew:160202.0,150379.0] ||  -> member(u,intersection(power_class(successor_relation),complement(v))) subclass(singleton(u),union(image(element_relation,universal_class),v))*.
% 299.82/300.45  161031[10:Rew:160202.0,150374.0] || member(u,symmetric_difference(complement(v),power_class(successor_relation)))* -> member(u,union(v,image(element_relation,universal_class))).
% 299.82/300.45  161015[10:Rew:160202.0,150373.0] ||  -> member(u,intersection(complement(v),power_class(successor_relation))) subclass(singleton(u),union(v,image(element_relation,universal_class)))*.
% 299.82/300.45  163388[10:Rew:160202.0,160754.0] || subclass(u,power_class(successor_relation)) member(regular(u),image(element_relation,universal_class))* -> equal(u,successor_relation).
% 299.82/300.45  160943[10:Rew:160202.0,150377.0] ||  -> subclass(complement(power_class(intersection(complement(u),power_class(successor_relation)))),image(element_relation,union(u,image(element_relation,universal_class))))*.
% 299.82/300.45  160912[10:Rew:160202.0,150406.0] ||  -> subclass(complement(power_class(intersection(power_class(successor_relation),complement(u)))),image(element_relation,union(image(element_relation,universal_class),u)))*.
% 299.82/300.45  160975[10:Rew:160202.0,148449.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,universal_class)))),union(u,image(element_relation,power_class(successor_relation))))**.
% 299.82/300.45  160974[10:Rew:160202.0,148448.0] ||  -> equal(complement(intersection(power_class(image(element_relation,universal_class)),complement(u))),union(image(element_relation,power_class(successor_relation)),u))**.
% 299.82/300.45  163392[10:Rew:160202.0,160901.1] || subclass(image(element_relation,universal_class),complement(power_class(successor_relation)))* -> equal(image(element_relation,universal_class),complement(power_class(successor_relation))).
% 299.82/300.45  163391[10:Rew:160202.0,160900.1] || member(not_subclass_element(u,complement(power_class(successor_relation))),image(element_relation,universal_class))* -> subclass(u,complement(power_class(successor_relation))).
% 299.82/300.45  163091[10:Rew:160202.0,159360.1] || subclass(domain_relation,symmetric_difference(complement(u),complement(v)))* -> member(ordered_pair(successor_relation,successor_relation),union(u,v)).
% 299.82/300.45  163401[10:Rew:160202.0,161362.0] || equal(intersection(complement(u),complement(v)),successor(successor_relation))** member(successor_relation,union(u,v)) -> .
% 299.82/300.45  162891[10:Rew:160202.0,152495.0] ||  -> equal(complement(intersection(power_class(complement(singleton(successor_relation))),complement(u))),union(image(element_relation,successor(successor_relation)),u))**.
% 299.82/300.45  162890[10:Rew:160202.0,152520.0] ||  -> equal(complement(intersection(complement(u),power_class(complement(singleton(successor_relation))))),union(u,image(element_relation,successor(successor_relation))))**.
% 299.82/300.45  163412[10:Rew:160202.0,162882.1] || subclass(complement(singleton(successor_relation)),complement(successor(successor_relation)))* -> equal(complement(successor(successor_relation)),complement(singleton(successor_relation))).
% 299.82/300.45  163402[10:Rew:160202.0,161366.0] || equal(intersection(complement(u),complement(v)),singleton(successor_relation))** member(successor_relation,union(u,v)) -> .
% 299.82/300.45  163411[10:Rew:160202.0,162857.1] || well_ordering(u,singleton(successor_relation)) -> equal(segment(u,successor(successor_relation),least(u,successor(successor_relation))),successor_relation)**.
% 299.82/300.45  163409[10:Rew:160202.0,162795.0] || member(u,symmetric_difference(successor(successor_relation),complement(v)))* -> member(u,union(complement(singleton(successor_relation)),v)).
% 299.82/300.45  163408[10:Rew:160202.0,162792.0] || member(u,symmetric_difference(complement(v),successor(successor_relation)))* -> member(u,union(v,complement(singleton(successor_relation)))).
% 299.82/300.45  163386[10:Rew:160202.0,160708.1,160202.0,160708.0] || subclass(u,successor(successor_relation)) member(regular(u),complement(singleton(successor_relation)))* -> equal(u,successor_relation).
% 299.82/300.45  47886[0:Res:34085.1,3.0] || member(u,rest_of(u)) subclass(element_relation,v) -> member(ordered_pair(u,rest_of(u)),v)*.
% 299.82/300.45  157421[8:MRR:156982.2,146185.0] || member(u,cross_product(universal_class,universal_class)) member(u,complement(compose(complement(element_relation),inverse(element_relation))))* -> .
% 299.82/300.45  48353[0:Res:1481.2,47888.0] || subclass(u,rest_of(not_subclass_element(u,v)))* subclass(universal_class,complement(element_relation)) -> subclass(u,v).
% 299.82/300.45  96327[0:SpL:44.0,48051.0] || member(inverse(restrict(u,v,universal_class)),image(u,v))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.45  108476[0:Res:1504.1,47888.0] || subclass(ordered_pair(u,v),rest_of(unordered_pair(u,singleton(v))))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.45  125119[0:Res:34427.0,6045.0] || subclass(power_class(u),v)* well_ordering(universal_class,v) -> subclass(w,image(element_relation,complement(u)))*.
% 299.82/300.45  107244[0:Rew:57.0,107160.1] ||  -> member(not_subclass_element(complement(power_class(u)),v),image(element_relation,complement(u)))* subclass(complement(power_class(u)),v).
% 299.82/300.45  10345[0:SpR:57.0,10292.0] ||  -> subclass(symmetric_difference(power_class(u),complement(inverse(image(element_relation,complement(u))))),symmetrization_of(image(element_relation,complement(u))))*.
% 299.82/300.45  10364[0:SpR:57.0,10293.0] ||  -> subclass(symmetric_difference(power_class(u),complement(singleton(image(element_relation,complement(u))))),successor(image(element_relation,complement(u))))*.
% 299.82/300.45  3601[0:SpL:208.0,3565.0] || equal(complement(power_class(image(element_relation,complement(u)))),universal_class)** -> member(omega,image(element_relation,power_class(u))).
% 299.82/300.45  152936[0:Res:1506.1,986.1] || equal(power_class(image(element_relation,complement(u))),universal_class) member(omega,image(element_relation,power_class(u)))* -> .
% 299.82/300.45  3422[0:SpL:208.0,3358.1] || equal(image(element_relation,power_class(u)),universal_class) equal(power_class(image(element_relation,complement(u))),universal_class)** -> .
% 299.82/300.45  10312[0:SpR:208.0,9898.0] ||  -> subclass(symmetric_difference(power_class(image(element_relation,complement(u))),complement(v)),union(image(element_relation,power_class(u)),v))*.
% 299.82/300.45  30575[0:SpL:208.0,30433.1] || subclass(universal_class,image(element_relation,power_class(u))) subclass(universal_class,power_class(image(element_relation,complement(u))))* -> .
% 299.82/300.45  10301[0:SpR:208.0,9898.0] ||  -> subclass(symmetric_difference(complement(u),power_class(image(element_relation,complement(v)))),union(u,image(element_relation,power_class(v))))*.
% 299.82/300.45  158382[2:SpR:208.0,142477.0] ||  -> equal(symmetric_difference(power_class(image(element_relation,power_class(u))),image(element_relation,power_class(image(element_relation,complement(u))))),universal_class)**.
% 299.82/300.45  158345[2:SpR:208.0,142475.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(image(element_relation,complement(u)))),power_class(image(element_relation,power_class(u)))),universal_class)**.
% 299.82/300.45  125157[2:Rew:2473.0,125097.1,28.0,125097.1,2473.0,125097.0,28.0,125097.0] ||  -> member(not_subclass_element(u,image(element_relation,kind_1_ordinals)),complement(image(element_relation,kind_1_ordinals)))* subclass(u,image(element_relation,kind_1_ordinals)).
% 299.82/300.45  155741[2:SpL:142543.0,9121.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(universal_class,v))* -> member(sum_class(u),complement(v))*.
% 299.82/300.45  126333[0:Res:8.1,9128.1] || equal(restrict(u,v,w),universal_class)** member(x,universal_class) -> member(sum_class(x),u)*.
% 299.82/300.45  37818[0:Obv:37807.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w) member(u,universal_class).
% 299.82/300.45  37819[0:Obv:37800.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),w),u)** subclass(unordered_pair(u,v),w) member(v,universal_class).
% 299.82/300.45  108444[0:Res:1504.1,595.0] || subclass(ordered_pair(u,v),restrict(w,x,y))* -> member(unordered_pair(u,singleton(v)),w).
% 299.82/300.45  48047[0:SpL:1948.0,3487.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v)))* -> member(unordered_pair(w,x),union(u,v))*.
% 299.82/300.45  155737[2:SpL:142543.0,9639.0] || subclass(u,symmetric_difference(universal_class,v)) -> subclass(u,w) member(not_subclass_element(u,w),complement(v))*.
% 299.82/300.45  155807[3:Res:34429.0,141576.1] || member(not_subclass_element(complement(complement(complement(kind_1_ordinals))),u),ordinal_numbers)* -> subclass(complement(complement(complement(kind_1_ordinals))),u).
% 299.82/300.45  107174[0:Res:34429.0,26.1] || member(not_subclass_element(complement(complement(complement(u))),v),u)* -> subclass(complement(complement(complement(u))),v).
% 299.82/300.45  108357[0:Res:4.1,9332.1] || member(not_subclass_element(intersection(u,v),w),symmetric_difference(u,v))* -> subclass(intersection(u,v),w).
% 299.82/300.45  126779[0:Rew:161.0,126696.1] || member(not_subclass_element(symmetric_difference(u,v),w),intersection(u,v))* -> subclass(symmetric_difference(u,v),w).
% 299.82/300.45  41930[0:SpL:2330.1,30556.0] || equal(complement(singleton(not_subclass_element(cross_product(u,v),w))),universal_class)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  41929[0:SpL:2330.1,30537.0] || subclass(universal_class,complement(singleton(not_subclass_element(cross_product(u,v),w))))* -> subclass(cross_product(u,v),w).
% 299.82/300.45  112652[0:MRR:112629.0,34189.1] ||  -> member(not_subclass_element(complement(union(u,v)),w),complement(u))* subclass(complement(union(u,v)),w).
% 299.82/300.45  112491[0:MRR:112462.0,34189.1] ||  -> member(not_subclass_element(complement(union(u,v)),w),complement(v))* subclass(complement(union(u,v)),w).
% 299.82/300.45  132296[0:Res:8.1,9647.0] || equal(restrict(u,v,w),x)* -> subclass(x,y) member(not_subclass_element(x,y),u)*.
% 299.82/300.45  125280[0:Res:8.1,28304.1] || equal(compose_class(u),rest_relation) member(v,universal_class) -> equal(compose(u,v),rest_of(v))**.
% 299.82/300.45  125239[0:Res:8.1,28281.1] || equal(singleton(u),rest_relation)** member(v,universal_class) -> equal(ordered_pair(v,rest_of(v)),u)*.
% 299.82/300.45  160062[3:Res:159952.1,1487.1] || subclass(complement(u),ordinal_numbers)* member(v,universal_class) -> member(v,u)* member(v,kind_1_ordinals)*.
% 299.82/300.45  30801[0:Res:18.2,3514.1] || member(u,v)* member(w,x)* subclass(universal_class,complement(cross_product(x,v)))* -> .
% 299.82/300.45  179998[11:Res:179843.1,513.0] || equal(intersection(complement(u),complement(v)),inverse(successor_relation))** member(successor_relation,union(u,v)) -> .
% 299.82/300.45  181065[10:SpR:181056.0,60.1] || member(ordered_pair(universal_class,u),compose(v,w))* -> member(u,image(v,image(w,successor_relation))).
% 299.82/300.45  181181[10:SpR:181067.0,28321.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(singleton(singleton(successor_relation)),rest_of(ordered_pair(universal_class,successor_relation))),u)*.
% 299.82/300.45  181183[10:SpR:181067.0,18.2] || member(universal_class,u) member(successor_relation,v) -> member(singleton(singleton(successor_relation)),cross_product(v,u))*.
% 299.82/300.45  181185[10:SpR:181067.0,28320.1] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(universal_class,rest_of(singleton(singleton(successor_relation)))),successor_relation),u)*.
% 299.82/300.45  181186[10:SpR:181067.0,28321.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(universal_class,successor_relation),rest_of(singleton(singleton(successor_relation)))),u)*.
% 299.82/300.45  181462[10:SpR:208.0,163005.0] ||  -> equal(intersection(symmetric_difference(universal_class,image(element_relation,power_class(u))),complement(power_class(image(element_relation,complement(u))))),successor_relation)**.
% 299.82/300.45  181496[10:Rew:113504.0,181439.0,160223.0,181439.0] ||  -> equal(symmetric_difference(symmetric_difference(universal_class,u),complement(complement(u))),union(symmetric_difference(universal_class,u),complement(complement(u))))**.
% 299.82/300.45  181532[10:Rew:113504.0,181502.0,160223.0,181502.0] ||  -> equal(symmetric_difference(symmetric_difference(universal_class,singleton(successor_relation)),successor(successor_relation)),union(symmetric_difference(universal_class,singleton(successor_relation)),successor(successor_relation)))**.
% 299.82/300.45  181607[10:Rew:113504.0,181577.0,160223.0,181577.0] ||  -> equal(symmetric_difference(symmetric_difference(universal_class,inverse(successor_relation)),symmetrization_of(successor_relation)),union(symmetric_difference(universal_class,inverse(successor_relation)),symmetrization_of(successor_relation)))**.
% 299.82/300.45  181640[10:SpR:208.0,163000.0] ||  -> equal(intersection(complement(power_class(image(element_relation,complement(u)))),symmetric_difference(universal_class,image(element_relation,power_class(u)))),successor_relation)**.
% 299.82/300.45  181669[10:Rew:113504.0,181613.0,160223.0,181613.0] ||  -> equal(symmetric_difference(complement(complement(u)),symmetric_difference(universal_class,u)),union(complement(complement(u)),symmetric_difference(universal_class,u)))**.
% 299.82/300.45  181704[10:Rew:113504.0,181675.0,160223.0,181675.0] ||  -> equal(symmetric_difference(successor(successor_relation),symmetric_difference(universal_class,singleton(successor_relation))),union(successor(successor_relation),symmetric_difference(universal_class,singleton(successor_relation))))**.
% 299.82/300.45  181739[10:Rew:113504.0,181710.0,160223.0,181710.0] ||  -> equal(symmetric_difference(symmetrization_of(successor_relation),symmetric_difference(universal_class,inverse(successor_relation))),union(symmetrization_of(successor_relation),symmetric_difference(universal_class,inverse(successor_relation))))**.
% 299.82/300.45  182263[10:SpR:181082.0,1479.2] || member(image(u,successor_relation),universal_class) subclass(universal_class,v) -> member(apply(u,universal_class),v)*.
% 299.82/300.45  182353[10:SpL:208.0,160544.0] || equal(complement(power_class(image(element_relation,complement(u)))),universal_class)** -> member(successor_relation,image(element_relation,power_class(u))).
% 299.82/300.45  183226[10:Rew:181135.1,183225.2] || member(u,universal_class)* member(singleton(singleton(successor_relation)),compose_class(v))* -> equal(successor(u),universal_class).
% 299.82/300.45  183231[10:Rew:181136.1,183230.2] || member(u,universal_class)* member(singleton(singleton(successor_relation)),rest_of(v))* -> equal(successor(u),universal_class).
% 299.82/300.45  183380[0:SpR:28.0,139600.0] ||  -> equal(intersection(intersection(complement(u),complement(v)),complement(union(u,v))),complement(union(u,v)))**.
% 299.82/300.45  183494[10:SpR:505.0,183420.0] ||  -> equal(symmetric_difference(image(element_relation,union(u,v)),complement(power_class(intersection(complement(u),complement(v))))),successor_relation)**.
% 299.82/300.45  183812[10:Res:340.1,183622.0] ||  -> subclass(intersection(successor(successor_relation),u),v) member(not_subclass_element(intersection(successor(successor_relation),u),v),singleton(successor_relation))*.
% 299.82/300.45  183817[10:Res:322.1,183622.0] ||  -> subclass(intersection(u,successor(successor_relation)),v) member(not_subclass_element(intersection(u,successor(successor_relation)),v),singleton(successor_relation))*.
% 299.82/300.45  183845[10:Res:340.1,183723.0] ||  -> subclass(intersection(symmetrization_of(successor_relation),u),v) member(not_subclass_element(intersection(symmetrization_of(successor_relation),u),v),inverse(successor_relation))*.
% 299.82/300.45  183850[10:Res:322.1,183723.0] ||  -> subclass(intersection(u,symmetrization_of(successor_relation)),v) member(not_subclass_element(intersection(u,symmetrization_of(successor_relation)),v),inverse(successor_relation))*.
% 299.82/300.45  183926[11:Res:183764.1,9322.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v)))* -> member(regular(symmetrization_of(successor_relation)),union(u,v)).
% 299.82/300.45  184645[10:SpR:163198.1,1938.0] || subclass(complement(restrict(u,v,w)),successor_relation)* -> equal(symmetric_difference(u,cross_product(v,w)),successor_relation).
% 299.82/300.45  184646[10:SpR:163198.1,1943.0] || subclass(complement(restrict(u,v,w)),successor_relation)* -> equal(symmetric_difference(cross_product(v,w),u),successor_relation).
% 299.82/300.45  184949[10:SpR:208.0,184676.1] || subclass(image(element_relation,power_class(u)),successor_relation) -> equal(complement(power_class(image(element_relation,complement(u)))),successor_relation)**.
% 299.82/300.45  185513[10:SpL:185302.1,307.0] || equal(successor_relation,u) member(v,image(element_relation,universal_class))* member(v,power_class(u))* -> .
% 299.82/300.45  185807[10:Res:185430.1,9146.1] || equal(complement(complement(u)),successor_relation) member(v,universal_class) member(power_class(v),u)* -> .
% 299.82/300.45  185817[10:Res:185430.1,9150.1] || equal(complement(intersection(u,v)),successor_relation)** member(w,universal_class) -> member(power_class(w),v)*.
% 299.82/300.45  185818[10:Res:185430.1,9149.1] || equal(complement(intersection(u,v)),successor_relation)** member(w,universal_class) -> member(power_class(w),u)*.
% 299.82/300.45  163398[10:Rew:160202.0,161185.0] || subclass(unordered_pair(u,v),successor_relation)* member(u,universal_class) well_ordering(w,inverse(successor_relation))* -> .
% 299.82/300.45  163399[10:Rew:160202.0,161186.0] || subclass(unordered_pair(u,v),successor_relation)* member(v,universal_class) well_ordering(w,inverse(successor_relation))* -> .
% 299.82/300.45  163403[10:Rew:160202.0,161450.2] || well_ordering(u,universal_class) -> equal(singleton(v),successor_relation) equal(segment(u,singleton(v),v),successor_relation)**.
% 299.82/300.45  155801[3:Res:31069.2,141576.1] inductive(complement(kind_1_ordinals)) || well_ordering(u,universal_class) member(least(u,complement(kind_1_ordinals)),ordinal_numbers)* -> .
% 299.82/300.45  108242[2:Res:31069.2,26.1] inductive(complement(u)) || well_ordering(v,universal_class) member(least(v,complement(u)),u)* -> .
% 299.82/300.45  161449[10:Rew:160202.0,146645.1] || well_ordering(u,singleton(v)) -> equal(singleton(v),successor_relation) equal(least(u,singleton(v)),v)**.
% 299.82/300.45  108838[2:Res:31076.2,2151.0] inductive(singleton(u)) || well_ordering(v,singleton(u)) -> equal(least(v,singleton(u)),u)**.
% 299.82/300.45  187774[10:Res:187500.1,513.0] || subclass(universal_class,intersection(complement(u),complement(v)))* member(power_class(successor_relation),union(u,v)) -> .
% 299.82/300.45  189168[10:SpR:185608.1,1938.0] || equal(complement(restrict(u,v,w)),successor_relation) -> equal(symmetric_difference(u,cross_product(v,w)),successor_relation)**.
% 299.82/300.45  189169[10:SpR:185608.1,1943.0] || equal(complement(restrict(u,v,w)),successor_relation) -> equal(symmetric_difference(cross_product(v,w),u),successor_relation)**.
% 299.82/300.45  189328[15:SpL:124.0,188793.1] || member(restrict(u,v,singleton(w)),universal_class)* member(x,segment(u,v,w))* -> .
% 299.82/300.45  189407[15:Rew:189339.1,184850.2] || member(u,universal_class) subclass(domain_relation,symmetrization_of(successor_relation)) -> member(ordered_pair(u,successor_relation),inverse(successor_relation))*.
% 299.82/300.45  189409[15:Rew:189339.1,184855.2] || member(u,universal_class) subclass(domain_relation,successor(successor_relation)) -> member(ordered_pair(u,successor_relation),singleton(successor_relation))*.
% 299.82/300.45  190612[10:Res:173.1,185639.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class)* equal(complement(intersection(y__dfg,ordinal_numbers)),successor_relation) -> .
% 299.82/300.45  190688[15:MRR:190652.1,160354.1] || equal(successor_relation,u) -> equal(integer_of(restrict(v,w,u)),successor_relation)** section(v,u,w).
% 299.82/300.45  190689[15:MRR:190654.1,160215.0] || subclass(u,v) -> equal(integer_of(restrict(w,v,u)),successor_relation)** section(w,u,v).
% 299.82/300.45  190773[15:MRR:190736.1,160354.1] || equal(successor_relation,u) -> equal(singleton(restrict(v,w,u)),successor_relation)** section(v,u,w).
% 299.82/300.45  190774[15:MRR:190738.1,160215.0] || subclass(u,v) -> equal(singleton(restrict(w,v,u)),successor_relation)** section(w,u,v).
% 299.82/300.45  191008[15:Obv:190979.0] ||  -> equal(regular(unordered_pair(u,v)),u)** equal(unordered_pair(u,v),successor_relation) equal(cantor(v),successor_relation).
% 299.82/300.45  191009[15:Obv:190978.0] ||  -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),successor_relation) equal(cantor(u),successor_relation).
% 299.82/300.45  191109[20:Res:191074.1,9300.0] || equal(symmetric_difference(u,cross_product(v,w)),omega) -> member(successor_relation,complement(restrict(u,v,w)))*.
% 299.82/300.45  191111[20:Res:191074.1,9306.0] || equal(symmetric_difference(cross_product(u,v),w),omega) -> member(successor_relation,complement(restrict(w,u,v)))*.
% 299.82/300.45  192234[15:Rew:181135.1,192233.2] || member(singleton(singleton(successor_relation)),compose_class(u))* -> equal(range_of(v),successor_relation)** equal(inverse(v),universal_class).
% 299.82/300.45  192237[15:Rew:181136.1,192236.2] || member(singleton(singleton(successor_relation)),rest_of(u))* -> equal(range_of(v),successor_relation)** equal(inverse(v),universal_class).
% 299.82/300.45  192293[20:Res:25.2,191095.1] || member(successor_relation,u) member(successor_relation,v) equal(complement(intersection(v,u)),omega)** -> .
% 299.82/300.45  192475[20:SpL:208.0,191129.1] || equal(image(element_relation,power_class(u)),omega) equal(power_class(image(element_relation,complement(u))),universal_class)** -> .
% 299.82/300.45  192885[20:SpL:208.0,192315.1] || equal(image(element_relation,power_class(u)),omega) equal(power_class(image(element_relation,complement(u))),omega)** -> .
% 299.82/300.45  192897[20:SpL:208.0,192321.1] || equal(image(element_relation,power_class(u)),universal_class) equal(power_class(image(element_relation,complement(u))),omega)** -> .
% 299.82/300.45  192922[20:SpL:208.0,192323.0] || equal(complement(power_class(image(element_relation,complement(u)))),omega)** -> member(successor_relation,image(element_relation,power_class(u))).
% 299.82/300.45  192945[10:SpL:208.0,188851.0] || subclass(power_class(image(element_relation,complement(u))),successor_relation)* -> member(singleton(v),image(element_relation,power_class(u)))*.
% 299.82/300.45  193411[10:Res:192947.1,9322.0] || equal(complement(symmetric_difference(complement(u),complement(v))),successor_relation)** -> member(singleton(w),union(u,v))*.
% 299.82/300.45  193598[10:SpR:208.0,161321.0] ||  -> equal(intersection(restrict(image(element_relation,power_class(u)),v,w),power_class(image(element_relation,complement(u)))),successor_relation)**.
% 299.82/300.45  193636[10:Rew:113504.0,193566.0,160223.0,193566.0] ||  -> equal(symmetric_difference(restrict(u,v,w),complement(u)),union(restrict(u,v,w),complement(u)))**.
% 299.82/300.45  193696[10:SpR:208.0,161320.0] ||  -> equal(intersection(power_class(image(element_relation,complement(u))),restrict(image(element_relation,power_class(u)),v,w)),successor_relation)**.
% 299.82/300.45  193724[10:Rew:113504.0,193655.0,160223.0,193655.0] ||  -> equal(symmetric_difference(complement(u),restrict(u,v,w)),union(complement(u),restrict(u,v,w)))**.
% 299.82/300.45  193937[10:SpL:161592.1,185803.0] || equal(complement(complement(singleton(regular(cross_product(u,v))))),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  194084[15:Res:189374.2,193819.0] || member(u,universal_class) subclass(domain_relation,cantor(complement(cross_product(singleton(ordered_pair(u,successor_relation)),universal_class))))* -> .
% 299.82/300.45  194457[10:Rew:181082.0,194430.0] || equal(apply(u,universal_class),image(u,successor_relation)) -> subclass(apply(u,universal_class),image(u,successor_relation))*.
% 299.82/300.45  194502[0:SpL:208.0,183398.0] || member(u,complement(power_class(image(element_relation,complement(v)))))* -> member(u,image(element_relation,power_class(v))).
% 299.82/300.45  194531[15:Res:189374.2,183398.0] || member(u,universal_class) subclass(domain_relation,complement(complement(v)))* -> member(ordered_pair(u,successor_relation),v)*.
% 299.82/300.45  195782[6:Res:195710.1,135.1] || equal(inverse(u),universal_class) subclass(inverse(u),v) -> section(w,inverse(u),v)*.
% 299.82/300.45  195784[17:Res:195710.1,188715.0] || equal(inverse(u),universal_class) well_ordering(v,inverse(u))* -> member(least(v,omega),omega)*.
% 299.82/300.45  195803[6:Res:195710.1,2609.1] function(inverse(u)) || equal(inverse(u),universal_class) -> equal(cross_product(universal_class,universal_class),inverse(u))*.
% 299.82/300.45  195814[6:Res:195710.1,31922.0] || equal(inverse(u),universal_class) well_ordering(v,inverse(u))* -> member(least(v,rest_relation),rest_relation)*.
% 299.82/300.45  195841[6:Res:195720.1,135.1] || equal(sum_class(u),universal_class) subclass(sum_class(u),v) -> section(w,sum_class(u),v)*.
% 299.82/300.45  195843[17:Res:195720.1,188715.0] || equal(sum_class(u),universal_class) well_ordering(v,sum_class(u))* -> member(least(v,omega),omega)*.
% 299.82/300.45  195862[6:Res:195720.1,2609.1] function(sum_class(u)) || equal(sum_class(u),universal_class) -> equal(cross_product(universal_class,universal_class),sum_class(u))*.
% 299.82/300.45  195873[6:Res:195720.1,31922.0] || equal(sum_class(u),universal_class) well_ordering(v,sum_class(u))* -> member(least(v,rest_relation),rest_relation)*.
% 299.82/300.45  196009[0:SpR:1948.0,195152.0] ||  -> equal(intersection(union(u,v),symmetric_difference(complement(u),complement(v))),symmetric_difference(complement(u),complement(v)))**.
% 299.82/300.45  196552[10:SpL:161137.0,2647.0] || subclass(universal_class,power_class(complement(inverse(successor_relation)))) member(singleton(u),image(element_relation,symmetrization_of(successor_relation)))* -> .
% 299.82/300.45  196663[10:SpL:2330.1,185804.0] || equal(complement(complement(not_subclass_element(cross_product(u,v),w))),successor_relation)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  196686[10:SpL:2330.1,188713.0] || equal(unordered_pair(not_subclass_element(cross_product(u,v),w),x),successor_relation)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  196699[10:SpL:2330.1,188646.0] || equal(unordered_pair(u,not_subclass_element(cross_product(v,w),x)),successor_relation)** -> subclass(cross_product(v,w),x).
% 299.82/300.45  196758[10:SpL:162889.0,2647.0] || subclass(universal_class,power_class(complement(singleton(successor_relation)))) member(singleton(u),image(element_relation,successor(successor_relation)))* -> .
% 299.82/300.45  197035[10:MRR:163609.1,197033.0] || well_ordering(u,complement(singleton(successor_relation))) -> member(least(u,complement(successor(successor_relation))),complement(successor(successor_relation)))*.
% 299.82/300.45  199990[6:Res:199848.1,513.0] || subclass(universal_class,intersection(complement(u),complement(v)))* member(regular(rest_relation),union(u,v)) -> .
% 299.82/300.45  200201[14:Rew:181135.1,200200.2] || member(u,universal_class)* member(singleton(singleton(successor_relation)),compose_class(v))* -> equal(range_of(u),universal_class).
% 299.82/300.45  200204[14:Rew:181136.1,200203.2] || member(u,universal_class)* member(singleton(singleton(successor_relation)),rest_of(v))* -> equal(range_of(u),universal_class).
% 299.82/300.45  200271[6:SpL:199964.0,95.0] || member(regular(rest_relation),compose_class(u)) -> equal(compose(u,first(regular(rest_relation))),second(regular(rest_relation)))**.
% 299.82/300.45  200306[6:MRR:200305.1,199831.0] || equal(compose(u,first(regular(rest_relation))),second(regular(rest_relation)))** -> member(regular(rest_relation),compose_class(u)).
% 299.82/300.45  200665[10:Res:161493.2,9332.1] inductive(intersection(u,v)) || member(w,symmetric_difference(u,v))* -> equal(integer_of(w),successor_relation).
% 299.82/300.45  200669[10:Res:161493.2,594.0] inductive(restrict(u,v,w)) ||  -> equal(integer_of(x),successor_relation) member(x,cross_product(v,w))*.
% 299.82/300.45  200688[10:Res:161493.2,10.0] inductive(unordered_pair(u,v)) ||  -> equal(integer_of(w),successor_relation)** equal(w,v)* equal(w,u)*.
% 299.82/300.45  200689[10:Res:161493.2,307.0] inductive(image(element_relation,complement(u))) || member(v,power_class(u))* -> equal(integer_of(v),successor_relation).
% 299.82/300.45  200691[10:Res:161493.2,160481.0] inductive(regular(u)) || member(v,u)* -> equal(integer_of(v),successor_relation) equal(u,successor_relation).
% 299.82/300.45  200695[10:Res:161493.2,175.0] inductive(intersection(intersection(y__dfg,ordinal_numbers),u)) ||  -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation)**.
% 299.82/300.45  200696[10:Res:161493.2,178.0] inductive(intersection(u,intersection(y__dfg,ordinal_numbers))) ||  -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation)**.
% 299.82/300.45  200712[10:Res:161493.2,95.0] inductive(compose_class(u)) ||  -> equal(integer_of(ordered_pair(v,w)),successor_relation)** equal(compose(u,v),w)*.
% 299.82/300.45  200756[10:Res:161493.2,1013.0] inductive(rest_relation) ||  -> equal(integer_of(singleton(singleton(singleton(u)))),successor_relation)** equal(rest_of(singleton(u)),u).
% 299.82/300.45  201380[6:Res:201231.1,513.0] || subclass(universal_class,intersection(complement(u),complement(v)))* member(regular(domain_relation),union(u,v)) -> .
% 299.82/300.45  201515[6:SpL:201355.0,95.0] || member(regular(domain_relation),compose_class(u)) -> equal(compose(u,first(regular(domain_relation))),second(regular(domain_relation)))**.
% 299.82/300.45  201550[6:MRR:201549.1,201221.0] || equal(compose(u,first(regular(domain_relation))),second(regular(domain_relation)))** -> member(regular(domain_relation),compose_class(u)).
% 299.82/300.45  201680[10:Res:201671.0,160373.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(segment(u,complement(kind_1_ordinals),least(u,complement(kind_1_ordinals))),successor_relation)**.
% 299.82/300.45  201723[10:Res:161419.0,183398.0] ||  -> equal(complement(complement(complement(complement(u)))),successor_relation) member(regular(complement(complement(complement(complement(u))))),u)*.
% 299.82/300.45  201769[10:Rew:160367.0,201700.1] ||  -> member(regular(complement(union(u,successor_relation))),symmetric_difference(universal_class,u))* equal(complement(union(u,successor_relation)),successor_relation).
% 299.82/300.45  201916[10:Res:161492.2,309.0] || equal(u,omega) -> equal(integer_of(not_subclass_element(complement(u),v)),successor_relation)** subclass(complement(u),v).
% 299.82/300.45  201923[10:Res:161492.2,3.0] || equal(u,omega) subclass(u,v)* -> equal(integer_of(w),successor_relation) member(w,v)*.
% 299.82/300.45  201927[10:Res:161492.2,148657.1] || equal(complement(compose(element_relation,universal_class)),omega)** member(u,element_relation)* -> equal(integer_of(u),successor_relation).
% 299.82/300.45  201936[10:Res:161492.2,1952.0] || equal(symmetric_difference(u,v),omega) -> equal(integer_of(w),successor_relation) member(w,union(u,v))*.
% 299.82/300.45  201937[10:Res:161492.2,10191.0] || equal(symmetric_difference(u,inverse(u)),omega)** -> equal(integer_of(v),successor_relation) member(v,symmetrization_of(u))*.
% 299.82/300.45  201938[10:Res:161492.2,10254.0] || equal(symmetric_difference(u,singleton(u)),omega)** -> equal(integer_of(v),successor_relation) member(v,successor(u))*.
% 299.82/300.45  202004[10:Res:161492.2,155787.0] || equal(omega,ordinal_numbers) -> equal(integer_of(not_subclass_element(complement(kind_1_ordinals),u)),successor_relation)** subclass(complement(kind_1_ordinals),u).
% 299.82/300.45  202007[10:Res:161492.2,157982.0] || equal(omega,ordinal_numbers) -> equal(integer_of(cross_product(universal_class,universal_class)),successor_relation) member(least(element_relation,domain_relation),domain_relation)*.
% 299.82/300.45  202009[10:Res:161492.2,155791.1] || equal(omega,ordinal_numbers) subclass(universal_class,complement(kind_1_ordinals)) -> equal(integer_of(unordered_pair(u,v)),successor_relation)**.
% 299.82/300.45  202031[10:Res:161492.2,1012.0] || equal(omega,element_relation) -> equal(integer_of(singleton(singleton(singleton(u)))),successor_relation)** member(singleton(u),u)*.
% 299.82/300.45  202388[2:Res:141787.0,3486.1] || subclass(universal_class,complement(inverse(singleton(unordered_pair(u,v)))))* -> asymmetric(singleton(unordered_pair(u,v)),w)*.
% 299.82/300.45  202394[10:Res:161492.2,3486.1] || equal(u,omega) subclass(universal_class,complement(u))* -> equal(integer_of(unordered_pair(v,w)),successor_relation)**.
% 299.82/300.45  202418[10:Res:163225.0,6045.0] || subclass(symmetric_difference(universal_class,u),v)* well_ordering(universal_class,v) -> member(successor_relation,union(u,successor_relation)).
% 299.82/300.45  202462[10:SpR:161137.0,163217.0] ||  -> member(successor_relation,image(element_relation,power_class(complement(inverse(successor_relation)))))* member(successor_relation,power_class(image(element_relation,symmetrization_of(successor_relation)))).
% 299.82/300.45  202463[10:SpR:162889.0,163217.0] ||  -> member(successor_relation,image(element_relation,power_class(complement(singleton(successor_relation)))))* member(successor_relation,power_class(image(element_relation,successor(successor_relation)))).
% 299.82/300.45  202465[10:Res:163217.0,6045.0] || subclass(image(element_relation,complement(u)),v)* well_ordering(universal_class,v) -> member(successor_relation,power_class(u)).
% 299.82/300.45  202487[10:SpR:202485.1,124.0] || equal(rest_of(restrict(u,v,singleton(w))),successor_relation)** -> equal(segment(u,v,w),successor_relation).
% 299.82/300.45  202710[10:SpR:161194.0,1951.1] || member(u,symmetric_difference(union(v,successor_relation),universal_class))* -> member(u,complement(symmetric_difference(complement(v),universal_class))).
% 299.82/300.45  202739[10:SpL:161194.0,9332.1] || member(u,symmetric_difference(union(v,successor_relation),universal_class))* member(u,symmetric_difference(complement(v),universal_class)) -> .
% 299.82/300.45  202759[10:Rew:161194.0,202704.0] ||  -> equal(symmetric_difference(complement(u),universal_class),successor_relation) member(regular(symmetric_difference(complement(u),universal_class)),union(u,successor_relation))*.
% 299.82/300.45  202766[10:MRR:202765.0,34067.1] || member(u,complement(symmetric_difference(complement(v),universal_class))) -> member(u,symmetric_difference(union(v,successor_relation),universal_class))*.
% 299.82/300.45  202769[10:Rew:142543.0,202695.0,142542.0,202695.0,142542.0,202695.0] ||  -> equal(symmetric_difference(complement(symmetric_difference(complement(u),universal_class)),universal_class),symmetric_difference(universal_class,symmetric_difference(union(u,successor_relation),universal_class)))**.
% 299.82/300.45  202845[11:Res:1951.1,168534.1] || member(successor_relation,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),symmetrization_of(successor_relation))** -> .
% 299.82/300.45  203121[11:SpL:208.0,202882.1] inductive(image(element_relation,power_class(u))) || equal(power_class(image(element_relation,complement(u))),symmetrization_of(successor_relation))** -> .
% 299.82/300.45  204581[6:Rew:203192.0,203154.1] || equal(cantor(u),universal_class) -> subclass(cantor(u),v) member(not_subclass_element(universal_class,v),cantor(u))*.
% 299.82/300.45  203561[6:Rew:203192.0,119999.0] || equal(cantor(cross_product(u,v)),v)** subclass(v,u) -> section(universal_class,v,u).
% 299.82/300.45  203564[6:Rew:203192.0,120014.1] || subclass(u,v) subclass(cantor(cross_product(v,u)),u)* -> section(universal_class,u,v).
% 299.82/300.45  204618[6:Rew:203192.0,203853.0] || member(u,cantor(u)) subclass(element_relation,v) -> member(ordered_pair(u,cantor(u)),v)*.
% 299.82/300.45  203883[6:Rew:203192.0,125961.1] || subclass(rest_relation,rotate(rest_of(u))) -> member(ordered_pair(v,rest_of(ordered_pair(w,v))),cantor(u))*.
% 299.82/300.45  203928[10:Rew:203192.0,201971.2] || equal(rest_of(u),omega) -> equal(integer_of(ordered_pair(v,w)),successor_relation)** member(v,cantor(u))*.
% 299.82/300.45  203960[6:Rew:203192.0,156845.2] inductive(domain_of(u)) || well_ordering(v,universal_class) -> member(least(v,cantor(u)),cantor(u))*.
% 299.82/300.45  206049[10:Res:1951.1,163205.1] || member(successor_relation,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),successor(successor_relation))** -> .
% 299.82/300.45  206204[10:SpL:208.0,206082.1] inductive(image(element_relation,power_class(u))) || equal(power_class(image(element_relation,complement(u))),successor(successor_relation))** -> .
% 299.82/300.45  206240[10:MRR:206233.2,160455.0] || member(successor_relation,ordinal_numbers) well_ordering(u,kind_1_ordinals) -> member(least(u,successor(successor_relation)),successor(successor_relation))*.
% 299.82/300.45  206274[10:MRR:206242.2,160455.0] || member(successor_relation,u) well_ordering(v,u)* -> member(least(v,successor(successor_relation)),successor(successor_relation))*.
% 299.82/300.45  206973[10:Res:206947.1,9300.0] || equal(symmetric_difference(u,cross_product(v,w)),kind_1_ordinals) -> member(successor_relation,complement(restrict(u,v,w)))*.
% 299.82/300.45  206975[10:Res:206947.1,9306.0] || equal(symmetric_difference(cross_product(u,v),w),kind_1_ordinals) -> member(successor_relation,complement(restrict(w,u,v)))*.
% 299.82/300.45  207551[10:MRR:207540.2,160455.0] || well_ordering(u,complement(v))* -> member(successor_relation,v) member(least(u,successor(successor_relation)),successor(successor_relation))*.
% 299.82/300.45  208223[10:Res:25.2,206958.1] || member(successor_relation,u) member(successor_relation,v) equal(complement(intersection(v,u)),kind_1_ordinals)** -> .
% 299.82/300.45  208360[10:SpL:208.0,206962.0] || equal(complement(power_class(image(element_relation,complement(u)))),kind_1_ordinals)** -> member(successor_relation,image(element_relation,power_class(u))).
% 299.82/300.45  208399[20:SpL:208.0,206996.1] || equal(image(element_relation,power_class(u)),kind_1_ordinals) equal(power_class(image(element_relation,complement(u))),omega)** -> .
% 299.82/300.45  208413[10:SpL:208.0,206997.1] || equal(image(element_relation,power_class(u)),kind_1_ordinals) equal(power_class(image(element_relation,complement(u))),universal_class)** -> .
% 299.82/300.45  208486[10:SpL:208.0,208250.1] || equal(image(element_relation,power_class(u)),kind_1_ordinals) equal(power_class(image(element_relation,complement(u))),kind_1_ordinals)** -> .
% 299.82/300.45  208500[20:SpL:208.0,208251.1] || equal(image(element_relation,power_class(u)),omega) equal(power_class(image(element_relation,complement(u))),kind_1_ordinals)** -> .
% 299.82/300.45  208514[10:SpL:208.0,208257.1] || equal(image(element_relation,power_class(u)),universal_class) equal(power_class(image(element_relation,complement(u))),kind_1_ordinals)** -> .
% 299.82/300.45  208810[21:Res:208805.0,160373.0] || well_ordering(u,symmetrization_of(successor_relation)) -> equal(segment(u,successor(successor_relation),least(u,successor(successor_relation))),successor_relation)**.
% 299.82/300.45  208888[10:SpL:28.0,162918.1] || equal(intersection(complement(u),complement(v)),successor(successor_relation))** equal(union(u,v),universal_class) -> .
% 299.82/300.45  208899[10:SpL:161137.0,162918.1] || equal(image(element_relation,symmetrization_of(successor_relation)),successor(successor_relation))** equal(power_class(complement(inverse(successor_relation))),universal_class) -> .
% 299.82/300.45  208900[10:SpL:162889.0,162918.1] || equal(image(element_relation,successor(successor_relation)),successor(successor_relation))** equal(power_class(complement(singleton(successor_relation))),universal_class) -> .
% 299.82/300.45  208909[10:Res:1951.1,163207.1] || member(successor_relation,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),singleton(successor_relation))** -> .
% 299.82/300.45  209070[10:SpL:208.0,208945.1] inductive(image(element_relation,power_class(u))) || equal(power_class(image(element_relation,complement(u))),singleton(successor_relation))** -> .
% 299.82/300.45  209075[10:SpL:28.0,162872.1] || equal(intersection(complement(u),complement(v)),singleton(successor_relation))** equal(union(u,v),universal_class) -> .
% 299.82/300.45  209086[10:SpL:161137.0,162872.1] || equal(image(element_relation,symmetrization_of(successor_relation)),singleton(successor_relation))** equal(power_class(complement(inverse(successor_relation))),universal_class) -> .
% 299.82/300.45  209087[10:SpL:162889.0,162872.1] || equal(image(element_relation,successor(successor_relation)),singleton(successor_relation))** equal(power_class(complement(singleton(successor_relation))),universal_class) -> .
% 299.82/300.45  209457[12:Res:209377.1,513.0] || subclass(universal_class,intersection(complement(u),complement(v)))* member(regular(element_relation),union(u,v)) -> .
% 299.82/300.45  209535[12:SpL:209433.0,95.0] || member(regular(element_relation),compose_class(u)) -> equal(compose(u,first(regular(element_relation))),second(regular(element_relation)))**.
% 299.82/300.45  209570[12:MRR:209569.1,209313.0] || equal(compose(u,first(regular(element_relation))),second(regular(element_relation)))** -> member(regular(element_relation),compose_class(u)).
% 299.82/300.45  210359[15:Res:189563.1,595.0] || subclass(domain_relation,flip(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,y),successor_relation),u)*.
% 299.82/300.45  210379[15:Res:189563.1,47888.0] || subclass(domain_relation,flip(rest_of(ordered_pair(ordered_pair(u,v),successor_relation))))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.45  210386[15:Res:189563.1,184007.1] || subclass(domain_relation,flip(cross_product(universal_class,universal_class)))* equal(sum_class(range_of(ordered_pair(u,v))),successor_relation)** -> .
% 299.82/300.45  210432[15:Res:189564.1,595.0] || subclass(domain_relation,rotate(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,successor_relation),y),u)*.
% 299.82/300.45  210687[10:Res:34429.0,183723.0] ||  -> subclass(complement(complement(symmetrization_of(successor_relation))),u) member(not_subclass_element(complement(complement(symmetrization_of(successor_relation))),u),inverse(successor_relation))*.
% 299.82/300.45  210689[10:Res:34429.0,183622.0] ||  -> subclass(complement(complement(successor(successor_relation))),u) member(not_subclass_element(complement(complement(successor(successor_relation))),u),singleton(successor_relation))*.
% 299.82/300.45  210885[15:MRR:210853.1,183757.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) -> member(ordered_pair(regular(symmetrization_of(successor_relation)),successor_relation),u)*.
% 299.82/300.45  211056[11:Res:1951.1,179992.1] || member(successor_relation,symmetric_difference(u,v)) equal(complement(complement(intersection(u,v))),inverse(successor_relation))** -> .
% 299.82/300.45  211266[11:SpL:208.0,211092.1] inductive(image(element_relation,power_class(u))) || equal(power_class(image(element_relation,complement(u))),inverse(successor_relation))** -> .
% 299.82/300.45  211331[10:SpL:181073.0,10.0] || member(u,ordered_pair(universal_class,v))* -> equal(u,unordered_pair(universal_class,singleton(v))) equal(u,successor_relation).
% 299.82/300.45  211386[10:SpL:211297.0,160488.0] || member(intersection(y__dfg,ordinal_numbers),ordered_pair(universal_class,universal_class))* -> equal(intersection(y__dfg,ordinal_numbers),unordered_pair(universal_class,successor_relation)).
% 299.82/300.45  211535[10:SpL:208.0,211448.0] || well_ordering(universal_class,power_class(image(element_relation,complement(u))))* -> member(singleton(successor_relation),image(element_relation,power_class(u))).
% 299.82/300.45  211631[10:SpR:208.0,211579.1] ||  -> member(singleton(successor_relation),image(element_relation,power_class(u))) member(singleton(successor_relation),power_class(image(element_relation,complement(u))))*.
% 299.82/300.45  211678[10:Res:181213.1,9332.1] || equal(intersection(u,v),singleton(singleton(successor_relation))) member(singleton(successor_relation),symmetric_difference(u,v))* -> .
% 299.82/300.45  211682[10:Res:181213.1,594.0] || equal(restrict(u,v,w),singleton(singleton(successor_relation)))** -> member(singleton(successor_relation),cross_product(v,w))*.
% 299.82/300.45  211700[10:Res:181213.1,307.0] || equal(image(element_relation,complement(u)),singleton(singleton(successor_relation))) member(singleton(successor_relation),power_class(u))* -> .
% 299.82/300.45  211702[10:Res:181213.1,160481.0] || equal(regular(u),singleton(singleton(successor_relation))) member(singleton(successor_relation),u)* -> equal(u,successor_relation).
% 299.82/300.45  211768[10:Rew:142543.0,211738.1] || equal(singleton(u),successor_relation) -> equal(complement(image(element_relation,successor(u))),power_class(symmetric_difference(universal_class,u)))**.
% 299.82/300.45  211785[11:SpL:28.0,182321.1] || equal(intersection(complement(u),complement(v)),inverse(successor_relation))** equal(union(u,v),universal_class) -> .
% 299.82/300.45  211796[11:SpL:161137.0,182321.1] || equal(image(element_relation,symmetrization_of(successor_relation)),inverse(successor_relation))** equal(power_class(complement(inverse(successor_relation))),universal_class) -> .
% 299.82/300.45  211797[11:SpL:162889.0,182321.1] || equal(image(element_relation,successor(successor_relation)),inverse(successor_relation))** equal(power_class(complement(singleton(successor_relation))),universal_class) -> .
% 299.82/300.45  211864[10:Rew:142543.0,211835.1] || equal(inverse(u),successor_relation) -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(symmetric_difference(universal_class,u)))**.
% 299.82/300.45  211952[10:SpR:161137.0,183456.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(complement(inverse(successor_relation)))),complement(power_class(image(element_relation,symmetrization_of(successor_relation))))),successor_relation)**.
% 299.82/300.45  211953[10:SpR:162889.0,183456.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(complement(singleton(successor_relation)))),complement(power_class(image(element_relation,successor(successor_relation))))),successor_relation)**.
% 299.82/300.45  211976[11:Res:183759.1,9332.1] || subclass(inverse(successor_relation),intersection(u,v)) member(regular(symmetrization_of(successor_relation)),symmetric_difference(u,v))* -> .
% 299.82/300.45  211980[11:Res:183759.1,594.0] || subclass(inverse(successor_relation),restrict(u,v,w))* -> member(regular(symmetrization_of(successor_relation)),cross_product(v,w)).
% 299.82/300.45  211998[11:Res:183759.1,307.0] || subclass(inverse(successor_relation),image(element_relation,complement(u)))* member(regular(symmetrization_of(successor_relation)),power_class(u)) -> .
% 299.82/300.45  212000[11:Res:183759.1,160481.0] || subclass(inverse(successor_relation),regular(u))* member(regular(symmetrization_of(successor_relation)),u) -> equal(u,successor_relation).
% 299.82/300.45  212049[10:SpR:161137.0,184090.1] || equal(symmetric_difference(universal_class,image(element_relation,symmetrization_of(successor_relation))),universal_class)** -> member(omega,power_class(complement(inverse(successor_relation)))).
% 299.82/300.45  212050[10:SpR:162889.0,184090.1] || equal(symmetric_difference(universal_class,image(element_relation,successor(successor_relation))),universal_class)** -> member(omega,power_class(complement(singleton(successor_relation)))).
% 299.82/300.45  212053[2:Res:184090.1,6045.0] || equal(symmetric_difference(universal_class,u),universal_class) subclass(complement(u),v)* well_ordering(universal_class,v) -> .
% 299.82/300.45  212104[10:MRR:212082.0,160295.1] ||  -> member(regular(regular(complement(u))),u)* equal(regular(complement(u)),successor_relation) equal(complement(u),successor_relation).
% 299.82/300.45  212138[10:SpL:161137.0,184637.0] || subclass(power_class(complement(inverse(successor_relation))),successor_relation) -> equal(symmetric_difference(universal_class,image(element_relation,symmetrization_of(successor_relation))),successor_relation)**.
% 299.82/300.45  212139[10:SpL:162889.0,184637.0] || subclass(power_class(complement(singleton(successor_relation))),successor_relation) -> equal(symmetric_difference(universal_class,image(element_relation,successor(successor_relation))),successor_relation)**.
% 299.82/300.45  212479[10:SpL:28.0,185801.0] || equal(complement(union(u,v)),successor_relation) subclass(universal_class,intersection(complement(u),complement(v)))* -> .
% 299.82/300.45  212490[10:SpL:161137.0,185801.0] || equal(complement(power_class(complement(inverse(successor_relation)))),successor_relation) subclass(universal_class,image(element_relation,symmetrization_of(successor_relation)))* -> .
% 299.82/300.45  212491[10:SpL:162889.0,185801.0] || equal(complement(power_class(complement(singleton(successor_relation)))),successor_relation) subclass(universal_class,image(element_relation,successor(successor_relation)))* -> .
% 299.82/300.45  212496[10:SpL:28.0,185935.0] || equal(complement(union(u,v)),successor_relation) member(successor_relation,intersection(complement(u),complement(v)))* -> .
% 299.82/300.45  212507[10:SpL:161137.0,185935.0] || equal(complement(power_class(complement(inverse(successor_relation)))),successor_relation) member(successor_relation,image(element_relation,symmetrization_of(successor_relation)))* -> .
% 299.82/300.45  212508[10:SpL:162889.0,185935.0] || equal(complement(power_class(complement(singleton(successor_relation)))),successor_relation) member(successor_relation,image(element_relation,successor(successor_relation)))* -> .
% 299.82/300.45  212513[13:MRR:163590.1,212512.0] || well_ordering(u,image(element_relation,successor_relation)) -> member(least(u,complement(power_class(universal_class))),complement(power_class(universal_class)))*.
% 299.82/300.45  212519[10:MRR:163591.1,212517.0] || well_ordering(u,image(element_relation,universal_class)) -> member(least(u,complement(power_class(successor_relation))),complement(power_class(successor_relation)))*.
% 299.82/300.45  212856[10:SpL:28.0,186009.0] || equal(complement(union(u,v)),successor_relation) member(omega,intersection(complement(u),complement(v)))* -> .
% 299.82/300.45  212867[10:SpL:161137.0,186009.0] || equal(complement(power_class(complement(inverse(successor_relation)))),successor_relation) member(omega,image(element_relation,symmetrization_of(successor_relation)))* -> .
% 299.82/300.45  212868[10:SpL:162889.0,186009.0] || equal(complement(power_class(complement(singleton(successor_relation)))),successor_relation) member(omega,image(element_relation,successor(successor_relation)))* -> .
% 299.82/300.45  212972[10:SpL:28.0,187767.0] || subclass(universal_class,union(u,v)) member(power_class(successor_relation),intersection(complement(u),complement(v)))* -> .
% 299.82/300.45  212983[10:SpL:161137.0,187767.0] || subclass(universal_class,power_class(complement(inverse(successor_relation)))) member(power_class(successor_relation),image(element_relation,symmetrization_of(successor_relation)))* -> .
% 299.82/300.45  212984[10:SpL:162889.0,187767.0] || subclass(universal_class,power_class(complement(singleton(successor_relation)))) member(power_class(successor_relation),image(element_relation,successor(successor_relation)))* -> .
% 299.82/300.45  213107[10:SpR:161137.0,188444.1] || equal(symmetric_difference(universal_class,image(element_relation,symmetrization_of(successor_relation))),universal_class)** -> member(successor_relation,power_class(complement(inverse(successor_relation)))).
% 299.82/300.45  213108[10:SpR:162889.0,188444.1] || equal(symmetric_difference(universal_class,image(element_relation,successor(successor_relation))),universal_class)** -> member(successor_relation,power_class(complement(singleton(successor_relation)))).
% 299.82/300.45  213147[10:SpL:160322.0,160800.0] || subclass(u,power_class(universal_class)) member(regular(u),image(element_relation,successor_relation))* -> equal(u,successor_relation).
% 299.82/300.45  213207[15:Res:189485.1,9332.1] || subclass(domain_relation,intersection(u,v)) member(singleton(singleton(singleton(successor_relation))),symmetric_difference(u,v))* -> .
% 299.82/300.45  213211[15:Res:189485.1,594.0] || subclass(domain_relation,restrict(u,v,w))* -> member(singleton(singleton(singleton(successor_relation))),cross_product(v,w))*.
% 299.82/300.45  213229[15:Res:189485.1,307.0] || subclass(domain_relation,image(element_relation,complement(u))) member(singleton(singleton(singleton(successor_relation))),power_class(u))* -> .
% 299.82/300.45  213231[15:Res:189485.1,160481.0] || subclass(domain_relation,regular(u)) member(singleton(singleton(singleton(successor_relation))),u)* -> equal(u,successor_relation).
% 299.82/300.45  213319[15:SpL:208.0,213296.1] || equal(image(element_relation,power_class(u)),domain_relation) equal(power_class(image(element_relation,complement(u))),universal_class)** -> .
% 299.82/300.45  213804[20:SpL:28.0,192317.1] || equal(intersection(complement(u),complement(v)),inverse(successor_relation))** equal(union(u,v),omega) -> .
% 299.82/300.45  213815[20:SpL:161137.0,192317.1] || equal(image(element_relation,symmetrization_of(successor_relation)),inverse(successor_relation))** equal(power_class(complement(inverse(successor_relation))),omega) -> .
% 299.82/300.45  213816[20:SpL:162889.0,192317.1] || equal(image(element_relation,successor(successor_relation)),inverse(successor_relation))** equal(power_class(complement(singleton(successor_relation))),omega) -> .
% 299.82/300.45  213818[20:SpL:28.0,192318.1] || equal(intersection(complement(u),complement(v)),singleton(successor_relation))** equal(union(u,v),omega) -> .
% 299.82/300.45  213829[20:SpL:161137.0,192318.1] || equal(image(element_relation,symmetrization_of(successor_relation)),singleton(successor_relation))** equal(power_class(complement(inverse(successor_relation))),omega) -> .
% 299.82/300.45  213830[20:SpL:162889.0,192318.1] || equal(image(element_relation,successor(successor_relation)),singleton(successor_relation))** equal(power_class(complement(singleton(successor_relation))),omega) -> .
% 299.82/300.45  213832[20:SpL:28.0,192319.1] || equal(intersection(complement(u),complement(v)),successor(successor_relation))** equal(union(u,v),omega) -> .
% 299.82/300.45  213843[20:SpL:161137.0,192319.1] || equal(image(element_relation,symmetrization_of(successor_relation)),successor(successor_relation))** equal(power_class(complement(inverse(successor_relation))),omega) -> .
% 299.82/300.45  213844[20:SpL:162889.0,192319.1] || equal(image(element_relation,successor(successor_relation)),successor(successor_relation))** equal(power_class(complement(singleton(successor_relation))),omega) -> .
% 299.82/300.45  214141[20:SpR:161137.0,193270.1] || equal(symmetric_difference(universal_class,image(element_relation,symmetrization_of(successor_relation))),omega)** -> member(successor_relation,power_class(complement(inverse(successor_relation)))).
% 299.82/300.45  214142[20:SpR:162889.0,193270.1] || equal(symmetric_difference(universal_class,image(element_relation,successor(successor_relation))),omega)** -> member(successor_relation,power_class(complement(singleton(successor_relation)))).
% 299.82/300.45  214144[20:Res:193270.1,6045.0] || equal(symmetric_difference(universal_class,u),omega) subclass(complement(u),v)* well_ordering(universal_class,v) -> .
% 299.82/300.45  214226[10:SpL:28.0,194513.0] || equal(complement(complement(union(u,v))),successor_relation) -> member(omega,intersection(complement(u),complement(v)))*.
% 299.82/300.45  214237[10:SpL:161137.0,194513.0] || equal(complement(complement(power_class(complement(inverse(successor_relation))))),successor_relation)** -> member(omega,image(element_relation,symmetrization_of(successor_relation))).
% 299.82/300.45  214238[10:SpL:162889.0,194513.0] || equal(complement(complement(power_class(complement(singleton(successor_relation))))),successor_relation)** -> member(omega,image(element_relation,successor(successor_relation))).
% 299.82/300.45  214256[10:SpL:28.0,194520.0] || subclass(universal_class,complement(union(u,v))) -> member(power_class(successor_relation),intersection(complement(u),complement(v)))*.
% 299.82/300.45  214267[10:SpL:161137.0,194520.0] || subclass(universal_class,complement(power_class(complement(inverse(successor_relation)))))* -> member(power_class(successor_relation),image(element_relation,symmetrization_of(successor_relation))).
% 299.82/300.45  214268[10:SpL:162889.0,194520.0] || subclass(universal_class,complement(power_class(complement(singleton(successor_relation)))))* -> member(power_class(successor_relation),image(element_relation,successor(successor_relation))).
% 299.82/300.45  214302[10:Res:214277.1,9322.0] || equal(complement(symmetric_difference(complement(u),complement(v))),successor_relation)** -> member(power_class(successor_relation),union(u,v)).
% 299.82/300.45  214337[10:SpL:28.0,194540.0] || equal(complement(complement(union(u,v))),successor_relation) -> member(successor_relation,intersection(complement(u),complement(v)))*.
% 299.82/300.45  214348[10:SpL:161137.0,194540.0] || equal(complement(complement(power_class(complement(inverse(successor_relation))))),successor_relation)** -> member(successor_relation,image(element_relation,symmetrization_of(successor_relation))).
% 299.82/300.45  214349[10:SpL:162889.0,194540.0] || equal(complement(complement(power_class(complement(singleton(successor_relation))))),successor_relation)** -> member(successor_relation,image(element_relation,successor(successor_relation))).
% 299.82/300.45  214584[11:SpL:28.0,194541.0] || equal(complement(union(u,v)),inverse(successor_relation)) -> member(successor_relation,intersection(complement(u),complement(v)))*.
% 299.82/300.45  214595[11:SpL:161137.0,194541.0] || equal(complement(power_class(complement(inverse(successor_relation)))),inverse(successor_relation)) -> member(successor_relation,image(element_relation,symmetrization_of(successor_relation)))*.
% 299.82/300.45  214596[11:SpL:162889.0,194541.0] || equal(complement(power_class(complement(singleton(successor_relation)))),inverse(successor_relation)) -> member(successor_relation,image(element_relation,successor(successor_relation)))*.
% 299.82/300.45  214607[10:SpR:204452.0,195540.1] || subclass(universal_class,segment(u,v,w)) -> equal(symmetric_difference(universal_class,segment(u,v,w)),successor_relation)**.
% 299.82/300.45  214653[10:SpL:28.0,194542.0] || equal(complement(union(u,v)),singleton(successor_relation)) -> member(successor_relation,intersection(complement(u),complement(v)))*.
% 299.82/300.45  214664[10:SpL:161137.0,194542.0] || equal(complement(power_class(complement(inverse(successor_relation)))),singleton(successor_relation)) -> member(successor_relation,image(element_relation,symmetrization_of(successor_relation)))*.
% 299.82/300.45  214665[10:SpL:162889.0,194542.0] || equal(complement(power_class(complement(singleton(successor_relation)))),singleton(successor_relation)) -> member(successor_relation,image(element_relation,successor(successor_relation)))*.
% 299.82/300.45  214672[10:SpL:28.0,194543.0] || equal(complement(union(u,v)),successor(successor_relation)) -> member(successor_relation,intersection(complement(u),complement(v)))*.
% 299.82/300.45  214683[10:SpL:161137.0,194543.0] || equal(complement(power_class(complement(inverse(successor_relation)))),successor(successor_relation)) -> member(successor_relation,image(element_relation,symmetrization_of(successor_relation)))*.
% 299.82/300.45  214684[10:SpL:162889.0,194543.0] || equal(complement(power_class(complement(singleton(successor_relation)))),successor(successor_relation)) -> member(successor_relation,image(element_relation,successor(successor_relation)))*.
% 299.82/300.45  214692[11:SpL:28.0,194544.0] || equal(complement(union(u,v)),symmetrization_of(successor_relation)) -> member(successor_relation,intersection(complement(u),complement(v)))*.
% 299.82/300.45  214703[11:SpL:161137.0,194544.0] || equal(complement(power_class(complement(inverse(successor_relation)))),symmetrization_of(successor_relation)) -> member(successor_relation,image(element_relation,symmetrization_of(successor_relation)))*.
% 299.82/300.45  214704[11:SpL:162889.0,194544.0] || equal(complement(power_class(complement(singleton(successor_relation)))),symmetrization_of(successor_relation)) -> member(successor_relation,image(element_relation,successor(successor_relation)))*.
% 299.82/300.45  214723[10:SpL:161137.0,195403.0] || subclass(universal_class,power_class(complement(inverse(successor_relation)))) -> equal(symmetric_difference(universal_class,image(element_relation,symmetrization_of(successor_relation))),universal_class)**.
% 299.82/300.45  214724[10:SpL:162889.0,195403.0] || subclass(universal_class,power_class(complement(singleton(successor_relation)))) -> equal(symmetric_difference(universal_class,image(element_relation,successor(successor_relation))),universal_class)**.
% 299.82/300.45  215249[10:Rew:162965.0,215146.1] || member(not_subclass_element(symmetric_difference(universal_class,u),successor_relation),union(u,successor_relation))* -> subclass(symmetric_difference(universal_class,u),successor_relation).
% 299.82/300.45  215251[10:Rew:163005.0,215114.1] || member(not_subclass_element(complement(complement(u)),successor_relation),symmetric_difference(universal_class,u))* -> subclass(complement(complement(u)),successor_relation).
% 299.82/300.45  215252[10:Rew:163000.0,215098.1] || member(not_subclass_element(symmetric_difference(universal_class,u),successor_relation),complement(complement(u)))* -> subclass(symmetric_difference(universal_class,u),successor_relation).
% 299.82/300.45  215253[10:Rew:161847.0,215160.1] || member(not_subclass_element(power_class(successor_relation),successor_relation),intersection(image(element_relation,universal_class),u))* -> subclass(power_class(successor_relation),successor_relation).
% 299.82/300.45  215254[10:Rew:161852.0,215159.1] || member(not_subclass_element(power_class(successor_relation),successor_relation),intersection(u,image(element_relation,universal_class)))* -> subclass(power_class(successor_relation),successor_relation).
% 299.82/300.45  215265[10:Rew:163006.0,215140.1] || member(not_subclass_element(power_class(universal_class),successor_relation),intersection(image(element_relation,successor_relation),u))* -> subclass(power_class(universal_class),successor_relation).
% 299.82/300.45  215266[10:Rew:163008.0,215139.1] || member(not_subclass_element(power_class(universal_class),successor_relation),intersection(u,image(element_relation,successor_relation)))* -> subclass(power_class(universal_class),successor_relation).
% 299.82/300.45  215505[10:Rew:160366.0,215301.1] || equal(inverse(u),universal_class) -> subclass(complement(complement(complement(inverse(inverse(u))))),symmetrization_of(inverse(u)))*.
% 299.82/300.45  215506[10:Rew:160366.0,215303.1] || equal(inverse(u),universal_class) -> subclass(complement(complement(complement(singleton(inverse(u))))),successor(inverse(u)))*.
% 299.82/300.45  215781[10:Rew:160366.0,215615.1] || equal(sum_class(u),universal_class) -> subclass(complement(complement(complement(inverse(sum_class(u))))),symmetrization_of(sum_class(u)))*.
% 299.82/300.45  215782[10:Rew:160366.0,215617.1] || equal(sum_class(u),universal_class) -> subclass(complement(complement(complement(singleton(sum_class(u))))),successor(sum_class(u)))*.
% 299.82/300.45  215870[10:Res:197082.1,9332.1] || subclass(universal_class,intersection(u,v)) member(regular(complement(successor(successor_relation))),symmetric_difference(u,v))* -> .
% 299.82/300.45  215874[10:Res:197082.1,594.0] || subclass(universal_class,restrict(u,v,w))* -> member(regular(complement(successor(successor_relation))),cross_product(v,w))*.
% 299.82/300.45  215892[10:Res:197082.1,307.0] || subclass(universal_class,image(element_relation,complement(u))) member(regular(complement(successor(successor_relation))),power_class(u))* -> .
% 299.82/300.45  215894[10:Res:197082.1,160481.0] || subclass(universal_class,regular(u)) member(regular(complement(successor(successor_relation))),u)* -> equal(u,successor_relation).
% 299.82/300.45  215912[10:Res:185430.1,155798.1] || equal(complement(complement(kind_1_ordinals)),successor_relation) member(u,universal_class) member(power_class(u),ordinal_numbers)* -> .
% 299.82/300.45  216111[6:Res:199830.1,9332.1] || equal(intersection(u,v),cross_product(universal_class,universal_class)) member(regular(rest_relation),symmetric_difference(u,v))* -> .
% 299.82/300.45  216115[6:Res:199830.1,594.0] || equal(restrict(u,v,w),cross_product(universal_class,universal_class))** -> member(regular(rest_relation),cross_product(v,w))*.
% 299.82/300.45  216133[6:Res:199830.1,307.0] || equal(image(element_relation,complement(u)),cross_product(universal_class,universal_class)) member(regular(rest_relation),power_class(u))* -> .
% 299.82/300.45  216135[10:Res:199830.1,160481.0] || equal(regular(u),cross_product(universal_class,universal_class)) member(regular(rest_relation),u)* -> equal(u,successor_relation).
% 299.82/300.45  216193[10:Res:185430.1,155799.1] || equal(complement(complement(kind_1_ordinals)),successor_relation) member(u,universal_class) member(sum_class(u),ordinal_numbers)* -> .
% 299.82/300.45  216369[14:Rew:160223.0,216226.1] || member(u,universal_class) -> subclass(symmetric_difference(complement(sum_class(range_of(u))),universal_class),successor(sum_class(range_of(u))))*.
% 299.82/300.45  216374[14:Rew:204010.0,216279.1] || member(u,universal_class) -> equal(segment(v,w,sum_class(range_of(u))),segment(v,w,universal_class))**.
% 299.82/300.45  216380[14:Rew:181085.0,216271.1] || member(u,universal_class) -> equal(range__dfg(v,sum_class(range_of(u)),w),range__dfg(v,universal_class,w))**.
% 299.82/300.45  216381[14:Rew:181087.0,216277.1] || member(u,universal_class) -> equal(domain__dfg(v,w,sum_class(range_of(u))),domain__dfg(v,w,universal_class))**.
% 299.82/300.45  216384[14:Rew:199971.1,216296.2] || member(u,universal_class) member(singleton(singleton(successor_relation)),element_relation)* -> member(successor_relation,sum_class(range_of(u)))*.
% 299.82/300.45  216393[14:Rew:181135.1,216392.2,200201.2,216392.2] || member(u,universal_class)* member(singleton(singleton(successor_relation)),compose_class(v))* -> equal(sum_class(universal_class),universal_class).
% 299.82/300.45  216396[14:Rew:181136.1,216395.2,200204.2,216395.2] || member(u,universal_class)* member(singleton(singleton(successor_relation)),rest_of(v))* -> equal(sum_class(universal_class),universal_class).
% 299.82/300.45  216423[6:SpL:28.0,199982.0] || subclass(universal_class,union(u,v)) member(regular(rest_relation),intersection(complement(u),complement(v)))* -> .
% 299.82/300.45  216435[10:SpL:161137.0,199982.0] || subclass(universal_class,power_class(complement(inverse(successor_relation)))) member(regular(rest_relation),image(element_relation,symmetrization_of(successor_relation)))* -> .
% 299.82/300.45  216436[10:SpL:162889.0,199982.0] || subclass(universal_class,power_class(complement(singleton(successor_relation)))) member(regular(rest_relation),image(element_relation,successor(successor_relation)))* -> .
% 299.82/300.45  216442[6:SpL:28.0,199986.0] || subclass(universal_class,complement(union(u,v))) -> member(regular(rest_relation),intersection(complement(u),complement(v)))*.
% 299.82/300.45  216454[10:SpL:161137.0,199986.0] || subclass(universal_class,complement(power_class(complement(inverse(successor_relation)))))* -> member(regular(rest_relation),image(element_relation,symmetrization_of(successor_relation))).
% 299.82/300.45  216455[10:SpL:162889.0,199986.0] || subclass(universal_class,complement(power_class(complement(singleton(successor_relation)))))* -> member(regular(rest_relation),image(element_relation,successor(successor_relation))).
% 299.82/300.45  216488[10:Res:216465.1,9322.0] || equal(complement(symmetric_difference(complement(u),complement(v))),successor_relation)** -> member(regular(rest_relation),union(u,v)).
% 299.82/300.45  216719[6:Res:201220.1,9332.1] || equal(intersection(u,v),cross_product(universal_class,universal_class)) member(regular(domain_relation),symmetric_difference(u,v))* -> .
% 299.82/300.45  216723[6:Res:201220.1,594.0] || equal(restrict(u,v,w),cross_product(universal_class,universal_class))** -> member(regular(domain_relation),cross_product(v,w))*.
% 299.82/300.45  216741[6:Res:201220.1,307.0] || equal(image(element_relation,complement(u)),cross_product(universal_class,universal_class)) member(regular(domain_relation),power_class(u))* -> .
% 299.82/300.45  216743[10:Res:201220.1,160481.0] || equal(regular(u),cross_product(universal_class,universal_class)) member(regular(domain_relation),u)* -> equal(u,successor_relation).
% 299.82/300.45  216805[6:SpL:28.0,201372.0] || subclass(universal_class,union(u,v)) member(regular(domain_relation),intersection(complement(u),complement(v)))* -> .
% 299.82/300.45  216817[10:SpL:161137.0,201372.0] || subclass(universal_class,power_class(complement(inverse(successor_relation)))) member(regular(domain_relation),image(element_relation,symmetrization_of(successor_relation)))* -> .
% 299.82/300.45  216818[10:SpL:162889.0,201372.0] || subclass(universal_class,power_class(complement(singleton(successor_relation)))) member(regular(domain_relation),image(element_relation,successor(successor_relation)))* -> .
% 299.82/300.45  216824[6:SpL:28.0,201376.0] || subclass(universal_class,complement(union(u,v))) -> member(regular(domain_relation),intersection(complement(u),complement(v)))*.
% 299.82/300.45  216836[10:SpL:161137.0,201376.0] || subclass(universal_class,complement(power_class(complement(inverse(successor_relation)))))* -> member(regular(domain_relation),image(element_relation,symmetrization_of(successor_relation))).
% 299.82/300.45  216837[10:SpL:162889.0,201376.0] || subclass(universal_class,complement(power_class(complement(singleton(successor_relation)))))* -> member(regular(domain_relation),image(element_relation,successor(successor_relation))).
% 299.82/300.45  216876[12:MRR:216867.2,185618.0] || member(apply(choice,regular(compose(element_relation,universal_class))),element_relation)* -> equal(regular(compose(element_relation,universal_class)),successor_relation).
% 299.82/300.45  216916[10:Res:216847.1,9322.0] || equal(complement(symmetric_difference(complement(u),complement(v))),successor_relation)** -> member(regular(domain_relation),union(u,v)).
% 299.82/300.45  217000[20:SpL:28.0,202875.1] || equal(intersection(complement(u),complement(v)),omega)** equal(union(u,v),symmetrization_of(successor_relation)) -> .
% 299.82/300.45  217010[20:SpL:161137.0,202875.1] || equal(image(element_relation,symmetrization_of(successor_relation)),omega)** equal(power_class(complement(inverse(successor_relation))),symmetrization_of(successor_relation)) -> .
% 299.82/300.45  217011[20:SpL:162889.0,202875.1] || equal(image(element_relation,successor(successor_relation)),omega)** equal(power_class(complement(singleton(successor_relation))),symmetrization_of(successor_relation)) -> .
% 299.82/300.45  217016[11:SpL:28.0,202881.1] || equal(intersection(complement(u),complement(v)),universal_class)** equal(union(u,v),symmetrization_of(successor_relation)) -> .
% 299.82/300.45  217026[11:SpL:161137.0,202881.1] || equal(image(element_relation,symmetrization_of(successor_relation)),universal_class)** equal(power_class(complement(inverse(successor_relation))),symmetrization_of(successor_relation)) -> .
% 299.82/300.45  217027[11:SpL:162889.0,202881.1] || equal(image(element_relation,successor(successor_relation)),universal_class)** equal(power_class(complement(singleton(successor_relation))),symmetrization_of(successor_relation)) -> .
% 299.82/300.45  217051[10:Res:185430.1,9118.1] || equal(complement(complement(u)),successor_relation) member(v,universal_class) member(sum_class(v),u)* -> .
% 299.82/300.45  217121[20:SpL:28.0,206075.1] || equal(intersection(complement(u),complement(v)),omega)** equal(union(u,v),successor(successor_relation)) -> .
% 299.82/300.45  217133[20:SpL:161137.0,206075.1] || equal(image(element_relation,symmetrization_of(successor_relation)),omega)** equal(power_class(complement(inverse(successor_relation))),successor(successor_relation)) -> .
% 299.82/300.45  217134[20:SpL:162889.0,206075.1] || equal(image(element_relation,successor(successor_relation)),omega)** equal(power_class(complement(singleton(successor_relation))),successor(successor_relation)) -> .
% 299.82/300.45  217138[10:SpL:28.0,206081.1] || equal(intersection(complement(u),complement(v)),universal_class)** equal(union(u,v),successor(successor_relation)) -> .
% 299.82/300.45  217150[10:SpL:161137.0,206081.1] || equal(image(element_relation,symmetrization_of(successor_relation)),universal_class)** equal(power_class(complement(inverse(successor_relation))),successor(successor_relation)) -> .
% 299.82/300.45  217151[10:SpL:162889.0,206081.1] || equal(image(element_relation,successor(successor_relation)),universal_class)** equal(power_class(complement(singleton(successor_relation))),successor(successor_relation)) -> .
% 299.82/300.45  217276[10:MRR:217242.2,185591.0] || equal(singleton(apply(choice,complement(singleton(successor_relation)))),kind_1_ordinals)** member(complement(singleton(successor_relation)),universal_class) -> .
% 299.82/300.45  217440[20:MRR:217405.2,185591.0] || equal(singleton(apply(choice,complement(singleton(successor_relation)))),omega)** member(complement(singleton(successor_relation)),universal_class) -> .
% 299.82/300.45  217588[10:MRR:217558.2,184594.0] || subclass(universal_class,regular(inverse(singleton(unordered_pair(u,v)))))* -> asymmetric(singleton(unordered_pair(u,v)),w)*.
% 299.82/300.45  217771[10:Res:185430.1,9122.1] || equal(complement(intersection(u,v)),successor_relation)** member(w,universal_class) -> member(sum_class(w),v)*.
% 299.82/300.45  217866[10:Res:185430.1,9121.1] || equal(complement(intersection(u,v)),successor_relation)** member(w,universal_class) -> member(sum_class(w),u)*.
% 299.82/300.45  218259[10:SpL:2330.1,217909.0] || equal(complement(regular(not_subclass_element(cross_product(u,v),w))),successor_relation)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  218308[12:MRR:218283.2,185618.0] || member(not_subclass_element(regular(compose(element_relation,universal_class)),u),element_relation)* -> subclass(regular(compose(element_relation,universal_class)),u).
% 299.82/300.45  218426[10:Res:218370.0,9.0] || subclass(successor(successor_relation),regular(complement(singleton(successor_relation))))* -> equal(regular(complement(singleton(successor_relation))),successor(successor_relation)).
% 299.82/300.45  218434[13:Res:218371.0,9.0] || subclass(power_class(universal_class),regular(image(element_relation,successor_relation)))* -> equal(regular(image(element_relation,successor_relation)),power_class(universal_class)).
% 299.82/300.45  218445[10:Res:218372.0,9.0] || subclass(power_class(successor_relation),regular(image(element_relation,universal_class)))* -> equal(regular(image(element_relation,universal_class)),power_class(successor_relation)).
% 299.82/300.45  218468[10:Res:185430.1,9587.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> member(unordered_pair(x,y),cross_product(v,w))*.
% 299.82/300.45  218492[6:Res:203330.1,217932.0] || section(u,complement(kind_1_ordinals),v) -> subclass(cantor(restrict(u,v,complement(kind_1_ordinals))),complement(ordinal_numbers))*.
% 299.82/300.45  218503[10:Res:218497.0,160373.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(segment(u,regular(kind_1_ordinals),least(u,regular(kind_1_ordinals))),successor_relation)**.
% 299.82/300.45  218532[3:Res:218494.0,9.0] || subclass(complement(ordinal_numbers),complement(complement(complement(kind_1_ordinals))))* -> equal(complement(complement(complement(kind_1_ordinals))),complement(ordinal_numbers)).
% 299.82/300.45  218622[3:Res:218475.0,9.0] || subclass(complement(ordinal_numbers),intersection(complement(kind_1_ordinals),u))* -> equal(intersection(complement(kind_1_ordinals),u),complement(ordinal_numbers)).
% 299.82/300.45  218656[3:Res:218485.0,9.0] || subclass(complement(ordinal_numbers),intersection(u,complement(kind_1_ordinals)))* -> equal(intersection(u,complement(kind_1_ordinals)),complement(ordinal_numbers)).
% 299.82/300.45  218887[22:Res:218867.1,513.0] || subclass(kind_1_ordinals,intersection(complement(u),complement(v)))* member(singleton(successor_relation),union(u,v)) -> .
% 299.82/300.45  219023[10:Res:185430.1,9639.0] || equal(complement(intersection(u,v)),successor_relation)** -> subclass(universal_class,w) member(not_subclass_element(universal_class,w),u)*.
% 299.82/300.45  219130[3:Res:218473.1,1485.1] || equal(unordered_pair(u,v),complement(kind_1_ordinals))** member(u,universal_class) -> member(u,complement(ordinal_numbers))*.
% 299.82/300.45  219132[3:Res:218473.1,1484.1] || equal(unordered_pair(u,v),complement(kind_1_ordinals))** member(v,universal_class) -> member(v,complement(ordinal_numbers))*.
% 299.82/300.45  219161[3:Res:218473.1,31922.0] || equal(complement(kind_1_ordinals),rest_relation) well_ordering(u,complement(ordinal_numbers)) -> member(least(u,rest_relation),rest_relation)*.
% 299.82/300.45  219180[3:Res:34429.0,218628.0] ||  -> subclass(complement(complement(complement(kind_1_ordinals))),u) member(not_subclass_element(complement(complement(complement(kind_1_ordinals))),u),complement(ordinal_numbers))*.
% 299.82/300.45  219181[3:Res:340.1,218628.0] ||  -> subclass(intersection(complement(kind_1_ordinals),u),v) member(not_subclass_element(intersection(complement(kind_1_ordinals),u),v),complement(ordinal_numbers))*.
% 299.82/300.45  219191[3:Res:322.1,218628.0] ||  -> subclass(intersection(u,complement(kind_1_ordinals)),v) member(not_subclass_element(intersection(u,complement(kind_1_ordinals)),v),complement(ordinal_numbers))*.
% 299.82/300.45  219198[10:Res:160482.2,218628.0] || well_ordering(u,universal_class) -> equal(complement(kind_1_ordinals),successor_relation) member(least(u,complement(kind_1_ordinals)),complement(ordinal_numbers))*.
% 299.82/300.45  219200[3:Res:31069.2,218628.0] inductive(complement(kind_1_ordinals)) || well_ordering(u,universal_class) -> member(least(u,complement(kind_1_ordinals)),complement(ordinal_numbers))*.
% 299.82/300.45  219201[15:Res:189374.2,218628.0] || member(u,universal_class) subclass(domain_relation,complement(kind_1_ordinals)) -> member(ordered_pair(u,successor_relation),complement(ordinal_numbers))*.
% 299.82/300.45  219337[10:Res:185430.1,9640.0] || equal(complement(intersection(u,v)),successor_relation)** -> subclass(universal_class,w) member(not_subclass_element(universal_class,w),v)*.
% 299.82/300.45  215268[10:Rew:163251.0,215117.1] || member(not_subclass_element(complement(kind_1_ordinals),successor_relation),symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> subclass(complement(kind_1_ordinals),successor_relation).
% 299.82/300.45  201942[10:Res:161492.2,163294.0] || equal(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),omega)** -> equal(integer_of(u),successor_relation) member(u,kind_1_ordinals)*.
% 299.82/300.45  163424[10:Rew:160202.0,160707.0,160305.0,160707.0] || subclass(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> equal(u,successor_relation) member(regular(u),kind_1_ordinals).
% 299.82/300.45  163507[10:Rew:160202.0,162824.1,160305.0,162824.1,160305.0,162824.0] || subclass(kind_1_ordinals,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> equal(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),kind_1_ordinals).
% 299.82/300.45  163509[10:Rew:160305.0,162859.0] ||  -> subclass(symmetric_difference(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals),complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation))))*.
% 299.82/300.45  193551[10:Res:141787.0,163256.1] || equal(inverse(singleton(successor_relation)),range_of(successor_relation)) -> asymmetric(singleton(successor_relation),u)* inductive(inverse(singleton(successor_relation)))*.
% 299.82/300.45  182943[10:Res:157922.1,163256.1] || member(successor_relation,element_relation) equal(compose(element_relation,universal_class),range_of(successor_relation)) -> inductive(compose(element_relation,universal_class))*.
% 299.82/300.45  163385[10:Rew:160202.0,160641.0] || member(ordered_pair(u,not_subclass_element(v,range_of(successor_relation))),compose(successor_relation,w))* -> subclass(v,range_of(successor_relation)).
% 299.82/300.45  163545[10:Rew:160305.0,163155.2] inductive(intersection(u,v)) ||  -> subclass(range_of(successor_relation),w) member(not_subclass_element(range_of(successor_relation),w),u)*.
% 299.82/300.45  163546[10:Rew:160305.0,163156.2] inductive(intersection(u,v)) ||  -> subclass(range_of(successor_relation),w) member(not_subclass_element(range_of(successor_relation),w),v)*.
% 299.82/300.45  166983[10:MRR:166962.0,160214.0] || equal(union(u,v),range_of(successor_relation)) -> member(successor_relation,complement(u)) inductive(union(u,v))*.
% 299.82/300.45  166984[10:MRR:166963.0,160214.0] || equal(union(u,v),range_of(successor_relation)) -> member(successor_relation,complement(v)) inductive(union(u,v))*.
% 299.82/300.45  167679[10:Res:9424.0,163335.1] inductive(restrict(range_of(successor_relation),u,v)) ||  -> equal(restrict(range_of(successor_relation),u,v),range_of(successor_relation))**.
% 299.82/300.45  213128[10:Res:188444.1,163256.1] || equal(symmetric_difference(universal_class,u),universal_class)** equal(range_of(successor_relation),complement(u)) -> inductive(complement(u)).
% 299.82/300.45  214162[20:Res:193270.1,163256.1] || equal(symmetric_difference(universal_class,u),omega)** equal(range_of(successor_relation),complement(u)) -> inductive(complement(u)).
% 299.82/300.45  163663[10:Rew:160305.0,162466.2,160305.0,162466.1] inductive(restrict(u,v,w)) ||  -> equal(range_of(successor_relation),successor_relation) member(regular(range_of(successor_relation)),u)*.
% 299.82/300.45  184375[10:SoR:164882.0,160511.2] single_valued_class(range_of(successor_relation)) || member(successor_relation,cross_product(universal_class,universal_class))* equal(range_of(successor_relation),successor_relation) -> .
% 299.82/300.45  211430[10:Rew:142543.0,211417.1] || equal(range_of(successor_relation),successor_relation) -> equal(power_class(symmetric_difference(universal_class,singleton(successor_relation))),complement(image(element_relation,kind_1_ordinals)))**.
% 299.82/300.45  216524[10:SpR:163341.1,181082.0] ||  -> equal(cross_product(successor_relation,universal_class),successor_relation) equal(apply(regular(cross_product(successor_relation,universal_class)),universal_class),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  203798[10:Rew:203192.0,160585.0] || subclass(universal_class,complement(cantor(u))) -> equal(apply(u,unordered_pair(v,w)),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  204617[10:Rew:203192.0,203793.0] ||  -> equal(apply(u,regular(complement(cantor(u)))),sum_class(range_of(successor_relation)))** equal(complement(cantor(u)),successor_relation).
% 299.82/300.45  220891[10:SpL:2330.1,219813.0] || subclass(universal_class,regular(singleton(not_subclass_element(cross_product(u,v),w))))* -> subclass(cross_product(u,v),w).
% 299.82/300.45  220929[10:SpL:2330.1,220897.0] || equal(regular(singleton(not_subclass_element(cross_product(u,v),w))),universal_class)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  221309[10:SpL:161592.1,220898.0] || equal(complement(regular(singleton(regular(cross_product(u,v))))),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  221389[6:SpL:203285.0,149509.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),range_of(u))* subclass(universal_class,intersection(y__dfg,ordinal_numbers)) -> .
% 299.82/300.45  221412[6:SpL:204209.0,149509.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),inverse(u))* subclass(universal_class,intersection(y__dfg,ordinal_numbers)) -> .
% 299.82/300.45  221413[6:SpL:204281.0,149509.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),sum_class(u))* subclass(universal_class,intersection(y__dfg,ordinal_numbers)) -> .
% 299.82/300.45  221429[6:Rew:194805.1,221423.2] || subclass(ordinal_numbers,y__dfg) member(least(element_relation,ordinal_numbers),cantor(u))* subclass(universal_class,ordinal_numbers) -> .
% 299.82/300.45  221442[10:Res:218373.0,9.0] || subclass(complement(singleton(u)),u)* -> equal(singleton(u),successor_relation) equal(complement(singleton(u)),u).
% 299.82/300.45  221509[10:Res:218373.0,206542.0] ||  -> equal(singleton(complement(complement(successor(successor_relation)))),successor_relation) member(successor_relation,complement(singleton(complement(complement(successor(successor_relation))))))*.
% 299.82/300.45  221510[10:Res:218373.0,31922.0] || well_ordering(u,complement(singleton(rest_relation)))* -> equal(singleton(rest_relation),successor_relation) member(least(u,rest_relation),rest_relation).
% 299.82/300.45  221737[6:Res:221565.0,9.0] || subclass(complement(element_relation),complement(compose(element_relation,universal_class)))* -> equal(complement(compose(element_relation,universal_class)),complement(element_relation)).
% 299.82/300.45  221785[10:Res:221522.0,163256.1] || equal(complement(singleton(ordered_pair(universal_class,u))),range_of(successor_relation)) -> inductive(complement(singleton(ordered_pair(universal_class,u))))*.
% 299.82/300.45  221851[10:Res:8.1,160703.0] || equal(complement(compose(element_relation,universal_class)),u)* member(regular(u),element_relation)* -> equal(u,successor_relation).
% 299.82/300.45  221929[10:Res:192947.1,33515.1] || equal(complement(u),successor_relation) member(u,universal_class) -> member(singleton(singleton(singleton(u))),element_relation)*.
% 299.82/300.45  222040[10:Res:206947.1,986.1] || equal(power_class(image(element_relation,complement(u))),kind_1_ordinals) member(successor_relation,image(element_relation,power_class(u)))* -> .
% 299.82/300.45  222041[20:Res:191074.1,986.1] || equal(power_class(image(element_relation,complement(u))),omega) member(successor_relation,image(element_relation,power_class(u)))* -> .
% 299.82/300.45  222118[10:Rew:185433.1,222087.2] || equal(complement(complement(kind_1_ordinals)),successor_relation) member(not_subclass_element(universal_class,u),ordinal_numbers)* -> subclass(universal_class,u).
% 299.82/300.45  222156[10:SpL:2330.1,222139.0] || subclass(complement(singleton(not_subclass_element(cross_product(u,v),w))),successor_relation)* -> subclass(cross_product(u,v),w).
% 299.82/300.45  222252[15:Res:160275.0,189380.2] || member(u,universal_class) subclass(domain_relation,complement(omega)) -> equal(integer_of(ordered_pair(u,successor_relation)),successor_relation)**.
% 299.82/300.45  222306[15:MRR:222261.2,34067.1] || member(successor_relation,u) member(v,w)* subclass(domain_relation,complement(cross_product(w,u)))* -> .
% 299.82/300.45  222334[24:SpR:222326.0,60.1] || member(ordered_pair(kind_1_ordinals,u),compose(v,w))* -> member(u,image(v,image(w,successor_relation))).
% 299.82/300.45  223133[24:Res:222474.0,9.0] || subclass(successor(kind_1_ordinals),symmetric_difference(complement(kind_1_ordinals),universal_class))* -> equal(symmetric_difference(complement(kind_1_ordinals),universal_class),successor(kind_1_ordinals)).
% 299.82/300.45  223146[24:Res:223096.0,9.0] || subclass(symmetric_difference(universal_class,kind_1_ordinals),complement(successor(kind_1_ordinals)))* -> equal(symmetric_difference(universal_class,kind_1_ordinals),complement(successor(kind_1_ordinals))).
% 299.82/300.45  223162[24:Res:222372.0,163256.1] || equal(complement(singleton(ordered_pair(kind_1_ordinals,u))),range_of(successor_relation)) -> inductive(complement(singleton(ordered_pair(kind_1_ordinals,u))))*.
% 299.82/300.45  223265[24:SpR:222479.0,28321.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,universal_class),rest_of(ordered_pair(kind_1_ordinals,v))),u)*.
% 299.82/300.45  223268[24:SpR:222479.0,28320.1] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(kind_1_ordinals,v))),universal_class),u)*.
% 299.82/300.45  223270[24:SpR:222479.0,18.2] || member(kind_1_ordinals,u) member(v,w) -> member(ordered_pair(v,universal_class),cross_product(w,u))*.
% 299.82/300.45  223280[24:SpR:222479.0,28320.1] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(kind_1_ordinals,rest_of(ordered_pair(v,universal_class))),v),u)*.
% 299.82/300.45  223281[24:SpR:222479.0,28321.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(kind_1_ordinals,v),rest_of(ordered_pair(v,universal_class))),u)*.
% 299.82/300.45  223366[24:Rew:222326.0,223329.1] || member(u,ordered_pair(v,universal_class))* -> equal(u,unordered_pair(v,successor_relation)) equal(u,singleton(v)).
% 299.82/300.45  224856[25:SoR:224736.0,6317.2] single_valued_class(regular(complement(successor(successor_relation)))) || equal(regular(complement(successor(successor_relation))),cross_product(universal_class,universal_class))** -> .
% 299.82/300.45  224859[25:SoR:224737.0,6317.2] single_valued_class(regular(complement(power_class(universal_class)))) || equal(regular(complement(power_class(universal_class))),cross_product(universal_class,universal_class))** -> .
% 299.82/300.45  224862[25:SoR:224738.0,6317.2] single_valued_class(regular(complement(power_class(successor_relation)))) || equal(regular(complement(power_class(successor_relation))),cross_product(universal_class,universal_class))** -> .
% 299.82/300.45  224898[25:SoR:224743.0,160511.2] single_valued_class(regular(complement(complement(symmetrization_of(successor_relation))))) || equal(regular(complement(complement(symmetrization_of(successor_relation)))),successor_relation)** -> .
% 299.82/300.45  224994[25:SpR:224739.1,105.0] function(single_valued1(u)) ||  -> equal(domain__dfg(u,image(inverse(u),successor_relation),single_valued2(u)),single_valued3(u))**.
% 299.82/300.45  225085[25:SpL:224739.1,203272.1] function(u) || member(u,cantor(v))* equal(restrict(v,successor_relation,universal_class),successor_relation)** -> .
% 299.82/300.45  226079[15:Res:8.1,189381.1] || equal(intersection(u,v),domain_relation)** member(w,universal_class) -> member(ordered_pair(w,successor_relation),u)*.
% 299.82/300.45  226174[15:Res:8.1,189386.1] || equal(intersection(u,v),domain_relation)** member(w,universal_class) -> member(ordered_pair(w,successor_relation),v)*.
% 299.82/300.45  226283[15:MRR:226184.2,160227.0] || member(u,universal_class) -> equal(singleton(v),successor_relation) equal(apply(v,u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226284[15:MRR:226194.2,160227.0] || member(u,universal_class) -> equal(v,successor_relation) equal(apply(regular(v),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226285[21:MRR:226198.1,160227.0] || member(u,universal_class) -> equal(apply(regular(complement(complement(symmetrization_of(successor_relation)))),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226352[25:SoR:224638.0,6317.2] single_valued_class(inverse(u)) || equal(cross_product(universal_class,universal_class),inverse(u))* -> equal(range_of(u),universal_class)**.
% 299.82/300.45  226383[25:SpR:226350.1,10417.0] one_to_one(restrict(cross_product(u,universal_class),v,w)) ||  -> equal(image(cross_product(v,w),u),universal_class)**.
% 299.82/300.45  226438[25:SoR:224774.0,6317.2] single_valued_class(power_class(u)) || member(u,universal_class)* equal(cross_product(universal_class,universal_class),power_class(u))* -> .
% 299.82/300.45  226441[25:SoR:224775.0,6317.2] single_valued_class(power_class(u)) || equal(successor_relation,u) equal(cross_product(universal_class,universal_class),power_class(u))* -> .
% 299.82/300.45  226444[25:SoR:224777.0,6317.2] single_valued_class(sum_class(u)) || member(u,universal_class)* equal(cross_product(universal_class,universal_class),sum_class(u))* -> .
% 299.82/300.45  226447[25:SoR:224778.0,6317.2] single_valued_class(rest_of(u)) || member(u,universal_class)* equal(cross_product(universal_class,universal_class),rest_of(u))* -> .
% 299.82/300.45  228745[10:Obv:228705.1] || equal(u,v) -> subclass(v,complement(unordered_pair(v,u)))* equal(unordered_pair(v,u),successor_relation).
% 299.82/300.45  228867[24:Rew:223107.0,228798.0] ||  -> subclass(symmetric_difference(complement(kind_1_ordinals),universal_class),u) member(not_subclass_element(symmetric_difference(complement(kind_1_ordinals),universal_class),u),successor(kind_1_ordinals))*.
% 299.82/300.45  228848[24:SpL:223107.0,160801.0] || subclass(u,symmetric_difference(complement(kind_1_ordinals),universal_class))* -> equal(u,successor_relation) member(regular(u),successor(kind_1_ordinals)).
% 299.82/300.45  228876[24:MRR:228852.0,34067.1] || member(u,successor(kind_1_ordinals))* subclass(symmetric_difference(complement(kind_1_ordinals),universal_class),v)* -> member(u,v)*.
% 299.82/300.45  228889[25:SoR:225054.0,160511.2] single_valued_class(first(regular(rest_relation))) || equal(first(regular(rest_relation)),successor_relation) -> member(successor_relation,regular(rest_relation))*.
% 299.82/300.45  228892[25:SoR:225055.0,160511.2] single_valued_class(first(regular(domain_relation))) || equal(first(regular(domain_relation)),successor_relation) -> member(successor_relation,regular(domain_relation))*.
% 299.82/300.45  228895[25:SoR:225056.0,160511.2] single_valued_class(first(regular(element_relation))) || equal(first(regular(element_relation)),successor_relation) -> member(successor_relation,regular(element_relation))*.
% 299.82/300.45  228898[10:Res:159952.1,160788.0] || subclass(u,ordinal_numbers) subclass(kind_1_ordinals,v) -> equal(u,successor_relation) member(regular(u),v)*.
% 299.82/300.45  228938[10:Res:159951.0,160788.0] || subclass(kind_1_ordinals,u) -> equal(intersection(v,ordinal_numbers),successor_relation) member(regular(intersection(v,ordinal_numbers)),u)*.
% 299.82/300.45  228939[10:Res:159950.0,160788.0] || subclass(kind_1_ordinals,u) -> equal(intersection(ordinal_numbers,v),successor_relation) member(regular(intersection(ordinal_numbers,v)),u)*.
% 299.82/300.45  228955[10:Res:159949.0,160788.0] || subclass(kind_1_ordinals,u) -> equal(complement(complement(ordinal_numbers)),successor_relation) member(regular(complement(complement(ordinal_numbers))),u)*.
% 299.82/300.45  229001[10:Rew:160824.1,228973.3] || subclass(complement(ordinal_numbers),u)* -> member(v,kind_1_ordinals)* equal(singleton(v),successor_relation) member(v,u)*.
% 299.82/300.45  229024[10:Res:228991.1,513.0] || subclass(kind_1_ordinals,intersection(complement(u),complement(v)))* member(regular(ordinal_numbers),union(u,v)) -> .
% 299.82/300.45  229252[10:Res:229228.1,513.0] || subclass(universal_class,intersection(complement(u),complement(v)))* member(regular(ordinal_numbers),union(u,v)) -> .
% 299.82/300.45  229290[25:SoR:225422.0,160511.2] single_valued_class(first(regular(rest_relation))) || member(successor_relation,rest_relation) equal(first(regular(rest_relation)),successor_relation)** -> .
% 299.82/300.45  229293[25:SoR:225423.0,160511.2] single_valued_class(first(regular(domain_relation))) || member(successor_relation,domain_relation) equal(first(regular(domain_relation)),successor_relation)** -> .
% 299.82/300.45  229321[25:SoR:225424.0,160511.2] single_valued_class(first(regular(element_relation))) || member(successor_relation,element_relation) equal(first(regular(element_relation)),successor_relation)** -> .
% 299.82/300.45  229441[10:Rew:185433.1,229376.2] || equal(complement(complement(u)),successor_relation) member(not_subclass_element(universal_class,v),u)* -> subclass(universal_class,v).
% 299.82/300.45  229832[10:MRR:229791.2,217612.0] ||  -> equal(integer_of(apply(choice,regular(complement(singleton(omega))))),successor_relation)** equal(regular(complement(singleton(omega))),successor_relation).
% 299.82/300.45  229833[10:MRR:229789.2,217612.0] ||  -> equal(integer_of(not_subclass_element(regular(complement(singleton(omega))),u)),successor_relation)** subclass(regular(complement(singleton(omega))),u).
% 299.82/300.45  230143[10:SpL:161592.1,222140.0] || equal(complement(complement(singleton(regular(cross_product(u,v))))),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  230166[15:SpL:208.0,222296.1] || subclass(domain_relation,image(element_relation,power_class(u))) subclass(domain_relation,power_class(image(element_relation,complement(u))))* -> .
% 299.82/300.45  230241[25:SoR:224783.0,160511.2] single_valued_class(least(u,ordinal_numbers)) || well_ordering(u,kind_1_ordinals) equal(least(u,ordinal_numbers),successor_relation)** -> .
% 299.82/300.45  230244[25:SoR:224784.0,160511.2] single_valued_class(least(u,universal_class)) || well_ordering(u,universal_class) equal(least(u,universal_class),successor_relation)** -> .
% 299.82/300.45  230280[25:SoR:224785.0,160511.2] single_valued_class(least(u,rest_relation)) || well_ordering(u,universal_class) equal(least(u,rest_relation),successor_relation)** -> .
% 299.82/300.45  230283[25:SoR:224786.0,160511.2] single_valued_class(least(u,rest_relation)) || well_ordering(u,rest_relation) equal(least(u,rest_relation),successor_relation)** -> .
% 299.82/300.45  230286[25:SoR:224787.0,160511.2] single_valued_class(least(u,omega)) || well_ordering(u,universal_class) equal(least(u,omega),successor_relation)** -> .
% 299.82/300.45  230289[25:SoR:224788.0,160511.2] single_valued_class(least(u,omega)) || well_ordering(u,omega) equal(least(u,omega),successor_relation)** -> .
% 299.82/300.45  230379[10:Rew:113504.0,230297.0,160223.0,230297.0] ||  -> equal(symmetric_difference(restrict(ordinal_numbers,u,v),complement(kind_1_ordinals)),union(restrict(ordinal_numbers,u,v),complement(kind_1_ordinals)))**.
% 299.82/300.45  230475[10:Rew:113504.0,230393.0,160223.0,230393.0] ||  -> equal(symmetric_difference(complement(kind_1_ordinals),restrict(ordinal_numbers,u,v)),union(complement(kind_1_ordinals),restrict(ordinal_numbers,u,v)))**.
% 299.82/300.45  230530[15:Res:189374.2,229800.0] || member(u,universal_class) subclass(domain_relation,singleton(omega)) -> equal(integer_of(ordered_pair(u,successor_relation)),successor_relation)**.
% 299.82/300.45  230643[15:SpL:208.0,230608.1] || equal(image(element_relation,power_class(u)),domain_relation) equal(power_class(image(element_relation,complement(u))),domain_relation)** -> .
% 299.82/300.45  230649[10:SpL:161592.1,219386.0] || subclass(universal_class,regular(unordered_pair(u,regular(cross_product(v,w)))))* -> equal(cross_product(v,w),successor_relation).
% 299.82/300.45  231107[10:Rew:160223.0,230985.1,160277.0,230985.1] || equal(inverse(image(element_relation,complement(u))),universal_class) -> equal(symmetrization_of(image(element_relation,complement(u))),universal_class)**.
% 299.82/300.45  231181[10:SpL:161592.1,221320.0] || subclass(universal_class,regular(unordered_pair(regular(cross_product(u,v)),w)))* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  231556[10:MRR:231532.1,160214.0] || equal(rest_relation,domain_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(successor_relation,successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231557[15:MRR:231533.1,54.0] || equal(rest_relation,domain_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(omega,successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231616[14:Res:3907.1,184011.1] || equal(complement(complement(cross_product(universal_class,universal_class))),universal_class)** equal(sum_class(range_of(singleton(u))),u)** -> .
% 299.82/300.45  231714[10:SpL:161592.1,230662.0] || equal(regular(unordered_pair(u,regular(cross_product(v,w)))),universal_class)** -> equal(cross_product(v,w),successor_relation).
% 299.82/300.45  231729[10:SpL:161592.1,231194.0] || equal(regular(unordered_pair(regular(cross_product(u,v)),w)),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.45  231843[10:Res:160271.1,161035.0] inductive(intersection(power_class(successor_relation),complement(u))) || member(successor_relation,union(image(element_relation,universal_class),u))* -> .
% 299.82/300.45  9331[0:Res:1951.1,3.0] || member(u,symmetric_difference(v,w))* subclass(complement(intersection(v,w)),x)* -> member(u,x)*.
% 299.82/300.45  28587[0:Res:25.2,513.0] || member(u,complement(v)) member(u,complement(w)) member(u,union(w,v))* -> .
% 299.82/300.45  29338[0:SpR:1948.0,9535.0] ||  -> subclass(symmetric_difference(union(u,v),union(complement(u),complement(v))),complement(symmetric_difference(complement(u),complement(v))))*.
% 299.82/300.45  29372[0:SpR:115.0,1948.0] ||  -> equal(intersection(symmetrization_of(u),union(complement(u),complement(inverse(u)))),symmetric_difference(complement(u),complement(inverse(u))))**.
% 299.82/300.45  35728[0:MRR:35703.0,34067.1] || member(u,union(v,w)) -> member(u,intersection(v,w))* member(u,symmetric_difference(v,w)).
% 299.82/300.45  29373[0:SpR:45.0,1948.0] ||  -> equal(intersection(successor(u),union(complement(u),complement(singleton(u)))),symmetric_difference(complement(u),complement(singleton(u))))**.
% 299.82/300.45  33914[0:SpL:1943.0,2648.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(singleton(x),complement(restrict(w,u,v)))*.
% 299.82/300.45  33839[0:SpL:1938.0,2648.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(singleton(x),complement(restrict(u,v,w)))*.
% 299.82/300.45  30783[0:Res:1951.1,3514.1] || member(ordered_pair(u,v),symmetric_difference(w,x))* subclass(universal_class,complement(complement(intersection(w,x))))* -> .
% 299.82/300.45  28596[0:Res:1499.1,513.0] || subclass(universal_class,intersection(complement(u),complement(v)))* member(ordered_pair(w,x),union(u,v))* -> .
% 299.82/300.45  6042[0:Res:1499.1,129.3] || subclass(universal_class,u) member(v,w)* subclass(w,x)* well_ordering(u,x)* -> .
% 299.82/300.45  31284[0:Res:8.1,5829.0] || equal(u,v)* well_ordering(w,u)* -> subclass(v,x)* member(least(w,v),v)*.
% 299.82/300.45  9145[0:Res:1478.2,3.0] || member(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(power_class(u),w)*.
% 299.82/300.45  9163[0:Res:1478.2,1952.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,w)) -> member(power_class(u),union(v,w))*.
% 299.82/300.45  48508[0:Res:1478.2,10191.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,inverse(v)))* -> member(power_class(u),symmetrization_of(v))*.
% 299.82/300.45  48610[0:Res:1478.2,10254.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,singleton(v)))* -> member(power_class(u),successor(v))*.
% 299.82/300.45  31071[2:Res:8.1,5832.1] inductive(u) || equal(v,u)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.45  33835[0:SpL:1938.0,5884.0] || equal(symmetric_difference(u,cross_product(v,w)),universal_class) -> member(singleton(x),complement(restrict(u,v,w)))*.
% 299.82/300.45  33910[0:SpL:1943.0,5884.0] || equal(symmetric_difference(cross_product(u,v),w),universal_class) -> member(singleton(x),complement(restrict(w,u,v)))*.
% 299.82/300.45  87691[0:SpR:124.0,31436.1] || equal(complement(rest_of(restrict(u,v,singleton(w)))),universal_class)** -> subclass(segment(u,v,w),x)*.
% 299.82/300.45  108181[2:MRR:108175.2,2492.1] || connected(u,singleton(v)) -> well_ordering(u,singleton(v)) equal(regular(not_well_ordering(u,singleton(v))),v)**.
% 299.82/300.45  109958[0:SpR:109924.1,134.1] || equal(cantor(restrict(u,v,w)),universal_class)** section(u,w,v) -> subclass(universal_class,w).
% 299.82/300.45  110146[0:MRR:110145.2,6.0] || equal(cantor(restrict(u,v,w)),universal_class)** section(u,w,v) -> equal(universal_class,w).
% 299.82/300.45  111797[0:Res:3907.1,9322.0] || equal(complement(complement(symmetric_difference(complement(u),complement(v)))),universal_class)** -> member(singleton(w),union(u,v))*.
% 299.82/300.45  122155[0:Rew:9494.1,122154.1] || member(u,v) member(u,w) -> subclass(intersection(singleton(u),x),intersection(w,v))*.
% 299.82/300.45  122366[0:Rew:9380.1,122365.1] || member(u,v) member(u,w) -> subclass(intersection(x,singleton(u)),intersection(w,v))*.
% 299.82/300.45  125968[0:Res:28320.1,95.0] || subclass(rest_relation,rotate(compose_class(u))) -> equal(compose(u,ordered_pair(v,rest_of(ordered_pair(w,v)))),w)**.
% 299.82/300.45  125978[0:Res:28320.1,35.0] || subclass(rest_relation,rotate(rotate(u))) -> member(ordered_pair(ordered_pair(rest_of(ordered_pair(v,w)),v),w),u)*.
% 299.82/300.45  125979[0:Res:28320.1,38.0] || subclass(rest_relation,rotate(flip(u))) -> member(ordered_pair(ordered_pair(rest_of(ordered_pair(v,w)),w),v),u)*.
% 299.82/300.45  125984[0:Res:28320.1,2151.0] || subclass(rest_relation,rotate(singleton(u)))* -> equal(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)*.
% 299.82/300.45  126098[0:Res:28321.1,95.0] || subclass(rest_relation,flip(compose_class(u))) -> equal(compose(u,ordered_pair(v,w)),rest_of(ordered_pair(w,v)))**.
% 299.82/300.45  126104[0:Res:28321.1,35.0] || subclass(rest_relation,flip(rotate(u))) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(v,w))),w),u)*.
% 299.82/300.45  126105[0:Res:28321.1,38.0] || subclass(rest_relation,flip(flip(u))) -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(v,w))),u)*.
% 299.82/300.45  126109[0:Res:28321.1,2151.0] || subclass(rest_relation,flip(singleton(u)))* -> equal(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)*.
% 299.82/300.45  130938[0:SpR:10422.0,134.1] || section(cross_product(u,singleton(v)),w,x) -> subclass(segment(cross_product(x,w),u,v),w)*.
% 299.82/300.45  144538[2:MRR:142025.1,144535.0] || asymmetric(cross_product(u,v),w) -> section(restrict(inverse(cross_product(u,v)),u,v),w,w)*.
% 299.82/300.45  162977[10:Rew:160202.0,156098.0] ||  -> subclass(symmetric_difference(power_class(intersection(complement(u),complement(v))),universal_class),union(image(element_relation,union(u,v)),successor_relation))*.
% 299.82/300.45  162966[10:Rew:160202.0,156063.0] || member(u,symmetric_difference(complement(v),union(w,successor_relation)))* -> member(u,union(v,symmetric_difference(universal_class,w))).
% 299.82/300.45  162761[10:Rew:160202.0,153435.0] || equal(cross_product(cross_product(universal_class,universal_class),universal_class),successor_relation) -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),flip(u))*.
% 299.82/300.45  162762[10:Rew:160202.0,153434.0] || equal(cross_product(cross_product(universal_class,universal_class),universal_class),successor_relation) -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(u))*.
% 299.82/300.45  162351[10:Rew:160202.0,150691.0] ||  -> equal(intersection(image(element_relation,union(u,image(element_relation,universal_class))),power_class(intersection(complement(u),power_class(successor_relation)))),successor_relation)**.
% 299.82/300.45  162350[10:Rew:160202.0,150690.0] ||  -> equal(intersection(power_class(intersection(complement(u),power_class(successor_relation))),image(element_relation,union(u,image(element_relation,universal_class)))),successor_relation)**.
% 299.82/300.45  162349[10:Rew:160202.0,150689.0] ||  -> equal(intersection(image(element_relation,union(image(element_relation,universal_class),u)),power_class(intersection(power_class(successor_relation),complement(u)))),successor_relation)**.
% 299.82/300.45  162348[10:Rew:160202.0,150688.0] ||  -> equal(intersection(power_class(intersection(power_class(successor_relation),complement(u))),image(element_relation,union(image(element_relation,universal_class),u))),successor_relation)**.
% 299.82/300.45  162015[10:Rew:160202.0,148532.1] || subclass(u,v) -> equal(cross_product(v,u),successor_relation) section(regular(cross_product(v,u)),u,v)*.
% 299.82/300.45  163451[10:Rew:160202.0,162002.1] ||  -> equal(cross_product(u,singleton(v)),successor_relation) equal(segment(regular(cross_product(u,singleton(v))),u,v),successor_relation)**.
% 299.82/300.45  161998[10:Rew:160202.0,147817.0] ||  -> equal(intersection(intersection(u,image(element_relation,union(v,w))),power_class(intersection(complement(v),complement(w)))),successor_relation)**.
% 299.82/300.45  161997[10:Rew:160202.0,147772.0] ||  -> equal(intersection(symmetric_difference(complement(intersection(u,v)),union(u,v)),complement(complement(symmetric_difference(u,v)))),successor_relation)**.
% 299.82/300.45  161996[10:Rew:160202.0,147771.0] ||  -> equal(intersection(intersection(image(element_relation,union(u,v)),w),power_class(intersection(complement(u),complement(v)))),successor_relation)**.
% 299.82/300.45  161995[10:Rew:160202.0,147753.0] ||  -> equal(intersection(power_class(intersection(complement(u),complement(v))),intersection(w,image(element_relation,union(u,v)))),successor_relation)**.
% 299.82/300.45  161994[10:Rew:160202.0,147659.0] ||  -> equal(intersection(power_class(intersection(complement(u),complement(v))),intersection(image(element_relation,union(u,v)),w)),successor_relation)**.
% 299.82/300.45  161993[10:Rew:160202.0,147658.0] ||  -> equal(intersection(complement(complement(symmetric_difference(u,v))),symmetric_difference(complement(intersection(u,v)),union(u,v))),successor_relation)**.
% 299.82/300.45  161992[10:Rew:160202.0,147600.2] || subclass(cross_product(u,v),w)* well_ordering(universal_class,w) -> equal(restrict(x,u,v),successor_relation)**.
% 299.82/300.45  161990[10:Rew:160202.0,147372.1] || member(regular(restrict(complement(u),v,w)),u)* -> equal(restrict(complement(u),v,w),successor_relation).
% 299.82/300.45  161983[10:Rew:160202.0,147319.1] || well_ordering(u,v) -> equal(segment(u,complement(complement(v)),least(u,complement(complement(v)))),successor_relation)**.
% 299.82/300.45  161967[10:Rew:160202.0,146923.1] || well_ordering(u,v) -> equal(segment(u,intersection(v,w),least(u,intersection(v,w))),successor_relation)**.
% 299.82/300.45  161966[10:Rew:160202.0,146922.1] || well_ordering(u,v) -> equal(segment(u,intersection(w,v),least(u,intersection(w,v))),successor_relation)**.
% 299.82/300.45  161961[10:Rew:160202.0,146917.2] inductive(segment(u,v,w)) || section(u,singleton(w),v)* -> member(successor_relation,singleton(w)).
% 299.82/300.45  162985[10:Rew:160202.0,159932.1] || well_ordering(universal_class,power_class(intersection(complement(u),complement(v))))* -> member(successor_relation,image(element_relation,union(u,v))).
% 299.82/300.45  161884[10:Rew:160202.0,146864.1] || member(regular(union(u,v)),intersection(complement(u),complement(v)))* -> equal(union(u,v),successor_relation).
% 299.82/300.45  161780[10:Rew:160202.0,146708.1] ||  -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),successor_relation) member(u,unordered_pair(u,v))*.
% 299.82/300.45  161781[10:Rew:160202.0,146707.1] ||  -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),successor_relation) member(v,unordered_pair(u,v))*.
% 299.82/300.45  161720[10:Rew:160202.0,146903.1] || subclass(u,singleton(v))* -> equal(intersection(u,w),successor_relation) equal(regular(intersection(u,w)),v)*.
% 299.82/300.45  161709[10:Rew:160202.0,146882.1] || subclass(u,singleton(v))* -> equal(intersection(w,u),successor_relation) equal(regular(intersection(w,u)),v)*.
% 299.82/300.45  161687[10:Rew:160202.0,146725.2] || subclass(complement(intersection(u,v)),w)* well_ordering(universal_class,w) -> equal(symmetric_difference(u,v),successor_relation).
% 299.82/300.45  161616[10:Rew:160202.0,147416.1] || subclass(complement(u),v) -> equal(symmetric_difference(universal_class,u),successor_relation) member(regular(symmetric_difference(universal_class,u)),v)*.
% 299.82/300.45  161609[10:Rew:160202.0,147216.1] || equal(u,v) -> equal(unordered_pair(v,u),successor_relation) equal(apply(choice,unordered_pair(v,u)),v)**.
% 299.82/300.45  163442[10:Rew:160202.0,161610.2] || equal(u,v) -> equal(unordered_pair(v,u),successor_relation) equal(intersection(unordered_pair(v,u),v),successor_relation)**.
% 299.82/300.45  161598[10:Rew:160202.0,146827.0] ||  -> equal(cross_product(u,v),successor_relation) member(singleton(first(regular(cross_product(u,v)))),regular(cross_product(u,v)))*.
% 299.82/300.45  161661[10:Rew:160202.0,156057.0] || member(u,symmetric_difference(union(v,successor_relation),complement(w)))* -> member(u,union(symmetric_difference(universal_class,v),w)).
% 299.82/300.45  161657[10:Rew:160202.0,156030.0] ||  -> equal(complement(intersection(complement(u),power_class(symmetric_difference(universal_class,v)))),union(u,image(element_relation,union(v,successor_relation))))**.
% 299.82/300.45  161431[10:Rew:160202.0,159720.2] || member(not_subclass_element(u,complement(regular(v))),v)* -> subclass(u,complement(regular(v))) equal(v,successor_relation).
% 299.82/300.45  161495[10:Rew:160202.0,155846.1] ||  -> equal(not_subclass_element(unordered_pair(u,v),omega),u)** equal(integer_of(v),successor_relation) subclass(unordered_pair(u,v),omega).
% 299.82/300.45  161282[10:Rew:160202.0,146733.1] || subclass(intersection(singleton(u),v),w)* -> equal(intersection(singleton(u),v),successor_relation) member(u,w).
% 299.82/300.45  161275[10:Rew:160202.0,146719.1] || subclass(intersection(u,singleton(v)),w)* -> equal(intersection(u,singleton(v)),successor_relation) member(v,w).
% 299.82/300.45  161295[10:Rew:160202.0,146574.1] || asymmetric(u,v) equal(compose(successor_relation,successor_relation),successor_relation) -> transitive(intersection(u,inverse(u)),v)*.
% 299.82/300.45  161296[10:Rew:160202.0,146573.2] || asymmetric(u,v) transitive(intersection(u,inverse(u)),v)* -> equal(compose(successor_relation,successor_relation),successor_relation).
% 299.82/300.45  161322[10:Rew:160202.0,146404.1] || asymmetric(universal_class,singleton(u)) -> equal(range__dfg(inverse(universal_class),u,singleton(u)),second(not_subclass_element(successor_relation,successor_relation)))**.
% 299.82/300.45  163044[10:Rew:160202.0,159265.1] single_valued_class(u) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued3(successor_relation))),single_valued2(u)),single_valued3(u))**.
% 299.82/300.45  163045[10:Rew:160202.0,159261.1] function(u) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued3(successor_relation))),single_valued2(u)),single_valued3(u))**.
% 299.82/300.45  161197[10:Rew:160202.0,155772.1] ||  -> subclass(symmetric_difference(complement(u),universal_class),v) member(not_subclass_element(symmetric_difference(complement(u),universal_class),v),union(u,successor_relation))*.
% 299.82/300.45  161208[10:Rew:160202.0,156004.0] ||  -> equal(complement(intersection(power_class(symmetric_difference(universal_class,u)),complement(v))),union(image(element_relation,union(u,successor_relation)),v))**.
% 299.82/300.45  163439[10:Rew:160202.0,161199.1] ||  -> member(not_subclass_element(complement(union(u,successor_relation)),v),symmetric_difference(universal_class,u))* subclass(complement(union(u,successor_relation)),v).
% 299.82/300.45  160817[10:Rew:160202.0,146396.1] || subclass(singleton(u),symmetric_difference(v,w))* -> equal(singleton(u),successor_relation) member(u,union(v,w)).
% 299.82/300.45  160877[10:Rew:160202.0,152632.2] || member(u,universal_class) subclass(universal_class,power_class(universal_class)) member(power_class(u),image(element_relation,successor_relation))* -> .
% 299.82/300.45  160876[10:Rew:160202.0,152631.2] || member(u,universal_class) subclass(universal_class,power_class(universal_class)) member(sum_class(u),image(element_relation,successor_relation))* -> .
% 299.82/300.45  160872[10:Rew:160202.0,152635.1] || member(u,intersection(complement(v),power_class(universal_class)))* member(u,union(v,image(element_relation,successor_relation))) -> .
% 299.82/300.45  160868[10:Rew:160202.0,152625.1] || member(u,intersection(power_class(universal_class),complement(v)))* member(u,union(image(element_relation,successor_relation),v)) -> .
% 299.82/300.45  160849[10:Rew:160202.0,152619.1] || subclass(universal_class,image(element_relation,power_class(universal_class))) member(unordered_pair(u,v),power_class(image(element_relation,successor_relation)))* -> .
% 299.82/300.45  160844[10:Rew:160202.0,152606.2] || member(u,universal_class) -> member(u,image(element_relation,power_class(universal_class)))* member(u,power_class(image(element_relation,successor_relation))).
% 299.82/300.45  163415[10:Rew:160202.0,160506.2] || equal(successor_relation,u) well_ordering(v,w)* -> equal(segment(v,u,least(v,u)),successor_relation)**.
% 299.82/300.45  160508[10:Rew:160202.0,153506.0] || equal(successor_relation,u) connected(v,u) -> well_ordering(v,u) equal(not_well_ordering(v,u),u)**.
% 299.82/300.45  163423[10:Rew:160202.0,160693.3] || subclass(u,regular(v))* member(regular(u),v) -> equal(u,successor_relation) equal(v,successor_relation).
% 299.82/300.45  160777[10:Rew:160202.0,146535.1] || subclass(u,restrict(v,w,x))* -> equal(u,successor_relation) member(regular(u),cross_product(w,x)).
% 299.82/300.45  160778[10:Rew:160202.0,146534.2] || subclass(u,image(element_relation,complement(v)))* member(regular(u),power_class(v)) -> equal(u,successor_relation).
% 299.82/300.45  160779[10:Rew:160202.0,146492.2] || subclass(u,intersection(v,w)) member(regular(u),symmetric_difference(v,w))* -> equal(u,successor_relation).
% 299.82/300.45  160780[10:Rew:160202.0,146488.2] || subclass(u,power_class(v)) member(regular(u),image(element_relation,complement(v)))* -> equal(u,successor_relation).
% 299.82/300.45  160781[10:Rew:160202.0,146476.1] || subclass(u,symmetric_difference(v,w)) -> equal(u,successor_relation) member(regular(u),complement(intersection(v,w)))*.
% 299.82/300.45  160782[10:Rew:160202.0,146465.2] function(u) || subclass(cross_product(universal_class,universal_class),v)* -> equal(u,successor_relation) member(regular(u),v)*.
% 299.82/300.45  162961[10:Rew:160202.0,155847.1] ||  -> equal(not_subclass_element(unordered_pair(u,v),omega),v)** equal(integer_of(u),successor_relation) subclass(unordered_pair(u,v),omega).
% 299.82/300.45  168560[11:Res:168384.1,986.1] || equal(power_class(image(element_relation,complement(u))),symmetrization_of(successor_relation)) member(successor_relation,image(element_relation,power_class(u)))* -> .
% 299.82/300.45  168550[11:Res:168384.1,9306.0] || equal(symmetric_difference(cross_product(u,v),w),symmetrization_of(successor_relation)) -> member(successor_relation,complement(restrict(w,u,v)))*.
% 299.82/300.45  168548[11:Res:168384.1,9300.0] || equal(symmetric_difference(u,cross_product(v,w)),symmetrization_of(successor_relation)) -> member(successor_relation,complement(restrict(u,v,w)))*.
% 299.82/300.45  163438[10:Rew:160202.0,161170.1] || member(regular(intersection(symmetrization_of(successor_relation),u)),complement(inverse(successor_relation)))* -> equal(intersection(symmetrization_of(successor_relation),u),successor_relation).
% 299.82/300.45  163437[10:Rew:160202.0,161169.1] || member(regular(intersection(u,symmetrization_of(successor_relation))),complement(inverse(successor_relation)))* -> equal(intersection(u,symmetrization_of(successor_relation)),successor_relation).
% 299.82/300.45  168377[11:Res:168372.0,127.0] || subclass(symmetrization_of(successor_relation),u)* well_ordering(v,u)* -> member(least(v,symmetrization_of(successor_relation)),symmetrization_of(successor_relation))*.
% 299.82/300.45  163421[10:Rew:160202.0,160530.3] || subclass(complement(u),successor_relation)* member(v,universal_class) -> member(v,u)* member(v,inverse(successor_relation))*.
% 299.82/300.45  168394[11:Res:168387.0,127.0] || subclass(inverse(successor_relation),u)* well_ordering(v,u)* -> member(least(v,inverse(successor_relation)),inverse(successor_relation))*.
% 299.82/300.45  163432[10:Rew:160202.0,161113.2] || member(u,universal_class) subclass(universal_class,symmetrization_of(successor_relation)) member(power_class(u),complement(inverse(successor_relation)))* -> .
% 299.82/300.45  163431[10:Rew:160202.0,161112.2] || member(u,universal_class) subclass(universal_class,symmetrization_of(successor_relation)) member(sum_class(u),complement(inverse(successor_relation)))* -> .
% 299.82/300.45  163434[10:Rew:160202.0,161133.1] || member(u,intersection(complement(v),symmetrization_of(successor_relation)))* member(u,union(v,complement(inverse(successor_relation)))) -> .
% 299.82/300.45  163433[10:Rew:160202.0,161131.1] || member(u,intersection(symmetrization_of(successor_relation),complement(v)))* member(u,union(complement(inverse(successor_relation)),v)) -> .
% 299.82/300.45  163429[10:Rew:160202.0,161094.1] || subclass(universal_class,image(element_relation,symmetrization_of(successor_relation))) member(unordered_pair(u,v),power_class(complement(inverse(successor_relation))))* -> .
% 299.82/300.45  163430[10:Rew:160202.0,161095.2] || member(u,universal_class) -> member(u,image(element_relation,symmetrization_of(successor_relation)))* member(u,power_class(complement(inverse(successor_relation)))).
% 299.82/300.45  163428[10:Rew:160202.0,161079.1] || member(regular(intersection(power_class(successor_relation),u)),image(element_relation,universal_class))* -> equal(intersection(power_class(successor_relation),u),successor_relation).
% 299.82/300.45  163427[10:Rew:160202.0,161075.1] || member(regular(intersection(u,power_class(successor_relation))),image(element_relation,universal_class))* -> equal(intersection(u,power_class(successor_relation)),successor_relation).
% 299.82/300.45  161058[10:Rew:160202.0,150476.0] || subclass(ordered_pair(u,v),power_class(successor_relation)) member(unordered_pair(u,singleton(v)),image(element_relation,universal_class))* -> .
% 299.82/300.45  161014[10:Rew:160202.0,150475.0] || member(u,intersection(complement(v),power_class(successor_relation)))* member(u,union(v,image(element_relation,universal_class))) -> .
% 299.82/300.45  161054[10:Rew:160202.0,150482.0] || subclass(u,power_class(successor_relation)) member(not_subclass_element(u,v),image(element_relation,universal_class))* -> subclass(u,v).
% 299.82/300.45  160951[10:Rew:160202.0,150479.0] || subclass(universal_class,intersection(complement(u),power_class(successor_relation)))* subclass(universal_class,union(u,image(element_relation,universal_class))) -> .
% 299.82/300.45  160950[10:Rew:160202.0,150478.0] || equal(intersection(complement(u),power_class(successor_relation)),universal_class)** equal(union(u,image(element_relation,universal_class)),universal_class) -> .
% 299.82/300.45  160920[10:Rew:160202.0,150496.0] || subclass(universal_class,intersection(power_class(successor_relation),complement(u)))* subclass(universal_class,union(image(element_relation,universal_class),u)) -> .
% 299.82/300.45  160919[10:Rew:160202.0,150495.0] || equal(intersection(power_class(successor_relation),complement(u)),universal_class)** equal(union(image(element_relation,universal_class),u),universal_class) -> .
% 299.82/300.45  160994[10:Rew:160202.0,150484.1] || member(u,universal_class) subclass(universal_class,power_class(successor_relation)) member(power_class(u),image(element_relation,universal_class))* -> .
% 299.82/300.45  160995[10:Rew:160202.0,150483.1] || member(u,universal_class) subclass(universal_class,power_class(successor_relation)) member(sum_class(u),image(element_relation,universal_class))* -> .
% 299.82/300.45  160976[10:Rew:160202.0,150497.0] || subclass(universal_class,image(element_relation,power_class(successor_relation))) member(unordered_pair(u,v),power_class(image(element_relation,universal_class)))* -> .
% 299.82/300.45  163426[10:Rew:160202.0,160897.1] || member(regular(complement(complement(power_class(successor_relation)))),image(element_relation,universal_class))* -> equal(complement(complement(power_class(successor_relation))),successor_relation).
% 299.82/300.45  163090[10:Rew:160202.0,159352.1] || subclass(domain_relation,intersection(complement(u),complement(v)))* member(ordered_pair(successor_relation,successor_relation),union(u,v)) -> .
% 299.82/300.45  163464[10:Rew:160202.0,163070.1] || subclass(domain_relation,unordered_pair(u,v))* -> equal(ordered_pair(successor_relation,successor_relation),v) equal(ordered_pair(successor_relation,successor_relation),u).
% 299.82/300.45  163462[10:Rew:160202.0,162912.1] || member(regular(intersection(u,successor(successor_relation))),complement(singleton(successor_relation)))* -> equal(intersection(u,successor(successor_relation)),successor_relation).
% 299.82/300.45  163461[10:Rew:160202.0,162910.1] || member(regular(intersection(successor(successor_relation),u)),complement(singleton(successor_relation)))* -> equal(intersection(successor(successor_relation),u),successor_relation).
% 299.82/300.45  163447[10:Rew:160202.0,161808.0] || equal(symmetric_difference(cross_product(u,v),w),successor(successor_relation)) -> member(successor_relation,complement(restrict(w,u,v)))*.
% 299.82/300.45  163445[10:Rew:160202.0,161804.0] || equal(symmetric_difference(u,cross_product(v,w)),successor(successor_relation)) -> member(successor_relation,complement(restrict(u,v,w)))*.
% 299.82/300.45  163443[10:Rew:160202.0,161799.0] || equal(power_class(image(element_relation,complement(u))),successor(successor_relation)) member(successor_relation,image(element_relation,power_class(u)))* -> .
% 299.82/300.45  163460[10:Rew:160202.0,162883.2] || subclass(successor(successor_relation),u)* well_ordering(v,u)* -> member(least(v,successor(successor_relation)),successor(successor_relation))*.
% 299.82/300.45  163448[10:Rew:160202.0,161809.0] || equal(symmetric_difference(cross_product(u,v),w),singleton(successor_relation)) -> member(successor_relation,complement(restrict(w,u,v)))*.
% 299.82/300.45  163446[10:Rew:160202.0,161805.0] || equal(symmetric_difference(u,cross_product(v,w)),singleton(successor_relation)) -> member(successor_relation,complement(restrict(u,v,w)))*.
% 299.82/300.45  163444[10:Rew:160202.0,161800.0] || equal(power_class(image(element_relation,complement(u))),singleton(successor_relation)) member(successor_relation,image(element_relation,power_class(u)))* -> .
% 299.82/300.45  163459[10:Rew:160202.0,162864.2] || subclass(singleton(successor_relation),u)* well_ordering(v,u)* -> member(least(v,singleton(successor_relation)),singleton(successor_relation))*.
% 299.82/300.45  163455[10:Rew:160202.0,162794.0] || member(u,intersection(successor(successor_relation),complement(v)))* member(u,union(complement(singleton(successor_relation)),v)) -> .
% 299.82/300.45  163454[10:Rew:160202.0,162791.0] || member(u,intersection(complement(v),successor(successor_relation)))* member(u,union(v,complement(singleton(successor_relation)))) -> .
% 299.82/300.45  163453[10:Rew:160202.0,162777.0] || subclass(universal_class,image(element_relation,successor(successor_relation))) member(unordered_pair(u,v),power_class(complement(singleton(successor_relation))))* -> .
% 299.82/300.45  163452[10:Rew:160202.0,162775.1] || member(u,universal_class) -> member(u,image(element_relation,successor(successor_relation)))* member(u,power_class(complement(singleton(successor_relation)))).
% 299.82/300.45  48053[0:SpL:124.0,47745.0] || member(restrict(u,v,singleton(w)),segment(u,v,w))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.45  157917[6:Res:1481.2,148657.1] || subclass(u,complement(compose(element_relation,universal_class)))* member(not_subclass_element(u,v),element_relation)* -> subclass(u,v).
% 299.82/300.45  157920[6:Res:1504.1,148657.1] || subclass(ordered_pair(u,v),complement(compose(element_relation,universal_class)))* member(unordered_pair(u,singleton(v)),element_relation) -> .
% 299.82/300.45  124613[0:Res:3907.1,33515.1] || equal(complement(complement(u)),universal_class) member(u,universal_class) -> member(singleton(singleton(singleton(u))),element_relation)*.
% 299.82/300.45  982[0:SpR:208.0,28.0] ||  -> equal(complement(intersection(power_class(image(element_relation,complement(u))),complement(v))),union(image(element_relation,power_class(u)),v))**.
% 299.82/300.45  984[0:SpR:208.0,28.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,complement(v))))),union(u,image(element_relation,power_class(v))))**.
% 299.82/300.45  9064[0:Res:4.1,307.0] || member(not_subclass_element(image(element_relation,complement(u)),v),power_class(u))* -> subclass(image(element_relation,complement(u)),v).
% 299.82/300.45  137680[0:SpR:10028.0,107233.0] ||  -> subclass(complement(symmetrization_of(image(element_relation,complement(u)))),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.82/300.45  137061[0:SpR:10029.0,107233.0] ||  -> subclass(complement(successor(image(element_relation,complement(u)))),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.82/300.45  3665[0:SpL:208.0,2647.0] || subclass(universal_class,power_class(image(element_relation,complement(u))))* member(singleton(v),image(element_relation,power_class(u)))* -> .
% 299.82/300.45  124235[0:Res:114897.1,986.1] || equal(power_class(image(element_relation,complement(u))),universal_class) member(singleton(v),image(element_relation,power_class(u)))* -> .
% 299.82/300.45  139660[0:SpR:982.0,107233.0] ||  -> subclass(complement(union(image(element_relation,power_class(u)),v)),intersection(power_class(image(element_relation,complement(u))),complement(v)))*.
% 299.82/300.45  140120[0:SpR:984.0,107233.0] ||  -> subclass(complement(union(u,image(element_relation,power_class(v)))),intersection(complement(u),power_class(image(element_relation,complement(v)))))*.
% 299.82/300.45  155721[2:SpR:505.0,142543.0] ||  -> equal(intersection(power_class(intersection(complement(u),complement(v))),universal_class),symmetric_difference(universal_class,image(element_relation,union(u,v))))**.
% 299.82/300.45  108219[0:SpR:505.0,107289.0] ||  -> subclass(complement(power_class(image(element_relation,union(u,v)))),image(element_relation,power_class(intersection(complement(u),complement(v)))))*.
% 299.82/300.45  89298[0:SpR:505.0,89275.1] ||  -> member(u,image(element_relation,union(v,w))) subclass(singleton(u),power_class(intersection(complement(v),complement(w))))*.
% 299.82/300.45  109255[0:SpR:9949.0,58.1] || member(intersection(complement(u),complement(singleton(u))),universal_class)* -> member(complement(image(element_relation,successor(u))),universal_class).
% 299.82/300.45  109323[0:SpR:9948.0,58.1] || member(intersection(complement(u),complement(inverse(u))),universal_class)* -> member(complement(image(element_relation,symmetrization_of(u))),universal_class).
% 299.82/300.45  48608[0:Res:1479.2,10254.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,singleton(v)))* -> member(sum_class(u),successor(v))*.
% 299.82/300.45  48506[0:Res:1479.2,10191.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,inverse(v)))* -> member(sum_class(u),symmetrization_of(v))*.
% 299.82/300.45  9135[0:Res:1479.2,1952.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,w)) -> member(sum_class(u),union(v,w))*.
% 299.82/300.45  9117[0:Res:1479.2,3.0] || member(u,universal_class) subclass(universal_class,v)* subclass(v,w)* -> member(sum_class(u),w)*.
% 299.82/300.45  9114[0:SpR:70.0,1479.2] || member(image(u,singleton(v)),universal_class)* subclass(universal_class,w) -> member(apply(u,v),w)*.
% 299.82/300.45  5758[0:SpL:70.0,5754.0] || subclass(apply(u,v),image(u,singleton(v)))* -> section(element_relation,image(u,singleton(v)),universal_class).
% 299.82/300.45  159779[6:SpL:505.0,159727.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),universal_class)** -> .
% 299.82/300.45  112485[0:Rew:57.0,112420.2] || member(u,universal_class) -> member(u,complement(intersection(complement(v),power_class(w))))* member(u,power_class(w)).
% 299.82/300.45  112587[0:SpR:509.0,30984.1] || member(u,universal_class) -> member(u,complement(intersection(complement(v),power_class(w))))* member(u,complement(v)).
% 299.82/300.45  112426[0:SpR:511.0,30985.1] || member(u,universal_class) -> member(u,complement(intersection(power_class(v),complement(w))))* member(u,complement(w)).
% 299.82/300.45  112646[0:Rew:57.0,112593.2] || member(u,universal_class) -> member(u,complement(intersection(power_class(v),complement(w))))* member(u,power_class(v)).
% 299.82/300.45  159958[3:Obv:159940.1] || member(u,ordinal_numbers) -> equal(not_subclass_element(unordered_pair(u,v),kind_1_ordinals),v)** subclass(unordered_pair(u,v),kind_1_ordinals).
% 299.82/300.45  30435[0:Res:1951.1,3486.1] || member(unordered_pair(u,v),symmetric_difference(w,x))* subclass(universal_class,complement(complement(intersection(w,x))))* -> .
% 299.82/300.45  5793[0:Res:3907.1,10.0] || equal(complement(complement(unordered_pair(u,v))),universal_class)** -> equal(singleton(w),v)* equal(singleton(w),u)*.
% 299.82/300.45  145039[2:MRR:51919.0,145036.0] ||  -> equal(unordered_pair(u,singleton(v)),regular(ordered_pair(u,v)))** equal(regular(ordered_pair(u,v)),singleton(u)).
% 299.82/300.45  143795[0:Res:1504.1,159.0] || subclass(ordered_pair(u,v),omega) -> equal(integer_of(unordered_pair(u,singleton(v))),unordered_pair(u,singleton(v)))**.
% 299.82/300.45  108448[0:Res:1504.1,10254.0] || subclass(ordered_pair(u,v),symmetric_difference(w,singleton(w)))* -> member(unordered_pair(u,singleton(v)),successor(w)).
% 299.82/300.45  108447[0:Res:1504.1,10191.0] || subclass(ordered_pair(u,v),symmetric_difference(w,inverse(w)))* -> member(unordered_pair(u,singleton(v)),symmetrization_of(w)).
% 299.82/300.45  108446[0:Res:1504.1,1952.0] || subclass(ordered_pair(u,v),symmetric_difference(w,x)) -> member(unordered_pair(u,singleton(v)),union(w,x))*.
% 299.82/300.45  108434[0:Res:1504.1,3.0] || subclass(ordered_pair(u,v),w)* subclass(w,x)* -> member(unordered_pair(u,singleton(v)),x)*.
% 299.82/300.45  41945[0:SpL:2330.1,30645.0] || equal(complement(unordered_pair(u,not_subclass_element(cross_product(v,w),x))),universal_class)** -> subclass(cross_product(v,w),x).
% 299.82/300.45  41944[0:SpL:2330.1,30584.0] || subclass(universal_class,complement(unordered_pair(u,not_subclass_element(cross_product(v,w),x))))* -> subclass(cross_product(v,w),x).
% 299.82/300.45  159957[3:Obv:159941.1] || member(u,ordinal_numbers) -> equal(not_subclass_element(unordered_pair(v,u),kind_1_ordinals),v)** subclass(unordered_pair(v,u),kind_1_ordinals).
% 299.82/300.45  37796[0:EqF:2143.1,2143.2] || equal(u,v) -> subclass(unordered_pair(v,u),w) equal(not_subclass_element(unordered_pair(v,u),w),v)**.
% 299.82/300.45  37823[0:Obv:37812.1] || member(u,v) -> equal(not_subclass_element(unordered_pair(w,u),v),w)** subclass(unordered_pair(w,u),v).
% 299.82/300.45  37821[0:Obv:37814.1] || member(u,v) -> equal(not_subclass_element(unordered_pair(u,w),v),w)** subclass(unordered_pair(u,w),v).
% 299.82/300.45  28581[0:Res:1476.1,513.0] || subclass(universal_class,intersection(complement(u),complement(v)))* member(unordered_pair(w,x),union(u,v))* -> .
% 299.82/300.45  41932[0:SpL:2330.1,30656.0] || equal(complement(unordered_pair(not_subclass_element(cross_product(u,v),w),x)),universal_class)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  41931[0:SpL:2330.1,30614.0] || subclass(universal_class,complement(unordered_pair(not_subclass_element(cross_product(u,v),w),x)))* -> subclass(cross_product(u,v),w).
% 299.82/300.45  89248[0:Res:51387.0,595.0] ||  -> subclass(u,complement(restrict(v,w,x))) member(not_subclass_element(u,complement(restrict(v,w,x))),v)*.
% 299.82/300.45  89250[0:Res:51387.0,1952.0] ||  -> subclass(u,complement(symmetric_difference(v,w))) member(not_subclass_element(u,complement(symmetric_difference(v,w))),union(v,w))*.
% 299.82/300.45  48505[0:Res:1481.2,10191.0] || subclass(u,symmetric_difference(v,inverse(v)))* -> subclass(u,w) member(not_subclass_element(u,w),symmetrization_of(v))*.
% 299.82/300.45  48607[0:Res:1481.2,10254.0] || subclass(u,symmetric_difference(v,singleton(v)))* -> subclass(u,w) member(not_subclass_element(u,w),successor(v))*.
% 299.82/300.45  122555[0:MRR:122501.0,34189.1] || subclass(u,complement(union(v,w)))* -> member(not_subclass_element(u,x),complement(v))* subclass(u,x).
% 299.82/300.45  122554[0:MRR:122502.0,34189.1] || subclass(u,complement(union(v,w)))* -> member(not_subclass_element(u,x),complement(w))* subclass(u,x).
% 299.82/300.45  9654[0:Res:1481.2,1952.0] || subclass(u,symmetric_difference(v,w)) -> subclass(u,x) member(not_subclass_element(u,x),union(v,w))*.
% 299.82/300.45  9635[0:Res:1481.2,3.0] || subclass(u,v)* subclass(v,w)* -> subclass(u,x) member(not_subclass_element(u,x),w)*.
% 299.82/300.45  89284[0:Rew:28.0,89223.1] ||  -> member(not_subclass_element(u,union(v,w)),intersection(complement(v),complement(w)))* subclass(u,union(v,w)).
% 299.82/300.45  126791[0:MRR:126714.0,34189.1] ||  -> member(not_subclass_element(intersection(complement(complement(u)),v),w),u)* subclass(intersection(complement(complement(u)),v),w).
% 299.82/300.45  126568[0:MRR:126496.0,34189.1] ||  -> member(not_subclass_element(intersection(u,complement(complement(v))),w),v)* subclass(intersection(u,complement(complement(v))),w).
% 299.82/300.45  107179[0:Res:34429.0,24.0] ||  -> subclass(complement(complement(intersection(u,v))),w) member(not_subclass_element(complement(complement(intersection(u,v))),w),v)*.
% 299.82/300.45  107178[0:Res:34429.0,23.0] ||  -> subclass(complement(complement(intersection(u,v))),w) member(not_subclass_element(complement(complement(intersection(u,v))),w),u)*.
% 299.82/300.45  107173[0:Res:34429.0,3.0] || subclass(u,v) -> subclass(complement(complement(u)),w) member(not_subclass_element(complement(complement(u)),w),v)*.
% 299.82/300.45  9407[0:Rew:30.0,9344.0] ||  -> subclass(restrict(u,v,w),x) member(not_subclass_element(restrict(u,v,w),x),cross_product(v,w))*.
% 299.82/300.45  113111[0:Res:9424.0,9649.0] ||  -> subclass(restrict(singleton(u),v,w),x) equal(not_subclass_element(restrict(singleton(u),v,w),x),u)**.
% 299.82/300.45  9367[0:Res:322.1,3.0] || subclass(u,v) -> subclass(intersection(w,u),x) member(not_subclass_element(intersection(w,u),x),v)*.
% 299.82/300.45  9371[0:Res:322.1,23.0] ||  -> subclass(intersection(u,intersection(v,w)),x) member(not_subclass_element(intersection(u,intersection(v,w)),x),v)*.
% 299.82/300.45  9372[0:Res:322.1,24.0] ||  -> subclass(intersection(u,intersection(v,w)),x) member(not_subclass_element(intersection(u,intersection(v,w)),x),w)*.
% 299.82/300.45  9481[0:Res:340.1,3.0] || subclass(u,v) -> subclass(intersection(u,w),x) member(not_subclass_element(intersection(u,w),x),v)*.
% 299.82/300.45  9485[0:Res:340.1,23.0] ||  -> subclass(intersection(intersection(u,v),w),x) member(not_subclass_element(intersection(intersection(u,v),w),x),u)*.
% 299.82/300.45  9486[0:Res:340.1,24.0] ||  -> subclass(intersection(intersection(u,v),w),x) member(not_subclass_element(intersection(intersection(u,v),w),x),v)*.
% 299.82/300.45  28297[0:Res:1495.2,144.0] || member(u,universal_class) subclass(rest_relation,rest_of(v)) -> equal(restrict(v,u,universal_class),rest_of(u))**.
% 299.82/300.45  28271[0:Res:1495.2,24.0] || member(u,universal_class) subclass(rest_relation,intersection(v,w))* -> member(ordered_pair(u,rest_of(u)),w)*.
% 299.82/300.45  28270[0:Res:1495.2,23.0] || member(u,universal_class) subclass(rest_relation,intersection(v,w))* -> member(ordered_pair(u,rest_of(u)),v)*.
% 299.82/300.45  28267[0:Res:1495.2,26.1] || member(u,universal_class) subclass(rest_relation,complement(v)) member(ordered_pair(u,rest_of(u)),v)* -> .
% 299.82/300.45  142021[2:Obv:142020.1] || member(u,universal_class) -> member(u,image(universal_class,singleton(u)))* asymmetric(cross_product(singleton(u),universal_class),v)*.
% 299.82/300.45  29645[0:Res:64.1,1487.1] function(complement(u)) || member(v,universal_class) -> member(v,u)* member(v,cross_product(universal_class,universal_class))*.
% 299.82/300.45  3638[0:Res:1477.1,19.0] || subclass(universal_class,cross_product(u,v))* -> equal(ordered_pair(first(singleton(w)),second(singleton(w))),singleton(w))**.
% 299.82/300.45  180005[11:Res:179843.1,9300.0] || equal(symmetric_difference(u,cross_product(v,w)),inverse(successor_relation)) -> member(successor_relation,complement(restrict(u,v,w)))*.
% 299.82/300.45  180007[11:Res:179843.1,9306.0] || equal(symmetric_difference(cross_product(u,v),w),inverse(successor_relation)) -> member(successor_relation,complement(restrict(w,u,v)))*.
% 299.82/300.45  181199[10:SpL:181067.0,35.0] || member(ordered_pair(singleton(singleton(successor_relation)),u),rotate(v))* -> member(ordered_pair(ordered_pair(universal_class,u),successor_relation),v).
% 299.82/300.45  181200[10:SpL:181067.0,38.0] || member(ordered_pair(singleton(singleton(successor_relation)),u),flip(v))* -> member(ordered_pair(ordered_pair(universal_class,successor_relation),u),v).
% 299.82/300.45  182937[6:Res:157922.1,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),element_relation) subclass(compose(element_relation,universal_class),intersection(y__dfg,ordinal_numbers))* -> .
% 299.82/300.45  183149[10:SpR:181044.1,15.0] || member(u,universal_class) -> equal(unordered_pair(successor_relation,unordered_pair(successor(u),singleton(v))),ordered_pair(successor(u),v))**.
% 299.82/300.45  183170[10:SpL:181044.1,1522.0] || member(u,universal_class) member(singleton(singleton(successor_relation)),cross_product(v,w))* -> member(successor(u),w)*.
% 299.82/300.45  183918[11:Res:183764.1,513.0] || subclass(universal_class,intersection(complement(u),complement(v)))* member(regular(symmetrization_of(successor_relation)),union(u,v)) -> .
% 299.82/300.45  185054[10:SpR:505.0,184981.1] || subclass(image(element_relation,union(u,v)),successor_relation) -> subclass(universal_class,power_class(intersection(complement(u),complement(v))))*.
% 299.82/300.45  185183[10:Res:1495.2,183723.0] || member(u,universal_class) subclass(rest_relation,symmetrization_of(successor_relation)) -> member(ordered_pair(u,rest_of(u)),inverse(successor_relation))*.
% 299.82/300.45  185188[10:Res:1495.2,183622.0] || member(u,universal_class) subclass(rest_relation,successor(successor_relation)) -> member(ordered_pair(u,rest_of(u)),singleton(successor_relation))*.
% 299.82/300.45  185389[10:SpR:185302.1,511.0] || equal(successor_relation,u) -> equal(complement(intersection(power_class(u),complement(v))),union(image(element_relation,universal_class),v))**.
% 299.82/300.45  185406[10:SpR:185302.1,509.0] || equal(successor_relation,u) -> equal(complement(intersection(complement(v),power_class(u))),union(v,image(element_relation,universal_class)))**.
% 299.82/300.45  185487[10:SpR:185302.1,505.0] || equal(image(element_relation,union(u,v)),successor_relation) -> equal(power_class(intersection(complement(u),complement(v))),universal_class)**.
% 299.82/300.45  185546[10:SpL:185302.1,9322.0] || equal(successor_relation,u) member(v,symmetric_difference(complement(w),universal_class))* -> member(v,union(w,u))*.
% 299.82/300.45  185675[10:Rew:142543.0,185545.1] || equal(successor_relation,u) member(v,symmetric_difference(universal_class,w))* member(v,union(w,u))* -> .
% 299.82/300.45  185770[10:SpL:505.0,185335.0] || equal(image(element_relation,power_class(intersection(complement(u),complement(v)))),power_class(image(element_relation,union(u,v))))** -> .
% 299.82/300.45  185819[10:Res:185430.1,9156.1] || equal(complement(restrict(u,v,w)),successor_relation)** member(x,universal_class) -> member(power_class(x),u)*.
% 299.82/300.45  185949[10:Res:185646.1,9300.0] || equal(complement(symmetric_difference(u,cross_product(v,w))),successor_relation) -> member(successor_relation,complement(restrict(u,v,w)))*.
% 299.82/300.45  185951[10:Res:185646.1,9306.0] || equal(complement(symmetric_difference(cross_product(u,v),w)),successor_relation) -> member(successor_relation,complement(restrict(w,u,v)))*.
% 299.82/300.45  186023[10:Res:185647.1,9300.0] || equal(complement(symmetric_difference(u,cross_product(v,w))),successor_relation) -> member(omega,complement(restrict(u,v,w)))*.
% 299.82/300.45  186025[10:Res:185647.1,9306.0] || equal(complement(symmetric_difference(cross_product(u,v),w)),successor_relation) -> member(omega,complement(restrict(w,u,v)))*.
% 299.82/300.45  186061[10:SpL:505.0,185795.0] || equal(power_class(intersection(complement(u),complement(v))),successor_relation)** -> equal(image(element_relation,union(u,v)),universal_class).
% 299.82/300.45  186349[10:Rew:160223.0,186320.1] || subclass(intersection(complement(u),complement(v)),successor_relation)* -> equal(complement(intersection(union(u,v),universal_class)),successor_relation).
% 299.82/300.45  183229[10:Rew:181137.1,183228.2] || member(u,universal_class)* member(ordered_pair(v,singleton(singleton(successor_relation))),composition_function)* -> equal(successor(u),universal_class).
% 299.82/300.45  107653[0:Res:99.1,6045.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,w) well_ordering(universal_class,w)* -> .
% 299.82/300.45  162019[10:Rew:160202.0,153413.0] || equal(sum_class(u),successor_relation) member(u,universal_class) well_ordering(element_relation,u)* -> member(u,ordinal_numbers).
% 299.82/300.45  107664[0:Res:34070.2,6045.0] || member(u,universal_class)* member(v,u)* subclass(element_relation,w) well_ordering(universal_class,w)* -> .
% 299.82/300.45  107570[0:Res:27.2,6045.0] || member(u,universal_class)* subclass(complement(v),w)* well_ordering(universal_class,w) -> member(u,v)*.
% 299.82/300.45  107651[0:Res:1495.2,6045.0] || member(u,universal_class)* subclass(rest_relation,v)* subclass(v,w)* well_ordering(universal_class,w)* -> .
% 299.82/300.45  163420[10:Rew:160202.0,160529.2] || subclass(complement(u),successor_relation)* member(v,universal_class)* well_ordering(w,successor_relation)* -> member(v,u)*.
% 299.82/300.45  163418[10:Rew:160202.0,160521.2,160202.0,160521.0] || subclass(sum_class(successor_relation),successor_relation)* member(ordinal_numbers,universal_class) well_ordering(element_relation,successor_relation) -> member(successor_relation,ordinal_numbers).
% 299.82/300.45  161923[10:Rew:160202.0,147194.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(rest_of(v),successor_relation) member(least(u,rest_of(v)),universal_class)*.
% 299.82/300.45  161928[10:Rew:160202.0,147198.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(compose_class(v),successor_relation) member(least(u,compose_class(v)),universal_class)*.
% 299.82/300.45  161985[10:Rew:160202.0,147320.2] || well_ordering(u,universal_class) -> member(least(u,complement(complement(v))),v)* equal(complement(complement(v)),successor_relation).
% 299.82/300.45  161973[10:Rew:160202.0,146930.1] || well_ordering(u,universal_class) -> equal(intersection(v,w),successor_relation) member(least(u,intersection(v,w)),v)*.
% 299.82/300.45  161974[10:Rew:160202.0,146929.1] || well_ordering(u,universal_class) -> equal(intersection(v,w),successor_relation) member(least(u,intersection(v,w)),w)*.
% 299.82/300.45  161437[10:Rew:160202.0,146635.2] || well_ordering(u,universal_class) subclass(v,w) -> equal(v,successor_relation) member(least(u,v),w)*.
% 299.82/300.45  108241[2:Res:31069.2,3.0] inductive(u) || well_ordering(v,universal_class) subclass(u,w) -> member(least(v,u),w)*.
% 299.82/300.45  108246[2:Res:31069.2,23.0] inductive(intersection(u,v)) || well_ordering(w,universal_class) -> member(least(w,intersection(u,v)),u)*.
% 299.82/300.45  108247[2:Res:31069.2,24.0] inductive(intersection(u,v)) || well_ordering(w,universal_class) -> member(least(w,intersection(u,v)),v)*.
% 299.82/300.45  163124[10:Rew:160202.0,160008.1] || well_ordering(u,kind_1_ordinals) -> equal(segment(u,intersection(v,ordinal_numbers),least(u,intersection(v,ordinal_numbers))),successor_relation)**.
% 299.82/300.45  163122[10:Rew:160202.0,159991.1] || well_ordering(u,kind_1_ordinals) -> equal(segment(u,intersection(ordinal_numbers,v),least(u,intersection(ordinal_numbers,v))),successor_relation)**.
% 299.82/300.45  163120[10:Rew:160202.0,159966.1] || well_ordering(u,kind_1_ordinals) -> equal(segment(u,complement(complement(ordinal_numbers)),least(u,complement(complement(ordinal_numbers)))),successor_relation)**.
% 299.82/300.45  160038[3:Res:159952.1,5829.0] || subclass(u,ordinal_numbers) well_ordering(v,kind_1_ordinals) -> subclass(u,w)* member(least(v,u),u)*.
% 299.82/300.45  160039[3:Res:159952.1,5832.1] inductive(u) || subclass(u,ordinal_numbers) well_ordering(v,kind_1_ordinals) -> member(least(v,u),u)*.
% 299.82/300.45  161978[10:Rew:160202.0,160036.2] || subclass(u,ordinal_numbers) well_ordering(v,kind_1_ordinals) -> equal(segment(v,u,least(v,u)),successor_relation)**.
% 299.82/300.45  160683[10:Rew:160202.0,160037.2] || subclass(u,ordinal_numbers) well_ordering(v,kind_1_ordinals) -> equal(u,successor_relation) member(least(v,u),u)*.
% 299.82/300.45  161438[10:Rew:160202.0,146631.2] || well_ordering(u,v) subclass(v,w) -> equal(v,successor_relation) member(least(u,v),w)*.
% 299.82/300.45  161866[10:Rew:160202.0,146909.2] || well_ordering(u,complement(v)) member(least(u,complement(v)),v)* -> equal(complement(v),successor_relation).
% 299.82/300.45  108795[2:Res:31076.2,26.1] inductive(complement(u)) || well_ordering(v,complement(u)) member(least(v,complement(u)),u)* -> .
% 299.82/300.45  155800[3:Res:31076.2,141576.1] inductive(complement(kind_1_ordinals)) || well_ordering(u,complement(kind_1_ordinals)) member(least(u,complement(kind_1_ordinals)),ordinal_numbers)* -> .
% 299.82/300.45  108794[2:Res:31076.2,3.0] inductive(u) || well_ordering(v,u) subclass(u,w) -> member(least(v,u),w)*.
% 299.82/300.45  161987[10:Rew:160202.0,147331.1] || member(singleton(u),ordinal_numbers) -> equal(sum_class(singleton(u)),successor_relation) equal(regular(sum_class(singleton(u))),u)**.
% 299.82/300.45  187777[10:Res:187500.1,19.0] || subclass(universal_class,cross_product(u,v))* -> equal(ordered_pair(first(power_class(successor_relation)),second(power_class(successor_relation))),power_class(successor_relation))**.
% 299.82/300.45  187781[10:Res:187500.1,9300.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(power_class(successor_relation),complement(restrict(u,v,w)))*.
% 299.82/300.45  187783[10:Res:187500.1,9306.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(power_class(successor_relation),complement(restrict(w,u,v)))*.
% 299.82/300.45  188830[10:Res:25.2,185065.1] || member(singleton(u),v)* member(singleton(u),w)* subclass(intersection(w,v),successor_relation)* -> .
% 299.82/300.45  189379[15:Rew:189339.1,28103.2] || member(u,universal_class) subclass(domain_relation,restrict(v,w,x))* -> member(ordered_pair(u,successor_relation),v)*.
% 299.82/300.45  189465[15:Rew:189339.1,189393.1] || member(u,universal_class) equal(compose(v,u),successor_relation) -> member(ordered_pair(u,successor_relation),compose_class(v))*.
% 299.82/300.45  190478[10:Obv:190472.1] || equal(singleton(u),successor_relation) -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),successor_relation).
% 299.82/300.45  190479[10:Obv:190470.1] || equal(singleton(u),successor_relation) -> equal(regular(unordered_pair(v,u)),v)** equal(unordered_pair(v,u),successor_relation).
% 299.82/300.45  191063[10:Rew:181056.0,191053.0] || asymmetric(u,successor_relation) -> equal(range__dfg(intersection(u,inverse(u)),universal_class,successor_relation),second(not_subclass_element(successor_relation,successor_relation)))**.
% 299.82/300.45  192131[15:SpR:190721.0,15.0] ||  -> equal(range_of(u),successor_relation) equal(unordered_pair(successor_relation,unordered_pair(inverse(u),singleton(v))),ordered_pair(inverse(u),v))**.
% 299.82/300.45  192160[15:SpL:190721.0,1522.0] || member(singleton(singleton(successor_relation)),cross_product(u,v))* -> equal(range_of(w),successor_relation) member(inverse(w),v)*.
% 299.82/300.45  192389[20:SpL:505.0,192322.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),omega)** -> .
% 299.82/300.45  192571[10:Res:160214.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(successor_relation,least(omega,universal_class))),successor_relation)**.
% 299.82/300.45  192613[20:Res:191039.0,162356.0] || subclass(omega,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(successor_relation,least(omega,omega))),successor_relation)**.
% 299.82/300.45  192626[15:Obv:192623.1] || equal(successor(u),successor_relation) -> equal(regular(unordered_pair(v,u)),v)** equal(unordered_pair(v,u),successor_relation).
% 299.82/300.45  192627[15:Obv:192622.1] || equal(successor(u),successor_relation) -> equal(regular(unordered_pair(u,v)),v)** equal(unordered_pair(u,v),successor_relation).
% 299.82/300.45  193504[15:SSi:193474.0,71.0] ||  -> equal(unordered_pair(u,v),successor_relation) equal(apply(choice,unordered_pair(u,v)),v)** equal(cantor(u),successor_relation).
% 299.82/300.45  193505[15:SSi:193475.0,71.0] ||  -> equal(unordered_pair(u,v),successor_relation) equal(apply(choice,unordered_pair(u,v)),u)** equal(cantor(v),successor_relation).
% 299.82/300.45  194056[10:Res:5768.2,185639.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,w)* equal(successor_relation,w) -> .
% 299.82/300.45  194085[10:Res:1495.2,193819.0] || member(u,universal_class) subclass(rest_relation,cantor(complement(cross_product(singleton(ordered_pair(u,rest_of(u))),universal_class))))* -> .
% 299.82/300.45  194532[0:Res:1495.2,183398.0] || member(u,universal_class) subclass(rest_relation,complement(complement(v))) -> member(ordered_pair(u,rest_of(u)),v)*.
% 299.82/300.45  194678[15:Obv:194643.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),w),u)** subclass(unordered_pair(u,v),w) equal(cantor(v),successor_relation).
% 299.82/300.45  194679[15:Obv:194642.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w) equal(cantor(u),successor_relation).
% 299.82/300.45  195383[0:SpR:194805.1,1933.0] || subclass(inverse(u),u) -> equal(intersection(complement(inverse(u)),symmetrization_of(u)),symmetric_difference(u,inverse(u)))**.
% 299.82/300.45  195385[10:SpR:194805.1,160364.1] || subclass(inverse(u),u)* asymmetric(u,v) -> equal(restrict(inverse(u),v,v),successor_relation)**.
% 299.82/300.45  195393[0:SpR:194805.1,1934.0] || subclass(singleton(u),u) -> equal(intersection(complement(singleton(u)),successor(u)),symmetric_difference(u,singleton(u)))**.
% 299.82/300.45  195407[0:SpR:194805.1,161.0] || subclass(union(u,v),complement(intersection(u,v)))* -> equal(symmetric_difference(u,v),union(u,v)).
% 299.82/300.45  195408[0:SpR:194805.1,1933.0] || subclass(symmetrization_of(u),complement(intersection(u,inverse(u))))* -> equal(symmetric_difference(u,inverse(u)),symmetrization_of(u)).
% 299.82/300.45  195409[0:SpR:194805.1,1934.0] || subclass(successor(u),complement(intersection(u,singleton(u))))* -> equal(symmetric_difference(u,singleton(u)),successor(u)).
% 299.82/300.45  195506[10:SpL:194805.1,160365.0] || subclass(inverse(u),u)* equal(restrict(inverse(u),v,v),successor_relation)** -> asymmetric(u,v).
% 299.82/300.45  195579[0:Rew:194805.1,195365.1] || subclass(ordinal_numbers,y__dfg) member(least(element_relation,ordinal_numbers),universal_class) -> member(least(element_relation,ordinal_numbers),complement(ordinal_numbers))*.
% 299.82/300.45  195929[0:SpR:195152.0,161.0] ||  -> equal(intersection(complement(intersection(u,v)),union(u,intersection(u,v))),symmetric_difference(u,intersection(u,v)))**.
% 299.82/300.45  196071[0:SpR:195339.0,161.0] ||  -> equal(intersection(complement(intersection(u,v)),union(v,intersection(u,v))),symmetric_difference(v,intersection(u,v)))**.
% 299.82/300.45  196514[10:SpR:161137.0,139600.0] ||  -> equal(intersection(image(element_relation,symmetrization_of(successor_relation)),complement(power_class(complement(inverse(successor_relation))))),complement(power_class(complement(inverse(successor_relation)))))**.
% 299.82/300.45  196560[10:SpL:161137.0,195436.0] || subclass(image(element_relation,symmetrization_of(successor_relation)),power_class(complement(inverse(successor_relation))))* -> equal(image(element_relation,symmetrization_of(successor_relation)),successor_relation).
% 299.82/300.45  196588[10:Rew:161137.0,196567.1] || subclass(power_class(complement(inverse(successor_relation))),image(element_relation,symmetrization_of(successor_relation)))* -> equal(power_class(complement(inverse(successor_relation))),successor_relation).
% 299.82/300.45  196666[10:SpL:2330.1,185803.0] || equal(complement(complement(singleton(not_subclass_element(cross_product(u,v),w)))),successor_relation)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  196720[10:SpR:162889.0,139600.0] ||  -> equal(intersection(image(element_relation,successor(successor_relation)),complement(power_class(complement(singleton(successor_relation))))),complement(power_class(complement(singleton(successor_relation)))))**.
% 299.82/300.45  196766[10:SpL:162889.0,195436.0] || subclass(image(element_relation,successor(successor_relation)),power_class(complement(singleton(successor_relation))))* -> equal(image(element_relation,successor(successor_relation)),successor_relation).
% 299.82/300.45  196793[10:Rew:162889.0,196773.1] || subclass(power_class(complement(singleton(successor_relation))),image(element_relation,successor(successor_relation)))* -> equal(power_class(complement(singleton(successor_relation))),successor_relation).
% 299.82/300.45  198309[10:SpR:163003.0,194805.1] || subclass(intersection(u,image(element_relation,successor_relation)),power_class(universal_class))* -> equal(intersection(u,image(element_relation,successor_relation)),successor_relation).
% 299.82/300.45  198382[10:SpR:163001.0,194805.1] || subclass(intersection(image(element_relation,successor_relation),u),power_class(universal_class))* -> equal(intersection(image(element_relation,successor_relation),u),successor_relation).
% 299.82/300.45  198460[10:SpR:162945.0,194805.1] || subclass(intersection(complement(singleton(successor_relation)),u),successor(successor_relation))* -> equal(intersection(complement(singleton(successor_relation)),u),successor_relation).
% 299.82/300.45  198569[10:SpR:162944.0,194805.1] || subclass(intersection(u,complement(singleton(successor_relation))),successor(successor_relation))* -> equal(intersection(u,complement(singleton(successor_relation))),successor_relation).
% 299.82/300.45  199201[10:SpR:162292.0,194805.1] || subclass(intersection(u,complement(inverse(successor_relation))),symmetrization_of(successor_relation))* -> equal(intersection(u,complement(inverse(successor_relation))),successor_relation).
% 299.82/300.45  199277[10:SpR:162291.0,194805.1] || subclass(intersection(complement(inverse(successor_relation)),u),symmetrization_of(successor_relation))* -> equal(intersection(complement(inverse(successor_relation)),u),successor_relation).
% 299.82/300.45  199516[10:SpR:161845.0,194805.1] || subclass(intersection(u,image(element_relation,universal_class)),power_class(successor_relation))* -> equal(intersection(u,image(element_relation,universal_class)),successor_relation).
% 299.82/300.45  199592[10:SpR:161843.0,194805.1] || subclass(intersection(image(element_relation,universal_class),u),power_class(successor_relation))* -> equal(intersection(image(element_relation,universal_class),u),successor_relation).
% 299.82/300.45  199997[6:Res:199848.1,9300.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(regular(rest_relation),complement(restrict(u,v,w)))*.
% 299.82/300.45  199999[6:Res:199848.1,9306.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(regular(rest_relation),complement(restrict(w,u,v)))*.
% 299.82/300.45  200071[14:SpR:200028.1,15.0] || member(u,universal_class) -> equal(unordered_pair(successor_relation,unordered_pair(range_of(u),singleton(v))),ordered_pair(range_of(u),v))**.
% 299.82/300.45  200117[14:SpL:200028.1,1522.0] || member(u,universal_class) member(singleton(singleton(successor_relation)),cross_product(v,w))* -> member(range_of(u),w)*.
% 299.82/300.45  200267[6:SpL:199964.0,144.0] || member(regular(rest_relation),rest_of(u)) -> equal(restrict(u,first(regular(rest_relation)),universal_class),second(regular(rest_relation)))**.
% 299.82/300.45  200292[6:SpL:199964.0,98.0] || member(ordered_pair(u,regular(rest_relation)),composition_function)* -> equal(compose(u,first(regular(rest_relation))),second(regular(rest_relation))).
% 299.82/300.45  200389[6:Res:200240.0,127.0] || subclass(regular(rest_relation),u)* well_ordering(v,u)* -> member(least(v,regular(rest_relation)),regular(rest_relation))*.
% 299.82/300.45  200676[10:Res:161493.2,9322.0] inductive(symmetric_difference(complement(u),complement(v))) ||  -> equal(integer_of(w),successor_relation) member(w,union(u,v))*.
% 299.82/300.45  200698[10:Res:161493.2,8846.0] inductive(restrict(intersection(y__dfg,ordinal_numbers),u,v)) ||  -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation)**.
% 299.82/300.45  200705[10:Res:161493.2,144.0] inductive(rest_of(u)) ||  -> equal(integer_of(ordered_pair(v,w)),successor_relation)** equal(restrict(u,v,universal_class),w)*.
% 299.82/300.45  200720[10:Res:161493.2,98.0] inductive(composition_function) ||  -> equal(integer_of(ordered_pair(u,ordered_pair(v,w))),successor_relation)** equal(compose(u,v),w).
% 299.82/300.45  200787[10:Res:161493.2,160488.0] inductive(unordered_pair(successor_relation,u)) ||  -> equal(integer_of(intersection(y__dfg,ordinal_numbers)),successor_relation)** equal(intersection(y__dfg,ordinal_numbers),u)*.
% 299.82/300.45  200788[10:Res:161493.2,160486.0] inductive(unordered_pair(u,successor_relation)) ||  -> equal(integer_of(intersection(y__dfg,ordinal_numbers)),successor_relation)** equal(intersection(y__dfg,ordinal_numbers),u)*.
% 299.82/300.45  200898[10:MRR:200849.2,160215.0] || equal(cantor(restrict(u,v,w)),successor_relation)** subclass(w,v) -> section(u,w,v).
% 299.82/300.45  201387[6:Res:201231.1,9300.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(regular(domain_relation),complement(restrict(u,v,w)))*.
% 299.82/300.45  201389[6:Res:201231.1,9306.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(regular(domain_relation),complement(restrict(w,u,v)))*.
% 299.82/300.45  201511[6:SpL:201355.0,144.0] || member(regular(domain_relation),rest_of(u)) -> equal(restrict(u,first(regular(domain_relation)),universal_class),second(regular(domain_relation)))**.
% 299.82/300.45  201536[6:SpL:201355.0,98.0] || member(ordered_pair(u,regular(domain_relation)),composition_function)* -> equal(compose(u,first(regular(domain_relation))),second(regular(domain_relation))).
% 299.82/300.45  201586[6:Res:201484.0,127.0] || subclass(regular(domain_relation),u)* well_ordering(v,u)* -> member(least(v,regular(domain_relation)),regular(domain_relation))*.
% 299.82/300.45  201679[10:Res:201671.0,160292.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(complement(kind_1_ordinals),successor_relation) member(least(u,complement(kind_1_ordinals)),complement(kind_1_ordinals))*.
% 299.82/300.45  201682[3:Res:201671.0,5832.1] inductive(complement(kind_1_ordinals)) || well_ordering(u,complement(ordinal_numbers)) -> member(least(u,complement(kind_1_ordinals)),complement(kind_1_ordinals))*.
% 299.82/300.45  201856[14:SpL:119971.0,184006.1] || member(cross_product(u,universal_class),universal_class)* equal(rest_of(cross_product(u,universal_class)),sum_class(image(universal_class,u))) -> .
% 299.82/300.45  201929[10:Res:161492.2,9332.1] || equal(intersection(u,v),omega) member(w,symmetric_difference(u,v))* -> equal(integer_of(w),successor_relation).
% 299.82/300.45  201933[10:Res:161492.2,594.0] || equal(restrict(u,v,w),omega)** -> equal(integer_of(x),successor_relation) member(x,cross_product(v,w))*.
% 299.82/300.45  201953[10:Res:161492.2,10.0] || equal(unordered_pair(u,v),omega)** -> equal(integer_of(w),successor_relation)** equal(w,v)* equal(w,u)*.
% 299.82/300.45  201954[10:Res:161492.2,307.0] || equal(image(element_relation,complement(u)),omega)** member(v,power_class(u))* -> equal(integer_of(v),successor_relation).
% 299.82/300.45  201956[10:Res:161492.2,160481.0] || equal(regular(u),omega) member(v,u)* -> equal(integer_of(v),successor_relation) equal(u,successor_relation).
% 299.82/300.45  201960[10:Res:161492.2,175.0] || equal(intersection(intersection(y__dfg,ordinal_numbers),u),omega)** -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation)**.
% 299.82/300.45  201961[10:Res:161492.2,178.0] || equal(intersection(u,intersection(y__dfg,ordinal_numbers)),omega)** -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation)**.
% 299.82/300.45  201977[10:Res:161492.2,95.0] || equal(compose_class(u),omega) -> equal(integer_of(ordered_pair(v,w)),successor_relation)** equal(compose(u,v),w)*.
% 299.82/300.45  202024[10:Res:161492.2,1013.0] || equal(rest_relation,omega) -> equal(integer_of(singleton(singleton(singleton(u)))),successor_relation)** equal(rest_of(singleton(u)),u).
% 299.82/300.45  202460[10:SpR:208.0,163217.0] ||  -> member(successor_relation,image(element_relation,power_class(image(element_relation,complement(u)))))* member(successor_relation,power_class(image(element_relation,power_class(u)))).
% 299.82/300.45  202598[10:MRR:202543.2,160215.0] || equal(rest_of(restrict(u,v,w)),successor_relation)** subclass(w,v) -> section(u,w,v).
% 299.82/300.45  202764[10:MRR:202748.0,34067.1] || member(u,union(v,successor_relation))* subclass(symmetric_difference(complement(v),universal_class),w)* -> member(u,w)*.
% 299.82/300.45  202781[10:Res:160827.1,9.0] || subclass(power_class(universal_class),singleton(u))* -> member(u,image(element_relation,successor_relation)) equal(power_class(universal_class),singleton(u)).
% 299.82/300.45  202846[11:Res:25.2,168534.1] || member(successor_relation,u) member(successor_relation,v) equal(complement(intersection(v,u)),symmetrization_of(successor_relation))** -> .
% 299.82/300.45  204663[6:Rew:203192.0,203856.2] inductive(domain_of(u)) || well_ordering(v,cantor(u)) -> member(least(v,cantor(u)),cantor(u))*.
% 299.82/300.45  203861[10:Rew:203192.0,200760.2] inductive(rest_of(u)) ||  -> equal(integer_of(singleton(singleton(singleton(v)))),successor_relation)** member(singleton(v),cantor(u))*.
% 299.82/300.45  204011[6:Rew:203192.0,160048.0] || subclass(cantor(restrict(u,v,kind_1_ordinals)),ordinal_numbers)* subclass(kind_1_ordinals,v) -> section(u,kind_1_ordinals,v).
% 299.82/300.45  204013[10:Rew:203192.0,160507.2] || equal(successor_relation,u) section(v,u,w) -> equal(cantor(restrict(v,w,u)),u)**.
% 299.82/300.45  204022[6:Rew:203192.0,10424.1] || section(cross_product(u,v),w,x) -> subclass(cantor(restrict(cross_product(x,w),u,v)),w)*.
% 299.82/300.45  204166[6:Rew:203285.0,108275.2] inductive(cantor(inverse(u))) || well_ordering(v,universal_class) -> member(least(v,range_of(u)),range_of(u))*.
% 299.82/300.45  206021[10:Res:163210.1,9.0] || subclass(symmetrization_of(successor_relation),singleton(u))* -> member(u,complement(inverse(successor_relation))) equal(symmetrization_of(successor_relation),singleton(u)).
% 299.82/300.45  206036[10:Res:160970.1,9.0] || subclass(power_class(successor_relation),singleton(u))* -> member(u,image(element_relation,universal_class)) equal(power_class(successor_relation),singleton(u)).
% 299.82/300.45  206050[10:Res:25.2,163205.1] || member(successor_relation,u) member(successor_relation,v) equal(complement(intersection(v,u)),successor(successor_relation))** -> .
% 299.82/300.45  206706[10:Res:206690.0,162356.0] || subclass(kind_1_ordinals,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(successor_relation,least(omega,kind_1_ordinals))),successor_relation)**.
% 299.82/300.45  207536[10:SpR:505.0,206226.1] ||  -> member(successor_relation,image(element_relation,union(u,v))) subclass(successor(successor_relation),power_class(intersection(complement(u),complement(v))))*.
% 299.82/300.45  208347[10:SpL:505.0,208258.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),kind_1_ordinals)** -> .
% 299.82/300.45  208897[10:SpL:208.0,162918.1] || equal(image(element_relation,power_class(u)),successor(successor_relation)) equal(power_class(image(element_relation,complement(u))),universal_class)** -> .
% 299.82/300.45  208910[10:Res:25.2,163207.1] || member(successor_relation,u) member(successor_relation,v) equal(complement(intersection(v,u)),singleton(successor_relation))** -> .
% 299.82/300.45  209084[10:SpL:208.0,162872.1] || equal(image(element_relation,power_class(u)),singleton(successor_relation)) equal(power_class(image(element_relation,complement(u))),universal_class)** -> .
% 299.82/300.45  209104[10:Res:163218.1,9.0] || subclass(successor(successor_relation),singleton(u))* -> member(u,complement(singleton(successor_relation))) equal(successor(successor_relation),singleton(u)).
% 299.82/300.45  209464[12:Res:209377.1,9300.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(regular(element_relation),complement(restrict(u,v,w)))*.
% 299.82/300.45  209466[12:Res:209377.1,9306.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(regular(element_relation),complement(restrict(w,u,v)))*.
% 299.82/300.45  209532[12:SpL:209433.0,144.0] || member(regular(element_relation),rest_of(u)) -> equal(restrict(u,first(regular(element_relation)),universal_class),second(regular(element_relation)))**.
% 299.82/300.45  209554[12:SpL:209433.0,98.0] || member(ordered_pair(u,regular(element_relation)),composition_function)* -> equal(compose(u,first(regular(element_relation))),second(regular(element_relation))).
% 299.82/300.45  209658[12:Res:209506.0,127.0] || subclass(regular(element_relation),u)* well_ordering(v,u)* -> member(least(v,regular(element_relation)),regular(element_relation))*.
% 299.82/300.45  210348[15:Res:189563.1,3.0] || subclass(domain_relation,flip(u))* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,x),successor_relation),v)*.
% 299.82/300.45  210352[15:Res:189563.1,148657.1] || subclass(domain_relation,flip(complement(compose(element_relation,universal_class))))* member(ordered_pair(ordered_pair(u,v),successor_relation),element_relation)* -> .
% 299.82/300.45  210361[15:Res:189563.1,1952.0] || subclass(domain_relation,flip(symmetric_difference(u,v))) -> member(ordered_pair(ordered_pair(w,x),successor_relation),union(u,v))*.
% 299.82/300.45  210362[15:Res:189563.1,10191.0] || subclass(domain_relation,flip(symmetric_difference(u,inverse(u))))* -> member(ordered_pair(ordered_pair(v,w),successor_relation),symmetrization_of(u))*.
% 299.82/300.45  210363[15:Res:189563.1,10254.0] || subclass(domain_relation,flip(symmetric_difference(u,singleton(u))))* -> member(ordered_pair(ordered_pair(v,w),successor_relation),successor(u))*.
% 299.82/300.45  210421[15:Res:189564.1,3.0] || subclass(domain_relation,rotate(u))* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,successor_relation),x),v)*.
% 299.82/300.45  210425[15:Res:189564.1,148657.1] || subclass(domain_relation,rotate(complement(compose(element_relation,universal_class))))* member(ordered_pair(ordered_pair(u,successor_relation),v),element_relation)* -> .
% 299.82/300.45  210434[15:Res:189564.1,1952.0] || subclass(domain_relation,rotate(symmetric_difference(u,v))) -> member(ordered_pair(ordered_pair(w,successor_relation),x),union(u,v))*.
% 299.82/300.45  210435[15:Res:189564.1,10191.0] || subclass(domain_relation,rotate(symmetric_difference(u,inverse(u))))* -> member(ordered_pair(ordered_pair(v,successor_relation),w),symmetrization_of(u))*.
% 299.82/300.45  210436[15:Res:189564.1,10254.0] || subclass(domain_relation,rotate(symmetric_difference(u,singleton(u))))* -> member(ordered_pair(ordered_pair(v,successor_relation),w),successor(u))*.
% 299.82/300.45  210672[0:Res:34429.0,183398.0] ||  -> subclass(complement(complement(complement(complement(u)))),v) member(not_subclass_element(complement(complement(complement(complement(u)))),v),u)*.
% 299.82/300.45  210774[2:Res:31069.2,183398.0] inductive(complement(complement(u))) || well_ordering(v,universal_class) -> member(least(v,complement(complement(u))),u)*.
% 299.82/300.45  211057[11:Res:25.2,179992.1] || member(successor_relation,u) member(successor_relation,v) equal(complement(intersection(v,u)),inverse(successor_relation))** -> .
% 299.82/300.45  211130[10:Res:161445.2,141576.1] || well_ordering(u,complement(kind_1_ordinals)) member(least(u,complement(kind_1_ordinals)),ordinal_numbers)* -> equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.45  211328[10:SpL:181073.0,160488.0] || member(intersection(y__dfg,ordinal_numbers),ordered_pair(universal_class,u))* -> equal(unordered_pair(universal_class,singleton(u)),intersection(y__dfg,ordinal_numbers)).
% 299.82/300.45  211399[10:MRR:211398.0,160315.0] ||  -> equal(apply(choice,ordered_pair(universal_class,universal_class)),unordered_pair(universal_class,successor_relation))** equal(apply(choice,ordered_pair(universal_class,universal_class)),successor_relation).
% 299.82/300.45  211481[10:Res:161493.2,187490.0] inductive(image(element_relation,universal_class)) ||  -> equal(integer_of(apply(choice,power_class(successor_relation))),successor_relation)** equal(power_class(successor_relation),successor_relation).
% 299.82/300.45  211490[10:Res:25.2,211446.0] || member(singleton(successor_relation),u) member(singleton(successor_relation),v) well_ordering(universal_class,intersection(v,u))* -> .
% 299.82/300.45  211540[10:SpL:185302.1,161505.0] || equal(successor_relation,u) member(regular(power_class(u)),image(element_relation,universal_class))* -> equal(power_class(u),successor_relation).
% 299.82/300.45  211560[10:Res:161493.2,161505.0] inductive(image(element_relation,complement(u))) ||  -> equal(integer_of(regular(power_class(u))),successor_relation)** equal(power_class(u),successor_relation).
% 299.82/300.45  211562[10:Rew:185302.1,211554.1] || equal(successor_relation,u) member(regular(power_class(successor_relation)),image(element_relation,universal_class))* -> equal(power_class(u),successor_relation)**.
% 299.82/300.45  211563[10:Rew:160223.0,211555.1] || equal(successor_relation,u) member(regular(power_class(u)),image(element_relation,universal_class))* -> equal(power_class(successor_relation),successor_relation).
% 299.82/300.45  211599[10:Res:9424.0,160705.0] || member(regular(restrict(complement(kind_1_ordinals),u,v)),ordinal_numbers)* -> equal(restrict(complement(kind_1_ordinals),u,v),successor_relation).
% 299.82/300.45  211689[10:Res:181213.1,9322.0] || equal(symmetric_difference(complement(u),complement(v)),singleton(singleton(successor_relation))) -> member(singleton(successor_relation),union(u,v))*.
% 299.82/300.45  211699[10:Res:181213.1,10.0] || equal(unordered_pair(u,v),singleton(singleton(successor_relation)))** -> equal(singleton(successor_relation),v) equal(singleton(successor_relation),u).
% 299.82/300.45  211779[10:Rew:142543.0,211735.1,160223.0,211735.1] || member(u,universal_class) -> equal(complement(image(element_relation,successor(successor(u)))),power_class(symmetric_difference(universal_class,successor(u))))**.
% 299.82/300.45  211780[15:Rew:142543.0,211736.1,160223.0,211736.1] ||  -> equal(range_of(u),successor_relation) equal(complement(image(element_relation,successor(inverse(u)))),power_class(symmetric_difference(universal_class,inverse(u))))**.
% 299.82/300.45  211781[14:Rew:142543.0,211737.1,160223.0,211737.1] || member(u,universal_class) -> equal(complement(image(element_relation,successor(range_of(u)))),power_class(symmetric_difference(universal_class,range_of(u))))**.
% 299.82/300.45  211794[11:SpL:208.0,182321.1] || equal(image(element_relation,power_class(u)),inverse(successor_relation)) equal(power_class(image(element_relation,complement(u))),universal_class)** -> .
% 299.82/300.45  211950[10:SpR:208.0,183456.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(image(element_relation,complement(u)))),complement(power_class(image(element_relation,power_class(u))))),successor_relation)**.
% 299.82/300.45  211987[11:Res:183759.1,9322.0] || subclass(inverse(successor_relation),symmetric_difference(complement(u),complement(v)))* -> member(regular(symmetrization_of(successor_relation)),union(u,v)).
% 299.82/300.45  212047[2:SpR:208.0,184090.1] || equal(symmetric_difference(universal_class,image(element_relation,power_class(u))),universal_class) -> member(omega,power_class(image(element_relation,complement(u))))*.
% 299.82/300.45  212094[10:Res:161493.2,163312.0] inductive(u) ||  -> equal(integer_of(regular(regular(u))),successor_relation)** equal(regular(u),successor_relation) equal(u,successor_relation).
% 299.82/300.45  212136[10:SpL:208.0,184637.0] || subclass(power_class(image(element_relation,complement(u))),successor_relation)* -> equal(symmetric_difference(universal_class,image(element_relation,power_class(u))),successor_relation).
% 299.82/300.45  212488[10:SpL:208.0,185801.0] || equal(complement(power_class(image(element_relation,complement(u)))),successor_relation)** subclass(universal_class,image(element_relation,power_class(u))) -> .
% 299.82/300.45  212505[10:SpL:208.0,185935.0] || equal(complement(power_class(image(element_relation,complement(u)))),successor_relation)** member(successor_relation,image(element_relation,power_class(u))) -> .
% 299.82/300.45  212852[10:Rew:9949.0,212837.0] || equal(complement(image(element_relation,successor(u))),successor_relation) member(successor_relation,complement(image(element_relation,successor(u))))* -> .
% 299.82/300.45  212853[10:Rew:9948.0,212838.0] || equal(complement(image(element_relation,symmetrization_of(u))),successor_relation) member(successor_relation,complement(image(element_relation,symmetrization_of(u))))* -> .
% 299.82/300.45  212865[10:SpL:208.0,186009.0] || equal(complement(power_class(image(element_relation,complement(u)))),successor_relation)** member(omega,image(element_relation,power_class(u))) -> .
% 299.82/300.45  212882[10:Rew:9949.0,212874.0] || equal(complement(image(element_relation,successor(u))),successor_relation) member(omega,complement(image(element_relation,successor(u))))* -> .
% 299.82/300.45  212883[10:Rew:9948.0,212875.0] || equal(complement(image(element_relation,symmetrization_of(u))),successor_relation) member(omega,complement(image(element_relation,symmetrization_of(u))))* -> .
% 299.82/300.45  212981[10:SpL:208.0,187767.0] || subclass(universal_class,power_class(image(element_relation,complement(u))))* member(power_class(successor_relation),image(element_relation,power_class(u))) -> .
% 299.82/300.45  213105[10:SpR:208.0,188444.1] || equal(symmetric_difference(universal_class,image(element_relation,power_class(u))),universal_class) -> member(successor_relation,power_class(image(element_relation,complement(u))))*.
% 299.82/300.45  213143[10:SpL:160367.0,160800.0] || subclass(u,union(v,successor_relation)) member(regular(u),symmetric_difference(universal_class,v))* -> equal(u,successor_relation).
% 299.82/300.45  213218[15:Res:189485.1,9322.0] || subclass(domain_relation,symmetric_difference(complement(u),complement(v))) -> member(singleton(singleton(singleton(successor_relation))),union(u,v))*.
% 299.82/300.45  213522[10:SpL:161194.0,160801.0] || subclass(u,symmetric_difference(complement(v),universal_class))* -> equal(u,successor_relation) member(regular(u),union(v,successor_relation)).
% 299.82/300.45  213813[20:SpL:208.0,192317.1] || equal(image(element_relation,power_class(u)),inverse(successor_relation)) equal(power_class(image(element_relation,complement(u))),omega)** -> .
% 299.82/300.45  213827[20:SpL:208.0,192318.1] || equal(image(element_relation,power_class(u)),singleton(successor_relation)) equal(power_class(image(element_relation,complement(u))),omega)** -> .
% 299.82/300.45  213841[20:SpL:208.0,192319.1] || equal(image(element_relation,power_class(u)),successor(successor_relation)) equal(power_class(image(element_relation,complement(u))),omega)** -> .
% 299.82/300.45  214139[20:SpR:208.0,193270.1] || equal(symmetric_difference(universal_class,image(element_relation,power_class(u))),omega) -> member(successor_relation,power_class(image(element_relation,complement(u))))*.
% 299.82/300.45  214235[10:SpL:208.0,194513.0] || equal(complement(complement(power_class(image(element_relation,complement(u))))),successor_relation)** -> member(omega,image(element_relation,power_class(u))).
% 299.82/300.45  214265[10:SpL:208.0,194520.0] || subclass(universal_class,complement(power_class(image(element_relation,complement(u)))))* -> member(power_class(successor_relation),image(element_relation,power_class(u))).
% 299.82/300.45  214346[10:SpL:208.0,194540.0] || equal(complement(complement(power_class(image(element_relation,complement(u))))),successor_relation)** -> member(successor_relation,image(element_relation,power_class(u))).
% 299.82/300.45  214532[10:SpR:163032.0,30984.1] || member(u,universal_class) -> member(u,complement(symmetric_difference(v,universal_class))) member(u,complement(intersection(v,universal_class)))*.
% 299.82/300.45  214593[11:SpL:208.0,194541.0] || equal(complement(power_class(image(element_relation,complement(u)))),inverse(successor_relation))** -> member(successor_relation,image(element_relation,power_class(u))).
% 299.82/300.45  214662[10:SpL:208.0,194542.0] || equal(complement(power_class(image(element_relation,complement(u)))),singleton(successor_relation))** -> member(successor_relation,image(element_relation,power_class(u))).
% 299.82/300.45  214681[10:SpL:208.0,194543.0] || equal(complement(power_class(image(element_relation,complement(u)))),successor(successor_relation))** -> member(successor_relation,image(element_relation,power_class(u))).
% 299.82/300.45  214701[11:SpL:208.0,194544.0] || equal(complement(power_class(image(element_relation,complement(u)))),symmetrization_of(successor_relation))** -> member(successor_relation,image(element_relation,power_class(u))).
% 299.82/300.45  214721[2:SpL:208.0,195403.0] || subclass(universal_class,power_class(image(element_relation,complement(u))))* -> equal(symmetric_difference(universal_class,image(element_relation,power_class(u))),universal_class).
% 299.82/300.45  214771[10:Res:161697.1,183723.0] ||  -> equal(restrict(symmetrization_of(successor_relation),u,v),successor_relation) member(regular(restrict(symmetrization_of(successor_relation),u,v)),inverse(successor_relation))*.
% 299.82/300.45  214773[10:Res:161697.1,183622.0] ||  -> equal(restrict(successor(successor_relation),u,v),successor_relation) member(regular(restrict(successor(successor_relation),u,v)),singleton(successor_relation))*.
% 299.82/300.45  215183[10:Res:161493.2,40234.0] inductive(u) ||  -> equal(integer_of(not_subclass_element(v,intersection(u,v))),successor_relation)** subclass(v,intersection(u,v)).
% 299.82/300.45  215263[10:Rew:181642.0,215145.1] || member(not_subclass_element(symmetric_difference(universal_class,inverse(successor_relation)),successor_relation),symmetrization_of(successor_relation))* -> subclass(symmetric_difference(universal_class,inverse(successor_relation)),successor_relation).
% 299.82/300.45  215264[10:Rew:181641.0,215144.1] || member(not_subclass_element(symmetric_difference(universal_class,singleton(successor_relation)),successor_relation),successor(successor_relation))* -> subclass(symmetric_difference(universal_class,singleton(successor_relation)),successor_relation).
% 299.82/300.45  215269[10:Rew:161320.0,215086.1] || member(not_subclass_element(restrict(u,v,w),successor_relation),complement(u))* -> subclass(restrict(u,v,w),successor_relation).
% 299.82/300.45  215881[10:Res:197082.1,9322.0] || subclass(universal_class,symmetric_difference(complement(u),complement(v))) -> member(regular(complement(successor(successor_relation))),union(u,v))*.
% 299.82/300.45  216122[6:Res:199830.1,9322.0] || equal(symmetric_difference(complement(u),complement(v)),cross_product(universal_class,universal_class)) -> member(regular(rest_relation),union(u,v))*.
% 299.82/300.45  216132[6:Res:199830.1,10.0] || equal(unordered_pair(u,v),cross_product(universal_class,universal_class))* -> equal(regular(rest_relation),v) equal(regular(rest_relation),u).
% 299.82/300.45  216433[6:SpL:208.0,199982.0] || subclass(universal_class,power_class(image(element_relation,complement(u))))* member(regular(rest_relation),image(element_relation,power_class(u))) -> .
% 299.82/300.45  216452[6:SpL:208.0,199986.0] || subclass(universal_class,complement(power_class(image(element_relation,complement(u)))))* -> member(regular(rest_relation),image(element_relation,power_class(u))).
% 299.82/300.45  216730[6:Res:201220.1,9322.0] || equal(symmetric_difference(complement(u),complement(v)),cross_product(universal_class,universal_class)) -> member(regular(domain_relation),union(u,v))*.
% 299.82/300.45  216740[6:Res:201220.1,10.0] || equal(unordered_pair(u,v),cross_product(universal_class,universal_class))* -> equal(regular(domain_relation),v) equal(regular(domain_relation),u).
% 299.82/300.45  216815[6:SpL:208.0,201372.0] || subclass(universal_class,power_class(image(element_relation,complement(u))))* member(regular(domain_relation),image(element_relation,power_class(u))) -> .
% 299.82/300.45  216834[6:SpL:208.0,201376.0] || subclass(universal_class,complement(power_class(image(element_relation,complement(u)))))* -> member(regular(domain_relation),image(element_relation,power_class(u))).
% 299.82/300.45  217008[20:SpL:208.0,202875.1] || equal(image(element_relation,power_class(u)),omega) equal(power_class(image(element_relation,complement(u))),symmetrization_of(successor_relation))** -> .
% 299.82/300.45  217024[11:SpL:208.0,202881.1] || equal(image(element_relation,power_class(u)),universal_class) equal(power_class(image(element_relation,complement(u))),symmetrization_of(successor_relation))** -> .
% 299.82/300.45  217131[20:SpL:208.0,206075.1] || equal(image(element_relation,power_class(u)),omega) equal(power_class(image(element_relation,complement(u))),successor(successor_relation))** -> .
% 299.82/300.45  217148[10:SpL:208.0,206081.1] || equal(image(element_relation,power_class(u)),universal_class) equal(power_class(image(element_relation,complement(u))),successor(successor_relation))** -> .
% 299.82/300.45  217195[10:Res:5771.1,206660.0] || equal(sum_class(complement(singleton(successor_relation))),complement(singleton(successor_relation))) member(successor_relation,sum_class(complement(singleton(successor_relation))))* -> .
% 299.82/300.45  217252[10:Res:217225.1,40234.0] || equal(singleton(not_subclass_element(u,intersection(singleton(successor_relation),u))),kind_1_ordinals)** -> subclass(u,intersection(singleton(successor_relation),u)).
% 299.82/300.45  217253[10:Res:217225.1,179.1] || equal(singleton(least(element_relation,intersection(y__dfg,ordinal_numbers))),kind_1_ordinals)** subclass(singleton(successor_relation),intersection(y__dfg,ordinal_numbers)) -> .
% 299.82/300.45  217375[10:Rew:160322.0,217293.1] || member(regular(intersection(power_class(universal_class),u)),image(element_relation,successor_relation))* -> equal(intersection(power_class(universal_class),u),successor_relation).
% 299.82/300.45  217415[20:Res:217226.1,40234.0] || equal(singleton(not_subclass_element(u,intersection(singleton(successor_relation),u))),omega)** -> subclass(u,intersection(singleton(successor_relation),u)).
% 299.82/300.45  217416[20:Res:217226.1,179.1] || equal(singleton(least(element_relation,intersection(y__dfg,ordinal_numbers))),omega)** subclass(singleton(successor_relation),intersection(y__dfg,ordinal_numbers)) -> .
% 299.82/300.45  217516[10:Rew:160322.0,217451.1] || member(regular(intersection(u,power_class(universal_class))),image(element_relation,successor_relation))* -> equal(intersection(u,power_class(universal_class)),successor_relation).
% 299.82/300.45  218034[10:SpR:194805.1,161690.1] || subclass(u,v) -> equal(symmetric_difference(v,u),successor_relation) member(regular(symmetric_difference(v,u)),complement(u))*.
% 299.82/300.45  218048[10:SpR:205791.1,161690.1] ||  -> equal(singleton(u),successor_relation) equal(symmetric_difference(u,universal_class),successor_relation) member(regular(symmetric_difference(u,universal_class)),complement(u))*.
% 299.82/300.45  218312[10:MRR:218273.0,34189.1] ||  -> member(not_subclass_element(regular(complement(u)),v),u)* subclass(regular(complement(u)),v) equal(complement(u),successor_relation).
% 299.82/300.45  218341[10:SpR:161137.0,218298.0] ||  -> subclass(regular(image(element_relation,symmetrization_of(successor_relation))),power_class(complement(inverse(successor_relation))))* equal(image(element_relation,symmetrization_of(successor_relation)),successor_relation).
% 299.82/300.45  218342[10:SpR:162889.0,218298.0] ||  -> subclass(regular(image(element_relation,successor(successor_relation))),power_class(complement(singleton(successor_relation))))* equal(image(element_relation,successor(successor_relation)),successor_relation).
% 299.82/300.45  218487[3:Res:131.2,217932.0] || connected(u,complement(kind_1_ordinals)) -> well_ordering(u,complement(kind_1_ordinals)) subclass(not_well_ordering(u,complement(kind_1_ordinals)),complement(ordinal_numbers))*.
% 299.82/300.45  218502[10:Res:218497.0,160292.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(regular(kind_1_ordinals),successor_relation) member(least(u,regular(kind_1_ordinals)),regular(kind_1_ordinals))*.
% 299.82/300.45  218505[10:Res:218497.0,5832.1] inductive(regular(kind_1_ordinals)) || well_ordering(u,complement(ordinal_numbers)) -> member(least(u,regular(kind_1_ordinals)),regular(kind_1_ordinals))*.
% 299.82/300.45  218565[20:Res:217226.1,9636.1] || equal(singleton(not_subclass_element(u,v)),omega)** subclass(u,complement(singleton(successor_relation)))* -> subclass(u,v).
% 299.82/300.45  218566[10:Res:217225.1,9636.1] || equal(singleton(not_subclass_element(u,v)),kind_1_ordinals)** subclass(u,complement(singleton(successor_relation)))* -> subclass(u,v).
% 299.82/300.45  218890[22:Res:218867.1,19.0] || subclass(kind_1_ordinals,cross_product(u,v))* -> equal(ordered_pair(first(singleton(successor_relation)),second(singleton(successor_relation))),singleton(successor_relation))**.
% 299.82/300.45  218894[22:Res:218867.1,9300.0] || subclass(kind_1_ordinals,symmetric_difference(u,cross_product(v,w))) -> member(singleton(successor_relation),complement(restrict(u,v,w)))*.
% 299.82/300.45  218896[22:Res:218867.1,9306.0] || subclass(kind_1_ordinals,symmetric_difference(cross_product(u,v),w)) -> member(singleton(successor_relation),complement(restrict(w,u,v)))*.
% 299.82/300.45  219168[10:MRR:219106.2,185324.0] || equal(sum_class(complement(ordinal_numbers)),complement(kind_1_ordinals)) well_ordering(element_relation,complement(ordinal_numbers))* -> member(complement(ordinal_numbers),ordinal_numbers).
% 299.82/300.45  219182[10:Res:160296.2,218628.0] || member(complement(kind_1_ordinals),universal_class) -> equal(complement(kind_1_ordinals),successor_relation) member(apply(choice,complement(kind_1_ordinals)),complement(ordinal_numbers))*.
% 299.82/300.45  219197[10:Res:161445.2,218628.0] || well_ordering(u,complement(kind_1_ordinals)) -> equal(complement(kind_1_ordinals),successor_relation) member(least(u,complement(kind_1_ordinals)),complement(ordinal_numbers))*.
% 299.82/300.45  219199[3:Res:31076.2,218628.0] inductive(complement(kind_1_ordinals)) || well_ordering(u,complement(kind_1_ordinals)) -> member(least(u,complement(kind_1_ordinals)),complement(ordinal_numbers))*.
% 299.82/300.45  219202[3:Res:1495.2,218628.0] || member(u,universal_class) subclass(rest_relation,complement(kind_1_ordinals)) -> member(ordered_pair(u,rest_of(u)),complement(ordinal_numbers))*.
% 299.82/300.45  219242[10:Res:161697.1,218628.0] ||  -> equal(restrict(complement(kind_1_ordinals),u,v),successor_relation) member(regular(restrict(complement(kind_1_ordinals),u,v)),complement(ordinal_numbers))*.
% 299.82/300.45  210440[15:Res:189564.1,163294.0] || subclass(domain_relation,rotate(symmetric_difference(singleton(successor_relation),range_of(successor_relation))))* -> member(ordered_pair(ordered_pair(u,successor_relation),v),kind_1_ordinals)*.
% 299.82/300.45  210367[15:Res:189563.1,163294.0] || subclass(domain_relation,flip(symmetric_difference(singleton(successor_relation),range_of(successor_relation))))* -> member(ordered_pair(ordered_pair(u,v),successor_relation),kind_1_ordinals)*.
% 299.82/300.45  163506[10:Rew:160305.0,162822.0] || subclass(ordered_pair(u,v),symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(unordered_pair(u,singleton(v)),kind_1_ordinals).
% 299.82/300.45  163505[10:Rew:160305.0,162821.0] || subclass(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> subclass(u,v) member(not_subclass_element(u,v),kind_1_ordinals)*.
% 299.82/300.45  195410[10:SpR:194805.1,163458.0] || subclass(kind_1_ordinals,complement(intersection(singleton(successor_relation),range_of(successor_relation))))* -> equal(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),kind_1_ordinals).
% 299.82/300.45  163503[10:Rew:160305.0,162808.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(power_class(u),kind_1_ordinals)*.
% 299.82/300.45  163504[10:Rew:160305.0,162809.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(sum_class(u),kind_1_ordinals)*.
% 299.82/300.45  202430[10:Res:163225.0,163256.1] || equal(symmetric_difference(universal_class,u),range_of(successor_relation)) -> member(successor_relation,union(u,successor_relation))* inductive(symmetric_difference(universal_class,u)).
% 299.82/300.45  195386[10:SpR:194805.1,160304.1] || subclass(inverse(u),u)* asymmetric(u,universal_class) -> equal(image(inverse(u),universal_class),range_of(successor_relation))**.
% 299.82/300.45  201468[20:MRR:201436.3,166686.1] single_valued_class(range_of(successor_relation)) || equal(cross_product(universal_class,universal_class),range_of(successor_relation))** equal(range_of(successor_relation),omega) -> .
% 299.82/300.45  163422[10:Rew:160202.0,160649.0] || member(ordered_pair(u,v),compose(successor_relation,w))* subclass(range_of(successor_relation),x)* -> member(v,x)*.
% 299.82/300.45  163614[10:Rew:160305.0,163154.2] inductive(restrict(u,v,w)) ||  -> subclass(range_of(successor_relation),x) member(not_subclass_element(range_of(successor_relation),x),u)*.
% 299.82/300.45  204047[10:Rew:203285.0,167691.1] inductive(restrict(cantor(inverse(successor_relation)),u,v)) ||  -> equal(restrict(range_of(successor_relation),u,v),range_of(successor_relation))**.
% 299.82/300.45  163501[10:Rew:160305.0,162789.0] || member(intersection(complement(singleton(successor_relation)),complement(range_of(successor_relation))),universal_class)* -> member(complement(image(element_relation,kind_1_ordinals)),universal_class).
% 299.82/300.45  163532[10:Rew:160305.0,162156.3,160305.0,162156.2] inductive(u) || subclass(u,v)* -> equal(range_of(successor_relation),successor_relation) member(regular(range_of(successor_relation)),v)*.
% 299.82/300.45  204662[10:Rew:203192.0,203797.1] ||  -> equal(apply(u,not_subclass_element(complement(cantor(u)),v)),sum_class(range_of(successor_relation)))** subclass(complement(cantor(u)),v).
% 299.82/300.45  160587[10:Rew:160202.0,146289.2] || member(u,universal_class) -> member(u,range_of(v)) equal(apply(inverse(v),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  160588[10:Rew:160202.0,146290.2] || member(u,universal_class) subclass(universal_class,complement(element_relation))* -> equal(apply(u,u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  220882[23:Res:220417.0,163137.0] || equal(rest_of(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),successor(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))))** -> .
% 299.82/300.45  221313[10:SpL:2330.1,220898.0] || equal(complement(regular(singleton(not_subclass_element(cross_product(u,v),w)))),successor_relation)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  221605[10:Res:1477.1,185698.1] inductive(singleton(u)) || subclass(universal_class,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.45  221610[10:Res:4.1,185698.1] inductive(not_subclass_element(ordinal_numbers,u)) ||  -> subclass(ordinal_numbers,u)* equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.45  221617[10:Res:187500.1,185698.1] inductive(power_class(successor_relation)) || subclass(universal_class,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.45  221644[22:Res:218867.1,185698.1] inductive(singleton(successor_relation)) || subclass(kind_1_ordinals,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.45  221664[10:Res:199848.1,185698.1] inductive(regular(rest_relation)) || subclass(universal_class,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.45  221667[10:Res:201231.1,185698.1] inductive(regular(domain_relation)) || subclass(universal_class,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.45  221668[12:Res:209377.1,185698.1] inductive(regular(element_relation)) || subclass(universal_class,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.45  221861[10:Res:163149.1,160703.0] inductive(complement(compose(element_relation,universal_class))) || member(regular(range_of(successor_relation)),element_relation)* -> equal(range_of(successor_relation),successor_relation).
% 299.82/300.45  221868[10:Res:114856.0,160703.0] || member(regular(symmetric_difference(universal_class,compose(element_relation,universal_class))),element_relation)* -> equal(symmetric_difference(universal_class,compose(element_relation,universal_class)),successor_relation).
% 299.82/300.45  222035[22:Res:218867.1,986.1] || subclass(kind_1_ordinals,power_class(image(element_relation,complement(u))))* member(singleton(successor_relation),image(element_relation,power_class(u))) -> .
% 299.82/300.45  222043[11:Res:179843.1,986.1] || equal(power_class(image(element_relation,complement(u))),inverse(successor_relation)) member(successor_relation,image(element_relation,power_class(u)))* -> .
% 299.82/300.45  222059[12:Res:209377.1,986.1] || subclass(universal_class,power_class(image(element_relation,complement(u))))* member(regular(element_relation),image(element_relation,power_class(u))) -> .
% 299.82/300.45  222312[15:MRR:222311.0,160214.0] || equal(compose(u,v),successor_relation)** member(v,universal_class) subclass(domain_relation,complement(compose_class(u)))* -> .
% 299.82/300.45  223304[24:SpL:222479.0,35.0] || member(ordered_pair(ordered_pair(u,universal_class),v),rotate(w))* -> member(ordered_pair(ordered_pair(kind_1_ordinals,v),u),w).
% 299.82/300.45  223305[24:SpL:222479.0,38.0] || member(ordered_pair(ordered_pair(u,universal_class),v),flip(w))* -> member(ordered_pair(ordered_pair(kind_1_ordinals,u),v),w).
% 299.82/300.45  225480[25:Rew:224739.1,224961.1] function(u) || member(image(v,successor_relation),ordinal_numbers) -> subclass(apply(v,u),image(v,successor_relation))*.
% 299.82/300.45  225481[25:Rew:224739.1,224966.1] function(u) || asymmetric(v,successor_relation) -> equal(segment(intersection(v,inverse(v)),successor_relation,u),successor_relation)**.
% 299.82/300.45  225484[25:Rew:224739.1,225070.1] function(u) || equal(successor(successor_relation),u)* member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> .
% 299.82/300.45  225835[14:Rew:181137.1,225834.2] || member(u,universal_class)* member(ordered_pair(v,singleton(singleton(successor_relation))),composition_function)* -> equal(range_of(u),universal_class).
% 299.82/300.45  225837[15:Rew:181137.1,225836.2] || member(ordered_pair(u,singleton(singleton(successor_relation))),composition_function)* -> equal(range_of(v),successor_relation)** equal(inverse(v),universal_class).
% 299.82/300.45  225841[14:Rew:181137.1,225840.2,225835.2,225840.2] || member(u,universal_class)* member(ordered_pair(v,singleton(singleton(successor_relation))),composition_function)* -> equal(sum_class(universal_class),universal_class).
% 299.82/300.45  226001[15:SpL:142543.0,189381.1] || member(u,universal_class) subclass(domain_relation,symmetric_difference(universal_class,v)) -> member(ordered_pair(u,successor_relation),complement(v))*.
% 299.82/300.45  226247[10:Res:203658.1,185639.1] || member(u,universal_class) equal(cantor(v),successor_relation) -> equal(apply(v,u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226292[15:MRR:226190.2,160227.0] || member(u,universal_class) member(v,universal_class) -> equal(apply(power_class(u),v),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226293[15:MRR:226191.2,160227.0] || equal(successor_relation,u) member(v,universal_class) -> equal(apply(power_class(u),v),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226294[23:MRR:226202.1,160227.0] || member(u,universal_class) -> equal(apply(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226295[15:MRR:226205.2,160227.0] || member(u,universal_class) member(v,universal_class) -> equal(apply(sum_class(u),v),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226296[15:MRR:226206.2,160227.0] || member(u,universal_class) member(v,universal_class) -> equal(apply(rest_of(u),v),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226297[15:MRR:226207.2,160227.0] function(u) || member(v,universal_class) -> equal(apply(apply(u,w),v),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226298[15:MRR:226208.2,160227.0] || member(u,universal_class) -> subclass(v,w) equal(apply(not_subclass_element(v,w),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.45  226299[10:MRR:226252.0,160214.0] || equal(range_of(successor_relation),cantor(u)) -> equal(apply(u,successor_relation),sum_class(range_of(successor_relation)))** inductive(cantor(u)).
% 299.82/300.45  226349[10:Res:185430.1,9128.1] || equal(complement(restrict(u,v,w)),successor_relation)** member(x,universal_class) -> member(sum_class(x),u)*.
% 299.82/300.45  226404[25:SpL:226350.1,184008.2] one_to_one(u) || member(v,universal_class)* member(u,universal_class)* equal(sum_class(universal_class),v) -> .
% 299.82/300.45  226454[25:SoR:224779.0,6317.2] function(u) single_valued_class(apply(u,v)) || equal(apply(u,v),cross_product(universal_class,universal_class))** -> .
% 299.82/300.45  226642[10:Rew:142543.0,226465.0] ||  -> equal(intersection(symmetric_difference(universal_class,u),v),successor_relation) member(regular(intersection(symmetric_difference(universal_class,u),v)),complement(u))*.
% 299.82/300.45  227341[25:SoR:224780.0,6317.2] single_valued_class(not_subclass_element(u,v)) || equal(cross_product(universal_class,universal_class),not_subclass_element(u,v))* -> subclass(u,v).
% 299.82/300.45  227532[10:Rew:142543.0,227352.0] ||  -> equal(intersection(u,symmetric_difference(universal_class,v)),successor_relation) member(regular(intersection(u,symmetric_difference(universal_class,v))),complement(v))*.
% 299.82/300.45  228840[24:SpL:223107.0,9121.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(kind_1_ordinals),universal_class))* -> member(sum_class(u),successor(kind_1_ordinals))*.
% 299.82/300.45  228843[24:SpL:223107.0,9149.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(kind_1_ordinals),universal_class))* -> member(power_class(u),successor(kind_1_ordinals))*.
% 299.82/300.45  228846[24:SpL:223107.0,9639.0] || subclass(u,symmetric_difference(complement(kind_1_ordinals),universal_class))* -> subclass(u,v) member(not_subclass_element(u,v),successor(kind_1_ordinals))*.
% 299.82/300.45  228869[24:Rew:223107.0,228853.1] || member(not_subclass_element(universal_class,symmetric_difference(complement(kind_1_ordinals),universal_class)),successor(kind_1_ordinals))* -> subclass(universal_class,symmetric_difference(complement(kind_1_ordinals),universal_class)).
% 299.82/300.45  228969[10:Res:218490.0,160788.0] || subclass(complement(ordinal_numbers),u) -> equal(symmetric_difference(universal_class,kind_1_ordinals),successor_relation) member(regular(symmetric_difference(universal_class,kind_1_ordinals)),u)*.
% 299.82/300.45  229027[10:Res:228991.1,19.0] || subclass(kind_1_ordinals,cross_product(u,v))* -> equal(ordered_pair(first(regular(ordinal_numbers)),second(regular(ordinal_numbers))),regular(ordinal_numbers))**.
% 299.82/300.45  229031[10:Res:228991.1,9300.0] || subclass(kind_1_ordinals,symmetric_difference(u,cross_product(v,w))) -> member(regular(ordinal_numbers),complement(restrict(u,v,w)))*.
% 299.82/300.45  229033[10:Res:228991.1,9306.0] || subclass(kind_1_ordinals,symmetric_difference(cross_product(u,v),w)) -> member(regular(ordinal_numbers),complement(restrict(w,u,v)))*.
% 299.82/300.45  229045[10:Res:228991.1,986.1] || subclass(kind_1_ordinals,power_class(image(element_relation,complement(u))))* member(regular(ordinal_numbers),image(element_relation,power_class(u))) -> .
% 299.82/300.45  229255[10:Res:229228.1,19.0] || subclass(universal_class,cross_product(u,v))* -> equal(ordered_pair(first(regular(ordinal_numbers)),second(regular(ordinal_numbers))),regular(ordinal_numbers))**.
% 299.82/300.45  229259[10:Res:229228.1,9300.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(regular(ordinal_numbers),complement(restrict(u,v,w)))*.
% 299.82/300.45  229261[10:Res:229228.1,9306.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(regular(ordinal_numbers),complement(restrict(w,u,v)))*.
% 299.82/300.45  229273[10:Res:229228.1,986.1] || subclass(universal_class,power_class(image(element_relation,complement(u))))* member(regular(ordinal_numbers),image(element_relation,power_class(u))) -> .
% 299.82/300.45  229802[10:Res:221521.1,9636.1] || subclass(u,complement(complement(singleton(omega))))* -> equal(integer_of(not_subclass_element(u,v)),successor_relation)** subclass(u,v).
% 299.82/300.45  229804[10:Res:221521.1,179.1] || subclass(complement(singleton(omega)),intersection(y__dfg,ordinal_numbers))* -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation).
% 299.82/300.45  230147[10:SpL:2330.1,222140.0] || equal(complement(complement(singleton(not_subclass_element(cross_product(u,v),w)))),universal_class)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  230258[10:Res:185430.1,9647.0] || equal(complement(restrict(u,v,w)),successor_relation)** -> subclass(universal_class,x) member(not_subclass_element(universal_class,x),u)*.
% 299.82/300.45  230482[10:Rew:227642.0,230466.1] || member(not_subclass_element(restrict(ordinal_numbers,u,v),successor_relation),complement(kind_1_ordinals))* -> subclass(restrict(ordinal_numbers,u,v),successor_relation).
% 299.82/300.45  230531[10:Res:1495.2,229800.0] || member(u,universal_class) subclass(rest_relation,singleton(omega)) -> equal(integer_of(ordered_pair(u,rest_of(u))),successor_relation)**.
% 299.82/300.45  230623[6:Res:8.1,157904.1] || equal(complement(compose(element_relation,universal_class)),universal_class)** member(u,universal_class) member(power_class(u),element_relation)* -> .
% 299.82/300.45  230653[10:SpL:2330.1,219386.0] || subclass(universal_class,regular(unordered_pair(u,not_subclass_element(cross_product(v,w),x))))* -> subclass(cross_product(v,w),x).
% 299.82/300.45  230668[6:Res:8.1,157905.1] || equal(complement(compose(element_relation,universal_class)),universal_class)** member(u,universal_class) member(sum_class(u),element_relation)* -> .
% 299.82/300.45  230706[10:Res:8.1,192570.0] || equal(u,universal_class) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(omega,least(omega,universal_class))),successor_relation)**.
% 299.82/300.45  231040[10:SpL:10028.0,185324.0] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),symmetrization_of(image(element_relation,complement(u))))** -> .
% 299.82/300.45  231096[10:Rew:160223.0,230994.1] || equal(complement(inverse(image(element_relation,complement(u)))),successor_relation)** -> equal(symmetrization_of(image(element_relation,complement(u))),universal_class).
% 299.82/300.45  231097[10:Rew:160223.0,230995.1] || subclass(complement(inverse(image(element_relation,complement(u)))),successor_relation)* -> equal(symmetrization_of(image(element_relation,complement(u))),universal_class).
% 299.82/300.45  231125[10:Rew:10028.0,231036.1] || equal(symmetrization_of(image(element_relation,complement(u))),successor_relation)** equal(symmetrization_of(image(element_relation,complement(u))),universal_class) -> .
% 299.82/300.45  231185[10:SpL:2330.1,221320.0] || subclass(universal_class,regular(unordered_pair(not_subclass_element(cross_product(u,v),w),x)))* -> subclass(cross_product(u,v),w).
% 299.82/300.45  231364[10:SpL:10029.0,185324.0] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),successor(image(element_relation,complement(u))))** -> .
% 299.82/300.45  231420[10:Rew:160223.0,231319.1] || subclass(complement(singleton(image(element_relation,complement(u)))),successor_relation)* -> equal(successor(image(element_relation,complement(u))),universal_class).
% 299.82/300.45  231450[10:Rew:10029.0,231360.1] || equal(successor(image(element_relation,complement(u))),successor_relation)** equal(successor(image(element_relation,complement(u))),universal_class) -> .
% 299.82/300.45  231558[15:MRR:231545.1,229170.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(regular(ordinal_numbers),successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231559[15:MRR:231544.1,229170.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(regular(ordinal_numbers),successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231560[15:MRR:231543.1,209309.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(regular(element_relation),successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231561[15:MRR:231542.1,209309.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(regular(element_relation),successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231562[15:MRR:231541.1,201216.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(regular(domain_relation),successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231563[15:MRR:231540.1,201216.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(regular(domain_relation),successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231564[15:MRR:231539.1,199826.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(regular(rest_relation),successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231565[15:MRR:231538.1,199826.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(regular(rest_relation),successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231566[15:MRR:231535.1,187489.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(power_class(successor_relation),successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231567[15:MRR:231534.1,187489.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(power_class(successor_relation),successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231568[15:MRR:231531.1,191.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(singleton(u),successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231569[15:MRR:231530.1,191.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(singleton(u),successor_relation),ordinal_numbers)* -> .
% 299.82/300.45  231718[10:SpL:2330.1,230662.0] || equal(regular(unordered_pair(u,not_subclass_element(cross_product(v,w),x))),universal_class)** -> subclass(cross_product(v,w),x).
% 299.82/300.45  231733[10:SpL:2330.1,231194.0] || equal(regular(unordered_pair(not_subclass_element(cross_product(u,v),w),x)),universal_class)** -> subclass(cross_product(u,v),w).
% 299.82/300.45  231796[10:Res:1506.1,161035.0] || equal(intersection(power_class(successor_relation),complement(u)),universal_class) member(omega,union(image(element_relation,universal_class),u))* -> .
% 299.82/300.45  231835[10:Res:206947.1,161035.0] || equal(intersection(power_class(successor_relation),complement(u)),kind_1_ordinals) member(successor_relation,union(image(element_relation,universal_class),u))* -> .
% 299.82/300.45  231836[20:Res:191074.1,161035.0] || equal(intersection(power_class(successor_relation),complement(u)),omega) member(successor_relation,union(image(element_relation,universal_class),u))* -> .
% 299.82/300.45  231842[10:Res:160268.1,161035.0] || equal(intersection(power_class(successor_relation),complement(u)),universal_class) member(successor_relation,union(image(element_relation,universal_class),u))* -> .
% 299.82/300.45  9303[0:SpR:161.0,1951.1] || member(u,symmetric_difference(complement(intersection(v,w)),union(v,w)))* -> member(u,complement(symmetric_difference(v,w))).
% 299.82/300.45  9907[0:Res:9535.0,9.0] || subclass(complement(intersection(u,v)),symmetric_difference(u,v))* -> equal(complement(intersection(u,v)),symmetric_difference(u,v)).
% 299.82/300.45  9926[0:Res:9418.0,9.0] || subclass(cross_product(u,v),restrict(w,u,v))* -> equal(restrict(w,u,v),cross_product(u,v)).
% 299.82/300.45  31646[0:Res:8.1,1316.0] || equal(rotate(u),cross_product(cross_product(universal_class,universal_class),universal_class))* -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(u)).
% 299.82/300.45  31768[0:Res:8.1,1315.0] || equal(flip(u),cross_product(cross_product(universal_class,universal_class),universal_class))* -> equal(cross_product(cross_product(universal_class,universal_class),universal_class),flip(u)).
% 299.82/300.45  34062[0:Res:8.1,3883.2] || equal(u,intersection(v,w))* member(x,w)* member(x,v)* -> member(x,u)*.
% 299.82/300.45  41272[0:Obv:41259.1] || member(ordered_pair(u,v),compose(w,x)) -> subclass(singleton(v),image(w,image(x,singleton(u))))*.
% 299.82/300.45  31433[0:SpL:124.0,31279.1] || equal(complement(rest_of(restrict(u,v,singleton(w)))),universal_class)** member(x,segment(u,v,w))* -> .
% 299.82/300.45  5552[0:SpR:1005.0,18.2] || member(u,v) member(singleton(u),w) -> member(singleton(singleton(singleton(u))),cross_product(w,v))*.
% 299.82/300.45  31305[0:Res:64.1,5829.0] function(u) || well_ordering(v,cross_product(universal_class,universal_class))* -> subclass(u,w)* member(least(v,u),u)*.
% 299.82/300.45  9597[0:Res:1478.2,594.0] || member(u,universal_class) subclass(universal_class,restrict(v,w,x))* -> member(power_class(u),cross_product(w,x))*.
% 299.82/300.45  5831[0:Res:1477.1,127.0] || subclass(universal_class,u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.45  3891[0:Res:25.2,3670.1] || member(singleton(u),v)* member(singleton(u),w)* equal(complement(intersection(w,v)),universal_class)** -> .
% 299.82/300.45  87705[0:Res:31436.1,135.1] || equal(complement(rest_of(restrict(u,v,w))),universal_class)** subclass(w,v) -> section(u,w,v).
% 299.82/300.45  89238[0:Res:51387.0,127.0] || subclass(u,v)* well_ordering(w,v)* -> subclass(x,complement(u))* member(least(w,u),u)*.
% 299.82/300.45  108320[0:SpL:161.0,9332.1] || member(u,symmetric_difference(complement(intersection(v,w)),union(v,w)))* member(u,symmetric_difference(v,w)) -> .
% 299.82/300.45  108373[0:Res:1478.2,9332.1] || member(u,universal_class) subclass(universal_class,intersection(v,w)) member(power_class(u),symmetric_difference(v,w))* -> .
% 299.82/300.45  111540[2:MRR:111510.3,2492.1] || connected(u,complement(v)) member(regular(not_well_ordering(u,complement(v))),v)* -> well_ordering(u,complement(v)).
% 299.82/300.45  120146[0:SpL:161.0,9149.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,w)) -> member(power_class(u),complement(intersection(v,w)))*.
% 299.82/300.45  125896[0:SpR:1005.0,28320.1] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(v,rest_of(singleton(singleton(singleton(v))))),singleton(v)),u)*.
% 299.82/300.45  125910[0:Res:28320.1,26.1] || subclass(rest_relation,rotate(complement(u))) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)* -> .
% 299.82/300.45  125915[0:Res:28320.1,23.0] || subclass(rest_relation,rotate(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),u)*.
% 299.82/300.45  125916[0:Res:28320.1,24.0] || subclass(rest_relation,rotate(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),v)*.
% 299.82/300.45  125960[0:Res:28320.1,144.0] || subclass(rest_relation,rotate(rest_of(u))) -> equal(restrict(u,ordered_pair(v,rest_of(ordered_pair(w,v))),universal_class),w)**.
% 299.82/300.45  126021[0:SpR:1005.0,28321.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(v,singleton(v)),rest_of(singleton(singleton(singleton(v))))),u)*.
% 299.82/300.45  126031[0:SpR:1005.0,28321.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(singleton(singleton(singleton(v))),rest_of(ordered_pair(v,singleton(v)))),u)*.
% 299.82/300.45  126040[0:Res:28321.1,26.1] || subclass(rest_relation,flip(complement(u))) member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)* -> .
% 299.82/300.45  126045[0:Res:28321.1,23.0] || subclass(rest_relation,flip(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),u)*.
% 299.82/300.45  126046[0:Res:28321.1,24.0] || subclass(rest_relation,flip(intersection(u,v)))* -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),v)*.
% 299.82/300.45  126090[0:Res:28321.1,144.0] || subclass(rest_relation,flip(rest_of(u))) -> equal(restrict(u,ordered_pair(v,w),universal_class),rest_of(ordered_pair(w,v)))**.
% 299.82/300.45  130001[2:MRR:129870.3,2492.1] || connected(u,v) subclass(v,w) -> well_ordering(u,v) member(regular(not_well_ordering(u,v)),w)*.
% 299.82/300.45  130400[0:Res:1499.1,9300.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(ordered_pair(x,y),complement(restrict(u,v,w)))*.
% 299.82/300.45  130493[0:Res:1499.1,9306.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(ordered_pair(x,y),complement(restrict(w,u,v)))*.
% 299.82/300.45  3840[0:Res:131.2,1322.1] inductive(not_well_ordering(u,omega)) || connected(u,omega) -> well_ordering(u,omega) equal(not_well_ordering(u,omega),omega)**.
% 299.82/300.45  119666[0:Res:114897.1,127.0] || equal(u,universal_class) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.45  142109[0:Res:54.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,omega)),second(ordered_pair(u,omega))),ordered_pair(u,omega))**.
% 299.82/300.45  150440[6:Rew:148462.0,149589.0] || equal(cross_product(u,u),complement(complement(symmetrization_of(v))))* -> equal(complement(complement(symmetrization_of(v))),cross_product(u,u)).
% 299.82/300.45  151031[6:MRR:151030.0,149715.0] || subclass(universal_class,restrict(cross_product(u,u),v,w))* -> equal(restrict(cross_product(v,w),u,u),universal_class).
% 299.82/300.45  155804[3:Res:28320.1,141576.1] || subclass(rest_relation,rotate(complement(kind_1_ordinals))) member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),ordinal_numbers)* -> .
% 299.82/300.45  155805[3:Res:28321.1,141576.1] || subclass(rest_relation,flip(complement(kind_1_ordinals))) member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),ordinal_numbers)* -> .
% 299.82/300.45  159343[6:Res:148538.1,127.0] || subclass(domain_relation,u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.45  160069[3:Res:159952.1,3883.2] || subclass(intersection(u,v),ordinal_numbers)* member(w,v)* member(w,u)* -> member(w,kind_1_ordinals)*.
% 299.82/300.45  163164[10:Rew:163163.1,92630.2] || well_ordering(u,cross_product(universal_class,universal_class)) subclass(singleton(least(u,successor_relation)),successor_relation)* -> section(u,successor_relation,successor_relation).
% 299.82/300.45  162324[10:Rew:160202.0,153500.0] || equal(segment(u,v,w),successor_relation) subclass(singleton(w),v) -> section(u,singleton(w),v)*.
% 299.82/300.45  162136[10:Rew:160202.0,148454.1] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,successor_relation)),second(ordered_pair(u,successor_relation))),ordered_pair(u,successor_relation))**.
% 299.82/300.45  162129[10:Rew:160202.0,147965.0] ||  -> equal(intersection(union(u,image(element_relation,power_class(v))),intersection(complement(u),power_class(image(element_relation,complement(v))))),successor_relation)**.
% 299.82/300.45  162128[10:Rew:160202.0,147964.0] ||  -> equal(intersection(intersection(complement(u),power_class(image(element_relation,complement(v)))),union(u,image(element_relation,power_class(v)))),successor_relation)**.
% 299.82/300.45  162127[10:Rew:160202.0,147945.0] ||  -> equal(intersection(union(image(element_relation,power_class(u)),v),intersection(power_class(image(element_relation,complement(u))),complement(v))),successor_relation)**.
% 299.82/300.45  162126[10:Rew:160202.0,147944.0] ||  -> equal(intersection(intersection(power_class(image(element_relation,complement(u))),complement(v)),union(image(element_relation,power_class(u)),v)),successor_relation)**.
% 299.82/300.45  162125[10:Rew:160202.0,147909.0] ||  -> equal(intersection(symmetrization_of(image(element_relation,complement(u))),intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))),successor_relation)**.
% 299.82/300.45  162124[10:Rew:160202.0,147908.0] ||  -> equal(intersection(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),symmetrization_of(image(element_relation,complement(u)))),successor_relation)**.
% 299.82/300.45  162123[10:Rew:160202.0,147889.0] ||  -> equal(intersection(successor(image(element_relation,complement(u))),intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))),successor_relation)**.
% 299.82/300.45  162122[10:Rew:160202.0,147888.0] ||  -> equal(intersection(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),successor(image(element_relation,complement(u)))),successor_relation)**.
% 299.82/300.45  162121[10:Rew:160202.0,147870.0] ||  -> equal(intersection(power_class(image(element_relation,union(u,v))),image(element_relation,power_class(intersection(complement(u),complement(v))))),successor_relation)**.
% 299.82/300.46  162120[10:Rew:160202.0,147850.0] ||  -> equal(intersection(image(element_relation,power_class(intersection(complement(u),complement(v)))),power_class(image(element_relation,union(u,v)))),successor_relation)**.
% 299.82/300.46  162119[10:Rew:160202.0,147819.1] || subclass(cross_product(cross_product(universal_class,universal_class),universal_class),u)* -> equal(flip(v),successor_relation) member(regular(flip(v)),u)*.
% 299.82/300.46  162117[10:Rew:160202.0,147818.1] || subclass(cross_product(cross_product(universal_class,universal_class),universal_class),u)* -> equal(rotate(v),successor_relation) member(regular(rotate(v)),u)*.
% 299.82/300.46  162115[10:Rew:160202.0,147776.0] ||  -> equal(intersection(intersection(u,singleton(v)),w),successor_relation) equal(regular(intersection(intersection(u,singleton(v)),w)),v)**.
% 299.82/300.46  162114[10:Rew:160202.0,147701.0] ||  -> equal(intersection(intersection(singleton(u),v),w),successor_relation) equal(regular(intersection(intersection(singleton(u),v),w)),u)**.
% 299.82/300.46  162113[10:Rew:160202.0,147663.0] ||  -> equal(intersection(u,intersection(v,singleton(w))),successor_relation) equal(regular(intersection(u,intersection(v,singleton(w)))),w)**.
% 299.82/300.46  162112[10:Rew:160202.0,147603.0] ||  -> equal(intersection(u,intersection(singleton(v),w)),successor_relation) equal(regular(intersection(u,intersection(singleton(v),w))),v)**.
% 299.82/300.46  162106[10:Rew:160202.0,147497.1] || member(regular(intersection(power_class(u),v)),image(element_relation,complement(u)))* -> equal(intersection(power_class(u),v),successor_relation).
% 299.82/300.46  162104[10:Rew:160202.0,147470.1] || member(regular(intersection(u,power_class(v))),image(element_relation,complement(v)))* -> equal(intersection(u,power_class(v)),successor_relation).
% 299.82/300.46  162102[10:Rew:160202.0,147419.1] || well_ordering(u,complement(v)) -> equal(segment(u,symmetric_difference(universal_class,v),least(u,symmetric_difference(universal_class,v))),successor_relation)**.
% 299.82/300.46  162100[10:Rew:160202.0,147403.0] ||  -> equal(restrict(intersection(u,v),w,x),successor_relation) member(regular(restrict(intersection(u,v),w,x)),u)*.
% 299.82/300.46  162101[10:Rew:160202.0,147402.0] ||  -> equal(restrict(intersection(u,v),w,x),successor_relation) member(regular(restrict(intersection(u,v),w,x)),v)*.
% 299.82/300.46  162095[10:Rew:160202.0,147273.0] ||  -> equal(complement(complement(symmetric_difference(u,v))),successor_relation) member(regular(complement(complement(symmetric_difference(u,v)))),union(u,v))*.
% 299.82/300.46  162094[10:Rew:160202.0,147272.0] ||  -> equal(complement(complement(restrict(u,v,w))),successor_relation) member(regular(complement(complement(restrict(u,v,w)))),u)*.
% 299.82/300.46  162092[10:Rew:160202.0,147221.1] || subclass(cross_product(universal_class,universal_class),u) -> equal(compose(v,w),successor_relation) member(regular(compose(v,w)),u)*.
% 299.82/300.46  162082[10:Rew:160202.0,147033.3] || subclass(u,v)* subclass(v,w)* well_ordering(universal_class,w)* -> equal(intersection(u,x),successor_relation)**.
% 299.82/300.46  162083[10:Rew:160202.0,147032.1] || subclass(u,intersection(v,w))* -> equal(intersection(u,x),successor_relation) member(regular(intersection(u,x)),v)*.
% 299.82/300.46  162084[10:Rew:160202.0,147031.1] || subclass(u,intersection(v,w))* -> equal(intersection(u,x),successor_relation) member(regular(intersection(u,x)),w)*.
% 299.82/300.46  162068[10:Rew:160202.0,147018.3] || subclass(u,v)* subclass(v,w)* well_ordering(universal_class,w)* -> equal(intersection(x,u),successor_relation)**.
% 299.82/300.46  162069[10:Rew:160202.0,147017.1] || subclass(u,intersection(v,w))* -> equal(intersection(x,u),successor_relation) member(regular(intersection(x,u)),v)*.
% 299.82/300.46  162070[10:Rew:160202.0,147016.1] || subclass(u,intersection(v,w))* -> equal(intersection(x,u),successor_relation) member(regular(intersection(x,u)),w)*.
% 299.82/300.46  162052[10:Rew:160202.0,146966.0] ||  -> equal(intersection(u,symmetric_difference(v,w)),successor_relation) member(regular(intersection(u,symmetric_difference(v,w))),union(v,w))*.
% 299.82/300.46  162049[10:Rew:160202.0,146963.0] ||  -> equal(intersection(symmetric_difference(u,v),w),successor_relation) member(regular(intersection(symmetric_difference(u,v),w)),union(u,v))*.
% 299.82/300.46  162046[10:Rew:160202.0,146960.0] ||  -> equal(intersection(restrict(u,v,w),x),successor_relation) member(regular(intersection(restrict(u,v,w),x)),u)*.
% 299.82/300.46  162041[10:Rew:160202.0,146955.0] ||  -> equal(intersection(u,restrict(v,w,x)),successor_relation) member(regular(intersection(u,restrict(v,w,x))),v)*.
% 299.82/300.46  162034[10:Rew:160202.0,146942.0] ||  -> equal(second(not_subclass_element(restrict(cross_product(singleton(u),v),w,x),successor_relation)),range__dfg(cross_product(w,x),u,v))**.
% 299.82/300.46  162033[10:Rew:160202.0,146941.0] ||  -> equal(first(not_subclass_element(restrict(cross_product(u,singleton(v)),w,x),successor_relation)),domain__dfg(cross_product(w,x),u,v))**.
% 299.82/300.46  162032[10:Rew:160202.0,146940.0] ||  -> equal(symmetric_difference(complement(u),complement(v)),successor_relation) member(regular(symmetric_difference(complement(u),complement(v))),union(u,v))*.
% 299.82/300.46  162968[10:Rew:160202.0,156062.0] || member(u,intersection(complement(v),union(w,successor_relation)))* member(u,union(v,symmetric_difference(universal_class,w))) -> .
% 299.82/300.46  161835[10:Rew:160202.0,147421.1] || subclass(u,v) -> equal(restrict(u,w,x),successor_relation) member(regular(restrict(u,w,x)),v)*.
% 299.82/300.46  161819[10:Rew:160202.0,147282.1] ||  -> member(regular(complement(union(u,v))),intersection(complement(u),complement(v)))* equal(complement(union(u,v)),successor_relation).
% 299.82/300.46  161777[10:Rew:160202.0,146700.1] ||  -> equal(apply(choice,unordered_pair(u,v)),v)** equal(unordered_pair(u,v),successor_relation) member(u,unordered_pair(u,v))*.
% 299.82/300.46  161778[10:Rew:160202.0,146699.1] ||  -> equal(apply(choice,unordered_pair(u,v)),u)** equal(unordered_pair(u,v),successor_relation) member(v,unordered_pair(u,v))*.
% 299.82/300.46  161726[10:Rew:160202.0,159722.2] || subclass(ordered_pair(u,v),regular(w))* member(unordered_pair(u,singleton(v)),w) -> equal(w,successor_relation).
% 299.82/300.46  161718[10:Rew:160202.0,146902.2] || subclass(u,complement(v)) member(regular(intersection(u,w)),v)* -> equal(intersection(u,w),successor_relation).
% 299.82/300.46  161707[10:Rew:160202.0,146881.2] || subclass(u,complement(v)) member(regular(intersection(w,u)),v)* -> equal(intersection(w,u),successor_relation).
% 299.82/300.46  161686[10:Rew:160202.0,146727.1] || subclass(union(u,v),w) -> equal(symmetric_difference(u,v),successor_relation) member(regular(symmetric_difference(u,v)),w)*.
% 299.82/300.46  161665[10:Rew:160202.0,156059.1] || member(u,universal_class) subclass(universal_class,union(v,successor_relation)) member(power_class(u),symmetric_difference(universal_class,v))* -> .
% 299.82/300.46  161666[10:Rew:160202.0,156058.1] || member(u,universal_class) subclass(universal_class,union(v,successor_relation)) member(sum_class(u),symmetric_difference(universal_class,v))* -> .
% 299.82/300.46  161663[10:Rew:160202.0,156052.0] || member(u,intersection(union(v,successor_relation),complement(w)))* member(u,union(symmetric_difference(universal_class,v),w)) -> .
% 299.82/300.46  161655[10:Rew:160202.0,156029.1] || member(u,universal_class) -> member(u,image(element_relation,union(v,successor_relation)))* member(u,power_class(symmetric_difference(universal_class,v))).
% 299.82/300.46  161427[10:Rew:160202.0,159719.3] || subclass(u,regular(v)) member(not_subclass_element(u,w),v)* -> subclass(u,w) equal(v,successor_relation).
% 299.82/300.46  163495[10:Rew:160202.0,161428.1] || member(regular(intersection(u,regular(v))),v)* -> equal(intersection(u,regular(v)),successor_relation) equal(v,successor_relation).
% 299.82/300.46  161429[10:Rew:160202.0,159703.3] || member(u,universal_class) subclass(universal_class,regular(v))* member(sum_class(u),v)* -> equal(v,successor_relation).
% 299.82/300.46  161430[10:Rew:160202.0,159702.3] || member(u,universal_class) subclass(universal_class,regular(v))* member(power_class(u),v)* -> equal(v,successor_relation).
% 299.82/300.46  163494[10:Rew:160202.0,161374.2] inductive(complement(intersection(u,v))) || member(successor_relation,union(u,v)) -> member(successor_relation,symmetric_difference(u,v))*.
% 299.82/300.46  162029[10:Rew:160202.0,146562.2] || member(u,ordinal_numbers) subclass(u,v) -> equal(sum_class(u),successor_relation) member(regular(sum_class(u)),v)*.
% 299.82/300.46  163491[10:Rew:160202.0,161293.1] || equal(compose(successor_relation,successor_relation),successor_relation) -> equal(cross_product(u,u),successor_relation) transitive(regular(cross_product(u,u)),u)*.
% 299.82/300.46  163492[10:Rew:160202.0,161294.1] || transitive(regular(cross_product(u,u)),u)* -> equal(cross_product(u,u),successor_relation) equal(compose(successor_relation,successor_relation),successor_relation).
% 299.82/300.46  163493[10:Rew:160202.0,161298.1] || subclass(compose(successor_relation,successor_relation),successor_relation) -> equal(cross_product(u,u),successor_relation) transitive(regular(cross_product(u,u)),u)*.
% 299.82/300.46  163496[10:Rew:160202.0,162001.1] ||  -> equal(cross_product(u,singleton(v)),successor_relation) equal(domain__dfg(regular(cross_product(u,singleton(v))),u,v),single_valued3(successor_relation))**.
% 299.82/300.46  163490[10:Rew:160202.0,161228.1] || subclass(union(u,successor_relation),symmetric_difference(complement(u),universal_class))* -> equal(symmetric_difference(complement(u),universal_class),union(u,successor_relation)).
% 299.82/300.46  161209[10:Rew:160202.0,156046.0] || subclass(universal_class,image(element_relation,union(u,successor_relation))) member(unordered_pair(v,w),power_class(symmetric_difference(universal_class,u)))* -> .
% 299.82/300.46  163489[10:Rew:160202.0,161200.1] || subclass(symmetric_difference(universal_class,u),complement(union(u,successor_relation)))* -> equal(complement(union(u,successor_relation)),symmetric_difference(universal_class,u)).
% 299.82/300.46  160882[10:Rew:160202.0,152646.0] || member(not_subclass_element(intersection(u,power_class(universal_class)),v),image(element_relation,successor_relation))* -> subclass(intersection(u,power_class(universal_class)),v).
% 299.82/300.46  160881[10:Rew:160202.0,152645.0] || member(not_subclass_element(intersection(power_class(universal_class),u),v),image(element_relation,successor_relation))* -> subclass(intersection(power_class(universal_class),u),v).
% 299.82/300.46  160878[10:Rew:160202.0,152634.2] || equal(u,power_class(universal_class)) member(v,universal_class) -> member(v,image(element_relation,successor_relation))* member(v,u)*.
% 299.82/300.46  160874[10:Rew:160202.0,152614.0] ||  -> equal(complement(intersection(complement(u),union(v,image(element_relation,successor_relation)))),union(u,intersection(complement(v),power_class(universal_class))))**.
% 299.82/300.46  160870[10:Rew:160202.0,152604.0] ||  -> equal(complement(intersection(complement(u),union(image(element_relation,successor_relation),v))),union(u,intersection(power_class(universal_class),complement(v))))**.
% 299.82/300.46  160865[10:Rew:160202.0,152589.0] ||  -> equal(power_class(intersection(power_class(universal_class),complement(singleton(image(element_relation,successor_relation))))),complement(image(element_relation,successor(image(element_relation,successor_relation)))))**.
% 299.82/300.46  160863[10:Rew:160202.0,152590.0] ||  -> equal(power_class(intersection(power_class(universal_class),complement(inverse(image(element_relation,successor_relation))))),complement(image(element_relation,symmetrization_of(image(element_relation,successor_relation)))))**.
% 299.82/300.46  160837[10:Rew:160202.0,152605.0] ||  -> equal(intersection(union(u,image(element_relation,successor_relation)),union(complement(u),power_class(universal_class))),symmetric_difference(complement(u),power_class(universal_class)))**.
% 299.82/300.46  160836[10:Rew:160202.0,152601.0] ||  -> equal(complement(intersection(union(u,image(element_relation,successor_relation)),complement(v))),union(intersection(complement(u),power_class(universal_class)),v))**.
% 299.82/300.46  160833[10:Rew:160202.0,152579.0] ||  -> equal(intersection(union(image(element_relation,successor_relation),u),union(power_class(universal_class),complement(u))),symmetric_difference(power_class(universal_class),complement(u)))**.
% 299.82/300.46  160832[10:Rew:160202.0,152576.0] ||  -> equal(complement(intersection(union(image(element_relation,successor_relation),u),complement(v))),union(intersection(power_class(universal_class),complement(u)),v))**.
% 299.82/300.46  160854[10:Rew:160202.0,152644.0] ||  -> member(not_subclass_element(u,image(element_relation,power_class(universal_class))),power_class(image(element_relation,successor_relation)))* subclass(u,image(element_relation,power_class(universal_class))).
% 299.82/300.46  160850[10:Rew:160202.0,152627.0] || member(u,image(element_relation,power_class(image(element_relation,successor_relation))))* member(u,power_class(image(element_relation,power_class(universal_class)))) -> .
% 299.82/300.46  160826[10:Rew:160202.0,152629.2] || member(u,universal_class) subclass(power_class(universal_class),v)* -> member(u,image(element_relation,successor_relation))* member(u,v)*.
% 299.82/300.46  163472[10:Rew:160202.0,160692.1] || member(regular(intersection(regular(u),v)),u)* -> equal(intersection(regular(u),v),successor_relation) equal(u,successor_relation).
% 299.82/300.46  160771[10:Rew:160202.0,146532.1] || subclass(u,unordered_pair(v,w))* -> equal(u,successor_relation) equal(regular(u),w) equal(regular(u),v).
% 299.82/300.46  160772[10:Rew:160202.0,146524.2] || member(u,universal_class) subclass(u,singleton(v))* -> equal(u,successor_relation) equal(apply(choice,u),v).
% 299.82/300.46  160773[10:Rew:160202.0,146502.2] function(u) || member(cross_product(universal_class,universal_class),ordinal_numbers)* -> equal(u,successor_relation) member(least(element_relation,u),u)*.
% 299.82/300.46  160774[10:Rew:160202.0,146481.1] || subclass(u,symmetric_difference(complement(v),complement(w)))* -> equal(u,successor_relation) member(regular(u),union(v,w)).
% 299.82/300.46  161159[10:Rew:160202.0,151135.0] ||  -> equal(power_class(intersection(symmetrization_of(successor_relation),complement(inverse(complement(inverse(successor_relation)))))),complement(image(element_relation,symmetrization_of(complement(inverse(successor_relation))))))**.
% 299.82/300.46  161157[10:Rew:160202.0,151133.0] ||  -> equal(power_class(intersection(symmetrization_of(successor_relation),complement(singleton(complement(inverse(successor_relation)))))),complement(image(element_relation,successor(complement(inverse(successor_relation))))))**.
% 299.82/300.46  161153[10:Rew:160202.0,152743.0] ||  -> equal(intersection(union(complement(inverse(successor_relation)),u),union(symmetrization_of(successor_relation),complement(u))),symmetric_difference(symmetrization_of(successor_relation),complement(u)))**.
% 299.82/300.46  161149[10:Rew:160202.0,152769.0] ||  -> equal(intersection(union(u,complement(inverse(successor_relation))),union(complement(u),symmetrization_of(successor_relation))),symmetric_difference(complement(u),symmetrization_of(successor_relation)))**.
% 299.82/300.46  163487[10:Rew:160202.0,161125.0] || member(not_subclass_element(intersection(symmetrization_of(successor_relation),u),v),complement(inverse(successor_relation)))* -> subclass(intersection(symmetrization_of(successor_relation),u),v).
% 299.82/300.46  163486[10:Rew:160202.0,161124.0] || member(not_subclass_element(intersection(u,symmetrization_of(successor_relation)),v),complement(inverse(successor_relation)))* -> subclass(intersection(u,symmetrization_of(successor_relation)),v).
% 299.82/300.46  161173[10:Rew:160202.0,152781.0] ||  -> equal(complement(intersection(complement(u),union(v,complement(inverse(successor_relation))))),union(u,intersection(complement(v),symmetrization_of(successor_relation))))**.
% 299.82/300.46  161172[10:Rew:160202.0,152768.0] ||  -> equal(complement(intersection(complement(u),union(complement(inverse(successor_relation)),v))),union(u,intersection(symmetrization_of(successor_relation),complement(v))))**.
% 299.82/300.46  161152[10:Rew:160202.0,152740.0] ||  -> equal(complement(intersection(union(complement(inverse(successor_relation)),u),complement(v))),union(intersection(symmetrization_of(successor_relation),complement(u)),v))**.
% 299.82/300.46  161148[10:Rew:160202.0,152765.0] ||  -> equal(complement(intersection(union(u,complement(inverse(successor_relation))),complement(v))),union(intersection(complement(u),symmetrization_of(successor_relation)),v))**.
% 299.82/300.46  163483[10:Rew:160202.0,161098.0] ||  -> member(not_subclass_element(u,image(element_relation,symmetrization_of(successor_relation))),power_class(complement(inverse(successor_relation))))* subclass(u,image(element_relation,symmetrization_of(successor_relation))).
% 299.82/300.46  163467[10:Rew:160202.0,160495.2,160202.0,160495.1] || subclass(u,successor_relation) well_ordering(v,inverse(successor_relation)) -> equal(segment(v,u,least(v,u)),successor_relation)**.
% 299.82/300.46  163485[10:Rew:160202.0,161123.2] || equal(u,symmetrization_of(successor_relation)) member(v,universal_class) -> member(v,complement(inverse(successor_relation)))* member(v,u)*.
% 299.82/300.46  163482[10:Rew:160202.0,161097.0] || member(u,image(element_relation,power_class(complement(inverse(successor_relation)))))* member(u,power_class(image(element_relation,symmetrization_of(successor_relation)))) -> .
% 299.82/300.46  163484[10:Rew:160202.0,161122.2] || member(u,universal_class) subclass(symmetrization_of(successor_relation),v)* -> member(u,complement(inverse(successor_relation)))* member(u,v)*.
% 299.82/300.46  161069[10:Rew:160202.0,150721.0] ||  -> equal(power_class(intersection(power_class(successor_relation),complement(inverse(image(element_relation,universal_class))))),complement(image(element_relation,symmetrization_of(image(element_relation,universal_class)))))**.
% 299.82/300.46  161068[10:Rew:160202.0,150720.0] ||  -> equal(power_class(intersection(power_class(successor_relation),complement(singleton(image(element_relation,universal_class))))),complement(image(element_relation,successor(image(element_relation,universal_class)))))**.
% 299.82/300.46  161066[10:Rew:160202.0,150719.0] ||  -> equal(intersection(union(image(element_relation,universal_class),u),union(power_class(successor_relation),complement(u))),symmetric_difference(power_class(successor_relation),complement(u)))**.
% 299.82/300.46  161062[10:Rew:160202.0,150706.0] ||  -> equal(intersection(union(u,image(element_relation,universal_class)),union(complement(u),power_class(successor_relation))),symmetric_difference(complement(u),power_class(successor_relation)))**.
% 299.82/300.46  161061[10:Rew:160202.0,150621.0] || equal(u,power_class(successor_relation)) member(v,universal_class) -> member(v,image(element_relation,universal_class))* member(v,u)*.
% 299.82/300.46  161060[10:Rew:160202.0,150620.1] || member(u,universal_class) subclass(power_class(successor_relation),v)* -> member(u,image(element_relation,universal_class))* member(u,v)*.
% 299.82/300.46  163480[10:Rew:160202.0,161078.1] || member(not_subclass_element(intersection(power_class(successor_relation),u),v),image(element_relation,universal_class))* -> subclass(intersection(power_class(successor_relation),u),v).
% 299.82/300.46  163479[10:Rew:160202.0,161074.1] || member(not_subclass_element(intersection(u,power_class(successor_relation)),v),image(element_relation,universal_class))* -> subclass(intersection(u,power_class(successor_relation)),v).
% 299.82/300.46  161037[10:Rew:160202.0,150619.0] ||  -> equal(complement(intersection(complement(u),union(image(element_relation,universal_class),v))),union(u,intersection(power_class(successor_relation),complement(v))))**.
% 299.82/300.46  161016[10:Rew:160202.0,150613.0] ||  -> equal(complement(intersection(complement(u),union(v,image(element_relation,universal_class)))),union(u,intersection(complement(v),power_class(successor_relation))))**.
% 299.82/300.46  160953[10:Rew:160202.0,150617.1] || subclass(universal_class,union(u,image(element_relation,universal_class))) member(singleton(v),intersection(complement(u),power_class(successor_relation)))* -> .
% 299.82/300.46  160952[10:Rew:160202.0,150616.0] ||  -> equal(complement(intersection(union(u,image(element_relation,universal_class)),complement(v))),union(intersection(complement(u),power_class(successor_relation)),v))**.
% 299.82/300.46  160922[10:Rew:160202.0,150629.1] || subclass(universal_class,union(image(element_relation,universal_class),u)) member(singleton(v),intersection(power_class(successor_relation),complement(u)))* -> .
% 299.82/300.46  160921[10:Rew:160202.0,150628.0] ||  -> equal(complement(intersection(union(image(element_relation,universal_class),u),complement(v))),union(intersection(power_class(successor_relation),complement(u)),v))**.
% 299.82/300.46  163478[10:Rew:160202.0,160983.1] || member(regular(image(element_relation,power_class(successor_relation))),power_class(image(element_relation,universal_class)))* -> equal(image(element_relation,power_class(successor_relation)),successor_relation).
% 299.82/300.46  163477[10:Rew:160202.0,160982.1] ||  -> member(not_subclass_element(u,image(element_relation,power_class(successor_relation))),power_class(image(element_relation,universal_class)))* subclass(u,image(element_relation,power_class(successor_relation))).
% 299.82/300.46  163476[10:Rew:160202.0,160981.1] || member(regular(power_class(image(element_relation,universal_class))),image(element_relation,power_class(successor_relation)))* -> equal(power_class(image(element_relation,universal_class)),successor_relation).
% 299.82/300.46  160977[10:Rew:160202.0,150618.1] || member(u,image(element_relation,power_class(image(element_relation,universal_class))))* member(u,power_class(image(element_relation,power_class(successor_relation)))) -> .
% 299.82/300.46  163475[10:Rew:160202.0,160896.1] || member(not_subclass_element(complement(complement(power_class(successor_relation))),u),image(element_relation,universal_class))* -> subclass(complement(complement(power_class(successor_relation))),u).
% 299.82/300.46  163101[10:Rew:160202.0,159371.1] || subclass(domain_relation,power_class(image(element_relation,complement(u)))) member(ordered_pair(successor_relation,successor_relation),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  163099[10:Rew:160202.0,159361.1] || subclass(domain_relation,symmetric_difference(cross_product(u,v),w)) -> member(ordered_pair(successor_relation,successor_relation),complement(restrict(w,u,v)))*.
% 299.82/300.46  163098[10:Rew:160202.0,159359.1] || subclass(domain_relation,symmetric_difference(u,cross_product(v,w))) -> member(ordered_pair(successor_relation,successor_relation),complement(restrict(u,v,w)))*.
% 299.82/300.46  162917[10:Rew:160202.0,151139.0] ||  -> equal(power_class(intersection(successor(successor_relation),complement(singleton(complement(singleton(successor_relation)))))),complement(image(element_relation,successor(complement(singleton(successor_relation))))))**.
% 299.82/300.46  162916[10:Rew:160202.0,151141.0] ||  -> equal(power_class(intersection(successor(successor_relation),complement(inverse(complement(singleton(successor_relation)))))),complement(image(element_relation,symmetrization_of(complement(singleton(successor_relation))))))**.
% 299.82/300.46  162915[10:Rew:160202.0,152492.0] ||  -> equal(intersection(union(complement(singleton(successor_relation)),u),union(successor(successor_relation),complement(u))),symmetric_difference(successor(successor_relation),complement(u)))**.
% 299.82/300.46  162914[10:Rew:160202.0,152518.0] ||  -> equal(intersection(union(u,complement(singleton(successor_relation))),union(complement(u),successor(successor_relation))),symmetric_difference(complement(u),successor(successor_relation)))**.
% 299.82/300.46  163512[10:Rew:160202.0,162913.1] || member(not_subclass_element(intersection(u,successor(successor_relation)),v),complement(singleton(successor_relation)))* -> subclass(intersection(u,successor(successor_relation)),v).
% 299.82/300.46  163511[10:Rew:160202.0,162911.1] || member(not_subclass_element(intersection(successor(successor_relation),u),v),complement(singleton(successor_relation)))* -> subclass(intersection(successor(successor_relation),u),v).
% 299.82/300.46  162909[10:Rew:160202.0,152517.0] ||  -> equal(complement(intersection(complement(u),union(complement(singleton(successor_relation)),v))),union(u,intersection(successor(successor_relation),complement(v))))**.
% 299.82/300.46  162908[10:Rew:160202.0,152530.0] ||  -> equal(complement(intersection(complement(u),union(v,complement(singleton(successor_relation))))),union(u,intersection(complement(v),successor(successor_relation))))**.
% 299.82/300.46  162904[10:Rew:160202.0,152514.0] ||  -> equal(complement(intersection(union(u,complement(singleton(successor_relation))),complement(v))),union(intersection(complement(u),successor(successor_relation)),v))**.
% 299.82/300.46  162902[10:Rew:160202.0,152489.0] ||  -> equal(complement(intersection(union(complement(singleton(successor_relation)),u),complement(v))),union(intersection(successor(successor_relation),complement(u)),v))**.
% 299.82/300.46  163510[10:Rew:160202.0,162892.1] ||  -> member(not_subclass_element(u,image(element_relation,successor(successor_relation))),power_class(complement(singleton(successor_relation))))* subclass(u,image(element_relation,successor(successor_relation))).
% 299.82/300.46  163502[10:Rew:160202.0,162798.0] || equal(u,successor(successor_relation)) member(v,universal_class) -> member(v,complement(singleton(successor_relation)))* member(v,u)*.
% 299.82/300.46  163500[10:Rew:160202.0,162778.1] || member(u,image(element_relation,power_class(complement(singleton(successor_relation)))))* member(u,power_class(image(element_relation,successor(successor_relation)))) -> .
% 299.82/300.46  163499[10:Rew:160202.0,162771.1] || member(u,universal_class) subclass(successor(successor_relation),v)* -> member(u,complement(singleton(successor_relation)))* member(u,v)*.
% 299.82/300.46  34092[0:MRR:33509.1,34067.1] || member(u,universal_class) member(v,u) subclass(element_relation,w) -> member(ordered_pair(v,u),w)*.
% 299.82/300.46  48359[0:Res:1495.2,47888.0] || member(u,universal_class) subclass(rest_relation,rest_of(ordered_pair(u,rest_of(u))))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.46  157918[6:Res:51387.0,148657.1] || member(not_subclass_element(u,complement(complement(compose(element_relation,universal_class)))),element_relation)* -> subclass(u,complement(complement(compose(element_relation,universal_class)))).
% 299.82/300.46  124645[0:MRR:124617.0,191.0] || member(complement(u),universal_class) -> member(singleton(complement(u)),u)* member(singleton(singleton(singleton(complement(u)))),element_relation)*.
% 299.82/300.46  47765[0:Rew:40.0,47722.0] || member(flip(cross_product(u,universal_class)),inverse(u)) -> member(ordered_pair(flip(cross_product(u,universal_class)),inverse(u)),element_relation)*.
% 299.82/300.46  47766[0:Rew:55.0,47720.0] || member(restrict(element_relation,universal_class,u),sum_class(u)) -> member(ordered_pair(restrict(element_relation,universal_class,u),sum_class(u)),element_relation)*.
% 299.82/300.46  108232[0:Res:107289.0,9.0] || subclass(image(element_relation,complement(u)),complement(power_class(u)))* -> equal(image(element_relation,complement(u)),complement(power_class(u))).
% 299.82/300.46  145338[2:SpR:10028.0,142420.0] ||  -> equal(symmetric_difference(symmetrization_of(image(element_relation,complement(u))),intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))),universal_class)**.
% 299.82/300.46  145206[2:SpR:10028.0,142419.0] ||  -> equal(symmetric_difference(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),symmetrization_of(image(element_relation,complement(u)))),universal_class)**.
% 299.82/300.46  145337[2:SpR:10029.0,142420.0] ||  -> equal(symmetric_difference(successor(image(element_relation,complement(u))),intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))),universal_class)**.
% 299.82/300.46  145205[2:SpR:10029.0,142419.0] ||  -> equal(symmetric_difference(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),successor(image(element_relation,complement(u)))),universal_class)**.
% 299.82/300.46  118677[0:SpL:57.0,9118.1] || member(u,universal_class) subclass(universal_class,power_class(v)) member(sum_class(u),image(element_relation,complement(v)))* -> .
% 299.82/300.46  118393[0:SpL:57.0,9146.1] || member(u,universal_class) subclass(universal_class,power_class(v)) member(power_class(u),image(element_relation,complement(v)))* -> .
% 299.82/300.46  9162[0:Res:1478.2,307.0] || member(u,universal_class) subclass(universal_class,image(element_relation,complement(v)))* member(power_class(u),power_class(v))* -> .
% 299.82/300.46  9134[0:Res:1479.2,307.0] || member(u,universal_class) subclass(universal_class,image(element_relation,complement(v)))* member(sum_class(u),power_class(v))* -> .
% 299.82/300.46  9653[0:Res:1481.2,307.0] || subclass(u,image(element_relation,complement(v)))* member(not_subclass_element(u,w),power_class(v))* -> subclass(u,w).
% 299.82/300.46  108466[0:Res:1504.1,307.0] || subclass(ordered_pair(u,v),image(element_relation,complement(w)))* member(unordered_pair(u,singleton(v)),power_class(w)) -> .
% 299.82/300.46  124284[0:Res:1499.1,986.1] || subclass(universal_class,power_class(image(element_relation,complement(u)))) member(ordered_pair(v,w),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  124240[0:Res:1476.1,986.1] || subclass(universal_class,power_class(image(element_relation,complement(u)))) member(unordered_pair(v,w),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  145333[2:SpR:982.0,142420.0] ||  -> equal(symmetric_difference(union(image(element_relation,power_class(u)),v),intersection(power_class(image(element_relation,complement(u))),complement(v))),universal_class)**.
% 299.82/300.46  145201[2:SpR:982.0,142419.0] ||  -> equal(symmetric_difference(intersection(power_class(image(element_relation,complement(u))),complement(v)),union(image(element_relation,power_class(u)),v)),universal_class)**.
% 299.82/300.46  118042[0:SpL:57.0,9069.0] || subclass(universal_class,image(element_relation,power_class(u))) member(unordered_pair(v,w),power_class(image(element_relation,complement(u))))* -> .
% 299.82/300.46  1029[0:SpR:208.0,27.2] || member(u,universal_class) -> member(u,image(element_relation,power_class(v))) member(u,power_class(image(element_relation,complement(v))))*.
% 299.82/300.46  145331[2:SpR:984.0,142420.0] ||  -> equal(symmetric_difference(union(u,image(element_relation,power_class(v))),intersection(complement(u),power_class(image(element_relation,complement(v))))),universal_class)**.
% 299.82/300.46  145199[2:SpR:984.0,142419.0] ||  -> equal(symmetric_difference(intersection(complement(u),power_class(image(element_relation,complement(v)))),union(u,image(element_relation,power_class(v)))),universal_class)**.
% 299.82/300.46  158314[0:SpL:505.0,3565.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),universal_class)** -> member(omega,image(element_relation,union(u,v))).
% 299.82/300.46  9957[0:SpL:505.0,3358.1] || equal(image(element_relation,union(u,v)),universal_class) equal(power_class(intersection(complement(u),complement(v))),universal_class)** -> .
% 299.82/300.46  158383[2:SpR:505.0,142477.0] ||  -> equal(symmetric_difference(power_class(image(element_relation,union(u,v))),image(element_relation,power_class(intersection(complement(u),complement(v))))),universal_class)**.
% 299.82/300.46  158346[2:SpR:505.0,142475.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(intersection(complement(u),complement(v)))),power_class(image(element_relation,union(u,v)))),universal_class)**.
% 299.82/300.46  10315[0:SpR:505.0,9898.0] ||  -> subclass(symmetric_difference(power_class(intersection(complement(u),complement(v))),complement(w)),union(image(element_relation,union(u,v)),w))*.
% 299.82/300.46  30576[0:SpL:505.0,30433.1] || subclass(universal_class,image(element_relation,union(u,v))) subclass(universal_class,power_class(intersection(complement(u),complement(v))))* -> .
% 299.82/300.46  9058[0:SpL:28.0,307.0] || member(u,image(element_relation,union(v,w))) member(u,power_class(intersection(complement(v),complement(w))))* -> .
% 299.82/300.46  10304[0:SpR:505.0,9898.0] ||  -> subclass(symmetric_difference(complement(u),power_class(intersection(complement(v),complement(w)))),union(u,image(element_relation,union(v,w))))*.
% 299.82/300.46  120267[0:SpL:161.0,9121.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,w)) -> member(sum_class(u),complement(intersection(v,w)))*.
% 299.82/300.46  108374[0:Res:1479.2,9332.1] || member(u,universal_class) subclass(universal_class,intersection(v,w)) member(sum_class(u),symmetric_difference(v,w))* -> .
% 299.82/300.46  9596[0:Res:1479.2,594.0] || member(u,universal_class) subclass(universal_class,restrict(v,w,x))* -> member(sum_class(u),cross_product(w,x))*.
% 299.82/300.46  158731[0:SpR:119971.0,474.1] || member(inverse(cross_product(u,universal_class)),universal_class) -> member(ordered_pair(inverse(cross_product(u,universal_class)),image(universal_class,u)),domain_relation)*.
% 299.82/300.46  143788[0:Res:34429.0,159.0] ||  -> subclass(complement(complement(omega)),u) equal(integer_of(not_subclass_element(complement(complement(omega)),u)),not_subclass_element(complement(complement(omega)),u))**.
% 299.82/300.46  93605[0:Obv:93570.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),complement(w)),u)** member(v,w) subclass(unordered_pair(u,v),complement(w)).
% 299.82/300.46  93604[0:Obv:93579.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),complement(w)),v)** member(u,w) subclass(unordered_pair(u,v),complement(w)).
% 299.82/300.46  37824[0:Obv:37806.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w) member(u,unordered_pair(u,v))*.
% 299.82/300.46  37825[0:Obv:37799.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),w),u)** subclass(unordered_pair(u,v),w) member(v,unordered_pair(u,v))*.
% 299.82/300.46  108443[0:Res:1504.1,594.0] || subclass(ordered_pair(u,v),restrict(w,x,y))* -> member(unordered_pair(u,singleton(v)),cross_product(x,y)).
% 299.82/300.46  108439[0:Res:1504.1,9332.1] || subclass(ordered_pair(u,v),intersection(w,x)) member(unordered_pair(u,singleton(v)),symmetric_difference(w,x))* -> .
% 299.82/300.46  111985[0:Res:6842.1,3.0] || subclass(universal_class,symmetric_difference(u,v)) subclass(union(u,v),w)* -> member(unordered_pair(x,y),w)*.
% 299.82/300.46  48022[0:SpL:1938.0,3487.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(unordered_pair(x,y),complement(restrict(u,v,w)))*.
% 299.82/300.46  48023[0:SpL:1943.0,3487.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(unordered_pair(x,y),complement(restrict(w,u,v)))*.
% 299.82/300.46  9333[0:Res:1951.1,5.0] || member(not_subclass_element(u,complement(intersection(v,w))),symmetric_difference(v,w))* -> subclass(u,complement(intersection(v,w))).
% 299.82/300.46  89251[0:Res:51387.0,10191.0] ||  -> subclass(u,complement(symmetric_difference(v,inverse(v)))) member(not_subclass_element(u,complement(symmetric_difference(v,inverse(v)))),symmetrization_of(v))*.
% 299.82/300.46  101364[0:Res:51387.0,10254.0] ||  -> subclass(u,complement(symmetric_difference(v,singleton(v)))) member(not_subclass_element(u,complement(symmetric_difference(v,singleton(v)))),successor(v))*.
% 299.82/300.46  40236[0:Obv:40229.2] || subclass(u,v) member(not_subclass_element(u,intersection(w,v)),w)* -> subclass(u,intersection(w,v)).
% 299.82/300.46  123398[0:SpL:161.0,9639.0] || subclass(u,symmetric_difference(v,w)) -> subclass(u,x) member(not_subclass_element(u,x),complement(intersection(v,w)))*.
% 299.82/300.46  108405[0:Res:1481.2,9332.1] || subclass(u,intersection(v,w)) member(not_subclass_element(u,x),symmetric_difference(v,w))* -> subclass(u,x).
% 299.82/300.46  9646[0:Res:1481.2,594.0] || subclass(u,restrict(v,w,x))* -> subclass(u,y) member(not_subclass_element(u,y),cross_product(w,x))*.
% 299.82/300.46  113238[0:Rew:31.0,113161.1] || member(not_subclass_element(u,restrict(u,v,w)),cross_product(v,w))* -> subclass(u,restrict(u,v,w)).
% 299.82/300.46  143789[0:Res:340.1,159.0] ||  -> subclass(intersection(omega,u),v) equal(integer_of(not_subclass_element(intersection(omega,u),v)),not_subclass_element(intersection(omega,u),v))**.
% 299.82/300.46  143791[0:Res:322.1,159.0] ||  -> subclass(intersection(u,omega),v) equal(integer_of(not_subclass_element(intersection(u,omega),v)),not_subclass_element(intersection(u,omega),v))**.
% 299.82/300.46  1091[0:Rew:28.0,1080.1] || member(not_subclass_element(union(u,v),w),intersection(complement(u),complement(v)))* -> subclass(union(u,v),w).
% 299.82/300.46  155809[3:Res:978.1,141576.1] || member(not_subclass_element(restrict(complement(kind_1_ordinals),u,v),w),ordinal_numbers)* -> subclass(restrict(complement(kind_1_ordinals),u,v),w).
% 299.82/300.46  40240[0:Obv:40228.1] || member(not_subclass_element(intersection(u,v),intersection(w,v)),w)* -> subclass(intersection(u,v),intersection(w,v)).
% 299.82/300.46  40241[0:Obv:40216.1] || member(not_subclass_element(intersection(u,v),intersection(w,u)),w)* -> subclass(intersection(u,v),intersection(w,u)).
% 299.82/300.46  113256[0:MRR:113198.0,34189.1] ||  -> member(not_subclass_element(u,intersection(union(v,w),u)),complement(v))* subclass(u,intersection(union(v,w),u)).
% 299.82/300.46  113255[0:MRR:113199.0,34189.1] ||  -> member(not_subclass_element(u,intersection(union(v,w),u)),complement(w))* subclass(u,intersection(union(v,w),u)).
% 299.82/300.46  107259[0:Obv:107218.1] || member(not_subclass_element(complement(complement(u)),intersection(v,u)),v)* -> subclass(complement(complement(u)),intersection(v,u)).
% 299.82/300.46  123492[0:Res:978.1,26.1] || member(not_subclass_element(restrict(complement(u),v,w),x),u)* -> subclass(restrict(complement(u),v,w),x).
% 299.82/300.46  151419[6:MRR:151418.0,34189.1] || member(not_subclass_element(u,symmetric_difference(universal_class,cantor(v))),complement(cantor(v)))* -> subclass(u,symmetric_difference(universal_class,cantor(v))).
% 299.82/300.46  28279[0:Res:1495.2,595.0] || member(u,universal_class) subclass(rest_relation,restrict(v,w,x))* -> member(ordered_pair(u,rest_of(u)),v)*.
% 299.82/300.46  112423[0:SpR:506.0,30985.1] || member(u,universal_class) -> member(u,complement(intersection(union(v,w),complement(x))))* member(u,complement(x)).
% 299.82/300.46  112449[0:Res:30985.1,3.0] || member(u,universal_class) subclass(union(v,w),x)* -> member(u,complement(w))* member(u,x)*.
% 299.82/300.46  112584[0:SpR:507.0,30984.1] || member(u,universal_class) -> member(u,complement(intersection(complement(v),union(w,x))))* member(u,complement(v)).
% 299.82/300.46  112616[0:Res:30984.1,3.0] || member(u,universal_class) subclass(union(v,w),x)* -> member(u,complement(v))* member(u,x)*.
% 299.82/300.46  141960[2:MRR:85403.3,120469.0] || asymmetric(u,v)* member(w,cross_product(v,v))* member(w,intersection(u,inverse(u)))* -> .
% 299.82/300.46  31092[2:Res:64.1,5832.1] function(u) inductive(u) || well_ordering(v,cross_product(universal_class,universal_class))* -> member(least(v,u),u)*.
% 299.82/300.46  34662[0:Res:173.1,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class) subclass(complement(intersection(y__dfg,ordinal_numbers)),intersection(y__dfg,ordinal_numbers))* -> .
% 299.82/300.46  183491[10:SpR:505.0,163005.0] ||  -> equal(intersection(symmetric_difference(universal_class,image(element_relation,union(u,v))),complement(power_class(intersection(complement(u),complement(v))))),successor_relation)**.
% 299.82/300.46  183492[10:SpR:505.0,163000.0] ||  -> equal(intersection(complement(power_class(intersection(complement(u),complement(v)))),symmetric_difference(universal_class,image(element_relation,union(u,v)))),successor_relation)**.
% 299.82/300.46  183553[10:SpL:505.0,160544.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),universal_class)** -> member(successor_relation,image(element_relation,union(u,v))).
% 299.82/300.46  183822[10:Res:28320.1,183622.0] || subclass(rest_relation,rotate(successor(successor_relation))) -> member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),singleton(successor_relation))*.
% 299.82/300.46  183823[10:Res:28321.1,183622.0] || subclass(rest_relation,flip(successor(successor_relation))) -> member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),singleton(successor_relation))*.
% 299.82/300.46  183855[10:Res:28320.1,183723.0] || subclass(rest_relation,rotate(symmetrization_of(successor_relation))) -> member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),inverse(successor_relation))*.
% 299.82/300.46  183856[10:Res:28321.1,183723.0] || subclass(rest_relation,flip(symmetrization_of(successor_relation))) -> member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),inverse(successor_relation))*.
% 299.82/300.46  183925[11:Res:183764.1,9300.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(regular(symmetrization_of(successor_relation)),complement(restrict(u,v,w)))*.
% 299.82/300.46  183927[11:Res:183764.1,9306.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(regular(symmetrization_of(successor_relation)),complement(restrict(w,u,v)))*.
% 299.82/300.46  184099[0:SpL:1931.0,1510.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),universal_class)** -> member(omega,complement(symmetric_difference(u,v))).
% 299.82/300.46  184647[10:SpR:163198.1,1931.0] || subclass(complement(symmetric_difference(u,v)),successor_relation) -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),successor_relation)**.
% 299.82/300.46  184792[14:SpL:119971.0,184008.2] || member(u,universal_class)* member(cross_product(v,universal_class),universal_class)* equal(sum_class(image(universal_class,v)),u)* -> .
% 299.82/300.46  184950[10:SpR:505.0,184676.1] || subclass(image(element_relation,union(u,v)),successor_relation) -> equal(complement(power_class(intersection(complement(u),complement(v)))),successor_relation)**.
% 299.82/300.46  185405[10:SpR:185302.1,1028.1] || equal(successor_relation,u) member(v,universal_class) -> member(v,image(element_relation,universal_class))* member(v,power_class(u))*.
% 299.82/300.46  185678[10:Rew:142543.0,185399.1] || equal(successor_relation,u) -> equal(complement(intersection(union(v,u),complement(w))),union(symmetric_difference(universal_class,v),w))**.
% 299.82/300.46  185681[10:Rew:142543.0,185456.1] || equal(successor_relation,u) -> equal(complement(intersection(complement(v),union(w,u))),union(v,symmetric_difference(universal_class,w)))**.
% 299.82/300.46  186160[10:Res:60.1,185639.1] || member(ordered_pair(u,v),compose(w,x))* equal(image(w,image(x,singleton(u))),successor_relation) -> .
% 299.82/300.46  39595[0:Res:5768.2,16.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,cross_product(w,x))* -> member(u,w)*.
% 299.82/300.46  39610[0:Res:5768.2,3514.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,w) subclass(universal_class,complement(w))* -> .
% 299.82/300.46  125976[0:Res:28320.1,98.0] || subclass(rest_relation,rotate(composition_function)) -> equal(compose(ordered_pair(u,rest_of(ordered_pair(ordered_pair(v,w),u))),v),w)**.
% 299.82/300.46  3628[0:SpL:1005.0,98.0] || member(singleton(singleton(singleton(ordered_pair(u,v)))),composition_function)* -> equal(compose(singleton(ordered_pair(u,v)),u),v)**.
% 299.82/300.46  41323[0:Res:6.0,5841.1] || member(u,universal_class) well_ordering(v,universal_class) -> member(least(v,unordered_pair(w,u)),unordered_pair(w,u))*.
% 299.82/300.46  41464[0:Res:6.0,5842.1] || member(u,universal_class) well_ordering(v,universal_class) -> member(least(v,unordered_pair(u,w)),unordered_pair(u,w))*.
% 299.82/300.46  163468[10:Rew:160202.0,160528.2] || subclass(complement(u),successor_relation)* member(v,universal_class)* well_ordering(w,inverse(successor_relation))* -> member(v,u)*.
% 299.82/300.46  163481[10:Rew:160202.0,161084.2] || well_ordering(u,universal_class) member(least(u,power_class(successor_relation)),image(element_relation,universal_class))* -> equal(power_class(successor_relation),successor_relation).
% 299.82/300.46  184600[10:Res:184565.1,127.0] || well_ordering(u,kind_1_ordinals)* subclass(ordinal_numbers,v) well_ordering(w,v)* -> member(least(w,ordinal_numbers),ordinal_numbers)*.
% 299.82/300.46  185784[10:Res:185430.1,160373.0] || equal(complement(u),successor_relation) well_ordering(v,u)* -> equal(segment(v,universal_class,least(v,universal_class)),successor_relation)**.
% 299.82/300.46  31090[2:Res:94.0,5832.1] inductive(compose_class(u)) || well_ordering(v,cross_product(universal_class,universal_class)) -> member(least(v,compose_class(u)),compose_class(u))*.
% 299.82/300.46  31089[2:Res:142.0,5832.1] inductive(rest_of(u)) || well_ordering(v,cross_product(universal_class,universal_class)) -> member(least(v,rest_of(u)),rest_of(u))*.
% 299.82/300.46  6320[0:Res:137.1,3926.1] single_valued_class(sum_class(cross_product(universal_class,universal_class))) || member(cross_product(universal_class,universal_class),ordinal_numbers) -> function(sum_class(cross_product(universal_class,universal_class)))*.
% 299.82/300.46  162098[10:Rew:160202.0,147374.2] || member(complement(u),ordinal_numbers) member(regular(sum_class(complement(u))),u)* -> equal(sum_class(complement(u)),successor_relation).
% 299.82/300.46  10118[0:Res:6219.1,1320.1] || member(u,sum_class(singleton(u)))* member(singleton(u),ordinal_numbers) -> equal(sum_class(singleton(u)),singleton(u)).
% 299.82/300.46  113113[0:Res:137.1,9649.0] || member(singleton(u),ordinal_numbers) -> subclass(sum_class(singleton(u)),v) equal(not_subclass_element(sum_class(singleton(u)),v),u)**.
% 299.82/300.46  163142[10:MRR:125965.2,160227.0] || subclass(rest_relation,rotate(cross_product(universal_class,universal_class))) equal(successor(ordered_pair(u,rest_of(ordered_pair(v,u)))),v)** -> .
% 299.82/300.46  163140[10:MRR:126095.2,160227.0] || subclass(rest_relation,flip(cross_product(universal_class,universal_class)))* equal(rest_of(ordered_pair(u,v)),successor(ordered_pair(v,u)))** -> .
% 299.82/300.46  188453[10:SpL:1931.0,160566.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),universal_class)** -> member(successor_relation,complement(symmetric_difference(u,v))).
% 299.82/300.46  188688[10:Res:3872.2,185639.1] || member(u,cross_product(v,w))* member(u,x)* equal(restrict(x,v,w),successor_relation)** -> .
% 299.82/300.46  189170[10:SpR:185608.1,1931.0] || equal(complement(symmetric_difference(u,v)),successor_relation) -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),successor_relation)**.
% 299.82/300.46  189385[15:Rew:189339.1,28090.3] || member(u,universal_class) subclass(domain_relation,v)* subclass(v,w)* -> member(ordered_pair(u,successor_relation),w)*.
% 299.82/300.46  189388[15:Rew:189339.1,80897.2] || member(u,universal_class) subclass(domain_relation,symmetric_difference(v,inverse(v)))* -> member(ordered_pair(u,successor_relation),symmetrization_of(v))*.
% 299.82/300.46  189392[15:Rew:189339.1,28110.2] || member(u,universal_class) subclass(domain_relation,symmetric_difference(v,w)) -> member(ordered_pair(u,successor_relation),union(v,w))*.
% 299.82/300.46  189397[15:Rew:189339.1,184836.2] || member(u,universal_class) subclass(domain_relation,complement(compose(element_relation,universal_class)))* member(ordered_pair(u,successor_relation),element_relation)* -> .
% 299.82/300.46  189410[15:Rew:189339.1,184846.2] || member(u,universal_class) subclass(domain_relation,symmetric_difference(v,singleton(v)))* -> member(ordered_pair(u,successor_relation),successor(v))*.
% 299.82/300.46  191093[20:Res:191074.1,127.0] || equal(u,omega) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  192476[20:SpL:505.0,191129.1] || equal(image(element_relation,union(u,v)),omega) equal(power_class(intersection(complement(u),complement(v))),universal_class)** -> .
% 299.82/300.46  192563[10:Res:191.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(singleton(v),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  192569[10:Res:187489.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(power_class(successor_relation),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  192886[20:SpL:505.0,192315.1] || equal(image(element_relation,union(u,v)),omega) equal(power_class(intersection(complement(u),complement(v))),omega)** -> .
% 299.82/300.46  192898[20:SpL:505.0,192321.1] || equal(image(element_relation,union(u,v)),universal_class) equal(power_class(intersection(complement(u),complement(v))),omega)** -> .
% 299.82/300.46  192923[20:SpL:505.0,192323.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),omega)** -> member(successor_relation,image(element_relation,union(u,v))).
% 299.82/300.46  192946[10:SpL:505.0,188851.0] || subclass(power_class(intersection(complement(u),complement(v))),successor_relation)* -> member(singleton(w),image(element_relation,union(u,v)))*.
% 299.82/300.46  193279[20:SpL:1931.0,191100.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),omega)** -> member(successor_relation,complement(symmetric_difference(u,v))).
% 299.82/300.46  193410[10:Res:192947.1,9300.0] || equal(complement(symmetric_difference(u,cross_product(v,w))),successor_relation) -> member(singleton(x),complement(restrict(u,v,w)))*.
% 299.82/300.46  193412[10:Res:192947.1,9306.0] || equal(complement(symmetric_difference(cross_product(u,v),w)),successor_relation) -> member(singleton(x),complement(restrict(w,u,v)))*.
% 299.82/300.46  193599[10:SpR:505.0,161321.0] ||  -> equal(intersection(restrict(image(element_relation,union(u,v)),w,x),power_class(intersection(complement(u),complement(v)))),successor_relation)**.
% 299.82/300.46  193697[10:SpR:505.0,161320.0] ||  -> equal(intersection(power_class(intersection(complement(u),complement(v))),restrict(image(element_relation,union(u,v)),w,x)),successor_relation)**.
% 299.82/300.46  194086[10:Res:28320.1,193819.0] || subclass(rest_relation,rotate(cantor(complement(cross_product(singleton(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v)),universal_class)))))* -> .
% 299.82/300.46  194087[10:Res:28321.1,193819.0] || subclass(rest_relation,flip(cantor(complement(cross_product(singleton(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u)))),universal_class)))))* -> .
% 299.82/300.46  194503[0:SpL:505.0,183398.0] || member(u,complement(power_class(intersection(complement(v),complement(w)))))* -> member(u,image(element_relation,union(v,w))).
% 299.82/300.46  194533[0:Res:28320.1,183398.0] || subclass(rest_relation,rotate(complement(complement(u)))) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)*.
% 299.82/300.46  194534[0:Res:28321.1,183398.0] || subclass(rest_relation,flip(complement(complement(u)))) -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)*.
% 299.82/300.46  195608[10:SpL:28.0,195436.0] || subclass(intersection(complement(u),complement(v)),union(u,v))* -> equal(intersection(complement(u),complement(v)),successor_relation).
% 299.82/300.46  195617[10:SpL:208.0,195436.0] || subclass(image(element_relation,power_class(u)),power_class(image(element_relation,complement(u))))* -> equal(image(element_relation,power_class(u)),successor_relation).
% 299.82/300.46  195810[6:Res:195710.1,5646.1] || equal(inverse(u),universal_class) member(ordered_pair(v,w),compose(x,y))* -> member(w,inverse(u))*.
% 299.82/300.46  195869[6:Res:195720.1,5646.1] || equal(sum_class(u),universal_class) member(ordered_pair(v,w),compose(x,y))* -> member(w,sum_class(u))*.
% 299.82/300.46  195980[0:SpR:1938.0,195152.0] ||  -> equal(intersection(complement(restrict(u,v,w)),symmetric_difference(u,cross_product(v,w))),symmetric_difference(u,cross_product(v,w)))**.
% 299.82/300.46  195981[0:SpR:1943.0,195152.0] ||  -> equal(intersection(complement(restrict(u,v,w)),symmetric_difference(cross_product(v,w),u)),symmetric_difference(cross_product(v,w),u))**.
% 299.82/300.46  196508[10:SpR:161137.0,10292.0] ||  -> subclass(symmetric_difference(power_class(complement(inverse(successor_relation))),complement(inverse(image(element_relation,symmetrization_of(successor_relation))))),symmetrization_of(image(element_relation,symmetrization_of(successor_relation))))*.
% 299.82/300.46  196510[10:SpR:161137.0,10293.0] ||  -> subclass(symmetric_difference(power_class(complement(inverse(successor_relation))),complement(singleton(image(element_relation,symmetrization_of(successor_relation))))),successor(image(element_relation,symmetrization_of(successor_relation))))*.
% 299.82/300.46  196589[10:Rew:161137.0,196564.1] || member(regular(power_class(complement(inverse(successor_relation)))),image(element_relation,symmetrization_of(successor_relation)))* -> equal(power_class(complement(inverse(successor_relation))),successor_relation).
% 299.82/300.46  196714[10:SpR:162889.0,10292.0] ||  -> subclass(symmetric_difference(power_class(complement(singleton(successor_relation))),complement(inverse(image(element_relation,successor(successor_relation))))),symmetrization_of(image(element_relation,successor(successor_relation))))*.
% 299.82/300.46  196716[10:SpR:162889.0,10293.0] ||  -> subclass(symmetric_difference(power_class(complement(singleton(successor_relation))),complement(singleton(image(element_relation,successor(successor_relation))))),successor(image(element_relation,successor(successor_relation))))*.
% 299.82/300.46  196794[10:Rew:162889.0,196770.1] || member(regular(power_class(complement(singleton(successor_relation)))),image(element_relation,successor(successor_relation)))* -> equal(power_class(complement(singleton(successor_relation))),successor_relation).
% 299.82/300.46  198129[10:Rew:113504.0,198063.0,160223.0,198063.0] ||  -> equal(symmetric_difference(intersection(u,image(element_relation,successor_relation)),power_class(universal_class)),union(intersection(u,image(element_relation,successor_relation)),power_class(universal_class)))**.
% 299.82/300.46  198279[10:Rew:113504.0,198208.0,160223.0,198208.0] ||  -> equal(symmetric_difference(intersection(image(element_relation,successor_relation),u),power_class(universal_class)),union(intersection(image(element_relation,successor_relation),u),power_class(universal_class)))**.
% 299.82/300.46  198352[10:Rew:113504.0,198286.0,160223.0,198286.0] ||  -> equal(symmetric_difference(power_class(universal_class),intersection(u,image(element_relation,successor_relation))),union(power_class(universal_class),intersection(u,image(element_relation,successor_relation))))**.
% 299.82/300.46  198430[10:Rew:113504.0,198359.0,160223.0,198359.0] ||  -> equal(symmetric_difference(power_class(universal_class),intersection(image(element_relation,successor_relation),u)),union(power_class(universal_class),intersection(image(element_relation,successor_relation),u)))**.
% 299.82/300.46  198512[10:Rew:113504.0,198437.0,160223.0,198437.0] ||  -> equal(symmetric_difference(successor(successor_relation),intersection(complement(singleton(successor_relation)),u)),union(successor(successor_relation),intersection(complement(singleton(successor_relation)),u)))**.
% 299.82/300.46  198617[10:Rew:113504.0,198546.0,160223.0,198546.0] ||  -> equal(symmetric_difference(successor(successor_relation),intersection(u,complement(singleton(successor_relation)))),union(successor(successor_relation),intersection(u,complement(singleton(successor_relation)))))**.
% 299.82/300.46  198698[10:Rew:113504.0,198624.0,160223.0,198624.0] ||  -> equal(symmetric_difference(intersection(complement(singleton(successor_relation)),u),successor(successor_relation)),union(intersection(complement(singleton(successor_relation)),u),successor(successor_relation)))**.
% 299.82/300.46  198910[10:Rew:113504.0,198841.0,160223.0,198841.0] ||  -> equal(symmetric_difference(intersection(u,complement(singleton(successor_relation))),successor(successor_relation)),union(intersection(u,complement(singleton(successor_relation))),successor(successor_relation)))**.
% 299.82/300.46  198987[10:Rew:113504.0,198917.0,160223.0,198917.0] ||  -> equal(symmetric_difference(intersection(u,complement(inverse(successor_relation))),symmetrization_of(successor_relation)),union(intersection(u,complement(inverse(successor_relation))),symmetrization_of(successor_relation)))**.
% 299.82/300.46  199117[10:Rew:113504.0,199041.0,160223.0,199041.0] ||  -> equal(symmetric_difference(intersection(complement(inverse(successor_relation)),u),symmetrization_of(successor_relation)),union(intersection(complement(inverse(successor_relation)),u),symmetrization_of(successor_relation)))**.
% 299.82/300.46  199247[10:Rew:113504.0,199178.0,160223.0,199178.0] ||  -> equal(symmetric_difference(symmetrization_of(successor_relation),intersection(u,complement(inverse(successor_relation)))),union(symmetrization_of(successor_relation),intersection(u,complement(inverse(successor_relation)))))**.
% 299.82/300.46  199329[10:Rew:113504.0,199254.0,160223.0,199254.0] ||  -> equal(symmetric_difference(symmetrization_of(successor_relation),intersection(complement(inverse(successor_relation)),u)),union(symmetrization_of(successor_relation),intersection(complement(inverse(successor_relation)),u)))**.
% 299.82/300.46  199405[10:Rew:113504.0,199336.0,160223.0,199336.0] ||  -> equal(symmetric_difference(intersection(u,image(element_relation,universal_class)),power_class(successor_relation)),union(intersection(u,image(element_relation,universal_class)),power_class(successor_relation)))**.
% 299.82/300.46  199486[10:Rew:113504.0,199412.0,160223.0,199412.0] ||  -> equal(symmetric_difference(intersection(image(element_relation,universal_class),u),power_class(successor_relation)),union(intersection(image(element_relation,universal_class),u),power_class(successor_relation)))**.
% 299.82/300.46  199562[10:Rew:113504.0,199493.0,160223.0,199493.0] ||  -> equal(symmetric_difference(power_class(successor_relation),intersection(u,image(element_relation,universal_class))),union(power_class(successor_relation),intersection(u,image(element_relation,universal_class))))**.
% 299.82/300.46  199643[10:Rew:113504.0,199569.0,160223.0,199569.0] ||  -> equal(symmetric_difference(power_class(successor_relation),intersection(image(element_relation,universal_class),u)),union(power_class(successor_relation),intersection(image(element_relation,universal_class),u)))**.
% 299.82/300.46  199843[10:Res:199826.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(rest_relation),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  200025[14:SpL:10417.0,199972.0] || member(image(cross_product(u,v),w),universal_class) member(restrict(cross_product(w,universal_class),u,v),universal_class)* -> .
% 299.82/300.46  200056[14:SpR:10417.0,200027.1] || member(restrict(cross_product(u,universal_class),v,w),universal_class)* -> equal(integer_of(image(cross_product(v,w),u)),successor_relation).
% 299.82/300.46  200110[14:SpR:10417.0,200028.1] || member(restrict(cross_product(u,universal_class),v,w),universal_class)* -> equal(singleton(image(cross_product(v,w),u)),successor_relation).
% 299.82/300.46  200562[10:Res:67.2,163137.0] function(u) || member(v,universal_class) equal(rest_of(image(u,v)),successor(image(u,v)))** -> .
% 299.82/300.46  200591[10:MRR:200540.1,6.0] || member(u,universal_class) equal(rest_of(apply(choice,u)),successor(apply(choice,u)))** -> equal(u,successor_relation).
% 299.82/300.46  200668[10:Res:161493.2,513.0] inductive(intersection(complement(u),complement(v))) || member(w,union(u,v))* -> equal(integer_of(w),successor_relation).
% 299.82/300.46  200697[10:Res:161493.2,179.1] inductive(u) || subclass(u,intersection(y__dfg,ordinal_numbers))* -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation)**.
% 299.82/300.46  200761[10:Res:161493.2,2031.0] inductive(compose_class(u)) ||  -> equal(integer_of(singleton(singleton(singleton(v)))),successor_relation)** equal(compose(u,singleton(v)),v)**.
% 299.82/300.46  201114[10:Rew:161137.0,201052.1] ||  -> member(not_subclass_element(u,power_class(complement(inverse(successor_relation)))),image(element_relation,symmetrization_of(successor_relation)))* subclass(u,power_class(complement(inverse(successor_relation)))).
% 299.82/300.46  201115[10:Rew:162889.0,201053.1] ||  -> member(not_subclass_element(u,power_class(complement(singleton(successor_relation)))),image(element_relation,successor(successor_relation)))* subclass(u,power_class(complement(singleton(successor_relation)))).
% 299.82/300.46  201226[10:Res:201216.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(domain_relation),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  201749[10:Res:161419.0,160481.0] || member(regular(complement(complement(regular(u)))),u)* -> equal(complement(complement(regular(u))),successor_relation) equal(u,successor_relation).
% 299.82/300.46  201940[10:Res:161492.2,9322.0] || equal(symmetric_difference(complement(u),complement(v)),omega)** -> equal(integer_of(w),successor_relation) member(w,union(u,v))*.
% 299.82/300.46  201963[10:Res:161492.2,8846.0] || equal(restrict(intersection(y__dfg,ordinal_numbers),u,v),omega)** -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation).
% 299.82/300.46  201970[10:Res:161492.2,144.0] || equal(rest_of(u),omega) -> equal(integer_of(ordered_pair(v,w)),successor_relation)** equal(restrict(u,v,universal_class),w)*.
% 299.82/300.46  201985[10:Res:161492.2,98.0] || equal(composition_function,omega) -> equal(integer_of(ordered_pair(u,ordered_pair(v,w))),successor_relation)** equal(compose(u,v),w).
% 299.82/300.46  202059[10:Res:161492.2,160488.0] || equal(unordered_pair(successor_relation,u),omega)** -> equal(integer_of(intersection(y__dfg,ordinal_numbers)),successor_relation)** equal(intersection(y__dfg,ordinal_numbers),u)*.
% 299.82/300.46  202060[10:Res:161492.2,160486.0] || equal(unordered_pair(u,successor_relation),omega)** -> equal(integer_of(intersection(y__dfg,ordinal_numbers)),successor_relation)** equal(intersection(y__dfg,ordinal_numbers),u)*.
% 299.82/300.46  202502[10:SpR:202485.1,114.2] function(u) || equal(rest_of(u),successor_relation) subclass(range_of(u),v) -> maps(u,successor_relation,v)*.
% 299.82/300.46  202745[10:SpL:161194.0,9149.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(v),universal_class))* -> member(power_class(u),union(v,successor_relation))*.
% 299.82/300.46  203122[11:SpL:505.0,202882.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),symmetrization_of(successor_relation))** -> .
% 299.82/300.46  203570[10:Rew:203192.0,162036.0] || member(u,cantor(cross_product(v,w))) equal(restrict(cross_product(singleton(u),universal_class),v,w),successor_relation)** -> .
% 299.82/300.46  203633[6:Rew:203192.0,39594.2] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,rest_of(w))* -> member(u,cantor(w))*.
% 299.82/300.46  203652[10:Rew:203192.0,188751.1] || member(u,universal_class) -> member(u,cantor(v)) equal(range__dfg(v,u,universal_class),range__dfg(successor_relation,w,x))*.
% 299.82/300.46  203763[10:Rew:203192.0,183186.1] || member(u,universal_class) member(successor(u),cantor(v))* equal(restrict(v,successor_relation,universal_class),successor_relation) -> .
% 299.82/300.46  203770[15:Rew:203192.0,192180.0] || member(inverse(u),cantor(v))* equal(restrict(v,successor_relation,universal_class),successor_relation) -> equal(range_of(u),successor_relation).
% 299.82/300.46  203771[14:Rew:203192.0,200144.1] || member(u,universal_class) member(range_of(u),cantor(v))* equal(restrict(v,successor_relation,universal_class),successor_relation) -> .
% 299.82/300.46  203860[10:Rew:203192.0,202028.2] || equal(rest_of(u),omega) -> equal(integer_of(singleton(singleton(singleton(v)))),successor_relation)** member(singleton(v),cantor(u))*.
% 299.82/300.46  203874[6:Rew:203192.0,109835.2] function(domain_of(u)) || subclass(cross_product(universal_class,universal_class),cantor(u))* -> equal(cross_product(universal_class,universal_class),cantor(u)).
% 299.82/300.46  203892[15:Rew:203192.0,186276.0] || member(successor_relation,cantor(u)) member(ordered_pair(u,singleton(singleton(successor_relation))),cross_product(universal_class,cross_product(universal_class,universal_class)))* -> .
% 299.82/300.46  204167[6:Rew:203285.0,52840.2] inductive(cantor(inverse(u))) || well_ordering(v,range_of(u)) -> member(least(v,range_of(u)),range_of(u))*.
% 299.82/300.46  205789[10:SpR:161774.2,205291.0] ||  -> equal(unordered_pair(u,v),successor_relation) equal(apply(choice,unordered_pair(u,v)),v)** equal(intersection(u,universal_class),u).
% 299.82/300.46  205790[10:SpR:161774.1,205291.0] ||  -> equal(unordered_pair(u,v),successor_relation) equal(apply(choice,unordered_pair(u,v)),u)** equal(intersection(v,universal_class),v).
% 299.82/300.46  206205[10:SpL:505.0,206082.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),successor(successor_relation))** -> .
% 299.82/300.46  206230[10:Obv:206219.1] || member(ordered_pair(u,successor_relation),compose(v,w)) -> subclass(successor(successor_relation),image(v,image(w,singleton(u))))*.
% 299.82/300.46  206249[10:Res:206224.1,1320.1] || member(successor_relation,sum_class(successor(successor_relation)))* member(successor(successor_relation),ordinal_numbers) -> equal(sum_class(successor(successor_relation)),successor(successor_relation)).
% 299.82/300.46  206956[10:Res:206947.1,127.0] || equal(u,kind_1_ordinals) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  207867[10:Res:206688.0,3874.1] || member(successor_relation,union(complement(singleton(successor_relation)),power_class(u))) -> member(successor_relation,symmetric_difference(complement(singleton(successor_relation)),power_class(u)))*.
% 299.82/300.46  208147[10:Res:207196.0,3874.1] || member(successor_relation,union(power_class(u),complement(singleton(successor_relation)))) -> member(successor_relation,symmetric_difference(power_class(u),complement(singleton(successor_relation))))*.
% 299.82/300.46  208361[10:SpL:505.0,206962.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),kind_1_ordinals)** -> member(successor_relation,image(element_relation,union(u,v))).
% 299.82/300.46  208400[20:SpL:505.0,206996.1] || equal(image(element_relation,union(u,v)),kind_1_ordinals) equal(power_class(intersection(complement(u),complement(v))),omega)** -> .
% 299.82/300.46  208414[10:SpL:505.0,206997.1] || equal(image(element_relation,union(u,v)),kind_1_ordinals) equal(power_class(intersection(complement(u),complement(v))),universal_class)** -> .
% 299.82/300.46  208487[10:SpL:505.0,208250.1] || equal(image(element_relation,union(u,v)),kind_1_ordinals) equal(power_class(intersection(complement(u),complement(v))),kind_1_ordinals)** -> .
% 299.82/300.46  208501[20:SpL:505.0,208251.1] || equal(image(element_relation,union(u,v)),omega) equal(power_class(intersection(complement(u),complement(v))),kind_1_ordinals)** -> .
% 299.82/300.46  208515[10:SpL:505.0,208257.1] || equal(image(element_relation,union(u,v)),universal_class) equal(power_class(intersection(complement(u),complement(v))),kind_1_ordinals)** -> .
% 299.82/300.46  208609[10:SpL:1931.0,206964.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),kind_1_ordinals)** -> member(successor_relation,complement(symmetric_difference(u,v))).
% 299.82/300.46  209071[10:SpL:505.0,208945.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),singleton(successor_relation))** -> .
% 299.82/300.46  209372[12:Res:209309.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(element_relation),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  209765[15:Res:67.2,189420.0] function(u) || member(v,universal_class) subclass(domain_relation,rest_relation) -> equal(rest_of(image(u,v)),successor_relation)**.
% 299.82/300.46  209801[15:MRR:209741.1,6.0] || member(u,universal_class) subclass(domain_relation,rest_relation) -> equal(u,successor_relation) equal(rest_of(apply(choice,u)),successor_relation)**.
% 299.82/300.46  209884[15:Res:67.2,189421.0] function(u) || member(v,universal_class) subclass(rest_relation,domain_relation) -> equal(rest_of(image(u,v)),successor_relation)**.
% 299.82/300.46  209920[15:MRR:209860.1,6.0] || member(u,universal_class) subclass(rest_relation,domain_relation) -> equal(u,successor_relation) equal(rest_of(apply(choice,u)),successor_relation)**.
% 299.82/300.46  210354[15:Res:189563.1,9332.1] || subclass(domain_relation,flip(intersection(u,v))) member(ordered_pair(ordered_pair(w,x),successor_relation),symmetric_difference(u,v))* -> .
% 299.82/300.46  210358[15:Res:189563.1,594.0] || subclass(domain_relation,flip(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,y),successor_relation),cross_product(v,w))*.
% 299.82/300.46  210372[15:Res:189563.1,159.0] || subclass(domain_relation,flip(omega)) -> equal(integer_of(ordered_pair(ordered_pair(u,v),successor_relation)),ordered_pair(ordered_pair(u,v),successor_relation))**.
% 299.82/300.46  210375[15:Res:189563.1,307.0] || subclass(domain_relation,flip(image(element_relation,complement(u)))) member(ordered_pair(ordered_pair(v,w),successor_relation),power_class(u))* -> .
% 299.82/300.46  210377[15:Res:189563.1,160481.0] || subclass(domain_relation,flip(regular(u))) member(ordered_pair(ordered_pair(v,w),successor_relation),u)* -> equal(u,successor_relation).
% 299.82/300.46  210427[15:Res:189564.1,9332.1] || subclass(domain_relation,rotate(intersection(u,v))) member(ordered_pair(ordered_pair(w,successor_relation),x),symmetric_difference(u,v))* -> .
% 299.82/300.46  210431[15:Res:189564.1,594.0] || subclass(domain_relation,rotate(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,successor_relation),y),cross_product(v,w))*.
% 299.82/300.46  210445[15:Res:189564.1,159.0] || subclass(domain_relation,rotate(omega)) -> equal(integer_of(ordered_pair(ordered_pair(u,successor_relation),v)),ordered_pair(ordered_pair(u,successor_relation),v))**.
% 299.82/300.46  210448[15:Res:189564.1,307.0] || subclass(domain_relation,rotate(image(element_relation,complement(u)))) member(ordered_pair(ordered_pair(v,successor_relation),w),power_class(u))* -> .
% 299.82/300.46  210450[15:Res:189564.1,160481.0] || subclass(domain_relation,rotate(regular(u))) member(ordered_pair(ordered_pair(v,successor_relation),w),u)* -> equal(u,successor_relation).
% 299.82/300.46  210468[15:Res:189564.1,5647.0] || subclass(domain_relation,rotate(compose(u,v))) -> subclass(w,image(u,image(v,singleton(ordered_pair(x,successor_relation)))))*.
% 299.82/300.46  211267[11:SpL:505.0,211092.1] inductive(image(element_relation,union(u,v))) || equal(power_class(intersection(complement(u),complement(v))),inverse(successor_relation))** -> .
% 299.82/300.46  211478[10:SpL:185605.1,187490.0] || equal(successor_relation,u) member(apply(choice,power_class(u)),image(element_relation,universal_class))* -> equal(power_class(successor_relation),successor_relation).
% 299.82/300.46  211480[10:Res:161492.2,187490.0] || equal(image(element_relation,universal_class),omega) -> equal(integer_of(apply(choice,power_class(successor_relation))),successor_relation)** equal(power_class(successor_relation),successor_relation).
% 299.82/300.46  211536[10:SpL:505.0,211448.0] || well_ordering(universal_class,power_class(intersection(complement(u),complement(v))))* -> member(singleton(successor_relation),image(element_relation,union(u,v))).
% 299.82/300.46  211548[10:SpL:160322.0,161505.0] || member(regular(power_class(image(element_relation,successor_relation))),image(element_relation,power_class(universal_class)))* -> equal(power_class(image(element_relation,successor_relation)),successor_relation).
% 299.82/300.46  211559[10:Res:161492.2,161505.0] || equal(image(element_relation,complement(u)),omega)** -> equal(integer_of(regular(power_class(u))),successor_relation) equal(power_class(u),successor_relation).
% 299.82/300.46  211598[10:Res:137.1,160705.0] || member(complement(kind_1_ordinals),ordinal_numbers) member(regular(sum_class(complement(kind_1_ordinals))),ordinal_numbers)* -> equal(sum_class(complement(kind_1_ordinals)),successor_relation).
% 299.82/300.46  211620[10:MRR:211605.3,160371.1] || connected(u,complement(kind_1_ordinals)) member(regular(not_well_ordering(u,complement(kind_1_ordinals))),ordinal_numbers)* -> well_ordering(u,complement(kind_1_ordinals)).
% 299.82/300.46  211632[10:SpR:505.0,211579.1] ||  -> member(singleton(successor_relation),image(element_relation,union(u,v))) member(singleton(successor_relation),power_class(intersection(complement(u),complement(v))))*.
% 299.82/300.46  211681[10:Res:181213.1,513.0] || equal(intersection(complement(u),complement(v)),singleton(singleton(successor_relation))) member(singleton(successor_relation),union(u,v))* -> .
% 299.82/300.46  211728[10:SpR:9949.0,185605.1] || equal(intersection(complement(u),complement(singleton(u))),successor_relation)** -> equal(complement(image(element_relation,successor(u))),power_class(successor_relation)).
% 299.82/300.46  211729[15:SpR:9949.0,191872.1] || member(intersection(complement(u),complement(singleton(u))),universal_class)* -> equal(cantor(complement(image(element_relation,successor(u)))),successor_relation).
% 299.82/300.46  211755[0:SpR:194805.1,9949.0] || subclass(complement(singleton(u)),complement(u))* -> equal(complement(image(element_relation,successor(u))),power_class(complement(singleton(u)))).
% 299.82/300.46  211829[10:SpR:9948.0,185605.1] || equal(intersection(complement(u),complement(inverse(u))),successor_relation)** -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(successor_relation)).
% 299.82/300.46  211830[15:SpR:9948.0,191872.1] || member(intersection(complement(u),complement(inverse(u))),universal_class)* -> equal(cantor(complement(image(element_relation,symmetrization_of(u)))),successor_relation).
% 299.82/300.46  211852[0:SpR:194805.1,9948.0] || subclass(complement(inverse(u)),complement(u))* -> equal(complement(image(element_relation,symmetrization_of(u))),power_class(complement(inverse(u)))).
% 299.82/300.46  211979[11:Res:183759.1,513.0] || subclass(inverse(successor_relation),intersection(complement(u),complement(v)))* member(regular(symmetrization_of(successor_relation)),union(u,v)) -> .
% 299.82/300.46  211997[11:Res:183759.1,10.0] || subclass(inverse(successor_relation),unordered_pair(u,v))* -> equal(regular(symmetrization_of(successor_relation)),v) equal(regular(symmetrization_of(successor_relation)),u).
% 299.82/300.46  212093[10:Res:161492.2,163312.0] || equal(u,omega) -> equal(integer_of(regular(regular(u))),successor_relation)** equal(regular(u),successor_relation) equal(u,successor_relation).
% 299.82/300.46  212952[10:Obv:212922.2] || member(u,v) member(u,intersection(singleton(v),w))* -> equal(intersection(singleton(v),w),successor_relation).
% 299.82/300.46  212953[10:Obv:212891.1] || subclass(intersection(singleton(u),v),omega)* -> equal(intersection(singleton(u),v),successor_relation) equal(integer_of(u),u).
% 299.82/300.46  212956[10:Rew:161284.1,212955.1] || member(regular(u),intersection(singleton(u),v))* -> equal(u,successor_relation) equal(intersection(singleton(u),v),successor_relation).
% 299.82/300.46  213063[10:Obv:213036.2] || member(u,v) member(u,intersection(w,singleton(v)))* -> equal(intersection(w,singleton(v)),successor_relation).
% 299.82/300.46  213064[10:Obv:213010.1] || subclass(intersection(u,singleton(v)),omega)* -> equal(intersection(u,singleton(v)),successor_relation) equal(integer_of(v),v).
% 299.82/300.46  213067[10:Rew:161277.1,213066.1] || member(regular(u),intersection(v,singleton(u)))* -> equal(u,successor_relation) equal(intersection(v,singleton(u)),successor_relation).
% 299.82/300.46  213210[15:Res:189485.1,513.0] || subclass(domain_relation,intersection(complement(u),complement(v))) member(singleton(singleton(singleton(successor_relation))),union(u,v))* -> .
% 299.82/300.46  213320[15:SpL:505.0,213296.1] || equal(image(element_relation,union(u,v)),domain_relation) equal(power_class(intersection(complement(u),complement(v))),universal_class)** -> .
% 299.82/300.46  213800[15:Rew:160223.0,213763.1] || equal(successor(intersection(complement(u),complement(v))),successor_relation) -> equal(complement(intersection(union(u,v),universal_class)),successor_relation)**.
% 299.82/300.46  214301[10:Res:214277.1,9300.0] || equal(complement(symmetric_difference(u,cross_product(v,w))),successor_relation) -> member(power_class(successor_relation),complement(restrict(u,v,w)))*.
% 299.82/300.46  214303[10:Res:214277.1,9306.0] || equal(complement(symmetric_difference(cross_product(u,v),w)),successor_relation) -> member(power_class(successor_relation),complement(restrict(w,u,v)))*.
% 299.82/300.46  214756[10:Res:161697.1,183398.0] ||  -> equal(restrict(complement(complement(u)),v,w),successor_relation) member(regular(restrict(complement(complement(u)),v,w)),u)*.
% 299.82/300.46  215178[6:Res:157922.1,40234.0] || member(not_subclass_element(u,intersection(compose(element_relation,universal_class),u)),element_relation)* -> subclass(u,intersection(compose(element_relation,universal_class),u)).
% 299.82/300.46  215182[10:Res:161492.2,40234.0] || equal(u,omega) -> equal(integer_of(not_subclass_element(v,intersection(u,v))),successor_relation)** subclass(v,intersection(u,v)).
% 299.82/300.46  215224[10:Rew:161194.0,215121.1] || member(not_subclass_element(universal_class,symmetric_difference(complement(u),universal_class)),union(u,successor_relation))* -> subclass(universal_class,symmetric_difference(complement(u),universal_class)).
% 299.82/300.46  215575[10:Res:161493.2,163021.0] inductive(element_relation) ||  -> equal(integer_of(regular(complement(compose(element_relation,universal_class)))),successor_relation)** equal(complement(compose(element_relation,universal_class)),successor_relation).
% 299.82/300.46  215873[10:Res:197082.1,513.0] || subclass(universal_class,intersection(complement(u),complement(v))) member(regular(complement(successor(successor_relation))),union(u,v))* -> .
% 299.82/300.46  215949[10:Res:161493.2,163029.0] inductive(ordinal_numbers) ||  -> equal(integer_of(regular(intersection(u,complement(kind_1_ordinals)))),successor_relation)** equal(intersection(u,complement(kind_1_ordinals)),successor_relation).
% 299.82/300.46  216084[10:Res:161493.2,163027.0] inductive(ordinal_numbers) ||  -> equal(integer_of(regular(intersection(complement(kind_1_ordinals),u))),successor_relation)** equal(intersection(complement(kind_1_ordinals),u),successor_relation).
% 299.82/300.46  216114[6:Res:199830.1,513.0] || equal(intersection(complement(u),complement(v)),cross_product(universal_class,universal_class)) member(regular(rest_relation),union(u,v))* -> .
% 299.82/300.46  216291[14:SpL:199971.1,1522.0] || member(u,universal_class) member(singleton(singleton(successor_relation)),cross_product(v,w))* -> member(sum_class(range_of(u)),w)*.
% 299.82/300.46  216487[10:Res:216465.1,9300.0] || equal(complement(symmetric_difference(u,cross_product(v,w))),successor_relation) -> member(regular(rest_relation),complement(restrict(u,v,w)))*.
% 299.82/300.46  216489[10:Res:216465.1,9306.0] || equal(complement(symmetric_difference(cross_product(u,v),w)),successor_relation) -> member(regular(rest_relation),complement(restrict(w,u,v)))*.
% 299.82/300.46  216722[6:Res:201220.1,513.0] || equal(intersection(complement(u),complement(v)),cross_product(universal_class,universal_class)) member(regular(domain_relation),union(u,v))* -> .
% 299.82/300.46  216871[10:Res:161493.2,163343.0] inductive(u) ||  -> equal(integer_of(apply(choice,regular(u))),successor_relation)** equal(regular(u),successor_relation) equal(u,successor_relation).
% 299.82/300.46  216915[10:Res:216847.1,9300.0] || equal(complement(symmetric_difference(u,cross_product(v,w))),successor_relation) -> member(regular(domain_relation),complement(restrict(u,v,w)))*.
% 299.82/300.46  216917[10:Res:216847.1,9306.0] || equal(complement(symmetric_difference(cross_product(u,v),w)),successor_relation) -> member(regular(domain_relation),complement(restrict(w,u,v)))*.
% 299.82/300.46  216977[10:SpL:185302.1,9069.0] || equal(successor_relation,u) subclass(universal_class,image(element_relation,universal_class)) member(unordered_pair(v,w),power_class(u))* -> .
% 299.82/300.46  217208[10:Res:203330.1,206660.0] || section(u,complement(singleton(successor_relation)),v) member(successor_relation,cantor(restrict(u,v,complement(singleton(successor_relation)))))* -> .
% 299.82/300.46  217349[10:Res:217225.1,161700.0] || equal(singleton(regular(intersection(complement(singleton(successor_relation)),u))),kind_1_ordinals)** -> equal(intersection(complement(singleton(successor_relation)),u),successor_relation).
% 299.82/300.46  217352[10:Res:161493.2,161700.0] inductive(u) ||  -> equal(integer_of(regular(intersection(complement(u),v))),successor_relation)** equal(intersection(complement(u),v),successor_relation).
% 299.82/300.46  217437[20:Res:217226.1,161700.0] || equal(singleton(regular(intersection(complement(singleton(successor_relation)),u))),omega)** -> equal(intersection(complement(singleton(successor_relation)),u),successor_relation).
% 299.82/300.46  217494[20:Res:217226.1,161380.0] || equal(singleton(regular(intersection(u,complement(singleton(successor_relation))))),omega)** -> equal(intersection(u,complement(singleton(successor_relation))),successor_relation).
% 299.82/300.46  217495[10:Res:217225.1,161380.0] || equal(singleton(regular(intersection(u,complement(singleton(successor_relation))))),kind_1_ordinals)** -> equal(intersection(u,complement(singleton(successor_relation))),successor_relation).
% 299.82/300.46  217498[10:Res:161493.2,161380.0] inductive(u) ||  -> equal(integer_of(regular(intersection(v,complement(u)))),successor_relation)** equal(intersection(v,complement(u)),successor_relation).
% 299.82/300.46  217567[10:Res:161493.2,160697.1] inductive(u) || subclass(universal_class,regular(u))* -> equal(integer_of(unordered_pair(v,w)),successor_relation)** equal(u,successor_relation).
% 299.82/300.46  217624[10:SpL:185302.1,1089.0] || equal(successor_relation,u) member(not_subclass_element(power_class(u),v),image(element_relation,universal_class))* -> subclass(power_class(u),v).
% 299.82/300.46  217649[10:Res:161493.2,1089.0] inductive(image(element_relation,complement(u))) ||  -> equal(integer_of(not_subclass_element(power_class(u),v)),successor_relation)** subclass(power_class(u),v).
% 299.82/300.46  217654[10:Rew:185302.1,217640.1] || equal(successor_relation,u) member(not_subclass_element(power_class(successor_relation),v),image(element_relation,universal_class))* -> subclass(power_class(u),v)*.
% 299.82/300.46  217655[10:Rew:160223.0,217641.1] || equal(successor_relation,u) member(not_subclass_element(power_class(u),v),image(element_relation,universal_class))* -> subclass(power_class(successor_relation),v).
% 299.82/300.46  217824[10:SpL:161194.0,9121.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(v),universal_class))* -> member(sum_class(u),union(v,successor_relation))*.
% 299.82/300.46  217930[10:Res:161493.2,155811.1] inductive(ordinal_numbers) || subclass(u,complement(kind_1_ordinals)) -> equal(integer_of(not_subclass_element(u,v)),successor_relation)** subclass(u,v).
% 299.82/300.46  218290[10:Res:161493.2,160698.0] inductive(u) ||  -> equal(integer_of(not_subclass_element(regular(u),v)),successor_relation)** subclass(regular(u),v) equal(u,successor_relation).
% 299.82/300.46  218329[10:SpR:28.0,218298.0] ||  -> subclass(regular(intersection(complement(u),complement(v))),union(u,v))* equal(intersection(complement(u),complement(v)),successor_relation).
% 299.82/300.46  218339[10:SpR:208.0,218298.0] ||  -> subclass(regular(image(element_relation,power_class(u))),power_class(image(element_relation,complement(u))))* equal(image(element_relation,power_class(u)),successor_relation).
% 299.82/300.46  218379[10:Obv:218351.0] ||  -> equal(regular(unordered_pair(u,v)),u) subclass(v,complement(unordered_pair(u,v)))* equal(unordered_pair(u,v),successor_relation).
% 299.82/300.46  218380[10:Obv:218350.0] ||  -> equal(regular(unordered_pair(u,v)),v) subclass(u,complement(unordered_pair(u,v)))* equal(unordered_pair(u,v),successor_relation).
% 299.82/300.46  218515[10:Res:218490.0,160373.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(segment(u,symmetric_difference(universal_class,kind_1_ordinals),least(u,symmetric_difference(universal_class,kind_1_ordinals))),successor_relation)**.
% 299.82/300.46  218569[10:Res:161493.2,9636.1] inductive(u) || subclass(v,complement(u))* -> equal(integer_of(not_subclass_element(v,w)),successor_relation)** subclass(v,w).
% 299.82/300.46  218758[3:Res:218481.0,9.0] || subclass(complement(ordinal_numbers),restrict(complement(kind_1_ordinals),u,v))* -> equal(restrict(complement(kind_1_ordinals),u,v),complement(ordinal_numbers)).
% 299.82/300.46  218862[22:Res:218858.0,162356.0] || subclass(kind_1_ordinals,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(singleton(successor_relation),least(omega,kind_1_ordinals))),successor_relation)**.
% 299.82/300.46  218877[22:Res:218867.1,127.0] || subclass(kind_1_ordinals,u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  218979[10:SpL:161194.0,9639.0] || subclass(u,symmetric_difference(complement(v),universal_class)) -> subclass(u,w) member(not_subclass_element(u,w),union(v,successor_relation))*.
% 299.82/300.46  219140[3:Res:218473.1,2609.1] function(complement(ordinal_numbers)) || equal(cross_product(universal_class,universal_class),complement(kind_1_ordinals))** -> equal(cross_product(universal_class,universal_class),complement(ordinal_numbers)).
% 299.82/300.46  219158[3:Res:218473.1,1487.1] || equal(complement(kind_1_ordinals),complement(u)) member(v,universal_class) -> member(v,u)* member(v,complement(ordinal_numbers))*.
% 299.82/300.46  219203[3:Res:28320.1,218628.0] || subclass(rest_relation,rotate(complement(kind_1_ordinals))) -> member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),complement(ordinal_numbers))*.
% 299.82/300.46  219205[3:Res:28321.1,218628.0] || subclass(rest_relation,flip(complement(kind_1_ordinals))) -> member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),complement(ordinal_numbers))*.
% 299.82/300.46  219579[3:Res:978.1,218628.0] ||  -> subclass(restrict(complement(kind_1_ordinals),u,v),w) member(not_subclass_element(restrict(complement(kind_1_ordinals),u,v),w),complement(ordinal_numbers))*.
% 299.82/300.46  219597[10:Res:978.1,183723.0] ||  -> subclass(restrict(symmetrization_of(successor_relation),u,v),w) member(not_subclass_element(restrict(symmetrization_of(successor_relation),u,v),w),inverse(successor_relation))*.
% 299.82/300.46  219599[10:Res:978.1,183622.0] ||  -> subclass(restrict(successor(successor_relation),u,v),w) member(not_subclass_element(restrict(successor(successor_relation),u,v),w),singleton(successor_relation))*.
% 299.82/300.46  201617[15:Res:189374.2,163294.0] || member(u,universal_class) subclass(domain_relation,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(ordered_pair(u,successor_relation),kind_1_ordinals)*.
% 299.82/300.46  196324[10:Rew:113504.0,196272.0,160223.0,196272.0] ||  -> equal(symmetric_difference(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),complement(kind_1_ordinals)),union(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),complement(kind_1_ordinals)))**.
% 299.82/300.46  196265[10:Rew:113504.0,196212.0,160223.0,196212.0] ||  -> equal(symmetric_difference(complement(kind_1_ordinals),symmetric_difference(singleton(successor_relation),range_of(successor_relation))),union(complement(kind_1_ordinals),symmetric_difference(singleton(successor_relation),range_of(successor_relation))))**.
% 299.82/300.46  195478[10:SpR:194805.1,163458.0] || subclass(range_of(successor_relation),singleton(successor_relation)) -> equal(intersection(complement(range_of(successor_relation)),kind_1_ordinals),symmetric_difference(singleton(successor_relation),range_of(successor_relation)))**.
% 299.82/300.46  168517[10:Rew:142543.0,168493.1] || equal(universal_class,ordinal_numbers) -> equal(symmetric_difference(universal_class,intersection(singleton(successor_relation),range_of(successor_relation))),symmetric_difference(singleton(successor_relation),range_of(successor_relation)))**.
% 299.82/300.46  188805[10:Res:136.1,163580.1] inductive(u) || member(u,ordinal_numbers)* -> equal(segment(element_relation,range_of(successor_relation),least(element_relation,range_of(successor_relation))),successor_relation)**.
% 299.82/300.46  166686[10:SoR:164882.0,6317.2] single_valued_class(range_of(successor_relation)) || member(successor_relation,cross_product(universal_class,universal_class))* equal(cross_product(universal_class,universal_class),range_of(successor_relation)) -> .
% 299.82/300.46  166985[10:MRR:166967.0,160214.0] || equal(image(element_relation,complement(u)),range_of(successor_relation)) -> member(successor_relation,power_class(u)) inductive(image(element_relation,complement(u)))*.
% 299.82/300.46  211421[10:SpR:194805.1,163369.0] || subclass(complement(range_of(successor_relation)),complement(singleton(successor_relation)))* -> equal(complement(image(element_relation,kind_1_ordinals)),power_class(complement(range_of(successor_relation)))).
% 299.82/300.46  163582[10:Rew:160305.0,162802.0] ||  -> equal(intersection(kind_1_ordinals,union(complement(singleton(successor_relation)),complement(range_of(successor_relation)))),symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation))))**.
% 299.82/300.46  211411[10:SpR:163369.0,185605.1] || equal(intersection(complement(singleton(successor_relation)),complement(range_of(successor_relation))),successor_relation)** -> equal(complement(image(element_relation,kind_1_ordinals)),power_class(successor_relation)).
% 299.82/300.46  211412[15:SpR:163369.0,191872.1] || member(intersection(complement(singleton(successor_relation)),complement(range_of(successor_relation))),universal_class)* -> equal(cantor(complement(image(element_relation,kind_1_ordinals))),successor_relation).
% 299.82/300.46  163579[10:Rew:160305.0,162155.3,160305.0,162155.2] inductive(u) || well_ordering(v,u)* -> equal(range_of(successor_relation),successor_relation) member(least(v,range_of(successor_relation)),universal_class)*.
% 299.82/300.46  163469[10:Rew:160202.0,160590.0] ||  -> equal(cross_product(singleton(u),universal_class),successor_relation) equal(apply(regular(cross_product(singleton(u),universal_class)),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  220410[23:MRR:163712.1,220405.0] || well_ordering(u,kind_1_ordinals) -> member(least(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),symmetric_difference(singleton(successor_relation),range_of(successor_relation)))*.
% 299.82/300.46  220411[23:MRR:163708.1,220405.0] || well_ordering(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))) -> member(least(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals)*.
% 299.82/300.46  220412[23:MRR:163709.1,220405.0] || member(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),universal_class) -> member(apply(choice,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals)*.
% 299.82/300.46  221414[6:SpL:203335.0,149509.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),segment(u,v,w))* subclass(universal_class,intersection(y__dfg,ordinal_numbers)) -> .
% 299.82/300.46  221484[10:Res:218373.0,163257.1] || member(successor_relation,complement(singleton(range_of(successor_relation))))* -> equal(singleton(range_of(successor_relation)),successor_relation) inductive(complement(singleton(range_of(successor_relation)))).
% 299.82/300.46  221615[10:Res:1476.1,185698.1] inductive(unordered_pair(u,v)) || subclass(universal_class,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221636[10:Res:1499.1,185698.1] inductive(ordered_pair(u,v)) || subclass(universal_class,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221637[10:Res:160251.1,185698.1] inductive(ordered_pair(successor_relation,successor_relation)) || subclass(domain_relation,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221642[10:Res:184565.1,185698.1] inductive(least(u,ordinal_numbers)) || well_ordering(u,kind_1_ordinals)* -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221659[11:Res:183764.1,185698.1] inductive(regular(symmetrization_of(successor_relation))) || subclass(universal_class,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221674[10:MRR:221628.2,184560.0] inductive(least(u,ordinal_numbers)) || well_ordering(u,universal_class)* -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221675[10:MRR:221627.2,184560.0] inductive(least(u,ordinal_numbers)) || well_ordering(u,ordinal_numbers)* -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221676[10:MRR:221613.2,184560.0] inductive(apply(choice,ordinal_numbers)) || member(ordinal_numbers,universal_class) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221819[10:Rew:160419.0,221800.1] || member(regular(image(element_relation,successor(successor_relation))),power_class(complement(singleton(successor_relation))))* -> equal(image(element_relation,successor(successor_relation)),successor_relation).
% 299.82/300.46  221820[10:Rew:160336.0,221801.1] || member(regular(image(element_relation,symmetrization_of(successor_relation))),power_class(complement(inverse(successor_relation))))* -> equal(image(element_relation,symmetrization_of(successor_relation)),successor_relation).
% 299.82/300.46  221821[10:Rew:160322.0,221807.1] || member(regular(image(element_relation,power_class(universal_class))),power_class(image(element_relation,successor_relation)))* -> equal(image(element_relation,power_class(universal_class)),successor_relation).
% 299.82/300.46  221952[10:Res:183719.1,33515.1] || equal(symmetrization_of(successor_relation),universal_class) member(inverse(successor_relation),universal_class) -> member(singleton(singleton(singleton(inverse(successor_relation)))),element_relation)*.
% 299.82/300.46  221953[10:Res:183720.1,33515.1] || subclass(universal_class,symmetrization_of(successor_relation)) member(inverse(successor_relation),universal_class) -> member(singleton(singleton(singleton(inverse(successor_relation)))),element_relation)*.
% 299.82/300.46  221994[10:Res:192947.1,986.1] || equal(complement(power_class(image(element_relation,complement(u)))),successor_relation) member(singleton(v),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  222008[10:Res:214277.1,986.1] || equal(complement(power_class(image(element_relation,complement(u)))),successor_relation) member(power_class(successor_relation),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  222050[11:Res:183764.1,986.1] || subclass(universal_class,power_class(image(element_relation,complement(u)))) member(regular(symmetrization_of(successor_relation)),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  222053[10:Res:216465.1,986.1] || equal(complement(power_class(image(element_relation,complement(u)))),successor_relation) member(regular(rest_relation),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  222056[10:Res:216847.1,986.1] || equal(complement(power_class(image(element_relation,complement(u)))),successor_relation) member(regular(domain_relation),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  222284[20:Res:217226.1,189380.2] || equal(singleton(ordered_pair(u,successor_relation)),omega)** member(u,universal_class) subclass(domain_relation,complement(singleton(successor_relation)))* -> .
% 299.82/300.46  222285[15:Res:217225.1,189380.2] || equal(singleton(ordered_pair(u,successor_relation)),kind_1_ordinals)** member(u,universal_class) subclass(domain_relation,complement(singleton(successor_relation)))* -> .
% 299.82/300.46  222309[15:MRR:222251.0,999.0] || member(u,universal_class) subclass(domain_relation,complement(union(v,w)))* -> member(ordered_pair(u,successor_relation),complement(w))*.
% 299.82/300.46  222310[15:MRR:222250.0,999.0] || member(u,universal_class) subclass(domain_relation,complement(union(v,w)))* -> member(ordered_pair(u,successor_relation),complement(v))*.
% 299.82/300.46  223369[24:Rew:222479.0,223311.2] || member(u,kind_1_ordinals) member(ordered_pair(u,universal_class),cross_product(universal_class,universal_class))* -> member(ordered_pair(u,universal_class),element_relation).
% 299.82/300.46  224014[10:Rew:185302.1,223977.2] || equal(successor_relation,u) -> member(not_subclass_element(v,image(element_relation,universal_class)),power_class(u))* subclass(v,image(element_relation,universal_class)).
% 299.82/300.46  224506[25:Rew:224236.1,224273.2] function(cantor(u)) function(v) || equal(cantor(cantor(w)),universal_class) -> compatible(v,w,u)*.
% 299.82/300.46  224526[25:SoR:224286.0,6317.2] single_valued_class(complement(cross_product(singleton(successor_relation),universal_class))) || equal(complement(cross_product(singleton(successor_relation),universal_class)),cross_product(universal_class,universal_class))** -> .
% 299.82/300.46  224897[25:SoR:224743.0,6317.2] single_valued_class(regular(complement(complement(symmetrization_of(successor_relation))))) || equal(regular(complement(complement(symmetrization_of(successor_relation)))),cross_product(universal_class,universal_class))** -> .
% 299.82/300.46  224900[25:SoR:224782.0,6317.2] single_valued_class(complement(cross_product(singleton(omega),universal_class))) || equal(complement(cross_product(singleton(omega),universal_class)),cross_product(universal_class,universal_class))** -> .
% 299.82/300.46  225485[25:Rew:224739.1,224967.1] function(u) || asymmetric(v,successor_relation) -> equal(domain__dfg(intersection(v,inverse(v)),successor_relation,u),single_valued3(successor_relation))**.
% 299.82/300.46  225969[10:Rew:160322.0,225942.2] || well_ordering(u,universal_class) member(least(u,power_class(universal_class)),image(element_relation,successor_relation))* -> equal(power_class(universal_class),successor_relation).
% 299.82/300.46  226086[25:SoR:224776.0,160511.2] single_valued_class(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))) || equal(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),successor_relation)** -> .
% 299.82/300.46  226263[15:Res:203658.1,212820.0] || member(second(regular(rest_relation)),universal_class) -> equal(apply(first(regular(rest_relation)),second(regular(rest_relation))),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  226264[15:Res:203658.1,212821.0] || member(second(regular(domain_relation)),universal_class) -> equal(apply(first(regular(domain_relation)),second(regular(domain_relation))),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  226265[15:Res:203658.1,212822.0] || member(second(regular(element_relation)),universal_class) -> equal(apply(first(regular(element_relation)),second(regular(element_relation))),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  226300[17:MRR:226217.2,160227.0] || well_ordering(u,omega) member(v,universal_class) -> equal(apply(least(u,omega),v),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  226301[17:MRR:226216.2,160227.0] || well_ordering(u,universal_class) member(v,universal_class) -> equal(apply(least(u,omega),v),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  226302[15:MRR:226215.2,160227.0] || well_ordering(u,rest_relation) member(v,universal_class) -> equal(apply(least(u,rest_relation),v),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  226303[15:MRR:226214.2,160227.0] || well_ordering(u,universal_class) member(v,universal_class) -> equal(apply(least(u,rest_relation),v),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  226304[15:MRR:226213.2,160227.0] || well_ordering(u,universal_class) member(v,universal_class) -> equal(apply(least(u,universal_class),v),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  226305[15:MRR:226212.2,160227.0] || well_ordering(u,kind_1_ordinals) member(v,universal_class) -> equal(apply(least(u,ordinal_numbers),v),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  228363[10:Res:161722.2,218628.0] || subclass(u,complement(kind_1_ordinals)) -> equal(intersection(u,v),successor_relation) member(regular(intersection(u,v)),complement(ordinal_numbers))*.
% 299.82/300.46  228364[10:Res:161722.2,141576.1] || subclass(u,complement(kind_1_ordinals)) member(regular(intersection(u,v)),ordinal_numbers)* -> equal(intersection(u,v),successor_relation).
% 299.82/300.46  228366[10:Res:161722.2,183398.0] || subclass(u,complement(complement(v))) -> equal(intersection(u,w),successor_relation) member(regular(intersection(u,w)),v)*.
% 299.82/300.46  228381[10:Res:161722.2,183723.0] || subclass(u,symmetrization_of(successor_relation)) -> equal(intersection(u,v),successor_relation) member(regular(intersection(u,v)),inverse(successor_relation))*.
% 299.82/300.46  228382[10:Res:161722.2,193819.0] || subclass(u,cantor(complement(cross_product(singleton(regular(intersection(u,v))),universal_class))))* -> equal(intersection(u,v),successor_relation).
% 299.82/300.46  228385[10:Res:161722.2,183622.0] || subclass(u,successor(successor_relation)) -> equal(intersection(u,v),successor_relation) member(regular(intersection(u,v)),singleton(successor_relation))*.
% 299.82/300.46  228584[10:Res:161711.2,218628.0] || subclass(u,complement(kind_1_ordinals)) -> equal(intersection(v,u),successor_relation) member(regular(intersection(v,u)),complement(ordinal_numbers))*.
% 299.82/300.46  228585[10:Res:161711.2,141576.1] || subclass(u,complement(kind_1_ordinals)) member(regular(intersection(v,u)),ordinal_numbers)* -> equal(intersection(v,u),successor_relation).
% 299.82/300.46  228587[10:Res:161711.2,183398.0] || subclass(u,complement(complement(v))) -> equal(intersection(w,u),successor_relation) member(regular(intersection(w,u)),v)*.
% 299.82/300.46  228602[10:Res:161711.2,183723.0] || subclass(u,symmetrization_of(successor_relation)) -> equal(intersection(v,u),successor_relation) member(regular(intersection(v,u)),inverse(successor_relation))*.
% 299.82/300.46  228603[10:Res:161711.2,193819.0] || subclass(u,cantor(complement(cross_product(singleton(regular(intersection(v,u))),universal_class))))* -> equal(intersection(v,u),successor_relation).
% 299.82/300.46  228606[10:Res:161711.2,183622.0] || subclass(u,successor(successor_relation)) -> equal(intersection(v,u),successor_relation) member(regular(intersection(v,u)),singleton(successor_relation))*.
% 299.82/300.46  228787[24:SpR:223107.0,161690.1] ||  -> equal(symmetric_difference(successor(kind_1_ordinals),universal_class),successor_relation) member(regular(symmetric_difference(successor(kind_1_ordinals),universal_class)),complement(symmetric_difference(complement(kind_1_ordinals),universal_class)))*.
% 299.82/300.46  228850[24:SpL:223107.0,189381.1] || member(u,universal_class) subclass(domain_relation,symmetric_difference(complement(kind_1_ordinals),universal_class))* -> member(ordered_pair(u,successor_relation),successor(kind_1_ordinals))*.
% 299.82/300.46  228888[25:SoR:225054.0,6317.2] single_valued_class(first(regular(rest_relation))) || equal(cross_product(universal_class,universal_class),first(regular(rest_relation))) -> member(successor_relation,regular(rest_relation))*.
% 299.82/300.46  228891[25:SoR:225055.0,6317.2] single_valued_class(first(regular(domain_relation))) || equal(cross_product(universal_class,universal_class),first(regular(domain_relation))) -> member(successor_relation,regular(domain_relation))*.
% 299.82/300.46  228894[25:SoR:225056.0,6317.2] single_valued_class(first(regular(element_relation))) || equal(cross_product(universal_class,universal_class),first(regular(element_relation))) -> member(successor_relation,regular(element_relation))*.
% 299.82/300.46  228952[10:Res:195710.1,160788.0] || equal(inverse(u),universal_class) subclass(inverse(u),v)* -> equal(w,successor_relation) member(regular(w),v)*.
% 299.82/300.46  228953[10:Res:195720.1,160788.0] || equal(sum_class(u),universal_class) subclass(sum_class(u),v)* -> equal(w,successor_relation) member(regular(w),v)*.
% 299.82/300.46  228964[24:Res:223096.0,160788.0] || subclass(symmetric_difference(universal_class,kind_1_ordinals),u) -> equal(complement(successor(kind_1_ordinals)),successor_relation) member(regular(complement(successor(kind_1_ordinals))),u)*.
% 299.82/300.46  228965[10:Res:218473.1,160788.0] || equal(complement(kind_1_ordinals),u) subclass(complement(ordinal_numbers),v)* -> equal(u,successor_relation) member(regular(u),v)*.
% 299.82/300.46  228966[10:Res:218373.0,160788.0] || subclass(complement(singleton(u)),v)* -> equal(singleton(u),successor_relation) equal(u,successor_relation) member(regular(u),v).
% 299.82/300.46  228975[10:Res:160337.0,160788.0] || subclass(complement(inverse(successor_relation)),u) -> equal(complement(symmetrization_of(successor_relation)),successor_relation) member(regular(complement(symmetrization_of(successor_relation))),u)*.
% 299.82/300.46  228977[10:Res:218298.0,160788.0] || subclass(complement(u),v) -> equal(u,successor_relation) equal(regular(u),successor_relation) member(regular(regular(u)),v)*.
% 299.82/300.46  228980[10:Res:159954.0,160788.0] || subclass(kind_1_ordinals,u) -> equal(restrict(ordinal_numbers,v,w),successor_relation) member(regular(restrict(ordinal_numbers,v,w)),u)*.
% 299.82/300.46  229004[10:Rew:160824.1,228948.3] || subclass(power_class(universal_class),u)* -> member(v,image(element_relation,successor_relation))* equal(singleton(v),successor_relation) member(v,u)*.
% 299.82/300.46  229005[10:Rew:160824.1,228949.3] || subclass(power_class(successor_relation),u)* -> member(v,image(element_relation,universal_class))* equal(singleton(v),successor_relation) member(v,u)*.
% 299.82/300.46  229006[10:Rew:160824.1,228950.3] || subclass(symmetrization_of(successor_relation),u)* -> member(v,complement(inverse(successor_relation)))* equal(singleton(v),successor_relation) member(v,u)*.
% 299.82/300.46  229007[10:Rew:160824.1,228951.3] || subclass(successor(successor_relation),u)* -> member(v,complement(singleton(successor_relation)))* equal(singleton(v),successor_relation) member(v,u)*.
% 299.82/300.46  229223[10:Res:229170.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(ordinal_numbers),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  229289[25:SoR:225422.0,6317.2] single_valued_class(first(regular(rest_relation))) || member(successor_relation,rest_relation) equal(cross_product(universal_class,universal_class),first(regular(rest_relation)))** -> .
% 299.82/300.46  229292[25:SoR:225423.0,6317.2] single_valued_class(first(regular(domain_relation))) || member(successor_relation,domain_relation) equal(cross_product(universal_class,universal_class),first(regular(domain_relation)))** -> .
% 299.82/300.46  229320[25:SoR:225424.0,6317.2] single_valued_class(first(regular(element_relation))) || member(successor_relation,element_relation) equal(cross_product(universal_class,universal_class),first(regular(element_relation)))** -> .
% 299.82/300.46  229803[10:Res:221521.1,40234.0] ||  -> equal(integer_of(not_subclass_element(u,intersection(complement(singleton(omega)),u))),successor_relation)** subclass(u,intersection(complement(singleton(omega)),u)).
% 299.82/300.46  229808[15:Res:221521.1,189380.2] || member(u,universal_class) subclass(domain_relation,complement(complement(singleton(omega))))* -> equal(integer_of(ordered_pair(u,successor_relation)),successor_relation)**.
% 299.82/300.46  229887[0:SpR:194805.1,9529.1] || subclass(u,v) -> subclass(symmetric_difference(v,u),w) member(not_subclass_element(symmetric_difference(v,u),w),complement(u))*.
% 299.82/300.46  229902[10:SpR:205791.1,9529.1] ||  -> equal(singleton(u),successor_relation) subclass(symmetric_difference(u,universal_class),v) member(not_subclass_element(symmetric_difference(u,universal_class),v),complement(u))*.
% 299.82/300.46  230167[15:SpL:505.0,222296.1] || subclass(domain_relation,image(element_relation,union(u,v))) subclass(domain_relation,power_class(intersection(complement(u),complement(v))))* -> .
% 299.82/300.46  230179[25:SpR:203327.0,224236.1] function(restrict(cross_product(u,singleton(v)),w,x)) ||  -> equal(segment(cross_product(w,x),u,v),universal_class)**.
% 299.82/300.46  230240[25:SoR:224783.0,6317.2] single_valued_class(least(u,ordinal_numbers)) || well_ordering(u,kind_1_ordinals) equal(cross_product(universal_class,universal_class),least(u,ordinal_numbers))* -> .
% 299.82/300.46  230243[25:SoR:224784.0,6317.2] single_valued_class(least(u,universal_class)) || well_ordering(u,universal_class) equal(cross_product(universal_class,universal_class),least(u,universal_class))* -> .
% 299.82/300.46  230279[25:SoR:224785.0,6317.2] single_valued_class(least(u,rest_relation)) || well_ordering(u,universal_class) equal(cross_product(universal_class,universal_class),least(u,rest_relation))* -> .
% 299.82/300.46  230282[25:SoR:224786.0,6317.2] single_valued_class(least(u,rest_relation)) || well_ordering(u,rest_relation) equal(cross_product(universal_class,universal_class),least(u,rest_relation))* -> .
% 299.82/300.46  230285[25:SoR:224787.0,6317.2] single_valued_class(least(u,omega)) || well_ordering(u,universal_class) equal(cross_product(universal_class,universal_class),least(u,omega))* -> .
% 299.82/300.46  230288[25:SoR:224788.0,6317.2] single_valued_class(least(u,omega)) || well_ordering(u,omega) equal(cross_product(universal_class,universal_class),least(u,omega))* -> .
% 299.82/300.46  230532[10:Res:28320.1,229800.0] || subclass(rest_relation,rotate(singleton(omega))) -> equal(integer_of(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v)),successor_relation)**.
% 299.82/300.46  230534[10:Res:28321.1,229800.0] || subclass(rest_relation,flip(singleton(omega))) -> equal(integer_of(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u)))),successor_relation)**.
% 299.82/300.46  230573[10:Res:161722.2,229800.0] || subclass(u,singleton(omega)) -> equal(intersection(u,v),successor_relation) equal(integer_of(regular(intersection(u,v))),successor_relation)**.
% 299.82/300.46  230575[10:Res:161711.2,229800.0] || subclass(u,singleton(omega)) -> equal(intersection(v,u),successor_relation) equal(integer_of(regular(intersection(v,u))),successor_relation)**.
% 299.82/300.46  230624[10:Res:185430.1,157904.1] || equal(complement(complement(compose(element_relation,universal_class))),successor_relation)** member(u,universal_class) member(power_class(u),element_relation)* -> .
% 299.82/300.46  230644[15:SpL:505.0,230608.1] || equal(image(element_relation,union(u,v)),domain_relation) equal(power_class(intersection(complement(u),complement(v))),domain_relation)** -> .
% 299.82/300.46  230669[10:Res:185430.1,157905.1] || equal(complement(complement(compose(element_relation,universal_class))),successor_relation)** member(u,universal_class) member(sum_class(u),element_relation)* -> .
% 299.82/300.46  230708[10:Res:185430.1,192570.0] || equal(complement(u),successor_relation) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(omega,least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  230832[10:Res:160972.1,185639.1] || member(u,universal_class) equal(image(element_relation,power_class(successor_relation)),successor_relation) -> member(u,power_class(image(element_relation,universal_class)))*.
% 299.82/300.46  231426[25:Rew:160223.0,231308.1] function(image(element_relation,complement(u))) ||  -> equal(complement(intersection(power_class(u),universal_class)),successor(image(element_relation,complement(u))))**.
% 299.82/300.46  231570[15:MRR:231537.1,183757.0] || subclass(domain_relation,rest_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(regular(symmetrization_of(successor_relation)),successor_relation),ordinal_numbers)* -> .
% 299.82/300.46  231571[15:MRR:231536.1,183757.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,complement(kind_1_ordinals)) member(ordered_pair(regular(symmetrization_of(successor_relation)),successor_relation),ordinal_numbers)* -> .
% 299.82/300.46  231624[25:Rew:224739.1,231605.1] function(u) || equal(sum_class(range_of(successor_relation)),u)* member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> .
% 299.82/300.46  231788[10:SpL:139600.0,161035.0] || member(u,complement(complement(power_class(successor_relation)))) member(u,union(image(element_relation,universal_class),complement(power_class(successor_relation))))* -> .
% 299.82/300.46  231790[10:Res:114897.1,161035.0] || equal(intersection(power_class(successor_relation),complement(u)),universal_class) member(singleton(v),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231792[10:Res:1477.1,161035.0] || subclass(universal_class,intersection(power_class(successor_relation),complement(u))) member(singleton(v),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231804[10:Res:187500.1,161035.0] || subclass(universal_class,intersection(power_class(successor_relation),complement(u))) member(power_class(successor_relation),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231830[22:Res:218867.1,161035.0] || subclass(kind_1_ordinals,intersection(power_class(successor_relation),complement(u))) member(singleton(successor_relation),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231838[11:Res:179843.1,161035.0] || equal(intersection(power_class(successor_relation),complement(u)),inverse(successor_relation)) member(successor_relation,union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231839[10:Res:163171.1,161035.0] || equal(intersection(power_class(successor_relation),complement(u)),singleton(successor_relation)) member(successor_relation,union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231840[10:Res:163169.1,161035.0] || equal(intersection(power_class(successor_relation),complement(u)),successor(successor_relation)) member(successor_relation,union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231841[11:Res:168384.1,161035.0] || equal(intersection(power_class(successor_relation),complement(u)),symmetrization_of(successor_relation)) member(successor_relation,union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231850[10:Res:199848.1,161035.0] || subclass(universal_class,intersection(power_class(successor_relation),complement(u))) member(regular(rest_relation),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231853[10:Res:201231.1,161035.0] || subclass(universal_class,intersection(power_class(successor_relation),complement(u))) member(regular(domain_relation),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231854[12:Res:209377.1,161035.0] || subclass(universal_class,intersection(power_class(successor_relation),complement(u))) member(regular(element_relation),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231856[10:Res:229228.1,161035.0] || subclass(universal_class,intersection(power_class(successor_relation),complement(u))) member(regular(ordinal_numbers),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231857[10:Res:228991.1,161035.0] || subclass(kind_1_ordinals,intersection(power_class(successor_relation),complement(u))) member(regular(ordinal_numbers),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  10177[0:SpR:1933.0,1951.1] || member(u,symmetric_difference(complement(intersection(v,inverse(v))),symmetrization_of(v)))* -> member(u,complement(symmetric_difference(v,inverse(v)))).
% 299.82/300.46  10350[0:SpR:28.0,10292.0] ||  -> subclass(symmetric_difference(union(u,v),complement(inverse(intersection(complement(u),complement(v))))),symmetrization_of(intersection(complement(u),complement(v))))*.
% 299.82/300.46  33806[0:SpR:1938.0,9535.0] ||  -> subclass(symmetric_difference(complement(restrict(u,v,w)),union(u,cross_product(v,w))),complement(symmetric_difference(u,cross_product(v,w))))*.
% 299.82/300.46  33878[0:SpR:1943.0,9535.0] ||  -> subclass(symmetric_difference(complement(restrict(u,v,w)),union(cross_product(v,w),u)),complement(symmetric_difference(cross_product(v,w),u)))*.
% 299.82/300.46  10239[0:SpR:1934.0,1951.1] || member(u,symmetric_difference(complement(intersection(v,singleton(v))),successor(v)))* -> member(u,complement(symmetric_difference(v,singleton(v)))).
% 299.82/300.46  40645[0:SpL:1931.0,2648.0] || subclass(universal_class,symmetric_difference(complement(intersection(u,v)),union(u,v)))* -> member(singleton(w),complement(symmetric_difference(u,v)))*.
% 299.82/300.46  31252[0:SpL:124.0,5751.0] || equal(segment(u,v,w),singleton(w)) subclass(singleton(w),v) -> section(u,singleton(w),v)*.
% 299.82/300.46  5797[0:Res:3907.1,19.0] || equal(complement(complement(cross_product(u,v))),universal_class)** -> equal(ordered_pair(first(singleton(w)),second(singleton(w))),singleton(w))**.
% 299.82/300.46  5641[0:SpL:1005.0,35.0] || member(ordered_pair(singleton(singleton(singleton(u))),v),rotate(w))* -> member(ordered_pair(ordered_pair(u,v),singleton(u)),w)*.
% 299.82/300.46  5584[0:SpL:1005.0,38.0] || member(ordered_pair(singleton(singleton(singleton(u))),v),flip(w))* -> member(ordered_pair(ordered_pair(u,singleton(u)),v),w)*.
% 299.82/300.46  10369[0:SpR:28.0,10293.0] ||  -> subclass(symmetric_difference(union(u,v),complement(singleton(intersection(complement(u),complement(v))))),successor(intersection(complement(u),complement(v))))*.
% 299.82/300.46  38405[0:MRR:38395.1,191.0] || member(u,universal_class) equal(compose(v,singleton(u)),u) -> member(singleton(singleton(singleton(u))),compose_class(v))*.
% 299.82/300.46  31086[2:Res:9395.0,5832.1] inductive(intersection(u,v)) || well_ordering(w,v) -> member(least(w,intersection(u,v)),intersection(u,v))*.
% 299.82/300.46  31077[2:Res:9509.0,5832.1] inductive(intersection(u,v)) || well_ordering(w,u) -> member(least(w,intersection(u,v)),intersection(u,v))*.
% 299.82/300.46  40639[0:SpL:1931.0,5884.0] || equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),universal_class)** -> member(singleton(w),complement(symmetric_difference(u,v)))*.
% 299.82/300.46  107300[2:Res:107233.0,5832.1] inductive(complement(complement(u))) || well_ordering(v,u) -> member(least(v,complement(complement(u))),complement(complement(u)))*.
% 299.82/300.46  107572[0:Res:25.2,6045.0] || member(u,v)* member(u,w)* subclass(intersection(w,v),x)* well_ordering(universal_class,x) -> .
% 299.82/300.46  107658[0:Res:18.2,6045.0] || member(u,v)* member(w,x)* subclass(cross_product(x,v),y)* well_ordering(universal_class,y) -> .
% 299.82/300.46  108321[0:SpL:1933.0,9332.1] || member(u,symmetric_difference(complement(intersection(v,inverse(v))),symmetrization_of(v)))* member(u,symmetric_difference(v,inverse(v))) -> .
% 299.82/300.46  108322[0:SpL:1934.0,9332.1] || member(u,symmetric_difference(complement(intersection(v,singleton(v))),successor(v)))* member(u,symmetric_difference(v,singleton(v))) -> .
% 299.82/300.46  108620[2:MRR:108618.2,2450.0] || well_ordering(u,v) subclass(singleton(least(u,v)),v) -> section(u,singleton(least(u,v)),v)*.
% 299.82/300.46  111809[0:Res:1478.2,9322.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(v),complement(w)))* -> member(power_class(u),union(v,w))*.
% 299.82/300.46  122558[0:Obv:122491.2] || subclass(intersection(u,singleton(v)),complement(w))* member(v,w) -> subclass(intersection(u,singleton(v)),x)*.
% 299.82/300.46  122559[0:Obv:122490.2] || subclass(intersection(singleton(u),v),complement(w))* member(u,w) -> subclass(intersection(singleton(u),v),x)*.
% 299.82/300.46  125908[0:Res:28320.1,127.0] || subclass(rest_relation,rotate(u)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  125919[0:Res:28320.1,595.0] || subclass(rest_relation,rotate(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,rest_of(ordered_pair(y,x))),y),u)*.
% 299.82/300.46  126038[0:Res:28321.1,127.0] || subclass(rest_relation,flip(u)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  126049[0:Res:28321.1,595.0] || subclass(rest_relation,flip(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,y),rest_of(ordered_pair(y,x))),u)*.
% 299.82/300.46  130342[0:Res:3907.1,9300.0] || equal(complement(complement(symmetric_difference(u,cross_product(v,w)))),universal_class) -> member(singleton(x),complement(restrict(u,v,w)))*.
% 299.82/300.46  130435[0:Res:3907.1,9306.0] || equal(complement(complement(symmetric_difference(cross_product(u,v),w))),universal_class) -> member(singleton(x),complement(restrict(w,u,v)))*.
% 299.82/300.46  149600[6:Rew:148462.0,20862.2] function(union(identity_relation,symmetrization_of(u))) || connected(u,universal_class) -> equal(complement(complement(symmetrization_of(u))),cross_product(universal_class,universal_class))**.
% 299.82/300.46  152875[6:Res:149580.1,2609.1] function(complement(complement(symmetrization_of(u)))) || connected(u,universal_class) -> equal(complement(complement(symmetrization_of(u))),cross_product(universal_class,universal_class))**.
% 299.82/300.46  152914[0:Res:1506.1,3874.1] || equal(complement(intersection(u,v)),universal_class) member(omega,union(u,v)) -> member(omega,symmetric_difference(u,v))*.
% 299.82/300.46  158204[0:Res:60.1,1509.1] || member(ordered_pair(u,omega),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),universal_class)** -> .
% 299.82/300.46  163031[10:Rew:160202.0,158450.1] || member(regular(intersection(u,complement(compose(element_relation,universal_class)))),element_relation)* -> equal(intersection(u,complement(compose(element_relation,universal_class))),successor_relation).
% 299.82/300.46  163028[10:Rew:160202.0,158259.1] || member(regular(intersection(complement(compose(element_relation,universal_class)),u)),element_relation)* -> equal(intersection(complement(compose(element_relation,universal_class)),u),successor_relation).
% 299.82/300.46  163544[10:Rew:160202.0,163014.3] || subclass(cross_product(u,v),successor_relation)* member(w,v)* member(x,u)* well_ordering(y,successor_relation)* -> .
% 299.82/300.46  163543[10:Rew:160202.0,162994.1] ||  -> member(successor_relation,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* member(successor_relation,symmetrization_of(image(element_relation,complement(u)))).
% 299.82/300.46  163542[10:Rew:160202.0,162992.1] ||  -> member(successor_relation,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* member(successor_relation,successor(image(element_relation,complement(u)))).
% 299.82/300.46  163541[10:Rew:160202.0,162990.1] ||  -> member(successor_relation,intersection(power_class(image(element_relation,complement(u))),complement(v)))* member(successor_relation,union(image(element_relation,power_class(u)),v)).
% 299.82/300.46  163540[10:Rew:160202.0,162988.1] ||  -> member(successor_relation,intersection(complement(u),power_class(image(element_relation,complement(v)))))* member(successor_relation,union(u,image(element_relation,power_class(v)))).
% 299.82/300.46  162764[10:Rew:160202.0,153602.1] || well_ordering(u,image(element_relation,universal_class)) -> equal(segment(u,complement(power_class(successor_relation)),least(u,complement(power_class(successor_relation)))),successor_relation)**.
% 299.82/300.46  162234[10:Rew:160202.0,148518.0] ||  -> equal(restrict(omega,u,v),successor_relation) equal(integer_of(regular(restrict(omega,u,v))),regular(restrict(omega,u,v)))**.
% 299.82/300.46  162222[10:Rew:160202.0,147777.1] || member(regular(intersection(intersection(u,complement(v)),w)),v)* -> equal(intersection(intersection(u,complement(v)),w),successor_relation).
% 299.82/300.46  162221[10:Rew:160202.0,147702.1] || member(regular(intersection(intersection(complement(u),v),w)),u)* -> equal(intersection(intersection(complement(u),v),w),successor_relation).
% 299.82/300.46  162220[10:Rew:160202.0,147697.1] || subclass(u,restrict(v,w,x))* -> equal(intersection(u,y),successor_relation) member(regular(intersection(u,y)),v)*.
% 299.82/300.46  162213[10:Rew:160202.0,147664.1] || member(regular(intersection(u,intersection(v,complement(w)))),w)* -> equal(intersection(u,intersection(v,complement(w))),successor_relation).
% 299.82/300.46  162212[10:Rew:160202.0,147604.1] || member(regular(intersection(u,intersection(complement(v),w))),v)* -> equal(intersection(u,intersection(complement(v),w)),successor_relation).
% 299.82/300.46  162211[10:Rew:160202.0,147598.1] || subclass(u,restrict(v,w,x))* -> equal(intersection(y,u),successor_relation) member(regular(intersection(y,u)),v)*.
% 299.82/300.46  162203[10:Rew:160202.0,147558.1] || member(regular(image(element_relation,successor(u))),complement(image(element_relation,successor(u))))* -> equal(image(element_relation,successor(u)),successor_relation).
% 299.82/300.46  162202[10:Rew:160202.0,147557.1] || member(regular(image(element_relation,symmetrization_of(u))),complement(image(element_relation,symmetrization_of(u))))* -> equal(image(element_relation,symmetrization_of(u)),successor_relation).
% 299.82/300.46  162200[10:Rew:160202.0,147513.1] ||  -> member(regular(intersection(complement(union(u,v)),w)),complement(v))* equal(intersection(complement(union(u,v)),w),successor_relation).
% 299.82/300.46  162201[10:Rew:160202.0,147512.1] ||  -> member(regular(intersection(complement(union(u,v)),w)),complement(u))* equal(intersection(complement(union(u,v)),w),successor_relation).
% 299.82/300.46  162197[10:Rew:160202.0,147486.1] ||  -> member(regular(intersection(u,complement(union(v,w)))),complement(w))* equal(intersection(u,complement(union(v,w))),successor_relation).
% 299.82/300.46  162198[10:Rew:160202.0,147485.1] ||  -> member(regular(intersection(u,complement(union(v,w)))),complement(v))* equal(intersection(u,complement(union(v,w))),successor_relation).
% 299.82/300.46  162186[10:Rew:160202.0,147296.0] ||  -> equal(complement(complement(symmetric_difference(u,singleton(u)))),successor_relation) member(regular(complement(complement(symmetric_difference(u,singleton(u))))),successor(u))*.
% 299.82/300.46  162185[10:Rew:160202.0,147274.0] ||  -> equal(complement(complement(symmetric_difference(u,inverse(u)))),successor_relation) member(regular(complement(complement(symmetric_difference(u,inverse(u))))),symmetrization_of(u))*.
% 299.82/300.46  162184[10:Rew:160202.0,147190.2] || well_ordering(u,complement(v))* -> member(w,v)* equal(segment(u,singleton(w),least(u,singleton(w))),successor_relation)**.
% 299.82/300.46  162182[10:Rew:160202.0,147004.2] || member(u,v)* well_ordering(w,v)* -> equal(segment(w,singleton(u),least(w,singleton(u))),successor_relation)**.
% 299.82/300.46  162181[10:Rew:160202.0,147003.1] || well_ordering(u,union(v,w)) -> equal(segment(u,symmetric_difference(v,w),least(u,symmetric_difference(v,w))),successor_relation)**.
% 299.82/300.46  162170[10:Rew:160202.0,146992.1] || well_ordering(u,v) -> equal(segment(u,restrict(v,w,x),least(u,restrict(v,w,x))),successor_relation)**.
% 299.82/300.46  162169[10:Rew:160202.0,146991.1] || well_ordering(u,v) -> equal(intersection(w,v),successor_relation) member(least(u,intersection(w,v)),intersection(w,v))*.
% 299.82/300.46  162167[10:Rew:160202.0,146986.1] || subclass(power_class(image(element_relation,complement(u))),image(element_relation,power_class(u)))* -> equal(power_class(image(element_relation,complement(u))),successor_relation).
% 299.82/300.46  162164[10:Rew:160202.0,146975.0] ||  -> equal(intersection(u,symmetric_difference(v,inverse(v))),successor_relation) member(regular(intersection(u,symmetric_difference(v,inverse(v)))),symmetrization_of(v))*.
% 299.82/300.46  162162[10:Rew:160202.0,146973.0] ||  -> equal(intersection(u,symmetric_difference(v,singleton(v))),successor_relation) member(regular(intersection(u,symmetric_difference(v,singleton(v)))),successor(v))*.
% 299.82/300.46  162160[10:Rew:160202.0,146971.0] ||  -> equal(intersection(symmetric_difference(u,inverse(u)),v),successor_relation) member(regular(intersection(symmetric_difference(u,inverse(u)),v)),symmetrization_of(u))*.
% 299.82/300.46  162158[10:Rew:160202.0,146969.0] ||  -> equal(intersection(symmetric_difference(u,singleton(u)),v),successor_relation) member(regular(intersection(symmetric_difference(u,singleton(u)),v)),successor(u))*.
% 299.82/300.46  162137[10:Rew:160202.0,159743.0] || member(ordered_pair(u,successor_relation),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),universal_class)** -> .
% 299.82/300.46  162110[10:Rew:160202.0,147541.1] || member(regular(image(element_relation,power_class(u))),power_class(image(element_relation,complement(u))))* -> equal(image(element_relation,power_class(u)),successor_relation).
% 299.82/300.46  162081[10:Rew:160202.0,147034.2] || subclass(u,v)* well_ordering(w,v)* -> equal(intersection(u,x),successor_relation)** member(least(w,u),u)*.
% 299.82/300.46  162067[10:Rew:160202.0,147019.2] || subclass(u,v)* well_ordering(w,v)* -> equal(intersection(x,u),successor_relation)** member(least(w,u),u)*.
% 299.82/300.46  162055[10:Rew:160202.0,146982.1] || member(regular(intersection(complement(u),complement(v))),union(u,v))* -> equal(intersection(complement(u),complement(v)),successor_relation).
% 299.82/300.46  162051[10:Rew:160202.0,146964.0] ||  -> equal(intersection(u,symmetric_difference(v,w)),successor_relation) member(regular(intersection(u,symmetric_difference(v,w))),complement(intersection(v,w)))*.
% 299.82/300.46  162048[10:Rew:160202.0,146961.0] ||  -> equal(intersection(symmetric_difference(u,v),w),successor_relation) member(regular(intersection(symmetric_difference(u,v),w)),complement(intersection(u,v)))*.
% 299.82/300.46  162969[10:Rew:160202.0,156039.0] ||  -> equal(complement(intersection(complement(u),union(v,symmetric_difference(universal_class,w)))),union(u,intersection(complement(v),union(w,successor_relation))))**.
% 299.82/300.46  161986[10:Rew:160202.0,147330.1] || equal(sum_class(singleton(u)),singleton(u)) -> equal(sum_class(singleton(u)),successor_relation) equal(regular(sum_class(singleton(u))),u)**.
% 299.82/300.46  161984[10:Rew:160202.0,147321.1] || well_ordering(u,v) -> equal(complement(complement(v)),successor_relation) member(least(u,complement(complement(v))),complement(complement(v)))*.
% 299.82/300.46  161970[10:Rew:160202.0,146928.1] || well_ordering(u,v) -> equal(intersection(v,w),successor_relation) member(least(u,intersection(v,w)),intersection(v,w))*.
% 299.82/300.46  161890[10:Rew:160202.0,146979.1] || member(regular(complement(complement(intersection(u,v)))),symmetric_difference(u,v))* -> equal(complement(complement(intersection(u,v))),successor_relation).
% 299.82/300.46  161879[10:Rew:160202.0,146906.1] || member(regular(intersection(intersection(u,v),w)),symmetric_difference(u,v))* -> equal(intersection(intersection(u,v),w),successor_relation).
% 299.82/300.46  161873[10:Rew:160202.0,146885.1] || member(regular(intersection(u,intersection(v,w))),symmetric_difference(v,w))* -> equal(intersection(u,intersection(v,w)),successor_relation).
% 299.82/300.46  163531[10:Rew:160202.0,161868.0] || member(successor_relation,cross_product(u,v)) member(successor_relation,w) equal(complement(restrict(w,u,v)),universal_class)** -> .
% 299.82/300.46  161815[10:Rew:160202.0,147269.1] || subclass(image(element_relation,complement(u)),v)* -> equal(complement(power_class(u)),successor_relation) member(regular(complement(power_class(u))),v).
% 299.82/300.46  161790[10:Rew:160202.0,146839.1] || subclass(symmetrization_of(u),v) -> equal(symmetric_difference(u,inverse(u)),successor_relation) member(regular(symmetric_difference(u,inverse(u))),v)*.
% 299.82/300.46  161787[10:Rew:160202.0,146836.1] || subclass(successor(u),v) -> equal(symmetric_difference(u,singleton(u)),successor_relation) member(regular(symmetric_difference(u,singleton(u))),v)*.
% 299.82/300.46  163513[10:Rew:160202.0,160534.3] || subclass(intersection(u,v),successor_relation)* member(w,v)* member(w,u)* well_ordering(x,successor_relation)* -> .
% 299.82/300.46  163529[10:Rew:160202.0,161775.2] ||  -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),successor_relation) equal(intersection(unordered_pair(u,v),u),successor_relation)**.
% 299.82/300.46  163530[10:Rew:160202.0,161776.2] ||  -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),successor_relation) equal(intersection(unordered_pair(u,v),v),successor_relation)**.
% 299.82/300.46  161685[10:Rew:160202.0,146724.1] || subclass(complement(intersection(u,v)),w)* -> equal(symmetric_difference(u,v),successor_relation) member(regular(symmetric_difference(u,v)),w).
% 299.82/300.46  161608[10:Rew:160202.0,147212.2] || equal(u,v) subclass(unordered_pair(v,u),w)* -> equal(unordered_pair(v,u),successor_relation) member(v,w).
% 299.82/300.46  161669[10:Rew:160202.0,156061.0] || equal(u,union(v,successor_relation))* member(w,universal_class) -> member(w,symmetric_difference(universal_class,v))* member(w,u)*.
% 299.82/300.46  161668[10:Rew:160202.0,156056.1] || member(u,universal_class) subclass(union(v,successor_relation),w)* -> member(u,symmetric_difference(universal_class,v))* member(u,w)*.
% 299.82/300.46  161664[10:Rew:160202.0,156027.0] ||  -> equal(complement(intersection(complement(u),union(symmetric_difference(universal_class,v),w))),union(u,intersection(union(v,successor_relation),complement(w))))**.
% 299.82/300.46  161658[10:Rew:160202.0,156054.1] || member(u,image(element_relation,power_class(symmetric_difference(universal_class,v))))* member(u,power_class(image(element_relation,union(v,successor_relation)))) -> .
% 299.82/300.46  161651[10:Rew:160202.0,156024.0] ||  -> equal(complement(intersection(union(u,symmetric_difference(universal_class,v)),complement(w))),union(intersection(complement(u),union(v,successor_relation)),w))**.
% 299.82/300.46  161425[10:Rew:160202.0,159718.2] || member(not_subclass_element(intersection(u,regular(v)),w),v)* -> subclass(intersection(u,regular(v)),w) equal(v,successor_relation).
% 299.82/300.46  161415[10:Rew:160202.0,146622.2] || member(complement(complement(u)),universal_class) -> member(apply(choice,complement(complement(u))),u)* equal(complement(complement(u)),successor_relation).
% 299.82/300.46  161416[10:Rew:160202.0,146620.2] || subclass(u,v)* well_ordering(w,v)* -> equal(complement(complement(u)),successor_relation) member(least(w,u),u)*.
% 299.82/300.46  163528[10:Rew:160202.0,161494.2] || well_ordering(u,omega) -> equal(integer_of(v),successor_relation) equal(segment(u,singleton(v),least(u,singleton(v))),successor_relation)**.
% 299.82/300.46  163526[10:Rew:160202.0,161370.2] || equal(complement(intersection(u,v)),universal_class) member(successor_relation,union(u,v)) -> member(successor_relation,symmetric_difference(u,v))*.
% 299.82/300.46  161308[10:Rew:160202.0,146611.2] || subclass(u,rest_of(regular(intersection(u,v))))* subclass(universal_class,complement(element_relation)) -> equal(intersection(u,v),successor_relation).
% 299.82/300.46  161316[10:Rew:160202.0,147369.2] || subclass(u,rest_of(regular(intersection(v,u))))* subclass(universal_class,complement(element_relation)) -> equal(intersection(v,u),successor_relation).
% 299.82/300.46  162028[10:Rew:160202.0,146561.2] || equal(sum_class(u),u) subclass(u,v) -> equal(sum_class(u),successor_relation) member(regular(sum_class(u)),v)*.
% 299.82/300.46  161224[10:Rew:160202.0,156012.0] ||  -> equal(power_class(intersection(union(u,successor_relation),complement(inverse(symmetric_difference(universal_class,u))))),complement(image(element_relation,symmetrization_of(symmetric_difference(universal_class,u)))))**.
% 299.82/300.46  161223[10:Rew:160202.0,156011.0] ||  -> equal(power_class(intersection(union(u,successor_relation),complement(singleton(symmetric_difference(universal_class,u))))),complement(image(element_relation,successor(symmetric_difference(universal_class,u)))))**.
% 299.82/300.46  161196[10:Rew:160202.0,155998.0] ||  -> equal(complement(intersection(union(symmetric_difference(universal_class,u),v),complement(w))),union(intersection(union(u,successor_relation),complement(v)),w))**.
% 299.82/300.46  163517[10:Rew:160202.0,160885.1] || well_ordering(u,image(element_relation,successor_relation)) -> equal(segment(u,complement(power_class(universal_class)),least(u,complement(power_class(universal_class)))),successor_relation)**.
% 299.82/300.46  160880[10:Rew:160202.0,152612.0] ||  -> equal(complement(intersection(power_class(image(element_relation,complement(u))),power_class(universal_class))),union(image(element_relation,power_class(u)),image(element_relation,successor_relation)))**.
% 299.82/300.46  160879[10:Rew:160202.0,152592.0] ||  -> equal(complement(intersection(power_class(universal_class),power_class(image(element_relation,complement(u))))),union(image(element_relation,successor_relation),image(element_relation,power_class(u))))**.
% 299.82/300.46  160871[10:Rew:160202.0,152613.2] || member(u,universal_class) -> member(u,intersection(complement(v),power_class(universal_class)))* member(u,union(v,image(element_relation,successor_relation))).
% 299.82/300.46  160867[10:Rew:160202.0,152603.2] || member(u,universal_class) -> member(u,intersection(power_class(universal_class),complement(v)))* member(u,union(image(element_relation,successor_relation),v)).
% 299.82/300.46  163516[10:Rew:160202.0,160853.1] || member(not_subclass_element(power_class(image(element_relation,successor_relation)),u),image(element_relation,power_class(universal_class)))* -> subclass(power_class(image(element_relation,successor_relation)),u).
% 299.82/300.46  160852[10:Rew:160202.0,152608.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,power_class(universal_class))))),union(u,image(element_relation,power_class(image(element_relation,successor_relation)))))**.
% 299.82/300.46  160851[10:Rew:160202.0,152581.0] ||  -> equal(complement(intersection(power_class(image(element_relation,power_class(universal_class))),complement(u))),union(image(element_relation,power_class(image(element_relation,successor_relation))),u))**.
% 299.82/300.46  160689[10:Rew:160202.0,159716.2] || member(not_subclass_element(intersection(regular(u),v),w),u)* -> subclass(intersection(regular(u),v),w) equal(u,successor_relation).
% 299.82/300.46  160690[10:Rew:160202.0,159715.2] || member(not_subclass_element(complement(complement(regular(u))),v),u)* -> subclass(complement(complement(regular(u))),v) equal(u,successor_relation).
% 299.82/300.46  160764[10:Rew:160202.0,146531.2] || subclass(u,intersection(complement(v),complement(w)))* member(regular(u),union(v,w)) -> equal(u,successor_relation).
% 299.82/300.46  160765[10:Rew:160202.0,146523.3] || member(u,universal_class) subclass(u,complement(v)) member(apply(choice,u),v)* -> equal(u,successor_relation).
% 299.82/300.46  160766[10:Rew:160202.0,146522.2] || member(u,universal_class) subclass(u,intersection(v,w))* -> equal(u,successor_relation) member(apply(choice,u),v).
% 299.82/300.46  160767[10:Rew:160202.0,146521.2] || member(u,universal_class) subclass(u,intersection(v,w))* -> equal(u,successor_relation) member(apply(choice,u),w).
% 299.82/300.46  160769[10:Rew:160202.0,146487.2] || subclass(u,union(v,w)) member(regular(u),intersection(complement(v),complement(w)))* -> equal(u,successor_relation).
% 299.82/300.46  161175[10:Rew:160202.0,152776.0] ||  -> equal(complement(intersection(power_class(image(element_relation,complement(u))),symmetrization_of(successor_relation))),union(image(element_relation,power_class(u)),complement(inverse(successor_relation))))**.
% 299.82/300.46  161174[10:Rew:160202.0,152756.0] ||  -> equal(complement(intersection(symmetrization_of(successor_relation),power_class(image(element_relation,complement(u))))),union(complement(inverse(successor_relation)),image(element_relation,power_class(u))))**.
% 299.82/300.46  168532[11:Res:168384.1,127.0] || equal(u,symmetrization_of(successor_relation)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  161142[10:Rew:160202.0,152772.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,symmetrization_of(successor_relation))))),union(u,image(element_relation,power_class(complement(inverse(successor_relation))))))**.
% 299.82/300.46  161141[10:Rew:160202.0,152745.0] ||  -> equal(complement(intersection(power_class(image(element_relation,symmetrization_of(successor_relation))),complement(u))),union(image(element_relation,power_class(complement(inverse(successor_relation)))),u))**.
% 299.82/300.46  163514[10:Rew:160202.0,160535.3] || subclass(intersection(u,v),successor_relation)* member(w,v)* member(w,u)* -> member(w,inverse(successor_relation))*.
% 299.82/300.46  163525[10:Rew:160202.0,161177.1] || well_ordering(u,complement(inverse(successor_relation))) -> equal(segment(u,complement(symmetrization_of(successor_relation)),least(u,complement(symmetrization_of(successor_relation)))),successor_relation)**.
% 299.82/300.46  163523[10:Rew:160202.0,161132.2] || member(u,universal_class) -> member(u,intersection(complement(v),symmetrization_of(successor_relation)))* member(u,union(v,complement(inverse(successor_relation)))).
% 299.82/300.46  163522[10:Rew:160202.0,161130.2] || member(u,universal_class) -> member(u,intersection(symmetrization_of(successor_relation),complement(v)))* member(u,union(complement(inverse(successor_relation)),v)).
% 299.82/300.46  163524[10:Rew:160202.0,161143.1] || member(not_subclass_element(power_class(complement(inverse(successor_relation))),u),image(element_relation,symmetrization_of(successor_relation)))* -> subclass(power_class(complement(inverse(successor_relation))),u).
% 299.82/300.46  163519[10:Rew:160202.0,161086.1] || member(regular(restrict(power_class(successor_relation),u,v)),image(element_relation,universal_class))* -> equal(restrict(power_class(successor_relation),u,v),successor_relation).
% 299.82/300.46  161070[10:Rew:160202.0,150722.0] ||  -> equal(complement(intersection(power_class(successor_relation),power_class(image(element_relation,complement(u))))),union(image(element_relation,universal_class),image(element_relation,power_class(u))))**.
% 299.82/300.46  161065[10:Rew:160202.0,150709.0] ||  -> equal(complement(intersection(power_class(image(element_relation,complement(u))),power_class(successor_relation))),union(image(element_relation,power_class(u)),image(element_relation,universal_class)))**.
% 299.82/300.46  161064[10:Rew:160202.0,150708.1] || member(u,universal_class) subclass(rest_relation,power_class(successor_relation)) member(ordered_pair(u,rest_of(u)),image(element_relation,universal_class))* -> .
% 299.82/300.46  161034[10:Rew:160202.0,150705.1] || member(u,universal_class) -> member(u,intersection(power_class(successor_relation),complement(v)))* member(u,union(image(element_relation,universal_class),v)).
% 299.82/300.46  161013[10:Rew:160202.0,150699.1] || member(u,universal_class) -> member(u,intersection(complement(v),power_class(successor_relation)))* member(u,union(v,image(element_relation,universal_class))).
% 299.82/300.46  160980[10:Rew:160202.0,150797.0] || member(not_subclass_element(power_class(image(element_relation,universal_class)),u),image(element_relation,power_class(successor_relation)))* -> subclass(power_class(image(element_relation,universal_class)),u).
% 299.82/300.46  160979[10:Rew:160202.0,150718.0] ||  -> equal(complement(intersection(power_class(image(element_relation,power_class(successor_relation))),complement(u))),union(image(element_relation,power_class(image(element_relation,universal_class))),u))**.
% 299.82/300.46  160978[10:Rew:160202.0,150704.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,power_class(successor_relation))))),union(u,image(element_relation,power_class(image(element_relation,universal_class)))))**.
% 299.82/300.46  162922[10:Rew:160202.0,152505.0] ||  -> equal(complement(intersection(successor(successor_relation),power_class(image(element_relation,complement(u))))),union(complement(singleton(successor_relation)),image(element_relation,power_class(u))))**.
% 299.82/300.46  162921[10:Rew:160202.0,152525.0] ||  -> equal(complement(intersection(power_class(image(element_relation,complement(u))),successor(successor_relation))),union(image(element_relation,power_class(u)),complement(singleton(successor_relation))))**.
% 299.82/300.46  162894[10:Rew:160202.0,152494.0] ||  -> equal(complement(intersection(power_class(image(element_relation,successor(successor_relation))),complement(u))),union(image(element_relation,power_class(complement(singleton(successor_relation)))),u))**.
% 299.82/300.46  162893[10:Rew:160202.0,152521.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,successor(successor_relation))))),union(u,image(element_relation,power_class(complement(singleton(successor_relation))))))**.
% 299.82/300.46  162919[10:Rew:160202.0,157829.0] || equal(u,successor(successor_relation)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  162873[10:Rew:160202.0,156275.0] || equal(u,singleton(successor_relation)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  163538[10:Rew:160202.0,162801.1] || well_ordering(u,complement(singleton(successor_relation))) -> equal(segment(u,complement(successor(successor_relation)),least(u,complement(successor(successor_relation)))),successor_relation)**.
% 299.82/300.46  163537[10:Rew:160202.0,162793.1] || member(u,universal_class) -> member(u,intersection(successor(successor_relation),complement(v)))* member(u,union(complement(singleton(successor_relation)),v)).
% 299.82/300.46  163536[10:Rew:160202.0,162790.1] || member(u,universal_class) -> member(u,intersection(complement(v),successor(successor_relation)))* member(u,union(v,complement(singleton(successor_relation)))).
% 299.82/300.46  163535[10:Rew:160202.0,162779.0] || member(not_subclass_element(power_class(complement(singleton(successor_relation))),u),image(element_relation,successor(successor_relation)))* -> subclass(power_class(complement(singleton(successor_relation))),u).
% 299.82/300.46  47885[0:Res:34085.1,127.0] || member(u,rest_of(u))* subclass(element_relation,v) well_ordering(w,v)* -> member(least(w,element_relation),element_relation)*.
% 299.82/300.46  125954[0:Res:28320.1,47888.0] || subclass(rest_relation,rotate(rest_of(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v))))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.46  126084[0:Res:28321.1,47888.0] || subclass(rest_relation,flip(rest_of(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))))))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.46  157908[6:Res:1495.2,148657.1] || member(u,universal_class) subclass(rest_relation,complement(compose(element_relation,universal_class)))* member(ordered_pair(u,rest_of(u)),element_relation)* -> .
% 299.82/300.46  126782[0:Rew:57.0,126683.1] || member(not_subclass_element(intersection(power_class(u),v),w),image(element_relation,complement(u)))* -> subclass(intersection(power_class(u),v),w).
% 299.82/300.46  126814[0:SpL:57.0,29643.0] || equal(u,power_class(v))* member(w,universal_class) -> member(w,image(element_relation,complement(v)))* member(w,u)*.
% 299.82/300.46  126561[0:Rew:57.0,126475.1] || member(not_subclass_element(intersection(u,power_class(v)),w),image(element_relation,complement(v)))* -> subclass(intersection(u,power_class(v)),w).
% 299.82/300.46  28530[0:Res:1028.1,3.0] || member(u,universal_class) subclass(image(element_relation,complement(v)),w)* -> member(u,power_class(v))* member(u,w)*.
% 299.82/300.46  29636[0:SpL:57.0,1487.1] || member(u,universal_class) subclass(power_class(v),w)* -> member(u,image(element_relation,complement(v)))* member(u,w)*.
% 299.82/300.46  10346[0:SpR:208.0,10292.0] ||  -> subclass(symmetric_difference(power_class(image(element_relation,complement(u))),complement(inverse(image(element_relation,power_class(u))))),symmetrization_of(image(element_relation,power_class(u))))*.
% 299.82/300.46  10365[0:SpR:208.0,10293.0] ||  -> subclass(symmetric_difference(power_class(image(element_relation,complement(u))),complement(singleton(image(element_relation,power_class(u))))),successor(image(element_relation,power_class(u))))*.
% 299.82/300.46  124236[0:Res:3907.1,986.1] || equal(complement(complement(power_class(image(element_relation,complement(u))))),universal_class)** member(singleton(v),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  125141[0:Rew:57.0,125105.1] ||  -> member(not_subclass_element(u,image(element_relation,power_class(v))),power_class(image(element_relation,complement(v))))* subclass(u,image(element_relation,power_class(v))).
% 299.82/300.46  9055[0:SpL:208.0,307.0] || member(u,image(element_relation,power_class(image(element_relation,complement(v)))))* member(u,power_class(image(element_relation,power_class(v)))) -> .
% 299.82/300.46  9955[0:SpL:505.0,2647.0] || subclass(universal_class,power_class(intersection(complement(u),complement(v))))* member(singleton(w),image(element_relation,union(u,v)))* -> .
% 299.82/300.46  9942[0:SpR:505.0,28.0] ||  -> equal(complement(intersection(power_class(intersection(complement(u),complement(v))),complement(w))),union(image(element_relation,union(u,v)),w))**.
% 299.82/300.46  9947[0:SpR:505.0,28.0] ||  -> equal(complement(intersection(complement(u),power_class(intersection(complement(v),complement(w))))),union(u,image(element_relation,union(v,w))))**.
% 299.82/300.46  125154[0:Rew:45.0,125095.1,28.0,125095.1,45.0,125095.0,28.0,125095.0] ||  -> member(not_subclass_element(u,image(element_relation,successor(v))),complement(image(element_relation,successor(v))))* subclass(u,image(element_relation,successor(v))).
% 299.82/300.46  125153[0:Rew:115.0,125096.1,28.0,125096.1,115.0,125096.0,28.0,125096.0] ||  -> member(not_subclass_element(u,image(element_relation,symmetrization_of(v))),complement(image(element_relation,symmetrization_of(v))))* subclass(u,image(element_relation,symmetrization_of(v))).
% 299.82/300.46  111810[0:Res:1479.2,9322.0] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(v),complement(w)))* -> member(sum_class(u),union(v,w))*.
% 299.82/300.46  145040[2:MRR:53160.0,145036.0] ||  -> equal(apply(choice,ordered_pair(u,v)),unordered_pair(u,singleton(v)))** equal(apply(choice,ordered_pair(u,v)),singleton(u)).
% 299.82/300.46  120032[0:Rew:114854.0,119995.0] || member(cross_product(u,singleton(v)),universal_class) -> member(ordered_pair(cross_product(u,singleton(v)),segment(universal_class,u,v)),domain_relation)*.
% 299.82/300.46  111849[0:Res:1504.1,9322.0] || subclass(ordered_pair(u,v),symmetric_difference(complement(w),complement(x)))* -> member(unordered_pair(u,singleton(v)),union(w,x)).
% 299.82/300.46  89247[0:Res:51387.0,594.0] ||  -> subclass(u,complement(restrict(v,w,x))) member(not_subclass_element(u,complement(restrict(v,w,x))),cross_product(w,x))*.
% 299.82/300.46  111843[0:Res:1481.2,9322.0] || subclass(u,symmetric_difference(complement(v),complement(w)))* -> subclass(u,x) member(not_subclass_element(u,x),union(v,w))*.
% 299.82/300.46  29428[0:Rew:1948.0,29340.0] ||  -> subclass(symmetric_difference(complement(u),complement(v)),w) member(not_subclass_element(symmetric_difference(complement(u),complement(v)),w),union(u,v))*.
% 299.82/300.46  41890[0:SpR:2330.1,1004.0] ||  -> subclass(cross_product(u,v),w) member(singleton(first(not_subclass_element(cross_product(u,v),w))),not_subclass_element(cross_product(u,v),w))*.
% 299.82/300.46  107184[0:Res:34429.0,1952.0] ||  -> subclass(complement(complement(symmetric_difference(u,v))),w) member(not_subclass_element(complement(complement(symmetric_difference(u,v))),w),union(u,v))*.
% 299.82/300.46  107256[0:Rew:28.0,107153.1] ||  -> member(not_subclass_element(complement(union(u,v)),w),intersection(complement(u),complement(v)))* subclass(complement(union(u,v)),w).
% 299.82/300.46  34428[0:MRR:30987.0,34189.1] ||  -> member(not_subclass_element(u,intersection(complement(v),complement(w))),union(v,w))* subclass(u,intersection(complement(v),complement(w))).
% 299.82/300.46  41939[0:SpL:2330.1,3514.1] || subclass(universal_class,complement(u)) member(not_subclass_element(cross_product(v,w),x),u)* -> subclass(cross_product(v,w),x).
% 299.82/300.46  9385[0:Res:322.1,1952.0] ||  -> subclass(intersection(u,symmetric_difference(v,w)),x) member(not_subclass_element(intersection(u,symmetric_difference(v,w)),x),union(v,w))*.
% 299.82/300.46  9499[0:Res:340.1,1952.0] ||  -> subclass(intersection(symmetric_difference(u,v),w),x) member(not_subclass_element(intersection(symmetric_difference(u,v),w),x),union(u,v))*.
% 299.82/300.46  122689[0:Res:6832.1,3.0] || subclass(union(u,v),w) -> subclass(symmetric_difference(u,v),x) member(not_subclass_element(symmetric_difference(u,v),x),w)*.
% 299.82/300.46  107182[0:Res:34429.0,595.0] ||  -> subclass(complement(complement(restrict(u,v,w))),x) member(not_subclass_element(complement(complement(restrict(u,v,w))),x),u)*.
% 299.82/300.46  9378[0:Res:322.1,595.0] ||  -> subclass(intersection(u,restrict(v,w,x)),y) member(not_subclass_element(intersection(u,restrict(v,w,x)),y),v)*.
% 299.82/300.46  9492[0:Res:340.1,595.0] ||  -> subclass(intersection(restrict(u,v,w),x),y) member(not_subclass_element(intersection(restrict(u,v,w),x),y),u)*.
% 299.82/300.46  123444[0:Res:9424.0,9639.0] ||  -> subclass(restrict(intersection(u,v),w,x),y) member(not_subclass_element(restrict(intersection(u,v),w,x),y),u)*.
% 299.82/300.46  122853[0:Res:9424.0,9640.0] ||  -> subclass(restrict(intersection(u,v),w,x),y) member(not_subclass_element(restrict(intersection(u,v),w,x),y),v)*.
% 299.82/300.46  123491[0:Res:978.1,3.0] || subclass(u,v) -> subclass(restrict(u,w,x),y) member(not_subclass_element(restrict(u,w,x),y),v)*.
% 299.82/300.46  143783[0:Res:1495.2,159.0] || member(u,universal_class) subclass(rest_relation,omega) -> equal(integer_of(ordered_pair(u,rest_of(u))),ordered_pair(u,rest_of(u)))**.
% 299.82/300.46  48616[0:Res:1495.2,10254.0] || member(u,universal_class) subclass(rest_relation,symmetric_difference(v,singleton(v)))* -> member(ordered_pair(u,rest_of(u)),successor(v))*.
% 299.82/300.46  48514[0:Res:1495.2,10191.0] || member(u,universal_class) subclass(rest_relation,symmetric_difference(v,inverse(v)))* -> member(ordered_pair(u,rest_of(u)),symmetrization_of(v))*.
% 299.82/300.46  28325[0:MRR:28316.1,146.0] || member(u,universal_class) equal(compose(v,u),rest_of(u)) -> member(ordered_pair(u,rest_of(u)),compose_class(v))*.
% 299.82/300.46  28286[0:Res:1495.2,1952.0] || member(u,universal_class) subclass(rest_relation,symmetric_difference(v,w)) -> member(ordered_pair(u,rest_of(u)),union(v,w))*.
% 299.82/300.46  28266[0:Res:1495.2,3.0] || member(u,universal_class) subclass(rest_relation,v)* subclass(v,w)* -> member(ordered_pair(u,rest_of(u)),w)*.
% 299.82/300.46  112489[0:Rew:28.0,112417.2] || member(u,universal_class) -> member(u,complement(intersection(complement(v),union(w,x))))* member(u,union(w,x)).
% 299.82/300.46  112650[0:Rew:28.0,112590.2] || member(u,universal_class) -> member(u,complement(intersection(union(v,w),complement(x))))* member(u,union(v,w)).
% 299.82/300.46  155813[3:Res:3595.3,141576.1] function(u) || member(v,universal_class) subclass(universal_class,complement(kind_1_ordinals)) member(image(u,v),ordinal_numbers)* -> .
% 299.82/300.46  30745[0:Res:3595.3,24.0] function(u) || member(v,universal_class) subclass(universal_class,intersection(w,x))* -> member(image(u,v),x)*.
% 299.82/300.46  30744[0:Res:3595.3,23.0] function(u) || member(v,universal_class) subclass(universal_class,intersection(w,x))* -> member(image(u,v),w)*.
% 299.82/300.46  30741[0:Res:3595.3,26.1] function(u) || member(v,universal_class) subclass(universal_class,complement(w)) member(image(u,v),w)* -> .
% 299.82/300.46  158193[0:Res:3872.2,1509.1] || member(omega,cross_product(u,v)) member(omega,w) equal(complement(restrict(w,u,v)),universal_class)** -> .
% 299.82/300.46  34066[0:Res:64.1,3883.2] function(intersection(u,v)) || member(w,v)* member(w,u)* -> member(w,cross_product(universal_class,universal_class))*.
% 299.82/300.46  179990[11:Res:179843.1,127.0] || equal(u,inverse(successor_relation)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  183389[0:SpR:208.0,139600.0] ||  -> equal(intersection(image(element_relation,power_class(u)),complement(power_class(image(element_relation,complement(u))))),complement(power_class(image(element_relation,complement(u)))))**.
% 299.82/300.46  184790[14:SpL:44.0,184008.2] || member(u,universal_class)* member(restrict(v,w,universal_class),universal_class)* equal(sum_class(image(v,w)),u)* -> .
% 299.82/300.46  185682[10:Rew:113504.0,185458.1] || equal(restrict(u,v,w),successor_relation) -> equal(symmetric_difference(cross_product(v,w),u),union(cross_product(v,w),u))**.
% 299.82/300.46  185683[10:Rew:113504.0,185457.1] || equal(restrict(u,v,w),successor_relation) -> equal(symmetric_difference(u,cross_product(v,w)),union(u,cross_product(v,w)))**.
% 299.82/300.46  185933[10:Res:185646.1,127.0] || equal(complement(u),successor_relation) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  187082[10:Rew:160322.0,187065.2,160322.0,187065.0] || member(power_class(universal_class),universal_class) member(apply(choice,power_class(universal_class)),image(element_relation,successor_relation))* -> equal(power_class(universal_class),successor_relation).
% 299.82/300.46  187511[10:Res:160784.3,141576.1] || member(u,universal_class) subclass(u,complement(kind_1_ordinals)) member(apply(choice,u),ordinal_numbers)* -> equal(u,successor_relation).
% 299.82/300.46  187526[10:Res:160784.3,183723.0] || member(u,universal_class) subclass(u,symmetrization_of(successor_relation)) -> equal(u,successor_relation) member(apply(choice,u),inverse(successor_relation))*.
% 299.82/300.46  187531[10:Res:160784.3,183622.0] || member(u,universal_class) subclass(u,successor(successor_relation)) -> equal(u,successor_relation) member(apply(choice,u),singleton(successor_relation))*.
% 299.82/300.46  41067[0:Res:6.0,5838.1] || member(u,universal_class)* well_ordering(v,universal_class) -> member(u,w)* member(least(v,complement(w)),complement(w))*.
% 299.82/300.46  112445[0:Res:30985.1,6045.0] || member(u,universal_class) subclass(union(v,w),x)* well_ordering(universal_class,x) -> member(u,complement(w))*.
% 299.82/300.46  112612[0:Res:30984.1,6045.0] || member(u,universal_class) subclass(union(v,w),x)* well_ordering(universal_class,x) -> member(u,complement(v))*.
% 299.82/300.46  39108[2:Res:5714.3,34067.0] || connected(u,v) well_ordering(w,v) -> well_ordering(u,v) member(least(w,not_well_ordering(u,v)),universal_class)*.
% 299.82/300.46  162027[10:Rew:160202.0,146567.2] || member(u,ordinal_numbers) well_ordering(v,u) -> equal(sum_class(u),successor_relation) member(least(v,sum_class(u)),universal_class)*.
% 299.82/300.46  162091[10:Rew:160202.0,147224.1] || well_ordering(u,cross_product(universal_class,universal_class)) -> equal(compose(v,w),successor_relation) member(least(u,compose(v,w)),universal_class)*.
% 299.82/300.46  162204[10:Rew:160202.0,147568.2] || well_ordering(u,universal_class) member(least(u,power_class(v)),image(element_relation,complement(v)))* -> equal(power_class(v),successor_relation).
% 299.82/300.46  162179[10:Rew:160202.0,147001.1] || well_ordering(u,universal_class) -> equal(symmetric_difference(v,w),successor_relation) member(least(u,symmetric_difference(v,w)),union(v,w))*.
% 299.82/300.46  162175[10:Rew:160202.0,146997.1] || well_ordering(u,universal_class) -> equal(restrict(v,w,x),successor_relation) member(least(u,restrict(v,w,x)),v)*.
% 299.82/300.46  163527[10:Rew:160202.0,161426.2] || well_ordering(u,universal_class) member(least(u,regular(v)),v)* -> equal(regular(v),successor_relation) equal(v,successor_relation).
% 299.82/300.46  56513[2:MRR:56511.2,2450.0] || well_ordering(u,universal_class) subclass(singleton(least(u,v)),v) -> section(u,singleton(least(u,v)),v)*.
% 299.82/300.46  160691[10:Rew:160202.0,159708.3] inductive(regular(u)) || well_ordering(v,universal_class) member(least(v,regular(u)),u)* -> equal(u,successor_relation).
% 299.82/300.46  108252[2:Res:31069.2,1952.0] inductive(symmetric_difference(u,v)) || well_ordering(w,universal_class) -> member(least(w,symmetric_difference(u,v)),union(u,v))*.
% 299.82/300.46  108250[2:Res:31069.2,595.0] inductive(restrict(u,v,w)) || well_ordering(x,universal_class) -> member(least(x,restrict(u,v,w)),u)*.
% 299.82/300.46  159969[3:Res:159949.0,5832.1] inductive(complement(complement(ordinal_numbers))) || well_ordering(u,kind_1_ordinals) -> member(least(u,complement(complement(ordinal_numbers))),complement(complement(ordinal_numbers)))*.
% 299.82/300.46  163126[10:Rew:160202.0,160024.1] || well_ordering(u,kind_1_ordinals) -> equal(segment(u,restrict(ordinal_numbers,v,w),least(u,restrict(ordinal_numbers,v,w))),successor_relation)**.
% 299.82/300.46  163125[10:Rew:160202.0,160009.1] || well_ordering(u,kind_1_ordinals) -> equal(intersection(v,ordinal_numbers),successor_relation) member(least(u,intersection(v,ordinal_numbers)),intersection(v,ordinal_numbers))*.
% 299.82/300.46  163123[10:Rew:160202.0,159992.1] || well_ordering(u,kind_1_ordinals) -> equal(intersection(ordinal_numbers,v),successor_relation) member(least(u,intersection(ordinal_numbers,v)),intersection(ordinal_numbers,v))*.
% 299.82/300.46  163121[10:Rew:160202.0,159967.1] || well_ordering(u,kind_1_ordinals) -> equal(complement(complement(ordinal_numbers)),successor_relation) member(least(u,complement(complement(ordinal_numbers))),complement(complement(ordinal_numbers)))*.
% 299.82/300.46  159994[3:Res:159950.0,5832.1] inductive(intersection(ordinal_numbers,u)) || well_ordering(v,kind_1_ordinals) -> member(least(v,intersection(ordinal_numbers,u)),intersection(ordinal_numbers,u))*.
% 299.82/300.46  160011[3:Res:159951.0,5832.1] inductive(intersection(u,ordinal_numbers)) || well_ordering(v,kind_1_ordinals) -> member(least(v,intersection(u,ordinal_numbers)),intersection(u,ordinal_numbers))*.
% 299.82/300.46  163128[10:Rew:160202.0,160193.2] || member(u,ordinal_numbers) well_ordering(v,kind_1_ordinals) -> equal(segment(v,singleton(u),least(v,singleton(u))),successor_relation)**.
% 299.82/300.46  161971[10:Rew:160202.0,146926.1] || well_ordering(u,intersection(v,w)) -> equal(intersection(v,w),successor_relation) member(least(u,intersection(v,w)),v)*.
% 299.82/300.46  161972[10:Rew:160202.0,146925.1] || well_ordering(u,intersection(v,w)) -> equal(intersection(v,w),successor_relation) member(least(u,intersection(v,w)),w)*.
% 299.82/300.46  163518[10:Rew:160202.0,161083.2,160202.0,161083.0] || well_ordering(u,power_class(successor_relation)) member(least(u,power_class(successor_relation)),image(element_relation,universal_class))* -> equal(power_class(successor_relation),successor_relation).
% 299.82/300.46  108801[2:Res:31076.2,24.0] inductive(intersection(u,v)) || well_ordering(w,intersection(u,v)) -> member(least(w,intersection(u,v)),v)*.
% 299.82/300.46  108800[2:Res:31076.2,23.0] inductive(intersection(u,v)) || well_ordering(w,intersection(u,v)) -> member(least(w,intersection(u,v)),u)*.
% 299.82/300.46  162183[10:Rew:160202.0,147035.2] inductive(apply(u,v)) || member(image(u,singleton(v)),ordinal_numbers)* -> member(successor_relation,image(u,singleton(v))).
% 299.82/300.46  184013[14:MRR:183990.2,160227.0] || subclass(rest_relation,rotate(cross_product(universal_class,universal_class))) equal(sum_class(range_of(ordered_pair(u,rest_of(ordered_pair(v,u))))),v)** -> .
% 299.82/300.46  184012[14:MRR:183989.2,160227.0] || subclass(rest_relation,flip(cross_product(universal_class,universal_class)))* equal(sum_class(range_of(ordered_pair(u,v))),rest_of(ordered_pair(v,u)))** -> .
% 299.82/300.46  188308[10:Res:3595.3,183723.0] function(u) || member(v,universal_class) subclass(universal_class,symmetrization_of(successor_relation)) -> member(image(u,v),inverse(successor_relation))*.
% 299.82/300.46  188404[10:Rew:142543.0,188341.2] || equal(successor_relation,u) member(v,universal_class) -> member(v,symmetric_difference(universal_class,w))* member(v,union(w,u))*.
% 299.82/300.46  188844[10:Res:60.1,185065.1] || member(ordered_pair(u,singleton(v)),compose(w,x))* subclass(image(w,image(x,singleton(u))),successor_relation)* -> .
% 299.82/300.46  189378[15:Rew:189339.1,184864.2] || member(u,universal_class) subclass(domain_relation,regular(v)) member(ordered_pair(u,successor_relation),v)* -> equal(v,successor_relation).
% 299.82/300.46  189394[15:Rew:189339.1,28102.2] || member(u,universal_class) subclass(domain_relation,restrict(v,w,x))* -> member(ordered_pair(u,successor_relation),cross_product(w,x))*.
% 299.82/300.46  189396[15:Rew:189339.1,184837.2] || member(u,universal_class) subclass(domain_relation,intersection(v,w)) member(ordered_pair(u,successor_relation),symmetric_difference(v,w))* -> .
% 299.82/300.46  189404[15:Rew:189339.1,28109.2] || member(u,universal_class) subclass(domain_relation,image(element_relation,complement(v)))* member(ordered_pair(u,successor_relation),power_class(v))* -> .
% 299.82/300.46  190620[15:SpR:189514.1,10422.0] ||  -> equal(integer_of(restrict(cross_product(u,singleton(v)),w,x)),successor_relation)** equal(segment(cross_product(w,x),u,v),successor_relation).
% 299.82/300.46  190703[15:SpR:189515.1,10422.0] ||  -> equal(singleton(restrict(cross_product(u,singleton(v)),w,x)),successor_relation)** equal(segment(cross_product(w,x),u,v),successor_relation).
% 299.82/300.46  191096[20:Res:191074.1,3874.1] || equal(complement(intersection(u,v)),omega) member(successor_relation,union(u,v)) -> member(successor_relation,symmetric_difference(u,v))*.
% 299.82/300.46  192295[20:Res:3872.2,191095.1] || member(successor_relation,cross_product(u,v)) member(successor_relation,w) equal(complement(restrict(w,u,v)),omega)** -> .
% 299.82/300.46  192305[20:Res:60.1,191095.1] || member(ordered_pair(u,successor_relation),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),omega)** -> .
% 299.82/300.46  192549[10:Res:160250.0,162356.0] || subclass(domain_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(successor_relation,successor_relation),least(omega,domain_relation))),successor_relation)**.
% 299.82/300.46  192564[10:Res:999.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(v,w),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  192572[10:Res:13.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(unordered_pair(v,w),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  192588[11:Res:168387.0,162356.0] || subclass(inverse(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(successor_relation,least(omega,inverse(successor_relation)))),successor_relation)**.
% 299.82/300.46  192589[11:Res:168372.0,162356.0] || subclass(symmetrization_of(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(successor_relation,least(omega,symmetrization_of(successor_relation)))),successor_relation)**.
% 299.82/300.46  192590[10:Res:160453.0,162356.0] || subclass(successor(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(successor_relation,least(omega,successor(successor_relation)))),successor_relation)**.
% 299.82/300.46  192591[10:Res:160414.0,162356.0] || subclass(singleton(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(successor_relation,least(omega,singleton(successor_relation)))),successor_relation)**.
% 299.82/300.46  192615[11:Res:183757.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(symmetrization_of(successor_relation)),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  192985[10:Rew:181056.0,192966.0] || member(restrict(u,v,successor_relation),universal_class) -> member(ordered_pair(restrict(u,v,successor_relation),segment(u,v,universal_class)),domain_relation)*.
% 299.82/300.46  194083[10:Res:160784.3,193819.0] || member(u,universal_class) subclass(u,cantor(complement(cross_product(singleton(apply(choice,u)),universal_class))))* -> equal(u,successor_relation).
% 299.82/300.46  194092[10:Res:3595.3,193819.0] function(u) || member(v,universal_class) subclass(universal_class,cantor(complement(cross_product(singleton(image(u,v)),universal_class))))* -> .
% 299.82/300.46  194528[10:Res:160784.3,183398.0] || member(u,universal_class) subclass(u,complement(complement(v)))* -> equal(u,successor_relation) member(apply(choice,u),v).
% 299.82/300.46  194538[0:Res:3595.3,183398.0] function(u) || member(v,universal_class) subclass(universal_class,complement(complement(w)))* -> member(image(u,v),w)*.
% 299.82/300.46  195387[10:SpR:194805.1,161953.1] || subclass(inverse(u),u)* asymmetric(u,singleton(v)) -> equal(segment(inverse(u),singleton(v),v),successor_relation)**.
% 299.82/300.46  195771[10:Res:195710.1,160292.0] || equal(inverse(u),universal_class) well_ordering(v,inverse(u))* -> equal(w,successor_relation) member(least(v,w),w)*.
% 299.82/300.46  195772[10:Res:195710.1,160373.0] || equal(inverse(u),universal_class) well_ordering(v,inverse(u))* -> equal(segment(v,w,least(v,w)),successor_relation)**.
% 299.82/300.46  195773[6:Res:195710.1,5829.0] || equal(inverse(u),universal_class) well_ordering(v,inverse(u))* -> subclass(w,x)* member(least(v,w),w)*.
% 299.82/300.46  195774[6:Res:195710.1,5832.1] inductive(u) || equal(inverse(v),universal_class) well_ordering(w,inverse(v))* -> member(least(w,u),u)*.
% 299.82/300.46  195829[10:Res:195720.1,160292.0] || equal(sum_class(u),universal_class) well_ordering(v,sum_class(u))* -> equal(w,successor_relation) member(least(v,w),w)*.
% 299.82/300.46  195830[10:Res:195720.1,160373.0] || equal(sum_class(u),universal_class) well_ordering(v,sum_class(u))* -> equal(segment(v,w,least(v,w)),successor_relation)**.
% 299.82/300.46  195831[6:Res:195720.1,5829.0] || equal(sum_class(u),universal_class) well_ordering(v,sum_class(u))* -> subclass(w,x)* member(least(v,w),w)*.
% 299.82/300.46  195832[6:Res:195720.1,5832.1] inductive(u) || equal(sum_class(v),universal_class) well_ordering(w,sum_class(v))* -> member(least(w,u),u)*.
% 299.82/300.46  196576[10:SpL:161137.0,9322.0] || member(u,symmetric_difference(power_class(complement(inverse(successor_relation))),complement(v)))* -> member(u,union(image(element_relation,symmetrization_of(successor_relation)),v)).
% 299.82/300.46  196583[10:SpL:161137.0,9322.0] || member(u,symmetric_difference(complement(v),power_class(complement(inverse(successor_relation)))))* -> member(u,union(v,image(element_relation,symmetrization_of(successor_relation)))).
% 299.82/300.46  196782[10:SpL:162889.0,9322.0] || member(u,symmetric_difference(power_class(complement(singleton(successor_relation))),complement(v)))* -> member(u,union(image(element_relation,successor(successor_relation)),v)).
% 299.82/300.46  196789[10:SpL:162889.0,9322.0] || member(u,symmetric_difference(complement(v),power_class(complement(singleton(successor_relation)))))* -> member(u,union(v,image(element_relation,successor(successor_relation)))).
% 299.82/300.46  196917[10:SoR:182364.0,6317.2] single_valued_class(image(element_relation,universal_class)) || equal(image(element_relation,universal_class),cross_product(universal_class,universal_class)) -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.46  196943[13:SoR:183119.0,6317.2] single_valued_class(image(element_relation,successor_relation)) || equal(image(element_relation,successor_relation),cross_product(universal_class,universal_class)) -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.82/300.46  199803[10:SpR:161327.1,105.0] function(u) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),second(not_subclass_element(successor_relation,successor_relation))),single_valued3(u))**.
% 299.82/300.46  199840[10:SpR:161328.1,105.0] single_valued_class(u) ||  -> equal(domain__dfg(u,image(inverse(u),singleton(single_valued1(u))),second(not_subclass_element(successor_relation,successor_relation))),single_valued3(u))**.
% 299.82/300.46  199967[14:SpL:10417.0,184789.0] || member(sum_class(image(cross_product(u,v),w)),universal_class) member(restrict(cross_product(w,universal_class),u,v),universal_class)* -> .
% 299.82/300.46  199974[15:SpL:10417.0,189423.1] || member(restrict(cross_product(u,universal_class),v,w),universal_class)* equal(sum_class(image(cross_product(v,w),u)),successor_relation) -> .
% 299.82/300.46  200248[6:SpR:199964.0,28321.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(regular(rest_relation),rest_of(ordered_pair(second(regular(rest_relation)),first(regular(rest_relation))))),u)*.
% 299.82/300.46  200251[6:SpR:199964.0,18.2] || member(second(regular(rest_relation)),u) member(first(regular(rest_relation)),v) -> member(regular(rest_relation),cross_product(v,u))*.
% 299.82/300.46  200254[6:SpR:199964.0,28320.1] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(second(regular(rest_relation)),rest_of(regular(rest_relation))),first(regular(rest_relation))),u)*.
% 299.82/300.46  200255[6:SpR:199964.0,28321.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(second(regular(rest_relation)),first(regular(rest_relation))),rest_of(regular(rest_relation))),u)*.
% 299.82/300.46  200675[10:Res:161493.2,9300.0] inductive(symmetric_difference(u,cross_product(v,w))) ||  -> equal(integer_of(x),successor_relation) member(x,complement(restrict(u,v,w)))*.
% 299.82/300.46  200677[10:Res:161493.2,9306.0] inductive(symmetric_difference(cross_product(u,v),w)) ||  -> equal(integer_of(x),successor_relation) member(x,complement(restrict(w,u,v)))*.
% 299.82/300.46  200683[10:Res:161493.2,1351.0] inductive(cantor(restrict(u,v,singleton(w)))) ||  -> equal(integer_of(x),successor_relation) member(x,segment(u,v,w))*.
% 299.82/300.46  200759[10:Res:161493.2,2320.0] inductive(rest_of(u)) ||  -> equal(integer_of(singleton(singleton(singleton(v)))),successor_relation) equal(restrict(u,singleton(v),universal_class),v)**.
% 299.82/300.46  200791[10:Rew:185228.1,200692.3] inductive(ordered_pair(u,v)) ||  -> equal(integer_of(w),successor_relation)** equal(w,unordered_pair(u,singleton(v)))* equal(w,successor_relation).
% 299.82/300.46  201492[6:SpR:201355.0,28321.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(regular(domain_relation),rest_of(ordered_pair(second(regular(domain_relation)),first(regular(domain_relation))))),u)*.
% 299.82/300.46  201495[6:SpR:201355.0,18.2] || member(second(regular(domain_relation)),u) member(first(regular(domain_relation)),v) -> member(regular(domain_relation),cross_product(v,u))*.
% 299.82/300.46  201498[6:SpR:201355.0,28320.1] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(second(regular(domain_relation)),rest_of(regular(domain_relation))),first(regular(domain_relation))),u)*.
% 299.82/300.46  201499[6:SpR:201355.0,28321.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(second(regular(domain_relation)),first(regular(domain_relation))),rest_of(regular(domain_relation))),u)*.
% 299.82/300.46  201722[10:Res:161419.0,148657.1] || member(regular(complement(complement(complement(compose(element_relation,universal_class))))),element_relation)* -> equal(complement(complement(complement(compose(element_relation,universal_class)))),successor_relation).
% 299.82/300.46  201771[10:Rew:161137.0,201708.1] ||  -> member(regular(complement(power_class(complement(inverse(successor_relation))))),image(element_relation,symmetrization_of(successor_relation)))* equal(complement(power_class(complement(inverse(successor_relation)))),successor_relation).
% 299.82/300.46  201772[10:Rew:162889.0,201709.1] ||  -> member(regular(complement(power_class(complement(singleton(successor_relation))))),image(element_relation,successor(successor_relation)))* equal(complement(power_class(complement(singleton(successor_relation)))),successor_relation).
% 299.82/300.46  201854[14:SpL:44.0,184006.1] || member(restrict(u,v,universal_class),universal_class)* equal(rest_of(restrict(u,v,universal_class)),sum_class(image(u,v))) -> .
% 299.82/300.46  201932[10:Res:161492.2,513.0] || equal(intersection(complement(u),complement(v)),omega)** member(w,union(u,v))* -> equal(integer_of(w),successor_relation).
% 299.82/300.46  201962[10:Res:161492.2,179.1] || equal(u,omega) subclass(u,intersection(y__dfg,ordinal_numbers))* -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation)**.
% 299.82/300.46  202029[10:Res:161492.2,2031.0] || equal(compose_class(u),omega) -> equal(integer_of(singleton(singleton(singleton(v)))),successor_relation)** equal(compose(u,singleton(v)),v)**.
% 299.82/300.46  202461[10:SpR:505.0,163217.0] ||  -> member(successor_relation,image(element_relation,power_class(intersection(complement(u),complement(v)))))* member(successor_relation,power_class(image(element_relation,union(u,v)))).
% 299.82/300.46  204712[6:Rew:203192.0,203566.2] || section(universal_class,u,v) subclass(u,cantor(cross_product(v,u)))* -> equal(cantor(cross_product(v,u)),u).
% 299.82/300.46  203628[10:Rew:203192.0,199837.2] single_valued_class(u) || member(v,universal_class) -> member(v,cantor(w)) equal(single_valued2(u),range__dfg(w,v,universal_class))*.
% 299.82/300.46  203629[10:Rew:203192.0,199801.2] function(u) || member(v,universal_class) -> member(v,cantor(w)) equal(single_valued2(u),range__dfg(w,v,universal_class))*.
% 299.82/300.46  203666[6:Rew:203192.0,40941.0] || member(u,cantor(v)) subclass(rest_of(v),w) -> member(ordered_pair(u,restrict(v,u,universal_class)),w)*.
% 299.82/300.46  203895[10:Rew:203192.0,181182.0] || member(successor_relation,cantor(u)) equal(restrict(u,successor_relation,universal_class),universal_class) -> member(singleton(singleton(successor_relation)),rest_of(u))*.
% 299.82/300.46  203916[6:Rew:203192.0,47742.0] || member(u,cantor(u))* subclass(element_relation,v) well_ordering(w,v)* -> member(least(w,element_relation),element_relation)*.
% 299.82/300.46  203976[15:Rew:203192.0,200298.0] || member(first(regular(rest_relation)),cantor(u)) member(ordered_pair(u,regular(rest_relation)),cross_product(universal_class,cross_product(universal_class,universal_class)))* -> .
% 299.82/300.46  203983[15:Rew:203192.0,201542.0] || member(first(regular(domain_relation)),cantor(u)) member(ordered_pair(u,regular(domain_relation)),cross_product(universal_class,cross_product(universal_class,universal_class)))* -> .
% 299.82/300.46  204271[6:Rew:204206.0,149766.2] inductive(cantor(flip(cross_product(u,universal_class)))) || well_ordering(v,universal_class) -> member(least(v,inverse(u)),inverse(u))*.
% 299.82/300.46  204340[6:Rew:204278.0,149811.2] inductive(cantor(restrict(element_relation,universal_class,u))) || well_ordering(v,universal_class) -> member(least(v,sum_class(u)),sum_class(u))*.
% 299.82/300.46  206234[10:Res:206225.1,160373.0] || member(successor_relation,ordinal_numbers) well_ordering(u,kind_1_ordinals) -> equal(segment(u,successor(successor_relation),least(u,successor(successor_relation))),successor_relation)**.
% 299.82/300.46  206243[10:Res:206224.1,160373.0] || member(successor_relation,u) well_ordering(v,u)* -> equal(segment(v,successor(successor_relation),least(v,successor(successor_relation))),successor_relation)**.
% 299.82/300.46  206959[10:Res:206947.1,3874.1] || equal(complement(intersection(u,v)),kind_1_ordinals) member(successor_relation,union(u,v)) -> member(successor_relation,symmetric_difference(u,v))*.
% 299.82/300.46  207541[10:Res:206226.1,160373.0] || well_ordering(u,complement(v))* -> member(successor_relation,v) equal(segment(u,successor(successor_relation),least(u,successor(successor_relation))),successor_relation)**.
% 299.82/300.46  208225[10:Res:3872.2,206958.1] || member(successor_relation,cross_product(u,v)) member(successor_relation,w) equal(complement(restrict(w,u,v)),kind_1_ordinals)** -> .
% 299.82/300.46  208235[10:Res:60.1,206958.1] || member(ordered_pair(u,successor_relation),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),kind_1_ordinals)** -> .
% 299.82/300.46  208898[10:SpL:505.0,162918.1] || equal(image(element_relation,union(u,v)),successor(successor_relation)) equal(power_class(intersection(complement(u),complement(v))),universal_class)** -> .
% 299.82/300.46  209085[10:SpL:505.0,162872.1] || equal(image(element_relation,union(u,v)),singleton(successor_relation)) equal(power_class(intersection(complement(u),complement(v))),universal_class)** -> .
% 299.82/300.46  209513[12:SpR:209433.0,28321.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(regular(element_relation),rest_of(ordered_pair(second(regular(element_relation)),first(regular(element_relation))))),u)*.
% 299.82/300.46  209516[12:SpR:209433.0,18.2] || member(second(regular(element_relation)),u) member(first(regular(element_relation)),v) -> member(regular(element_relation),cross_product(v,u))*.
% 299.82/300.46  209519[12:SpR:209433.0,28320.1] || subclass(rest_relation,rotate(u)) -> member(ordered_pair(ordered_pair(second(regular(element_relation)),rest_of(regular(element_relation))),first(regular(element_relation))),u)*.
% 299.82/300.46  209520[12:SpR:209433.0,28321.1] || subclass(rest_relation,flip(u)) -> member(ordered_pair(ordered_pair(second(regular(element_relation)),first(regular(element_relation))),rest_of(regular(element_relation))),u)*.
% 299.82/300.46  209562[15:SpL:209433.0,203269.1] || member(first(regular(element_relation)),cantor(u)) member(ordered_pair(u,regular(element_relation)),cross_product(universal_class,cross_product(universal_class,universal_class)))* -> .
% 299.82/300.46  210335[15:SpR:161592.1,189563.1] || subclass(domain_relation,flip(u)) -> equal(cross_product(v,w),successor_relation) member(ordered_pair(regular(cross_product(v,w)),successor_relation),u)*.
% 299.82/300.46  210347[15:Res:189563.1,127.0] || subclass(domain_relation,flip(u)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  210365[15:Res:189563.1,9322.0] || subclass(domain_relation,flip(symmetric_difference(complement(u),complement(v)))) -> member(ordered_pair(ordered_pair(w,x),successor_relation),union(u,v))*.
% 299.82/300.46  210420[15:Res:189564.1,127.0] || subclass(domain_relation,rotate(u)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  210438[15:Res:189564.1,9322.0] || subclass(domain_relation,rotate(symmetric_difference(complement(u),complement(v)))) -> member(ordered_pair(ordered_pair(w,successor_relation),x),union(u,v))*.
% 299.82/300.46  210551[10:Res:160482.2,149475.0] || well_ordering(u,universal_class) subclass(universal_class,v) -> equal(cantor(w),successor_relation) member(least(u,cantor(w)),v)*.
% 299.82/300.46  210790[6:Res:31069.2,149475.0] inductive(cantor(u)) || well_ordering(v,universal_class) subclass(universal_class,w) -> member(least(v,cantor(u)),w)*.
% 299.82/300.46  211132[10:Res:161445.2,183398.0] || well_ordering(u,complement(complement(v))) -> equal(complement(complement(v)),successor_relation) member(least(u,complement(complement(v))),v)*.
% 299.82/300.46  211186[2:Res:31076.2,183398.0] inductive(complement(complement(u))) || well_ordering(v,complement(complement(u))) -> member(least(v,complement(complement(u))),u)*.
% 299.82/300.46  211503[10:Res:60.1,211446.0] || member(ordered_pair(u,singleton(successor_relation)),compose(v,w)) well_ordering(universal_class,image(v,image(w,singleton(u))))* -> .
% 299.82/300.46  211544[10:SpL:160367.0,161505.0] || member(regular(power_class(symmetric_difference(universal_class,u))),image(element_relation,union(u,successor_relation)))* -> equal(power_class(symmetric_difference(universal_class,u)),successor_relation).
% 299.82/300.46  211684[10:Res:181213.1,19.0] || equal(cross_product(u,v),singleton(singleton(successor_relation)))** -> equal(ordered_pair(first(singleton(successor_relation)),second(singleton(successor_relation))),singleton(successor_relation))**.
% 299.82/300.46  211688[10:Res:181213.1,9300.0] || equal(symmetric_difference(u,cross_product(v,w)),singleton(singleton(successor_relation))) -> member(singleton(successor_relation),complement(restrict(u,v,w)))*.
% 299.82/300.46  211690[10:Res:181213.1,9306.0] || equal(symmetric_difference(cross_product(u,v),w),singleton(singleton(successor_relation))) -> member(singleton(successor_relation),complement(restrict(w,u,v)))*.
% 299.82/300.46  211795[11:SpL:505.0,182321.1] || equal(image(element_relation,union(u,v)),inverse(successor_relation)) equal(power_class(intersection(complement(u),complement(v))),universal_class)** -> .
% 299.82/300.46  211951[10:SpR:505.0,183456.0] ||  -> equal(symmetric_difference(image(element_relation,power_class(intersection(complement(u),complement(v)))),complement(power_class(image(element_relation,union(u,v))))),successor_relation)**.
% 299.82/300.46  211969[11:Res:183759.1,127.0] || subclass(inverse(successor_relation),u) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  211986[11:Res:183759.1,9300.0] || subclass(inverse(successor_relation),symmetric_difference(u,cross_product(v,w))) -> member(regular(symmetrization_of(successor_relation)),complement(restrict(u,v,w)))*.
% 299.82/300.46  211988[11:Res:183759.1,9306.0] || subclass(inverse(successor_relation),symmetric_difference(cross_product(u,v),w)) -> member(regular(symmetrization_of(successor_relation)),complement(restrict(w,u,v)))*.
% 299.82/300.46  212048[2:SpR:505.0,184090.1] || equal(symmetric_difference(universal_class,image(element_relation,union(u,v))),universal_class) -> member(omega,power_class(intersection(complement(u),complement(v))))*.
% 299.82/300.46  212137[10:SpL:505.0,184637.0] || subclass(power_class(intersection(complement(u),complement(v))),successor_relation)* -> equal(symmetric_difference(universal_class,image(element_relation,union(u,v))),successor_relation).
% 299.82/300.46  212489[10:SpL:505.0,185801.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),successor_relation)** subclass(universal_class,image(element_relation,union(u,v))) -> .
% 299.82/300.46  212506[10:SpL:505.0,185935.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),successor_relation)** member(successor_relation,image(element_relation,union(u,v))) -> .
% 299.82/300.46  212866[10:SpL:505.0,186009.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),successor_relation)** member(omega,image(element_relation,union(u,v))) -> .
% 299.82/300.46  212982[10:SpL:505.0,187767.0] || subclass(universal_class,power_class(intersection(complement(u),complement(v))))* member(power_class(successor_relation),image(element_relation,union(u,v))) -> .
% 299.82/300.46  213001[10:SpL:9949.0,188181.1] || member(intersection(complement(u),complement(singleton(u))),universal_class)* equal(singleton(complement(image(element_relation,successor(u)))),successor_relation) -> .
% 299.82/300.46  213002[10:SpL:9948.0,188181.1] || member(intersection(complement(u),complement(inverse(u))),universal_class)* equal(singleton(complement(image(element_relation,symmetrization_of(u)))),successor_relation) -> .
% 299.82/300.46  213106[10:SpR:505.0,188444.1] || equal(symmetric_difference(universal_class,image(element_relation,union(u,v))),universal_class) -> member(successor_relation,power_class(intersection(complement(u),complement(v))))*.
% 299.82/300.46  213151[10:SpL:161137.0,160800.0] || subclass(u,power_class(complement(inverse(successor_relation)))) member(regular(u),image(element_relation,symmetrization_of(successor_relation)))* -> equal(u,successor_relation).
% 299.82/300.46  213152[10:SpL:162889.0,160800.0] || subclass(u,power_class(complement(singleton(successor_relation)))) member(regular(u),image(element_relation,successor(successor_relation)))* -> equal(u,successor_relation).
% 299.82/300.46  213178[10:Res:149580.1,160800.0] || connected(u,v) member(regular(cross_product(v,v)),complement(symmetrization_of(u)))* -> equal(cross_product(v,v),successor_relation).
% 299.82/300.46  213217[15:Res:189485.1,9300.0] || subclass(domain_relation,symmetric_difference(u,cross_product(v,w))) -> member(singleton(singleton(singleton(successor_relation))),complement(restrict(u,v,w)))*.
% 299.82/300.46  213219[15:Res:189485.1,9306.0] || subclass(domain_relation,symmetric_difference(cross_product(u,v),w)) -> member(singleton(singleton(singleton(successor_relation))),complement(restrict(w,u,v)))*.
% 299.82/300.46  213228[15:Res:189485.1,10.0] || subclass(domain_relation,unordered_pair(u,v))* -> equal(singleton(singleton(singleton(successor_relation))),v) equal(singleton(singleton(singleton(successor_relation))),u).
% 299.82/300.46  213604[15:SpL:9949.0,191623.1] || member(intersection(complement(u),complement(singleton(u))),universal_class)* equal(successor(complement(image(element_relation,successor(u)))),successor_relation) -> .
% 299.82/300.46  213605[15:SpL:9948.0,191623.1] || member(intersection(complement(u),complement(inverse(u))),universal_class)* equal(successor(complement(image(element_relation,symmetrization_of(u)))),successor_relation) -> .
% 299.82/300.46  213814[20:SpL:505.0,192317.1] || equal(image(element_relation,union(u,v)),inverse(successor_relation)) equal(power_class(intersection(complement(u),complement(v))),omega)** -> .
% 299.82/300.46  213828[20:SpL:505.0,192318.1] || equal(image(element_relation,union(u,v)),singleton(successor_relation)) equal(power_class(intersection(complement(u),complement(v))),omega)** -> .
% 299.82/300.46  213842[20:SpL:505.0,192319.1] || equal(image(element_relation,union(u,v)),successor(successor_relation)) equal(power_class(intersection(complement(u),complement(v))),omega)** -> .
% 299.82/300.46  214140[20:SpR:505.0,193270.1] || equal(symmetric_difference(universal_class,image(element_relation,union(u,v))),omega) -> member(successor_relation,power_class(intersection(complement(u),complement(v))))*.
% 299.82/300.46  214236[10:SpL:505.0,194513.0] || equal(complement(complement(power_class(intersection(complement(u),complement(v))))),successor_relation)** -> member(omega,image(element_relation,union(u,v))).
% 299.82/300.46  214266[10:SpL:505.0,194520.0] || subclass(universal_class,complement(power_class(intersection(complement(u),complement(v)))))* -> member(power_class(successor_relation),image(element_relation,union(u,v))).
% 299.82/300.46  214347[10:SpL:505.0,194540.0] || equal(complement(complement(power_class(intersection(complement(u),complement(v))))),successor_relation)** -> member(successor_relation,image(element_relation,union(u,v))).
% 299.82/300.46  214594[11:SpL:505.0,194541.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),inverse(successor_relation))** -> member(successor_relation,image(element_relation,union(u,v))).
% 299.82/300.46  214663[10:SpL:505.0,194542.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),singleton(successor_relation))** -> member(successor_relation,image(element_relation,union(u,v))).
% 299.82/300.46  214682[10:SpL:505.0,194543.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),successor(successor_relation))** -> member(successor_relation,image(element_relation,union(u,v))).
% 299.82/300.46  214702[11:SpL:505.0,194544.0] || equal(complement(power_class(intersection(complement(u),complement(v)))),symmetrization_of(successor_relation))** -> member(successor_relation,image(element_relation,union(u,v))).
% 299.82/300.46  214722[2:SpL:505.0,195403.0] || subclass(universal_class,power_class(intersection(complement(u),complement(v))))* -> equal(symmetric_difference(universal_class,image(element_relation,union(u,v))),universal_class).
% 299.82/300.46  215270[10:Rew:161843.0,215154.1] || member(not_subclass_element(intersection(image(element_relation,universal_class),u),successor_relation),power_class(successor_relation))* -> subclass(intersection(image(element_relation,universal_class),u),successor_relation).
% 299.82/300.46  215271[10:Rew:161845.0,215153.1] || member(not_subclass_element(intersection(u,image(element_relation,universal_class)),successor_relation),power_class(successor_relation))* -> subclass(intersection(u,image(element_relation,universal_class)),successor_relation).
% 299.82/300.46  215272[10:Rew:162291.0,215152.1] || member(not_subclass_element(intersection(complement(inverse(successor_relation)),u),successor_relation),symmetrization_of(successor_relation))* -> subclass(intersection(complement(inverse(successor_relation)),u),successor_relation).
% 299.82/300.46  215273[10:Rew:162292.0,215151.1] || member(not_subclass_element(intersection(u,complement(inverse(successor_relation))),successor_relation),symmetrization_of(successor_relation))* -> subclass(intersection(u,complement(inverse(successor_relation))),successor_relation).
% 299.82/300.46  215274[10:Rew:162944.0,215150.1] || member(not_subclass_element(intersection(u,complement(singleton(successor_relation))),successor_relation),successor(successor_relation))* -> subclass(intersection(u,complement(singleton(successor_relation))),successor_relation).
% 299.82/300.46  215275[10:Rew:162945.0,215149.1] || member(not_subclass_element(intersection(complement(singleton(successor_relation)),u),successor_relation),successor(successor_relation))* -> subclass(intersection(complement(singleton(successor_relation)),u),successor_relation).
% 299.82/300.46  215276[10:Rew:163001.0,215135.1] || member(not_subclass_element(intersection(image(element_relation,successor_relation),u),successor_relation),power_class(universal_class))* -> subclass(intersection(image(element_relation,successor_relation),u),successor_relation).
% 299.82/300.46  215277[10:Rew:163003.0,215134.1] || member(not_subclass_element(intersection(u,image(element_relation,successor_relation)),successor_relation),power_class(universal_class))* -> subclass(intersection(u,image(element_relation,successor_relation)),successor_relation).
% 299.82/300.46  215574[10:Res:161492.2,163021.0] || equal(omega,element_relation) -> equal(integer_of(regular(complement(compose(element_relation,universal_class)))),successor_relation)** equal(complement(compose(element_relation,universal_class)),successor_relation).
% 299.82/300.46  215880[10:Res:197082.1,9300.0] || subclass(universal_class,symmetric_difference(u,cross_product(v,w))) -> member(regular(complement(successor(successor_relation))),complement(restrict(u,v,w)))*.
% 299.82/300.46  215882[10:Res:197082.1,9306.0] || subclass(universal_class,symmetric_difference(cross_product(u,v),w)) -> member(regular(complement(successor(successor_relation))),complement(restrict(w,u,v)))*.
% 299.82/300.46  215948[10:Res:161492.2,163029.0] || equal(omega,ordinal_numbers) -> equal(integer_of(regular(intersection(u,complement(kind_1_ordinals)))),successor_relation)** equal(intersection(u,complement(kind_1_ordinals)),successor_relation).
% 299.82/300.46  216083[10:Res:161492.2,163027.0] || equal(omega,ordinal_numbers) -> equal(integer_of(regular(intersection(complement(kind_1_ordinals),u))),successor_relation)** equal(intersection(complement(kind_1_ordinals),u),successor_relation).
% 299.82/300.46  216121[6:Res:199830.1,9300.0] || equal(symmetric_difference(u,cross_product(v,w)),cross_product(universal_class,universal_class)) -> member(regular(rest_relation),complement(restrict(u,v,w)))*.
% 299.82/300.46  216123[6:Res:199830.1,9306.0] || equal(symmetric_difference(cross_product(u,v),w),cross_product(universal_class,universal_class)) -> member(regular(rest_relation),complement(restrict(w,u,v)))*.
% 299.82/300.46  216205[14:SpR:10417.0,199970.1] || member(restrict(cross_product(u,universal_class),v,w),universal_class)* -> equal(integer_of(sum_class(image(cross_product(v,w),u))),successor_relation).
% 299.82/300.46  216236[14:SpR:199971.1,15.0] || member(u,universal_class) -> equal(unordered_pair(successor_relation,unordered_pair(sum_class(range_of(u)),singleton(v))),ordered_pair(sum_class(range_of(u)),v))**.
% 299.82/300.46  216284[14:SpR:10417.0,199971.1] || member(restrict(cross_product(u,universal_class),v,w),universal_class)* -> equal(singleton(sum_class(image(cross_product(v,w),u))),successor_relation).
% 299.82/300.46  216326[14:SpL:199971.1,203272.1] || member(u,universal_class) member(sum_class(range_of(u)),cantor(v))* equal(restrict(v,successor_relation,universal_class),successor_relation) -> .
% 299.82/300.46  216391[14:Rew:142543.0,216227.1,160223.0,216227.1] || member(u,universal_class) -> equal(complement(image(element_relation,successor(sum_class(range_of(u))))),power_class(symmetric_difference(universal_class,sum_class(range_of(u)))))**.
% 299.82/300.46  216434[6:SpL:505.0,199982.0] || subclass(universal_class,power_class(intersection(complement(u),complement(v))))* member(regular(rest_relation),image(element_relation,union(u,v))) -> .
% 299.82/300.46  216453[6:SpL:505.0,199986.0] || subclass(universal_class,complement(power_class(intersection(complement(u),complement(v)))))* -> member(regular(rest_relation),image(element_relation,union(u,v))).
% 299.82/300.46  216729[6:Res:201220.1,9300.0] || equal(symmetric_difference(u,cross_product(v,w)),cross_product(universal_class,universal_class)) -> member(regular(domain_relation),complement(restrict(u,v,w)))*.
% 299.82/300.46  216731[6:Res:201220.1,9306.0] || equal(symmetric_difference(cross_product(u,v),w),cross_product(universal_class,universal_class)) -> member(regular(domain_relation),complement(restrict(w,u,v)))*.
% 299.82/300.46  216767[10:SpR:181082.0,143767.2] || member(image(u,successor_relation),universal_class)* subclass(universal_class,omega) -> equal(integer_of(apply(u,universal_class)),apply(u,universal_class)).
% 299.82/300.46  216816[6:SpL:505.0,201372.0] || subclass(universal_class,power_class(intersection(complement(u),complement(v))))* member(regular(domain_relation),image(element_relation,union(u,v))) -> .
% 299.82/300.46  216835[6:SpL:505.0,201376.0] || subclass(universal_class,complement(power_class(intersection(complement(u),complement(v)))))* -> member(regular(domain_relation),image(element_relation,union(u,v))).
% 299.82/300.46  216870[10:Res:161492.2,163343.0] || equal(u,omega) -> equal(integer_of(apply(choice,regular(u))),successor_relation)** equal(regular(u),successor_relation) equal(u,successor_relation).
% 299.82/300.46  216882[10:Rew:161277.1,216881.1] || member(apply(choice,u),intersection(v,singleton(u)))* -> equal(u,successor_relation) equal(intersection(v,singleton(u)),successor_relation).
% 299.82/300.46  216884[10:Rew:161284.1,216883.1] || member(apply(choice,u),intersection(singleton(u),v))* -> equal(u,successor_relation) equal(intersection(singleton(u),v),successor_relation).
% 299.82/300.46  217009[20:SpL:505.0,202875.1] || equal(image(element_relation,union(u,v)),omega) equal(power_class(intersection(complement(u),complement(v))),symmetrization_of(successor_relation))** -> .
% 299.82/300.46  217025[11:SpL:505.0,202881.1] || equal(image(element_relation,union(u,v)),universal_class) equal(power_class(intersection(complement(u),complement(v))),symmetrization_of(successor_relation))** -> .
% 299.82/300.46  217132[20:SpL:505.0,206075.1] || equal(image(element_relation,union(u,v)),omega) equal(power_class(intersection(complement(u),complement(v))),successor(successor_relation))** -> .
% 299.82/300.46  217149[10:SpL:505.0,206081.1] || equal(image(element_relation,union(u,v)),universal_class) equal(power_class(intersection(complement(u),complement(v))),successor(successor_relation))** -> .
% 299.82/300.46  217351[10:Res:161492.2,161700.0] || equal(u,omega) -> equal(integer_of(regular(intersection(complement(u),v))),successor_relation)** equal(intersection(complement(u),v),successor_relation).
% 299.82/300.46  217378[10:Rew:160367.0,217289.1] || member(regular(intersection(union(u,successor_relation),v)),symmetric_difference(universal_class,u))* -> equal(intersection(union(u,successor_relation),v),successor_relation).
% 299.82/300.46  217497[10:Res:161492.2,161380.0] || equal(u,omega) -> equal(integer_of(regular(intersection(v,complement(u)))),successor_relation)** equal(intersection(v,complement(u)),successor_relation).
% 299.82/300.46  217519[10:Rew:160367.0,217447.1] || member(regular(intersection(u,union(v,successor_relation))),symmetric_difference(universal_class,v))* -> equal(intersection(u,union(v,successor_relation)),successor_relation).
% 299.82/300.46  217566[10:Res:161492.2,160697.1] || equal(u,omega) subclass(universal_class,regular(u))* -> equal(integer_of(unordered_pair(v,w)),successor_relation)** equal(u,successor_relation).
% 299.82/300.46  217572[10:Res:6842.1,160697.1] || subclass(universal_class,symmetric_difference(u,v)) subclass(universal_class,regular(union(u,v)))* -> equal(union(u,v),successor_relation).
% 299.82/300.46  217591[10:MRR:217551.0,13.0] || subclass(universal_class,regular(union(u,v)))* -> member(unordered_pair(w,x),complement(v))* equal(union(u,v),successor_relation).
% 299.82/300.46  217592[10:MRR:217550.0,13.0] || subclass(universal_class,regular(union(u,v)))* -> member(unordered_pair(w,x),complement(u))* equal(union(u,v),successor_relation).
% 299.82/300.46  217648[10:Res:161492.2,1089.0] || equal(image(element_relation,complement(u)),omega) -> equal(integer_of(not_subclass_element(power_class(u),v)),successor_relation)** subclass(power_class(u),v).
% 299.82/300.46  217929[10:Res:161492.2,155811.1] || equal(omega,ordinal_numbers) subclass(u,complement(kind_1_ordinals)) -> equal(integer_of(not_subclass_element(u,v)),successor_relation)** subclass(u,v).
% 299.82/300.46  218004[10:SpR:195152.0,161690.1] ||  -> equal(symmetric_difference(u,intersection(u,v)),successor_relation) member(regular(symmetric_difference(u,intersection(u,v))),complement(intersection(u,v)))*.
% 299.82/300.46  218005[10:SpR:195339.0,161690.1] ||  -> equal(symmetric_difference(u,intersection(v,u)),successor_relation) member(regular(symmetric_difference(u,intersection(v,u))),complement(intersection(v,u)))*.
% 299.82/300.46  218289[10:Res:161492.2,160698.0] || equal(u,omega) -> equal(integer_of(not_subclass_element(regular(u),v)),successor_relation)** subclass(regular(u),v) equal(u,successor_relation).
% 299.82/300.46  218314[10:Rew:161277.1,218313.1] || member(not_subclass_element(u,v),intersection(w,singleton(u)))* -> subclass(u,v) equal(intersection(w,singleton(u)),successor_relation).
% 299.82/300.46  218316[10:Rew:161284.1,218315.1] || member(not_subclass_element(u,v),intersection(singleton(u),w))* -> subclass(u,v) equal(intersection(singleton(u),w),successor_relation).
% 299.82/300.46  218355[10:Res:218298.0,160373.0] || well_ordering(u,complement(v)) -> equal(v,successor_relation) equal(segment(u,regular(v),least(u,regular(v))),successor_relation)**.
% 299.82/300.46  218559[2:Res:141787.0,9636.1] || subclass(u,complement(inverse(singleton(not_subclass_element(u,v)))))* -> asymmetric(singleton(not_subclass_element(u,v)),w)* subclass(u,v).
% 299.82/300.46  218568[10:Res:161492.2,9636.1] || equal(u,omega) subclass(v,complement(u))* -> equal(integer_of(not_subclass_element(v,w)),successor_relation)** subclass(v,w).
% 299.82/300.46  218743[3:Obv:218698.2] || subclass(intersection(singleton(u),v),complement(kind_1_ordinals))* member(u,ordinal_numbers) -> subclass(intersection(singleton(u),v),w)*.
% 299.82/300.46  218770[10:Res:218493.1,160373.0] || well_ordering(u,complement(ordinal_numbers)) -> member(v,kind_1_ordinals) equal(segment(u,singleton(v),least(u,singleton(v))),successor_relation)**.
% 299.82/300.46  218853[3:Obv:218811.2] || subclass(intersection(u,singleton(v)),complement(kind_1_ordinals))* member(v,ordinal_numbers) -> subclass(intersection(u,singleton(v)),w)*.
% 299.82/300.46  218909[22:Res:218867.1,2142.0] || subclass(kind_1_ordinals,ordered_pair(u,v))* -> equal(unordered_pair(u,singleton(v)),singleton(successor_relation)) equal(singleton(successor_relation),singleton(u)).
% 299.82/300.46  219085[10:Res:218473.1,160292.0] || equal(complement(kind_1_ordinals),u) well_ordering(v,complement(ordinal_numbers)) -> equal(u,successor_relation) member(least(v,u),u)*.
% 299.82/300.46  219086[10:Res:218473.1,160373.0] || equal(complement(kind_1_ordinals),u) well_ordering(v,complement(ordinal_numbers)) -> equal(segment(v,u,least(v,u)),successor_relation)**.
% 299.82/300.46  219087[3:Res:218473.1,5829.0] || equal(complement(kind_1_ordinals),u) well_ordering(v,complement(ordinal_numbers)) -> subclass(u,w)* member(least(v,u),u)*.
% 299.82/300.46  219088[3:Res:218473.1,5832.1] inductive(u) || equal(complement(kind_1_ordinals),u) well_ordering(v,complement(ordinal_numbers)) -> member(least(v,u),u)*.
% 299.82/300.46  219195[10:Res:160784.3,218628.0] || member(u,universal_class) subclass(u,complement(kind_1_ordinals)) -> equal(u,successor_relation) member(apply(choice,u),complement(ordinal_numbers))*.
% 299.82/300.46  219217[3:Res:3595.3,218628.0] function(u) || member(v,universal_class) subclass(universal_class,complement(kind_1_ordinals)) -> member(image(u,v),complement(ordinal_numbers))*.
% 299.82/300.46  219582[0:Res:978.1,183398.0] ||  -> subclass(restrict(complement(complement(u)),v,w),x) member(not_subclass_element(restrict(complement(complement(u)),v,w),x),u)*.
% 299.82/300.46  215278[10:Rew:163252.0,215099.1] || member(not_subclass_element(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),successor_relation),complement(kind_1_ordinals))* -> subclass(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),successor_relation).
% 299.82/300.46  163583[10:Rew:160305.0,162828.1] || member(u,universal_class) subclass(rest_relation,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(ordered_pair(u,rest_of(u)),kind_1_ordinals)*.
% 299.82/300.46  163610[10:Rew:160202.0,162817.1,160305.0,162817.1,160305.0,162817.0] ||  -> subclass(u,complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))) member(not_subclass_element(u,complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),kind_1_ordinals)*.
% 299.82/300.46  160652[10:Rew:160202.0,146346.1] || asymmetric(cross_product(u,v),universal_class) -> equal(image(restrict(inverse(cross_product(u,v)),u,v),universal_class),range_of(successor_relation))**.
% 299.82/300.46  193778[10:SpR:193730.0,3595.3] function(complement(cross_product(u,universal_class))) || member(u,universal_class)* subclass(universal_class,v) -> member(range_of(successor_relation),v)*.
% 299.82/300.46  163515[10:Rew:160202.0,160630.0] || member(ordered_pair(u,v),compose(w,successor_relation))* subclass(image(w,range_of(successor_relation)),x)* -> member(v,x)*.
% 299.82/300.46  193780[10:SpR:193730.0,60.1] || member(ordered_pair(u,v),compose(w,complement(cross_product(singleton(u),universal_class))))* -> member(v,image(w,range_of(successor_relation))).
% 299.82/300.46  193784[10:SpR:193730.0,60.1] || member(ordered_pair(u,v),compose(complement(cross_product(image(w,singleton(u)),universal_class)),w))* -> member(v,range_of(successor_relation)).
% 299.82/300.46  213003[10:SpL:163369.0,188181.1] || member(intersection(complement(singleton(successor_relation)),complement(range_of(successor_relation))),universal_class)* equal(singleton(complement(image(element_relation,kind_1_ordinals))),successor_relation) -> .
% 299.82/300.46  213606[15:SpL:163369.0,191623.1] || member(intersection(complement(singleton(successor_relation)),complement(range_of(successor_relation))),universal_class)* equal(successor(complement(image(element_relation,kind_1_ordinals))),successor_relation) -> .
% 299.82/300.46  184385[10:Rew:160305.0,184376.2] single_valued_class(image(successor_relation,cross_product(universal_class,universal_class))) || member(successor_relation,cross_product(universal_class,universal_class))* equal(range_of(successor_relation),successor_relation) -> .
% 299.82/300.46  204718[10:Rew:203192.0,203942.1] ||  -> equal(apply(u,not_subclass_element(v,intersection(cantor(u),v))),sum_class(range_of(successor_relation)))** subclass(v,intersection(cantor(u),v)).
% 299.82/300.46  203669[10:Rew:203192.0,160593.0] || subclass(u,complement(cantor(v))) -> equal(apply(v,not_subclass_element(u,w)),sum_class(range_of(successor_relation)))** subclass(u,w).
% 299.82/300.46  160591[10:Rew:160202.0,146291.2] || member(u,universal_class) -> member(u,sum_class(v)) equal(apply(restrict(element_relation,universal_class,v),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  160592[10:Rew:160202.0,146295.2] || member(u,universal_class) -> member(u,inverse(v)) equal(apply(flip(cross_product(v,universal_class)),u),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  221438[10:Res:218373.0,160292.0] || well_ordering(u,complement(singleton(v)))* -> equal(singleton(v),successor_relation) equal(v,successor_relation) member(least(u,v),v)*.
% 299.82/300.46  221439[10:Res:218373.0,160373.0] || well_ordering(u,complement(singleton(v))) -> equal(singleton(v),successor_relation) equal(segment(u,v,least(u,v)),successor_relation)**.
% 299.82/300.46  221440[10:Res:218373.0,5829.0] || well_ordering(u,complement(singleton(v)))* -> equal(singleton(v),successor_relation) subclass(v,w)* member(least(u,v),v)*.
% 299.82/300.46  221441[10:Res:218373.0,5832.1] inductive(u) || well_ordering(v,complement(singleton(u)))* -> equal(singleton(u),successor_relation) member(least(v,u),u)*.
% 299.82/300.46  221507[10:Res:218373.0,1487.1] || member(u,universal_class) -> equal(singleton(complement(v)),successor_relation) member(u,v) member(u,complement(singleton(complement(v))))*.
% 299.82/300.46  221564[10:Res:161493.2,157891.0] inductive(element_relation) ||  -> equal(integer_of(not_subclass_element(complement(compose(element_relation,universal_class)),u)),successor_relation)** subclass(complement(compose(element_relation,universal_class)),u).
% 299.82/300.46  221588[10:Res:161493.2,162951.1] inductive(ordinal_numbers) || well_ordering(u,universal_class) -> equal(integer_of(least(u,complement(kind_1_ordinals))),successor_relation)** equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.46  221604[10:Res:3907.1,185698.1] inductive(singleton(u)) || equal(complement(complement(ordinal_numbers)),universal_class) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221620[10:Res:51387.0,185698.1] inductive(not_subclass_element(u,complement(ordinal_numbers))) ||  -> subclass(u,complement(ordinal_numbers))* equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221641[10:Res:161493.2,185698.1] inductive(ordinal_numbers) inductive(u) ||  -> equal(integer_of(u),successor_relation)** equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221643[15:Res:189485.1,185698.1] inductive(singleton(singleton(singleton(successor_relation)))) || subclass(domain_relation,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221645[10:Res:181213.1,185698.1] inductive(singleton(successor_relation)) || equal(singleton(singleton(successor_relation)),ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221658[11:Res:183759.1,185698.1] inductive(regular(symmetrization_of(successor_relation))) || subclass(inverse(successor_relation),ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221660[10:Res:197082.1,185698.1] inductive(regular(complement(successor(successor_relation)))) || subclass(universal_class,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221663[10:Res:199830.1,185698.1] inductive(regular(rest_relation)) || equal(cross_product(universal_class,universal_class),ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221666[10:Res:201220.1,185698.1] inductive(regular(domain_relation)) || equal(cross_product(universal_class,universal_class),ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221686[15:Res:161493.2,189406.2] inductive(ordinal_numbers) || member(u,universal_class) subclass(domain_relation,complement(kind_1_ordinals)) -> equal(integer_of(ordered_pair(u,successor_relation)),successor_relation)**.
% 299.82/300.46  221816[10:Res:161493.2,161795.0] inductive(power_class(u)) ||  -> equal(integer_of(regular(image(element_relation,complement(u)))),successor_relation)** equal(image(element_relation,complement(u)),successor_relation).
% 299.82/300.46  221912[14:Rew:200028.1,221902.1] || member(u,universal_class)* equal(range_of(u),successor(successor_relation)) member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> .
% 299.82/300.46  221913[15:Rew:190721.0,221901.0] || equal(successor(successor_relation),inverse(u)) member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> equal(range_of(u),successor_relation)**.
% 299.82/300.46  221914[10:Rew:181044.1,221900.1] || member(u,universal_class)* equal(successor(successor_relation),successor(u)) member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> .
% 299.82/300.46  221948[10:Res:161493.2,33515.1] inductive(u) || member(u,universal_class) -> equal(integer_of(singleton(u)),successor_relation) member(singleton(singleton(singleton(u))),element_relation)*.
% 299.82/300.46  221977[10:SpL:185302.1,986.1] || equal(successor_relation,u) member(v,image(element_relation,power_class(u)))* member(v,power_class(image(element_relation,universal_class))) -> .
% 299.82/300.46  222033[10:Res:161493.2,986.1] inductive(power_class(image(element_relation,complement(u)))) || member(v,image(element_relation,power_class(u)))* -> equal(integer_of(v),successor_relation).
% 299.82/300.46  222034[15:Res:189485.1,986.1] || subclass(domain_relation,power_class(image(element_relation,complement(u)))) member(singleton(singleton(singleton(successor_relation))),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  222036[10:Res:181213.1,986.1] || equal(power_class(image(element_relation,complement(u))),singleton(singleton(successor_relation))) member(singleton(successor_relation),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  222049[11:Res:183759.1,986.1] || subclass(inverse(successor_relation),power_class(image(element_relation,complement(u))))* member(regular(symmetrization_of(successor_relation)),image(element_relation,power_class(u))) -> .
% 299.82/300.46  222051[10:Res:197082.1,986.1] || subclass(universal_class,power_class(image(element_relation,complement(u)))) member(regular(complement(successor(successor_relation))),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  222054[6:Res:199830.1,986.1] || equal(power_class(image(element_relation,complement(u))),cross_product(universal_class,universal_class)) member(regular(rest_relation),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  222057[6:Res:201220.1,986.1] || equal(power_class(image(element_relation,complement(u))),cross_product(universal_class,universal_class)) member(regular(domain_relation),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  222094[10:Res:161493.2,155808.0] inductive(ordinal_numbers) ||  -> equal(integer_of(not_subclass_element(intersection(complement(kind_1_ordinals),u),v)),successor_relation)** subclass(intersection(complement(kind_1_ordinals),u),v).
% 299.82/300.46  222125[10:SpR:161592.1,221525.0] ||  -> equal(cross_product(u,v),successor_relation) member(singleton(first(regular(cross_product(u,v)))),complement(singleton(regular(cross_product(u,v)))))*.
% 299.82/300.46  222187[10:Res:161493.2,155810.0] inductive(ordinal_numbers) ||  -> equal(integer_of(not_subclass_element(intersection(u,complement(kind_1_ordinals)),v)),successor_relation)** subclass(intersection(u,complement(kind_1_ordinals)),v).
% 299.82/300.46  222222[10:SpL:161592.1,222147.0] || member(singleton(first(regular(cross_product(u,v)))),singleton(regular(cross_product(u,v))))* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.46  222288[15:Res:161493.2,189380.2] inductive(u) || member(v,universal_class) subclass(domain_relation,complement(u))* -> equal(integer_of(ordered_pair(v,successor_relation)),successor_relation)**.
% 299.82/300.46  222308[15:MRR:222260.2,34067.1] || member(u,cantor(v)) equal(restrict(v,u,universal_class),successor_relation)** subclass(domain_relation,complement(rest_of(v)))* -> .
% 299.82/300.46  223143[24:Res:223096.0,160373.0] || well_ordering(u,symmetric_difference(universal_class,kind_1_ordinals)) -> equal(segment(u,complement(successor(kind_1_ordinals)),least(u,complement(successor(kind_1_ordinals)))),successor_relation)**.
% 299.82/300.46  223269[24:SpR:222479.0,203278.2] || member(u,cantor(v)) equal(restrict(v,u,universal_class),kind_1_ordinals) -> member(ordered_pair(u,universal_class),rest_of(v))*.
% 299.82/300.46  224369[25:Rew:224236.1,204734.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,successor_relation)*.
% 299.82/300.46  224370[25:Rew:224236.1,204733.2] function(u) || equal(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,w)*.
% 299.82/300.46  224371[25:Rew:224236.1,204732.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,omega)*.
% 299.82/300.46  224508[25:Rew:224236.1,224274.2] function(range_of(u)) function(v) || equal(cantor(cantor(w)),universal_class) -> compatible(v,w,inverse(u))*.
% 299.82/300.46  224716[25:SpL:224236.1,203329.1] function(restrict(u,v,w)) || subclass(w,v) subclass(universal_class,w) -> section(u,w,v)*.
% 299.82/300.46  224717[25:SpL:224236.1,203334.0] function(restrict(u,v,w)) || equal(universal_class,w) subclass(w,v) -> section(u,w,v)*.
% 299.82/300.46  224915[25:SpR:224739.1,60.1] function(u) || member(ordered_pair(u,v),compose(w,x))* -> member(v,image(w,image(x,successor_relation))).
% 299.82/300.46  225828[10:Res:161493.2,3627.0] inductive(composition_function) ||  -> equal(integer_of(ordered_pair(u,singleton(singleton(singleton(v))))),successor_relation)** equal(compose(u,singleton(v)),v).
% 299.82/300.46  225964[10:Res:161493.2,161867.1] inductive(u) || well_ordering(v,universal_class) -> equal(integer_of(least(v,complement(u))),successor_relation)** equal(complement(u),successor_relation).
% 299.82/300.46  226005[15:SpL:161.0,189381.1] || member(u,universal_class) subclass(domain_relation,symmetric_difference(v,w)) -> member(ordered_pair(u,successor_relation),complement(intersection(v,w)))*.
% 299.82/300.46  226037[15:SpL:161194.0,189381.1] || member(u,universal_class) subclass(domain_relation,symmetric_difference(complement(v),universal_class)) -> member(ordered_pair(u,successor_relation),union(v,successor_relation))*.
% 299.82/300.46  226355[25:Rew:226350.1,40343.1] one_to_one(flip(cross_product(u,universal_class))) || subclass(universal_class,v) -> maps(flip(cross_product(u,universal_class)),inverse(u),v)*.
% 299.82/300.46  226359[25:Rew:226350.1,40432.1] one_to_one(restrict(element_relation,universal_class,u)) || subclass(universal_class,v) -> maps(restrict(element_relation,universal_class,u),sum_class(u),v)*.
% 299.82/300.46  226577[10:Res:161880.1,218628.0] ||  -> equal(intersection(intersection(complement(kind_1_ordinals),u),v),successor_relation) member(regular(intersection(intersection(complement(kind_1_ordinals),u),v)),complement(ordinal_numbers))*.
% 299.82/300.46  226578[10:Res:161880.1,141576.1] || member(regular(intersection(intersection(complement(kind_1_ordinals),u),v)),ordinal_numbers)* -> equal(intersection(intersection(complement(kind_1_ordinals),u),v),successor_relation).
% 299.82/300.46  226595[10:Res:161880.1,183723.0] ||  -> equal(intersection(intersection(symmetrization_of(successor_relation),u),v),successor_relation) member(regular(intersection(intersection(symmetrization_of(successor_relation),u),v)),inverse(successor_relation))*.
% 299.82/300.46  226597[10:Res:161880.1,183622.0] ||  -> equal(intersection(intersection(successor(successor_relation),u),v),successor_relation) member(regular(intersection(intersection(successor(successor_relation),u),v)),singleton(successor_relation))*.
% 299.82/300.46  227168[10:Res:161881.1,218628.0] ||  -> equal(intersection(intersection(u,complement(kind_1_ordinals)),v),successor_relation) member(regular(intersection(intersection(u,complement(kind_1_ordinals)),v)),complement(ordinal_numbers))*.
% 299.82/300.46  227169[10:Res:161881.1,141576.1] || member(regular(intersection(intersection(u,complement(kind_1_ordinals)),v)),ordinal_numbers)* -> equal(intersection(intersection(u,complement(kind_1_ordinals)),v),successor_relation).
% 299.82/300.46  227186[10:Res:161881.1,183723.0] ||  -> equal(intersection(intersection(u,symmetrization_of(successor_relation)),v),successor_relation) member(regular(intersection(intersection(u,symmetrization_of(successor_relation)),v)),inverse(successor_relation))*.
% 299.82/300.46  227188[10:Res:161881.1,183622.0] ||  -> equal(intersection(intersection(u,successor(successor_relation)),v),successor_relation) member(regular(intersection(intersection(u,successor(successor_relation)),v)),singleton(successor_relation))*.
% 299.82/300.46  227316[25:SpR:161592.1,224913.1] function(first(regular(cross_product(u,v)))) ||  -> equal(cross_product(u,v),successor_relation) member(successor_relation,regular(cross_product(u,v)))*.
% 299.82/300.46  227464[10:Res:161874.1,218628.0] ||  -> equal(intersection(u,intersection(complement(kind_1_ordinals),v)),successor_relation) member(regular(intersection(u,intersection(complement(kind_1_ordinals),v))),complement(ordinal_numbers))*.
% 299.82/300.46  227465[10:Res:161874.1,141576.1] || member(regular(intersection(u,intersection(complement(kind_1_ordinals),v))),ordinal_numbers)* -> equal(intersection(u,intersection(complement(kind_1_ordinals),v)),successor_relation).
% 299.82/300.46  227482[10:Res:161874.1,183723.0] ||  -> equal(intersection(u,intersection(symmetrization_of(successor_relation),v)),successor_relation) member(regular(intersection(u,intersection(symmetrization_of(successor_relation),v))),inverse(successor_relation))*.
% 299.82/300.46  227484[10:Res:161874.1,183622.0] ||  -> equal(intersection(u,intersection(successor(successor_relation),v)),successor_relation) member(regular(intersection(u,intersection(successor(successor_relation),v))),singleton(successor_relation))*.
% 299.82/300.46  228070[10:Res:161875.1,218628.0] ||  -> equal(intersection(u,intersection(v,complement(kind_1_ordinals))),successor_relation) member(regular(intersection(u,intersection(v,complement(kind_1_ordinals)))),complement(ordinal_numbers))*.
% 299.82/300.46  228071[10:Res:161875.1,141576.1] || member(regular(intersection(u,intersection(v,complement(kind_1_ordinals)))),ordinal_numbers)* -> equal(intersection(u,intersection(v,complement(kind_1_ordinals))),successor_relation).
% 299.82/300.46  228088[10:Res:161875.1,183723.0] ||  -> equal(intersection(u,intersection(v,symmetrization_of(successor_relation))),successor_relation) member(regular(intersection(u,intersection(v,symmetrization_of(successor_relation)))),inverse(successor_relation))*.
% 299.82/300.46  228090[10:Res:161875.1,183622.0] ||  -> equal(intersection(u,intersection(v,successor(successor_relation))),successor_relation) member(regular(intersection(u,intersection(v,successor(successor_relation)))),singleton(successor_relation))*.
% 299.82/300.46  228873[24:Rew:223107.0,228802.0] ||  -> equal(intersection(symmetric_difference(complement(kind_1_ordinals),universal_class),u),successor_relation) member(regular(intersection(symmetric_difference(complement(kind_1_ordinals),universal_class),u)),successor(kind_1_ordinals))*.
% 299.82/300.46  228874[24:Rew:223107.0,228805.0] ||  -> equal(intersection(u,symmetric_difference(complement(kind_1_ordinals),universal_class)),successor_relation) member(regular(intersection(u,symmetric_difference(complement(kind_1_ordinals),universal_class))),successor(kind_1_ordinals))*.
% 299.82/300.46  228875[24:Rew:223107.0,228807.1] || subclass(successor(kind_1_ordinals),u) -> equal(symmetric_difference(complement(kind_1_ordinals),universal_class),successor_relation) member(regular(symmetric_difference(complement(kind_1_ordinals),universal_class)),u)*.
% 299.82/300.46  228968[10:Res:218494.0,160788.0] || subclass(complement(ordinal_numbers),u) -> equal(complement(complement(complement(kind_1_ordinals))),successor_relation) member(regular(complement(complement(complement(kind_1_ordinals)))),u)*.
% 299.82/300.46  228970[10:Res:218475.0,160788.0] || subclass(complement(ordinal_numbers),u) -> equal(intersection(complement(kind_1_ordinals),v),successor_relation) member(regular(intersection(complement(kind_1_ordinals),v)),u)*.
% 299.82/300.46  228971[10:Res:218485.0,160788.0] || subclass(complement(ordinal_numbers),u) -> equal(intersection(v,complement(kind_1_ordinals)),successor_relation) member(regular(intersection(v,complement(kind_1_ordinals))),u)*.
% 299.82/300.46  228978[10:Res:221565.0,160788.0] || subclass(complement(element_relation),u) -> equal(complement(compose(element_relation,universal_class)),successor_relation) member(regular(complement(compose(element_relation,universal_class))),u)*.
% 299.82/300.46  228987[10:Res:218370.0,160788.0] || subclass(successor(successor_relation),u) -> equal(regular(complement(singleton(successor_relation))),successor_relation) member(regular(regular(complement(singleton(successor_relation)))),u)*.
% 299.82/300.46  228988[13:Res:218371.0,160788.0] || subclass(power_class(universal_class),u) -> equal(regular(image(element_relation,successor_relation)),successor_relation) member(regular(regular(image(element_relation,successor_relation))),u)*.
% 299.82/300.46  228989[10:Res:218372.0,160788.0] || subclass(power_class(successor_relation),u) -> equal(regular(image(element_relation,universal_class)),successor_relation) member(regular(regular(image(element_relation,universal_class))),u)*.
% 299.82/300.46  229047[10:Res:228991.1,2142.0] || subclass(kind_1_ordinals,ordered_pair(u,v))* -> equal(unordered_pair(u,singleton(v)),regular(ordinal_numbers)) equal(regular(ordinal_numbers),singleton(u)).
% 299.82/300.46  229396[20:Res:217226.1,9482.0] || equal(singleton(not_subclass_element(intersection(complement(singleton(successor_relation)),u),v)),omega)** -> subclass(intersection(complement(singleton(successor_relation)),u),v).
% 299.82/300.46  229397[10:Res:217225.1,9482.0] || equal(singleton(not_subclass_element(intersection(complement(singleton(successor_relation)),u),v)),kind_1_ordinals)** -> subclass(intersection(complement(singleton(successor_relation)),u),v).
% 299.82/300.46  229400[10:Res:161493.2,9482.0] inductive(u) ||  -> equal(integer_of(not_subclass_element(intersection(complement(u),v),w)),successor_relation)** subclass(intersection(complement(u),v),w).
% 299.82/300.46  229562[20:Res:217226.1,9368.0] || equal(singleton(not_subclass_element(intersection(u,complement(singleton(successor_relation))),v)),omega)** -> subclass(intersection(u,complement(singleton(successor_relation))),v).
% 299.82/300.46  229563[10:Res:217225.1,9368.0] || equal(singleton(not_subclass_element(intersection(u,complement(singleton(successor_relation))),v)),kind_1_ordinals)** -> subclass(intersection(u,complement(singleton(successor_relation))),v).
% 299.82/300.46  229566[10:Res:161493.2,9368.0] inductive(u) ||  -> equal(integer_of(not_subclass_element(intersection(v,complement(u)),w)),successor_relation)** subclass(intersection(v,complement(u)),w).
% 299.82/300.46  229823[10:Res:221521.1,161700.0] ||  -> equal(integer_of(regular(intersection(complement(complement(singleton(omega))),u))),successor_relation)** equal(intersection(complement(complement(singleton(omega))),u),successor_relation).
% 299.82/300.46  229824[10:Res:221521.1,161380.0] ||  -> equal(integer_of(regular(intersection(u,complement(complement(singleton(omega)))))),successor_relation)** equal(intersection(u,complement(complement(singleton(omega)))),successor_relation).
% 299.82/300.46  229903[24:SpR:223107.0,9529.1] ||  -> subclass(symmetric_difference(successor(kind_1_ordinals),universal_class),u) member(not_subclass_element(symmetric_difference(successor(kind_1_ordinals),universal_class),u),complement(symmetric_difference(complement(kind_1_ordinals),universal_class)))*.
% 299.82/300.46  230524[10:Res:160784.3,229800.0] || member(u,universal_class) subclass(u,singleton(omega)) -> equal(u,successor_relation) equal(integer_of(apply(choice,u)),successor_relation)**.
% 299.82/300.46  230910[10:SpR:10028.0,183420.0] ||  -> equal(symmetric_difference(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),complement(symmetrization_of(image(element_relation,complement(u))))),successor_relation)**.
% 299.82/300.46  231232[10:SpR:10029.0,183420.0] ||  -> equal(symmetric_difference(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),complement(successor(image(element_relation,complement(u))))),successor_relation)**.
% 299.82/300.46  231766[10:SpL:160419.0,161035.0] || member(u,intersection(power_class(successor_relation),successor(successor_relation))) member(u,union(image(element_relation,universal_class),complement(singleton(successor_relation))))* -> .
% 299.82/300.46  231767[10:SpL:160336.0,161035.0] || member(u,intersection(power_class(successor_relation),symmetrization_of(successor_relation))) member(u,union(image(element_relation,universal_class),complement(inverse(successor_relation))))* -> .
% 299.82/300.46  231773[10:SpL:160322.0,161035.0] || member(u,intersection(power_class(successor_relation),power_class(universal_class))) member(u,union(image(element_relation,universal_class),image(element_relation,successor_relation)))* -> .
% 299.82/300.46  231802[10:Res:1476.1,161035.0] || subclass(universal_class,intersection(power_class(successor_relation),complement(u))) member(unordered_pair(v,w),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231805[10:Res:25.2,161035.0] || member(u,complement(v)) member(u,power_class(successor_relation)) member(u,union(image(element_relation,universal_class),v))* -> .
% 299.82/300.46  231824[10:Res:1499.1,161035.0] || subclass(universal_class,intersection(power_class(successor_relation),complement(u))) member(ordered_pair(v,w),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231825[10:Res:160251.1,161035.0] || subclass(domain_relation,intersection(power_class(successor_relation),complement(u))) member(ordered_pair(successor_relation,successor_relation),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231845[11:Res:183764.1,161035.0] || subclass(universal_class,intersection(power_class(successor_relation),complement(u))) member(regular(symmetrization_of(successor_relation)),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  10178[0:SpR:1933.0,25.2] || member(u,symmetrization_of(v)) member(u,complement(intersection(v,inverse(v))))* -> member(u,symmetric_difference(v,inverse(v))).
% 299.82/300.46  10326[0:Res:9898.0,9.0] || subclass(union(u,v),symmetric_difference(complement(u),complement(v)))* -> equal(symmetric_difference(complement(u),complement(v)),union(u,v)).
% 299.82/300.46  10360[0:Res:10292.0,9.0] || subclass(symmetrization_of(u),symmetric_difference(complement(u),complement(inverse(u))))* -> equal(symmetric_difference(complement(u),complement(inverse(u))),symmetrization_of(u)).
% 299.82/300.46  10497[0:Res:1951.1,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),symmetric_difference(u,v))* subclass(complement(intersection(u,v)),intersection(y__dfg,ordinal_numbers)) -> .
% 299.82/300.46  29190[0:SpR:506.0,115.0] ||  -> equal(complement(intersection(union(u,v),complement(inverse(intersection(complement(u),complement(v)))))),symmetrization_of(intersection(complement(u),complement(v))))**.
% 299.82/300.46  35754[0:MRR:35713.0,34067.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),union(y__dfg,ordinal_numbers)) -> member(least(element_relation,intersection(y__dfg,ordinal_numbers)),symmetric_difference(y__dfg,ordinal_numbers))*.
% 299.82/300.46  10379[0:Res:10293.0,9.0] || subclass(successor(u),symmetric_difference(complement(u),complement(singleton(u))))* -> equal(symmetric_difference(complement(u),complement(singleton(u))),successor(u)).
% 299.82/300.46  10240[0:SpR:1934.0,25.2] || member(u,successor(v)) member(u,complement(intersection(v,singleton(v))))* -> member(u,symmetric_difference(v,singleton(v))).
% 299.82/300.46  29191[0:SpR:506.0,45.0] ||  -> equal(complement(intersection(union(u,v),complement(singleton(intersection(complement(u),complement(v)))))),successor(intersection(complement(u),complement(v))))**.
% 299.82/300.46  30784[0:Res:25.2,3514.1] || member(ordered_pair(u,v),w)* member(ordered_pair(u,v),x)* subclass(universal_class,complement(intersection(x,w)))* -> .
% 299.82/300.46  36244[0:Res:8.1,5553.2] || equal(u,cross_product(v,w))* member(x,w)* member(y,v)* -> member(ordered_pair(y,x),u)*.
% 299.82/300.46  5855[0:Res:1004.0,127.0] || subclass(ordered_pair(u,v),w)* well_ordering(x,w)* -> member(least(x,ordered_pair(u,v)),ordered_pair(u,v))*.
% 299.82/300.46  28591[0:Res:1478.2,513.0] || member(u,universal_class) subclass(universal_class,intersection(complement(v),complement(w)))* member(power_class(u),union(v,w))* -> .
% 299.82/300.46  31099[2:Res:34.0,5832.1] inductive(rotate(u)) || well_ordering(v,cross_product(cross_product(universal_class,universal_class),universal_class))* -> member(least(v,rotate(u)),rotate(u))*.
% 299.82/300.46  31100[2:Res:37.0,5832.1] inductive(flip(u)) || well_ordering(v,cross_product(cross_product(universal_class,universal_class),universal_class))* -> member(least(v,flip(u)),flip(u))*.
% 299.82/300.46  5740[0:Res:60.1,3670.1] || member(ordered_pair(u,singleton(v)),compose(w,x))* equal(complement(image(w,image(x,singleton(u)))),universal_class) -> .
% 299.82/300.46  108433[0:Res:1504.1,127.0] || subclass(ordered_pair(u,v),w)* subclass(w,x)* well_ordering(y,x)* -> member(least(y,w),w)*.
% 299.82/300.46  112954[2:MRR:112944.2,2492.1] || connected(u,intersection(v,w)) -> well_ordering(u,intersection(v,w)) member(regular(not_well_ordering(u,intersection(v,w))),v)*.
% 299.82/300.46  113076[2:MRR:113066.2,2492.1] || connected(u,intersection(v,w)) -> well_ordering(u,intersection(v,w)) member(regular(not_well_ordering(u,intersection(v,w))),w)*.
% 299.82/300.46  115622[2:Res:114856.0,5832.1] inductive(symmetric_difference(universal_class,u)) || well_ordering(v,complement(u)) -> member(least(v,symmetric_difference(universal_class,u)),symmetric_difference(universal_class,u))*.
% 299.82/300.46  118386[0:SpL:28.0,9146.1] || member(u,universal_class) subclass(universal_class,union(v,w)) member(power_class(u),intersection(complement(v),complement(w)))* -> .
% 299.82/300.46  122153[0:Obv:122108.1] || member(ordered_pair(u,v),compose(w,x)) -> subclass(intersection(singleton(v),y),image(w,image(x,singleton(u))))*.
% 299.82/300.46  122364[0:Obv:122317.1] || member(ordered_pair(u,v),compose(w,x)) -> subclass(intersection(y,singleton(v)),image(w,image(x,singleton(u))))*.
% 299.82/300.46  125909[0:Res:28320.1,3.0] || subclass(rest_relation,rotate(u))* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),v)*.
% 299.82/300.46  125922[0:Res:28320.1,1952.0] || subclass(rest_relation,rotate(symmetric_difference(u,v))) -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),union(u,v))*.
% 299.82/300.46  125923[0:Res:28320.1,10191.0] || subclass(rest_relation,rotate(symmetric_difference(u,inverse(u))))* -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),symmetrization_of(u))*.
% 299.82/300.46  125924[0:Res:28320.1,10254.0] || subclass(rest_relation,rotate(symmetric_difference(u,singleton(u))))* -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),successor(u))*.
% 299.82/300.46  126039[0:Res:28321.1,3.0] || subclass(rest_relation,flip(u))* subclass(u,v)* -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),v)*.
% 299.82/300.46  126052[0:Res:28321.1,1952.0] || subclass(rest_relation,flip(symmetric_difference(u,v))) -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),union(u,v))*.
% 299.82/300.46  126053[0:Res:28321.1,10191.0] || subclass(rest_relation,flip(symmetric_difference(u,inverse(u))))* -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),symmetrization_of(u))*.
% 299.82/300.46  126054[0:Res:28321.1,10254.0] || subclass(rest_relation,flip(symmetric_difference(u,singleton(u))))* -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),successor(u))*.
% 299.82/300.46  160067[3:Res:159952.1,5553.2] || subclass(cross_product(u,v),ordinal_numbers)* member(w,v)* member(x,u)* -> member(ordered_pair(x,w),kind_1_ordinals)*.
% 299.82/300.46  162320[10:Rew:160202.0,148533.2] || member(u,universal_class) -> member(u,segment(universal_class,v,w)) equal(segment(cross_product(singleton(u),universal_class),v,w),successor_relation)**.
% 299.82/300.46  162310[10:Rew:160202.0,147969.0] ||  -> equal(intersection(intersection(u,intersection(complement(v),power_class(image(element_relation,complement(w))))),union(v,image(element_relation,power_class(w)))),successor_relation)**.
% 299.82/300.46  162309[10:Rew:160202.0,147968.0] ||  -> equal(intersection(intersection(intersection(complement(u),power_class(image(element_relation,complement(v)))),w),union(u,image(element_relation,power_class(v)))),successor_relation)**.
% 299.82/300.46  162308[10:Rew:160202.0,147967.0] ||  -> equal(intersection(union(u,image(element_relation,power_class(v))),intersection(w,intersection(complement(u),power_class(image(element_relation,complement(v)))))),successor_relation)**.
% 299.82/300.46  162307[10:Rew:160202.0,147966.0] ||  -> equal(intersection(union(u,image(element_relation,power_class(v))),intersection(intersection(complement(u),power_class(image(element_relation,complement(v)))),w)),successor_relation)**.
% 299.82/300.46  162306[10:Rew:160202.0,147949.0] ||  -> equal(intersection(intersection(u,intersection(power_class(image(element_relation,complement(v))),complement(w))),union(image(element_relation,power_class(v)),w)),successor_relation)**.
% 299.82/300.46  162305[10:Rew:160202.0,147948.0] ||  -> equal(intersection(intersection(intersection(power_class(image(element_relation,complement(u))),complement(v)),w),union(image(element_relation,power_class(u)),v)),successor_relation)**.
% 299.82/300.46  162304[10:Rew:160202.0,147947.0] ||  -> equal(intersection(union(image(element_relation,power_class(u)),v),intersection(w,intersection(power_class(image(element_relation,complement(u))),complement(v)))),successor_relation)**.
% 299.82/300.46  162303[10:Rew:160202.0,147946.0] ||  -> equal(intersection(union(image(element_relation,power_class(u)),v),intersection(intersection(power_class(image(element_relation,complement(u))),complement(v)),w)),successor_relation)**.
% 299.82/300.46  162302[10:Rew:160202.0,147913.0] ||  -> equal(intersection(intersection(u,intersection(power_class(v),complement(inverse(image(element_relation,complement(v)))))),symmetrization_of(image(element_relation,complement(v)))),successor_relation)**.
% 299.82/300.46  162301[10:Rew:160202.0,147912.0] ||  -> equal(intersection(intersection(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),v),symmetrization_of(image(element_relation,complement(u)))),successor_relation)**.
% 299.82/300.46  162300[10:Rew:160202.0,147911.0] ||  -> equal(intersection(symmetrization_of(image(element_relation,complement(u))),intersection(v,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))),successor_relation)**.
% 299.82/300.46  162299[10:Rew:160202.0,147910.0] ||  -> equal(intersection(symmetrization_of(image(element_relation,complement(u))),intersection(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),v)),successor_relation)**.
% 299.82/300.46  162298[10:Rew:160202.0,147893.0] ||  -> equal(intersection(intersection(u,intersection(power_class(v),complement(singleton(image(element_relation,complement(v)))))),successor(image(element_relation,complement(v)))),successor_relation)**.
% 299.82/300.46  162297[10:Rew:160202.0,147892.0] ||  -> equal(intersection(intersection(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),v),successor(image(element_relation,complement(u)))),successor_relation)**.
% 299.82/300.46  162296[10:Rew:160202.0,147891.0] ||  -> equal(intersection(successor(image(element_relation,complement(u))),intersection(v,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))),successor_relation)**.
% 299.82/300.46  162295[10:Rew:160202.0,147890.0] ||  -> equal(intersection(successor(image(element_relation,complement(u))),intersection(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),v)),successor_relation)**.
% 299.82/300.46  162289[10:Rew:160202.0,147781.0] ||  -> equal(intersection(intersection(u,intersection(v,w)),x),successor_relation) member(regular(intersection(intersection(u,intersection(v,w)),x)),v)*.
% 299.82/300.46  162290[10:Rew:160202.0,147780.0] ||  -> equal(intersection(intersection(u,intersection(v,w)),x),successor_relation) member(regular(intersection(intersection(u,intersection(v,w)),x)),w)*.
% 299.82/300.46  162287[10:Rew:160202.0,147778.1] || subclass(u,v) -> equal(intersection(intersection(w,u),x),successor_relation) member(regular(intersection(intersection(w,u),x)),v)*.
% 299.82/300.46  162285[10:Rew:160202.0,147708.0] ||  -> equal(intersection(intersection(intersection(u,v),w),x),successor_relation) member(regular(intersection(intersection(intersection(u,v),w),x)),u)*.
% 299.82/300.46  162286[10:Rew:160202.0,147707.0] ||  -> equal(intersection(intersection(intersection(u,v),w),x),successor_relation) member(regular(intersection(intersection(intersection(u,v),w),x)),v)*.
% 299.82/300.46  162283[10:Rew:160202.0,147705.1] || subclass(u,v) -> equal(intersection(intersection(u,w),x),successor_relation) member(regular(intersection(intersection(u,w),x)),v)*.
% 299.82/300.46  162281[10:Rew:160202.0,147668.0] ||  -> equal(intersection(u,intersection(v,intersection(w,x))),successor_relation) member(regular(intersection(u,intersection(v,intersection(w,x)))),w)*.
% 299.82/300.46  162282[10:Rew:160202.0,147667.0] ||  -> equal(intersection(u,intersection(v,intersection(w,x))),successor_relation) member(regular(intersection(u,intersection(v,intersection(w,x)))),x)*.
% 299.82/300.46  162279[10:Rew:160202.0,147665.1] || subclass(u,v) -> equal(intersection(w,intersection(x,u)),successor_relation) member(regular(intersection(w,intersection(x,u))),v)*.
% 299.82/300.46  162277[10:Rew:160202.0,147610.0] ||  -> equal(intersection(u,intersection(intersection(v,w),x)),successor_relation) member(regular(intersection(u,intersection(intersection(v,w),x))),v)*.
% 299.82/300.46  162278[10:Rew:160202.0,147609.0] ||  -> equal(intersection(u,intersection(intersection(v,w),x)),successor_relation) member(regular(intersection(u,intersection(intersection(v,w),x))),w)*.
% 299.82/300.46  162275[10:Rew:160202.0,147607.1] || subclass(u,v) -> equal(intersection(w,intersection(u,x)),successor_relation) member(regular(intersection(w,intersection(u,x))),v)*.
% 299.82/300.46  162271[10:Rew:160202.0,147430.0] ||  -> equal(restrict(symmetric_difference(u,v),w,x),successor_relation) member(regular(restrict(symmetric_difference(u,v),w,x)),union(u,v))*.
% 299.82/300.46  162270[10:Rew:160202.0,147429.0] ||  -> equal(restrict(restrict(u,v,w),x,y),successor_relation) member(regular(restrict(restrict(u,v,w),x,y)),u)*.
% 299.82/300.46  162268[10:Rew:160202.0,147427.2] || subclass(u,v)* well_ordering(w,v)* -> equal(restrict(u,x,y),successor_relation)** member(least(w,u),u)*.
% 299.82/300.46  162266[10:Rew:160202.0,147426.0] ||  -> equal(restrict(cross_product(u,v),w,x),successor_relation) member(regular(restrict(cross_product(w,x),u,v)),cross_product(u,v))*.
% 299.82/300.46  162267[10:Rew:160202.0,147425.0] ||  -> equal(restrict(cross_product(u,v),w,x),successor_relation) member(regular(restrict(cross_product(w,x),u,v)),cross_product(w,x))*.
% 299.82/300.46  162265[10:Rew:160202.0,147420.1] || well_ordering(u,complement(v)) -> equal(symmetric_difference(universal_class,v),successor_relation) member(least(u,symmetric_difference(universal_class,v)),symmetric_difference(universal_class,v))*.
% 299.82/300.46  162260[10:Rew:160202.0,147335.1] || well_ordering(u,image(element_relation,complement(v))) -> equal(segment(u,complement(power_class(v)),least(u,complement(power_class(v)))),successor_relation)**.
% 299.82/300.46  162256[10:Rew:160202.0,147135.1] || section(u,singleton(v),w) -> equal(segment(u,w,v),successor_relation) equal(regular(segment(u,w,v)),v)**.
% 299.82/300.46  162254[10:Rew:160202.0,147063.1] || well_ordering(u,symmetrization_of(v)) -> equal(segment(u,symmetric_difference(v,inverse(v)),least(u,symmetric_difference(v,inverse(v)))),successor_relation)**.
% 299.82/300.46  162253[10:Rew:160202.0,147062.1] || well_ordering(u,successor(v)) -> equal(segment(u,symmetric_difference(v,singleton(v)),least(u,symmetric_difference(v,singleton(v)))),successor_relation)**.
% 299.82/300.46  162246[10:Rew:160202.0,147052.1] || member(regular(intersection(u,image(element_relation,complement(v)))),power_class(v))* -> equal(intersection(u,image(element_relation,complement(v))),successor_relation).
% 299.82/300.46  162244[10:Rew:160202.0,147050.1] || member(regular(intersection(image(element_relation,complement(u)),v)),power_class(u))* -> equal(intersection(image(element_relation,complement(u)),v),successor_relation).
% 299.82/300.46  162241[10:Rew:160202.0,147048.0] ||  -> equal(symmetric_difference(cross_product(u,v),w),successor_relation) member(regular(symmetric_difference(cross_product(u,v),w)),complement(restrict(w,u,v)))*.
% 299.82/300.46  162242[10:Rew:160202.0,147046.1] || member(regular(symmetric_difference(cross_product(u,v),w)),restrict(w,u,v))* -> equal(symmetric_difference(cross_product(u,v),w),successor_relation).
% 299.82/300.46  162238[10:Rew:160202.0,147045.0] ||  -> equal(symmetric_difference(u,cross_product(v,w)),successor_relation) member(regular(symmetric_difference(u,cross_product(v,w))),complement(restrict(u,v,w)))*.
% 299.82/300.46  162239[10:Rew:160202.0,147043.1] || member(regular(symmetric_difference(u,cross_product(v,w))),restrict(u,v,w))* -> equal(symmetric_difference(u,cross_product(v,w)),successor_relation).
% 299.82/300.46  162993[10:Rew:160202.0,159926.1] || well_ordering(universal_class,symmetrization_of(image(element_relation,complement(u)))) -> member(successor_relation,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.82/300.46  162991[10:Rew:160202.0,159925.1] || well_ordering(universal_class,successor(image(element_relation,complement(u)))) -> member(successor_relation,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.82/300.46  162989[10:Rew:160202.0,159924.1] || well_ordering(universal_class,union(image(element_relation,power_class(u)),v)) -> member(successor_relation,intersection(power_class(image(element_relation,complement(u))),complement(v)))*.
% 299.82/300.46  162987[10:Rew:160202.0,159923.1] || well_ordering(universal_class,union(u,image(element_relation,power_class(v)))) -> member(successor_relation,intersection(complement(u),power_class(image(element_relation,complement(v)))))*.
% 299.82/300.46  162199[10:Rew:160202.0,147511.1] || subclass(intersection(complement(union(u,v)),w),symmetric_difference(u,v))* -> equal(intersection(complement(union(u,v)),w),successor_relation).
% 299.82/300.46  162196[10:Rew:160202.0,147484.1] || subclass(intersection(u,complement(union(v,w))),symmetric_difference(v,w))* -> equal(intersection(u,complement(union(v,w))),successor_relation).
% 299.82/300.46  162180[10:Rew:160202.0,147002.1] || well_ordering(u,complement(intersection(v,w))) -> equal(segment(u,symmetric_difference(v,w),least(u,symmetric_difference(v,w))),successor_relation)**.
% 299.82/300.46  162166[10:Rew:160202.0,146984.1] || member(regular(power_class(image(element_relation,complement(u)))),image(element_relation,power_class(u)))* -> equal(power_class(image(element_relation,complement(u))),successor_relation).
% 299.82/300.46  162147[10:Rew:160202.0,147244.2] || section(element_relation,u,universal_class) well_ordering(v,u) -> equal(segment(v,sum_class(u),least(v,sum_class(u))),successor_relation)**.
% 299.82/300.46  162142[10:Rew:160202.0,147220.1] || member(cross_product(cross_product(universal_class,universal_class),universal_class),ordinal_numbers)* -> equal(flip(u),successor_relation) member(least(element_relation,flip(u)),flip(u))*.
% 299.82/300.46  162140[10:Rew:160202.0,147219.1] || member(cross_product(cross_product(universal_class,universal_class),universal_class),ordinal_numbers)* -> equal(rotate(u),successor_relation) member(least(element_relation,rotate(u)),rotate(u))*.
% 299.82/300.46  162097[10:Rew:160202.0,147373.2] || equal(sum_class(complement(u)),complement(u)) member(regular(sum_class(complement(u))),u)* -> equal(sum_class(complement(u)),successor_relation).
% 299.82/300.46  162093[10:Rew:160202.0,147271.0] ||  -> equal(complement(complement(restrict(u,v,w))),successor_relation) member(regular(complement(complement(restrict(u,v,w)))),cross_product(v,w))*.
% 299.82/300.46  162079[10:Rew:160202.0,147030.2] || subclass(u,v)* subclass(v,w)* -> equal(intersection(u,x),successor_relation) member(regular(intersection(u,x)),w)*.
% 299.82/300.46  162080[10:Rew:160202.0,147029.1] || subclass(u,symmetric_difference(v,w)) -> equal(intersection(u,x),successor_relation) member(regular(intersection(u,x)),union(v,w))*.
% 299.82/300.46  162065[10:Rew:160202.0,147015.2] || subclass(u,v)* subclass(v,w)* -> equal(intersection(x,u),successor_relation) member(regular(intersection(x,u)),w)*.
% 299.82/300.46  162066[10:Rew:160202.0,147014.1] || subclass(u,symmetric_difference(v,w)) -> equal(intersection(x,u),successor_relation) member(regular(intersection(x,u)),union(v,w))*.
% 299.82/300.46  162045[10:Rew:160202.0,146959.0] ||  -> equal(intersection(restrict(u,v,w),x),successor_relation) member(regular(intersection(restrict(u,v,w),x)),cross_product(v,w))*.
% 299.82/300.46  162040[10:Rew:160202.0,146954.0] ||  -> equal(intersection(u,restrict(v,w,x)),successor_relation) member(regular(intersection(u,restrict(v,w,x))),cross_product(w,x))*.
% 299.82/300.46  162967[10:Rew:160202.0,156038.1] || member(u,universal_class) -> member(u,intersection(complement(v),union(w,successor_relation)))* member(u,union(v,symmetric_difference(universal_class,w))).
% 299.82/300.46  161991[10:Rew:160202.0,147601.1] || subclass(cross_product(u,v),w) -> equal(restrict(x,u,v),successor_relation) member(regular(restrict(x,u,v)),w)*.
% 299.82/300.46  161897[10:Rew:160202.0,147086.2] || well_ordering(u,complement(v))* -> member(w,v)* equal(singleton(w),successor_relation) member(least(u,singleton(w)),singleton(w))*.
% 299.82/300.46  161792[10:Rew:160202.0,146848.1] || subclass(singleton(least(element_relation,intersection(y__dfg,ordinal_numbers))),intersection(y__dfg,ordinal_numbers))* -> equal(singleton(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation).
% 299.82/300.46  161715[10:Rew:160202.0,146900.1] || subclass(u,symmetric_difference(v,inverse(v)))* -> equal(intersection(u,w),successor_relation) member(regular(intersection(u,w)),symmetrization_of(v))*.
% 299.82/300.46  161716[10:Rew:160202.0,146899.1] || subclass(u,symmetric_difference(v,singleton(v)))* -> equal(intersection(u,w),successor_relation) member(regular(intersection(u,w)),successor(v))*.
% 299.82/300.46  161704[10:Rew:160202.0,146879.1] || subclass(u,symmetric_difference(v,inverse(v)))* -> equal(intersection(w,u),successor_relation) member(regular(intersection(w,u)),symmetrization_of(v))*.
% 299.82/300.46  161705[10:Rew:160202.0,146878.1] || subclass(u,symmetric_difference(v,singleton(v)))* -> equal(intersection(w,u),successor_relation) member(regular(intersection(w,u)),successor(v))*.
% 299.82/300.46  163576[10:Rew:160202.0,161634.2] || section(u,successor_relation,v) subclass(singleton(w),x)* -> equal(segment(u,v,w),successor_relation)** member(w,x).
% 299.82/300.46  163574[10:Rew:160202.0,161596.1] || member(cross_product(u,v),universal_class) subclass(apply(choice,cross_product(u,v)),successor_relation)* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.46  163575[10:Rew:160202.0,161597.1] || member(cross_product(u,v),universal_class) equal(apply(choice,cross_product(u,v)),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.46  161504[10:Rew:160202.0,146652.2] || member(power_class(u),universal_class) member(apply(choice,power_class(u)),image(element_relation,complement(u)))* -> equal(power_class(u),successor_relation).
% 299.82/300.46  163578[10:Rew:160202.0,161672.1] || member(not_subclass_element(intersection(u,union(v,successor_relation)),w),symmetric_difference(universal_class,v))* -> subclass(intersection(u,union(v,successor_relation)),w).
% 299.82/300.46  161671[10:Rew:160202.0,156035.0] ||  -> equal(complement(intersection(power_class(image(element_relation,complement(u))),union(v,successor_relation))),union(image(element_relation,power_class(u)),symmetric_difference(universal_class,v)))**.
% 299.82/300.46  161670[10:Rew:160202.0,156028.0] ||  -> equal(intersection(union(u,symmetric_difference(universal_class,v)),union(complement(u),union(v,successor_relation))),symmetric_difference(complement(u),union(v,successor_relation)))**.
% 299.82/300.46  161662[10:Rew:160202.0,156026.1] || member(u,universal_class) -> member(u,intersection(union(v,successor_relation),complement(w)))* member(u,union(symmetric_difference(universal_class,v),w)).
% 299.82/300.46  163577[10:Rew:160202.0,161660.1] ||  -> member(not_subclass_element(u,image(element_relation,union(v,successor_relation))),power_class(symmetric_difference(universal_class,v)))* subclass(u,image(element_relation,union(v,successor_relation))).
% 299.82/300.46  161659[10:Rew:160202.0,156031.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,union(v,successor_relation))))),union(u,image(element_relation,power_class(symmetric_difference(universal_class,v)))))**.
% 299.82/300.46  161424[10:Rew:160202.0,159709.3] || member(u,universal_class) subclass(rest_relation,regular(v)) member(ordered_pair(u,rest_of(u)),v)* -> equal(v,successor_relation).
% 299.82/300.46  163573[10:Rew:160202.0,161448.1] || well_ordering(u,omega) -> equal(integer_of(v),successor_relation) equal(singleton(v),successor_relation) member(least(u,singleton(v)),singleton(v))*.
% 299.82/300.46  161307[10:Rew:160202.0,146602.1] || subclass(u,omega) -> equal(intersection(u,v),successor_relation) equal(integer_of(regular(intersection(u,v))),regular(intersection(u,v)))**.
% 299.82/300.46  161315[10:Rew:160202.0,147361.1] || subclass(u,omega) -> equal(intersection(v,u),successor_relation) equal(integer_of(regular(intersection(v,u))),regular(intersection(v,u)))**.
% 299.82/300.46  163570[10:Rew:160202.0,161325.0] ||  -> equal(cross_product(singleton(u),v),successor_relation) equal(range__dfg(regular(cross_product(singleton(u),v)),u,v),second(not_subclass_element(successor_relation,successor_relation)))**.
% 299.82/300.46  163569[10:Rew:160202.0,161227.1] || member(not_subclass_element(intersection(union(u,successor_relation),v),w),symmetric_difference(universal_class,u))* -> subclass(intersection(union(u,successor_relation),v),w).
% 299.82/300.46  161226[10:Rew:160202.0,156014.0] ||  -> equal(complement(intersection(union(u,successor_relation),power_class(image(element_relation,complement(v))))),union(symmetric_difference(universal_class,u),image(element_relation,power_class(v))))**.
% 299.82/300.46  161225[10:Rew:160202.0,156001.0] ||  -> equal(intersection(union(symmetric_difference(universal_class,u),v),union(union(u,successor_relation),complement(v))),symmetric_difference(union(u,successor_relation),complement(v)))**.
% 299.82/300.46  161211[10:Rew:160202.0,156047.0] || member(not_subclass_element(power_class(symmetric_difference(universal_class,u)),v),image(element_relation,union(u,successor_relation)))* -> subclass(power_class(symmetric_difference(universal_class,u)),v).
% 299.82/300.46  161210[10:Rew:160202.0,156003.0] ||  -> equal(complement(intersection(power_class(image(element_relation,union(u,successor_relation))),complement(v))),union(image(element_relation,power_class(symmetric_difference(universal_class,u))),v))**.
% 299.82/300.46  160815[10:Rew:160202.0,146400.2] || member(u,v)* well_ordering(w,v)* -> equal(singleton(u),successor_relation) member(least(w,singleton(u)),singleton(u))*.
% 299.82/300.46  160749[10:Rew:160202.0,146530.1] || subclass(u,cross_product(v,w))* -> equal(u,successor_relation) equal(ordered_pair(first(regular(u)),second(regular(u))),regular(u))**.
% 299.82/300.46  160750[10:Rew:160202.0,146519.2] || member(u,universal_class) subclass(u,restrict(v,w,x))* -> equal(u,successor_relation) member(apply(choice,u),v).
% 299.82/300.46  160752[10:Rew:160202.0,146517.3] || member(u,universal_class) subclass(u,rest_of(apply(choice,u)))* subclass(universal_class,complement(element_relation)) -> equal(u,successor_relation).
% 299.82/300.46  160753[10:Rew:160202.0,146485.2] || subclass(u,power_class(image(element_relation,complement(v))))* member(regular(u),image(element_relation,power_class(v))) -> equal(u,successor_relation).
% 299.82/300.46  160755[10:Rew:160202.0,146475.1] || subclass(u,symmetric_difference(v,cross_product(w,x))) -> equal(u,successor_relation) member(regular(u),complement(restrict(v,w,x)))*.
% 299.82/300.46  160756[10:Rew:160202.0,146474.1] || subclass(u,symmetric_difference(cross_product(v,w),x)) -> equal(u,successor_relation) member(regular(u),complement(restrict(x,v,w)))*.
% 299.82/300.46  160758[10:Rew:160202.0,146464.2] || subclass(u,symmetric_difference(v,w))* subclass(union(v,w),x)* -> equal(u,successor_relation) member(regular(u),x)*.
% 299.82/300.46  160762[10:Rew:160202.0,146411.2] || member(u,universal_class) subclass(u,omega) -> equal(u,successor_relation) equal(integer_of(apply(choice,u)),apply(choice,u))**.
% 299.82/300.46  160560[10:Rew:160202.0,156188.2] || subclass(complement(u),v)* well_ordering(w,v)* -> member(successor_relation,u) member(least(w,complement(u)),complement(u))*.
% 299.82/300.46  168535[11:Res:168384.1,3874.1] || equal(complement(intersection(u,v)),symmetrization_of(successor_relation)) member(successor_relation,union(u,v)) -> member(successor_relation,symmetric_difference(u,v))*.
% 299.82/300.46  163568[10:Rew:160202.0,161191.0] || subclass(cross_product(u,v),successor_relation)* member(w,v)* member(x,u)* well_ordering(y,inverse(successor_relation))* -> .
% 299.82/300.46  163547[10:Rew:160202.0,160533.3] || subclass(intersection(u,v),successor_relation)* member(w,v)* member(w,u)* well_ordering(x,inverse(successor_relation))* -> .
% 299.82/300.46  161072[10:Rew:160202.0,150801.0] || subclass(rest_relation,rotate(power_class(successor_relation))) member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),image(element_relation,universal_class))* -> .
% 299.82/300.46  161071[10:Rew:160202.0,150800.0] || subclass(rest_relation,flip(power_class(successor_relation))) member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),image(element_relation,universal_class))* -> .
% 299.82/300.46  163564[10:Rew:160202.0,161085.1] || member(not_subclass_element(restrict(power_class(successor_relation),u,v),w),image(element_relation,universal_class))* -> subclass(restrict(power_class(successor_relation),u,v),w).
% 299.82/300.46  161039[10:Rew:160202.0,150793.1] || member(u,image(element_relation,union(image(element_relation,universal_class),v)))* member(u,power_class(intersection(power_class(successor_relation),complement(v)))) -> .
% 299.82/300.46  161018[10:Rew:160202.0,150791.1] || member(u,image(element_relation,union(v,image(element_relation,universal_class))))* member(u,power_class(intersection(complement(v),power_class(successor_relation)))) -> .
% 299.82/300.46  163562[10:Rew:160202.0,161052.2] || subclass(u,power_class(successor_relation)) member(regular(intersection(u,v)),image(element_relation,universal_class))* -> equal(intersection(u,v),successor_relation).
% 299.82/300.46  163563[10:Rew:160202.0,161053.2] || subclass(u,power_class(successor_relation)) member(regular(intersection(v,u)),image(element_relation,universal_class))* -> equal(intersection(v,u),successor_relation).
% 299.82/300.46  163559[10:Rew:160202.0,160961.1] || subclass(intersection(complement(u),power_class(successor_relation)),union(u,image(element_relation,universal_class)))* -> subclass(intersection(complement(u),power_class(successor_relation)),v)*.
% 299.82/300.46  163557[10:Rew:160202.0,160959.1] || equal(intersection(complement(u),power_class(successor_relation)),union(u,image(element_relation,universal_class)))** -> equal(intersection(complement(u),power_class(successor_relation)),successor_relation).
% 299.82/300.46  163558[10:Rew:160202.0,160960.1] || equal(intersection(complement(u),power_class(successor_relation)),union(u,image(element_relation,universal_class)))** -> equal(union(u,image(element_relation,universal_class)),successor_relation).
% 299.82/300.46  163556[10:Rew:160202.0,160958.1] || subclass(union(u,image(element_relation,universal_class)),intersection(complement(u),power_class(successor_relation)))* -> equal(union(u,image(element_relation,universal_class)),successor_relation).
% 299.82/300.46  163555[10:Rew:160202.0,160930.1] || subclass(intersection(power_class(successor_relation),complement(u)),union(image(element_relation,universal_class),u))* -> subclass(intersection(power_class(successor_relation),complement(u)),v)*.
% 299.82/300.46  163553[10:Rew:160202.0,160928.1] || equal(intersection(power_class(successor_relation),complement(u)),union(image(element_relation,universal_class),u))** -> equal(intersection(power_class(successor_relation),complement(u)),successor_relation).
% 299.82/300.46  163554[10:Rew:160202.0,160929.1] || equal(intersection(power_class(successor_relation),complement(u)),union(image(element_relation,universal_class),u))** -> equal(union(image(element_relation,universal_class),u),successor_relation).
% 299.82/300.46  163552[10:Rew:160202.0,160927.1] || subclass(union(image(element_relation,universal_class),u),intersection(power_class(successor_relation),complement(u)))* -> equal(union(image(element_relation,universal_class),u),successor_relation).
% 299.82/300.46  163561[10:Rew:160202.0,161002.0] ||  -> equal(symmetric_difference(power_class(successor_relation),complement(u)),successor_relation) member(regular(symmetric_difference(power_class(successor_relation),complement(u))),union(image(element_relation,universal_class),u))*.
% 299.82/300.46  163560[10:Rew:160202.0,160992.0] ||  -> equal(symmetric_difference(complement(u),power_class(successor_relation)),successor_relation) member(regular(symmetric_difference(complement(u),power_class(successor_relation))),union(u,image(element_relation,universal_class)))*.
% 299.82/300.46  163104[10:Rew:160202.0,159355.1] || subclass(domain_relation,cross_product(u,v))* -> equal(ordered_pair(first(ordered_pair(successor_relation,successor_relation)),second(ordered_pair(successor_relation,successor_relation))),ordered_pair(successor_relation,successor_relation))**.
% 299.82/300.46  163571[10:Rew:160202.0,161361.2,160202.0,161361.0] || equal(complement(intersection(u,v)),successor(successor_relation)) member(successor_relation,union(u,v)) -> member(successor_relation,symmetric_difference(u,v))*.
% 299.82/300.46  163572[10:Rew:160202.0,161365.2,160202.0,161365.0] || equal(complement(intersection(u,v)),singleton(successor_relation)) member(successor_relation,union(u,v)) -> member(successor_relation,symmetric_difference(u,v))*.
% 299.82/300.46  111915[0:SpL:10417.0,48051.0] || member(inverse(restrict(cross_product(u,universal_class),v,w)),image(cross_product(v,w),u))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.46  157911[6:Res:28321.1,148657.1] || subclass(rest_relation,flip(complement(compose(element_relation,universal_class)))) member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),element_relation)* -> .
% 299.82/300.46  157910[6:Res:28320.1,148657.1] || subclass(rest_relation,rotate(complement(compose(element_relation,universal_class)))) member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),element_relation)* -> .
% 299.82/300.46  157913[6:Res:34429.0,148657.1] || member(not_subclass_element(complement(complement(complement(compose(element_relation,universal_class)))),u),element_relation)* -> subclass(complement(complement(complement(compose(element_relation,universal_class)))),u).
% 299.82/300.46  157916[6:Res:322.1,148657.1] || member(not_subclass_element(intersection(u,complement(compose(element_relation,universal_class))),v),element_relation)* -> subclass(intersection(u,complement(compose(element_relation,universal_class))),v).
% 299.82/300.46  157914[6:Res:340.1,148657.1] || member(not_subclass_element(intersection(complement(compose(element_relation,universal_class)),u),v),element_relation)* -> subclass(intersection(complement(compose(element_relation,universal_class)),u),v).
% 299.82/300.46  125123[0:Res:34427.0,3.0] || subclass(power_class(u),v) -> subclass(w,image(element_relation,complement(u))) member(not_subclass_element(w,image(element_relation,complement(u))),v)*.
% 299.82/300.46  155716[2:SpR:10028.0,142543.0] ||  -> equal(symmetric_difference(universal_class,intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))),intersection(symmetrization_of(image(element_relation,complement(u))),universal_class))**.
% 299.82/300.46  159773[6:SpL:10028.0,159727.1] inductive(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))) || equal(symmetrization_of(image(element_relation,complement(u))),universal_class)** -> .
% 299.82/300.46  155715[2:SpR:10029.0,142543.0] ||  -> equal(symmetric_difference(universal_class,intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))),intersection(successor(image(element_relation,complement(u))),universal_class))**.
% 299.82/300.46  159772[6:SpL:10029.0,159727.1] inductive(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))) || equal(successor(image(element_relation,complement(u))),universal_class)** -> .
% 299.82/300.46  111965[0:SpR:511.0,6842.1] || subclass(universal_class,symmetric_difference(image(element_relation,complement(u)),v)) -> member(unordered_pair(w,x),complement(intersection(power_class(u),complement(v))))*.
% 299.82/300.46  137722[0:SpR:10028.0,1951.1] || member(u,symmetric_difference(power_class(v),complement(inverse(image(element_relation,complement(v))))))* -> member(u,symmetrization_of(image(element_relation,complement(v)))).
% 299.82/300.46  137715[0:SpR:10028.0,89275.1] ||  -> member(u,intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))* subclass(singleton(u),symmetrization_of(image(element_relation,complement(v)))).
% 299.82/300.46  137103[0:SpR:10029.0,1951.1] || member(u,symmetric_difference(power_class(v),complement(singleton(image(element_relation,complement(v))))))* -> member(u,successor(image(element_relation,complement(v)))).
% 299.82/300.46  137096[0:SpR:10029.0,89275.1] ||  -> member(u,intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))* subclass(singleton(u),successor(image(element_relation,complement(v)))).
% 299.82/300.46  113258[0:MRR:113205.0,34189.1] ||  -> member(not_subclass_element(u,intersection(image(element_relation,complement(v)),u)),power_class(v))* subclass(u,intersection(image(element_relation,complement(v)),u)).
% 299.82/300.46  28285[0:Res:1495.2,307.0] || member(u,universal_class) subclass(rest_relation,image(element_relation,complement(v))) member(ordered_pair(u,rest_of(u)),power_class(v))* -> .
% 299.82/300.46  111959[0:SpR:509.0,6842.1] || subclass(universal_class,symmetric_difference(u,image(element_relation,complement(v)))) -> member(unordered_pair(w,x),complement(intersection(complement(u),power_class(v))))*.
% 299.82/300.46  155714[2:SpR:982.0,142543.0] ||  -> equal(symmetric_difference(universal_class,intersection(power_class(image(element_relation,complement(u))),complement(v))),intersection(union(image(element_relation,power_class(u)),v),universal_class))**.
% 299.82/300.46  159771[6:SpL:982.0,159727.1] inductive(intersection(power_class(image(element_relation,complement(u))),complement(v))) || equal(union(image(element_relation,power_class(u)),v),universal_class)** -> .
% 299.82/300.46  89285[0:Rew:208.0,89229.1] ||  -> member(not_subclass_element(u,power_class(image(element_relation,complement(v)))),image(element_relation,power_class(v)))* subclass(u,power_class(image(element_relation,complement(v)))).
% 299.82/300.46  139696[0:SpR:982.0,89275.1] ||  -> member(u,intersection(power_class(image(element_relation,complement(v))),complement(w)))* subclass(singleton(u),union(image(element_relation,power_class(v)),w)).
% 299.82/300.46  111786[0:SpL:208.0,9322.0] || member(u,symmetric_difference(power_class(image(element_relation,complement(v))),complement(w)))* -> member(u,union(image(element_relation,power_class(v)),w)).
% 299.82/300.46  155713[2:SpR:984.0,142543.0] ||  -> equal(symmetric_difference(universal_class,intersection(complement(u),power_class(image(element_relation,complement(v))))),intersection(union(u,image(element_relation,power_class(v))),universal_class))**.
% 299.82/300.46  159770[6:SpL:984.0,159727.1] inductive(intersection(complement(u),power_class(image(element_relation,complement(v))))) || equal(union(u,image(element_relation,power_class(v))),universal_class)** -> .
% 299.82/300.46  9997[0:SpR:208.0,509.0] ||  -> equal(union(u,image(element_relation,power_class(image(element_relation,complement(v))))),complement(intersection(complement(u),power_class(image(element_relation,power_class(v))))))**.
% 299.82/300.46  10038[0:SpR:208.0,511.0] ||  -> equal(union(image(element_relation,power_class(image(element_relation,complement(u)))),v),complement(intersection(power_class(image(element_relation,power_class(u))),complement(v))))**.
% 299.82/300.46  140158[0:SpR:984.0,89275.1] ||  -> member(u,intersection(complement(v),power_class(image(element_relation,complement(w)))))* subclass(singleton(u),union(v,image(element_relation,power_class(w)))).
% 299.82/300.46  111770[0:SpL:208.0,9322.0] || member(u,symmetric_difference(complement(v),power_class(image(element_relation,complement(w)))))* -> member(u,union(v,image(element_relation,power_class(w)))).
% 299.82/300.46  118036[0:SpL:28.0,9069.0] || subclass(universal_class,image(element_relation,union(u,v))) member(unordered_pair(w,x),power_class(intersection(complement(u),complement(v))))* -> .
% 299.82/300.46  140110[0:SpR:984.0,107289.0] ||  -> subclass(complement(power_class(intersection(complement(u),power_class(image(element_relation,complement(v)))))),image(element_relation,union(u,image(element_relation,power_class(v)))))*.
% 299.82/300.46  9946[0:SpR:505.0,27.2] || member(u,universal_class) -> member(u,image(element_relation,union(v,w))) member(u,power_class(intersection(complement(v),complement(w))))*.
% 299.82/300.46  139650[0:SpR:982.0,107289.0] ||  -> subclass(complement(power_class(intersection(power_class(image(element_relation,complement(u))),complement(v)))),image(element_relation,union(image(element_relation,power_class(u)),v)))*.
% 299.82/300.46  109283[0:SpR:57.0,9949.0] ||  -> equal(power_class(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))),complement(image(element_relation,successor(image(element_relation,complement(u))))))**.
% 299.82/300.46  109340[0:SpR:57.0,9948.0] ||  -> equal(power_class(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))),complement(image(element_relation,symmetrization_of(image(element_relation,complement(u))))))**.
% 299.82/300.46  157928[9:Res:157923.0,127.0] || subclass(image(element_relation,universal_class),u)* well_ordering(v,u)* -> member(least(v,image(element_relation,universal_class)),image(element_relation,universal_class))*.
% 299.82/300.46  118670[0:SpL:28.0,9118.1] || member(u,universal_class) subclass(universal_class,union(v,w)) member(sum_class(u),intersection(complement(v),complement(w)))* -> .
% 299.82/300.46  28590[0:Res:1479.2,513.0] || member(u,universal_class) subclass(universal_class,intersection(complement(v),complement(w)))* member(sum_class(u),union(v,w))* -> .
% 299.82/300.46  113114[0:Res:5771.1,9649.0] || equal(sum_class(singleton(u)),singleton(u)) -> subclass(sum_class(singleton(u)),v) equal(not_subclass_element(sum_class(singleton(u)),v),u)**.
% 299.82/300.46  9030[0:SpR:44.0,474.1] || member(inverse(restrict(u,v,universal_class)),universal_class) -> member(ordered_pair(inverse(restrict(u,v,universal_class)),image(u,v)),domain_relation)*.
% 299.82/300.46  10503[0:Res:305.1,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class) subclass(singleton(least(element_relation,intersection(y__dfg,ordinal_numbers))),intersection(y__dfg,ordinal_numbers))* -> .
% 299.82/300.46  30436[0:Res:25.2,3486.1] || member(unordered_pair(u,v),w)* member(unordered_pair(u,v),x)* subclass(universal_class,complement(intersection(x,w)))* -> .
% 299.82/300.46  108442[0:Res:1504.1,513.0] || subclass(ordered_pair(u,v),intersection(complement(w),complement(x)))* member(unordered_pair(u,singleton(v)),union(w,x)) -> .
% 299.82/300.46  9648[0:Res:1481.2,10.0] || subclass(u,unordered_pair(v,w))* -> subclass(u,x) equal(not_subclass_element(u,x),w)* equal(not_subclass_element(u,x),v)*.
% 299.82/300.46  3642[0:Res:1476.1,19.0] || subclass(universal_class,cross_product(u,v))* -> equal(ordered_pair(first(unordered_pair(w,x)),second(unordered_pair(w,x))),unordered_pair(w,x))**.
% 299.82/300.46  48024[0:SpL:1931.0,3487.0] || subclass(universal_class,symmetric_difference(complement(intersection(u,v)),union(u,v)))* -> member(unordered_pair(w,x),complement(symmetric_difference(u,v)))*.
% 299.82/300.46  122496[0:Res:1951.1,9636.1] || member(not_subclass_element(u,v),symmetric_difference(w,x))* subclass(u,complement(complement(intersection(w,x))))* -> subclass(u,v).
% 299.82/300.46  28589[0:Res:1481.2,513.0] || subclass(u,intersection(complement(v),complement(w)))* member(not_subclass_element(u,x),union(v,w))* -> subclass(u,x).
% 299.82/300.46  107185[0:Res:34429.0,10191.0] ||  -> subclass(complement(complement(symmetric_difference(u,inverse(u)))),v) member(not_subclass_element(complement(complement(symmetric_difference(u,inverse(u)))),v),symmetrization_of(u))*.
% 299.82/300.46  107186[0:Res:34429.0,10254.0] ||  -> subclass(complement(complement(symmetric_difference(u,singleton(u)))),v) member(not_subclass_element(complement(complement(symmetric_difference(u,singleton(u)))),v),successor(u))*.
% 299.82/300.46  48587[0:Res:340.1,10254.0] ||  -> subclass(intersection(symmetric_difference(u,singleton(u)),v),w) member(not_subclass_element(intersection(symmetric_difference(u,singleton(u)),v),w),successor(u))*.
% 299.82/300.46  48485[0:Res:340.1,10191.0] ||  -> subclass(intersection(symmetric_difference(u,inverse(u)),v),w) member(not_subclass_element(intersection(symmetric_difference(u,inverse(u)),v),w),symmetrization_of(u))*.
% 299.82/300.46  48606[0:Res:322.1,10254.0] ||  -> subclass(intersection(u,symmetric_difference(v,singleton(v))),w) member(not_subclass_element(intersection(u,symmetric_difference(v,singleton(v))),w),successor(v))*.
% 299.82/300.46  48504[0:Res:322.1,10191.0] ||  -> subclass(intersection(u,symmetric_difference(v,inverse(v))),w) member(not_subclass_element(intersection(u,symmetric_difference(v,inverse(v))),w),symmetrization_of(v))*.
% 299.82/300.46  28575[0:Res:4.1,513.0] || member(not_subclass_element(intersection(complement(u),complement(v)),w),union(u,v))* -> subclass(intersection(complement(u),complement(v)),w).
% 299.82/300.46  126374[0:Res:10258.1,3.0] || subclass(successor(u),v) -> subclass(symmetric_difference(u,singleton(u)),w) member(not_subclass_element(symmetric_difference(u,singleton(u)),w),v)*.
% 299.82/300.46  126442[0:Res:10194.1,3.0] || subclass(symmetrization_of(u),v) -> subclass(symmetric_difference(u,inverse(u)),w) member(not_subclass_element(symmetric_difference(u,inverse(u)),w),v)*.
% 299.82/300.46  9325[0:Res:1951.1,309.0] || member(not_subclass_element(complement(complement(intersection(u,v))),w),symmetric_difference(u,v))* -> subclass(complement(complement(intersection(u,v))),w).
% 299.82/300.46  123571[0:Obv:123537.1] || member(not_subclass_element(restrict(u,v,w),intersection(x,u)),x)* -> subclass(restrict(u,v,w),intersection(x,u)).
% 299.82/300.46  108404[0:Res:322.1,9332.1] || member(not_subclass_element(intersection(u,intersection(v,w)),x),symmetric_difference(v,w))* -> subclass(intersection(u,intersection(v,w)),x).
% 299.82/300.46  126572[0:MRR:126504.0,34189.1] ||  -> member(not_subclass_element(intersection(u,complement(union(v,w))),x),complement(v))* subclass(intersection(u,complement(union(v,w))),x).
% 299.82/300.46  126571[0:MRR:126505.0,34189.1] ||  -> member(not_subclass_element(intersection(u,complement(union(v,w))),x),complement(w))* subclass(intersection(u,complement(union(v,w))),x).
% 299.82/300.46  108403[0:Res:340.1,9332.1] || member(not_subclass_element(intersection(intersection(u,v),w),x),symmetric_difference(u,v))* -> subclass(intersection(intersection(u,v),w),x).
% 299.82/300.46  126799[0:MRR:126722.0,34189.1] ||  -> member(not_subclass_element(intersection(complement(union(u,v)),w),x),complement(u))* subclass(intersection(complement(union(u,v)),w),x).
% 299.82/300.46  126798[0:MRR:126723.0,34189.1] ||  -> member(not_subclass_element(intersection(complement(union(u,v)),w),x),complement(v))* subclass(intersection(complement(union(u,v)),w),x).
% 299.82/300.46  131861[0:Res:9529.1,3.0] || subclass(complement(intersection(u,v)),w) -> subclass(symmetric_difference(u,v),x) member(not_subclass_element(symmetric_difference(u,v),x),w)*.
% 299.82/300.46  113248[0:Rew:30.0,113145.1] || member(not_subclass_element(cross_product(u,v),restrict(w,u,v)),w)* -> subclass(cross_product(u,v),restrict(w,u,v)).
% 299.82/300.46  108394[0:Res:1495.2,9332.1] || member(u,universal_class) subclass(rest_relation,intersection(v,w)) member(ordered_pair(u,rest_of(u)),symmetric_difference(v,w))* -> .
% 299.82/300.46  28278[0:Res:1495.2,594.0] || member(u,universal_class) subclass(rest_relation,restrict(v,w,x))* -> member(ordered_pair(u,rest_of(u)),cross_product(w,x))*.
% 299.82/300.46  143794[0:Res:3595.3,159.0] function(u) || member(v,universal_class) subclass(universal_class,omega) -> equal(integer_of(image(u,v)),image(u,v))**.
% 299.82/300.46  30754[0:Res:3595.3,595.0] function(u) || member(v,universal_class) subclass(universal_class,restrict(w,x,y))* -> member(image(u,v),w)*.
% 299.82/300.46  3643[0:Res:1499.1,19.0] || subclass(universal_class,cross_product(u,v))* -> equal(ordered_pair(first(ordered_pair(w,x)),second(ordered_pair(w,x))),ordered_pair(w,x))**.
% 299.82/300.46  179993[11:Res:179843.1,3874.1] || equal(complement(intersection(u,v)),inverse(successor_relation)) member(successor_relation,union(u,v)) -> member(successor_relation,symmetric_difference(u,v))*.
% 299.82/300.46  180587[13:Res:180583.0,127.0] || subclass(image(element_relation,successor_relation),u)* well_ordering(v,u)* -> member(least(v,image(element_relation,successor_relation)),image(element_relation,successor_relation))*.
% 299.82/300.46  181102[10:SpL:181056.0,5646.1] || member(ordered_pair(universal_class,u),compose(v,w))* subclass(image(v,image(w,successor_relation)),x)* -> member(u,x)*.
% 299.82/300.46  181152[10:Res:181060.0,127.0] || subclass(singleton(singleton(successor_relation)),u)* well_ordering(v,u)* -> member(least(v,singleton(singleton(successor_relation))),singleton(singleton(successor_relation)))*.
% 299.82/300.46  183483[10:Rew:183390.0,183482.0] ||  -> equal(symmetric_difference(complement(successor(successor_relation)),union(singleton(successor_relation),successor(successor_relation))),union(complement(successor(successor_relation)),union(singleton(successor_relation),successor(successor_relation))))**.
% 299.82/300.46  183600[10:Rew:183391.0,183599.0] ||  -> equal(symmetric_difference(complement(symmetrization_of(successor_relation)),union(inverse(successor_relation),symmetrization_of(successor_relation))),union(complement(symmetrization_of(successor_relation)),union(inverse(successor_relation),symmetrization_of(successor_relation))))**.
% 299.82/300.46  183921[11:Res:183764.1,19.0] || subclass(universal_class,cross_product(u,v))* -> equal(ordered_pair(first(regular(symmetrization_of(successor_relation))),second(regular(symmetrization_of(successor_relation)))),regular(symmetrization_of(successor_relation)))**.
% 299.82/300.46  185936[10:Res:185646.1,3874.1] || equal(complement(complement(intersection(u,v))),successor_relation)** member(successor_relation,union(u,v)) -> member(successor_relation,symmetric_difference(u,v)).
% 299.82/300.46  186010[10:Res:185647.1,3874.1] || equal(complement(complement(intersection(u,v))),successor_relation)** member(omega,union(u,v)) -> member(omega,symmetric_difference(u,v)).
% 299.82/300.46  186148[10:Res:6010.3,185639.1] || member(u,universal_class)* member(v,universal_class) equal(compose(w,v),u)* equal(compose_class(w),successor_relation) -> .
% 299.82/300.46  39605[0:Res:5768.2,21.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,element_relation) -> member(u,ordered_pair(v,compose(u,v)))*.
% 299.82/300.46  125977[0:Res:28320.1,3627.0] || subclass(rest_relation,rotate(composition_function)) -> equal(compose(ordered_pair(u,rest_of(ordered_pair(singleton(singleton(singleton(v))),u))),singleton(v)),v)**.
% 299.82/300.46  107585[0:Res:1028.1,6045.0] || member(u,universal_class) subclass(image(element_relation,complement(v)),w)* well_ordering(universal_class,w) -> member(u,power_class(v))*.
% 299.82/300.46  41328[0:Res:314.0,5841.1] || member(u,universal_class) well_ordering(v,unordered_pair(w,u)) -> member(least(v,unordered_pair(w,u)),unordered_pair(w,u))*.
% 299.82/300.46  41469[0:Res:314.0,5842.1] || member(u,universal_class) well_ordering(v,unordered_pair(u,w)) -> member(least(v,unordered_pair(u,w)),unordered_pair(u,w))*.
% 299.82/300.46  41072[0:Res:314.0,5838.1] || member(u,universal_class)* well_ordering(v,complement(w)) -> member(u,w)* member(least(v,complement(w)),complement(w))*.
% 299.82/300.46  107594[0:Res:173.1,6045.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class)* subclass(complement(intersection(y__dfg,ordinal_numbers)),u)* well_ordering(universal_class,u) -> .
% 299.82/300.46  163565[10:Rew:160202.0,161187.3,160202.0,161187.0] || subclass(sum_class(inverse(successor_relation)),successor_relation)* member(ordinal_numbers,universal_class) well_ordering(element_relation,inverse(successor_relation)) -> member(inverse(successor_relation),ordinal_numbers).
% 299.82/300.46  162273[10:Rew:160202.0,147576.2] || well_ordering(u,universal_class) -> member(least(u,complement(union(v,w))),complement(w))* equal(complement(union(v,w)),successor_relation).
% 299.82/300.46  162274[10:Rew:160202.0,147575.2] || well_ordering(u,universal_class) -> member(least(u,complement(union(v,w))),complement(v))* equal(complement(union(v,w)),successor_relation).
% 299.82/300.46  162252[10:Rew:160202.0,147058.1] || well_ordering(u,universal_class) -> equal(symmetric_difference(v,singleton(v)),successor_relation) member(least(u,symmetric_difference(v,singleton(v))),successor(v))*.
% 299.82/300.46  162249[10:Rew:160202.0,147055.1] || well_ordering(u,universal_class) -> equal(symmetric_difference(v,inverse(v)),successor_relation) member(least(u,symmetric_difference(v,inverse(v))),symmetrization_of(v))*.
% 299.82/300.46  161969[10:Rew:160202.0,146927.2] || well_ordering(u,universal_class) member(least(u,intersection(v,w)),symmetric_difference(v,w))* -> equal(intersection(v,w),successor_relation).
% 299.82/300.46  163019[10:Rew:160202.0,159510.2] || well_ordering(u,universal_class) member(least(u,complement(compose(element_relation,universal_class))),element_relation)* -> equal(complement(compose(element_relation,universal_class)),successor_relation).
% 299.82/300.46  157907[6:Res:31069.2,148657.1] inductive(complement(compose(element_relation,universal_class))) || well_ordering(u,universal_class) member(least(u,complement(compose(element_relation,universal_class))),element_relation)* -> .
% 299.82/300.46  108253[2:Res:31069.2,10191.0] inductive(symmetric_difference(u,inverse(u))) || well_ordering(v,universal_class) -> member(least(v,symmetric_difference(u,inverse(u))),symmetrization_of(u))*.
% 299.82/300.46  108254[2:Res:31069.2,10254.0] inductive(symmetric_difference(u,singleton(u))) || well_ordering(v,universal_class) -> member(least(v,symmetric_difference(u,singleton(u))),successor(u))*.
% 299.82/300.46  108380[2:Res:31069.2,9332.1] inductive(intersection(u,v)) || well_ordering(w,universal_class) member(least(w,intersection(u,v)),symmetric_difference(u,v))* -> .
% 299.82/300.46  160808[10:Rew:160202.0,160194.2] || member(u,ordinal_numbers) well_ordering(v,kind_1_ordinals) -> equal(singleton(u),successor_relation) member(least(v,singleton(u)),singleton(u))*.
% 299.82/300.46  160196[3:Res:159953.1,5832.1] inductive(singleton(u)) || member(u,ordinal_numbers) well_ordering(v,kind_1_ordinals) -> member(least(v,singleton(u)),singleton(u))*.
% 299.82/300.46  30058[0:SoR:2610.0,6317.2] single_valued_class(intersection(y__dfg,ordinal_numbers)) || well_ordering(element_relation,cross_product(universal_class,universal_class))* equal(intersection(y__dfg,ordinal_numbers),cross_product(universal_class,universal_class)) -> .
% 299.82/300.46  163566[10:Rew:160202.0,161188.3,160202.0,161188.2,160202.0,161188.0] || subclass(sum_class(inverse(successor_relation)),successor_relation)* well_ordering(element_relation,inverse(successor_relation)) -> equal(inverse(successor_relation),ordinal_numbers) member(inverse(successor_relation),ordinal_numbers).
% 299.82/300.46  160687[10:Rew:160202.0,159707.3] inductive(regular(u)) || well_ordering(v,regular(u)) member(least(v,regular(u)),u)* -> equal(u,successor_relation).
% 299.82/300.46  31085[2:Res:6219.1,5832.1] inductive(singleton(u)) || member(u,v)* well_ordering(w,v)* -> member(least(w,singleton(u)),singleton(u))*.
% 299.82/300.46  89901[2:Res:89275.1,5832.1] inductive(singleton(u)) || well_ordering(v,complement(w))* -> member(u,w)* member(least(v,singleton(u)),singleton(u))*.
% 299.82/300.46  31074[2:Res:137.1,5832.1] inductive(sum_class(u)) || member(u,ordinal_numbers) well_ordering(v,u) -> member(least(v,sum_class(u)),sum_class(u))*.
% 299.82/300.46  162263[10:Rew:160202.0,147407.1] || member(intersection(u,v),ordinal_numbers) -> equal(sum_class(intersection(u,v)),successor_relation) member(regular(sum_class(intersection(u,v))),u)*.
% 299.82/300.46  162264[10:Rew:160202.0,147405.1] || member(intersection(u,v),ordinal_numbers) -> equal(sum_class(intersection(u,v)),successor_relation) member(regular(sum_class(intersection(u,v))),v)*.
% 299.82/300.46  160816[10:Rew:160202.0,146399.1] || member(image(choice,singleton(singleton(u))),ordinal_numbers) -> equal(singleton(u),successor_relation) subclass(u,image(choice,singleton(singleton(u))))*.
% 299.82/300.46  188832[10:Res:3872.2,185065.1] || member(singleton(u),cross_product(v,w))* member(singleton(u),x)* subclass(restrict(x,v,w),successor_relation)* -> .
% 299.82/300.46  189330[15:SpL:10422.0,188793.1] || member(restrict(cross_product(u,singleton(v)),w,x),universal_class)* member(y,segment(cross_product(w,x),u,v))* -> .
% 299.82/300.46  189389[15:Rew:189339.1,184848.2] || member(u,universal_class) subclass(domain_relation,symmetric_difference(complement(v),complement(w)))* -> member(ordered_pair(u,successor_relation),union(v,w))*.
% 299.82/300.46  191242[10:Rew:142543.0,191146.1,142543.0,191146.0] || member(symmetric_difference(universal_class,u),universal_class) -> equal(symmetric_difference(universal_class,u),successor_relation) member(apply(choice,symmetric_difference(universal_class,u)),complement(u))*.
% 299.82/300.46  192585[15:Res:189478.0,162356.0] || subclass(domain_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(singleton(singleton(singleton(successor_relation))),least(omega,domain_relation))),successor_relation)**.
% 299.82/300.46  192601[10:Res:160271.1,162356.0] inductive(u) || subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(successor_relation,least(omega,u))),successor_relation)**.
% 299.82/300.46  193646[10:Res:160354.1,150815.1] || equal(complement(complement(symmetrization_of(u))),successor_relation) connected(u,v)* -> equal(complement(complement(symmetrization_of(u))),cross_product(v,v))*.
% 299.82/300.46  195388[10:SpR:194805.1,161299.2] || subclass(inverse(u),u)* asymmetric(u,v) subclass(compose(successor_relation,successor_relation),successor_relation)* -> transitive(inverse(u),v)*.
% 299.82/300.46  195389[10:SpR:194805.1,163042.1] || subclass(inverse(u),u)* asymmetric(u,singleton(v)) -> equal(domain__dfg(inverse(u),singleton(v),v),single_valued3(successor_relation))**.
% 299.82/300.46  195805[6:Res:195710.1,5553.2] || equal(inverse(u),universal_class) member(v,w)* member(x,y)* -> member(ordered_pair(x,v),inverse(u))*.
% 299.82/300.46  195864[6:Res:195720.1,5553.2] || equal(sum_class(u),universal_class) member(v,w)* member(x,y)* -> member(ordered_pair(x,v),sum_class(u))*.
% 299.82/300.46  196547[10:SpR:161137.0,1028.1] || member(u,universal_class) -> member(u,image(element_relation,power_class(complement(inverse(successor_relation)))))* member(u,power_class(image(element_relation,symmetrization_of(successor_relation)))).
% 299.82/300.46  196575[10:SpL:161137.0,513.0] || member(u,intersection(power_class(complement(inverse(successor_relation))),complement(v)))* member(u,union(image(element_relation,symmetrization_of(successor_relation)),v)) -> .
% 299.82/300.46  196577[10:SpL:161137.0,9146.1] || member(u,universal_class) subclass(universal_class,power_class(complement(inverse(successor_relation)))) member(power_class(u),image(element_relation,symmetrization_of(successor_relation)))* -> .
% 299.82/300.46  196582[10:SpL:161137.0,513.0] || member(u,intersection(complement(v),power_class(complement(inverse(successor_relation)))))* member(u,union(v,image(element_relation,symmetrization_of(successor_relation)))) -> .
% 299.82/300.46  196753[10:SpR:162889.0,1028.1] || member(u,universal_class) -> member(u,image(element_relation,power_class(complement(singleton(successor_relation)))))* member(u,power_class(image(element_relation,successor(successor_relation)))).
% 299.82/300.46  196781[10:SpL:162889.0,513.0] || member(u,intersection(power_class(complement(singleton(successor_relation))),complement(v)))* member(u,union(image(element_relation,successor(successor_relation)),v)) -> .
% 299.82/300.46  196783[10:SpL:162889.0,9146.1] || member(u,universal_class) subclass(universal_class,power_class(complement(singleton(successor_relation)))) member(power_class(u),image(element_relation,successor(successor_relation)))* -> .
% 299.82/300.46  196788[10:SpL:162889.0,513.0] || member(u,intersection(complement(v),power_class(complement(singleton(successor_relation)))))* member(u,union(v,image(element_relation,successor(successor_relation)))) -> .
% 299.82/300.46  197072[10:Res:197034.0,127.0] || subclass(complement(singleton(successor_relation)),u)* well_ordering(v,u)* -> member(least(v,complement(singleton(successor_relation))),complement(singleton(successor_relation)))*.
% 299.82/300.46  197077[10:Res:197071.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(complement(successor(successor_relation))),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  199962[6:Res:199831.0,127.0] || subclass(cross_product(universal_class,universal_class),u)* well_ordering(v,u)* -> member(least(v,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class))*.
% 299.82/300.46  200272[6:SpL:199964.0,35.0] || member(ordered_pair(regular(rest_relation),u),rotate(v)) -> member(ordered_pair(ordered_pair(second(regular(rest_relation)),u),first(regular(rest_relation))),v)*.
% 299.82/300.46  200273[6:SpL:199964.0,38.0] || member(ordered_pair(regular(rest_relation),u),flip(v)) -> member(ordered_pair(ordered_pair(second(regular(rest_relation)),first(regular(rest_relation))),u),v)*.
% 299.82/300.46  200653[10:Res:161493.2,161270.1] inductive(u) || member(complement(u),universal_class) -> equal(integer_of(apply(choice,complement(u))),successor_relation)** equal(complement(u),successor_relation).
% 299.82/300.46  200722[10:Res:161493.2,35.0] inductive(rotate(u)) ||  -> equal(integer_of(ordered_pair(ordered_pair(v,w),x)),successor_relation) member(ordered_pair(ordered_pair(w,x),v),u)*.
% 299.82/300.46  200723[10:Res:161493.2,38.0] inductive(flip(u)) ||  -> equal(integer_of(ordered_pair(ordered_pair(v,w),x)),successor_relation) member(ordered_pair(ordered_pair(w,v),x),u)*.
% 299.82/300.46  200739[10:Res:161493.2,176.0] inductive(ordinal_numbers) || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),y__dfg)* -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation).
% 299.82/300.46  201516[6:SpL:201355.0,35.0] || member(ordered_pair(regular(domain_relation),u),rotate(v)) -> member(ordered_pair(ordered_pair(second(regular(domain_relation)),u),first(regular(domain_relation))),v)*.
% 299.82/300.46  201517[6:SpL:201355.0,38.0] || member(ordered_pair(regular(domain_relation),u),flip(v)) -> member(ordered_pair(ordered_pair(second(regular(domain_relation)),first(regular(domain_relation))),u),v)*.
% 299.82/300.46  201684[3:Res:201671.0,5838.1] || member(u,universal_class) well_ordering(v,complement(ordinal_numbers)) -> member(u,kind_1_ordinals)* member(least(v,complement(kind_1_ordinals)),complement(kind_1_ordinals))*.
% 299.82/300.46  201939[10:Res:161492.2,9300.0] || equal(symmetric_difference(u,cross_product(v,w)),omega) -> equal(integer_of(x),successor_relation) member(x,complement(restrict(u,v,w)))*.
% 299.82/300.46  201941[10:Res:161492.2,9306.0] || equal(symmetric_difference(cross_product(u,v),w),omega) -> equal(integer_of(x),successor_relation) member(x,complement(restrict(w,u,v)))*.
% 299.82/300.46  202027[10:Res:161492.2,2320.0] || equal(rest_of(u),omega) -> equal(integer_of(singleton(singleton(singleton(v)))),successor_relation) equal(restrict(u,singleton(v),universal_class),v)**.
% 299.82/300.46  202065[20:Rew:191138.1,201957.3] || equal(ordered_pair(u,v),omega) -> equal(integer_of(w),successor_relation)** equal(w,unordered_pair(u,singleton(v)))* equal(w,successor_relation).
% 299.82/300.46  202492[10:SpR:202485.1,10422.0] || equal(rest_of(restrict(cross_product(u,singleton(v)),w,x)),successor_relation)** -> equal(segment(cross_product(w,x),u,v),successor_relation).
% 299.82/300.46  202850[11:Res:3872.2,168534.1] || member(successor_relation,cross_product(u,v)) member(successor_relation,w) equal(complement(restrict(w,u,v)),symmetrization_of(successor_relation))** -> .
% 299.82/300.46  202862[11:Res:60.1,168534.1] || member(ordered_pair(u,successor_relation),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),symmetrization_of(successor_relation))** -> .
% 299.82/300.46  203569[10:Rew:203192.0,162035.1] || member(u,universal_class) -> member(u,cantor(cross_product(v,w))) equal(restrict(cross_product(singleton(u),universal_class),v,w),successor_relation)**.
% 299.82/300.46  203634[6:Rew:203192.0,141997.3] || member(u,universal_class) member(v,cross_product(singleton(u),universal_class))* member(v,w)* -> member(u,cantor(w))*.
% 299.82/300.46  203677[15:Rew:203192.0,186277.0] || member(singleton(u),cantor(v)) member(ordered_pair(v,singleton(singleton(singleton(u)))),cross_product(universal_class,cross_product(universal_class,universal_class)))* -> .
% 299.82/300.46  204009[10:Rew:203192.0,163567.0] || subclass(cantor(restrict(u,v,inverse(successor_relation))),successor_relation)* subclass(inverse(successor_relation),v) -> section(u,inverse(successor_relation),v).
% 299.82/300.46  204012[6:Rew:203192.0,3841.2] inductive(domain_of(restrict(u,v,omega))) || section(u,omega,v) -> equal(cantor(restrict(u,v,omega)),omega)**.
% 299.82/300.46  204272[6:Rew:204206.0,149767.2] inductive(cantor(flip(cross_product(u,universal_class)))) || well_ordering(v,inverse(u)) -> member(least(v,inverse(u)),inverse(u))*.
% 299.82/300.46  204341[6:Rew:204278.0,149812.2] inductive(cantor(restrict(element_relation,universal_class,u))) || well_ordering(v,sum_class(u)) -> member(least(v,sum_class(u)),sum_class(u))*.
% 299.82/300.46  206052[10:Res:3872.2,163205.1] || member(successor_relation,cross_product(u,v)) member(successor_relation,w) equal(complement(restrict(w,u,v)),successor(successor_relation))** -> .
% 299.82/300.46  206062[10:Res:60.1,163205.1] || member(ordered_pair(u,successor_relation),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),successor(successor_relation))** -> .
% 299.82/300.46  206170[6:Res:203330.1,1322.1] inductive(cantor(restrict(u,v,omega))) || section(u,omega,v) -> equal(cantor(restrict(u,v,omega)),omega)**.
% 299.82/300.46  206722[10:Res:206682.0,127.0] || subclass(symmetrization_of(singleton(successor_relation)),u)* well_ordering(v,u)* -> member(least(v,symmetrization_of(singleton(successor_relation))),symmetrization_of(singleton(successor_relation)))*.
% 299.82/300.46  206736[10:Res:206684.0,127.0] || subclass(successor(singleton(successor_relation)),u)* well_ordering(v,u)* -> member(least(v,successor(singleton(successor_relation))),successor(singleton(successor_relation)))*.
% 299.82/300.46  208912[10:Res:3872.2,163207.1] || member(successor_relation,cross_product(u,v)) member(successor_relation,w) equal(complement(restrict(w,u,v)),singleton(successor_relation))** -> .
% 299.82/300.46  208922[10:Res:60.1,163207.1] || member(ordered_pair(u,successor_relation),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),singleton(successor_relation))** -> .
% 299.82/300.46  209536[12:SpL:209433.0,35.0] || member(ordered_pair(regular(element_relation),u),rotate(v)) -> member(ordered_pair(ordered_pair(second(regular(element_relation)),u),first(regular(element_relation))),v)*.
% 299.82/300.46  209537[12:SpL:209433.0,38.0] || member(ordered_pair(regular(element_relation),u),flip(v)) -> member(ordered_pair(ordered_pair(second(regular(element_relation)),first(regular(element_relation))),u),v)*.
% 299.82/300.46  210339[15:SpR:2330.1,189563.1] || subclass(domain_relation,flip(u)) -> subclass(cross_product(v,w),x) member(ordered_pair(not_subclass_element(cross_product(v,w),x),successor_relation),u)*.
% 299.82/300.46  210357[15:Res:189563.1,513.0] || subclass(domain_relation,flip(intersection(complement(u),complement(v)))) member(ordered_pair(ordered_pair(w,x),successor_relation),union(u,v))* -> .
% 299.82/300.46  210430[15:Res:189564.1,513.0] || subclass(domain_relation,rotate(intersection(complement(u),complement(v)))) member(ordered_pair(ordered_pair(w,successor_relation),x),union(u,v))* -> .
% 299.82/300.46  210465[15:Res:189564.1,129.3] || subclass(domain_relation,rotate(u))* member(ordered_pair(v,successor_relation),w)* subclass(w,x)* well_ordering(u,x)* -> .
% 299.82/300.46  210538[10:Res:160296.2,149475.0] || member(cantor(u),universal_class) subclass(universal_class,v) -> equal(cantor(u),successor_relation) member(apply(choice,cantor(u)),v)*.
% 299.82/300.46  210729[10:Rew:162889.0,210658.1] ||  -> member(not_subclass_element(complement(power_class(complement(singleton(successor_relation)))),u),image(element_relation,successor(successor_relation)))* subclass(complement(power_class(complement(singleton(successor_relation)))),u).
% 299.82/300.46  210730[10:Rew:161137.0,210657.1] ||  -> member(not_subclass_element(complement(power_class(complement(inverse(successor_relation)))),u),image(element_relation,symmetrization_of(successor_relation)))* subclass(complement(power_class(complement(inverse(successor_relation)))),u).
% 299.82/300.46  211059[11:Res:3872.2,179992.1] || member(successor_relation,cross_product(u,v)) member(successor_relation,w) equal(complement(restrict(w,u,v)),inverse(successor_relation))** -> .
% 299.82/300.46  211069[11:Res:60.1,179992.1] || member(ordered_pair(u,successor_relation),compose(v,w)) equal(complement(image(v,image(w,singleton(u)))),inverse(successor_relation))** -> .
% 299.82/300.46  211148[10:Res:161445.2,149475.0] || well_ordering(u,cantor(v)) subclass(universal_class,w) -> equal(cantor(v),successor_relation) member(least(u,cantor(v)),w)*.
% 299.82/300.46  211155[10:Res:161445.2,160481.0] || well_ordering(u,regular(v)) member(least(u,regular(v)),v)* -> equal(regular(v),successor_relation) equal(v,successor_relation).
% 299.82/300.46  211202[6:Res:31076.2,149475.0] inductive(cantor(u)) || well_ordering(v,cantor(u)) subclass(universal_class,w) -> member(least(v,cantor(u)),w)*.
% 299.82/300.46  211492[10:Res:3872.2,211446.0] || member(singleton(successor_relation),cross_product(u,v)) member(singleton(successor_relation),w) well_ordering(universal_class,restrict(w,u,v))* -> .
% 299.82/300.46  211597[10:Res:5771.1,160705.0] || equal(sum_class(complement(kind_1_ordinals)),complement(kind_1_ordinals)) member(regular(sum_class(complement(kind_1_ordinals))),ordinal_numbers)* -> equal(sum_class(complement(kind_1_ordinals)),successor_relation).
% 299.82/300.46  211671[10:Res:181213.1,127.0] || equal(u,singleton(singleton(successor_relation))) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  212059[2:Res:184090.1,3874.1] || equal(symmetric_difference(universal_class,intersection(u,v)),universal_class)** member(omega,union(u,v)) -> member(omega,symmetric_difference(u,v)).
% 299.82/300.46  212554[13:Res:212548.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(complement(power_class(universal_class))),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  212661[10:Res:212652.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(complement(power_class(successor_relation))),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  212954[10:Obv:212889.0] ||  -> equal(intersection(singleton(u),v),successor_relation) equal(symmetric_difference(intersection(singleton(u),v),u),union(intersection(singleton(u),v),u))**.
% 299.82/300.46  213065[10:Obv:213008.0] ||  -> equal(intersection(u,singleton(v)),successor_relation) equal(symmetric_difference(intersection(u,singleton(v)),v),union(intersection(u,singleton(v)),v))**.
% 299.82/300.46  213116[10:Res:188444.1,3874.1] || equal(symmetric_difference(universal_class,intersection(u,v)),universal_class)** member(successor_relation,union(u,v)) -> member(successor_relation,symmetric_difference(u,v)).
% 299.82/300.46  214150[20:Res:193270.1,3874.1] || equal(symmetric_difference(universal_class,intersection(u,v)),omega)** member(successor_relation,union(u,v)) -> member(successor_relation,symmetric_difference(u,v)).
% 299.82/300.46  214427[10:MRR:214415.0,160295.1] ||  -> member(regular(regular(union(u,v))),complement(v))* equal(regular(union(u,v)),successor_relation) equal(union(u,v),successor_relation).
% 299.82/300.46  214576[10:MRR:214562.0,160295.1] ||  -> member(regular(regular(union(u,v))),complement(u))* equal(regular(union(u,v)),successor_relation) equal(union(u,v),successor_relation).
% 299.82/300.46  214779[10:Res:161697.1,160481.0] || member(regular(restrict(regular(u),v,w)),u)* -> equal(restrict(regular(u),v,w),successor_relation) equal(u,successor_relation).
% 299.82/300.46  216104[6:Res:199830.1,127.0] || equal(u,cross_product(universal_class,universal_class)) subclass(u,v)* well_ordering(w,v)* -> member(least(w,u),u)*.
% 299.82/300.46  216766[0:SpR:70.0,143767.2] || member(image(u,singleton(v)),universal_class)* subclass(universal_class,omega) -> equal(integer_of(apply(u,v)),apply(u,v)).
% 299.82/300.46  216990[10:SpL:161137.0,9069.0] || subclass(universal_class,image(element_relation,power_class(complement(inverse(successor_relation))))) member(unordered_pair(u,v),power_class(image(element_relation,symmetrization_of(successor_relation))))* -> .
% 299.82/300.46  216991[10:SpL:162889.0,9069.0] || subclass(universal_class,image(element_relation,power_class(complement(singleton(successor_relation))))) member(unordered_pair(u,v),power_class(image(element_relation,successor(successor_relation))))* -> .
% 299.82/300.46  217046[10:SpL:161137.0,9118.1] || member(u,universal_class) subclass(universal_class,power_class(complement(inverse(successor_relation)))) member(sum_class(u),image(element_relation,symmetrization_of(successor_relation)))* -> .
% 299.82/300.46  217047[10:SpL:162889.0,9118.1] || member(u,universal_class) subclass(universal_class,power_class(complement(singleton(successor_relation)))) member(sum_class(u),image(element_relation,successor(successor_relation)))* -> .
% 299.82/300.46  217203[10:Res:131.2,206660.0] || connected(u,complement(singleton(successor_relation))) member(successor_relation,not_well_ordering(u,complement(singleton(successor_relation))))* -> well_ordering(u,complement(singleton(successor_relation))).
% 299.82/300.46  217593[10:MRR:217547.3,186121.2] || member(unordered_pair(u,v),w)* member(unordered_pair(u,v),x)* subclass(universal_class,regular(intersection(x,w)))* -> .
% 299.82/300.46  217666[10:SpL:161565.2,217599.0] || member(cross_product(u,v),universal_class) subclass(universal_class,apply(choice,cross_product(u,v)))* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.46  217882[10:SpL:161565.2,217670.0] || member(cross_product(u,v),universal_class) equal(apply(choice,cross_product(u,v)),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.46  218049[10:SpR:161194.0,161690.1] ||  -> equal(symmetric_difference(union(u,successor_relation),universal_class),successor_relation) member(regular(symmetric_difference(union(u,successor_relation),universal_class)),complement(symmetric_difference(complement(u),universal_class)))*.
% 299.82/300.46  218354[10:Res:218298.0,160292.0] || well_ordering(u,complement(v)) -> equal(v,successor_relation) equal(regular(v),successor_relation) member(least(u,regular(v)),regular(v))*.
% 299.82/300.46  218357[10:Res:218298.0,5832.1] inductive(regular(u)) || well_ordering(v,complement(u)) -> equal(u,successor_relation) member(least(v,regular(u)),regular(u))*.
% 299.82/300.46  218423[10:Res:218370.0,160373.0] || well_ordering(u,successor(successor_relation)) -> equal(segment(u,regular(complement(singleton(successor_relation))),least(u,regular(complement(singleton(successor_relation))))),successor_relation)**.
% 299.82/300.46  218431[13:Res:218371.0,160373.0] || well_ordering(u,power_class(universal_class)) -> equal(segment(u,regular(image(element_relation,successor_relation)),least(u,regular(image(element_relation,successor_relation)))),successor_relation)**.
% 299.82/300.46  218442[10:Res:218372.0,160373.0] || well_ordering(u,power_class(successor_relation)) -> equal(segment(u,regular(image(element_relation,universal_class)),least(u,regular(image(element_relation,universal_class)))),successor_relation)**.
% 299.82/300.46  218514[10:Res:218490.0,160292.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(symmetric_difference(universal_class,kind_1_ordinals),successor_relation) member(least(u,symmetric_difference(universal_class,kind_1_ordinals)),symmetric_difference(universal_class,kind_1_ordinals))*.
% 299.82/300.46  218517[3:Res:218490.0,5832.1] inductive(symmetric_difference(universal_class,kind_1_ordinals)) || well_ordering(u,complement(ordinal_numbers)) -> member(least(u,symmetric_difference(universal_class,kind_1_ordinals)),symmetric_difference(universal_class,kind_1_ordinals))*.
% 299.82/300.46  218529[10:Res:218494.0,160373.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(segment(u,complement(complement(complement(kind_1_ordinals))),least(u,complement(complement(complement(kind_1_ordinals))))),successor_relation)**.
% 299.82/300.46  218619[10:Res:218475.0,160373.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(segment(u,intersection(complement(kind_1_ordinals),v),least(u,intersection(complement(kind_1_ordinals),v))),successor_relation)**.
% 299.82/300.46  218653[10:Res:218485.0,160373.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(segment(u,intersection(v,complement(kind_1_ordinals)),least(u,intersection(v,complement(kind_1_ordinals)))),successor_relation)**.
% 299.82/300.46  218769[10:Res:218493.1,160292.0] || well_ordering(u,complement(ordinal_numbers)) -> member(v,kind_1_ordinals) equal(singleton(v),successor_relation) member(least(u,singleton(v)),singleton(v))*.
% 299.82/300.46  218772[3:Res:218493.1,5832.1] inductive(singleton(u)) || well_ordering(v,complement(ordinal_numbers)) -> member(u,kind_1_ordinals) member(least(v,singleton(u)),singleton(u))*.
% 299.82/300.46  219152[3:Res:218473.1,3883.2] || equal(intersection(u,v),complement(kind_1_ordinals))** member(w,v)* member(w,u)* -> member(w,complement(ordinal_numbers))*.
% 299.82/300.46  163611[10:Rew:160305.0,162829.0] || subclass(rest_relation,rotate(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))) -> member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),kind_1_ordinals)*.
% 299.82/300.46  163612[10:Rew:160305.0,162830.0] || subclass(rest_relation,flip(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))) -> member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),kind_1_ordinals)*.
% 299.82/300.46  163631[10:Rew:160305.0,162831.1,160305.0,162831.0,160202.0,162831.0] ||  -> equal(intersection(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),successor_relation) member(regular(intersection(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),kind_1_ordinals)*.
% 299.82/300.46  163632[10:Rew:160305.0,162835.1,160305.0,162835.0,160202.0,162835.0] ||  -> equal(intersection(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u),successor_relation) member(regular(intersection(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u)),kind_1_ordinals)*.
% 299.82/300.46  163603[10:Rew:160202.0,161301.0,160305.0,161301.0] || subclass(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> equal(intersection(u,v),successor_relation) member(regular(intersection(u,v)),kind_1_ordinals)*.
% 299.82/300.46  163604[10:Rew:160202.0,161314.0,160305.0,161314.0] || subclass(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> equal(intersection(v,u),successor_relation) member(regular(intersection(v,u)),kind_1_ordinals)*.
% 299.82/300.46  163629[10:Rew:160305.0,162819.1,160202.0,162819.0,160305.0,162819.0] || member(u,symmetric_difference(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals))* -> member(u,complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))).
% 299.82/300.46  163628[10:Rew:160305.0,162815.1,160305.0,162815.0,160202.0,162815.0] ||  -> equal(complement(complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),successor_relation) member(regular(complement(complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation))))),kind_1_ordinals)*.
% 299.82/300.46  163626[10:Rew:160305.0,162805.1,160202.0,162805.0,160305.0,162805.0] || member(u,symmetric_difference(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals))* member(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))) -> .
% 299.82/300.46  208153[10:Res:207196.0,163256.1] || equal(complement(intersection(power_class(u),complement(singleton(successor_relation)))),range_of(successor_relation)) -> inductive(complement(intersection(power_class(u),complement(singleton(successor_relation)))))*.
% 299.82/300.46  207873[10:Res:206688.0,163256.1] || equal(complement(intersection(complement(singleton(successor_relation)),power_class(u))),range_of(successor_relation)) -> inductive(complement(intersection(complement(singleton(successor_relation)),power_class(u))))*.
% 299.82/300.46  203563[10:Rew:203192.0,160655.1] || member(u,universal_class) -> member(u,cantor(cross_product(v,universal_class))) equal(image(cross_product(singleton(u),universal_class),v),range_of(successor_relation))**.
% 299.82/300.46  166959[10:Res:25.2,163256.1] || member(successor_relation,u) member(successor_relation,v) equal(intersection(v,u),range_of(successor_relation)) -> inductive(intersection(v,u))*.
% 299.82/300.46  160653[10:Rew:160202.0,146347.2] || member(single_valued1(u),universal_class) -> member(single_valued1(u),range_of(u)) equal(domain__dfg(u,range_of(successor_relation),single_valued2(u)),single_valued3(u))**.
% 299.82/300.46  166958[10:Res:1951.1,163256.1] || member(successor_relation,symmetric_difference(u,v)) equal(complement(intersection(u,v)),range_of(successor_relation)) -> inductive(complement(intersection(u,v)))*.
% 299.82/300.46  163551[10:Rew:160202.0,160633.0] || member(ordered_pair(u,not_subclass_element(v,image(w,range_of(successor_relation)))),compose(w,successor_relation))* -> subclass(v,image(w,range_of(successor_relation))).
% 299.82/300.46  163624[10:Rew:160202.0,162781.1,160305.0,162781.1,160305.0,162781.0] || subclass(kind_1_ordinals,symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation))))* -> equal(symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation))),kind_1_ordinals).
% 299.82/300.46  204739[10:Rew:203192.0,203803.1] ||  -> equal(apply(u,regular(intersection(v,complement(cantor(u))))),sum_class(range_of(successor_relation)))** equal(intersection(v,complement(cantor(u))),successor_relation).
% 299.82/300.46  204738[10:Rew:203192.0,203800.1] ||  -> equal(apply(u,regular(intersection(complement(cantor(u)),v))),sum_class(range_of(successor_relation)))** equal(intersection(complement(cantor(u)),v),successor_relation).
% 299.82/300.46  203756[10:Rew:203192.0,160583.1] || member(u,universal_class) subclass(cantor(v),w)* -> equal(apply(v,u),sum_class(range_of(successor_relation)))** member(u,w)*.
% 299.82/300.46  221537[20:Res:221515.0,127.0] || subclass(complement(singleton(omega)),u)* well_ordering(v,u)* -> member(least(v,complement(singleton(omega))),complement(singleton(omega)))*.
% 299.82/300.46  221563[10:Res:161492.2,157891.0] || equal(omega,element_relation) -> equal(integer_of(not_subclass_element(complement(compose(element_relation,universal_class)),u)),successor_relation)** subclass(complement(compose(element_relation,universal_class)),u).
% 299.82/300.46  221587[10:Res:161492.2,162951.1] || equal(omega,ordinal_numbers) well_ordering(u,universal_class) -> equal(integer_of(least(u,complement(kind_1_ordinals))),successor_relation)** equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.46  221607[10:Res:160466.1,185698.1] inductive(regular(intersection(ordinal_numbers,u))) ||  -> equal(intersection(ordinal_numbers,u),successor_relation)** equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221622[10:Res:160465.1,185698.1] inductive(regular(intersection(u,ordinal_numbers))) ||  -> equal(intersection(u,ordinal_numbers),successor_relation)** equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221623[10:Res:160290.2,185698.1] inductive(regular(u)) || subclass(u,ordinal_numbers)* -> equal(u,successor_relation) equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221640[10:Res:161492.2,185698.1] inductive(u) || equal(omega,ordinal_numbers) -> equal(integer_of(u),successor_relation)** equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221661[10:Res:161419.0,185698.1] inductive(regular(complement(complement(ordinal_numbers)))) ||  -> equal(complement(complement(ordinal_numbers)),successor_relation) equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221685[15:Res:161492.2,189406.2] || equal(omega,ordinal_numbers) member(u,universal_class) subclass(domain_relation,complement(kind_1_ordinals)) -> equal(integer_of(ordered_pair(u,successor_relation)),successor_relation)**.
% 299.82/300.46  221734[10:Res:221565.0,160373.0] || well_ordering(u,complement(element_relation)) -> equal(segment(u,complement(compose(element_relation,universal_class)),least(u,complement(compose(element_relation,universal_class)))),successor_relation)**.
% 299.82/300.46  221815[10:Res:161492.2,161795.0] || equal(power_class(u),omega) -> equal(integer_of(regular(image(element_relation,complement(u)))),successor_relation)** equal(image(element_relation,complement(u)),successor_relation).
% 299.82/300.46  221824[10:Rew:160367.0,221803.1] || member(regular(image(element_relation,union(u,successor_relation))),power_class(symmetric_difference(universal_class,u)))* -> equal(image(element_relation,union(u,successor_relation)),successor_relation).
% 299.82/300.46  221915[14:Rew:199971.1,221903.1] || member(u,universal_class) equal(sum_class(range_of(u)),successor(successor_relation))** member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> .
% 299.82/300.46  221947[10:Res:161492.2,33515.1] || equal(u,omega) member(u,universal_class) -> equal(integer_of(singleton(u)),successor_relation) member(singleton(singleton(singleton(u))),element_relation)*.
% 299.82/300.46  222032[10:Res:161492.2,986.1] || equal(power_class(image(element_relation,complement(u))),omega) member(v,image(element_relation,power_class(u)))* -> equal(integer_of(v),successor_relation).
% 299.82/300.46  222093[10:Res:161492.2,155808.0] || equal(omega,ordinal_numbers) -> equal(integer_of(not_subclass_element(intersection(complement(kind_1_ordinals),u),v)),successor_relation)** subclass(intersection(complement(kind_1_ordinals),u),v).
% 299.82/300.46  222186[10:Res:161492.2,155810.0] || equal(omega,ordinal_numbers) -> equal(integer_of(not_subclass_element(intersection(u,complement(kind_1_ordinals)),v)),successor_relation)** subclass(intersection(u,complement(kind_1_ordinals)),v).
% 299.82/300.46  222258[15:Res:141787.0,189380.2] || member(u,universal_class) subclass(domain_relation,complement(inverse(singleton(ordered_pair(u,successor_relation)))))* -> asymmetric(singleton(ordered_pair(u,successor_relation)),v)*.
% 299.82/300.46  222287[15:Res:161492.2,189380.2] || equal(u,omega) member(v,universal_class) subclass(domain_relation,complement(u))* -> equal(integer_of(ordered_pair(v,successor_relation)),successor_relation)**.
% 299.82/300.46  222419[24:SpL:222326.0,5646.1] || member(ordered_pair(kind_1_ordinals,u),compose(v,w))* subclass(image(v,image(w,successor_relation)),x)* -> member(u,x)*.
% 299.82/300.46  223130[24:Res:222474.0,160373.0] || well_ordering(u,successor(kind_1_ordinals)) -> equal(segment(u,symmetric_difference(complement(kind_1_ordinals),universal_class),least(u,symmetric_difference(complement(kind_1_ordinals),universal_class))),successor_relation)**.
% 299.82/300.46  224352[25:Rew:224236.1,209424.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,regular(element_relation))*.
% 299.82/300.46  224365[25:Rew:224236.1,204762.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,power_class(successor_relation))*.
% 299.82/300.46  224366[25:Rew:224236.1,204761.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,singleton(w))*.
% 299.82/300.46  224367[25:Rew:224236.1,204760.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,regular(rest_relation))*.
% 299.82/300.46  224368[25:Rew:224236.1,204759.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,regular(domain_relation))*.
% 299.82/300.46  224397[25:Rew:224236.1,204755.2] function(u) || equal(cantor(cantor(v)),universal_class) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,v)*.
% 299.82/300.46  224757[25:MRR:202602.4,224753.0] function(u) || equal(rest_of(u),successor_relation) subclass(range_of(u),successor_relation)* equal(cross_product(successor_relation,successor_relation),successor_relation) -> .
% 299.82/300.46  225488[25:Rew:224739.1,224968.1] function(u) || asymmetric(v,successor_relation) -> equal(range__dfg(intersection(v,inverse(v)),u,successor_relation),second(not_subclass_element(successor_relation,successor_relation)))**.
% 299.82/300.46  225827[10:Res:161492.2,3627.0] || equal(composition_function,omega) -> equal(integer_of(ordered_pair(u,singleton(singleton(singleton(v))))),successor_relation)** equal(compose(u,singleton(v)),v).
% 299.82/300.46  225963[10:Res:161492.2,161867.1] || equal(u,omega) well_ordering(v,universal_class) -> equal(integer_of(least(v,complement(u))),successor_relation)** equal(complement(u),successor_relation).
% 299.82/300.46  225971[10:Rew:160367.0,225938.2] || well_ordering(u,universal_class) member(least(u,union(v,successor_relation)),symmetric_difference(universal_class,v))* -> equal(union(v,successor_relation),successor_relation).
% 299.82/300.46  225981[25:SoR:224285.0,6317.2] single_valued_class(complement(cross_product(singleton(power_class(successor_relation)),universal_class))) || equal(complement(cross_product(singleton(power_class(successor_relation)),universal_class)),cross_product(universal_class,universal_class))** -> .
% 299.82/300.46  225984[25:SoR:224288.0,6317.2] single_valued_class(complement(cross_product(singleton(regular(rest_relation)),universal_class))) || equal(complement(cross_product(singleton(regular(rest_relation)),universal_class)),cross_product(universal_class,universal_class))** -> .
% 299.82/300.46  225987[25:SoR:224289.0,6317.2] single_valued_class(complement(cross_product(singleton(regular(domain_relation)),universal_class))) || equal(complement(cross_product(singleton(regular(domain_relation)),universal_class)),cross_product(universal_class,universal_class))** -> .
% 299.82/300.46  225990[25:SoR:224290.0,6317.2] single_valued_class(complement(cross_product(singleton(regular(element_relation)),universal_class))) || equal(complement(cross_product(singleton(regular(element_relation)),universal_class)),cross_product(universal_class,universal_class))** -> .
% 299.82/300.46  226085[25:SoR:224776.0,6317.2] single_valued_class(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))) || equal(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),cross_product(universal_class,universal_class))** -> .
% 299.82/300.46  226306[15:MRR:226246.0,999.0] || member(u,universal_class) subclass(domain_relation,complement(cantor(v))) -> equal(apply(v,ordered_pair(u,successor_relation)),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  226307[10:MRR:226226.0,13.0] || subclass(universal_class,regular(cantor(u))) -> equal(apply(u,unordered_pair(v,w)),sum_class(range_of(successor_relation)))** equal(cantor(u),successor_relation).
% 299.82/300.46  226308[10:MRR:226260.0,160295.1] ||  -> equal(apply(u,regular(regular(cantor(u)))),sum_class(range_of(successor_relation)))** equal(regular(cantor(u)),successor_relation) equal(cantor(u),successor_relation).
% 299.82/300.46  226336[25:SoR:224287.0,6317.2] single_valued_class(complement(cross_product(singleton(singleton(u)),universal_class))) || equal(complement(cross_product(singleton(singleton(u)),universal_class)),cross_product(universal_class,universal_class))** -> .
% 299.82/300.46  226435[25:SSi:226402.1,73.1] one_to_one(u) || subclass(universal_class,cantor(cantor(v)))* equal(cantor(cantor(w)),universal_class) -> compatible(u,w,v)*.
% 299.82/300.46  226580[10:Res:161880.1,183398.0] ||  -> equal(intersection(intersection(complement(complement(u)),v),w),successor_relation) member(regular(intersection(intersection(complement(complement(u)),v),w)),u)*.
% 299.82/300.46  226700[10:Rew:161194.0,226501.0] ||  -> equal(intersection(symmetric_difference(complement(u),universal_class),v),successor_relation) member(regular(intersection(symmetric_difference(complement(u),universal_class),v)),union(u,successor_relation))*.
% 299.82/300.46  227171[10:Res:161881.1,183398.0] ||  -> equal(intersection(intersection(u,complement(complement(v))),w),successor_relation) member(regular(intersection(intersection(u,complement(complement(v))),w)),v)*.
% 299.82/300.46  227467[10:Res:161874.1,183398.0] ||  -> equal(intersection(u,intersection(complement(complement(v)),w)),successor_relation) member(regular(intersection(u,intersection(complement(complement(v)),w))),v)*.
% 299.82/300.46  227588[10:Rew:161194.0,227389.0] ||  -> equal(intersection(u,symmetric_difference(complement(v),universal_class)),successor_relation) member(regular(intersection(u,symmetric_difference(complement(v),universal_class))),union(v,successor_relation))*.
% 299.82/300.46  228073[10:Res:161875.1,183398.0] ||  -> equal(intersection(u,intersection(v,complement(complement(w)))),successor_relation) member(regular(intersection(u,intersection(v,complement(complement(w))))),w)*.
% 299.82/300.46  228365[10:Res:161722.2,148657.1] || subclass(u,complement(compose(element_relation,universal_class)))* member(regular(intersection(u,v)),element_relation)* -> equal(intersection(u,v),successor_relation).
% 299.82/300.46  228437[10:Rew:161194.0,228308.1] || subclass(union(u,successor_relation),v) -> equal(symmetric_difference(complement(u),universal_class),successor_relation) member(regular(symmetric_difference(complement(u),universal_class)),v)*.
% 299.82/300.46  228586[10:Res:161711.2,148657.1] || subclass(u,complement(compose(element_relation,universal_class)))* member(regular(intersection(v,u)),element_relation)* -> equal(intersection(v,u),successor_relation).
% 299.82/300.46  228749[10:Obv:228718.3] || equal(u,v) member(w,v) member(w,unordered_pair(v,u))* -> equal(unordered_pair(v,u),successor_relation).
% 299.82/300.46  228752[10:Obv:228704.2] || equal(u,v) subclass(unordered_pair(v,u),omega)* -> equal(unordered_pair(v,u),successor_relation) equal(integer_of(v),v).
% 299.82/300.46  228755[10:Rew:161611.2,228754.2] || equal(u,v) member(regular(v),unordered_pair(v,u))* -> equal(v,successor_relation) equal(unordered_pair(v,u),successor_relation).
% 299.82/300.46  228963[10:Res:160369.0,160788.0] || subclass(symmetric_difference(universal_class,u),v) -> equal(complement(union(u,successor_relation)),successor_relation) member(regular(complement(union(u,successor_relation))),v)*.
% 299.82/300.46  229091[25:Rew:160225.0,229084.1] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,regular(ordinal_numbers))*.
% 299.82/300.46  229399[10:Res:161492.2,9482.0] || equal(u,omega) -> equal(integer_of(not_subclass_element(intersection(complement(u),v),w)),successor_relation)** subclass(intersection(complement(u),v),w).
% 299.82/300.46  229565[10:Res:161492.2,9368.0] || equal(u,omega) -> equal(integer_of(not_subclass_element(intersection(v,complement(u)),w)),successor_relation)** subclass(intersection(v,complement(u)),w).
% 299.82/300.46  229806[10:Res:221521.1,161867.1] || well_ordering(u,universal_class) -> equal(integer_of(least(u,complement(complement(singleton(omega))))),successor_relation)** equal(complement(complement(singleton(omega))),successor_relation).
% 299.82/300.46  229825[10:Res:221521.1,9368.0] ||  -> equal(integer_of(not_subclass_element(intersection(u,complement(complement(singleton(omega)))),v)),successor_relation)** subclass(intersection(u,complement(complement(singleton(omega)))),v).
% 299.82/300.46  229826[10:Res:221521.1,9482.0] ||  -> equal(integer_of(not_subclass_element(intersection(complement(complement(singleton(omega))),u),v)),successor_relation)** subclass(intersection(complement(complement(singleton(omega))),u),v).
% 299.82/300.46  229859[0:SpR:195152.0,9529.1] ||  -> subclass(symmetric_difference(u,intersection(u,v)),w) member(not_subclass_element(symmetric_difference(u,intersection(u,v)),w),complement(intersection(u,v)))*.
% 299.82/300.46  229860[0:SpR:195339.0,9529.1] ||  -> subclass(symmetric_difference(u,intersection(v,u)),w) member(not_subclass_element(symmetric_difference(u,intersection(v,u)),w),complement(intersection(v,u)))*.
% 299.82/300.46  230294[10:Res:161493.2,162952.1] inductive(ordinal_numbers) || member(complement(kind_1_ordinals),universal_class) -> equal(integer_of(apply(choice,complement(kind_1_ordinals))),successor_relation)** equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.46  230601[10:Res:161493.2,161960.0] inductive(ordinal_numbers) ||  -> equal(integer_of(cross_product(universal_class,cross_product(universal_class,universal_class))),successor_relation) equal(segment(element_relation,composition_function,least(element_relation,composition_function)),successor_relation)**.
% 299.82/300.46  230863[10:MRR:230837.0,160214.0] || equal(image(element_relation,power_class(successor_relation)),range_of(successor_relation)) -> member(successor_relation,power_class(image(element_relation,universal_class)))* inductive(image(element_relation,power_class(successor_relation))).
% 299.82/300.46  230901[10:SpR:10028.0,185302.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),successor_relation)** -> equal(symmetrization_of(image(element_relation,complement(u))),universal_class).
% 299.82/300.46  230940[10:SpR:10028.0,206226.1] ||  -> member(successor_relation,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* subclass(successor(successor_relation),symmetrization_of(image(element_relation,complement(u)))).
% 299.82/300.46  230984[10:SpR:185302.1,10028.0] || equal(inverse(image(element_relation,complement(u))),successor_relation) -> equal(symmetrization_of(image(element_relation,complement(u))),complement(intersection(power_class(u),universal_class)))**.
% 299.82/300.46  231037[10:SpL:10028.0,185795.0] || equal(symmetrization_of(image(element_relation,complement(u))),successor_relation) -> equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),universal_class)**.
% 299.82/300.46  231048[20:SpL:10028.0,192322.1] inductive(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))) || equal(symmetrization_of(image(element_relation,complement(u))),omega)** -> .
% 299.82/300.46  231060[10:SpL:10028.0,208258.1] inductive(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))) || equal(symmetrization_of(image(element_relation,complement(u))),kind_1_ordinals)** -> .
% 299.82/300.46  231223[10:SpR:10029.0,185302.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),successor_relation)** -> equal(successor(image(element_relation,complement(u))),universal_class).
% 299.82/300.46  231263[10:SpR:10029.0,206226.1] ||  -> member(successor_relation,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* subclass(successor(successor_relation),successor(image(element_relation,complement(u)))).
% 299.82/300.46  231309[10:SpR:185302.1,10029.0] || equal(singleton(image(element_relation,complement(u))),successor_relation) -> equal(complement(intersection(power_class(u),universal_class)),successor(image(element_relation,complement(u))))**.
% 299.82/300.46  231372[20:SpL:10029.0,192322.1] inductive(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))) || equal(successor(image(element_relation,complement(u))),omega)** -> .
% 299.82/300.46  231384[10:SpL:10029.0,208258.1] inductive(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))) || equal(successor(image(element_relation,complement(u))),kind_1_ordinals)** -> .
% 299.82/300.46  231551[10:Res:161493.2,155802.2] inductive(ordinal_numbers) || member(u,universal_class) subclass(rest_relation,complement(kind_1_ordinals)) -> equal(integer_of(ordered_pair(u,rest_of(u))),successor_relation)**.
% 299.82/300.46  231625[14:Rew:200028.1,231609.1] || member(u,universal_class)* equal(sum_class(range_of(successor_relation)),range_of(u))* member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> .
% 299.82/300.46  231626[15:Rew:190721.0,231608.0] || equal(sum_class(range_of(successor_relation)),inverse(u))* member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> equal(range_of(u),successor_relation)**.
% 299.82/300.46  231627[14:Rew:181044.1,231607.1] || member(u,universal_class)* equal(sum_class(range_of(successor_relation)),successor(u))* member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> .
% 299.82/300.46  231762[10:SpL:185302.1,161035.0] || equal(successor_relation,u) member(v,intersection(power_class(successor_relation),universal_class)) member(v,union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231769[10:SpL:160367.0,161035.0] || member(u,intersection(power_class(successor_relation),union(v,successor_relation))) member(u,union(image(element_relation,universal_class),symmetric_difference(universal_class,v)))* -> .
% 299.82/300.46  231785[10:SpL:194805.1,161035.0] || subclass(complement(u),power_class(successor_relation)) member(v,complement(u)) member(v,union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231828[10:Res:161493.2,161035.0] inductive(intersection(power_class(successor_relation),complement(u))) || member(v,union(image(element_relation,universal_class),u))* -> equal(integer_of(v),successor_relation).
% 299.82/300.46  231829[15:Res:189485.1,161035.0] || subclass(domain_relation,intersection(power_class(successor_relation),complement(u))) member(singleton(singleton(singleton(successor_relation))),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231831[10:Res:181213.1,161035.0] || equal(intersection(power_class(successor_relation),complement(u)),singleton(singleton(successor_relation))) member(singleton(successor_relation),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231844[11:Res:183759.1,161035.0] || subclass(inverse(successor_relation),intersection(power_class(successor_relation),complement(u))) member(regular(symmetrization_of(successor_relation)),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231846[10:Res:197082.1,161035.0] || subclass(universal_class,intersection(power_class(successor_relation),complement(u))) member(regular(complement(successor(successor_relation))),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231849[10:Res:199830.1,161035.0] || equal(intersection(power_class(successor_relation),complement(u)),cross_product(universal_class,universal_class)) member(regular(rest_relation),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  231852[10:Res:201220.1,161035.0] || equal(intersection(power_class(successor_relation),complement(u)),cross_product(universal_class,universal_class)) member(regular(domain_relation),union(image(element_relation,universal_class),u))* -> .
% 299.82/300.46  29345[0:SpR:1948.0,1951.1] || member(u,symmetric_difference(union(v,w),union(complement(v),complement(w))))* -> member(u,complement(symmetric_difference(complement(v),complement(w)))).
% 299.82/300.46  38888[0:Res:8.1,5646.1] || equal(u,image(v,image(w,singleton(x))))* member(ordered_pair(x,y),compose(v,w))* -> member(y,u)*.
% 299.82/300.46  35692[0:Res:1477.1,3874.1] || subclass(universal_class,complement(intersection(u,v)))* member(singleton(w),union(u,v)) -> member(singleton(w),symmetric_difference(u,v))*.
% 299.82/300.46  30817[0:Res:60.1,3514.1] || member(ordered_pair(u,ordered_pair(v,w)),compose(x,y))* subclass(universal_class,complement(image(x,image(y,singleton(u)))))* -> .
% 299.82/300.46  39029[0:Rew:124.0,39020.2,124.0,39020.0] || member(u,segment(v,w,u))* section(v,singleton(u),w) -> equal(segment(v,w,u),singleton(u)).
% 299.82/300.46  9634[0:Res:1481.2,127.0] || subclass(u,v)* subclass(v,w)* well_ordering(x,w)* -> subclass(u,y)* member(least(x,v),v)*.
% 299.82/300.46  39955[0:Res:191.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,singleton(w))),second(ordered_pair(u,singleton(w)))),ordered_pair(u,singleton(w)))**.
% 299.82/300.46  31106[2:Res:9421.0,5832.1] inductive(symmetric_difference(u,v)) || well_ordering(w,union(u,v)) -> member(least(w,symmetric_difference(u,v)),symmetric_difference(u,v))*.
% 299.82/300.46  38401[0:Res:6010.3,3514.1] || member(u,universal_class)* member(v,universal_class) equal(compose(w,v),u)* subclass(universal_class,complement(compose_class(w)))* -> .
% 299.82/300.46  92631[2:MRR:92610.2,2450.0] || well_ordering(u,cross_product(universal_class,universal_class)) subclass(singleton(least(u,domain_relation)),domain_relation) -> section(u,singleton(least(u,domain_relation)),domain_relation)*.
% 299.82/300.46  92632[2:MRR:92609.2,2450.0] || well_ordering(u,cross_product(universal_class,universal_class)) subclass(singleton(least(u,rest_relation)),rest_relation) -> section(u,singleton(least(u,rest_relation)),rest_relation)*.
% 299.82/300.46  108348[0:SpL:1948.0,9332.1] || member(u,symmetric_difference(union(v,w),union(complement(v),complement(w))))* member(u,symmetric_difference(complement(v),complement(w))) -> .
% 299.82/300.46  110015[0:SpL:109924.1,135.1] || equal(cantor(restrict(u,v,w)),universal_class)** subclass(w,v) subclass(universal_class,w) -> section(u,w,v).
% 299.82/300.46  110013[0:SpL:109924.1,5751.0] || equal(cantor(restrict(u,v,w)),universal_class)** equal(universal_class,w) subclass(w,v) -> section(u,w,v).
% 299.82/300.46  119669[0:Res:114897.1,3874.1] || equal(complement(intersection(u,v)),universal_class) member(singleton(w),union(u,v)) -> member(singleton(w),symmetric_difference(u,v))*.
% 299.82/300.46  120151[0:SpL:1943.0,9149.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(cross_product(v,w),x)) -> member(power_class(u),complement(restrict(x,v,w)))*.
% 299.82/300.46  120150[0:SpL:1938.0,9149.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,cross_product(w,x))) -> member(power_class(u),complement(restrict(v,w,x)))*.
% 299.82/300.46  125918[0:Res:28320.1,594.0] || subclass(rest_relation,rotate(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,rest_of(ordered_pair(y,x))),y),cross_product(v,w))*.
% 299.82/300.46  125914[0:Res:28320.1,9332.1] || subclass(rest_relation,rotate(intersection(u,v))) member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),symmetric_difference(u,v))* -> .
% 299.82/300.46  126048[0:Res:28321.1,594.0] || subclass(rest_relation,flip(restrict(u,v,w)))* -> member(ordered_pair(ordered_pair(x,y),rest_of(ordered_pair(y,x))),cross_product(v,w))*.
% 299.82/300.46  126044[0:Res:28321.1,9332.1] || subclass(rest_relation,flip(intersection(u,v))) member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),symmetric_difference(u,v))* -> .
% 299.82/300.46  130985[0:SpL:10422.0,135.1] || subclass(u,v) subclass(segment(cross_product(v,u),w,x),u)* -> section(cross_product(w,singleton(x)),u,v).
% 299.82/300.46  130983[0:SpL:10422.0,5751.0] || equal(segment(cross_product(u,v),w,x),v) subclass(v,u) -> section(cross_product(w,singleton(x)),v,u)*.
% 299.82/300.46  94755[2:Res:2457.1,5919.0] inductive(domain_of(u)) || subclass(rest_of(u),v)* well_ordering(w,v)* -> member(least(w,rest_of(u)),rest_of(u))*.
% 299.82/300.46  149601[6:Rew:148462.0,36246.3] || connected(u,v)* member(w,v)* member(x,v)* -> member(ordered_pair(x,w),complement(complement(symmetrization_of(u))))*.
% 299.82/300.46  155826[3:Res:155815.1,129.3] || member(ordered_pair(u,least(kind_1_ordinals,v)),ordinal_numbers)* member(u,v) subclass(v,w)* well_ordering(kind_1_ordinals,w)* -> .
% 299.82/300.46  160071[3:Res:159952.1,5646.1] || subclass(image(u,image(v,singleton(w))),ordinal_numbers)* member(ordered_pair(w,x),compose(u,v))* -> member(x,kind_1_ordinals).
% 299.82/300.46  31202[0:Res:3872.2,3670.1] || member(singleton(u),cross_product(v,w))* member(singleton(u),x)* equal(complement(restrict(x,v,w)),universal_class)** -> .
% 299.82/300.46  31209[0:Res:3872.2,3.0] || member(u,cross_product(v,w))* member(u,x)* subclass(restrict(x,v,w),y)* -> member(u,y)*.
% 299.82/300.46  123483[0:SpR:955.0,978.1] ||  -> subclass(restrict(cross_product(u,v),w,x),y) member(not_subclass_element(restrict(cross_product(w,x),u,v),y),cross_product(u,v))*.
% 299.82/300.46  30740[0:Res:3595.3,3.0] function(u) || member(v,universal_class) subclass(universal_class,w)* subclass(w,x)* -> member(image(u,v),x)*.
% 299.82/300.46  30763[0:Res:3595.3,1952.0] function(u) || member(v,universal_class) subclass(universal_class,symmetric_difference(w,x)) -> member(image(u,v),union(w,x))*.
% 299.82/300.46  48532[0:Res:3595.3,10191.0] function(u) || member(v,universal_class) subclass(universal_class,symmetric_difference(w,inverse(w)))* -> member(image(u,v),symmetrization_of(w))*.
% 299.82/300.46  48634[0:Res:3595.3,10254.0] function(u) || member(v,universal_class) subclass(universal_class,symmetric_difference(w,singleton(w)))* -> member(image(u,v),successor(w))*.
% 299.82/300.46  126807[0:SpL:28.0,29643.0] || equal(u,union(v,w))* member(x,universal_class) -> member(x,intersection(complement(v),complement(w)))* member(x,u)*.
% 299.82/300.46  29629[0:SpL:28.0,1487.1] || member(u,universal_class) subclass(union(v,w),x)* -> member(u,intersection(complement(v),complement(w)))* member(u,x)*.
% 299.82/300.46  30983[0:Res:1032.1,3.0] || member(u,universal_class) subclass(intersection(complement(v),complement(w)),x)* -> member(u,union(v,w))* member(u,x)*.
% 299.82/300.46  111832[0:Res:1495.2,9322.0] || member(u,universal_class) subclass(rest_relation,symmetric_difference(complement(v),complement(w))) -> member(ordered_pair(u,rest_of(u)),union(v,w))*.
% 299.82/300.46  123501[0:Res:978.1,595.0] ||  -> subclass(restrict(restrict(u,v,w),x,y),z) member(not_subclass_element(restrict(restrict(u,v,w),x,y),z),u)*.
% 299.82/300.46  113253[0:Rew:161.0,113149.1] || member(not_subclass_element(union(u,v),symmetric_difference(u,v)),complement(intersection(u,v)))* -> subclass(union(u,v),symmetric_difference(u,v)).
% 299.82/300.46  123503[0:Res:978.1,1952.0] ||  -> subclass(restrict(symmetric_difference(u,v),w,x),y) member(not_subclass_element(restrict(symmetric_difference(u,v),w,x),y),union(u,v))*.
% 299.82/300.46  9582[0:Res:340.1,594.0] ||  -> subclass(intersection(restrict(u,v,w),x),y) member(not_subclass_element(intersection(restrict(u,v,w),x),y),cross_product(v,w))*.
% 299.82/300.46  9593[0:Res:322.1,594.0] ||  -> subclass(intersection(u,restrict(v,w,x)),y) member(not_subclass_element(intersection(u,restrict(v,w,x)),y),cross_product(w,x))*.
% 299.82/300.46  113122[0:Res:2126.1,9649.0] || section(u,singleton(v),w) -> subclass(segment(u,w,v),x) equal(not_subclass_element(segment(u,w,v),x),v)**.
% 299.82/300.46  107181[0:Res:34429.0,594.0] ||  -> subclass(complement(complement(restrict(u,v,w))),x) member(not_subclass_element(complement(complement(restrict(u,v,w))),x),cross_product(v,w))*.
% 299.82/300.46  33855[0:Rew:1938.0,33808.0] ||  -> subclass(symmetric_difference(u,cross_product(v,w)),x) member(not_subclass_element(symmetric_difference(u,cross_product(v,w)),x),complement(restrict(u,v,w)))*.
% 299.82/300.46  126793[0:Rew:1938.0,126700.1] || member(not_subclass_element(symmetric_difference(u,cross_product(v,w)),x),restrict(u,v,w))* -> subclass(symmetric_difference(u,cross_product(v,w)),x).
% 299.82/300.46  33933[0:Rew:1943.0,33880.0] ||  -> subclass(symmetric_difference(cross_product(u,v),w),x) member(not_subclass_element(symmetric_difference(cross_product(u,v),w),x),complement(restrict(w,u,v)))*.
% 299.82/300.46  126792[0:Rew:1943.0,126701.1] || member(not_subclass_element(symmetric_difference(cross_product(u,v),w),x),restrict(w,u,v))* -> subclass(symmetric_difference(cross_product(u,v),w),x).
% 299.82/300.46  143790[0:Res:978.1,159.0] ||  -> subclass(restrict(omega,u,v),w) equal(integer_of(not_subclass_element(restrict(omega,u,v),w)),not_subclass_element(restrict(omega,u,v),w))**.
% 299.82/300.46  123403[0:SpL:1943.0,9639.0] || subclass(u,symmetric_difference(cross_product(v,w),x)) -> subclass(u,y) member(not_subclass_element(u,y),complement(restrict(x,v,w)))*.
% 299.82/300.46  123402[0:SpL:1938.0,9639.0] || subclass(u,symmetric_difference(v,cross_product(w,x))) -> subclass(u,y) member(not_subclass_element(u,y),complement(restrict(v,w,x)))*.
% 299.82/300.46  111844[0:Res:51387.0,9322.0] ||  -> subclass(u,complement(symmetric_difference(complement(v),complement(w)))) member(not_subclass_element(u,complement(symmetric_difference(complement(v),complement(w)))),union(v,w))*.
% 299.82/300.46  108451[0:Res:1504.1,10.0] || subclass(ordered_pair(u,v),unordered_pair(w,x))* -> equal(unordered_pair(u,singleton(v)),x) equal(unordered_pair(u,singleton(v)),w).
% 299.82/300.46  30449[0:Res:60.1,3486.1] || member(ordered_pair(u,unordered_pair(v,w)),compose(x,y))* subclass(universal_class,complement(image(x,image(y,singleton(u)))))* -> .
% 299.82/300.46  31033[0:Res:3907.1,2142.0] || equal(complement(complement(ordered_pair(u,v))),universal_class)** -> equal(singleton(w),unordered_pair(u,singleton(v)))* equal(singleton(w),singleton(u)).
% 299.82/300.46  130414[0:Res:1504.1,9300.0] || subclass(ordered_pair(u,v),symmetric_difference(w,cross_product(x,y))) -> member(unordered_pair(u,singleton(v)),complement(restrict(w,x,y)))*.
% 299.82/300.46  130507[0:Res:1504.1,9306.0] || subclass(ordered_pair(u,v),symmetric_difference(cross_product(w,x),y)) -> member(unordered_pair(u,singleton(v)),complement(restrict(y,w,x)))*.
% 299.82/300.46  9160[0:Res:1478.2,19.0] || member(u,universal_class) subclass(universal_class,cross_product(v,w))* -> equal(ordered_pair(first(power_class(u)),second(power_class(u))),power_class(u))**.
% 299.82/300.46  10501[0:Res:11.1,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class) subclass(unordered_pair(least(element_relation,intersection(y__dfg,ordinal_numbers)),u),intersection(y__dfg,ordinal_numbers))* -> .
% 299.82/300.46  10500[0:Res:12.1,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class) subclass(unordered_pair(u,least(element_relation,intersection(y__dfg,ordinal_numbers))),intersection(y__dfg,ordinal_numbers))* -> .
% 299.82/300.46  28087[0:SpR:40.0,1496.2] || member(flip(cross_product(u,universal_class)),universal_class) subclass(domain_relation,v) -> member(ordered_pair(flip(cross_product(u,universal_class)),inverse(u)),v)*.
% 299.82/300.46  92629[2:MRR:92612.2,2450.0] || well_ordering(u,cross_product(universal_class,universal_class)) subclass(singleton(least(u,element_relation)),element_relation) -> section(u,singleton(least(u,element_relation)),element_relation)*.
% 299.82/300.46  9132[0:Res:1479.2,19.0] || member(u,universal_class) subclass(universal_class,cross_product(v,w))* -> equal(ordered_pair(first(sum_class(u)),second(sum_class(u))),sum_class(u))**.
% 299.82/300.46  120272[0:SpL:1943.0,9121.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(cross_product(v,w),x)) -> member(sum_class(u),complement(restrict(x,v,w)))*.
% 299.82/300.46  120271[0:SpL:1938.0,9121.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(v,cross_product(w,x))) -> member(sum_class(u),complement(restrict(v,w,x)))*.
% 299.82/300.46  28085[0:SpR:55.0,1496.2] || member(restrict(element_relation,universal_class,u),universal_class) subclass(domain_relation,v) -> member(ordered_pair(restrict(element_relation,universal_class,u),sum_class(u)),v)*.
% 299.82/300.46  109324[0:SpR:9948.0,1478.2] || member(intersection(complement(u),complement(inverse(u))),universal_class)* subclass(universal_class,v) -> member(complement(image(element_relation,symmetrization_of(u))),v)*.
% 299.82/300.46  109256[0:SpR:9949.0,1478.2] || member(intersection(complement(u),complement(singleton(u))),universal_class)* subclass(universal_class,v) -> member(complement(image(element_relation,successor(u))),v)*.
% 299.82/300.46  158338[2:SpR:982.0,142475.0] ||  -> equal(symmetric_difference(image(element_relation,union(image(element_relation,power_class(u)),v)),power_class(intersection(power_class(image(element_relation,complement(u))),complement(v)))),universal_class)**.
% 299.82/300.46  158375[2:SpR:982.0,142477.0] ||  -> equal(symmetric_difference(power_class(intersection(power_class(image(element_relation,complement(u))),complement(v))),image(element_relation,union(image(element_relation,power_class(u)),v))),universal_class)**.
% 299.82/300.46  9964[0:SpL:505.0,307.0] || member(u,image(element_relation,power_class(intersection(complement(v),complement(w)))))* member(u,power_class(image(element_relation,union(v,w)))) -> .
% 299.82/300.46  158337[2:SpR:984.0,142475.0] ||  -> equal(symmetric_difference(image(element_relation,union(u,image(element_relation,power_class(v)))),power_class(intersection(complement(u),power_class(image(element_relation,complement(v)))))),universal_class)**.
% 299.82/300.46  158374[2:SpR:984.0,142477.0] ||  -> equal(symmetric_difference(power_class(intersection(complement(u),power_class(image(element_relation,complement(v))))),image(element_relation,union(u,image(element_relation,power_class(v))))),universal_class)**.
% 299.82/300.46  28559[0:SpL:208.0,513.0] || member(u,intersection(complement(v),power_class(image(element_relation,complement(w)))))* member(u,union(v,image(element_relation,power_class(w)))) -> .
% 299.82/300.46  124298[0:Res:1504.1,986.1] || subclass(ordered_pair(u,v),power_class(image(element_relation,complement(w))))* member(unordered_pair(u,singleton(v)),image(element_relation,power_class(w))) -> .
% 299.82/300.46  118043[0:SpL:208.0,9069.0] || subclass(universal_class,image(element_relation,power_class(image(element_relation,complement(u)))))* member(unordered_pair(v,w),power_class(image(element_relation,power_class(u))))* -> .
% 299.82/300.46  28520[0:SpR:208.0,1028.1] || member(u,universal_class) -> member(u,image(element_relation,power_class(image(element_relation,complement(v)))))* member(u,power_class(image(element_relation,power_class(v)))).
% 299.82/300.46  158305[0:SpL:984.0,3565.0] || equal(complement(union(u,image(element_relation,power_class(v)))),universal_class) -> member(omega,intersection(complement(u),power_class(image(element_relation,complement(v)))))*.
% 299.82/300.46  140220[0:SpL:984.0,3358.1] || equal(intersection(complement(u),power_class(image(element_relation,complement(v)))),universal_class)** equal(union(u,image(element_relation,power_class(v))),universal_class) -> .
% 299.82/300.46  140217[0:SpL:984.0,30433.1] || subclass(universal_class,intersection(complement(u),power_class(image(element_relation,complement(v)))))* subclass(universal_class,union(u,image(element_relation,power_class(v)))) -> .
% 299.82/300.46  28571[0:SpL:208.0,513.0] || member(u,intersection(power_class(image(element_relation,complement(v))),complement(w)))* member(u,union(image(element_relation,power_class(v)),w)) -> .
% 299.82/300.46  118394[0:SpL:208.0,9146.1] || member(u,universal_class) subclass(universal_class,power_class(image(element_relation,complement(v))))* member(power_class(u),image(element_relation,power_class(v)))* -> .
% 299.82/300.46  118678[0:SpL:208.0,9118.1] || member(u,universal_class) subclass(universal_class,power_class(image(element_relation,complement(v))))* member(sum_class(u),image(element_relation,power_class(v)))* -> .
% 299.82/300.46  124292[0:Res:1481.2,986.1] || subclass(u,power_class(image(element_relation,complement(v)))) member(not_subclass_element(u,w),image(element_relation,power_class(v)))* -> subclass(u,w).
% 299.82/300.46  158306[0:SpL:982.0,3565.0] || equal(complement(union(image(element_relation,power_class(u)),v)),universal_class) -> member(omega,intersection(power_class(image(element_relation,complement(u))),complement(v)))*.
% 299.82/300.46  139758[0:SpL:982.0,3358.1] || equal(intersection(power_class(image(element_relation,complement(u))),complement(v)),universal_class)** equal(union(image(element_relation,power_class(u)),v),universal_class) -> .
% 299.82/300.46  139755[0:SpL:982.0,30433.1] || subclass(universal_class,intersection(power_class(image(element_relation,complement(u))),complement(v)))* subclass(universal_class,union(image(element_relation,power_class(u)),v)) -> .
% 299.82/300.46  1093[0:Rew:208.0,1076.1] || member(not_subclass_element(power_class(image(element_relation,complement(u))),v),image(element_relation,power_class(u)))* -> subclass(power_class(image(element_relation,complement(u))),v).
% 299.82/300.46  9384[0:Res:322.1,307.0] || member(not_subclass_element(intersection(u,image(element_relation,complement(v))),w),power_class(v))* -> subclass(intersection(u,image(element_relation,complement(v))),w).
% 299.82/300.46  137170[0:SpL:10029.0,26.1] || member(u,intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))* member(u,successor(image(element_relation,complement(v)))) -> .
% 299.82/300.46  137788[0:SpL:10028.0,26.1] || member(u,intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))* member(u,symmetrization_of(image(element_relation,complement(v)))) -> .
% 299.82/300.46  158307[0:SpL:10029.0,3565.0] || equal(complement(successor(image(element_relation,complement(u)))),universal_class) -> member(omega,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.82/300.46  137135[0:SpL:10029.0,3358.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),universal_class)** equal(successor(image(element_relation,complement(u))),universal_class) -> .
% 299.82/300.46  137132[0:SpL:10029.0,30433.1] || subclass(universal_class,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* subclass(universal_class,successor(image(element_relation,complement(u)))) -> .
% 299.82/300.46  158308[0:SpL:10028.0,3565.0] || equal(complement(symmetrization_of(image(element_relation,complement(u)))),universal_class) -> member(omega,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.82/300.46  137753[0:SpL:10028.0,3358.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),universal_class)** equal(symmetrization_of(image(element_relation,complement(u))),universal_class) -> .
% 299.82/300.46  137750[0:SpL:10028.0,30433.1] || subclass(universal_class,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* subclass(universal_class,symmetrization_of(image(element_relation,complement(u)))) -> .
% 299.82/300.46  9498[0:Res:340.1,307.0] || member(not_subclass_element(intersection(image(element_relation,complement(u)),v),w),power_class(u))* -> subclass(intersection(image(element_relation,complement(u)),v),w).
% 299.82/300.46  125941[0:Res:28320.1,307.0] || subclass(rest_relation,rotate(image(element_relation,complement(u)))) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),power_class(u))* -> .
% 299.82/300.46  126071[0:Res:28321.1,307.0] || subclass(rest_relation,flip(image(element_relation,complement(u)))) member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),power_class(u))* -> .
% 299.82/300.46  157919[6:Res:3595.3,148657.1] function(u) || member(v,universal_class) subclass(universal_class,complement(compose(element_relation,universal_class)))* member(image(u,v),element_relation)* -> .
% 299.82/300.46  130996[0:SpL:10422.0,47745.0] || member(restrict(cross_product(u,singleton(v)),w,x),segment(cross_product(w,x),u,v))* subclass(universal_class,complement(element_relation)) -> .
% 299.82/300.46  52162[0:Res:50.1,5646.1] inductive(image(u,singleton(v))) || member(ordered_pair(v,w),compose(successor_relation,u))* -> member(w,image(u,singleton(v))).
% 299.82/300.46  163613[10:Rew:160202.0,163105.2] || subclass(domain_relation,ordered_pair(u,v))* -> equal(unordered_pair(u,singleton(v)),ordered_pair(successor_relation,successor_relation)) equal(ordered_pair(successor_relation,successor_relation),singleton(u)).
% 299.82/300.46  163594[10:Rew:160202.0,160991.1] ||  -> subclass(symmetric_difference(complement(u),power_class(successor_relation)),v) member(not_subclass_element(symmetric_difference(complement(u),power_class(successor_relation)),v),union(u,image(element_relation,universal_class)))*.
% 299.82/300.46  160993[10:Rew:160202.0,150849.2] function(u) || member(v,universal_class) subclass(universal_class,power_class(successor_relation)) member(image(u,v),image(element_relation,universal_class))* -> .
% 299.82/300.46  163595[10:Rew:160202.0,161001.1] ||  -> subclass(symmetric_difference(power_class(successor_relation),complement(u)),v) member(not_subclass_element(symmetric_difference(power_class(successor_relation),complement(u)),v),union(image(element_relation,universal_class),u))*.
% 299.82/300.46  160913[10:Rew:160202.0,150868.0] ||  -> equal(complement(intersection(power_class(intersection(power_class(successor_relation),complement(u))),complement(v))),union(image(element_relation,union(image(element_relation,universal_class),u)),v))**.
% 299.82/300.46  160923[10:Rew:160202.0,150975.0] ||  -> subclass(symmetric_difference(union(image(element_relation,universal_class),u),complement(singleton(intersection(power_class(successor_relation),complement(u))))),successor(intersection(power_class(successor_relation),complement(u))))*.
% 299.82/300.46  160925[10:Rew:160202.0,150976.0] ||  -> subclass(symmetric_difference(union(image(element_relation,universal_class),u),complement(inverse(intersection(power_class(successor_relation),complement(u))))),symmetrization_of(intersection(power_class(successor_relation),complement(u))))*.
% 299.82/300.46  163592[10:Rew:160202.0,160932.1] || member(regular(union(image(element_relation,universal_class),u)),intersection(power_class(successor_relation),complement(u)))* -> equal(union(image(element_relation,universal_class),u),successor_relation).
% 299.82/300.46  160944[10:Rew:160202.0,150853.0] ||  -> equal(complement(intersection(power_class(intersection(complement(u),power_class(successor_relation))),complement(v))),union(image(element_relation,union(u,image(element_relation,universal_class))),v))**.
% 299.82/300.46  160954[10:Rew:160202.0,150956.0] ||  -> subclass(symmetric_difference(union(u,image(element_relation,universal_class)),complement(singleton(intersection(complement(u),power_class(successor_relation))))),successor(intersection(complement(u),power_class(successor_relation))))*.
% 299.82/300.46  160956[10:Rew:160202.0,150957.0] ||  -> subclass(symmetric_difference(union(u,image(element_relation,universal_class)),complement(inverse(intersection(complement(u),power_class(successor_relation))))),symmetrization_of(intersection(complement(u),power_class(successor_relation))))*.
% 299.82/300.46  163593[10:Rew:160202.0,160963.1] || member(regular(union(u,image(element_relation,universal_class))),intersection(complement(u),power_class(successor_relation)))* -> equal(union(u,image(element_relation,universal_class)),successor_relation).
% 299.82/300.46  163587[10:Rew:160202.0,160716.1] || member(u,universal_class) subclass(u,power_class(successor_relation)) member(apply(choice,u),image(element_relation,universal_class))* -> equal(u,successor_relation).
% 299.82/300.46  161019[10:Rew:160202.0,150848.0] ||  -> equal(complement(intersection(complement(u),power_class(intersection(complement(v),power_class(successor_relation))))),union(u,image(element_relation,union(v,image(element_relation,universal_class)))))**.
% 299.82/300.46  163589[10:Rew:160202.0,160726.1] || subclass(u,union(v,image(element_relation,universal_class))) member(regular(u),intersection(complement(v),power_class(successor_relation)))* -> equal(u,successor_relation).
% 299.82/300.46  161025[10:Rew:160202.0,150954.0] ||  -> member(not_subclass_element(u,union(v,image(element_relation,universal_class))),intersection(complement(v),power_class(successor_relation)))* subclass(u,union(v,image(element_relation,universal_class))).
% 299.82/300.46  161040[10:Rew:160202.0,150855.0] ||  -> equal(complement(intersection(complement(u),power_class(intersection(power_class(successor_relation),complement(v))))),union(u,image(element_relation,union(image(element_relation,universal_class),v))))**.
% 299.82/300.46  163588[10:Rew:160202.0,160725.1] || subclass(u,union(image(element_relation,universal_class),v)) member(regular(u),intersection(power_class(successor_relation),complement(v)))* -> equal(u,successor_relation).
% 299.82/300.46  161046[10:Rew:160202.0,150961.0] ||  -> member(not_subclass_element(u,union(image(element_relation,universal_class),v)),intersection(power_class(successor_relation),complement(v)))* subclass(u,union(image(element_relation,universal_class),v)).
% 299.82/300.46  163596[10:Rew:160202.0,161076.1] || member(regular(intersection(intersection(u,power_class(successor_relation)),v)),image(element_relation,universal_class))* -> equal(intersection(intersection(u,power_class(successor_relation)),v),successor_relation).
% 299.82/300.46  163597[10:Rew:160202.0,161080.1] || member(regular(intersection(intersection(power_class(successor_relation),u),v)),image(element_relation,universal_class))* -> equal(intersection(intersection(power_class(successor_relation),u),v),successor_relation).
% 299.82/300.46  161073[10:Rew:160202.0,150850.0] ||  -> equal(complement(intersection(power_class(intersection(complement(u),complement(v))),power_class(successor_relation))),union(image(element_relation,union(u,v)),image(element_relation,universal_class)))**.
% 299.82/300.46  161082[10:Rew:160202.0,150872.0] ||  -> equal(complement(intersection(power_class(successor_relation),power_class(intersection(complement(u),complement(v))))),union(image(element_relation,universal_class),image(element_relation,union(u,v))))**.
% 299.82/300.46  163598[10:Rew:160202.0,161087.1] || member(regular(intersection(u,intersection(power_class(successor_relation),v))),image(element_relation,universal_class))* -> equal(intersection(u,intersection(power_class(successor_relation),v)),successor_relation).
% 299.82/300.46  163599[10:Rew:160202.0,161088.1] || member(regular(intersection(u,intersection(v,power_class(successor_relation)))),image(element_relation,universal_class))* -> equal(intersection(u,intersection(v,power_class(successor_relation))),successor_relation).
% 299.82/300.46  163600[10:Rew:160202.0,161100.1,160202.0,161100.0] || well_ordering(u,complement(inverse(successor_relation))) -> equal(complement(symmetrization_of(successor_relation)),successor_relation) member(least(u,complement(symmetrization_of(successor_relation))),complement(symmetrization_of(successor_relation)))*.
% 299.82/300.46  163602[10:Rew:160202.0,161192.0] || subclass(cross_product(u,v),successor_relation)* member(w,v)* member(x,u)* -> member(ordered_pair(x,w),inverse(successor_relation))*.
% 299.82/300.46  160746[10:Rew:160202.0,146501.2] || member(u,universal_class) subclass(u,symmetric_difference(v,singleton(v)))* -> equal(u,successor_relation) member(apply(choice,u),successor(v)).
% 299.82/300.46  160745[10:Rew:160202.0,146514.3] || member(u,universal_class) subclass(u,v)* subclass(v,w)* -> equal(u,successor_relation) member(apply(choice,u),w)*.
% 299.82/300.46  160744[10:Rew:160202.0,146515.2] || member(u,universal_class) subclass(u,symmetric_difference(v,w)) -> equal(u,successor_relation) member(apply(choice,u),union(v,w))*.
% 299.82/300.46  160743[10:Rew:160202.0,146516.2] || member(u,universal_class) subclass(u,symmetric_difference(v,inverse(v)))* -> equal(u,successor_relation) member(apply(choice,u),symmetrization_of(v)).
% 299.82/300.46  160742[10:Rew:160202.0,146529.3] || subclass(u,v)* subclass(v,w)* well_ordering(x,w)* -> equal(u,successor_relation) member(least(x,v),v)*.
% 299.82/300.46  160686[10:Rew:160202.0,159717.2] || member(not_subclass_element(restrict(regular(u),v,w),x),u)* -> subclass(restrict(regular(u),v,w),x) equal(u,successor_relation).
% 299.82/300.46  160685[10:Rew:160202.0,159712.2] || subclass(rest_relation,flip(regular(u))) member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),u)* -> equal(u,successor_relation).
% 299.82/300.46  160684[10:Rew:160202.0,159711.2] || subclass(rest_relation,rotate(regular(u))) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),u)* -> equal(u,successor_relation).
% 299.82/300.46  162025[10:Rew:160202.0,146563.2] || section(element_relation,u,universal_class) well_ordering(v,u) -> equal(sum_class(u),successor_relation) member(least(v,sum_class(u)),sum_class(u))*.
% 299.82/300.46  162024[10:Rew:160202.0,146568.2] || equal(sum_class(u),u) well_ordering(v,u) -> equal(sum_class(u),successor_relation) member(least(v,sum_class(u)),sum_class(u))*.
% 299.82/300.46  161274[10:Rew:160202.0,146718.1] || subclass(intersection(u,singleton(v)),symmetric_difference(w,x))* -> equal(intersection(u,singleton(v)),successor_relation) member(v,union(w,x)).
% 299.82/300.46  161281[10:Rew:160202.0,146732.1] || subclass(intersection(singleton(u),v),symmetric_difference(w,x))* -> equal(intersection(singleton(u),v),successor_relation) member(u,union(w,x)).
% 299.82/300.46  161353[10:Rew:160202.0,146597.2] || subclass(rest_of(u),v)* well_ordering(w,v)* -> equal(cantor(u),successor_relation) member(least(w,rest_of(u)),rest_of(u))*.
% 299.82/300.46  163605[10:Rew:160202.0,161674.1] || well_ordering(u,union(v,successor_relation)) -> equal(segment(u,symmetric_difference(complement(v),universal_class),least(u,symmetric_difference(complement(v),universal_class))),successor_relation)**.
% 299.82/300.46  161595[10:Rew:160202.0,146803.2] || member(cross_product(u,v),universal_class) subclass(universal_class,complement(apply(choice,cross_product(u,v))))* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.46  161594[10:Rew:160202.0,146804.2] || member(cross_product(u,v),universal_class) equal(complement(apply(choice,cross_product(u,v))),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.46  161593[10:Rew:160202.0,146826.1] || subclass(regular(cross_product(u,v)),w) -> equal(cross_product(u,v),successor_relation) member(singleton(first(regular(cross_product(u,v)))),w)*.
% 299.82/300.46  161684[10:Rew:160202.0,146731.1] || member(symmetric_difference(u,v),universal_class) -> equal(symmetric_difference(u,v),successor_relation) member(apply(choice,symmetric_difference(u,v)),union(u,v))*.
% 299.82/300.46  161703[10:Rew:160202.0,146874.2] || subclass(u,image(element_relation,complement(v))) member(regular(intersection(w,u)),power_class(v))* -> equal(intersection(w,u),successor_relation).
% 299.82/300.46  161714[10:Rew:160202.0,146895.2] || subclass(u,image(element_relation,complement(v))) member(regular(intersection(u,w)),power_class(v))* -> equal(intersection(u,w),successor_relation).
% 299.82/300.46  161773[10:Rew:160202.0,146703.2] || subclass(unordered_pair(u,v),w)* -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),successor_relation) member(v,w).
% 299.82/300.46  161772[10:Rew:160202.0,146704.2] || subclass(unordered_pair(u,v),w)* -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),successor_relation) member(u,w).
% 299.82/300.46  161917[10:Rew:160202.0,147156.1] || equal(u,regular(cross_product(v,w))) -> equal(cross_product(v,w),successor_relation) member(singleton(first(regular(cross_product(v,w)))),u)*.
% 299.82/300.46  162064[10:Rew:160202.0,147013.2] || subclass(u,intersection(v,w)) member(regular(intersection(x,u)),symmetric_difference(v,w))* -> equal(intersection(x,u),successor_relation).
% 299.82/300.46  162078[10:Rew:160202.0,147028.2] || subclass(u,intersection(v,w)) member(regular(intersection(u,x)),symmetric_difference(v,w))* -> equal(intersection(u,x),successor_relation).
% 299.82/300.46  162099[10:Rew:160202.0,147401.1] || member(regular(restrict(intersection(u,v),w,x)),symmetric_difference(u,v))* -> equal(restrict(intersection(u,v),w,x),successor_relation).
% 299.82/300.46  162177[10:Rew:160202.0,147000.1] || well_ordering(u,union(v,w)) -> equal(symmetric_difference(v,w),successor_relation) member(least(u,symmetric_difference(v,w)),symmetric_difference(v,w))*.
% 299.82/300.46  162210[10:Rew:160202.0,147597.1] || subclass(u,restrict(v,w,x))* -> equal(intersection(y,u),successor_relation) member(regular(intersection(y,u)),cross_product(w,x))*.
% 299.82/300.46  162219[10:Rew:160202.0,147696.1] || subclass(u,restrict(v,w,x))* -> equal(intersection(u,y),successor_relation) member(regular(intersection(u,y)),cross_product(w,x))*.
% 299.82/300.46  162323[10:Rew:160202.0,147071.1] || well_ordering(u,cross_product(v,w)) -> equal(segment(u,restrict(x,v,w),least(u,restrict(x,v,w))),successor_relation)**.
% 299.82/300.46  162328[10:Rew:160202.0,147276.1] ||  -> member(regular(complement(power_class(image(element_relation,complement(u))))),image(element_relation,power_class(u)))* equal(complement(power_class(image(element_relation,complement(u)))),successor_relation).
% 299.82/300.46  162332[10:Rew:160202.0,147432.0] ||  -> equal(restrict(symmetric_difference(u,singleton(u)),v,w),successor_relation) member(regular(restrict(symmetric_difference(u,singleton(u)),v,w)),successor(u))*.
% 299.82/300.46  162333[10:Rew:160202.0,147433.0] ||  -> equal(restrict(symmetric_difference(u,inverse(u)),v,w),successor_relation) member(regular(restrict(symmetric_difference(u,inverse(u)),v,w)),symmetrization_of(u))*.
% 299.82/300.46  162334[10:Rew:160202.0,147479.1] || member(regular(intersection(u,union(v,w))),intersection(complement(v),complement(w)))* -> equal(intersection(u,union(v,w)),successor_relation).
% 299.82/300.46  162335[10:Rew:160202.0,147506.1] || member(regular(intersection(union(u,v),w)),intersection(complement(u),complement(v)))* -> equal(intersection(union(u,v),w),successor_relation).
% 299.82/300.46  162344[10:Rew:160202.0,147950.0] ||  -> equal(intersection(power_class(intersection(power_class(image(element_relation,complement(u))),complement(v))),image(element_relation,union(image(element_relation,power_class(u)),v))),successor_relation)**.
% 299.82/300.46  162345[10:Rew:160202.0,147951.0] ||  -> equal(intersection(image(element_relation,union(image(element_relation,power_class(u)),v)),power_class(intersection(power_class(image(element_relation,complement(u))),complement(v)))),successor_relation)**.
% 299.82/300.46  162346[10:Rew:160202.0,147970.0] ||  -> equal(intersection(power_class(intersection(complement(u),power_class(image(element_relation,complement(v))))),image(element_relation,union(u,image(element_relation,power_class(v))))),successor_relation)**.
% 299.82/300.46  162347[10:Rew:160202.0,147971.0] ||  -> equal(intersection(image(element_relation,union(u,image(element_relation,power_class(v)))),power_class(intersection(complement(u),power_class(image(element_relation,complement(v)))))),successor_relation)**.
% 299.82/300.46  162357[10:Rew:160202.0,148534.1] || asymmetric(cross_product(u,v),singleton(w)) -> equal(segment(restrict(inverse(cross_product(u,v)),u,v),singleton(w),w),successor_relation)**.
% 299.82/300.46  162995[10:Rew:160202.0,156254.1] || well_ordering(u,symmetric_difference(universal_class,v)) -> equal(segment(u,complement(union(v,successor_relation)),least(u,complement(union(v,successor_relation)))),successor_relation)**.
% 299.82/300.46  183141[10:SpR:181044.1,60.1] || member(u,universal_class) member(ordered_pair(successor(u),v),compose(w,x))* -> member(v,image(w,image(x,successor_relation))).
% 299.82/300.46  183972[14:Rew:183958.0,101309.1] single_valued_class(recursion(u,successor_relation,union_of_range_map)) || equal(recursion(u,successor_relation,successor_relation),cross_product(universal_class,universal_class)) -> member(ordinal_add(u,v),universal_class)*.
% 299.82/300.46  185847[10:MRR:162600.0,185804.0] ||  -> equal(regular(complement(complement(ordered_pair(u,v)))),unordered_pair(u,singleton(v)))** equal(regular(complement(complement(ordered_pair(u,v)))),singleton(u)).
% 299.82/300.46  187497[10:Res:187489.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,power_class(successor_relation))),second(ordered_pair(u,power_class(successor_relation)))),ordered_pair(u,power_class(successor_relation)))**.
% 299.82/300.46  187512[10:Res:160784.3,148657.1] || member(u,universal_class) subclass(u,complement(compose(element_relation,universal_class)))* member(apply(choice,u),element_relation) -> equal(u,successor_relation).
% 299.82/300.46  5804[0:Rew:1005.0,5801.2] || member(singleton(u),u)* member(singleton(singleton(singleton(u))),cross_product(universal_class,universal_class))* -> member(singleton(singleton(singleton(u))),element_relation).
% 299.82/300.46  181224[10:Rew:181067.0,181214.2] || equal(compose(u,successor_relation),universal_class) member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> member(singleton(singleton(successor_relation)),compose_class(u))*.
% 299.82/300.46  122855[0:Res:137.1,9640.0] || member(intersection(u,v),ordinal_numbers) -> subclass(sum_class(intersection(u,v)),w) member(not_subclass_element(sum_class(intersection(u,v)),w),v)*.
% 299.82/300.46  123446[0:Res:137.1,9639.0] || member(intersection(u,v),ordinal_numbers) -> subclass(sum_class(intersection(u,v)),w) member(not_subclass_element(sum_class(intersection(u,v)),w),u)*.
% 299.82/300.46  31091[2:Res:59.0,5832.1] inductive(compose(u,v)) || well_ordering(w,cross_product(universal_class,universal_class)) -> member(least(w,compose(u,v)),compose(u,v))*.
% 299.82/300.46  108806[2:Res:31076.2,1952.0] inductive(symmetric_difference(u,v)) || well_ordering(w,symmetric_difference(u,v)) -> member(least(w,symmetric_difference(u,v)),union(u,v))*.
% 299.82/300.46  162178[10:Rew:160202.0,146998.1] || well_ordering(u,symmetric_difference(v,w)) -> equal(symmetric_difference(v,w),successor_relation) member(least(u,symmetric_difference(v,w)),union(v,w))*.
% 299.82/300.46  110649[0:MRR:110640.2,34067.1] || well_ordering(cross_product(u,universal_class),universal_class)* member(v,u)* subclass(universal_class,w) well_ordering(cross_product(u,universal_class),w)* -> .
% 299.82/300.46  108249[2:Res:31069.2,594.0] inductive(restrict(u,v,w)) || well_ordering(x,universal_class) -> member(least(x,restrict(u,v,w)),cross_product(v,w))*.
% 299.82/300.46  108271[2:Res:31069.2,307.0] inductive(image(element_relation,complement(u))) || well_ordering(v,universal_class) member(least(v,image(element_relation,complement(u))),power_class(u))* -> .
% 299.82/300.46  162322[10:Rew:160202.0,147068.2] || well_ordering(u,universal_class) member(least(u,image(element_relation,complement(v))),power_class(v))* -> equal(image(element_relation,complement(v)),successor_relation).
% 299.82/300.46  162174[10:Rew:160202.0,146996.1] || well_ordering(u,universal_class) -> equal(restrict(v,w,x),successor_relation) member(least(u,restrict(v,w,x)),cross_product(w,x))*.
% 299.82/300.46  5844[0:Res:305.1,127.0] || member(u,universal_class) subclass(singleton(u),v)* well_ordering(w,v)* -> member(least(w,singleton(u)),singleton(u))*.
% 299.82/300.46  36247[0:Res:64.1,5553.2] function(cross_product(u,v)) || member(w,v)* member(x,u)* -> member(ordered_pair(x,w),cross_product(universal_class,universal_class))*.
% 299.82/300.46  125672[0:SpL:1005.0,3627.0] || member(singleton(singleton(singleton(singleton(singleton(singleton(u)))))),composition_function)* -> equal(compose(singleton(singleton(singleton(singleton(u)))),singleton(u)),u)**.
% 299.82/300.46  107654[0:Res:5768.2,6045.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,w)* subclass(w,x)* well_ordering(universal_class,x)* -> .
% 299.82/300.46  39602[0:Res:5768.2,147.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,rest_relation) -> equal(ordered_pair(v,compose(u,v)),rest_of(u))**.
% 299.82/300.46  162996[10:Rew:160202.0,156354.2] function(u) || member(ordered_pair(u,inverse(u)),cross_product(universal_class,universal_class)) -> member(ordered_pair(u,ordered_pair(inverse(u),successor_relation)),composition_function)*.
% 299.82/300.46  162997[10:Rew:160202.0,156319.2] single_valued_class(u) || member(ordered_pair(u,inverse(u)),cross_product(universal_class,universal_class)) -> member(ordered_pair(u,ordered_pair(inverse(u),successor_relation)),composition_function)*.
% 299.82/300.46  187768[10:Res:187500.1,3874.1] || subclass(universal_class,complement(intersection(u,v)))* member(power_class(successor_relation),union(u,v)) -> member(power_class(successor_relation),symmetric_difference(u,v)).
% 299.82/300.46  189391[15:Rew:189339.1,28594.2] || member(u,universal_class) subclass(domain_relation,intersection(complement(v),complement(w)))* member(ordered_pair(u,successor_relation),union(v,w))* -> .
% 299.82/300.46  189466[15:Rew:189339.1,189382.2] || member(u,universal_class) subclass(domain_relation,unordered_pair(v,w))* -> equal(ordered_pair(u,successor_relation),w)* equal(ordered_pair(u,successor_relation),v)*.
% 299.82/300.46  192123[15:SpR:190721.0,60.1] || member(ordered_pair(inverse(u),v),compose(w,x))* -> equal(range_of(u),successor_relation) member(v,image(w,image(x,successor_relation))).
% 299.82/300.46  192614[11:Res:183734.0,162356.0] || subclass(inverse(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(symmetrization_of(successor_relation)),least(omega,inverse(successor_relation)))),successor_relation)**.
% 299.82/300.46  192607[10:Res:181063.0,162356.0] || subclass(ordered_pair(universal_class,u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(successor_relation,least(omega,ordered_pair(universal_class,u)))),successor_relation)**.
% 299.82/300.46  192600[10:Res:160268.1,162356.0] || equal(u,universal_class) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(successor_relation,least(omega,u))),successor_relation)**.
% 299.82/300.46  192594[20:Res:191074.1,162356.0] || equal(u,omega) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(successor_relation,least(omega,u))),successor_relation)**.
% 299.82/300.46  192593[13:Res:180583.0,162356.0] || subclass(image(element_relation,successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(successor_relation,least(omega,image(element_relation,successor_relation)))),successor_relation)**.
% 299.82/300.46  192592[10:Res:160460.0,162356.0] || subclass(image(element_relation,universal_class),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(successor_relation,least(omega,image(element_relation,universal_class)))),successor_relation)**.
% 299.82/300.46  192574[10:Res:160295.1,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(v,successor_relation) equal(integer_of(ordered_pair(regular(v),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  192566[10:Res:160362.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(singleton(v),successor_relation) equal(integer_of(ordered_pair(v,least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  192565[10:Res:160274.1,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(v),successor_relation) equal(integer_of(ordered_pair(v,least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  192516[10:Res:155815.1,162356.0] || member(u,ordinal_numbers) subclass(kind_1_ordinals,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(u,least(omega,kind_1_ordinals))),successor_relation)**.
% 299.82/300.46  192515[10:Res:160275.0,162356.0] || subclass(omega,u) well_ordering(omega,u)* -> equal(integer_of(v),successor_relation) equal(integer_of(ordered_pair(v,least(omega,omega))),successor_relation)**.
% 299.82/300.46  192502[10:Res:1506.1,162356.0] || equal(u,universal_class) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(omega,least(omega,u))),successor_relation)**.
% 299.82/300.46  192499[10:Res:160298.1,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(u,successor_relation) equal(integer_of(ordered_pair(regular(u),least(omega,u))),successor_relation)**.
% 299.82/300.46  193547[2:Res:141787.0,179.1] || subclass(inverse(singleton(least(element_relation,intersection(y__dfg,ordinal_numbers)))),intersection(y__dfg,ordinal_numbers))* -> asymmetric(singleton(least(element_relation,intersection(y__dfg,ordinal_numbers))),u)*.
% 299.82/300.46  195512[0:SpL:194805.1,3874.1] || subclass(u,v) member(w,union(v,u)) member(w,complement(u)) -> member(w,symmetric_difference(v,u))*.
% 299.82/300.46  195618[10:SpL:505.0,195436.0] || subclass(image(element_relation,union(u,v)),power_class(intersection(complement(u),complement(v))))* -> equal(image(element_relation,union(u,v)),successor_relation).
% 299.82/300.46  196580[10:SpL:161137.0,1487.1] || member(u,universal_class) subclass(power_class(complement(inverse(successor_relation))),v)* -> member(u,image(element_relation,symmetrization_of(successor_relation)))* member(u,v)*.
% 299.82/300.46  196550[10:SpR:161137.0,507.0] ||  -> equal(complement(intersection(complement(u),union(v,image(element_relation,symmetrization_of(successor_relation))))),union(u,intersection(complement(v),power_class(complement(inverse(successor_relation))))))**.
% 299.82/300.46  196543[10:SpR:161137.0,507.0] ||  -> equal(complement(intersection(complement(u),union(image(element_relation,symmetrization_of(successor_relation)),v))),union(u,intersection(power_class(complement(inverse(successor_relation))),complement(v))))**.
% 299.82/300.46  196540[10:SpR:161137.0,506.0] ||  -> equal(complement(intersection(union(u,image(element_relation,symmetrization_of(successor_relation))),complement(v))),union(intersection(complement(u),power_class(complement(inverse(successor_relation)))),v))**.
% 299.82/300.46  196505[10:SpR:161137.0,506.0] ||  -> equal(complement(intersection(union(image(element_relation,symmetrization_of(successor_relation)),u),complement(v))),union(intersection(power_class(complement(inverse(successor_relation))),complement(u)),v))**.
% 299.82/300.46  196786[10:SpL:162889.0,1487.1] || member(u,universal_class) subclass(power_class(complement(singleton(successor_relation))),v)* -> member(u,image(element_relation,successor(successor_relation)))* member(u,v)*.
% 299.82/300.46  196756[10:SpR:162889.0,507.0] ||  -> equal(complement(intersection(complement(u),union(v,image(element_relation,successor(successor_relation))))),union(u,intersection(complement(v),power_class(complement(singleton(successor_relation))))))**.
% 299.82/300.46  196749[10:SpR:162889.0,507.0] ||  -> equal(complement(intersection(complement(u),union(image(element_relation,successor(successor_relation)),v))),union(u,intersection(power_class(complement(singleton(successor_relation))),complement(v))))**.
% 299.82/300.46  196746[10:SpR:162889.0,506.0] ||  -> equal(complement(intersection(union(u,image(element_relation,successor(successor_relation))),complement(v))),union(intersection(complement(u),power_class(complement(singleton(successor_relation)))),v))**.
% 299.82/300.46  196711[10:SpR:162889.0,506.0] ||  -> equal(complement(intersection(union(image(element_relation,successor(successor_relation)),u),complement(v))),union(intersection(power_class(complement(singleton(successor_relation))),complement(u)),v))**.
% 299.82/300.46  197429[10:SpL:161565.2,185068.0] || member(cross_product(u,v),universal_class) subclass(singleton(apply(choice,cross_product(u,v))),successor_relation)* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.46  199845[6:Res:199826.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,regular(rest_relation))),second(ordered_pair(u,regular(rest_relation)))),ordered_pair(u,regular(rest_relation)))**.
% 299.82/300.46  199983[6:Res:199848.1,3874.1] || subclass(universal_class,complement(intersection(u,v)))* member(regular(rest_relation),union(u,v)) -> member(regular(rest_relation),symmetric_difference(u,v)).
% 299.82/300.46  200063[14:SpR:200028.1,60.1] || member(u,universal_class) member(ordered_pair(range_of(u),v),compose(w,x))* -> member(v,image(w,image(x,successor_relation))).
% 299.82/300.46  201228[6:Res:201216.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,regular(domain_relation))),second(ordered_pair(u,regular(domain_relation)))),ordered_pair(u,regular(domain_relation)))**.
% 299.82/300.46  201373[6:Res:201231.1,3874.1] || subclass(universal_class,complement(intersection(u,v)))* member(regular(domain_relation),union(u,v)) -> member(regular(domain_relation),symmetric_difference(u,v)).
% 299.82/300.46  202005[10:Res:161492.2,176.0] || equal(omega,ordinal_numbers) member(least(element_relation,intersection(y__dfg,ordinal_numbers)),y__dfg)* -> equal(integer_of(least(element_relation,intersection(y__dfg,ordinal_numbers))),successor_relation).
% 299.82/300.46  201988[10:Res:161492.2,38.0] || equal(flip(u),omega) -> equal(integer_of(ordered_pair(ordered_pair(v,w),x)),successor_relation) member(ordered_pair(ordered_pair(w,v),x),u)*.
% 299.82/300.46  201987[10:Res:161492.2,35.0] || equal(rotate(u),omega) -> equal(integer_of(ordered_pair(ordered_pair(v,w),x)),successor_relation) member(ordered_pair(ordered_pair(w,x),v),u)*.
% 299.82/300.46  201917[10:Res:161492.2,161270.1] || equal(u,omega) member(complement(u),universal_class) -> equal(integer_of(apply(choice,complement(u))),successor_relation)** equal(complement(u),successor_relation).
% 299.82/300.46  202778[10:Res:160827.1,160373.0] || well_ordering(u,power_class(universal_class)) -> member(v,image(element_relation,successor_relation)) equal(segment(u,singleton(v),least(u,singleton(v))),successor_relation)**.
% 299.82/300.46  203782[6:Rew:203192.0,119254.2] inductive(complement(domain_of(u))) || well_ordering(v,complement(cantor(u))) -> member(least(v,complement(cantor(u))),complement(cantor(u)))*.
% 299.82/300.46  204767[6:Rew:203192.0,203870.3,203192.0,203870.0] || subclass(sum_class(cantor(u)),cantor(u))* member(ordinal_numbers,universal_class) well_ordering(element_relation,cantor(u)) -> member(cantor(u),ordinal_numbers).
% 299.82/300.46  203961[6:Rew:203192.0,39592.2] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,domain_relation) -> equal(ordered_pair(v,compose(u,v)),cantor(u))**.
% 299.82/300.46  204018[6:Rew:203192.0,10460.1] || subclass(u,v) subclass(cantor(restrict(cross_product(v,u),w,x)),u)* -> section(cross_product(w,x),u,v).
% 299.82/300.46  204019[6:Rew:203192.0,31248.0] || equal(cantor(restrict(cross_product(u,v),w,x)),v)** subclass(v,u) -> section(cross_product(w,x),v,u).
% 299.82/300.46  206018[10:Res:163210.1,160373.0] || well_ordering(u,symmetrization_of(successor_relation)) -> member(v,complement(inverse(successor_relation))) equal(segment(u,singleton(v),least(u,singleton(v))),successor_relation)**.
% 299.82/300.46  206033[10:Res:160970.1,160373.0] || well_ordering(u,power_class(successor_relation)) -> member(v,image(element_relation,universal_class)) equal(segment(u,singleton(v),least(u,singleton(v))),successor_relation)**.
% 299.82/300.46  206718[10:Res:206682.0,162356.0] || subclass(symmetrization_of(singleton(successor_relation)),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(successor_relation,least(omega,symmetrization_of(singleton(successor_relation))))),successor_relation)**.
% 299.82/300.46  206732[10:Res:206684.0,162356.0] || subclass(successor(singleton(successor_relation)),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(successor_relation,least(omega,successor(singleton(successor_relation))))),successor_relation)**.
% 299.82/300.46  206952[10:Res:206947.1,162356.0] || equal(u,kind_1_ordinals) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(successor_relation,least(omega,u))),successor_relation)**.
% 299.82/300.46  209101[10:Res:163218.1,160373.0] || well_ordering(u,successor(successor_relation)) -> member(v,complement(singleton(successor_relation))) equal(segment(u,singleton(v),least(u,singleton(v))),successor_relation)**.
% 299.82/300.46  209374[12:Res:209309.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,regular(element_relation))),second(ordered_pair(u,regular(element_relation)))),ordered_pair(u,regular(element_relation)))**.
% 299.82/300.46  209450[12:Res:209377.1,3874.1] || subclass(universal_class,complement(intersection(u,v)))* member(regular(element_relation),union(u,v)) -> member(regular(element_relation),symmetric_difference(u,v)).
% 299.82/300.46  210366[15:Res:189563.1,9306.0] || subclass(domain_relation,flip(symmetric_difference(cross_product(u,v),w))) -> member(ordered_pair(ordered_pair(x,y),successor_relation),complement(restrict(w,u,v)))*.
% 299.82/300.46  210364[15:Res:189563.1,9300.0] || subclass(domain_relation,flip(symmetric_difference(u,cross_product(v,w)))) -> member(ordered_pair(ordered_pair(x,y),successor_relation),complement(restrict(u,v,w)))*.
% 299.82/300.46  210439[15:Res:189564.1,9306.0] || subclass(domain_relation,rotate(symmetric_difference(cross_product(u,v),w))) -> member(ordered_pair(ordered_pair(x,successor_relation),y),complement(restrict(w,u,v)))*.
% 299.82/300.46  210437[15:Res:189564.1,9300.0] || subclass(domain_relation,rotate(symmetric_difference(u,cross_product(v,w)))) -> member(ordered_pair(ordered_pair(x,successor_relation),y),complement(restrict(u,v,w)))*.
% 299.82/300.46  211641[10:Res:211579.1,127.0] || subclass(complement(u),v)* well_ordering(w,v)* -> member(singleton(successor_relation),u) member(least(w,complement(u)),complement(u))*.
% 299.82/300.46  211703[10:Res:181213.1,2142.0] || equal(ordered_pair(u,v),singleton(singleton(successor_relation))) -> equal(unordered_pair(u,singleton(v)),singleton(successor_relation))** equal(singleton(successor_relation),singleton(u)).
% 299.82/300.46  211982[11:Res:183759.1,19.0] || subclass(inverse(successor_relation),cross_product(u,v))* -> equal(ordered_pair(first(regular(symmetrization_of(successor_relation))),second(regular(symmetrization_of(successor_relation)))),regular(symmetrization_of(successor_relation)))**.
% 299.82/300.46  214440[21:Res:214433.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(complement(complement(symmetrization_of(successor_relation)))),least(omega,universal_class))),successor_relation)**.
% 299.82/300.46  214755[10:Res:161697.1,148657.1] || member(regular(restrict(complement(compose(element_relation,universal_class)),u,v)),element_relation)* -> equal(restrict(complement(compose(element_relation,universal_class)),u,v),successor_relation).
% 299.82/300.46  216136[6:Res:199830.1,2142.0] || equal(ordered_pair(u,v),cross_product(universal_class,universal_class)) -> equal(unordered_pair(u,singleton(v)),regular(rest_relation))** equal(regular(rest_relation),singleton(u)).
% 299.82/300.46  216744[6:Res:201220.1,2142.0] || equal(ordered_pair(u,v),cross_product(universal_class,universal_class)) -> equal(unordered_pair(u,singleton(v)),regular(domain_relation))** equal(regular(domain_relation),singleton(u)).
% 299.82/300.46  216880[10:MRR:216857.3,161269.0] || member(apply(choice,regular(complement(u))),universal_class)* -> member(apply(choice,regular(complement(u))),u)* equal(regular(complement(u)),successor_relation).
% 299.82/300.46  216956[10:SpR:202307.1,99.1] || equal(compose_class(u),domain_relation) member(ordered_pair(u,successor_relation),cross_product(universal_class,universal_class)) -> member(ordered_pair(u,ordered_pair(successor_relation,successor_relation)),composition_function)*.
% 299.82/300.46  217594[10:MRR:217556.0,13.0] || subclass(universal_class,regular(image(element_relation,complement(u))))* -> member(unordered_pair(v,w),power_class(u))* equal(image(element_relation,complement(u)),successor_relation).
% 299.82/300.46  217595[10:MRR:217565.2,186160.1] || member(ordered_pair(u,unordered_pair(v,w)),compose(x,y))* subclass(universal_class,regular(image(x,image(y,singleton(u)))))* -> .
% 299.82/300.46  217904[10:SpL:161565.2,217574.0] || member(cross_product(u,v),universal_class) subclass(universal_class,regular(apply(choice,cross_product(u,v))))* -> equal(cross_product(u,v),successor_relation).
% 299.82/300.46  217987[10:SpL:161565.2,217671.0] || member(cross_product(u,v),universal_class) equal(complement(apply(choice,cross_product(u,v))),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.46  217996[10:SpL:161565.2,217908.0] || member(cross_product(u,v),universal_class) equal(regular(apply(choice,cross_product(u,v))),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.82/300.46  218317[10:MRR:218279.0,34189.1] ||  -> member(not_subclass_element(regular(union(u,v)),w),complement(v))* subclass(regular(union(u,v)),w) equal(union(u,v),successor_relation).
% 299.82/300.46  218318[10:MRR:218278.0,34189.1] ||  -> member(not_subclass_element(regular(union(u,v)),w),complement(u))* subclass(regular(union(u,v)),w) equal(union(u,v),successor_relation).
% 299.82/300.46  218340[10:SpR:505.0,218298.0] ||  -> subclass(regular(image(element_relation,union(u,v))),power_class(intersection(complement(u),complement(v))))* equal(image(element_relation,union(u,v)),successor_relation).
% 299.82/300.46  218880[22:Res:218867.1,3874.1] || subclass(kind_1_ordinals,complement(intersection(u,v)))* member(singleton(successor_relation),union(u,v)) -> member(singleton(successor_relation),symmetric_difference(u,v)).
% 299.82/300.46  219153[6:Res:218473.1,203329.1] || equal(cantor(restrict(u,v,complement(ordinal_numbers))),complement(kind_1_ordinals))** subclass(complement(ordinal_numbers),v) -> section(u,complement(ordinal_numbers),v).
% 299.82/300.46  203748[10:Rew:203192.0,160582.1] || member(u,universal_class) subclass(cantor(v),w)* well_ordering(universal_class,w) -> equal(apply(v,u),sum_class(range_of(successor_relation)))**.
% 299.82/300.46  204757[10:Rew:203192.0,203674.2] || well_ordering(u,universal_class) -> equal(apply(v,least(u,complement(cantor(v)))),sum_class(range_of(successor_relation)))** equal(complement(cantor(v)),successor_relation).
% 299.82/300.46  204764[10:Rew:203192.0,203802.1] ||  -> equal(apply(u,not_subclass_element(intersection(complement(cantor(u)),v),w)),sum_class(range_of(successor_relation)))** subclass(intersection(complement(cantor(u)),v),w).
% 299.82/300.46  204765[10:Rew:203192.0,203804.1] ||  -> equal(apply(u,not_subclass_element(intersection(v,complement(cantor(u))),w)),sum_class(range_of(successor_relation)))** subclass(intersection(v,complement(cantor(u))),w).
% 299.82/300.46  163625[10:Rew:160305.0,162788.0] || member(intersection(complement(singleton(successor_relation)),complement(range_of(successor_relation))),universal_class)* subclass(universal_class,u) -> member(complement(image(element_relation,kind_1_ordinals)),u)*.
% 299.82/300.46  163585[10:Rew:160202.0,160657.2] || member(u,range_of(successor_relation)) member(ordered_pair(v,u),cross_product(universal_class,universal_class)) -> member(ordered_pair(v,u),compose(successor_relation,w))*.
% 299.82/300.46  163659[10:Rew:160305.0,161255.2] single_valued_class(image(successor_relation,cross_product(universal_class,universal_class))) || member(successor_relation,cross_product(universal_class,universal_class))* equal(cross_product(universal_class,universal_class),range_of(successor_relation)) -> .
% 299.82/300.46  166986[10:MRR:166960.0,160214.0] || equal(intersection(complement(u),complement(v)),range_of(successor_relation)) -> member(successor_relation,union(u,v)) inductive(intersection(complement(u),complement(v)))*.
% 299.82/300.46  163586[10:Rew:160202.0,160660.3,160202.0,160660.2] || member(ordinal_numbers,universal_class) well_ordering(element_relation,range_of(successor_relation)) subclass(sum_class(range_of(successor_relation)),range_of(successor_relation))* -> member(range_of(successor_relation),ordinal_numbers).
% 299.82/300.46  163639[10:Rew:160305.0,162804.2,160202.0,162804.1,160305.0,162804.1] || member(u,kind_1_ordinals) member(u,complement(intersection(singleton(successor_relation),range_of(successor_relation))))* -> member(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))).
% 299.82/300.46  163627[10:Rew:160305.0,162807.2] function(u) || member(v,universal_class) subclass(universal_class,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> member(image(u,v),kind_1_ordinals)*.
% 299.82/300.46  163640[10:Rew:160202.0,162816.1,160305.0,162816.1,160305.0,162816.0] ||  -> subclass(complement(complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),u) member(not_subclass_element(complement(complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),u),kind_1_ordinals)*.
% 299.82/300.46  163615[10:Rew:160202.0,160706.1,160305.0,160706.1] || member(u,universal_class) subclass(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))* -> equal(u,successor_relation) member(apply(choice,u),kind_1_ordinals).
% 299.82/300.46  163642[10:Rew:160202.0,162836.1,160305.0,162836.1,160305.0,162836.0] ||  -> subclass(intersection(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u),v) member(not_subclass_element(intersection(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u),v),kind_1_ordinals)*.
% 299.82/300.46  163641[10:Rew:160202.0,162832.1,160305.0,162832.1,160305.0,162832.0] ||  -> subclass(intersection(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),v) member(not_subclass_element(intersection(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),v),kind_1_ordinals)*.
% 299.82/300.46  163645[10:Rew:160305.0,162949.1] || well_ordering(u,kind_1_ordinals) -> equal(segment(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation)),least(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),successor_relation)**.
% 299.82/300.46  221533[20:Res:221515.0,162356.0] || subclass(complement(singleton(omega)),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(successor_relation,least(omega,complement(singleton(omega))))),successor_relation)**.
% 299.82/300.46  221648[10:Res:1504.1,185698.1] inductive(unordered_pair(u,singleton(v))) || subclass(ordered_pair(u,v),ordinal_numbers)* -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221638[15:Res:189563.1,185698.1] inductive(ordered_pair(ordered_pair(u,v),successor_relation)) || subclass(domain_relation,flip(ordinal_numbers)) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221634[15:Res:189564.1,185698.1] inductive(ordered_pair(ordered_pair(u,successor_relation),v)) || subclass(domain_relation,rotate(ordinal_numbers)) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221624[10:Res:1479.2,185698.1] inductive(sum_class(u)) || member(u,universal_class)* subclass(universal_class,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221621[10:Res:322.1,185698.1] inductive(not_subclass_element(intersection(u,ordinal_numbers),v)) ||  -> subclass(intersection(u,ordinal_numbers),v)* equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221619[10:Res:1481.2,185698.1] inductive(not_subclass_element(u,v)) || subclass(u,ordinal_numbers)* -> subclass(u,v)* equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221618[10:Res:1478.2,185698.1] inductive(power_class(u)) || member(u,universal_class)* subclass(universal_class,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221612[10:Res:340.1,185698.1] inductive(not_subclass_element(intersection(ordinal_numbers,u),v)) ||  -> subclass(intersection(ordinal_numbers,u),v)* equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  221611[10:Res:34429.0,185698.1] inductive(not_subclass_element(complement(complement(ordinal_numbers)),u)) ||  -> subclass(complement(complement(ordinal_numbers)),u)* equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.82/300.46  222030[15:Res:189563.1,986.1] || subclass(domain_relation,flip(power_class(image(element_relation,complement(u))))) member(ordered_pair(ordered_pair(v,w),successor_relation),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  222026[15:Res:189564.1,986.1] || subclass(domain_relation,rotate(power_class(image(element_relation,complement(u))))) member(ordered_pair(ordered_pair(v,successor_relation),w),image(element_relation,power_class(u)))* -> .
% 299.82/300.46  221991[10:SpL:162889.0,986.1] || member(u,image(element_relation,power_class(image(element_relation,successor(successor_relation)))))* member(u,power_class(image(element_relation,power_class(complement(singleton(successor_relation)))))) -> .
% 299.82/300.46  221990[10:SpL:161137.0,986.1] || member(u,image(element_relation,power_class(image(element_relation,symmetrization_of(successor_relation)))))* member(u,power_class(image(element_relation,power_class(complement(inverse(successor_relation)))))) -> .
% 299.82/300.46  222129[10:SpR:2330.1,221525.0] ||  -> subclass(cross_product(u,v),w) member(singleton(first(not_subclass_element(cross_product(u,v),w))),complement(singleton(not_subclass_element(cross_product(u,v),w))))*.
% 299.82/300.46  222226[10:SpL:2330.1,222147.0] || member(singleton(first(not_subclass_element(cross_product(u,v),w))),singleton(not_subclass_element(cross_product(u,v),w)))* -> subclass(cross_product(u,v),w).
% 299.82/300.46  222246[15:Res:1951.1,189380.2] || member(ordered_pair(u,successor_relation),symmetric_difference(v,w))* member(u,universal_class) subclass(domain_relation,complement(complement(intersection(v,w))))* -> .
% 299.82/300.46  222614[24:Res:222332.0,162356.0] || subclass(ordered_pair(kind_1_ordinals,u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(successor_relation,least(omega,ordered_pair(kind_1_ordinals,u)))),successor_relation)**.
% 299.82/300.46  223145[24:Res:223096.0,5832.1] inductive(complement(successor(kind_1_ordinals))) || well_ordering(u,symmetric_difference(universal_class,kind_1_ordinals)) -> member(least(u,complement(successor(kind_1_ordinals))),complement(successor(kind_1_ordinals)))*.
% 299.82/300.46  223142[24:Res:223096.0,160292.0] || well_ordering(u,symmetric_difference(universal_class,kind_1_ordinals)) -> equal(complement(successor(kind_1_ordinals)),successor_relation) member(least(u,complement(successor(kind_1_ordinals))),complement(successor(kind_1_ordinals)))*.
% 299.82/300.46  223370[24:Rew:222479.0,223328.2] || equal(compose(u,v),kind_1_ordinals) member(ordered_pair(v,universal_class),cross_product(universal_class,universal_class))* -> member(ordered_pair(v,universal_class),compose_class(u))*.
% 299.82/300.46  224362[25:Rew:224236.1,204794.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,regular(symmetrization_of(successor_relation)))*.
% 299.82/300.46  224363[25:Rew:224236.1,204793.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,ordered_pair(w,x))*.
% 299.82/300.46  224364[25:Rew:224236.1,204792.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,unordered_pair(w,x))*.
% 299.82/300.46  224396[25:Rew:224236.1,204787.2] function(u) || equal(cantor(range_of(v)),universal_class) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,inverse(v))*.
% 299.82/300.46  224802[25:MRR:224801.3,3567.0] function(restrict(u,v,w)) || section(u,w,v)* well_ordering(x,w)* -> member(least(x,universal_class),universal_class)*.
% 299.82/300.46  226310[10:MRR:226223.0,34189.1] ||  -> equal(apply(u,not_subclass_element(regular(cantor(u)),v)),sum_class(range_of(successor_relation)))** subclass(regular(cantor(u)),v) equal(cantor(u),successor_relation).
% 299.82/300.46  226356[25:Rew:226350.1,224762.1] one_to_one(flip(cross_product(u,universal_class))) || subclass(universal_class,range_of(u)) equal(cross_product(range_of(u),range_of(u)),inverse(u))** -> .
% 299.82/300.46  226364[25:Rew:226353.2,187302.3] single_valued_class(inverse(u)) || subclass(range_of(inverse(u)),v) equal(inverse(u),successor_relation) -> maps(inverse(u),universal_class,v)*.
% 299.82/300.46  226436[25:SSi:226403.1,73.1] one_to_one(u) || subclass(universal_class,cantor(range_of(v))) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,inverse(v))*.
% 299.82/300.46  227320[25:SpR:2330.1,224913.1] function(first(not_subclass_element(cross_product(u,v),w))) ||  -> subclass(cross_product(u,v),w) member(successor_relation,not_subclass_element(cross_product(u,v),w))*.
% 299.82/300.46  228392[10:Res:161722.2,160481.0] || subclass(u,regular(v)) member(regular(intersection(u,w)),v)* -> equal(intersection(u,w),successor_relation) equal(v,successor_relation).
% 299.82/300.46  228613[10:Res:161711.2,160481.0] || subclass(u,regular(v)) member(regular(intersection(w,u)),v)* -> equal(intersection(w,u),successor_relation) equal(v,successor_relation).
% 299.82/300.46  228753[10:Obv:228702.1] || equal(u,v) -> equal(unordered_pair(v,u),successor_relation) equal(symmetric_difference(unordered_pair(v,u),v),union(unordered_pair(v,u),v))**.
% 299.82/300.46  228757[10:Rew:161611.2,228756.2] || equal(u,v) member(not_subclass_element(v,w),unordered_pair(v,u))* -> subclass(v,w) equal(unordered_pair(v,u),successor_relation).
% 299.82/300.46  228759[10:Rew:161611.2,228758.2] || equal(u,v) member(apply(choice,v),unordered_pair(v,u))* -> equal(v,successor_relation) equal(unordered_pair(v,u),successor_relation).
% 299.82/300.46  228972[10:Res:218481.0,160788.0] || subclass(complement(ordinal_numbers),u) -> equal(restrict(complement(kind_1_ordinals),v,w),successor_relation) member(regular(restrict(complement(kind_1_ordinals),v,w)),u)*.
% 299.82/300.46  229008[10:Rew:162256.2,228942.3] || section(u,singleton(v),w)* subclass(singleton(v),x)* -> equal(segment(u,w,v),successor_relation) member(v,x).
% 299.82/300.46  229016[10:Res:228991.1,3874.1] || subclass(kind_1_ordinals,complement(intersection(u,v)))* member(regular(ordinal_numbers),union(u,v)) -> member(regular(ordinal_numbers),symmetric_difference(u,v)).
% 299.82/300.46  229158[10:Obv:229141.1] || subclass(regular(union(u,v)),symmetric_difference(u,v))* -> equal(regular(union(u,v)),successor_relation) equal(union(u,v),successor_relation).
% 299.82/300.46  229225[10:Res:229170.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,regular(ordinal_numbers))),second(ordered_pair(u,regular(ordinal_numbers)))),ordered_pair(u,regular(ordinal_numbers)))**.
% 299.82/300.46  229244[10:Res:229228.1,3874.1] || subclass(universal_class,complement(intersection(u,v)))* member(regular(ordinal_numbers),union(u,v)) -> member(regular(ordinal_numbers),symmetric_difference(u,v)).
% 299.82/300.46  229712[10:SpL:162889.0,29643.0] || equal(u,power_class(complement(singleton(successor_relation))))* member(v,universal_class) -> member(v,image(element_relation,successor(successor_relation)))* member(v,u)*.
% 299.82/300.46  229711[10:SpL:161137.0,29643.0] || equal(u,power_class(complement(inverse(successor_relation))))* member(v,universal_class) -> member(v,image(element_relation,symmetrization_of(successor_relation)))* member(v,u)*.
% 299.82/300.46  229904[10:SpR:161194.0,9529.1] ||  -> subclass(symmetric_difference(union(u,successor_relation),universal_class),v) member(not_subclass_element(symmetric_difference(union(u,successor_relation),universal_class),v),complement(symmetric_difference(complement(u),universal_class)))*.
% 299.82/300.46  230293[10:Res:161492.2,162952.1] || equal(omega,ordinal_numbers) member(complement(kind_1_ordinals),universal_class) -> equal(integer_of(apply(choice,complement(kind_1_ordinals))),successor_relation)** equal(complement(kind_1_ordinals),successor_relation).
% 299.82/300.46  230600[10:Res:161492.2,161960.0] || equal(omega,ordinal_numbers) -> equal(integer_of(cross_product(universal_class,cross_product(universal_class,universal_class))),successor_relation) equal(segment(element_relation,composition_function,least(element_relation,composition_function)),successor_relation)**.
% 299.82/300.46  230749[10:Res:163539.1,3.0] || subclass(kind_1_ordinals,u) -> subclass(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),v) member(not_subclass_element(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),v),u)*.
% 299.82/300.46  230823[10:Res:160972.1,3.0] || member(u,universal_class) subclass(image(element_relation,power_class(successor_relation)),v)* -> member(u,power_class(image(element_relation,universal_class)))* member(u,v)*.
% 299.82/300.46  230807[10:SpR:185605.1,160972.1] || equal(successor_relation,u) member(v,universal_class) -> member(v,image(element_relation,power_class(u)))* member(v,power_class(image(element_relation,universal_class))).
% 299.82/300.46  231076[0:SpL:10028.0,183398.0] || member(u,complement(symmetrization_of(image(element_relation,complement(v))))) -> member(u,intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))*.
% 299.82/300.46  231066[15:SpL:10028.0,230608.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),domain_relation)** equal(symmetrization_of(image(element_relation,complement(u))),domain_relation) -> .
% 299.82/300.46  231065[15:SpL:10028.0,222296.1] || subclass(domain_relation,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* subclass(domain_relation,symmetrization_of(image(element_relation,complement(u)))) -> .
% 299.82/300.46  231062[11:SpL:10028.0,211092.1] inductive(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))) || equal(symmetrization_of(image(element_relation,complement(u))),inverse(successor_relation))** -> .
% 299.82/300.46  231061[10:SpL:10028.0,208945.1] inductive(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))) || equal(symmetrization_of(image(element_relation,complement(u))),singleton(successor_relation))** -> .
% 299.82/300.46  231059[10:SpL:10028.0,208250.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),kind_1_ordinals)** equal(symmetrization_of(image(element_relation,complement(u))),kind_1_ordinals) -> .
% 299.82/300.46  231058[20:SpL:10028.0,208251.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),omega)** equal(symmetrization_of(image(element_relation,complement(u))),kind_1_ordinals) -> .
% 299.82/300.46  231057[10:SpL:10028.0,208257.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),universal_class)** equal(symmetrization_of(image(element_relation,complement(u))),kind_1_ordinals) -> .
% 299.82/300.46  231056[10:SpL:10028.0,206082.1] inductive(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))) || equal(symmetrization_of(image(element_relation,complement(u))),successor(successor_relation))** -> .
% 299.82/300.46  231053[11:SpL:10028.0,202882.1] inductive(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))) || equal(symmetrization_of(image(element_relation,complement(u))),symmetrization_of(successor_relation))** -> .
% 299.82/300.46  231050[10:SpL:10028.0,188851.0] || subclass(symmetrization_of(image(element_relation,complement(u))),successor_relation) -> member(singleton(v),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.82/300.46  231047[20:SpL:10028.0,192315.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),omega)** equal(symmetrization_of(image(element_relation,complement(u))),omega) -> .
% 299.82/300.46  231046[20:SpL:10028.0,192321.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),universal_class)** equal(symmetrization_of(image(element_relation,complement(u))),omega) -> .
% 299.82/300.46  231045[20:SpL:10028.0,206996.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),kind_1_ordinals)** equal(symmetrization_of(image(element_relation,complement(u))),omega) -> .
% 299.82/300.46  231033[10:SpL:10028.0,211448.0] || well_ordering(universal_class,symmetrization_of(image(element_relation,complement(u)))) -> member(singleton(successor_relation),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.82/300.46  231016[10:SpL:10028.0,206962.0] || equal(complement(symmetrization_of(image(element_relation,complement(u)))),kind_1_ordinals) -> member(successor_relation,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.82/300.46  231012[20:SpL:10028.0,192323.0] || equal(complement(symmetrization_of(image(element_relation,complement(u)))),omega) -> member(successor_relation,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.82/300.46  231010[10:SpL:10028.0,160544.0] || equal(complement(symmetrization_of(image(element_relation,complement(u)))),universal_class) -> member(successor_relation,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.82/300.46  231007[20:SpL:10028.0,191129.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),omega)** equal(symmetrization_of(image(element_relation,complement(u))),universal_class) -> .
% 299.82/300.46  231006[10:SpL:10028.0,206997.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),kind_1_ordinals)** equal(symmetrization_of(image(element_relation,complement(u))),universal_class) -> .
% 299.82/300.46  231002[15:SpL:10028.0,213296.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),domain_relation)** equal(symmetrization_of(image(element_relation,complement(u))),universal_class) -> .
% 299.82/300.46  230941[10:SpR:10028.0,211579.1] ||  -> member(singleton(successor_relation),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* member(singleton(successor_relation),symmetrization_of(image(element_relation,complement(u)))).
% 299.82/300.46  230939[10:SpR:10028.0,161320.0] ||  -> equal(intersection(symmetrization_of(image(element_relation,complement(u))),restrict(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),v,w)),successor_relation)**.
% 299.82/300.46  230938[10:SpR:10028.0,161321.0] ||  -> equal(intersection(restrict(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),v,w),symmetrization_of(image(element_relation,complement(u)))),successor_relation)**.
% 299.82/300.46  231400[0:SpL:10029.0,183398.0] || member(u,complement(successor(image(element_relation,complement(v))))) -> member(u,intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))*.
% 299.82/300.46  231390[15:SpL:10029.0,230608.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),domain_relation)** equal(successor(image(element_relation,complement(u))),domain_relation) -> .
% 299.82/300.46  231389[15:SpL:10029.0,222296.1] || subclass(domain_relation,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* subclass(domain_relation,successor(image(element_relation,complement(u)))) -> .
% 299.82/300.46  231386[11:SpL:10029.0,211092.1] inductive(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))) || equal(successor(image(element_relation,complement(u))),inverse(successor_relation))** -> .
% 299.82/300.46  231385[10:SpL:10029.0,208945.1] inductive(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))) || equal(successor(image(element_relation,complement(u))),singleton(successor_relation))** -> .
% 299.82/300.46  231383[10:SpL:10029.0,208250.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),kind_1_ordinals)** equal(successor(image(element_relation,complement(u))),kind_1_ordinals) -> .
% 299.82/300.46  231382[20:SpL:10029.0,208251.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),omega)** equal(successor(image(element_relation,complement(u))),kind_1_ordinals) -> .
% 299.82/300.46  231381[10:SpL:10029.0,208257.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),universal_class)** equal(successor(image(element_relation,complement(u))),kind_1_ordinals) -> .
% 299.82/300.46  231380[10:SpL:10029.0,206082.1] inductive(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))) || equal(successor(image(element_relation,complement(u))),successor(successor_relation))** -> .
% 299.82/300.46  231377[11:SpL:10029.0,202882.1] inductive(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))) || equal(successor(image(element_relation,complement(u))),symmetrization_of(successor_relation))** -> .
% 299.82/300.46  231374[10:SpL:10029.0,188851.0] || subclass(successor(image(element_relation,complement(u))),successor_relation) -> member(singleton(v),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.82/300.46  231371[20:SpL:10029.0,192315.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),omega)** equal(successor(image(element_relation,complement(u))),omega) -> .
% 299.82/300.46  231370[20:SpL:10029.0,192321.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),universal_class)** equal(successor(image(element_relation,complement(u))),omega) -> .
% 299.82/300.46  231369[20:SpL:10029.0,206996.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),kind_1_ordinals)** equal(successor(image(element_relation,complement(u))),omega) -> .
% 299.82/300.46  231357[10:SpL:10029.0,211448.0] || well_ordering(universal_class,successor(image(element_relation,complement(u)))) -> member(singleton(successor_relation),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.82/300.46  231340[10:SpL:10029.0,206962.0] || equal(complement(successor(image(element_relation,complement(u)))),kind_1_ordinals) -> member(successor_relation,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.82/300.46  231336[20:SpL:10029.0,192323.0] || equal(complement(successor(image(element_relation,complement(u)))),omega) -> member(successor_relation,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.82/300.46  231334[10:SpL:10029.0,160544.0] || equal(complement(successor(image(element_relation,complement(u)))),universal_class) -> member(successor_relation,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.82/300.46  231331[20:SpL:10029.0,191129.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),omega)** equal(successor(image(element_relation,complement(u))),universal_class) -> .
% 299.82/300.46  231330[10:SpL:10029.0,206997.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),kind_1_ordinals)** equal(successor(image(element_relation,complement(u))),universal_class) -> .
% 299.82/300.46  231326[15:SpL:10029.0,213296.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),domain_relation)** equal(successor(image(element_relation,complement(u))),universal_class) -> .
% 299.82/300.46  231264[10:SpR:10029.0,211579.1] ||  -> member(singleton(successor_relation),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* member(singleton(successor_relation),successor(image(element_relation,complement(u)))).
% 299.82/300.46  231262[10:SpR:10029.0,161320.0] ||  -> equal(intersection(successor(image(element_relation,complement(u))),restrict(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),v,w)),successor_relation)**.
% 299.82/300.46  231261[10:SpR:10029.0,161321.0] ||  -> equal(intersection(restrict(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),v,w),successor(image(element_relation,complement(u)))),successor_relation)**.
% 299.82/300.46  231550[10:Res:161492.2,155802.2] || equal(omega,ordinal_numbers) member(u,universal_class) subclass(rest_relation,complement(kind_1_ordinals)) -> equal(integer_of(ordered_pair(u,rest_of(u))),successor_relation)**.
% 299.82/300.46  231628[14:Rew:199971.1,231610.1] || member(u,universal_class) equal(sum_class(range_of(successor_relation)),sum_class(range_of(u)))* member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class))* -> .
% 299.82/300.46  231687[25:Rew:160223.0,231656.1] function(intersection(complement(u),complement(v))) ||  -> equal(complement(intersection(union(u,v),universal_class)),successor(intersection(complement(u),complement(v))))**.
% 299.82/300.46  231827[10:Res:161492.2,161035.0] || equal(intersection(power_class(successor_relation),complement(u)),omega) member(v,union(image(element_relation,universal_class),u))* -> equal(integer_of(v),successor_relation).
% 299.82/300.46  231811[10:Res:160290.2,161035.0] || subclass(u,intersection(power_class(successor_relation),complement(v))) member(regular(u),union(image(element_relation,universal_class),v))* -> equal(u,successor_relation).
% 299.82/300.46  231793[10:Res:160298.1,161035.0] || member(regular(intersection(power_class(successor_relation),complement(u))),union(image(element_relation,universal_class),u))* -> equal(intersection(power_class(successor_relation),complement(u)),successor_relation).
% 299.82/300.46  231781[10:SpL:185605.1,161035.0] || equal(successor_relation,u) member(v,intersection(power_class(u),complement(w)))* member(v,union(image(element_relation,universal_class),w)) -> .
% 299.82/300.46  29346[0:SpR:1948.0,25.2] || member(u,union(complement(v),complement(w))) member(u,union(v,w)) -> member(u,symmetric_difference(complement(v),complement(w)))*.
% 299.82/300.46  39290[0:SoR:5753.0,73.1] one_to_one(domain_of(restrict(u,v,cross_product(universal_class,universal_class)))) || subclass(cross_product(universal_class,universal_class),v) -> section(u,cross_product(universal_class,universal_class),v)*.
% 299.82/300.46  10395[0:Res:2126.1,9.0] || section(u,singleton(v),w) subclass(singleton(v),segment(u,w,v))* -> equal(segment(u,w,v),singleton(v)).
% 299.82/300.46  42960[0:Res:9395.0,5839.2] || member(u,v)* member(u,w)* well_ordering(x,v) -> member(least(x,intersection(w,v)),intersection(w,v))*.
% 299.82/300.46  42959[0:Res:9509.0,5839.2] || member(u,v)* member(u,w)* well_ordering(x,w) -> member(least(x,intersection(w,v)),intersection(w,v))*.
% 299.82/300.46  31079[2:Res:9424.0,5832.1] inductive(restrict(u,v,w)) || well_ordering(x,u) -> member(least(x,restrict(u,v,w)),restrict(u,v,w))*.
% 299.82/300.46  31107[2:Res:9535.0,5832.1] inductive(symmetric_difference(u,v)) || well_ordering(w,complement(intersection(u,v))) -> member(least(w,symmetric_difference(u,v)),symmetric_difference(u,v))*.
% 299.82/300.46  107698[0:Res:60.1,6045.0] || member(ordered_pair(u,v),compose(w,x))* subclass(image(w,image(x,singleton(u))),y)* well_ordering(universal_class,y) -> .
% 299.82/300.46  125926[0:Res:28320.1,9322.0] || subclass(rest_relation,rotate(symmetric_difference(complement(u),complement(v)))) -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),union(u,v))*.
% 299.82/300.46  126056[0:Res:28321.1,9322.0] || subclass(rest_relation,flip(symmetric_difference(complement(u),complement(v)))) -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),union(u,v))*.
% 299.82/300.46  142648[2:Rew:113504.0,142519.1] || asymmetric(u,v) -> equal(symmetric_difference(intersection(u,inverse(u)),cross_product(v,v)),union(intersection(u,inverse(u)),cross_product(v,v)))**.
% 299.82/300.46  142649[2:Rew:113504.0,142520.1] || asymmetric(u,v) -> equal(symmetric_difference(cross_product(v,v),intersection(u,inverse(u))),union(cross_product(v,v),intersection(u,inverse(u))))**.
% 299.82/300.46  38890[0:Res:64.1,5646.1] function(image(u,image(v,singleton(w)))) || member(ordered_pair(w,x),compose(u,v))* -> member(x,cross_product(universal_class,universal_class)).
% 299.82/300.46  107574[0:Res:3872.2,6045.0] || member(u,cross_product(v,w))* member(u,x)* subclass(restrict(x,v,w),y)* well_ordering(universal_class,y) -> .
% 299.82/300.46  30753[0:Res:3595.3,594.0] function(u) || member(v,universal_class) subclass(universal_class,restrict(w,x,y))* -> member(image(u,v),cross_product(x,y))*.
% 299.82/300.46  108410[0:Res:3595.3,9332.1] function(u) || member(v,universal_class) subclass(universal_class,intersection(w,x)) member(image(u,v),symmetric_difference(w,x))* -> .
% 299.82/300.46  28595[0:Res:1495.2,513.0] || member(u,universal_class) subclass(rest_relation,intersection(complement(v),complement(w))) member(ordered_pair(u,rest_of(u)),union(v,w))* -> .
% 299.82/300.46  113252[0:Rew:1933.0,113150.1] || member(not_subclass_element(symmetrization_of(u),symmetric_difference(u,inverse(u))),complement(intersection(u,inverse(u))))* -> subclass(symmetrization_of(u),symmetric_difference(u,inverse(u))).
% 299.82/300.46  113251[0:Rew:1934.0,113151.1] || member(not_subclass_element(successor(u),symmetric_difference(u,singleton(u))),complement(intersection(u,singleton(u))))* -> subclass(successor(u),symmetric_difference(u,singleton(u))).
% 299.82/300.46  123496[0:Res:978.1,9332.1] || member(not_subclass_element(restrict(intersection(u,v),w,x),y),symmetric_difference(u,v))* -> subclass(restrict(intersection(u,v),w,x),y).
% 299.82/300.46  126789[0:Rew:28.0,126676.1] || member(not_subclass_element(intersection(union(u,v),w),x),intersection(complement(u),complement(v)))* -> subclass(intersection(union(u,v),w),x).
% 299.82/300.46  126566[0:Rew:28.0,126468.1] || member(not_subclass_element(intersection(u,union(v,w)),x),intersection(complement(v),complement(w)))* -> subclass(intersection(u,union(v,w)),x).
% 299.82/300.46  123504[0:Res:978.1,10191.0] ||  -> subclass(restrict(symmetric_difference(u,inverse(u)),v,w),x) member(not_subclass_element(restrict(symmetric_difference(u,inverse(u)),v,w),x),symmetrization_of(u))*.
% 299.82/300.46  123505[0:Res:978.1,10254.0] ||  -> subclass(restrict(symmetric_difference(u,singleton(u)),v,w),x) member(not_subclass_element(restrict(symmetric_difference(u,singleton(u)),v,w),x),successor(u))*.
% 299.82/300.46  126451[0:Obv:126444.1] || member(not_subclass_element(symmetric_difference(u,inverse(u)),intersection(v,symmetrization_of(u))),v)* -> subclass(symmetric_difference(u,inverse(u)),intersection(v,symmetrization_of(u))).
% 299.82/300.46  126396[0:Obv:126376.1] || member(not_subclass_element(symmetric_difference(u,singleton(u)),intersection(v,successor(u))),v)* -> subclass(symmetric_difference(u,singleton(u)),intersection(v,successor(u))).
% 299.82/300.46  113190[0:Res:1951.1,40234.0] || member(not_subclass_element(u,intersection(complement(intersection(v,w)),u)),symmetric_difference(v,w))* -> subclass(u,intersection(complement(intersection(v,w)),u)).
% 299.82/300.46  122730[0:Obv:122692.1] || member(not_subclass_element(symmetric_difference(u,v),intersection(w,union(u,v))),w)* -> subclass(symmetric_difference(u,v),intersection(w,union(u,v))).
% 299.82/300.46  111962[0:SpR:506.0,6842.1] || subclass(universal_class,symmetric_difference(intersection(complement(u),complement(v)),w)) -> member(unordered_pair(x,y),complement(intersection(union(u,v),complement(w))))*.
% 299.82/300.46  111956[0:SpR:507.0,6842.1] || subclass(universal_class,symmetric_difference(u,intersection(complement(v),complement(w)))) -> member(unordered_pair(x,y),complement(intersection(complement(u),union(v,w))))*.
% 299.82/300.46  37828[0:Obv:37809.1] || subclass(unordered_pair(u,v),w)* -> equal(not_subclass_element(unordered_pair(u,v),x),v)** subclass(unordered_pair(u,v),x) member(u,w).
% 299.82/300.46  37829[0:Obv:37802.1] || subclass(unordered_pair(u,v),w)* -> equal(not_subclass_element(unordered_pair(u,v),x),u)** subclass(unordered_pair(u,v),x) member(v,w).
% 299.82/300.46  111772[0:SpL:505.0,9322.0] || member(u,symmetric_difference(complement(v),power_class(intersection(complement(w),complement(x)))))* -> member(u,union(v,image(element_relation,union(w,x)))).
% 299.82/300.46  10000[0:SpR:505.0,509.0] ||  -> equal(union(u,image(element_relation,power_class(intersection(complement(v),complement(w))))),complement(intersection(complement(u),power_class(image(element_relation,union(v,w))))))**.
% 299.82/300.46  111788[0:SpL:505.0,9322.0] || member(u,symmetric_difference(power_class(intersection(complement(v),complement(w))),complement(x)))* -> member(u,union(image(element_relation,union(v,w)),x)).
% 299.82/300.46  125150[0:Rew:28.0,125098.1] ||  -> member(not_subclass_element(u,image(element_relation,union(v,w))),power_class(intersection(complement(v),complement(w))))* subclass(u,image(element_relation,union(v,w))).
% 299.82/300.46  10041[0:SpR:505.0,511.0] ||  -> equal(union(image(element_relation,power_class(intersection(complement(u),complement(v)))),w),complement(intersection(power_class(image(element_relation,union(u,v))),complement(w))))**.
% 299.82/300.46  10349[0:SpR:505.0,10292.0] ||  -> subclass(symmetric_difference(power_class(intersection(complement(u),complement(v))),complement(inverse(image(element_relation,union(u,v))))),symmetrization_of(image(element_relation,union(u,v))))*.
% 299.82/300.46  10368[0:SpR:505.0,10293.0] ||  -> subclass(symmetric_difference(power_class(intersection(complement(u),complement(v))),complement(singleton(image(element_relation,union(u,v))))),successor(image(element_relation,union(u,v))))*.
% 299.82/300.46  29299[0:SpR:208.0,507.0] ||  -> equal(union(u,intersection(complement(v),power_class(image(element_relation,complement(w))))),complement(intersection(complement(u),union(v,image(element_relation,power_class(w))))))**.
% 299.82/300.46  124224[0:SpL:208.0,986.1] || member(u,image(element_relation,power_class(image(element_relation,power_class(v))))) member(u,power_class(image(element_relation,power_class(image(element_relation,complement(v))))))* -> .
% 299.82/300.46  29215[0:SpR:208.0,506.0] ||  -> equal(union(intersection(complement(u),power_class(image(element_relation,complement(v)))),w),complement(intersection(union(u,image(element_relation,power_class(v))),complement(w))))**.
% 299.82/300.46  140214[0:SpL:984.0,2647.0] || subclass(universal_class,union(u,image(element_relation,power_class(v)))) member(singleton(w),intersection(complement(u),power_class(image(element_relation,complement(v)))))* -> .
% 299.82/300.46  29637[0:SpL:208.0,1487.1] || member(u,universal_class) subclass(power_class(image(element_relation,complement(v))),w)* -> member(u,image(element_relation,power_class(v)))* member(u,w)*.
% 299.82/300.46  29311[0:SpR:208.0,507.0] ||  -> equal(union(u,intersection(power_class(image(element_relation,complement(v))),complement(w))),complement(intersection(complement(u),union(image(element_relation,power_class(v)),w))))**.
% 299.82/300.46  126815[0:SpL:208.0,29643.0] || equal(u,power_class(image(element_relation,complement(v))))* member(w,universal_class) -> member(w,image(element_relation,power_class(v)))* member(w,u)*.
% 299.82/300.46  29227[0:SpR:208.0,506.0] ||  -> equal(union(intersection(power_class(image(element_relation,complement(u))),complement(v)),w),complement(intersection(union(image(element_relation,power_class(u)),v),complement(w))))**.
% 299.82/300.46  139752[0:SpL:982.0,2647.0] || subclass(universal_class,union(image(element_relation,power_class(u)),v)) member(singleton(w),intersection(power_class(image(element_relation,complement(u))),complement(v)))* -> .
% 299.82/300.46  107255[0:Rew:208.0,107161.1] ||  -> member(not_subclass_element(complement(power_class(image(element_relation,complement(u)))),v),image(element_relation,power_class(u)))* subclass(complement(power_class(image(element_relation,complement(u)))),v).
% 299.82/300.46  30759[0:Res:3595.3,307.0] function(u) || member(v,universal_class) subclass(universal_class,image(element_relation,complement(w)))* member(image(u,v),power_class(w))* -> .
% 299.82/300.46  9990[0:SpR:509.0,161.0] ||  -> equal(intersection(complement(intersection(u,image(element_relation,complement(v)))),complement(intersection(complement(u),power_class(v)))),symmetric_difference(u,image(element_relation,complement(v))))**.
% 299.82/300.46  137086[0:SpR:10029.0,28.0] ||  -> equal(union(u,intersection(power_class(v),complement(singleton(image(element_relation,complement(v)))))),complement(intersection(complement(u),successor(image(element_relation,complement(v))))))**.
% 299.82/300.46  137705[0:SpR:10028.0,28.0] ||  -> equal(union(u,intersection(power_class(v),complement(inverse(image(element_relation,complement(v)))))),complement(intersection(complement(u),symmetrization_of(image(element_relation,complement(v))))))**.
% 299.82/300.46  137129[0:SpL:10029.0,2647.0] || subclass(universal_class,successor(image(element_relation,complement(u)))) member(singleton(v),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* -> .
% 299.82/300.46  137045[0:SpR:10029.0,28.0] ||  -> equal(union(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),v),complement(intersection(successor(image(element_relation,complement(u))),complement(v))))**.
% 299.82/300.46  137747[0:SpL:10028.0,2647.0] || subclass(universal_class,symmetrization_of(image(element_relation,complement(u)))) member(singleton(v),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* -> .
% 299.82/300.46  137663[0:SpR:10028.0,28.0] ||  -> equal(union(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),v),complement(intersection(symmetrization_of(image(element_relation,complement(u))),complement(v))))**.
% 299.82/300.46  10030[0:SpR:511.0,161.0] ||  -> equal(intersection(complement(intersection(image(element_relation,complement(u)),v)),complement(intersection(power_class(u),complement(v)))),symmetric_difference(image(element_relation,complement(u)),v))**.
% 299.82/300.46  108227[2:Res:107289.0,5832.1] inductive(complement(power_class(u))) || well_ordering(v,image(element_relation,complement(u))) -> member(least(v,complement(power_class(u))),complement(power_class(u)))*.
% 299.82/300.46  124648[0:MRR:124625.0,191.0] || member(union(u,v),universal_class) -> member(singleton(union(u,v)),complement(v))* member(singleton(singleton(singleton(union(u,v)))),element_relation)*.
% 299.82/300.46  124649[0:MRR:124624.0,191.0] || member(union(u,v),universal_class) -> member(singleton(union(u,v)),complement(u))* member(singleton(singleton(singleton(union(u,v)))),element_relation)*.
% 299.82/300.46  157915[6:Res:978.1,148657.1] || member(not_subclass_element(restrict(complement(compose(element_relation,universal_class)),u,v),w),element_relation)* -> subclass(restrict(complement(compose(element_relation,universal_class)),u,v),w).
% 299.82/300.46  160914[10:Rew:160202.0,150974.1] || subclass(universal_class,image(element_relation,union(image(element_relation,universal_class),u))) member(unordered_pair(v,w),power_class(intersection(power_class(successor_relation),complement(u))))* -> .
% 299.82/300.46  160931[10:Rew:160202.0,151055.0] || member(not_subclass_element(union(image(element_relation,universal_class),u),v),intersection(power_class(successor_relation),complement(u)))* -> subclass(union(image(element_relation,universal_class),u),v).
% 299.82/300.46  163616[10:Rew:160202.0,160934.1] ||  -> member(regular(complement(union(image(element_relation,universal_class),u))),intersection(power_class(successor_relation),complement(u)))* equal(complement(union(image(element_relation,universal_class),u)),successor_relation).
% 299.82/300.46  160945[10:Rew:160202.0,150955.1] || subclass(universal_class,image(element_relation,union(u,image(element_relation,universal_class)))) member(unordered_pair(v,w),power_class(intersection(complement(u),power_class(successor_relation))))* -> .
% 299.82/300.46  160962[10:Rew:160202.0,151039.0] || member(not_subclass_element(union(u,image(element_relation,universal_class)),v),intersection(complement(u),power_class(successor_relation)))* -> subclass(union(u,image(element_relation,universal_class)),v).
% 299.82/300.46  163617[10:Rew:160202.0,160965.1] ||  -> member(regular(complement(union(u,image(element_relation,universal_class)))),intersection(complement(u),power_class(successor_relation)))* equal(complement(union(u,image(element_relation,universal_class))),successor_relation).
% 299.82/300.46  161017[10:Rew:160202.0,150951.2] || member(u,universal_class) -> member(u,image(element_relation,union(v,image(element_relation,universal_class))))* member(u,power_class(intersection(complement(v),power_class(successor_relation)))).
% 299.82/300.46  161023[10:Rew:160202.0,150952.2] || member(u,universal_class) subclass(universal_class,union(v,image(element_relation,universal_class))) member(power_class(u),intersection(complement(v),power_class(successor_relation)))* -> .
% 299.82/300.46  161024[10:Rew:160202.0,150953.2] || member(u,universal_class) subclass(universal_class,union(v,image(element_relation,universal_class))) member(sum_class(u),intersection(complement(v),power_class(successor_relation)))* -> .
% 299.82/300.46  161038[10:Rew:160202.0,150958.2] || member(u,universal_class) -> member(u,image(element_relation,union(image(element_relation,universal_class),v)))* member(u,power_class(intersection(power_class(successor_relation),complement(v)))).
% 299.82/300.46  161044[10:Rew:160202.0,150959.2] || member(u,universal_class) subclass(universal_class,union(image(element_relation,universal_class),v)) member(power_class(u),intersection(power_class(successor_relation),complement(v)))* -> .
% 299.82/300.46  161045[10:Rew:160202.0,150960.2] || member(u,universal_class) subclass(universal_class,union(image(element_relation,universal_class),v)) member(sum_class(u),intersection(power_class(successor_relation),complement(v)))* -> .
% 299.82/300.46  163620[10:Rew:160202.0,161193.0] || subclass(image(u,image(v,singleton(w))),successor_relation)* member(ordered_pair(w,x),compose(u,v))* -> member(x,inverse(successor_relation)).
% 299.82/300.46  160741[10:Rew:160202.0,146461.1] || subclass(u,symmetric_difference(v,image(element_relation,complement(w)))) -> equal(u,successor_relation) member(regular(u),complement(intersection(complement(v),power_class(w))))*.
% 299.82/300.46  160740[10:Rew:160202.0,146463.1] || subclass(u,symmetric_difference(image(element_relation,complement(v)),w)) -> equal(u,successor_relation) member(regular(u),complement(intersection(power_class(v),complement(w))))*.
% 299.82/300.46  160739[10:Rew:160202.0,146471.1] || subclass(u,symmetric_difference(complement(intersection(v,w)),union(v,w)))* -> equal(u,successor_relation) member(regular(u),complement(symmetric_difference(v,w))).
% 299.82/300.46  160738[10:Rew:160202.0,146482.2] || subclass(u,power_class(intersection(complement(v),complement(w))))* member(regular(u),image(element_relation,union(v,w))) -> equal(u,successor_relation).
% 299.82/300.46  160737[10:Rew:160202.0,146491.3] || member(u,universal_class) subclass(u,intersection(v,w)) member(apply(choice,u),symmetric_difference(v,w))* -> equal(u,successor_relation).
% 299.82/300.46  160736[10:Rew:160202.0,146511.2] || member(u,universal_class) subclass(u,restrict(v,w,x))* -> equal(u,successor_relation) member(apply(choice,u),cross_product(w,x))*.
% 299.82/300.46  160735[10:Rew:160202.0,146513.3] || member(u,universal_class) subclass(u,image(element_relation,complement(v)))* member(apply(choice,u),power_class(v)) -> equal(u,successor_relation).
% 299.82/300.46  160734[10:Rew:160202.0,146528.1] || subclass(u,ordered_pair(v,w))* -> equal(u,successor_relation) equal(regular(u),unordered_pair(v,singleton(w))) equal(regular(u),singleton(v)).
% 299.82/300.46  163043[10:Rew:160202.0,158811.1] || asymmetric(cross_product(u,v),singleton(w)) -> equal(domain__dfg(restrict(inverse(cross_product(u,v)),u,v),singleton(w),w),single_valued3(successor_relation))**.
% 299.89/300.46  161297[10:Rew:160202.0,146577.1] || asymmetric(cross_product(u,v),w) subclass(compose(successor_relation,successor_relation),successor_relation) -> transitive(restrict(inverse(cross_product(u,v)),u,v),w)*.
% 299.89/300.46  161291[10:Rew:160202.0,146571.2] || asymmetric(cross_product(u,v),w) transitive(restrict(inverse(cross_product(u,v)),u,v),w)* -> equal(compose(successor_relation,successor_relation),successor_relation).
% 299.89/300.46  161290[10:Rew:160202.0,146572.1] || asymmetric(cross_product(u,v),w) equal(compose(successor_relation,successor_relation),successor_relation) -> transitive(restrict(inverse(cross_product(u,v)),u,v),w)*.
% 299.89/300.46  161306[10:Rew:160202.0,146613.2] || member(intersection(u,v),universal_class) member(apply(choice,intersection(u,v)),symmetric_difference(u,v))* -> equal(intersection(u,v),successor_relation).
% 299.89/300.46  161273[10:Rew:160202.0,146722.1] || member(intersection(u,singleton(v)),universal_class) -> equal(intersection(u,singleton(v)),successor_relation) equal(apply(choice,intersection(u,singleton(v))),v)**.
% 299.89/300.46  161280[10:Rew:160202.0,146736.1] || member(intersection(singleton(u),v),universal_class) -> equal(intersection(singleton(u),v),successor_relation) equal(apply(choice,intersection(singleton(u),v)),u)**.
% 299.89/300.46  161591[10:Rew:160202.0,146801.2] || member(cross_product(u,v),universal_class) subclass(universal_class,complement(singleton(apply(choice,cross_product(u,v)))))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.46  161590[10:Rew:160202.0,146802.2] || member(cross_product(u,v),universal_class) equal(complement(singleton(apply(choice,cross_product(u,v)))),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.89/300.46  161588[10:Rew:160202.0,146824.1] || member(regular(cross_product(u,v)),cross_product(w,x))* -> equal(cross_product(u,v),successor_relation) member(first(regular(cross_product(u,v))),w).
% 299.89/300.46  161587[10:Rew:160202.0,146825.1] || member(regular(cross_product(u,v)),cross_product(w,x))* -> equal(cross_product(u,v),successor_relation) member(second(regular(cross_product(u,v))),x).
% 299.89/300.46  161683[10:Rew:160202.0,146730.1] || member(symmetric_difference(u,v),universal_class) -> equal(symmetric_difference(u,v),successor_relation) member(apply(choice,symmetric_difference(u,v)),complement(intersection(u,v)))*.
% 299.89/300.46  161695[10:Rew:160202.0,146714.1] || member(restrict(u,v,w),universal_class) -> equal(restrict(u,v,w),successor_relation) member(apply(choice,restrict(u,v,w)),u)*.
% 299.89/300.46  161725[10:Rew:160202.0,159721.4] function(u) || member(v,universal_class) subclass(universal_class,regular(w)) member(image(u,v),w)* -> equal(w,successor_relation).
% 299.89/300.46  161771[10:Rew:160202.0,146695.2] || subclass(unordered_pair(u,v),w)* -> equal(apply(choice,unordered_pair(u,v)),u)** equal(unordered_pair(u,v),successor_relation) member(v,w).
% 299.89/300.46  161770[10:Rew:160202.0,146696.2] || subclass(unordered_pair(u,v),w)* -> equal(apply(choice,unordered_pair(u,v)),v)** equal(unordered_pair(u,v),successor_relation) member(u,w).
% 299.89/300.46  161896[10:Rew:160202.0,147087.1] || member(u,v)* -> equal(singleton(w),successor_relation) equal(ordered_pair(first(ordered_pair(u,w)),second(ordered_pair(u,w))),ordered_pair(u,w))**.
% 299.89/300.46  162031[10:Rew:160202.0,146938.1] || subclass(union(u,v),w) -> equal(symmetric_difference(complement(u),complement(v)),successor_relation) member(regular(symmetric_difference(complement(u),complement(v))),w)*.
% 299.89/300.46  162063[10:Rew:160202.0,147011.1] || subclass(u,symmetric_difference(complement(v),complement(w))) -> equal(intersection(x,u),successor_relation) member(regular(intersection(x,u)),union(v,w))*.
% 299.89/300.46  162077[10:Rew:160202.0,147026.1] || subclass(u,symmetric_difference(complement(v),complement(w))) -> equal(intersection(u,x),successor_relation) member(regular(intersection(u,x)),union(v,w))*.
% 299.89/300.46  162138[10:Rew:160202.0,148482.1] || member(u,v)* -> equal(integer_of(w),successor_relation) equal(ordered_pair(first(ordered_pair(u,w)),second(ordered_pair(u,w))),ordered_pair(u,w))**.
% 299.89/300.46  162172[10:Rew:160202.0,146995.1] || well_ordering(u,v) -> equal(restrict(v,w,x),successor_relation) member(least(u,restrict(v,w,x)),restrict(v,w,x))*.
% 299.89/300.46  162176[10:Rew:160202.0,146999.1] || well_ordering(u,complement(intersection(v,w))) -> equal(symmetric_difference(v,w),successor_relation) member(least(u,symmetric_difference(v,w)),symmetric_difference(v,w))*.
% 299.89/300.46  163633[10:Rew:160202.0,163015.0] || subclass(image(u,image(v,singleton(w))),successor_relation)* member(ordered_pair(w,x),compose(u,v))* well_ordering(y,successor_relation)* -> .
% 299.89/300.46  162269[10:Rew:160202.0,147428.0] ||  -> equal(restrict(restrict(u,v,w),x,y),successor_relation) member(regular(restrict(restrict(u,v,w),x,y)),cross_product(v,w))*.
% 299.89/300.46  162336[10:Rew:160202.0,147549.1] || member(regular(image(element_relation,union(u,v))),power_class(intersection(complement(u),complement(v))))* -> equal(image(element_relation,union(u,v)),successor_relation).
% 299.89/300.46  163622[10:Rew:160202.0,162358.2] || connected(complement(u),successor_relation) member(v,w) subclass(w,successor_relation) -> member(ordered_pair(v,least(complement(u),w)),u)*.
% 299.89/300.46  162362[10:Rew:160202.0,147078.1] || subclass(power_class(intersection(complement(u),complement(v))),image(element_relation,union(u,v)))* -> equal(power_class(intersection(complement(u),complement(v))),successor_relation).
% 299.89/300.46  162363[10:Rew:160202.0,147088.2] inductive(compose(restrict(u,v,v),restrict(u,v,v))) || transitive(u,v) -> member(successor_relation,restrict(u,v,v))*.
% 299.89/300.46  162364[10:Rew:160202.0,147336.1] || well_ordering(u,image(element_relation,complement(v))) -> equal(complement(power_class(v)),successor_relation) member(least(u,complement(power_class(v))),complement(power_class(v)))*.
% 299.89/300.46  162370[10:Rew:160202.0,147377.0] ||  -> equal(complement(complement(symmetric_difference(complement(u),complement(v)))),successor_relation) member(regular(complement(complement(symmetric_difference(complement(u),complement(v))))),union(u,v))*.
% 299.89/300.46  162372[10:Rew:160202.0,147379.0] ||  -> equal(intersection(u,symmetric_difference(complement(v),complement(w))),successor_relation) member(regular(intersection(u,symmetric_difference(complement(v),complement(w)))),union(v,w))*.
% 299.89/300.46  162374[10:Rew:160202.0,147381.0] ||  -> equal(intersection(symmetric_difference(complement(u),complement(v)),w),successor_relation) member(regular(intersection(symmetric_difference(complement(u),complement(v)),w)),union(u,v))*.
% 299.89/300.46  162375[10:Rew:160202.0,147435.1] || member(regular(restrict(image(element_relation,complement(u)),v,w)),power_class(u))* -> equal(restrict(image(element_relation,complement(u)),v,w),successor_relation).
% 299.89/300.46  162378[10:Rew:160202.0,147612.0] ||  -> equal(intersection(u,intersection(symmetric_difference(v,w),x)),successor_relation) member(regular(intersection(u,intersection(symmetric_difference(v,w),x))),union(v,w))*.
% 299.89/300.46  162380[10:Rew:160202.0,147614.0] ||  -> equal(intersection(u,intersection(restrict(v,w,x),y)),successor_relation) member(regular(intersection(u,intersection(restrict(v,w,x),y))),v)*.
% 299.89/300.46  162381[10:Rew:160202.0,147670.0] ||  -> equal(intersection(u,intersection(v,symmetric_difference(w,x))),successor_relation) member(regular(intersection(u,intersection(v,symmetric_difference(w,x)))),union(w,x))*.
% 299.89/300.46  162383[10:Rew:160202.0,147672.0] ||  -> equal(intersection(u,intersection(v,restrict(w,x,y))),successor_relation) member(regular(intersection(u,intersection(v,restrict(w,x,y)))),w)*.
% 299.89/300.46  162384[10:Rew:160202.0,147710.0] ||  -> equal(intersection(intersection(symmetric_difference(u,v),w),x),successor_relation) member(regular(intersection(intersection(symmetric_difference(u,v),w),x)),union(u,v))*.
% 299.89/300.46  162386[10:Rew:160202.0,147712.0] ||  -> equal(intersection(intersection(restrict(u,v,w),x),y),successor_relation) member(regular(intersection(intersection(restrict(u,v,w),x),y)),u)*.
% 299.89/300.46  162387[10:Rew:160202.0,147783.0] ||  -> equal(intersection(intersection(u,symmetric_difference(v,w)),x),successor_relation) member(regular(intersection(intersection(u,symmetric_difference(v,w)),x)),union(v,w))*.
% 299.89/300.46  162389[10:Rew:160202.0,147785.0] ||  -> equal(intersection(intersection(u,restrict(v,w,x)),y),successor_relation) member(regular(intersection(intersection(u,restrict(v,w,x)),y)),v)*.
% 299.89/300.46  162392[10:Rew:160202.0,148485.1] || member(not_subclass_element(u,intersection(v,omega)),v)* -> equal(integer_of(not_subclass_element(u,intersection(v,omega))),successor_relation) subclass(u,intersection(v,omega)).
% 299.89/300.46  162393[10:Rew:160202.0,148519.0] ||  -> equal(intersection(u,intersection(v,omega)),successor_relation) equal(integer_of(regular(intersection(u,intersection(v,omega)))),regular(intersection(u,intersection(v,omega))))**.
% 299.89/300.46  162394[10:Rew:160202.0,148520.0] ||  -> equal(intersection(intersection(u,omega),v),successor_relation) equal(integer_of(regular(intersection(intersection(u,omega),v))),regular(intersection(intersection(u,omega),v)))**.
% 299.89/300.46  162395[10:Rew:160202.0,148521.0] ||  -> equal(intersection(u,intersection(omega,v)),successor_relation) equal(integer_of(regular(intersection(u,intersection(omega,v)))),regular(intersection(u,intersection(omega,v))))**.
% 299.89/300.46  162396[10:Rew:160202.0,148522.0] ||  -> equal(intersection(intersection(omega,u),v),successor_relation) equal(integer_of(regular(intersection(intersection(omega,u),v))),regular(intersection(intersection(omega,u),v)))**.
% 299.89/300.46  183493[0:SpR:505.0,139600.0] ||  -> equal(intersection(image(element_relation,union(u,v)),complement(power_class(intersection(complement(u),complement(v))))),complement(power_class(intersection(complement(u),complement(v)))))**.
% 299.89/300.46  187029[10:SpR:181082.0,475.1] || member(restrict(element_relation,universal_class,image(u,successor_relation)),universal_class) -> member(ordered_pair(restrict(element_relation,universal_class,image(u,successor_relation)),apply(u,universal_class)),domain_relation)*.
% 299.89/300.46  187085[10:Rew:160367.0,187061.2,160367.0,187061.0] || member(union(u,successor_relation),universal_class) member(apply(choice,union(u,successor_relation)),symmetric_difference(universal_class,u))* -> equal(union(u,successor_relation),successor_relation).
% 299.89/300.46  187539[10:Res:160784.3,160481.0] || member(u,universal_class) subclass(u,regular(v)) member(apply(choice,u),v)* -> equal(u,successor_relation) equal(v,successor_relation).
% 299.89/300.46  155827[3:Res:155815.1,3886.0] || member(not_subclass_element(u,intersection(v,kind_1_ordinals)),ordinal_numbers)* member(not_subclass_element(u,intersection(v,kind_1_ordinals)),v)* -> subclass(u,intersection(v,kind_1_ordinals)).
% 299.89/300.46  184010[14:Rew:183958.0,183975.1] || member(image(recursion(u,successor_relation,successor_relation),singleton(v)),ordinal_numbers) -> subclass(ordinal_add(u,v),image(recursion(u,successor_relation,successor_relation),singleton(v)))*.
% 299.89/300.46  183700[10:Rew:181082.0,183688.2] || member(image(u,successor_relation),ordinal_numbers) subclass(image(u,successor_relation),apply(u,universal_class))* -> equal(apply(u,universal_class),image(u,successor_relation)).
% 299.89/300.46  107600[2:Res:5714.3,6045.0] || connected(u,v) well_ordering(w,v)* subclass(not_well_ordering(u,v),x)* well_ordering(universal_class,x) -> well_ordering(u,v).
% 299.89/300.46  161921[10:Rew:160202.0,147193.2] || well_ordering(u,cross_product(universal_class,universal_class)) subclass(rest_of(v),w) -> equal(rest_of(v),successor_relation) member(least(u,rest_of(v)),w)*.
% 299.89/300.46  161926[10:Rew:160202.0,147197.2] || well_ordering(u,cross_product(universal_class,universal_class)) subclass(compose_class(v),w) -> equal(compose_class(v),successor_relation) member(least(u,compose_class(v)),w)*.
% 299.89/300.46  108804[2:Res:31076.2,595.0] inductive(restrict(u,v,w)) || well_ordering(x,restrict(u,v,w)) -> member(least(x,restrict(u,v,w)),u)*.
% 299.89/300.46  108799[2:Res:31076.2,9332.1] inductive(intersection(u,v)) || well_ordering(w,intersection(u,v)) member(least(w,intersection(u,v)),symmetric_difference(u,v))* -> .
% 299.89/300.46  161968[10:Rew:160202.0,146924.2] || well_ordering(u,intersection(v,w)) member(least(u,intersection(v,w)),symmetric_difference(v,w))* -> equal(intersection(v,w),successor_relation).
% 299.89/300.46  162173[10:Rew:160202.0,146994.1] || well_ordering(u,restrict(v,w,x)) -> equal(restrict(v,w,x),successor_relation) member(least(u,restrict(v,w,x)),v)*.
% 299.89/300.46  160027[3:Res:159954.0,5832.1] inductive(restrict(ordinal_numbers,u,v)) || well_ordering(w,kind_1_ordinals) -> member(least(w,restrict(ordinal_numbers,u,v)),restrict(ordinal_numbers,u,v))*.
% 299.89/300.46  160014[3:Res:159951.0,5839.2] || member(u,ordinal_numbers)* member(u,v)* well_ordering(w,kind_1_ordinals) -> member(least(w,intersection(v,ordinal_numbers)),intersection(v,ordinal_numbers))*.
% 299.89/300.46  159996[3:Res:159950.0,5839.2] || member(u,v)* member(u,ordinal_numbers)* well_ordering(w,kind_1_ordinals) -> member(least(w,intersection(ordinal_numbers,v)),intersection(ordinal_numbers,v))*.
% 299.89/300.46  163127[10:Rew:160202.0,160025.1] || well_ordering(u,kind_1_ordinals) -> equal(restrict(ordinal_numbers,v,w),successor_relation) member(least(u,restrict(ordinal_numbers,v,w)),restrict(ordinal_numbers,v,w))*.
% 299.89/300.46  42836[0:Res:6.0,5853.2] || member(u,v)* member(w,x)* well_ordering(y,universal_class) -> member(least(y,cross_product(x,v)),cross_product(x,v))*.
% 299.89/300.46  42953[0:Res:6.0,5839.2] || member(u,v)* member(u,w)* well_ordering(x,universal_class) -> member(least(x,intersection(w,v)),intersection(w,v))*.
% 299.89/300.46  162377[10:Rew:160202.0,147572.2] || well_ordering(u,universal_class) member(least(u,union(v,w)),intersection(complement(v),complement(w)))* -> equal(union(v,w),successor_relation).
% 299.89/300.46  56514[2:Obv:56510.3] || well_ordering(u,universal_class) connected(u,v) member(least(u,not_well_ordering(u,v)),not_well_ordering(u,v))* -> well_ordering(u,v).
% 299.89/300.46  39282[0:SoR:5564.0,73.1] one_to_one(sum_class(cross_product(universal_class,universal_class))) || member(ordinal_numbers,universal_class) well_ordering(element_relation,cross_product(universal_class,universal_class))* -> member(cross_product(universal_class,universal_class),ordinal_numbers).
% 299.89/300.46  34093[0:MRR:33508.1,34067.1] || member(u,universal_class)* member(v,u)* subclass(element_relation,w) well_ordering(x,w)* -> member(least(x,element_relation),element_relation)*.
% 299.89/300.46  107310[0:Res:107233.0,5838.1] || member(u,universal_class) well_ordering(v,w) -> member(u,complement(w))* member(least(v,complement(complement(w))),complement(complement(w)))*.
% 299.89/300.46  107573[0:Res:1032.1,6045.0] || member(u,universal_class) subclass(intersection(complement(v),complement(w)),x)* well_ordering(universal_class,x) -> member(u,union(v,w))*.
% 299.89/300.46  159971[3:Res:159949.0,5838.1] || member(u,universal_class) well_ordering(v,kind_1_ordinals) -> member(u,complement(ordinal_numbers))* member(least(v,complement(complement(ordinal_numbers))),complement(complement(ordinal_numbers)))*.
% 299.89/300.46  28265[0:Res:1495.2,127.0] || member(u,universal_class)* subclass(rest_relation,v) subclass(v,w)* well_ordering(x,w)* -> member(least(x,v),v)*.
% 299.89/300.46  39596[0:Res:5768.2,17.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,cross_product(w,x))* -> member(ordered_pair(v,compose(u,v)),x)*.
% 299.89/300.46  189413[15:Rew:189339.1,184849.2] || member(u,universal_class) subclass(domain_relation,symmetric_difference(cross_product(v,w),x)) -> member(ordered_pair(u,successor_relation),complement(restrict(x,v,w)))*.
% 299.89/300.46  189414[15:Rew:189339.1,184847.2] || member(u,universal_class) subclass(domain_relation,symmetric_difference(v,cross_product(w,x))) -> member(ordered_pair(u,successor_relation),complement(restrict(v,w,x)))*.
% 299.89/300.46  190488[10:Obv:190473.2] || member(u,v) member(u,unordered_pair(v,w))* -> equal(regular(unordered_pair(v,w)),w) equal(unordered_pair(v,w),successor_relation).
% 299.89/300.46  190489[10:Obv:190471.2] || member(u,v) member(u,unordered_pair(w,v))* -> equal(regular(unordered_pair(w,v)),w) equal(unordered_pair(w,v),successor_relation).
% 299.89/300.46  192602[10:Res:163162.1,162356.0] || subclass(complement(u),v)* well_ordering(omega,v) -> member(successor_relation,u) equal(integer_of(ordered_pair(successor_relation,least(omega,complement(u)))),successor_relation)**.
% 299.89/300.46  192599[11:Res:168384.1,162356.0] || equal(u,symmetrization_of(successor_relation)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(successor_relation,least(omega,u))),successor_relation)**.
% 299.89/300.46  192598[10:Res:163169.1,162356.0] || equal(u,successor(successor_relation)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(successor_relation,least(omega,u))),successor_relation)**.
% 299.89/300.46  192597[10:Res:163171.1,162356.0] || equal(u,singleton(successor_relation)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(successor_relation,least(omega,u))),successor_relation)**.
% 299.89/300.46  192596[11:Res:179843.1,162356.0] || equal(u,inverse(successor_relation)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(successor_relation,least(omega,u))),successor_relation)**.
% 299.89/300.46  192595[10:Res:185646.1,162356.0] || equal(complement(u),successor_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(successor_relation,least(omega,u))),successor_relation)**.
% 299.89/300.46  192586[10:Res:181060.0,162356.0] || subclass(singleton(singleton(successor_relation)),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(singleton(successor_relation),least(omega,singleton(singleton(successor_relation))))),successor_relation)**.
% 299.89/300.46  192578[10:Res:34189.1,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> subclass(v,w) equal(integer_of(ordered_pair(not_subclass_element(v,w),least(omega,universal_class))),successor_relation)**.
% 299.89/300.46  192577[10:Res:9089.1,162356.0] function(u) || subclass(universal_class,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(apply(u,w),least(omega,universal_class))),successor_relation)**.
% 299.89/300.46  192576[10:Res:120366.1,162356.0] || member(u,universal_class) subclass(universal_class,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(rest_of(u),least(omega,universal_class))),successor_relation)**.
% 299.89/300.46  192573[10:Res:56.1,162356.0] || member(u,universal_class) subclass(universal_class,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(sum_class(u),least(omega,universal_class))),successor_relation)**.
% 299.89/300.46  192568[10:Res:58.1,162356.0] || member(u,universal_class) subclass(universal_class,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(power_class(u),least(omega,universal_class))),successor_relation)**.
% 299.89/300.46  192567[10:Res:186499.1,162356.0] || equal(successor_relation,u) subclass(universal_class,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(power_class(u),least(omega,universal_class))),successor_relation)**.
% 299.89/300.46  192555[10:Res:1004.0,162356.0] || subclass(ordered_pair(u,v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(singleton(u),least(omega,ordered_pair(u,v)))),successor_relation)**.
% 299.89/300.46  192508[10:Res:187500.1,162356.0] || subclass(universal_class,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(power_class(successor_relation),least(omega,u))),successor_relation)**.
% 299.89/300.46  192503[10:Res:4.1,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> subclass(u,w) equal(integer_of(ordered_pair(not_subclass_element(u,w),least(omega,u))),successor_relation)**.
% 299.89/300.46  192501[10:Res:185647.1,162356.0] || equal(complement(u),successor_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(omega,least(omega,u))),successor_relation)**.
% 299.89/300.46  192498[10:Res:1477.1,162356.0] || subclass(universal_class,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(w),least(omega,u))),successor_relation)**.
% 299.89/300.46  192496[10:Res:114897.1,162356.0] || equal(u,universal_class) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(w),least(omega,u))),successor_relation)**.
% 299.89/300.46  193397[10:Res:192947.1,3874.1] || equal(complement(complement(intersection(u,v))),successor_relation) member(singleton(w),union(u,v)) -> member(singleton(w),symmetric_difference(u,v))*.
% 299.89/300.46  195450[0:SpR:194805.1,1948.0] || subclass(union(complement(u),complement(v)),union(u,v))* -> equal(symmetric_difference(complement(u),complement(v)),union(complement(u),complement(v))).
% 299.89/300.46  195390[10:SpR:194805.1,161324.1] || subclass(inverse(u),u)* asymmetric(u,singleton(v)) -> equal(range__dfg(inverse(u),v,singleton(v)),second(not_subclass_element(successor_relation,successor_relation)))**.
% 299.89/300.46  195917[6:Res:157922.1,5647.0] || member(ordered_pair(u,not_subclass_element(v,image(element_relation,image(universal_class,singleton(u))))),element_relation)* -> subclass(v,image(element_relation,image(universal_class,singleton(u)))).
% 299.89/300.46  195921[10:Rew:181056.0,195907.1] || member(ordered_pair(universal_class,not_subclass_element(u,image(v,image(w,successor_relation)))),compose(v,w))* -> subclass(u,image(v,image(w,successor_relation))).
% 299.89/300.46  196447[10:Res:160848.0,9.0] || subclass(image(element_relation,power_class(universal_class)),complement(power_class(image(element_relation,successor_relation))))* -> equal(complement(power_class(image(element_relation,successor_relation))),image(element_relation,power_class(universal_class))).
% 299.89/300.46  196499[10:Res:161138.0,9.0] || subclass(image(element_relation,symmetrization_of(successor_relation)),complement(power_class(complement(inverse(successor_relation)))))* -> equal(complement(power_class(complement(inverse(successor_relation)))),image(element_relation,symmetrization_of(successor_relation))).
% 299.89/300.46  196549[10:SpR:161137.0,1032.1] || member(u,universal_class) -> member(u,intersection(complement(v),power_class(complement(inverse(successor_relation)))))* member(u,union(v,image(element_relation,symmetrization_of(successor_relation)))).
% 299.89/300.46  196542[10:SpR:161137.0,1032.1] || member(u,universal_class) -> member(u,intersection(power_class(complement(inverse(successor_relation))),complement(v)))* member(u,union(image(element_relation,symmetrization_of(successor_relation)),v)).
% 299.89/300.46  196639[10:Res:160971.0,9.0] || subclass(image(element_relation,power_class(successor_relation)),complement(power_class(image(element_relation,universal_class))))* -> equal(complement(power_class(image(element_relation,universal_class))),image(element_relation,power_class(successor_relation))).
% 299.89/300.46  196755[10:SpR:162889.0,1032.1] || member(u,universal_class) -> member(u,intersection(complement(v),power_class(complement(singleton(successor_relation)))))* member(u,union(v,image(element_relation,successor(successor_relation)))).
% 299.89/300.46  196748[10:SpR:162889.0,1032.1] || member(u,universal_class) -> member(u,intersection(power_class(complement(singleton(successor_relation))),complement(v)))* member(u,union(image(element_relation,successor(successor_relation)),v)).
% 299.89/300.46  196807[10:Res:162888.0,9.0] || subclass(image(element_relation,successor(successor_relation)),complement(power_class(complement(singleton(successor_relation)))))* -> equal(complement(power_class(complement(singleton(successor_relation)))),image(element_relation,successor(successor_relation))).
% 299.89/300.46  197461[10:SpL:161565.2,188646.0] || member(cross_product(u,v),universal_class) equal(unordered_pair(w,apply(choice,cross_product(u,v))),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.89/300.46  197448[10:SpL:161565.2,188713.0] || member(cross_product(u,v),universal_class) equal(unordered_pair(apply(choice,cross_product(u,v)),w),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.89/300.46  197425[10:SpL:161565.2,185804.0] || member(cross_product(u,v),universal_class) equal(complement(complement(apply(choice,cross_product(u,v)))),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.89/300.46  199958[10:Res:199831.0,162356.0] || subclass(cross_product(universal_class,universal_class),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(rest_relation),least(omega,cross_product(universal_class,universal_class)))),successor_relation)**.
% 299.89/300.46  199976[10:Res:199848.1,162356.0] || subclass(universal_class,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(rest_relation),least(omega,u))),successor_relation)**.
% 299.89/300.47  200294[6:SpL:199964.0,2142.0] || member(u,regular(rest_relation))* -> equal(u,unordered_pair(first(regular(rest_relation)),singleton(second(regular(rest_relation)))))* equal(u,singleton(first(regular(rest_relation)))).
% 299.89/300.47  200385[10:Res:200240.0,162356.0] || subclass(regular(rest_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(singleton(first(regular(rest_relation))),least(omega,regular(rest_relation)))),successor_relation)**.
% 299.89/300.47  200661[10:Res:161493.2,3874.1] inductive(complement(intersection(u,v))) || member(w,union(u,v)) -> equal(integer_of(w),successor_relation) member(w,symmetric_difference(u,v))*.
% 299.89/300.47  201349[10:Res:201221.0,162356.0] || subclass(cross_product(universal_class,universal_class),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(domain_relation),least(omega,cross_product(universal_class,universal_class)))),successor_relation)**.
% 299.89/300.47  201366[10:Res:201231.1,162356.0] || subclass(universal_class,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(domain_relation),least(omega,u))),successor_relation)**.
% 299.89/300.47  201441[10:EmS:161261.0,161261.1,6317.2,195817.1] single_valued_class(inverse(u)) || equal(cross_product(universal_class,universal_class),inverse(u))* equal(inverse(u),universal_class) -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.89/300.47  201424[10:EmS:161261.0,161261.1,6317.2,195883.1] single_valued_class(sum_class(u)) || equal(cross_product(universal_class,universal_class),sum_class(u))* equal(sum_class(u),universal_class) -> member(successor_relation,cross_product(universal_class,universal_class))*.
% 299.89/300.47  201538[6:SpL:201355.0,2142.0] || member(u,regular(domain_relation))* -> equal(u,unordered_pair(first(regular(domain_relation)),singleton(second(regular(domain_relation)))))* equal(u,singleton(first(regular(domain_relation)))).
% 299.89/300.47  201582[10:Res:201484.0,162356.0] || subclass(regular(domain_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(singleton(first(regular(domain_relation))),least(omega,regular(domain_relation)))),successor_relation)**.
% 299.89/300.47  202780[10:Res:160827.1,5832.1] inductive(singleton(u)) || well_ordering(v,power_class(universal_class)) -> member(u,image(element_relation,successor_relation)) member(least(v,singleton(u)),singleton(u))*.
% 299.89/300.47  202777[10:Res:160827.1,160292.0] || well_ordering(u,power_class(universal_class)) -> member(v,image(element_relation,successor_relation)) equal(singleton(v),successor_relation) member(least(u,singleton(v)),singleton(v))*.
% 299.89/300.47  203522[6:Rew:203192.0,120010.0] || member(u,cantor(universal_class)) equal(cross_product(u,universal_class),v) subclass(rest_of(universal_class),w) -> member(ordered_pair(u,v),w)*.
% 299.89/300.47  203640[10:Rew:203192.0,161589.2] || member(regular(cross_product(u,v)),rest_of(w)) -> equal(cross_product(u,v),successor_relation) member(first(regular(cross_product(u,v))),cantor(w))*.
% 299.89/300.47  203656[6:Rew:203192.0,142646.1] || member(u,universal_class) -> member(u,cantor(v)) equal(symmetric_difference(v,cross_product(singleton(u),universal_class)),union(v,cross_product(singleton(u),universal_class)))**.
% 299.89/300.47  203657[6:Rew:203192.0,142647.1] || member(u,universal_class) -> member(u,cantor(v)) equal(symmetric_difference(cross_product(singleton(u),universal_class),v),union(cross_product(singleton(u),universal_class),v))**.
% 299.89/300.47  203678[6:Rew:203192.0,5914.0] || member(singleton(u),cantor(v)) equal(restrict(v,singleton(u),universal_class),u) -> member(singleton(singleton(singleton(u))),rest_of(v))*.
% 299.89/300.47  206020[10:Res:163210.1,5832.1] inductive(singleton(u)) || well_ordering(v,symmetrization_of(successor_relation)) -> member(u,complement(inverse(successor_relation))) member(least(v,singleton(u)),singleton(u))*.
% 299.89/300.47  206017[10:Res:163210.1,160292.0] || well_ordering(u,symmetrization_of(successor_relation)) -> member(v,complement(inverse(successor_relation))) equal(singleton(v),successor_relation) member(least(u,singleton(v)),singleton(v))*.
% 299.89/300.47  206035[10:Res:160970.1,5832.1] inductive(singleton(u)) || well_ordering(v,power_class(successor_relation)) -> member(u,image(element_relation,universal_class)) member(least(v,singleton(u)),singleton(u))*.
% 299.89/300.47  206032[10:Res:160970.1,160292.0] || well_ordering(u,power_class(successor_relation)) -> member(v,image(element_relation,universal_class)) equal(singleton(v),successor_relation) member(least(u,singleton(v)),singleton(v))*.
% 299.89/300.47  208472[6:SoR:206609.0,73.1] one_to_one(cantor(restrict(u,v,cross_product(universal_class,universal_class)))) || subclass(cross_product(universal_class,universal_class),v) -> section(u,cross_product(universal_class,universal_class),v)*.
% 299.89/300.47  209103[10:Res:163218.1,5832.1] inductive(singleton(u)) || well_ordering(v,successor(successor_relation)) -> member(u,complement(singleton(successor_relation))) member(least(v,singleton(u)),singleton(u))*.
% 299.89/300.47  209100[10:Res:163218.1,160292.0] || well_ordering(u,successor(successor_relation)) -> member(v,complement(singleton(successor_relation))) equal(singleton(v),successor_relation) member(least(u,singleton(v)),singleton(v))*.
% 299.89/300.47  209427[12:Res:209313.0,162356.0] || subclass(cross_product(universal_class,universal_class),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(element_relation),least(omega,cross_product(universal_class,universal_class)))),successor_relation)**.
% 299.89/300.47  209443[12:Res:209377.1,162356.0] || subclass(universal_class,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(element_relation),least(omega,u))),successor_relation)**.
% 299.89/300.47  209556[12:SpL:209433.0,2142.0] || member(u,regular(element_relation))* -> equal(u,unordered_pair(first(regular(element_relation)),singleton(second(regular(element_relation)))))* equal(u,singleton(first(regular(element_relation)))).
% 299.89/300.47  209654[12:Res:209506.0,162356.0] || subclass(regular(element_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(singleton(first(regular(element_relation))),least(omega,regular(element_relation)))),successor_relation)**.
% 299.89/300.47  210374[15:Res:189563.1,10.0] || subclass(domain_relation,flip(unordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,x),successor_relation),v)* equal(ordered_pair(ordered_pair(w,x),successor_relation),u)*.
% 299.89/300.47  210447[15:Res:189564.1,10.0] || subclass(domain_relation,rotate(unordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,successor_relation),x),v)* equal(ordered_pair(ordered_pair(w,successor_relation),x),u)*.
% 299.89/300.47  210549[10:Res:160784.3,149475.0] || member(u,universal_class) subclass(u,cantor(v))* subclass(universal_class,w) -> equal(u,successor_relation) member(apply(choice,u),w)*.
% 299.89/300.47  211397[10:Rew:211297.0,211353.2,211297.0,211353.0] ||  -> subclass(ordered_pair(universal_class,universal_class),u) equal(not_subclass_element(ordered_pair(universal_class,universal_class),u),unordered_pair(universal_class,successor_relation))** equal(not_subclass_element(ordered_pair(universal_class,universal_class),u),successor_relation).
% 299.89/300.47  211553[10:SpL:162889.0,161505.0] || member(regular(power_class(image(element_relation,successor(successor_relation)))),image(element_relation,power_class(complement(singleton(successor_relation)))))* -> equal(power_class(image(element_relation,successor(successor_relation))),successor_relation).
% 299.89/300.47  211552[10:SpL:161137.0,161505.0] || member(regular(power_class(image(element_relation,symmetrization_of(successor_relation)))),image(element_relation,power_class(complement(inverse(successor_relation)))))* -> equal(power_class(image(element_relation,symmetrization_of(successor_relation))),successor_relation).
% 299.89/300.47  211752[10:SpR:162889.0,9949.0] ||  -> equal(power_class(intersection(power_class(complement(singleton(successor_relation))),complement(singleton(image(element_relation,successor(successor_relation)))))),complement(image(element_relation,successor(image(element_relation,successor(successor_relation))))))**.
% 299.89/300.47  211751[10:SpR:161137.0,9949.0] ||  -> equal(power_class(intersection(power_class(complement(inverse(successor_relation))),complement(singleton(image(element_relation,symmetrization_of(successor_relation)))))),complement(image(element_relation,successor(image(element_relation,symmetrization_of(successor_relation))))))**.
% 299.89/300.47  211849[10:SpR:162889.0,9948.0] ||  -> equal(power_class(intersection(power_class(complement(singleton(successor_relation))),complement(inverse(image(element_relation,successor(successor_relation)))))),complement(image(element_relation,symmetrization_of(image(element_relation,successor(successor_relation))))))**.
% 299.89/300.47  211848[10:SpR:161137.0,9948.0] ||  -> equal(power_class(intersection(power_class(complement(inverse(successor_relation))),complement(inverse(image(element_relation,symmetrization_of(successor_relation)))))),complement(image(element_relation,symmetrization_of(image(element_relation,symmetrization_of(successor_relation))))))**.
% 299.89/300.47  212001[11:Res:183759.1,2142.0] || subclass(inverse(successor_relation),ordered_pair(u,v))* -> equal(unordered_pair(u,singleton(v)),regular(symmetrization_of(successor_relation))) equal(regular(symmetrization_of(successor_relation)),singleton(u)).
% 299.89/300.47  212107[10:Rew:161779.1,212106.2] || member(regular(u),unordered_pair(v,u))* -> equal(regular(unordered_pair(v,u)),v) equal(u,successor_relation) equal(unordered_pair(v,u),successor_relation).
% 299.89/300.47  212109[10:Rew:161779.2,212108.2] || member(regular(u),unordered_pair(u,v))* -> equal(regular(unordered_pair(u,v)),v) equal(u,successor_relation) equal(unordered_pair(u,v),successor_relation).
% 299.89/300.47  212168[10:Obv:212165.1] || subclass(unordered_pair(u,v),omega)* -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),successor_relation) equal(integer_of(v),v).
% 299.89/300.47  212169[10:Obv:212164.1] || subclass(unordered_pair(u,v),omega)* -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),successor_relation) equal(integer_of(u),u).
% 299.89/300.47  214287[10:Res:214277.1,3874.1] || equal(complement(complement(intersection(u,v))),successor_relation) member(power_class(successor_relation),union(u,v)) -> member(power_class(successor_relation),symmetric_difference(u,v))*.
% 299.89/300.47  216225[14:SpR:199971.1,60.1] || member(u,universal_class) member(ordered_pair(sum_class(range_of(u)),v),compose(w,x))* -> member(v,image(w,image(x,successor_relation))).
% 299.89/300.47  216473[10:Res:216465.1,3874.1] || equal(complement(complement(intersection(u,v))),successor_relation) member(regular(rest_relation),union(u,v)) -> member(regular(rest_relation),symmetric_difference(u,v))*.
% 299.89/300.47  216901[10:Res:216847.1,3874.1] || equal(complement(complement(intersection(u,v))),successor_relation) member(regular(domain_relation),union(u,v)) -> member(regular(domain_relation),symmetric_difference(u,v))*.
% 299.89/300.47  217386[10:Rew:162889.0,217298.1] || member(regular(intersection(power_class(complement(singleton(successor_relation))),u)),image(element_relation,successor(successor_relation)))* -> equal(intersection(power_class(complement(singleton(successor_relation))),u),successor_relation).
% 299.89/300.47  217387[10:Rew:161137.0,217297.1] || member(regular(intersection(power_class(complement(inverse(successor_relation))),u)),image(element_relation,symmetrization_of(successor_relation)))* -> equal(intersection(power_class(complement(inverse(successor_relation))),u),successor_relation).
% 299.89/300.47  217524[10:Rew:162889.0,217456.1] || member(regular(intersection(u,power_class(complement(singleton(successor_relation))))),image(element_relation,successor(successor_relation)))* -> equal(intersection(u,power_class(complement(singleton(successor_relation)))),successor_relation).
% 299.89/300.47  217525[10:Rew:161137.0,217455.1] || member(regular(intersection(u,power_class(complement(inverse(successor_relation))))),image(element_relation,symmetrization_of(successor_relation)))* -> equal(intersection(u,power_class(complement(inverse(successor_relation)))),successor_relation).
% 299.89/300.47  218260[10:SpL:161565.2,217909.0] || member(cross_product(u,v),universal_class) equal(complement(regular(apply(choice,cross_product(u,v)))),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  218755[10:Res:218481.0,160373.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(segment(u,restrict(complement(kind_1_ordinals),v,w),least(u,restrict(complement(kind_1_ordinals),v,w))),successor_relation)**.
% 299.89/300.47  218873[22:Res:218867.1,162356.0] || subclass(kind_1_ordinals,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(successor_relation),least(omega,u))),successor_relation)**.
% 299.89/300.47  219142[3:Res:218473.1,5553.2] || equal(cross_product(u,v),complement(kind_1_ordinals))** member(w,v)* member(x,u)* -> member(ordered_pair(x,w),complement(ordinal_numbers))*.
% 299.89/300.47  219378[22:Rew:219376.1,217262.1] || equal(singleton(not_subclass_element(u,intersection(v,singleton(successor_relation)))),kind_1_ordinals)** member(singleton(successor_relation),v) -> subclass(u,intersection(v,singleton(successor_relation))).
% 299.89/300.47  160600[10:Rew:160202.0,146301.2] || member(u,universal_class) -> member(u,segment(v,w,x)) equal(apply(restrict(v,w,singleton(x)),u),sum_class(range_of(successor_relation)))**.
% 299.89/300.47  204796[10:Rew:203192.0,203946.2,203192.0,203946.1] || member(cantor(u),universal_class) -> equal(apply(u,singleton(cantor(u))),sum_class(range_of(successor_relation)))** member(singleton(singleton(singleton(cantor(u)))),element_relation)*.
% 299.89/300.47  195926[10:Rew:193730.0,195914.1] || member(ordered_pair(u,not_subclass_element(v,range_of(successor_relation))),compose(complement(cross_product(image(w,singleton(u)),universal_class)),w))* -> subclass(v,range_of(successor_relation)).
% 299.89/300.47  163665[10:Rew:160305.0,162843.1,160305.0,162843.0,160202.0,162843.0] ||  -> equal(restrict(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u,v),successor_relation) member(regular(restrict(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u,v)),kind_1_ordinals)*.
% 299.89/300.47  220414[23:Res:220406.0,162356.0] || subclass(kind_1_ordinals,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),least(omega,kind_1_ordinals))),successor_relation)**.
% 299.89/300.47  220873[23:Res:220417.0,162356.0] || subclass(universal_class,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),least(omega,universal_class))),successor_relation)**.
% 299.89/300.47  220892[10:SpL:161565.2,219813.0] || member(cross_product(u,v),universal_class) subclass(universal_class,regular(singleton(apply(choice,cross_product(u,v)))))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  220930[10:SpL:161565.2,220897.0] || member(cross_product(u,v),universal_class) equal(regular(singleton(apply(choice,cross_product(u,v)))),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  221503[10:Res:218373.0,3883.2] || member(u,v) member(u,w) -> equal(singleton(intersection(w,v)),successor_relation) member(u,complement(singleton(intersection(w,v))))*.
% 299.89/300.47  221530[10:MRR:221482.2,185246.0] || member(u,universal_class) well_ordering(v,complement(singleton(unordered_pair(w,u)))) -> member(least(v,unordered_pair(w,u)),unordered_pair(w,u))*.
% 299.89/300.47  221531[10:MRR:221480.2,185246.0] || member(u,universal_class) well_ordering(v,complement(singleton(unordered_pair(u,w)))) -> member(least(v,unordered_pair(u,w)),unordered_pair(u,w))*.
% 299.89/300.47  221669[10:Res:161697.1,185698.1] inductive(regular(restrict(ordinal_numbers,u,v))) ||  -> equal(restrict(ordinal_numbers,u,v),successor_relation)** equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  221631[15:Res:189374.2,185698.1] inductive(ordered_pair(u,successor_relation)) || member(u,universal_class)* subclass(domain_relation,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  221943[6:Res:157922.1,33515.1] || member(singleton(compose(element_relation,universal_class)),element_relation) member(compose(element_relation,universal_class),universal_class) -> member(singleton(singleton(singleton(compose(element_relation,universal_class)))),element_relation)*.
% 299.89/300.47  222023[15:Res:189374.2,986.1] || member(u,universal_class) subclass(domain_relation,power_class(image(element_relation,complement(v)))) member(ordered_pair(u,successor_relation),image(element_relation,power_class(v)))* -> .
% 299.89/300.47  222157[10:SpL:161565.2,222139.0] || member(cross_product(u,v),universal_class) subclass(complement(singleton(apply(choice,cross_product(u,v)))),successor_relation)* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  222518[24:Rew:222326.0,222421.1] || member(ordered_pair(kind_1_ordinals,not_subclass_element(u,image(v,image(w,successor_relation)))),compose(v,w))* -> subclass(u,image(v,image(w,successor_relation))).
% 299.89/300.47  224350[25:Rew:224236.1,212722.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,regular(complement(power_class(successor_relation))))*.
% 299.89/300.47  224351[25:Rew:224236.1,212639.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,regular(complement(power_class(universal_class))))*.
% 299.89/300.47  224361[25:Rew:224236.1,204808.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,regular(complement(successor(successor_relation))))*.
% 299.89/300.47  224395[25:Rew:224236.1,204804.2] function(u) || equal(cantor(range_of(v)),range_of(u)) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,inverse(v))*.
% 299.89/300.47  225489[25:Rew:224739.1,224991.1] function(u) || member(restrict(v,w,successor_relation),universal_class) -> member(ordered_pair(restrict(v,w,successor_relation),segment(v,w,u)),domain_relation)*.
% 299.89/300.47  226604[10:Res:161880.1,160481.0] || member(regular(intersection(intersection(regular(u),v),w)),u)* -> equal(intersection(intersection(regular(u),v),w),successor_relation) equal(u,successor_relation).
% 299.89/300.47  227195[10:Res:161881.1,160481.0] || member(regular(intersection(intersection(u,regular(v)),w)),v)* -> equal(intersection(intersection(u,regular(v)),w),successor_relation) equal(v,successor_relation).
% 299.89/300.47  227491[10:Res:161874.1,160481.0] || member(regular(intersection(u,intersection(regular(v),w))),v)* -> equal(intersection(u,intersection(regular(v),w)),successor_relation) equal(v,successor_relation).
% 299.89/300.47  228097[10:Res:161875.1,160481.0] || member(regular(intersection(u,intersection(v,regular(w)))),w)* -> equal(intersection(u,intersection(v,regular(w))),successor_relation) equal(w,successor_relation).
% 299.89/300.47  229009[10:Res:228991.1,162356.0] || subclass(kind_1_ordinals,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(ordinal_numbers),least(omega,u))),successor_relation)**.
% 299.89/300.47  229237[10:Res:229228.1,162356.0] || subclass(universal_class,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(ordinal_numbers),least(omega,u))),successor_relation)**.
% 299.89/300.47  229810[10:Res:221521.1,33515.1] || member(complement(singleton(omega)),universal_class) -> equal(integer_of(singleton(complement(singleton(omega)))),successor_relation) member(singleton(singleton(singleton(complement(singleton(omega))))),element_relation)*.
% 299.89/300.47  230759[10:Obv:230754.1] || member(not_subclass_element(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),intersection(u,kind_1_ordinals)),u)* -> subclass(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),intersection(u,kind_1_ordinals)).
% 299.89/300.47  230819[10:Res:160972.1,6045.0] || member(u,universal_class) subclass(image(element_relation,power_class(successor_relation)),v)* well_ordering(universal_class,v) -> member(u,power_class(image(element_relation,universal_class)))*.
% 299.89/300.47  230869[10:MRR:230826.0,34189.1] ||  -> member(not_subclass_element(u,intersection(image(element_relation,power_class(successor_relation)),u)),power_class(image(element_relation,universal_class)))* subclass(u,intersection(image(element_relation,power_class(successor_relation)),u)).
% 299.89/300.47  231055[20:SpL:10028.0,206075.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),omega)** equal(symmetrization_of(image(element_relation,complement(u))),successor(successor_relation)) -> .
% 299.89/300.47  231054[10:SpL:10028.0,206081.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),universal_class)** equal(symmetrization_of(image(element_relation,complement(u))),successor(successor_relation)) -> .
% 299.89/300.47  231052[20:SpL:10028.0,202875.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),omega)** equal(symmetrization_of(image(element_relation,complement(u))),symmetrization_of(successor_relation)) -> .
% 299.89/300.47  231051[11:SpL:10028.0,202881.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),universal_class)** equal(symmetrization_of(image(element_relation,complement(u))),symmetrization_of(successor_relation)) -> .
% 299.89/300.47  231044[20:SpL:10028.0,192317.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),inverse(successor_relation))** equal(symmetrization_of(image(element_relation,complement(u))),omega) -> .
% 299.89/300.47  231043[20:SpL:10028.0,192318.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),singleton(successor_relation))** equal(symmetrization_of(image(element_relation,complement(u))),omega) -> .
% 299.89/300.47  231042[20:SpL:10028.0,192319.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),successor(successor_relation))** equal(symmetrization_of(image(element_relation,complement(u))),omega) -> .
% 299.89/300.47  231025[11:SpL:10028.0,194544.0] || equal(complement(symmetrization_of(image(element_relation,complement(u)))),symmetrization_of(successor_relation)) -> member(successor_relation,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.89/300.47  231024[10:SpL:10028.0,194543.0] || equal(complement(symmetrization_of(image(element_relation,complement(u)))),successor(successor_relation)) -> member(successor_relation,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.89/300.47  231023[10:SpL:10028.0,194542.0] || equal(complement(symmetrization_of(image(element_relation,complement(u)))),singleton(successor_relation)) -> member(successor_relation,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.89/300.47  231022[11:SpL:10028.0,194541.0] || equal(complement(symmetrization_of(image(element_relation,complement(u)))),inverse(successor_relation)) -> member(successor_relation,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.89/300.47  231021[10:SpL:10028.0,194520.0] || subclass(universal_class,complement(symmetrization_of(image(element_relation,complement(u))))) -> member(power_class(successor_relation),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.89/300.47  231020[6:SpL:10028.0,199986.0] || subclass(universal_class,complement(symmetrization_of(image(element_relation,complement(u))))) -> member(regular(rest_relation),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.89/300.47  231019[6:SpL:10028.0,201376.0] || subclass(universal_class,complement(symmetrization_of(image(element_relation,complement(u))))) -> member(regular(domain_relation),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.89/300.47  231018[10:SpL:10028.0,194513.0] || equal(complement(complement(symmetrization_of(image(element_relation,complement(u))))),successor_relation) -> member(omega,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.89/300.47  231017[10:SpL:10028.0,194540.0] || equal(complement(complement(symmetrization_of(image(element_relation,complement(u))))),successor_relation) -> member(successor_relation,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))*.
% 299.89/300.47  231015[10:SpL:10028.0,185801.0] || equal(complement(symmetrization_of(image(element_relation,complement(u)))),successor_relation) subclass(universal_class,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  231014[10:SpL:10028.0,185935.0] || equal(complement(symmetrization_of(image(element_relation,complement(u)))),successor_relation) member(successor_relation,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  231013[10:SpL:10028.0,186009.0] || equal(complement(symmetrization_of(image(element_relation,complement(u)))),successor_relation) member(omega,intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  231005[10:SpL:10028.0,162918.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),successor(successor_relation))** equal(symmetrization_of(image(element_relation,complement(u))),universal_class) -> .
% 299.89/300.47  231004[10:SpL:10028.0,162872.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),singleton(successor_relation))** equal(symmetrization_of(image(element_relation,complement(u))),universal_class) -> .
% 299.89/300.47  231003[11:SpL:10028.0,182321.1] || equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),inverse(successor_relation))** equal(symmetrization_of(image(element_relation,complement(u))),universal_class) -> .
% 299.89/300.47  230999[10:SpL:10028.0,187767.0] || subclass(universal_class,symmetrization_of(image(element_relation,complement(u)))) member(power_class(successor_relation),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  230997[6:SpL:10028.0,199982.0] || subclass(universal_class,symmetrization_of(image(element_relation,complement(u)))) member(regular(rest_relation),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  230996[6:SpL:10028.0,201372.0] || subclass(universal_class,symmetrization_of(image(element_relation,complement(u)))) member(regular(domain_relation),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  231379[20:SpL:10029.0,206075.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),omega)** equal(successor(image(element_relation,complement(u))),successor(successor_relation)) -> .
% 299.89/300.47  231378[10:SpL:10029.0,206081.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),universal_class)** equal(successor(image(element_relation,complement(u))),successor(successor_relation)) -> .
% 299.89/300.47  231376[20:SpL:10029.0,202875.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),omega)** equal(successor(image(element_relation,complement(u))),symmetrization_of(successor_relation)) -> .
% 299.89/300.47  231375[11:SpL:10029.0,202881.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),universal_class)** equal(successor(image(element_relation,complement(u))),symmetrization_of(successor_relation)) -> .
% 299.89/300.47  231368[20:SpL:10029.0,192317.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),inverse(successor_relation))** equal(successor(image(element_relation,complement(u))),omega) -> .
% 299.89/300.47  231367[20:SpL:10029.0,192318.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),singleton(successor_relation))** equal(successor(image(element_relation,complement(u))),omega) -> .
% 299.89/300.47  231366[20:SpL:10029.0,192319.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),successor(successor_relation))** equal(successor(image(element_relation,complement(u))),omega) -> .
% 299.89/300.47  231349[11:SpL:10029.0,194544.0] || equal(complement(successor(image(element_relation,complement(u)))),symmetrization_of(successor_relation)) -> member(successor_relation,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.89/300.47  231348[10:SpL:10029.0,194543.0] || equal(complement(successor(image(element_relation,complement(u)))),successor(successor_relation)) -> member(successor_relation,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.89/300.47  231347[10:SpL:10029.0,194542.0] || equal(complement(successor(image(element_relation,complement(u)))),singleton(successor_relation)) -> member(successor_relation,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.89/300.47  231346[11:SpL:10029.0,194541.0] || equal(complement(successor(image(element_relation,complement(u)))),inverse(successor_relation)) -> member(successor_relation,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.89/300.47  231345[10:SpL:10029.0,194520.0] || subclass(universal_class,complement(successor(image(element_relation,complement(u))))) -> member(power_class(successor_relation),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.89/300.47  231344[6:SpL:10029.0,199986.0] || subclass(universal_class,complement(successor(image(element_relation,complement(u))))) -> member(regular(rest_relation),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.89/300.47  231343[6:SpL:10029.0,201376.0] || subclass(universal_class,complement(successor(image(element_relation,complement(u))))) -> member(regular(domain_relation),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.89/300.47  231342[10:SpL:10029.0,194513.0] || equal(complement(complement(successor(image(element_relation,complement(u))))),successor_relation) -> member(omega,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.89/300.47  231341[10:SpL:10029.0,194540.0] || equal(complement(complement(successor(image(element_relation,complement(u))))),successor_relation) -> member(successor_relation,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))*.
% 299.89/300.47  231339[10:SpL:10029.0,185801.0] || equal(complement(successor(image(element_relation,complement(u)))),successor_relation) subclass(universal_class,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  231338[10:SpL:10029.0,185935.0] || equal(complement(successor(image(element_relation,complement(u)))),successor_relation) member(successor_relation,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  231337[10:SpL:10029.0,186009.0] || equal(complement(successor(image(element_relation,complement(u)))),successor_relation) member(omega,intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  231329[10:SpL:10029.0,162918.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),successor(successor_relation))** equal(successor(image(element_relation,complement(u))),universal_class) -> .
% 299.89/300.47  231328[10:SpL:10029.0,162872.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),singleton(successor_relation))** equal(successor(image(element_relation,complement(u))),universal_class) -> .
% 299.89/300.47  231327[11:SpL:10029.0,182321.1] || equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),inverse(successor_relation))** equal(successor(image(element_relation,complement(u))),universal_class) -> .
% 299.89/300.47  231323[10:SpL:10029.0,187767.0] || subclass(universal_class,successor(image(element_relation,complement(u)))) member(power_class(successor_relation),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  231321[6:SpL:10029.0,199982.0] || subclass(universal_class,successor(image(element_relation,complement(u)))) member(regular(rest_relation),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  231320[6:SpL:10029.0,201372.0] || subclass(universal_class,successor(image(element_relation,complement(u)))) member(regular(domain_relation),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  231834[10:Res:1504.1,161035.0] || subclass(ordered_pair(u,v),intersection(power_class(successor_relation),complement(w))) member(unordered_pair(u,singleton(v)),union(image(element_relation,universal_class),w))* -> .
% 299.89/300.47  231826[15:Res:189563.1,161035.0] || subclass(domain_relation,flip(intersection(power_class(successor_relation),complement(u)))) member(ordered_pair(ordered_pair(v,w),successor_relation),union(image(element_relation,universal_class),u))* -> .
% 299.89/300.47  231822[15:Res:189564.1,161035.0] || subclass(domain_relation,rotate(intersection(power_class(successor_relation),complement(u)))) member(ordered_pair(ordered_pair(v,successor_relation),w),union(image(element_relation,universal_class),u))* -> .
% 299.89/300.47  231812[10:Res:1479.2,161035.0] || member(u,universal_class) subclass(universal_class,intersection(power_class(successor_relation),complement(v))) member(sum_class(u),union(image(element_relation,universal_class),v))* -> .
% 299.89/300.47  231807[10:Res:1481.2,161035.0] || subclass(u,intersection(power_class(successor_relation),complement(v))) member(not_subclass_element(u,w),union(image(element_relation,universal_class),v))* -> subclass(u,w).
% 299.89/300.47  231806[10:Res:1478.2,161035.0] || member(u,universal_class) subclass(universal_class,intersection(power_class(successor_relation),complement(v))) member(power_class(u),union(image(element_relation,universal_class),v))* -> .
% 299.89/300.47  231797[10:Res:4.1,161035.0] || member(not_subclass_element(intersection(power_class(successor_relation),complement(u)),v),union(image(element_relation,universal_class),u))* -> subclass(intersection(power_class(successor_relation),complement(u)),v).
% 299.89/300.47  231778[10:SpL:162889.0,161035.0] || member(u,intersection(power_class(successor_relation),power_class(complement(singleton(successor_relation))))) member(u,union(image(element_relation,universal_class),image(element_relation,successor(successor_relation))))* -> .
% 299.89/300.47  231777[10:SpL:161137.0,161035.0] || member(u,intersection(power_class(successor_relation),power_class(complement(inverse(successor_relation))))) member(u,union(image(element_relation,universal_class),image(element_relation,symmetrization_of(successor_relation))))* -> .
% 299.89/300.47  10180[0:SpR:31.0,1933.0] ||  -> equal(intersection(complement(restrict(inverse(cross_product(u,v)),u,v)),symmetrization_of(cross_product(u,v))),symmetric_difference(cross_product(u,v),inverse(cross_product(u,v))))**.
% 299.89/300.47  33814[0:SpR:1938.0,1951.1] || member(u,symmetric_difference(complement(restrict(v,w,x)),union(v,cross_product(w,x))))* -> member(u,complement(symmetric_difference(v,cross_product(w,x)))).
% 299.89/300.47  33887[0:SpR:1943.0,1951.1] || member(u,symmetric_difference(complement(restrict(v,w,x)),union(cross_product(w,x),v)))* -> member(u,complement(symmetric_difference(cross_product(w,x),v))).
% 299.89/300.47  34028[0:SpL:161.0,3883.2] || member(u,union(v,w)) member(u,complement(intersection(v,w)))* subclass(symmetric_difference(v,w),x)* -> member(u,x)*.
% 299.89/300.47  35717[0:Res:1499.1,3874.1] || subclass(universal_class,complement(intersection(u,v))) member(ordered_pair(w,x),union(u,v)) -> member(ordered_pair(w,x),symmetric_difference(u,v))*.
% 299.89/300.47  35691[0:Res:3907.1,3874.1] || equal(complement(complement(complement(intersection(u,v)))),universal_class)** member(singleton(w),union(u,v)) -> member(singleton(w),symmetric_difference(u,v))*.
% 299.89/300.47  70410[0:SpR:31.0,1934.0] ||  -> equal(intersection(complement(restrict(singleton(cross_product(u,v)),u,v)),successor(cross_product(u,v))),symmetric_difference(cross_product(u,v),singleton(cross_product(u,v))))**.
% 299.89/300.47  31108[2:Res:9811.0,5832.1] inductive(symmetric_difference(u,inverse(u))) || well_ordering(v,symmetrization_of(u)) -> member(least(v,symmetric_difference(u,inverse(u))),symmetric_difference(u,inverse(u)))*.
% 299.89/300.47  31109[2:Res:9812.0,5832.1] inductive(symmetric_difference(u,singleton(u))) || well_ordering(v,successor(u)) -> member(least(v,symmetric_difference(u,singleton(u))),symmetric_difference(u,singleton(u)))*.
% 299.89/300.47  5865[0:Res:1009.0,127.0] || subclass(singleton(singleton(singleton(u))),v)* well_ordering(w,v)* -> member(least(w,singleton(singleton(singleton(u)))),singleton(singleton(singleton(u))))*.
% 299.89/300.47  108325[0:SpL:1943.0,9332.1] || member(u,symmetric_difference(complement(restrict(v,w,x)),union(cross_product(w,x),v)))* member(u,symmetric_difference(cross_product(w,x),v)) -> .
% 299.89/300.47  108324[0:SpL:1938.0,9332.1] || member(u,symmetric_difference(complement(restrict(v,w,x)),union(v,cross_product(w,x))))* member(u,symmetric_difference(v,cross_product(w,x))) -> .
% 299.89/300.47  120152[0:SpL:1931.0,9149.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(intersection(v,w)),union(v,w)))* -> member(power_class(u),complement(symmetric_difference(v,w)))*.
% 299.89/300.47  122603[2:MRR:122596.2,2492.1] || connected(u,restrict(v,w,x)) -> well_ordering(u,restrict(v,w,x)) member(regular(not_well_ordering(u,restrict(v,w,x))),v)*.
% 299.89/300.47  125917[0:Res:28320.1,513.0] || subclass(rest_relation,rotate(intersection(complement(u),complement(v)))) member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),union(u,v))* -> .
% 299.89/300.47  126047[0:Res:28321.1,513.0] || subclass(rest_relation,flip(intersection(complement(u),complement(v)))) member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),union(u,v))* -> .
% 299.89/300.47  126373[0:Res:10258.1,127.0] || subclass(successor(u),v)* well_ordering(w,v)* -> subclass(symmetric_difference(u,singleton(u)),x)* member(least(w,successor(u)),successor(u))*.
% 299.89/300.47  126441[0:Res:10194.1,127.0] || subclass(symmetrization_of(u),v)* well_ordering(w,v)* -> subclass(symmetric_difference(u,inverse(u)),x)* member(least(w,symmetrization_of(u)),symmetrization_of(u))*.
% 299.89/300.47  142023[2:MRR:92724.3,120469.0] || asymmetric(cross_product(u,v),w)* member(x,cross_product(w,w))* member(x,restrict(inverse(cross_product(u,v)),u,v))* -> .
% 299.89/300.47  31215[0:Res:3872.2,3514.1] || member(ordered_pair(u,v),cross_product(w,x))* member(ordered_pair(u,v),y)* subclass(universal_class,complement(restrict(y,w,x)))* -> .
% 299.89/300.47  111848[0:Res:3595.3,9322.0] function(u) || member(v,universal_class) subclass(universal_class,symmetric_difference(complement(w),complement(x)))* -> member(image(u,v),union(w,x))*.
% 299.89/300.47  130394[0:Res:1495.2,9300.0] || member(u,universal_class) subclass(rest_relation,symmetric_difference(v,cross_product(w,x))) -> member(ordered_pair(u,rest_of(u)),complement(restrict(v,w,x)))*.
% 299.89/300.47  130487[0:Res:1495.2,9306.0] || member(u,universal_class) subclass(rest_relation,symmetric_difference(cross_product(v,w),x)) -> member(ordered_pair(u,rest_of(u)),complement(restrict(x,v,w)))*.
% 299.89/300.47  123500[0:Res:978.1,594.0] ||  -> subclass(restrict(restrict(u,v,w),x,y),z) member(not_subclass_element(restrict(restrict(u,v,w),x,y),z),cross_product(v,w))*.
% 299.89/300.47  111841[0:Res:340.1,9322.0] ||  -> subclass(intersection(symmetric_difference(complement(u),complement(v)),w),x) member(not_subclass_element(intersection(symmetric_difference(complement(u),complement(v)),w),x),union(u,v))*.
% 299.89/300.47  111842[0:Res:322.1,9322.0] ||  -> subclass(intersection(u,symmetric_difference(complement(v),complement(w))),x) member(not_subclass_element(intersection(u,symmetric_difference(complement(v),complement(w))),x),union(v,w))*.
% 299.89/300.47  41940[0:SpL:2330.1,6210.0] || equal(u,not_subclass_element(cross_product(v,w),x)) -> subclass(cross_product(v,w),x) member(singleton(first(not_subclass_element(cross_product(v,w),x))),u)*.
% 299.89/300.47  113264[0:MRR:113192.0,34189.1] ||  -> member(not_subclass_element(u,intersection(intersection(complement(v),complement(w)),u)),union(v,w))* subclass(u,intersection(intersection(complement(v),complement(w)),u)).
% 299.89/300.47  111840[0:Res:34429.0,9322.0] ||  -> subclass(complement(complement(symmetric_difference(complement(u),complement(v)))),w) member(not_subclass_element(complement(complement(symmetric_difference(complement(u),complement(v)))),w),union(u,v))*.
% 299.89/300.47  41919[0:SpL:2330.1,1503.0] || subclass(not_subclass_element(cross_product(u,v),w),x) -> subclass(cross_product(u,v),w) member(singleton(first(not_subclass_element(cross_product(u,v),w))),x)*.
% 299.89/300.47  9651[0:Res:1481.2,19.0] || subclass(u,cross_product(v,w))* -> subclass(u,x) equal(ordered_pair(first(not_subclass_element(u,x)),second(not_subclass_element(u,x))),not_subclass_element(u,x))**.
% 299.89/300.47  123404[0:SpL:1931.0,9639.0] || subclass(u,symmetric_difference(complement(intersection(v,w)),union(v,w)))* -> subclass(u,x) member(not_subclass_element(u,x),complement(symmetric_difference(v,w)))*.
% 299.89/300.47  130502[0:Res:51387.0,9306.0] ||  -> subclass(u,complement(symmetric_difference(cross_product(v,w),x))) member(not_subclass_element(u,complement(symmetric_difference(cross_product(v,w),x))),complement(restrict(x,v,w)))*.
% 299.89/300.47  130409[0:Res:51387.0,9300.0] ||  -> subclass(u,complement(symmetric_difference(v,cross_product(w,x)))) member(not_subclass_element(u,complement(symmetric_difference(v,cross_product(w,x)))),complement(restrict(v,w,x)))*.
% 299.89/300.47  122497[0:Res:25.2,9636.1] || member(not_subclass_element(u,v),w)* member(not_subclass_element(u,v),x)* subclass(u,complement(intersection(x,w)))* -> subclass(u,v).
% 299.89/300.47  35695[0:Res:1476.1,3874.1] || subclass(universal_class,complement(intersection(u,v))) member(unordered_pair(w,x),union(u,v)) -> member(unordered_pair(w,x),symmetric_difference(u,v))*.
% 299.89/300.47  28280[0:Res:1495.2,10.0] || member(u,universal_class) subclass(rest_relation,unordered_pair(v,w))* -> equal(ordered_pair(u,rest_of(u)),w)* equal(ordered_pair(u,rest_of(u)),v)*.
% 299.89/300.47  89252[0:Res:51387.0,10.0] ||  -> subclass(u,complement(unordered_pair(v,w))) equal(not_subclass_element(u,complement(unordered_pair(v,w))),w)** equal(not_subclass_element(u,complement(unordered_pair(v,w))),v)**.
% 299.89/300.47  31204[0:Res:3872.2,3486.1] || member(unordered_pair(u,v),cross_product(w,x))* member(unordered_pair(u,v),y)* subclass(universal_class,complement(restrict(y,w,x)))* -> .
% 299.89/300.47  10496[0:Res:27.2,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class)* subclass(complement(u),intersection(y__dfg,ordinal_numbers)) -> member(least(element_relation,intersection(y__dfg,ordinal_numbers)),u)*.
% 299.89/300.47  34660[0:Res:173.1,3.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class)* subclass(complement(intersection(y__dfg,ordinal_numbers)),u) -> member(least(element_relation,intersection(y__dfg,ordinal_numbers)),u)*.
% 299.89/300.47  120273[0:SpL:1931.0,9121.1] || member(u,universal_class) subclass(universal_class,symmetric_difference(complement(intersection(v,w)),union(v,w)))* -> member(sum_class(u),complement(symmetric_difference(v,w)))*.
% 299.89/300.47  109334[0:SpR:28.0,9948.0] ||  -> equal(power_class(intersection(union(u,v),complement(inverse(intersection(complement(u),complement(v)))))),complement(image(element_relation,symmetrization_of(intersection(complement(u),complement(v))))))**.
% 299.89/300.47  109341[0:SpR:208.0,9948.0] ||  -> equal(power_class(intersection(power_class(image(element_relation,complement(u))),complement(inverse(image(element_relation,power_class(u)))))),complement(image(element_relation,symmetrization_of(image(element_relation,power_class(u))))))**.
% 299.89/300.47  109277[0:SpR:28.0,9949.0] ||  -> equal(power_class(intersection(union(u,v),complement(singleton(intersection(complement(u),complement(v)))))),complement(image(element_relation,successor(intersection(complement(u),complement(v))))))**.
% 299.89/300.47  109284[0:SpR:208.0,9949.0] ||  -> equal(power_class(intersection(power_class(image(element_relation,complement(u))),complement(singleton(image(element_relation,power_class(u)))))),complement(image(element_relation,successor(image(element_relation,power_class(u))))))**.
% 299.89/300.47  28560[0:SpL:505.0,513.0] || member(u,intersection(complement(v),power_class(intersection(complement(w),complement(x)))))* member(u,union(v,image(element_relation,union(w,x)))) -> .
% 299.89/300.47  28521[0:SpR:505.0,1028.1] || member(u,universal_class) -> member(u,image(element_relation,power_class(intersection(complement(v),complement(w)))))* member(u,power_class(image(element_relation,union(v,w)))).
% 299.89/300.47  28572[0:SpL:505.0,513.0] || member(u,intersection(power_class(intersection(complement(v),complement(w))),complement(x)))* member(u,union(image(element_relation,union(v,w)),x)) -> .
% 299.89/300.47  89289[0:Rew:505.0,89231.1] ||  -> member(not_subclass_element(u,power_class(intersection(complement(v),complement(w)))),image(element_relation,union(v,w)))* subclass(u,power_class(intersection(complement(v),complement(w)))).
% 299.89/300.47  118396[0:SpL:505.0,9146.1] || member(u,universal_class) subclass(universal_class,power_class(intersection(complement(v),complement(w))))* member(power_class(u),image(element_relation,union(v,w)))* -> .
% 299.89/300.47  118680[0:SpL:505.0,9118.1] || member(u,universal_class) subclass(universal_class,power_class(intersection(complement(v),complement(w))))* member(sum_class(u),image(element_relation,union(v,w)))* -> .
% 299.89/300.47  118045[0:SpL:505.0,9069.0] || subclass(universal_class,image(element_relation,power_class(intersection(complement(u),complement(v)))))* member(unordered_pair(w,x),power_class(image(element_relation,union(u,v))))* -> .
% 299.89/300.47  30957[0:SpR:208.0,1032.1] || member(u,universal_class) -> member(u,intersection(complement(v),power_class(image(element_relation,complement(w)))))* member(u,union(v,image(element_relation,power_class(w)))).
% 299.89/300.47  139742[0:SpR:208.0,982.0] ||  -> equal(complement(intersection(power_class(image(element_relation,power_class(image(element_relation,complement(u))))),complement(v))),union(image(element_relation,power_class(image(element_relation,power_class(u)))),v))**.
% 299.89/300.47  140183[0:SpR:208.0,984.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,power_class(image(element_relation,complement(v))))))),union(u,image(element_relation,power_class(image(element_relation,power_class(v))))))**.
% 299.89/300.47  30970[0:SpR:208.0,1032.1] || member(u,universal_class) -> member(u,intersection(power_class(image(element_relation,complement(v))),complement(w)))* member(u,union(image(element_relation,power_class(v)),w)).
% 299.89/300.47  124293[0:Res:51387.0,986.1] || member(not_subclass_element(u,complement(power_class(image(element_relation,complement(v))))),image(element_relation,power_class(v)))* -> subclass(u,complement(power_class(image(element_relation,complement(v))))).
% 299.89/300.47  124280[0:Res:1495.2,986.1] || member(u,universal_class) subclass(rest_relation,power_class(image(element_relation,complement(v)))) member(ordered_pair(u,rest_of(u)),image(element_relation,power_class(v)))* -> .
% 299.89/300.47  139722[0:SpR:208.0,982.0] ||  -> equal(complement(intersection(power_class(image(element_relation,complement(u))),power_class(image(element_relation,complement(v))))),union(image(element_relation,power_class(u)),image(element_relation,power_class(v))))**.
% 299.89/300.47  125155[0:Obv:125118.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),image(element_relation,complement(w))),u)** member(v,power_class(w)) subclass(unordered_pair(u,v),image(element_relation,complement(w))).
% 299.89/300.47  125156[0:Obv:125117.0] ||  -> equal(not_subclass_element(unordered_pair(u,v),image(element_relation,complement(w))),v)** member(u,power_class(w)) subclass(unordered_pair(u,v),image(element_relation,complement(w))).
% 299.89/300.47  137085[0:SpR:10029.0,27.2] || member(u,universal_class) -> member(u,intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))* member(u,successor(image(element_relation,complement(v)))).
% 299.89/300.47  137704[0:SpR:10028.0,27.2] || member(u,universal_class) -> member(u,intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))* member(u,symmetrization_of(image(element_relation,complement(v)))).
% 299.89/300.47  123521[0:Res:978.1,307.0] || member(not_subclass_element(restrict(image(element_relation,complement(u)),v,w),x),power_class(u))* -> subclass(restrict(image(element_relation,complement(u)),v,w),x).
% 299.89/300.47  125122[0:Res:34427.0,127.0] || subclass(power_class(u),v)* well_ordering(w,v)* -> subclass(x,image(element_relation,complement(u)))* member(least(w,power_class(u)),power_class(u))*.
% 299.89/300.47  163646[10:Rew:160202.0,163089.2] || subclass(domain_relation,complement(intersection(u,v))) member(ordered_pair(successor_relation,successor_relation),union(u,v)) -> member(ordered_pair(successor_relation,successor_relation),symmetric_difference(u,v))*.
% 299.89/300.47  160933[10:Rew:160202.0,151107.0] ||  -> member(not_subclass_element(complement(union(image(element_relation,universal_class),u)),v),intersection(power_class(successor_relation),complement(u)))* subclass(complement(union(image(element_relation,universal_class),u)),v).
% 299.89/300.47  160964[10:Rew:160202.0,151099.0] ||  -> member(not_subclass_element(complement(union(u,image(element_relation,universal_class))),v),intersection(complement(u),power_class(successor_relation)))* subclass(complement(union(u,image(element_relation,universal_class))),v).
% 299.89/300.47  161012[10:Rew:160202.0,151032.2] || member(u,universal_class) subclass(union(v,image(element_relation,universal_class)),w)* -> member(u,intersection(complement(v),power_class(successor_relation)))* member(u,w)*.
% 299.89/300.47  161020[10:Rew:160202.0,151033.0] || member(u,image(element_relation,power_class(intersection(complement(v),power_class(successor_relation)))))* member(u,power_class(image(element_relation,union(v,image(element_relation,universal_class))))) -> .
% 299.89/300.47  161026[10:Rew:160202.0,151034.2] || equal(u,union(v,image(element_relation,universal_class)))* member(w,universal_class) -> member(w,intersection(complement(v),power_class(successor_relation)))* member(w,u)*.
% 299.89/300.47  161033[10:Rew:160202.0,151040.2] || member(u,universal_class) subclass(union(image(element_relation,universal_class),v),w)* -> member(u,intersection(power_class(successor_relation),complement(v)))* member(u,w)*.
% 299.89/300.47  161041[10:Rew:160202.0,151041.0] || member(u,image(element_relation,power_class(intersection(power_class(successor_relation),complement(v)))))* member(u,power_class(image(element_relation,union(image(element_relation,universal_class),v)))) -> .
% 299.89/300.47  161047[10:Rew:160202.0,151042.2] || equal(u,union(image(element_relation,universal_class),v))* member(w,universal_class) -> member(w,intersection(power_class(successor_relation),complement(v)))* member(w,u)*.
% 299.89/300.47  163638[10:Rew:160202.0,161190.0] || subclass(image(u,image(v,singleton(w))),successor_relation)* member(ordered_pair(w,x),compose(u,v))* well_ordering(y,inverse(successor_relation))* -> .
% 299.89/300.47  160732[10:Rew:160202.0,146480.2] || member(u,universal_class) subclass(u,symmetric_difference(complement(v),complement(w)))* -> equal(u,successor_relation) member(apply(choice,u),union(v,w)).
% 299.89/300.47  161305[10:Rew:160202.0,146615.2] || member(intersection(u,v),universal_class) subclass(v,w) -> equal(intersection(u,v),successor_relation) member(apply(choice,intersection(u,v)),w)*.
% 299.89/300.47  161304[10:Rew:160202.0,146616.2] || member(intersection(u,v),universal_class) subclass(u,w) -> equal(intersection(u,v),successor_relation) member(apply(choice,intersection(u,v)),w)*.
% 299.89/300.47  161379[10:Rew:160202.0,146845.2] || member(intersection(u,complement(v)),universal_class) member(apply(choice,intersection(u,complement(v))),v)* -> equal(intersection(u,complement(v)),successor_relation).
% 299.89/300.47  161586[10:Rew:160202.0,146745.0] ||  -> equal(cross_product(u,v),successor_relation) equal(symmetric_difference(regular(cross_product(u,v)),cross_product(u,v)),union(regular(cross_product(u,v)),cross_product(u,v)))**.
% 299.89/300.47  161585[10:Rew:160202.0,146796.2] || member(cross_product(u,v),universal_class) subclass(universal_class,w) -> equal(cross_product(u,v),successor_relation) member(apply(choice,cross_product(u,v)),w)*.
% 299.89/300.47  161584[10:Rew:160202.0,146797.2] || member(cross_product(u,v),universal_class) subclass(universal_class,complement(unordered_pair(apply(choice,cross_product(u,v)),w)))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  161583[10:Rew:160202.0,146798.2] || member(cross_product(u,v),universal_class) equal(complement(unordered_pair(apply(choice,cross_product(u,v)),w)),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  161582[10:Rew:160202.0,146799.2] || member(cross_product(u,v),universal_class) subclass(universal_class,complement(unordered_pair(w,apply(choice,cross_product(u,v)))))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  161581[10:Rew:160202.0,146800.2] || member(cross_product(u,v),universal_class) equal(complement(unordered_pair(w,apply(choice,cross_product(u,v)))),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  161580[10:Rew:160202.0,146822.0] ||  -> equal(cross_product(u,v),successor_relation) member(unordered_pair(first(regular(cross_product(u,v))),singleton(second(regular(cross_product(u,v))))),regular(cross_product(u,v)))*.
% 299.89/300.47  161607[10:Rew:160202.0,147211.2] || equal(u,v) subclass(unordered_pair(v,u),symmetric_difference(w,x))* -> equal(unordered_pair(v,u),successor_relation) member(v,union(w,x)).
% 299.89/300.47  161699[10:Rew:160202.0,146847.2] || member(intersection(complement(u),v),universal_class) member(apply(choice,intersection(complement(u),v)),u)* -> equal(intersection(complement(u),v),successor_relation).
% 299.89/300.47  161786[10:Rew:160202.0,146837.1] || member(symmetric_difference(u,singleton(u)),universal_class) -> equal(symmetric_difference(u,singleton(u)),successor_relation) member(apply(choice,symmetric_difference(u,singleton(u))),successor(u))*.
% 299.89/300.47  161789[10:Rew:160202.0,146840.1] || member(symmetric_difference(u,inverse(u)),universal_class) -> equal(symmetric_difference(u,inverse(u)),successor_relation) member(apply(choice,symmetric_difference(u,inverse(u))),symmetrization_of(u))*.
% 299.89/300.47  161818[10:Rew:160202.0,147278.2] || member(complement(union(u,v)),universal_class) -> member(apply(choice,complement(union(u,v))),complement(u))* equal(complement(union(u,v)),successor_relation).
% 299.89/300.47  161817[10:Rew:160202.0,147280.2] || member(complement(union(u,v)),universal_class) -> member(apply(choice,complement(union(u,v))),complement(v))* equal(complement(union(u,v)),successor_relation).
% 299.89/300.47  163020[10:Rew:160202.0,157901.2] || member(complement(compose(element_relation,universal_class)),universal_class) member(apply(choice,complement(compose(element_relation,universal_class))),element_relation)* -> equal(complement(compose(element_relation,universal_class)),successor_relation).
% 299.89/300.47  162061[10:Rew:160202.0,147010.2] || subclass(u,intersection(complement(v),complement(w))) member(regular(intersection(x,u)),union(v,w))* -> equal(intersection(x,u),successor_relation).
% 299.89/300.47  162075[10:Rew:160202.0,147025.2] || subclass(u,intersection(complement(v),complement(w))) member(regular(intersection(u,x)),union(v,w))* -> equal(intersection(u,x),successor_relation).
% 299.89/300.47  162209[10:Rew:160202.0,147596.3] || subclass(u,v)* subclass(v,w)* well_ordering(x,w)* -> equal(intersection(y,u),successor_relation)** member(least(x,v),v)*.
% 299.89/300.47  162218[10:Rew:160202.0,147695.3] || subclass(u,v)* subclass(v,w)* well_ordering(x,w)* -> equal(intersection(u,y),successor_relation)** member(least(x,v),v)*.
% 299.89/300.47  162247[10:Rew:160202.0,147054.1] || well_ordering(u,symmetrization_of(v)) -> equal(symmetric_difference(v,inverse(v)),successor_relation) member(least(u,symmetric_difference(v,inverse(v))),symmetric_difference(v,inverse(v)))*.
% 299.89/300.47  162250[10:Rew:160202.0,147057.1] || well_ordering(u,successor(v)) -> equal(symmetric_difference(v,singleton(v)),successor_relation) member(least(u,symmetric_difference(v,singleton(v))),symmetric_difference(v,singleton(v)))*.
% 299.89/300.47  162262[10:Rew:160202.0,147404.1] || equal(sum_class(intersection(u,v)),intersection(u,v)) -> equal(sum_class(intersection(u,v)),successor_relation) member(regular(sum_class(intersection(u,v))),v)*.
% 299.89/300.47  162261[10:Rew:160202.0,147406.1] || equal(sum_class(intersection(u,v)),intersection(u,v)) -> equal(sum_class(intersection(u,v)),successor_relation) member(regular(sum_class(intersection(u,v))),u)*.
% 299.89/300.47  162276[10:Rew:160202.0,147608.1] || member(regular(intersection(u,intersection(intersection(v,w),x))),symmetric_difference(v,w))* -> equal(intersection(u,intersection(intersection(v,w),x)),successor_relation).
% 299.89/300.47  162280[10:Rew:160202.0,147666.1] || member(regular(intersection(u,intersection(v,intersection(w,x)))),symmetric_difference(w,x))* -> equal(intersection(u,intersection(v,intersection(w,x))),successor_relation).
% 299.89/300.47  162284[10:Rew:160202.0,147706.1] || member(regular(intersection(intersection(intersection(u,v),w),x)),symmetric_difference(u,v))* -> equal(intersection(intersection(intersection(u,v),w),x),successor_relation).
% 299.89/300.47  162288[10:Rew:160202.0,147779.1] || member(regular(intersection(intersection(u,intersection(v,w)),x)),symmetric_difference(v,w))* -> equal(intersection(intersection(u,intersection(v,w)),x),successor_relation).
% 299.89/300.47  162411[10:Rew:160202.0,150826.2] || connected(u,v)* subclass(complement(complement(symmetrization_of(u))),w)* -> equal(cross_product(v,v),successor_relation) member(regular(cross_product(v,v)),w)*.
% 299.89/300.47  162360[10:Rew:160202.0,147077.1] || member(regular(power_class(intersection(complement(u),complement(v)))),image(element_relation,union(u,v)))* -> equal(power_class(intersection(complement(u),complement(v))),successor_relation).
% 299.89/300.47  162400[10:Rew:160202.0,147092.2] || member(regular(complement(intersection(u,v))),v)* member(regular(complement(intersection(u,v))),u)* -> equal(complement(intersection(u,v)),successor_relation).
% 299.89/300.47  162402[10:Rew:160202.0,147094.1] || member(regular(intersection(u,intersection(complement(v),complement(w)))),union(v,w))* -> equal(intersection(u,intersection(complement(v),complement(w))),successor_relation).
% 299.89/300.47  162404[10:Rew:160202.0,147096.1] || member(regular(intersection(intersection(complement(u),complement(v)),w)),union(u,v))* -> equal(intersection(intersection(complement(u),complement(v)),w),successor_relation).
% 299.89/300.47  162405[10:Rew:160202.0,147097.1] || well_ordering(u,union(v,w)) -> equal(segment(u,symmetric_difference(complement(v),complement(w)),least(u,symmetric_difference(complement(v),complement(w)))),successor_relation)**.
% 299.89/300.47  162415[10:Rew:160202.0,147354.1] || member(regular(power_class(image(element_relation,power_class(u)))),image(element_relation,power_class(image(element_relation,complement(u)))))* -> equal(power_class(image(element_relation,power_class(u))),successor_relation).
% 299.89/300.47  162416[10:Rew:160202.0,147395.0] ||  -> equal(symmetric_difference(image(element_relation,complement(u)),v),successor_relation) member(regular(symmetric_difference(image(element_relation,complement(u)),v)),complement(intersection(power_class(u),complement(v))))*.
% 299.89/300.47  162417[10:Rew:160202.0,147397.0] ||  -> equal(symmetric_difference(u,image(element_relation,complement(v))),successor_relation) member(regular(symmetric_difference(u,image(element_relation,complement(v)))),complement(intersection(complement(u),power_class(v))))*.
% 299.89/300.47  162418[10:Rew:160202.0,147472.1] || member(regular(intersection(u,complement(complement(intersection(v,w))))),symmetric_difference(v,w))* -> equal(intersection(u,complement(complement(intersection(v,w)))),successor_relation).
% 299.89/300.47  162419[10:Rew:160202.0,147499.1] || member(regular(intersection(complement(complement(intersection(u,v))),w)),symmetric_difference(u,v))* -> equal(intersection(complement(complement(intersection(u,v))),w),successor_relation).
% 299.89/300.47  162424[10:Rew:160202.0,147616.0] ||  -> equal(intersection(u,intersection(symmetric_difference(v,singleton(v)),w)),successor_relation) member(regular(intersection(u,intersection(symmetric_difference(v,singleton(v)),w))),successor(v))*.
% 299.89/300.47  162425[10:Rew:160202.0,147617.0] ||  -> equal(intersection(u,intersection(symmetric_difference(v,inverse(v)),w)),successor_relation) member(regular(intersection(u,intersection(symmetric_difference(v,inverse(v)),w))),symmetrization_of(v))*.
% 299.89/300.47  162427[10:Rew:160202.0,147674.0] ||  -> equal(intersection(u,intersection(v,symmetric_difference(w,singleton(w)))),successor_relation) member(regular(intersection(u,intersection(v,symmetric_difference(w,singleton(w))))),successor(w))*.
% 299.89/300.47  162428[10:Rew:160202.0,147675.0] ||  -> equal(intersection(u,intersection(v,symmetric_difference(w,inverse(w)))),successor_relation) member(regular(intersection(u,intersection(v,symmetric_difference(w,inverse(w))))),symmetrization_of(w))*.
% 299.89/300.47  162430[10:Rew:160202.0,147714.0] ||  -> equal(intersection(intersection(symmetric_difference(u,singleton(u)),v),w),successor_relation) member(regular(intersection(intersection(symmetric_difference(u,singleton(u)),v),w)),successor(u))*.
% 299.89/300.47  162431[10:Rew:160202.0,147715.0] ||  -> equal(intersection(intersection(symmetric_difference(u,inverse(u)),v),w),successor_relation) member(regular(intersection(intersection(symmetric_difference(u,inverse(u)),v),w)),symmetrization_of(u))*.
% 299.89/300.47  162433[10:Rew:160202.0,147787.0] ||  -> equal(intersection(intersection(u,symmetric_difference(v,singleton(v))),w),successor_relation) member(regular(intersection(intersection(u,symmetric_difference(v,singleton(v))),w)),successor(v))*.
% 299.89/300.47  162434[10:Rew:160202.0,147788.0] ||  -> equal(intersection(intersection(u,symmetric_difference(v,inverse(v))),w),successor_relation) member(regular(intersection(intersection(u,symmetric_difference(v,inverse(v))),w)),symmetrization_of(v))*.
% 299.89/300.47  162436[10:Rew:160202.0,147824.1] || subclass(successor(u),v) -> equal(symmetric_difference(complement(u),complement(singleton(u))),successor_relation) member(regular(symmetric_difference(complement(u),complement(singleton(u)))),v)*.
% 299.89/300.47  162437[10:Rew:160202.0,147825.1] || subclass(symmetrization_of(u),v) -> equal(symmetric_difference(complement(u),complement(inverse(u))),successor_relation) member(regular(symmetric_difference(complement(u),complement(inverse(u)))),v)*.
% 299.89/300.47  183912[11:Res:183764.1,3874.1] || subclass(universal_class,complement(intersection(u,v))) member(regular(symmetrization_of(successor_relation)),union(u,v)) -> member(regular(symmetrization_of(successor_relation)),symmetric_difference(u,v))*.
% 299.89/300.47  184791[14:SpL:10417.0,184008.2] || member(u,universal_class)* member(restrict(cross_product(v,universal_class),w,x),universal_class)* equal(sum_class(image(cross_product(w,x),v)),u)* -> .
% 299.89/300.47  162421[10:Rew:160202.0,147538.1] || member(restrict(u,v,w),ordinal_numbers) -> equal(sum_class(restrict(u,v,w)),successor_relation) member(regular(sum_class(restrict(u,v,w))),u)*.
% 299.89/300.47  108808[2:Res:31076.2,10254.0] inductive(symmetric_difference(u,singleton(u))) || well_ordering(v,symmetric_difference(u,singleton(u))) -> member(least(v,symmetric_difference(u,singleton(u))),successor(u))*.
% 299.89/300.47  108807[2:Res:31076.2,10191.0] inductive(symmetric_difference(u,inverse(u))) || well_ordering(v,symmetric_difference(u,inverse(u))) -> member(least(v,symmetric_difference(u,inverse(u))),symmetrization_of(u))*.
% 299.89/300.47  157906[6:Res:31076.2,148657.1] inductive(complement(compose(element_relation,universal_class))) || well_ordering(u,complement(compose(element_relation,universal_class))) member(least(u,complement(compose(element_relation,universal_class))),element_relation)* -> .
% 299.89/300.47  40326[0:SoR:5540.0,73.1] one_to_one(sum_class(cross_product(universal_class,universal_class))) || well_ordering(element_relation,cross_product(universal_class,universal_class))* -> equal(cross_product(universal_class,universal_class),ordinal_numbers) member(cross_product(universal_class,universal_class),ordinal_numbers).
% 299.89/300.47  162251[10:Rew:160202.0,147056.1] || well_ordering(u,symmetric_difference(v,singleton(v))) -> equal(symmetric_difference(v,singleton(v)),successor_relation) member(least(u,symmetric_difference(v,singleton(v))),successor(v))*.
% 299.89/300.47  162248[10:Rew:160202.0,147053.1] || well_ordering(u,symmetric_difference(v,inverse(v))) -> equal(symmetric_difference(v,inverse(v)),successor_relation) member(least(u,symmetric_difference(v,inverse(v))),symmetrization_of(v))*.
% 299.89/300.47  111818[2:Res:31069.2,9322.0] inductive(symmetric_difference(complement(u),complement(v))) || well_ordering(w,universal_class) -> member(least(w,symmetric_difference(complement(u),complement(v))),union(u,v))*.
% 299.89/300.47  162408[10:Rew:160202.0,147125.1] || well_ordering(u,universal_class) -> equal(symmetric_difference(complement(v),complement(w)),successor_relation) member(least(u,symmetric_difference(complement(v),complement(w))),union(v,w))*.
% 299.89/300.47  145041[2:MRR:56582.1,145036.0] || well_ordering(u,universal_class) -> equal(least(u,ordered_pair(v,w)),unordered_pair(v,singleton(w)))** equal(least(u,ordered_pair(v,w)),singleton(v)).
% 299.89/300.47  110150[3:MRR:110149.3,2717.0] || equal(cantor(restrict(u,v,w)),universal_class)** section(u,w,v) well_ordering(x,w)* -> member(least(x,universal_class),universal_class)*.
% 299.89/300.47  39578[0:Res:5768.2,2151.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,singleton(w))* -> equal(ordered_pair(u,ordered_pair(v,compose(u,v))),w)*.
% 299.89/300.47  39600[0:Res:5768.2,95.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,compose_class(w))* -> equal(compose(w,u),ordered_pair(v,compose(u,v)))*.
% 299.89/300.47  190490[10:Obv:190467.0] ||  -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),successor_relation) equal(symmetric_difference(unordered_pair(u,v),u),union(unordered_pair(u,v),u))**.
% 299.89/300.47  190491[10:Obv:190459.0] ||  -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),successor_relation) equal(symmetric_difference(unordered_pair(u,v),v),union(unordered_pair(u,v),v))**.
% 299.89/300.47  191226[10:Res:161311.2,183622.0] || member(intersection(successor(successor_relation),u),universal_class) -> equal(intersection(successor(successor_relation),u),successor_relation) member(apply(choice,intersection(successor(successor_relation),u)),singleton(successor_relation))*.
% 299.89/300.47  191221[10:Res:161311.2,183723.0] || member(intersection(symmetrization_of(successor_relation),u),universal_class) -> equal(intersection(symmetrization_of(successor_relation),u),successor_relation) member(apply(choice,intersection(symmetrization_of(successor_relation),u)),inverse(successor_relation))*.
% 299.89/300.47  191206[10:Res:161311.2,141576.1] || member(intersection(complement(kind_1_ordinals),u),universal_class) member(apply(choice,intersection(complement(kind_1_ordinals),u)),ordinal_numbers)* -> equal(intersection(complement(kind_1_ordinals),u),successor_relation).
% 299.89/300.47  191353[10:Res:161312.2,183622.0] || member(intersection(u,successor(successor_relation)),universal_class) -> equal(intersection(u,successor(successor_relation)),successor_relation) member(apply(choice,intersection(u,successor(successor_relation))),singleton(successor_relation))*.
% 299.89/300.47  191348[10:Res:161312.2,183723.0] || member(intersection(u,symmetrization_of(successor_relation)),universal_class) -> equal(intersection(u,symmetrization_of(successor_relation)),successor_relation) member(apply(choice,intersection(u,symmetrization_of(successor_relation))),inverse(successor_relation))*.
% 299.89/300.47  191333[10:Res:161312.2,141576.1] || member(intersection(u,complement(kind_1_ordinals)),universal_class) member(apply(choice,intersection(u,complement(kind_1_ordinals))),ordinal_numbers)* -> equal(intersection(u,complement(kind_1_ordinals)),successor_relation).
% 299.89/300.47  192616[11:Res:183764.1,162356.0] || subclass(universal_class,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(symmetrization_of(successor_relation)),least(omega,u))),successor_relation)**.
% 299.89/300.47  192584[17:Res:188729.1,162356.0] || well_ordering(u,universal_class) subclass(universal_class,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,omega),least(omega,universal_class))),successor_relation)**.
% 299.89/300.47  192583[17:Res:188737.1,162356.0] || well_ordering(u,omega) subclass(universal_class,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,omega),least(omega,universal_class))),successor_relation)**.
% 299.89/300.47  192582[10:Res:110382.1,162356.0] || well_ordering(u,universal_class) subclass(universal_class,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,rest_relation),least(omega,universal_class))),successor_relation)**.
% 299.89/300.47  192581[10:Res:110388.1,162356.0] || well_ordering(u,rest_relation) subclass(universal_class,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,rest_relation),least(omega,universal_class))),successor_relation)**.
% 299.89/300.47  192580[10:Res:110623.1,162356.0] || well_ordering(u,universal_class) subclass(universal_class,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,universal_class),least(omega,universal_class))),successor_relation)**.
% 299.89/300.47  192579[10:Res:184599.1,162356.0] || well_ordering(u,kind_1_ordinals) subclass(universal_class,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,ordinal_numbers),least(omega,universal_class))),successor_relation)**.
% 299.89/300.47  192562[10:Res:184565.1,162356.0] || well_ordering(u,kind_1_ordinals) subclass(ordinal_numbers,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,ordinal_numbers),least(omega,ordinal_numbers))),successor_relation)**.
% 299.89/300.47  192559[10:Res:160361.1,162356.0] || subclass(singleton(u),v)* well_ordering(omega,v) -> equal(singleton(u),successor_relation) equal(integer_of(ordered_pair(u,least(omega,singleton(u)))),successor_relation)**.
% 299.89/300.47  192558[10:Res:305.1,162356.0] || member(u,universal_class) subclass(singleton(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(u,least(omega,singleton(u)))),successor_relation)**.
% 299.89/300.47  192557[10:Res:181084.0,162356.0] || subclass(ordered_pair(u,universal_class),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(unordered_pair(u,successor_relation),least(omega,ordered_pair(u,universal_class)))),successor_relation)**.
% 299.89/300.47  192554[15:Res:189373.1,162356.0] || member(u,universal_class) subclass(domain_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(u,successor_relation),least(omega,domain_relation))),successor_relation)**.
% 299.89/300.47  192551[10:Res:160251.1,162356.0] || subclass(domain_relation,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(successor_relation,successor_relation),least(omega,u))),successor_relation)**.
% 299.89/300.47  192550[10:Res:160252.1,162356.0] || equal(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(successor_relation,successor_relation),least(omega,rest_relation))),successor_relation)**.
% 299.89/300.47  192546[10:Res:1499.1,162356.0] || subclass(universal_class,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(w,x),least(omega,u))),successor_relation)**.
% 299.89/300.47  192534[17:Res:188716.1,162356.0] || well_ordering(u,universal_class) subclass(omega,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,omega),least(omega,omega))),successor_relation)**.
% 299.89/300.47  192533[17:Res:188721.1,162356.0] || well_ordering(u,omega) subclass(omega,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,omega),least(omega,omega))),successor_relation)**.
% 299.89/300.47  192532[10:Res:110376.1,162356.0] || well_ordering(u,rest_relation) subclass(rest_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,rest_relation),least(omega,rest_relation))),successor_relation)**.
% 299.89/300.47  192531[10:Res:110370.1,162356.0] || well_ordering(u,universal_class) subclass(rest_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(least(u,rest_relation),least(omega,rest_relation))),successor_relation)**.
% 299.89/300.47  192507[10:Res:1476.1,162356.0] || subclass(universal_class,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(unordered_pair(w,x),least(omega,u))),successor_relation)**.
% 299.89/300.47  193390[10:Res:192947.1,162356.0] || equal(complement(u),successor_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(w),least(omega,u))),successor_relation)**.
% 299.89/300.47  195369[0:SpR:194805.1,1931.0] || subclass(u,v) -> equal(intersection(complement(symmetric_difference(v,u)),union(complement(u),union(v,u))),symmetric_difference(complement(u),union(v,u)))**.
% 299.89/300.47  196043[0:SpL:195152.0,3874.1] || member(u,union(v,intersection(v,w))) member(u,complement(intersection(v,w))) -> member(u,symmetric_difference(v,intersection(v,w)))*.
% 299.89/300.47  195982[0:SpR:1931.0,195152.0] ||  -> equal(intersection(complement(symmetric_difference(u,v)),symmetric_difference(complement(intersection(u,v)),union(u,v))),symmetric_difference(complement(intersection(u,v)),union(u,v)))**.
% 299.89/300.47  196188[0:SpL:195339.0,3874.1] || member(u,union(v,intersection(w,v))) member(u,complement(intersection(w,v))) -> member(u,symmetric_difference(v,intersection(w,v)))*.
% 299.89/300.47  196544[10:SpR:161137.0,1948.0] ||  -> equal(intersection(union(u,image(element_relation,symmetrization_of(successor_relation))),union(complement(u),power_class(complement(inverse(successor_relation))))),symmetric_difference(complement(u),power_class(complement(inverse(successor_relation)))))**.
% 299.89/300.47  196509[10:SpR:161137.0,1948.0] ||  -> equal(intersection(union(image(element_relation,symmetrization_of(successor_relation)),u),union(power_class(complement(inverse(successor_relation))),complement(u))),symmetric_difference(power_class(complement(inverse(successor_relation))),complement(u)))**.
% 299.89/300.47  196750[10:SpR:162889.0,1948.0] ||  -> equal(intersection(union(u,image(element_relation,successor(successor_relation))),union(complement(u),power_class(complement(singleton(successor_relation))))),symmetric_difference(complement(u),power_class(complement(singleton(successor_relation)))))**.
% 299.89/300.47  196715[10:SpR:162889.0,1948.0] ||  -> equal(intersection(union(image(element_relation,successor(successor_relation)),u),union(power_class(complement(singleton(successor_relation))),complement(u))),symmetric_difference(power_class(complement(singleton(successor_relation))),complement(u)))**.
% 299.89/300.47  197428[10:SpL:161565.2,185803.0] || member(cross_product(u,v),universal_class) equal(complement(complement(singleton(apply(choice,cross_product(u,v))))),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  201925[10:Res:161492.2,3874.1] || equal(complement(intersection(u,v)),omega) member(w,union(u,v)) -> equal(integer_of(w),successor_relation) member(w,symmetric_difference(u,v))*.
% 299.89/300.47  204863[6:Rew:119971.0,204056.2] inductive(cantor(inverse(cross_product(u,universal_class)))) || well_ordering(v,image(universal_class,u)) -> member(least(v,image(universal_class,u)),image(universal_class,u))*.
% 299.89/300.47  206583[10:Res:206541.0,127.0] || subclass(complement(complement(successor(successor_relation))),u)* well_ordering(v,u)* -> member(least(v,complement(complement(successor(successor_relation)))),complement(complement(successor(successor_relation))))*.
% 299.89/300.47  206579[10:Res:206541.0,162356.0] || subclass(complement(complement(successor(successor_relation))),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(successor_relation,least(omega,complement(complement(successor(successor_relation)))))),successor_relation)**.
% 299.89/300.47  206695[10:Res:206681.0,127.0] || subclass(union(singleton(successor_relation),u),v)* well_ordering(w,v)* -> member(least(w,union(singleton(successor_relation),u)),union(singleton(successor_relation),u))*.
% 299.89/300.47  206691[10:Res:206681.0,162356.0] || subclass(union(singleton(successor_relation),u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(successor_relation,least(omega,union(singleton(successor_relation),u)))),successor_relation)**.
% 299.89/300.47  207201[10:Res:207189.0,127.0] || subclass(union(u,singleton(successor_relation)),v)* well_ordering(w,v)* -> member(least(w,union(u,singleton(successor_relation))),union(u,singleton(successor_relation)))*.
% 299.89/300.47  207197[10:Res:207189.0,162356.0] || subclass(union(u,singleton(successor_relation)),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(successor_relation,least(omega,union(u,singleton(successor_relation))))),successor_relation)**.
% 299.89/300.47  210062[15:Res:209831.1,162356.0] || equal(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(omega,successor_relation),least(omega,rest_relation))),successor_relation)**.
% 299.89/300.47  211037[15:Res:211024.1,162356.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(successor_relation,successor_relation),least(omega,rest_relation))),successor_relation)**.
% 299.89/300.47  211131[10:Res:161445.2,148657.1] || well_ordering(u,complement(compose(element_relation,universal_class))) member(least(u,complement(compose(element_relation,universal_class))),element_relation)* -> equal(complement(compose(element_relation,universal_class)),successor_relation).
% 299.89/300.47  211674[10:Res:181213.1,3874.1] || equal(complement(intersection(u,v)),singleton(singleton(successor_relation))) member(singleton(successor_relation),union(u,v)) -> member(singleton(successor_relation),symmetric_difference(u,v))*.
% 299.89/300.47  212056[2:Res:184090.1,127.0] || equal(symmetric_difference(universal_class,u),universal_class) subclass(complement(u),v)* well_ordering(w,v)* -> member(least(w,complement(u)),complement(u))*.
% 299.89/300.47  212105[10:MRR:212084.3,186121.2] || member(regular(regular(intersection(u,v))),v)* member(regular(regular(intersection(u,v))),u)* -> equal(regular(intersection(u,v)),successor_relation).
% 299.89/300.47  212110[10:MRR:212089.0,160295.1] ||  -> member(regular(regular(image(element_relation,complement(u)))),power_class(u))* equal(regular(image(element_relation,complement(u))),successor_relation) equal(image(element_relation,complement(u)),successor_relation).
% 299.89/300.47  213232[15:Res:189485.1,2142.0] || subclass(domain_relation,ordered_pair(u,v))* -> equal(unordered_pair(u,singleton(v)),singleton(singleton(singleton(successor_relation)))) equal(singleton(singleton(singleton(successor_relation))),singleton(u)).
% 299.89/300.47  213213[15:Res:189485.1,19.0] || subclass(domain_relation,cross_product(u,v))* -> equal(ordered_pair(first(singleton(singleton(singleton(successor_relation)))),second(singleton(singleton(singleton(successor_relation))))),singleton(singleton(singleton(successor_relation))))**.
% 299.89/300.47  214147[20:Res:193270.1,127.0] || equal(symmetric_difference(universal_class,u),omega) subclass(complement(u),v)* well_ordering(w,v)* -> member(least(w,complement(u)),complement(u))*.
% 299.89/300.47  214280[10:Res:214277.1,162356.0] || equal(complement(u),successor_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(power_class(successor_relation),least(omega,u))),successor_relation)**.
% 299.89/300.47  214430[21:Res:214356.0,162356.0] || subclass(inverse(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(complement(complement(symmetrization_of(successor_relation)))),least(omega,inverse(successor_relation)))),successor_relation)**.
% 299.89/300.47  215876[10:Res:197082.1,19.0] || subclass(universal_class,cross_product(u,v))* -> equal(ordered_pair(first(regular(complement(successor(successor_relation)))),second(regular(complement(successor(successor_relation))))),regular(complement(successor(successor_relation))))**.
% 299.89/300.47  216107[6:Res:199830.1,3874.1] || equal(complement(intersection(u,v)),cross_product(universal_class,universal_class)) member(regular(rest_relation),union(u,v)) -> member(regular(rest_relation),symmetric_difference(u,v))*.
% 299.89/300.47  216466[10:Res:216465.1,162356.0] || equal(complement(u),successor_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(rest_relation),least(omega,u))),successor_relation)**.
% 299.89/300.47  216715[6:Res:201220.1,3874.1] || equal(complement(intersection(u,v)),cross_product(universal_class,universal_class)) member(regular(domain_relation),union(u,v)) -> member(regular(domain_relation),symmetric_difference(u,v))*.
% 299.89/300.47  216889[10:Rew:161779.1,216888.2] || member(apply(choice,u),unordered_pair(v,u))* -> equal(regular(unordered_pair(v,u)),v) equal(u,successor_relation) equal(unordered_pair(v,u),successor_relation).
% 299.89/300.47  216891[10:Rew:161779.2,216890.2] || member(apply(choice,u),unordered_pair(u,v))* -> equal(regular(unordered_pair(u,v)),v) equal(u,successor_relation) equal(unordered_pair(u,v),successor_relation).
% 299.89/300.47  216894[10:Res:216847.1,162356.0] || equal(complement(u),successor_relation) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(domain_relation),least(omega,u))),successor_relation)**.
% 299.89/300.47  217546[10:Res:1951.1,160697.1] || member(unordered_pair(u,v),symmetric_difference(w,x))* subclass(universal_class,regular(complement(intersection(w,x))))* -> equal(complement(intersection(w,x)),successor_relation).
% 299.89/300.47  217596[10:MRR:217549.3,188688.2] || member(unordered_pair(u,v),cross_product(w,x))* member(unordered_pair(u,v),y)* subclass(universal_class,regular(restrict(y,w,x)))* -> .
% 299.89/300.47  217638[10:SpL:162889.0,1089.0] || member(not_subclass_element(power_class(image(element_relation,successor(successor_relation))),u),image(element_relation,power_class(complement(singleton(successor_relation)))))* -> subclass(power_class(image(element_relation,successor(successor_relation))),u).
% 299.89/300.47  217637[10:SpL:161137.0,1089.0] || member(not_subclass_element(power_class(image(element_relation,symmetrization_of(successor_relation))),u),image(element_relation,power_class(complement(inverse(successor_relation)))))* -> subclass(power_class(image(element_relation,symmetrization_of(successor_relation))),u).
% 299.89/300.47  218321[10:Rew:161779.1,218320.2] || member(not_subclass_element(u,v),unordered_pair(w,u))* -> equal(regular(unordered_pair(w,u)),w) subclass(u,v) equal(unordered_pair(w,u),successor_relation).
% 299.89/300.47  218323[10:Rew:161779.2,218322.2] || member(not_subclass_element(u,v),unordered_pair(u,w))* -> equal(regular(unordered_pair(u,w)),w) subclass(u,v) equal(unordered_pair(u,w),successor_relation).
% 299.89/300.47  218425[10:Res:218370.0,5832.1] inductive(regular(complement(singleton(successor_relation)))) || well_ordering(u,successor(successor_relation)) -> member(least(u,regular(complement(singleton(successor_relation)))),regular(complement(singleton(successor_relation))))*.
% 299.89/300.47  218422[10:Res:218370.0,160292.0] || well_ordering(u,successor(successor_relation)) -> equal(regular(complement(singleton(successor_relation))),successor_relation) member(least(u,regular(complement(singleton(successor_relation)))),regular(complement(singleton(successor_relation))))*.
% 299.89/300.47  218433[13:Res:218371.0,5832.1] inductive(regular(image(element_relation,successor_relation))) || well_ordering(u,power_class(universal_class)) -> member(least(u,regular(image(element_relation,successor_relation))),regular(image(element_relation,successor_relation)))*.
% 299.89/300.47  218430[13:Res:218371.0,160292.0] || well_ordering(u,power_class(universal_class)) -> equal(regular(image(element_relation,successor_relation)),successor_relation) member(least(u,regular(image(element_relation,successor_relation))),regular(image(element_relation,successor_relation)))*.
% 299.89/300.47  218444[10:Res:218372.0,5832.1] inductive(regular(image(element_relation,universal_class))) || well_ordering(u,power_class(successor_relation)) -> member(least(u,regular(image(element_relation,universal_class))),regular(image(element_relation,universal_class)))*.
% 299.89/300.47  218441[10:Res:218372.0,160292.0] || well_ordering(u,power_class(successor_relation)) -> equal(regular(image(element_relation,universal_class)),successor_relation) member(least(u,regular(image(element_relation,universal_class))),regular(image(element_relation,universal_class)))*.
% 299.89/300.47  218531[3:Res:218494.0,5832.1] inductive(complement(complement(complement(kind_1_ordinals)))) || well_ordering(u,complement(ordinal_numbers)) -> member(least(u,complement(complement(complement(kind_1_ordinals)))),complement(complement(complement(kind_1_ordinals))))*.
% 299.89/300.47  218528[10:Res:218494.0,160292.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(complement(complement(complement(kind_1_ordinals))),successor_relation) member(least(u,complement(complement(complement(kind_1_ordinals)))),complement(complement(complement(kind_1_ordinals))))*.
% 299.89/300.47  218621[3:Res:218475.0,5832.1] inductive(intersection(complement(kind_1_ordinals),u)) || well_ordering(v,complement(ordinal_numbers)) -> member(least(v,intersection(complement(kind_1_ordinals),u)),intersection(complement(kind_1_ordinals),u))*.
% 299.89/300.47  218618[10:Res:218475.0,160292.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(intersection(complement(kind_1_ordinals),v),successor_relation) member(least(u,intersection(complement(kind_1_ordinals),v)),intersection(complement(kind_1_ordinals),v))*.
% 299.89/300.47  218655[3:Res:218485.0,5832.1] inductive(intersection(u,complement(kind_1_ordinals))) || well_ordering(v,complement(ordinal_numbers)) -> member(least(v,intersection(u,complement(kind_1_ordinals))),intersection(u,complement(kind_1_ordinals)))*.
% 299.89/300.47  218652[10:Res:218485.0,160292.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(intersection(v,complement(kind_1_ordinals)),successor_relation) member(least(u,intersection(v,complement(kind_1_ordinals))),intersection(v,complement(kind_1_ordinals)))*.
% 299.89/300.47  219155[3:Res:218473.1,5646.1] || equal(image(u,image(v,singleton(w))),complement(kind_1_ordinals)) member(ordered_pair(w,x),compose(u,v))* -> member(x,complement(ordinal_numbers)).
% 299.89/300.47  219196[10:Res:161312.2,218628.0] || member(intersection(u,complement(kind_1_ordinals)),universal_class) -> equal(intersection(u,complement(kind_1_ordinals)),successor_relation) member(apply(choice,intersection(u,complement(kind_1_ordinals))),complement(ordinal_numbers))*.
% 299.89/300.47  219183[10:Res:161311.2,218628.0] || member(intersection(complement(kind_1_ordinals),u),universal_class) -> equal(intersection(complement(kind_1_ordinals),u),successor_relation) member(apply(choice,intersection(complement(kind_1_ordinals),u)),complement(ordinal_numbers))*.
% 299.89/300.47  204810[10:Rew:203192.0,203790.1,203192.0,203790.0] || member(complement(cantor(u)),universal_class) -> equal(apply(u,apply(choice,complement(cantor(u)))),sum_class(range_of(successor_relation)))** equal(complement(cantor(u)),successor_relation).
% 299.89/300.47  163691[10:Rew:160305.0,162153.4,160305.0,162153.3,160305.0,162153.2] inductive(u) || well_ordering(v,u)* subclass(range_of(successor_relation),w) -> equal(range_of(successor_relation),successor_relation) member(least(v,range_of(successor_relation)),w)*.
% 299.89/300.47  203583[10:Rew:203192.0,160625.2] || member(u,universal_class) member(ordered_pair(u,v),compose(w,x))* -> member(u,cantor(x)) member(v,image(w,range_of(successor_relation))).
% 299.89/300.47  193788[10:SpL:193730.0,5646.1] || member(ordered_pair(u,v),compose(w,complement(cross_product(singleton(u),universal_class))))* subclass(image(w,range_of(successor_relation)),x)* -> member(v,x)*.
% 299.89/300.47  193793[10:SpL:193730.0,5646.1] || member(ordered_pair(u,v),compose(complement(cross_product(image(w,singleton(u)),universal_class)),w))* subclass(range_of(successor_relation),x)* -> member(v,x)*.
% 299.89/300.47  164292[10:Res:163149.1,2078.1] inductive(not_well_ordering(u,range_of(successor_relation))) || connected(u,range_of(successor_relation)) -> well_ordering(u,range_of(successor_relation)) equal(not_well_ordering(u,range_of(successor_relation)),range_of(successor_relation))**.
% 299.89/300.47  163636[10:Rew:160202.0,160663.2] || member(u,image(v,range_of(successor_relation))) member(ordered_pair(w,u),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,u),compose(v,successor_relation))*.
% 299.89/300.47  163694[10:Rew:160305.0,162823.1,160202.0,162823.0,160305.0,162823.0] || member(not_subclass_element(kind_1_ordinals,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),complement(intersection(singleton(successor_relation),range_of(successor_relation))))* -> subclass(kind_1_ordinals,symmetric_difference(singleton(successor_relation),range_of(successor_relation))).
% 299.89/300.47  163680[10:Rew:160202.0,162844.1,160305.0,162844.1,160305.0,162844.0] ||  -> subclass(restrict(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u,v),w) member(not_subclass_element(restrict(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u,v),w),kind_1_ordinals)*.
% 299.89/300.47  221314[10:SpL:161565.2,220898.0] || member(cross_product(u,v),universal_class) equal(complement(regular(singleton(apply(choice,cross_product(u,v))))),successor_relation)** -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  221491[10:Res:218373.0,2609.1] function(complement(singleton(cross_product(universal_class,universal_class)))) ||  -> equal(singleton(cross_product(universal_class,universal_class)),successor_relation) equal(complement(singleton(cross_product(universal_class,universal_class))),cross_product(universal_class,universal_class))**.
% 299.89/300.47  221573[10:Res:221516.0,127.0] || subclass(complement(singleton(singleton(successor_relation))),u)* well_ordering(v,u)* -> member(least(v,complement(singleton(singleton(successor_relation)))),complement(singleton(singleton(successor_relation))))*.
% 299.89/300.47  221569[10:Res:221516.0,162356.0] || subclass(complement(singleton(singleton(successor_relation))),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(successor_relation,least(omega,complement(singleton(singleton(successor_relation)))))),successor_relation)**.
% 299.89/300.47  221670[10:Res:978.1,185698.1] inductive(not_subclass_element(restrict(ordinal_numbers,u,v),w)) ||  -> subclass(restrict(ordinal_numbers,u,v),w)* equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  221632[10:Res:1495.2,185698.1] inductive(ordered_pair(u,rest_of(u))) || member(u,universal_class)* subclass(rest_relation,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  221736[6:Res:221565.0,5832.1] inductive(complement(compose(element_relation,universal_class))) || well_ordering(u,complement(element_relation)) -> member(least(u,complement(compose(element_relation,universal_class))),complement(compose(element_relation,universal_class)))*.
% 299.89/300.47  221733[10:Res:221565.0,160292.0] || well_ordering(u,complement(element_relation)) -> equal(complement(compose(element_relation,universal_class)),successor_relation) member(least(u,complement(compose(element_relation,universal_class))),complement(compose(element_relation,universal_class)))*.
% 299.89/300.47  221830[10:Rew:162889.0,221812.1] || member(regular(image(element_relation,power_class(complement(singleton(successor_relation))))),power_class(image(element_relation,successor(successor_relation))))* -> equal(image(element_relation,power_class(complement(singleton(successor_relation)))),successor_relation).
% 299.89/300.47  221831[10:Rew:161137.0,221811.1] || member(regular(image(element_relation,power_class(complement(inverse(successor_relation))))),power_class(image(element_relation,symmetrization_of(successor_relation))))* -> equal(image(element_relation,power_class(complement(inverse(successor_relation)))),successor_relation).
% 299.89/300.47  222316[15:MRR:222265.0,222265.3,160214.0,34067.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(v,u),successor_relation),w)* subclass(domain_relation,complement(flip(w))) -> .
% 299.89/300.47  222317[15:MRR:222264.0,222264.3,160214.0,34067.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(v,successor_relation),u),w)* subclass(domain_relation,complement(rotate(w))) -> .
% 299.89/300.47  223132[24:Res:222474.0,5832.1] inductive(symmetric_difference(complement(kind_1_ordinals),universal_class)) || well_ordering(u,successor(kind_1_ordinals)) -> member(least(u,symmetric_difference(complement(kind_1_ordinals),universal_class)),symmetric_difference(complement(kind_1_ordinals),universal_class))*.
% 299.89/300.47  223129[24:Res:222474.0,160292.0] || well_ordering(u,successor(kind_1_ordinals)) -> equal(symmetric_difference(complement(kind_1_ordinals),universal_class),successor_relation) member(least(u,symmetric_difference(complement(kind_1_ordinals),universal_class)),symmetric_difference(complement(kind_1_ordinals),universal_class))*.
% 299.89/300.47  224033[10:Rew:162889.0,223991.1] ||  -> member(not_subclass_element(u,image(element_relation,power_class(complement(singleton(successor_relation))))),power_class(image(element_relation,successor(successor_relation))))* subclass(u,image(element_relation,power_class(complement(singleton(successor_relation))))).
% 299.89/300.47  224034[10:Rew:161137.0,223990.1] ||  -> member(not_subclass_element(u,image(element_relation,power_class(complement(inverse(successor_relation))))),power_class(image(element_relation,symmetrization_of(successor_relation))))* subclass(u,image(element_relation,power_class(complement(inverse(successor_relation))))).
% 299.89/300.47  224349[25:Rew:224236.1,214498.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,regular(complement(complement(symmetrization_of(successor_relation)))))*.
% 299.89/300.47  224358[25:Rew:224236.1,204827.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> equal(integer_of(w),successor_relation) compatible(u,v,w)*.
% 299.89/300.47  224359[25:Rew:224236.1,204826.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> equal(singleton(w),successor_relation) compatible(u,v,w)*.
% 299.89/300.47  224360[25:Rew:224236.1,204825.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> equal(w,successor_relation) compatible(u,v,regular(w))*.
% 299.89/300.47  224691[25:SpL:224236.1,224320.1] function(u) function(v) || subclass(range_of(v),cantor(universal_class))* equal(cantor(cantor(w)),universal_class) -> compatible(v,w,u)*.
% 299.89/300.47  225080[25:SpL:224739.1,5646.1] function(u) || member(ordered_pair(u,v),compose(w,x))* subclass(image(w,image(x,successor_relation)),y)* -> member(v,y)*.
% 299.89/300.47  225973[10:Rew:162889.0,225947.2] || well_ordering(u,universal_class) member(least(u,power_class(complement(singleton(successor_relation)))),image(element_relation,successor(successor_relation)))* -> equal(power_class(complement(singleton(successor_relation))),successor_relation).
% 299.89/300.47  225974[10:Rew:161137.0,225946.2] || well_ordering(u,universal_class) member(least(u,power_class(complement(inverse(successor_relation)))),image(element_relation,symmetrization_of(successor_relation)))* -> equal(power_class(complement(inverse(successor_relation))),successor_relation).
% 299.89/300.47  226361[25:Rew:226350.1,42809.1] one_to_one(restrict(u,v,singleton(w))) || subclass(universal_class,x) -> maps(restrict(u,v,singleton(w)),segment(u,v,w),x)*.
% 299.89/300.47  226367[25:Rew:226352.2,30725.3] single_valued_class(inverse(u)) || subclass(range_of(inverse(u)),v) equal(cross_product(universal_class,universal_class),inverse(u)) -> maps(inverse(u),universal_class,v)*.
% 299.89/300.47  226579[10:Res:161880.1,148657.1] || member(regular(intersection(intersection(complement(compose(element_relation,universal_class)),u),v)),element_relation)* -> equal(intersection(intersection(complement(compose(element_relation,universal_class)),u),v),successor_relation).
% 299.89/300.47  227170[10:Res:161881.1,148657.1] || member(regular(intersection(intersection(u,complement(compose(element_relation,universal_class))),v)),element_relation)* -> equal(intersection(intersection(u,complement(compose(element_relation,universal_class))),v),successor_relation).
% 299.89/300.47  227466[10:Res:161874.1,148657.1] || member(regular(intersection(u,intersection(complement(compose(element_relation,universal_class)),v))),element_relation)* -> equal(intersection(u,intersection(complement(compose(element_relation,universal_class)),v)),successor_relation).
% 299.89/300.47  228072[10:Res:161875.1,148657.1] || member(regular(intersection(u,intersection(v,complement(compose(element_relation,universal_class))))),element_relation)* -> equal(intersection(u,intersection(v,complement(compose(element_relation,universal_class)))),successor_relation).
% 299.89/300.47  228257[10:Res:222126.0,127.0] || subclass(complement(singleton(regular(rest_relation))),u)* well_ordering(v,u)* -> member(least(v,complement(singleton(regular(rest_relation)))),complement(singleton(regular(rest_relation))))*.
% 299.89/300.47  228461[10:Res:222127.0,127.0] || subclass(complement(singleton(regular(domain_relation))),u)* well_ordering(v,u)* -> member(least(v,complement(singleton(regular(domain_relation)))),complement(singleton(regular(domain_relation))))*.
% 299.89/300.47  228478[12:Res:222128.0,127.0] || subclass(complement(singleton(regular(element_relation))),u)* well_ordering(v,u)* -> member(least(v,complement(singleton(regular(element_relation)))),complement(singleton(regular(element_relation))))*.
% 299.89/300.47  228880[24:Rew:223107.0,228799.1,223107.0,228799.0] || member(symmetric_difference(complement(kind_1_ordinals),universal_class),universal_class) -> equal(symmetric_difference(complement(kind_1_ordinals),universal_class),successor_relation) member(apply(choice,symmetric_difference(complement(kind_1_ordinals),universal_class)),successor(kind_1_ordinals))*.
% 299.89/300.47  228962[10:Res:162888.0,160788.0] || subclass(image(element_relation,successor(successor_relation)),u) -> equal(complement(power_class(complement(singleton(successor_relation)))),successor_relation) member(regular(complement(power_class(complement(singleton(successor_relation))))),u)*.
% 299.89/300.47  228961[10:Res:161138.0,160788.0] || subclass(image(element_relation,symmetrization_of(successor_relation)),u) -> equal(complement(power_class(complement(inverse(successor_relation)))),successor_relation) member(regular(complement(power_class(complement(inverse(successor_relation))))),u)*.
% 299.89/300.47  228960[10:Res:160971.0,160788.0] || subclass(image(element_relation,power_class(successor_relation)),u) -> equal(complement(power_class(image(element_relation,universal_class))),successor_relation) member(regular(complement(power_class(image(element_relation,universal_class)))),u)*.
% 299.89/300.47  228959[10:Res:160848.0,160788.0] || subclass(image(element_relation,power_class(universal_class)),u) -> equal(complement(power_class(image(element_relation,successor_relation))),successor_relation) member(regular(complement(power_class(image(element_relation,successor_relation)))),u)*.
% 299.89/300.47  229459[10:Rew:162889.0,229341.1] || member(not_subclass_element(intersection(power_class(complement(singleton(successor_relation))),u),v),image(element_relation,successor(successor_relation)))* -> subclass(intersection(power_class(complement(singleton(successor_relation))),u),v).
% 299.89/300.47  229460[10:Rew:161137.0,229340.1] || member(not_subclass_element(intersection(power_class(complement(inverse(successor_relation))),u),v),image(element_relation,symmetrization_of(successor_relation)))* -> subclass(intersection(power_class(complement(inverse(successor_relation))),u),v).
% 299.89/300.47  229616[10:Rew:162889.0,229520.1] || member(not_subclass_element(intersection(u,power_class(complement(singleton(successor_relation)))),v),image(element_relation,successor(successor_relation)))* -> subclass(intersection(u,power_class(complement(singleton(successor_relation)))),v).
% 299.89/300.47  229617[10:Rew:161137.0,229519.1] || member(not_subclass_element(intersection(u,power_class(complement(inverse(successor_relation)))),v),image(element_relation,symmetrization_of(successor_relation)))* -> subclass(intersection(u,power_class(complement(inverse(successor_relation)))),v).
% 299.89/300.47  229684[0:Obv:229674.1] || subclass(unordered_pair(u,v),omega) -> equal(not_subclass_element(unordered_pair(u,v),w),u)** subclass(unordered_pair(u,v),w) equal(integer_of(v),v).
% 299.89/300.47  229685[0:Obv:229673.1] || subclass(unordered_pair(u,v),omega) -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w) equal(integer_of(u),u).
% 299.89/300.47  229790[10:Res:221521.1,161270.1] || member(complement(complement(singleton(omega))),universal_class) -> equal(integer_of(apply(choice,complement(complement(singleton(omega))))),successor_relation)** equal(complement(complement(singleton(omega))),successor_relation).
% 299.89/300.47  230148[10:SpL:161565.2,222140.0] || member(cross_product(u,v),universal_class) equal(complement(complement(singleton(apply(choice,cross_product(u,v))))),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  230654[10:SpL:161565.2,219386.0] || member(cross_product(u,v),universal_class) subclass(universal_class,regular(unordered_pair(w,apply(choice,cross_product(u,v)))))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  230867[10:MRR:230816.0,13.0] || subclass(universal_class,regular(image(element_relation,power_class(successor_relation)))) -> member(unordered_pair(u,v),power_class(image(element_relation,universal_class)))* equal(image(element_relation,power_class(successor_relation)),successor_relation).
% 299.89/300.47  231186[10:SpL:161565.2,221320.0] || member(cross_product(u,v),universal_class) subclass(universal_class,regular(unordered_pair(apply(choice,cross_product(u,v)),w)))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  231719[10:SpL:161565.2,230662.0] || member(cross_product(u,v),universal_class) equal(regular(unordered_pair(w,apply(choice,cross_product(u,v)))),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  231734[10:SpL:161565.2,231194.0] || member(cross_product(u,v),universal_class) equal(regular(unordered_pair(apply(choice,cross_product(u,v)),w)),universal_class)** -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  231754[24:SpL:222482.0,160396.2] || connected(u,v) member(kind_1_ordinals,not_well_ordering(u,v)) equal(segment(u,not_well_ordering(u,v),universal_class),successor_relation)** -> well_ordering(u,v).
% 299.89/300.47  231819[15:Res:189374.2,161035.0] || member(u,universal_class) subclass(domain_relation,intersection(power_class(successor_relation),complement(v))) member(ordered_pair(u,successor_relation),union(image(element_relation,universal_class),v))* -> .
% 299.89/300.47  231775[10:SpL:208.0,161035.0] || member(u,intersection(power_class(successor_relation),power_class(image(element_relation,complement(v)))))* member(u,union(image(element_relation,universal_class),image(element_relation,power_class(v)))) -> .
% 299.89/300.47  10168[0:SpR:1933.0,161.0] ||  -> equal(intersection(complement(symmetric_difference(u,inverse(u))),union(complement(intersection(u,inverse(u))),symmetrization_of(u))),symmetric_difference(complement(intersection(u,inverse(u))),symmetrization_of(u)))**.
% 299.89/300.47  33815[0:SpR:1938.0,25.2] || member(u,union(v,cross_product(w,x))) member(u,complement(restrict(v,w,x))) -> member(u,symmetric_difference(v,cross_product(w,x)))*.
% 299.89/300.47  33888[0:SpR:1943.0,25.2] || member(u,union(cross_product(v,w),x)) member(u,complement(restrict(x,v,w))) -> member(u,symmetric_difference(cross_product(v,w),x))*.
% 299.89/300.47  34029[0:SpL:1933.0,3883.2] || member(u,symmetrization_of(v)) member(u,complement(intersection(v,inverse(v))))* subclass(symmetric_difference(v,inverse(v)),w)* -> member(u,w)*.
% 299.89/300.47  40549[0:SpR:1931.0,9535.0] ||  -> subclass(symmetric_difference(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v))),complement(symmetric_difference(complement(intersection(u,v)),union(u,v))))*.
% 299.89/300.47  34030[0:SpL:1934.0,3883.2] || member(u,successor(v)) member(u,complement(intersection(v,singleton(v))))* subclass(symmetric_difference(v,singleton(v)),w)* -> member(u,w)*.
% 299.89/300.47  10511[0:Res:60.1,179.1] || member(ordered_pair(u,least(element_relation,intersection(y__dfg,ordinal_numbers))),compose(v,w))* subclass(image(v,image(w,singleton(u))),intersection(y__dfg,ordinal_numbers)) -> .
% 299.89/300.47  10230[0:SpR:1934.0,161.0] ||  -> equal(intersection(complement(symmetric_difference(u,singleton(u))),union(complement(intersection(u,singleton(u))),successor(u))),symmetric_difference(complement(intersection(u,singleton(u))),successor(u)))**.
% 299.89/300.47  35968[0:Res:6219.1,2078.1] || member(u,not_well_ordering(v,singleton(u)))* connected(v,singleton(u)) -> well_ordering(v,singleton(u)) equal(not_well_ordering(v,singleton(u)),singleton(u)).
% 299.89/300.47  43888[0:Res:1499.1,6044.0] || subclass(universal_class,compose(u,v)) member(w,x)* subclass(x,y)* well_ordering(image(u,image(v,singleton(z))),y)* -> .
% 299.89/300.47  39957[0:Res:999.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,ordered_pair(w,x))),second(ordered_pair(u,ordered_pair(w,x)))),ordered_pair(u,ordered_pair(w,x)))**.
% 299.89/300.47  31101[2:Res:9418.0,5832.1] inductive(restrict(u,v,w)) || well_ordering(x,cross_product(v,w)) -> member(least(x,restrict(u,v,w)),restrict(u,v,w))*.
% 299.89/300.47  92635[2:MRR:92619.3,2450.0] function(u) || well_ordering(v,cross_product(universal_class,universal_class)) subclass(singleton(least(v,u)),u) -> section(v,singleton(least(v,u)),u)*.
% 299.89/300.47  130399[0:Res:28321.1,9300.0] || subclass(rest_relation,flip(symmetric_difference(u,cross_product(v,w)))) -> member(ordered_pair(ordered_pair(x,y),rest_of(ordered_pair(y,x))),complement(restrict(u,v,w)))*.
% 299.89/300.47  130398[0:Res:28320.1,9300.0] || subclass(rest_relation,rotate(symmetric_difference(u,cross_product(v,w)))) -> member(ordered_pair(ordered_pair(x,rest_of(ordered_pair(y,x))),y),complement(restrict(u,v,w)))*.
% 299.89/300.47  130492[0:Res:28321.1,9306.0] || subclass(rest_relation,flip(symmetric_difference(cross_product(u,v),w))) -> member(ordered_pair(ordered_pair(x,y),rest_of(ordered_pair(y,x))),complement(restrict(w,u,v)))*.
% 299.89/300.47  130491[0:Res:28320.1,9306.0] || subclass(rest_relation,rotate(symmetric_difference(cross_product(u,v),w))) -> member(ordered_pair(ordered_pair(x,rest_of(ordered_pair(y,x))),y),complement(restrict(w,u,v)))*.
% 299.89/300.47  143786[0:Res:28321.1,159.0] || subclass(rest_relation,flip(omega)) -> equal(integer_of(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u)))),ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))))**.
% 299.89/300.47  143785[0:Res:28320.1,159.0] || subclass(rest_relation,rotate(omega)) -> equal(integer_of(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v)),ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v))**.
% 299.89/300.47  30746[0:Res:3595.3,513.0] function(u) || member(v,universal_class) subclass(universal_class,intersection(complement(w),complement(x)))* member(image(u,v),union(w,x))* -> .
% 299.89/300.47  126715[0:Res:1951.1,9482.0] || member(not_subclass_element(intersection(complement(complement(intersection(u,v))),w),x),symmetric_difference(u,v))* -> subclass(intersection(complement(complement(intersection(u,v))),w),x).
% 299.89/300.47  28576[0:Res:340.1,513.0] || member(not_subclass_element(intersection(intersection(complement(u),complement(v)),w),x),union(u,v))* -> subclass(intersection(intersection(complement(u),complement(v)),w),x).
% 299.89/300.47  126497[0:Res:1951.1,9368.0] || member(not_subclass_element(intersection(u,complement(complement(intersection(v,w)))),x),symmetric_difference(v,w))* -> subclass(intersection(u,complement(complement(intersection(v,w)))),x).
% 299.89/300.47  28588[0:Res:322.1,513.0] || member(not_subclass_element(intersection(u,intersection(complement(v),complement(w))),x),union(v,w))* -> subclass(intersection(u,intersection(complement(v),complement(w))),x).
% 299.89/300.47  40261[0:MRR:40217.0,34189.1] || member(not_subclass_element(u,intersection(v,complement(w))),v)* -> member(not_subclass_element(u,intersection(v,complement(w))),w)* subclass(u,intersection(v,complement(w))).
% 299.89/300.47  131944[0:Obv:131865.1] || member(not_subclass_element(symmetric_difference(u,v),intersection(w,complement(intersection(u,v)))),w)* -> subclass(symmetric_difference(u,v),intersection(w,complement(intersection(u,v)))).
% 299.89/300.47  113121[0:Res:131.2,9649.0] || connected(u,singleton(v)) -> well_ordering(u,singleton(v)) subclass(not_well_ordering(u,singleton(v)),w) equal(not_subclass_element(not_well_ordering(u,singleton(v)),w),v)**.
% 299.89/300.47  41912[0:SpL:2330.1,16.0] || member(not_subclass_element(cross_product(u,v),w),cross_product(x,y))* -> subclass(cross_product(u,v),w) member(first(not_subclass_element(cross_product(u,v),w)),x).
% 299.89/300.47  41913[0:SpL:2330.1,17.0] || member(not_subclass_element(cross_product(u,v),w),cross_product(x,y))* -> subclass(cross_product(u,v),w) member(second(not_subclass_element(cross_product(u,v),w)),y).
% 299.89/300.47  122525[0:Res:60.1,9636.1] || member(ordered_pair(u,not_subclass_element(v,w)),compose(x,y))* subclass(v,complement(image(x,image(y,singleton(u)))))* -> subclass(v,w).
% 299.89/300.47  31044[0:Res:1481.2,2142.0] || subclass(u,ordered_pair(v,w))* -> subclass(u,x) equal(not_subclass_element(u,x),unordered_pair(v,singleton(w)))* equal(not_subclass_element(u,x),singleton(v)).
% 299.89/300.47  39956[0:Res:13.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,unordered_pair(w,x))),second(ordered_pair(u,unordered_pair(w,x)))),ordered_pair(u,unordered_pair(w,x)))**.
% 299.89/300.47  31031[0:Res:4.1,2142.0] ||  -> subclass(ordered_pair(u,v),w) equal(not_subclass_element(ordered_pair(u,v),w),unordered_pair(u,singleton(v)))** equal(not_subclass_element(ordered_pair(u,v),w),singleton(u)).
% 299.89/300.47  122561[0:Obv:122493.2] || subclass(unordered_pair(u,v),complement(w))* member(v,w) -> equal(not_subclass_element(unordered_pair(u,v),x),u)** subclass(unordered_pair(u,v),x).
% 299.89/300.47  122562[0:Obv:122492.2] || subclass(unordered_pair(u,v),complement(w))* member(u,w) -> equal(not_subclass_element(unordered_pair(u,v),x),v)** subclass(unordered_pair(u,v),x).
% 299.89/300.47  123447[0:Res:5771.1,9639.0] || equal(sum_class(intersection(u,v)),intersection(u,v)) -> subclass(sum_class(intersection(u,v)),w) member(not_subclass_element(sum_class(intersection(u,v)),w),u)*.
% 299.89/300.47  122856[0:Res:5771.1,9640.0] || equal(sum_class(intersection(u,v)),intersection(u,v)) -> subclass(sum_class(intersection(u,v)),w) member(not_subclass_element(sum_class(intersection(u,v)),w),v)*.
% 299.89/300.47  30311[0:SpR:70.0,475.1] || member(restrict(element_relation,universal_class,image(u,singleton(v))),universal_class) -> member(ordered_pair(restrict(element_relation,universal_class,image(u,singleton(v))),apply(u,v)),domain_relation)*.
% 299.89/300.47  137851[0:Rew:109340.0,137757.1] || subclass(universal_class,image(element_relation,symmetrization_of(image(element_relation,complement(u))))) member(unordered_pair(v,w),complement(image(element_relation,symmetrization_of(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  137235[0:Rew:109283.0,137139.1] || subclass(universal_class,image(element_relation,successor(image(element_relation,complement(u))))) member(unordered_pair(v,w),complement(image(element_relation,successor(image(element_relation,complement(u))))))* -> .
% 299.89/300.47  139799[0:SpL:982.0,307.0] || member(u,image(element_relation,union(image(element_relation,power_class(v)),w))) member(u,power_class(intersection(power_class(image(element_relation,complement(v))),complement(w))))* -> .
% 299.89/300.47  29300[0:SpR:505.0,507.0] ||  -> equal(union(u,intersection(complement(v),power_class(intersection(complement(w),complement(x))))),complement(intersection(complement(u),union(v,image(element_relation,union(w,x))))))**.
% 299.89/300.47  140261[0:SpL:984.0,307.0] || member(u,image(element_relation,union(v,image(element_relation,power_class(w))))) member(u,power_class(intersection(complement(v),power_class(image(element_relation,complement(w))))))* -> .
% 299.89/300.47  29216[0:SpR:505.0,506.0] ||  -> equal(union(intersection(complement(u),power_class(intersection(complement(v),complement(w)))),x),complement(intersection(union(u,image(element_relation,union(v,w))),complement(x))))**.
% 299.89/300.47  29638[0:SpL:505.0,1487.1] || member(u,universal_class) subclass(power_class(intersection(complement(v),complement(w))),x)* -> member(u,image(element_relation,union(v,w)))* member(u,x)*.
% 299.89/300.47  124226[0:SpL:505.0,986.1] || member(u,image(element_relation,power_class(image(element_relation,union(v,w))))) member(u,power_class(image(element_relation,power_class(intersection(complement(v),complement(w))))))* -> .
% 299.89/300.47  29312[0:SpR:505.0,507.0] ||  -> equal(union(u,intersection(power_class(intersection(complement(v),complement(w))),complement(x))),complement(intersection(complement(u),union(image(element_relation,union(v,w)),x))))**.
% 299.89/300.47  126817[0:SpL:505.0,29643.0] || equal(u,power_class(intersection(complement(v),complement(w))))* member(x,universal_class) -> member(x,image(element_relation,union(v,w)))* member(x,u)*.
% 299.89/300.47  29228[0:SpR:505.0,506.0] ||  -> equal(union(intersection(power_class(intersection(complement(u),complement(v))),complement(w)),x),complement(intersection(union(image(element_relation,union(u,v)),w),complement(x))))**.
% 299.89/300.47  9972[0:Rew:505.0,9954.1] || member(not_subclass_element(power_class(intersection(complement(u),complement(v))),w),image(element_relation,union(u,v)))* -> subclass(power_class(intersection(complement(u),complement(v))),w).
% 299.89/300.47  118918[0:SpL:208.0,1089.0] || member(not_subclass_element(power_class(image(element_relation,power_class(u))),v),image(element_relation,power_class(image(element_relation,complement(u)))))* -> subclass(power_class(image(element_relation,power_class(u))),v).
% 299.89/300.47  125951[0:Res:28320.1,986.1] || subclass(rest_relation,rotate(power_class(image(element_relation,complement(u))))) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),image(element_relation,power_class(u)))* -> .
% 299.89/300.47  126081[0:Res:28321.1,986.1] || subclass(rest_relation,flip(power_class(image(element_relation,complement(u))))) member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),image(element_relation,power_class(u)))* -> .
% 299.89/300.47  122640[0:SpR:509.0,6832.1] ||  -> subclass(symmetric_difference(u,image(element_relation,complement(v))),w) member(not_subclass_element(symmetric_difference(u,image(element_relation,complement(v))),w),complement(intersection(complement(u),power_class(v))))*.
% 299.89/300.47  122652[0:SpR:511.0,6832.1] ||  -> subclass(symmetric_difference(image(element_relation,complement(u)),v),w) member(not_subclass_element(symmetric_difference(image(element_relation,complement(u)),v),w),complement(intersection(power_class(u),complement(v))))*.
% 299.89/300.47  47767[0:Rew:124.0,47721.0] || member(restrict(u,v,singleton(w)),segment(u,v,w)) -> member(ordered_pair(restrict(u,v,singleton(w)),segment(u,v,w)),element_relation)*.
% 299.89/300.47  163666[10:Rew:160202.0,162923.3] || member(u,v) subclass(v,w)* well_ordering(successor(successor_relation),w)* -> member(ordered_pair(u,least(successor(successor_relation),v)),complement(singleton(successor_relation)))*.
% 299.89/300.47  160915[10:Rew:160202.0,151106.0] ||  -> equal(complement(intersection(power_class(image(element_relation,union(image(element_relation,universal_class),u))),complement(v))),union(image(element_relation,power_class(intersection(power_class(successor_relation),complement(u)))),v))**.
% 299.89/300.47  160946[10:Rew:160202.0,151098.0] ||  -> equal(complement(intersection(power_class(image(element_relation,union(u,image(element_relation,universal_class)))),complement(v))),union(image(element_relation,power_class(intersection(complement(u),power_class(successor_relation)))),v))**.
% 299.89/300.47  161021[10:Rew:160202.0,151096.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,union(v,image(element_relation,universal_class)))))),union(u,image(element_relation,power_class(intersection(complement(v),power_class(successor_relation))))))**.
% 299.89/300.47  163653[10:Rew:160202.0,161030.0] || member(u,union(complement(v),power_class(successor_relation))) member(u,union(v,image(element_relation,universal_class))) -> member(u,symmetric_difference(complement(v),power_class(successor_relation)))*.
% 299.89/300.47  161042[10:Rew:160202.0,151100.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,union(image(element_relation,universal_class),v))))),union(u,image(element_relation,power_class(intersection(power_class(successor_relation),complement(v))))))**.
% 299.89/300.47  163654[10:Rew:160202.0,161055.0] || member(u,union(power_class(successor_relation),complement(v))) member(u,union(image(element_relation,universal_class),v)) -> member(u,symmetric_difference(power_class(successor_relation),complement(v)))*.
% 299.89/300.47  163655[10:Rew:160202.0,161091.3] || member(u,v) subclass(v,w)* well_ordering(power_class(successor_relation),w)* -> member(ordered_pair(u,least(power_class(successor_relation),v)),image(element_relation,universal_class))*.
% 299.89/300.47  163657[10:Rew:160202.0,161127.3] || member(u,v) subclass(v,w)* well_ordering(symmetrization_of(successor_relation),w)* -> member(ordered_pair(u,least(symmetrization_of(successor_relation),v)),complement(inverse(successor_relation)))*.
% 299.89/300.47  160731[10:Rew:160202.0,146458.1] || subclass(u,symmetric_difference(v,intersection(complement(w),complement(x)))) -> equal(u,successor_relation) member(regular(u),complement(intersection(complement(v),union(w,x))))*.
% 299.89/300.47  160730[10:Rew:160202.0,146459.1] || subclass(u,symmetric_difference(intersection(complement(v),complement(w)),x)) -> equal(u,successor_relation) member(regular(u),complement(intersection(union(v,w),complement(x))))*.
% 299.89/300.47  160729[10:Rew:160202.0,146509.3] || member(u,universal_class) subclass(u,intersection(complement(v),complement(w)))* member(apply(choice,u),union(v,w)) -> equal(u,successor_relation).
% 299.89/300.47  160728[10:Rew:160202.0,146510.2] || member(u,universal_class) subclass(u,unordered_pair(v,w))* -> equal(u,successor_relation) equal(apply(choice,u),w) equal(apply(choice,u),v).
% 299.89/300.47  160727[10:Rew:160202.0,146527.2] || subclass(u,complement(intersection(v,w)))* member(regular(u),union(v,w)) -> equal(u,successor_relation) member(regular(u),symmetric_difference(v,w)).
% 299.89/300.47  160883[10:Rew:160202.0,152647.3] || member(u,v) subclass(v,w)* well_ordering(power_class(universal_class),w)* -> member(ordered_pair(u,least(power_class(universal_class),v)),image(element_relation,successor_relation))*.
% 299.89/300.47  167521[10:Res:160369.0,5832.1] inductive(complement(union(u,successor_relation))) || well_ordering(v,symmetric_difference(universal_class,u)) -> member(least(v,complement(union(u,successor_relation))),complement(union(u,successor_relation)))*.
% 299.89/300.47  161201[10:Rew:160202.0,156257.2] inductive(complement(union(u,identity_relation))) || well_ordering(v,symmetric_difference(universal_class,u)) -> member(least(v,complement(union(u,successor_relation))),complement(union(u,successor_relation)))*.
% 299.89/300.47  161229[10:Rew:160202.0,156107.1] inductive(symmetric_difference(complement(u),universal_class)) || well_ordering(v,union(u,successor_relation)) -> member(least(v,symmetric_difference(complement(u),universal_class)),symmetric_difference(complement(u),universal_class))*.
% 299.89/300.47  161326[10:Rew:160202.0,146403.1] || asymmetric(cross_product(u,v),singleton(w)) -> equal(range__dfg(restrict(inverse(cross_product(u,v)),u,v),w,singleton(w)),second(not_subclass_element(successor_relation,successor_relation)))**.
% 299.89/300.47  163660[10:Rew:160202.0,161673.1] || well_ordering(u,union(v,successor_relation)) -> equal(symmetric_difference(complement(v),universal_class),successor_relation) member(least(u,symmetric_difference(complement(v),universal_class)),symmetric_difference(complement(v),universal_class))*.
% 299.89/300.47  163661[10:Rew:160202.0,161675.1] || well_ordering(u,symmetric_difference(universal_class,v)) -> equal(complement(union(v,successor_relation)),successor_relation) member(least(u,complement(union(v,successor_relation))),complement(union(v,successor_relation)))*.
% 299.89/300.47  161579[10:Rew:160202.0,146821.1] || member(regular(cross_product(u,v)),element_relation) -> equal(cross_product(u,v),successor_relation) member(first(regular(cross_product(u,v))),second(regular(cross_product(u,v))))*.
% 299.89/300.47  161694[10:Rew:160202.0,146713.1] || member(restrict(u,v,w),universal_class) -> equal(restrict(u,v,w),successor_relation) member(apply(choice,restrict(u,v,w)),cross_product(v,w))*.
% 299.89/300.47  161702[10:Rew:160202.0,146871.2] || subclass(u,power_class(image(element_relation,complement(v)))) member(regular(intersection(w,u)),image(element_relation,power_class(v)))* -> equal(intersection(w,u),successor_relation).
% 299.89/300.47  161713[10:Rew:160202.0,146892.2] || subclass(u,power_class(image(element_relation,complement(v)))) member(regular(intersection(u,w)),image(element_relation,power_class(v)))* -> equal(intersection(u,w),successor_relation).
% 299.89/300.47  161727[10:Rew:160202.0,147074.1] || member(u,v)* -> equal(w,successor_relation) equal(ordered_pair(first(ordered_pair(u,regular(w))),second(ordered_pair(u,regular(w)))),ordered_pair(u,regular(w)))**.
% 299.89/300.47  161794[10:Rew:160202.0,146856.2] || member(image(element_relation,complement(u)),universal_class) member(apply(choice,image(element_relation,complement(u))),power_class(u))* -> equal(image(element_relation,complement(u)),successor_relation).
% 299.89/300.47  161883[10:Rew:160202.0,146863.2] || member(union(u,v),universal_class) member(apply(choice,union(u,v)),intersection(complement(u),complement(v)))* -> equal(union(u,v),successor_relation).
% 299.89/300.47  161948[10:Rew:160202.0,148513.1] || member(intersection(omega,u),universal_class) -> equal(intersection(omega,u),successor_relation) equal(integer_of(apply(choice,intersection(omega,u))),apply(choice,intersection(omega,u)))**.
% 299.89/300.47  161950[10:Rew:160202.0,148515.1] || member(intersection(u,omega),universal_class) -> equal(intersection(u,omega),successor_relation) equal(integer_of(apply(choice,intersection(u,omega))),apply(choice,intersection(u,omega)))**.
% 299.89/300.47  162060[10:Rew:160202.0,147008.1] || subclass(u,unordered_pair(v,w))* -> equal(intersection(x,u),successor_relation) equal(regular(intersection(x,u)),w)* equal(regular(intersection(x,u)),v)*.
% 299.89/300.47  162074[10:Rew:160202.0,147023.1] || subclass(u,unordered_pair(v,w))* -> equal(intersection(u,x),successor_relation) equal(regular(intersection(u,x)),w)* equal(regular(intersection(u,x)),v)*.
% 299.89/300.47  162207[10:Rew:160202.0,147593.1] || subclass(u,symmetric_difference(cross_product(v,w),x)) -> equal(intersection(y,u),successor_relation) member(regular(intersection(y,u)),complement(restrict(x,v,w)))*.
% 299.89/300.47  162206[10:Rew:160202.0,147594.1] || subclass(u,symmetric_difference(v,cross_product(w,x))) -> equal(intersection(y,u),successor_relation) member(regular(intersection(y,u)),complement(restrict(v,w,x)))*.
% 299.89/300.47  162216[10:Rew:160202.0,147692.1] || subclass(u,symmetric_difference(cross_product(v,w),x)) -> equal(intersection(u,y),successor_relation) member(regular(intersection(u,y)),complement(restrict(x,v,w)))*.
% 299.89/300.47  162215[10:Rew:160202.0,147693.1] || subclass(u,symmetric_difference(v,cross_product(w,x))) -> equal(intersection(u,y),successor_relation) member(regular(intersection(u,y)),complement(restrict(v,w,x)))*.
% 299.89/300.47  162237[10:Rew:160202.0,147042.1] || subclass(complement(restrict(u,v,w)),x) -> equal(symmetric_difference(u,cross_product(v,w)),successor_relation) member(regular(symmetric_difference(u,cross_product(v,w))),x)*.
% 299.89/300.47  162379[10:Rew:160202.0,147613.0] ||  -> equal(intersection(u,intersection(restrict(v,w,x),y)),successor_relation) member(regular(intersection(u,intersection(restrict(v,w,x),y))),cross_product(w,x))*.
% 299.89/300.47  162382[10:Rew:160202.0,147671.0] ||  -> equal(intersection(u,intersection(v,restrict(w,x,y))),successor_relation) member(regular(intersection(u,intersection(v,restrict(w,x,y)))),cross_product(x,y))*.
% 299.89/300.47  162385[10:Rew:160202.0,147711.0] ||  -> equal(intersection(intersection(restrict(u,v,w),x),y),successor_relation) member(regular(intersection(intersection(restrict(u,v,w),x),y)),cross_product(v,w))*.
% 299.89/300.47  162388[10:Rew:160202.0,147784.0] ||  -> equal(intersection(intersection(u,restrict(v,w,x)),y),successor_relation) member(regular(intersection(intersection(u,restrict(v,w,x)),y)),cross_product(w,x))*.
% 299.89/300.47  162446[10:Rew:160202.0,147100.0] ||  -> equal(intersection(u,unordered_pair(v,w)),successor_relation) equal(regular(intersection(u,unordered_pair(v,w))),w)** equal(regular(intersection(u,unordered_pair(v,w))),v)**.
% 299.89/300.47  162448[10:Rew:160202.0,147102.0] ||  -> equal(intersection(unordered_pair(u,v),w),successor_relation) equal(regular(intersection(unordered_pair(u,v),w)),v)** equal(regular(intersection(unordered_pair(u,v),w)),u)**.
% 299.89/300.47  162449[10:Rew:160202.0,147103.1] || well_ordering(u,symmetrization_of(v)) -> equal(segment(u,symmetric_difference(complement(v),complement(inverse(v))),least(u,symmetric_difference(complement(v),complement(inverse(v))))),successor_relation)**.
% 299.89/300.47  162450[10:Rew:160202.0,147104.1] || well_ordering(u,successor(v)) -> equal(segment(u,symmetric_difference(complement(v),complement(singleton(v))),least(u,symmetric_difference(complement(v),complement(singleton(v))))),successor_relation)**.
% 299.89/300.47  162455[10:Rew:160202.0,147109.1] || well_ordering(u,cross_product(v,w)) -> equal(restrict(x,v,w),successor_relation) member(least(u,restrict(x,v,w)),restrict(x,v,w))*.
% 299.89/300.47  162456[10:Rew:160202.0,150914.2] || member(complement(complement(symmetrization_of(u))),ordinal_numbers)* connected(u,v)* -> equal(segment(element_relation,cross_product(v,v),least(element_relation,cross_product(v,v))),successor_relation)**.
% 299.89/300.47  162457[10:Rew:160202.0,147284.0] ||  -> equal(complement(complement(unordered_pair(u,v))),successor_relation) equal(regular(complement(complement(unordered_pair(u,v)))),v)** equal(regular(complement(complement(unordered_pair(u,v)))),u)**.
% 299.89/300.47  162458[10:Rew:160202.0,147285.1] ||  -> member(regular(complement(power_class(intersection(complement(u),complement(v))))),image(element_relation,union(u,v)))* equal(complement(power_class(intersection(complement(u),complement(v)))),successor_relation).
% 299.89/300.47  162460[10:Rew:160202.0,147439.0] ||  -> equal(restrict(symmetric_difference(complement(u),complement(v)),w,x),successor_relation) member(regular(restrict(symmetric_difference(complement(u),complement(v)),w,x)),union(u,v))*.
% 299.89/300.47  162463[10:Rew:160202.0,147478.1] || member(regular(intersection(u,power_class(image(element_relation,complement(v))))),image(element_relation,power_class(v)))* -> equal(intersection(u,power_class(image(element_relation,complement(v)))),successor_relation).
% 299.89/300.47  162465[10:Rew:160202.0,147505.1] || member(regular(intersection(power_class(image(element_relation,complement(u))),v)),image(element_relation,power_class(u)))* -> equal(intersection(power_class(image(element_relation,complement(u))),v),successor_relation).
% 299.89/300.47  162467[10:Rew:160202.0,147560.1] || member(regular(complement(complement(power_class(image(element_relation,complement(u)))))),image(element_relation,power_class(u)))* -> equal(complement(complement(power_class(image(element_relation,complement(u))))),successor_relation).
% 299.89/300.47  162469[10:Rew:160202.0,147619.1] || member(regular(intersection(u,intersection(image(element_relation,complement(v)),w))),power_class(v))* -> equal(intersection(u,intersection(image(element_relation,complement(v)),w)),successor_relation).
% 299.89/300.47  162471[10:Rew:160202.0,147630.0] ||  -> equal(intersection(u,symmetric_difference(cross_product(v,w),x)),successor_relation) member(regular(intersection(u,symmetric_difference(cross_product(v,w),x))),complement(restrict(x,v,w)))*.
% 299.89/300.47  162473[10:Rew:160202.0,147632.0] ||  -> equal(intersection(u,symmetric_difference(v,cross_product(w,x))),successor_relation) member(regular(intersection(u,symmetric_difference(v,cross_product(w,x)))),complement(restrict(v,w,x)))*.
% 299.89/300.47  162474[10:Rew:160202.0,147677.1] || member(regular(intersection(u,intersection(v,image(element_relation,complement(w))))),power_class(w))* -> equal(intersection(u,intersection(v,image(element_relation,complement(w)))),successor_relation).
% 299.89/300.47  162475[10:Rew:160202.0,147699.1] || subclass(complement(restrict(u,v,w)),x) -> equal(symmetric_difference(cross_product(v,w),u),successor_relation) member(regular(symmetric_difference(cross_product(v,w),u)),x)*.
% 299.89/300.47  162476[10:Rew:160202.0,147717.1] || member(regular(intersection(intersection(image(element_relation,complement(u)),v),w)),power_class(u))* -> equal(intersection(intersection(image(element_relation,complement(u)),v),w),successor_relation).
% 299.89/300.47  162478[10:Rew:160202.0,147728.0] ||  -> equal(intersection(symmetric_difference(cross_product(u,v),w),x),successor_relation) member(regular(intersection(symmetric_difference(cross_product(u,v),w),x)),complement(restrict(w,u,v)))*.
% 299.89/300.47  162480[10:Rew:160202.0,147730.0] ||  -> equal(intersection(symmetric_difference(u,cross_product(v,w)),x),successor_relation) member(regular(intersection(symmetric_difference(u,cross_product(v,w)),x)),complement(restrict(u,v,w)))*.
% 299.89/300.47  162481[10:Rew:160202.0,147790.1] || member(regular(intersection(intersection(u,image(element_relation,complement(v))),w)),power_class(v))* -> equal(intersection(intersection(u,image(element_relation,complement(v))),w),successor_relation).
% 299.89/300.47  162482[10:Rew:160202.0,147830.0] ||  -> equal(complement(complement(symmetric_difference(u,cross_product(v,w)))),successor_relation) member(regular(complement(complement(symmetric_difference(u,cross_product(v,w))))),complement(restrict(u,v,w)))*.
% 299.89/300.47  162483[10:Rew:160202.0,147838.0] ||  -> equal(complement(complement(symmetric_difference(cross_product(u,v),w))),successor_relation) member(regular(complement(complement(symmetric_difference(cross_product(u,v),w)))),complement(restrict(w,u,v)))*.
% 299.89/300.47  162487[10:Rew:160202.0,147898.1] || subclass(successor(image(element_relation,complement(u))),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* -> equal(successor(image(element_relation,complement(u))),successor_relation).
% 299.89/300.47  162491[10:Rew:160202.0,147918.1] || subclass(symmetrization_of(image(element_relation,complement(u))),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* -> equal(symmetrization_of(image(element_relation,complement(u))),successor_relation).
% 299.89/300.47  182934[6:Res:157922.1,127.0] || member(u,element_relation)* subclass(compose(element_relation,universal_class),v)* well_ordering(w,v)* -> member(least(w,compose(element_relation,universal_class)),compose(element_relation,universal_class))*.
% 299.89/300.47  183756[11:Res:183734.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,regular(symmetrization_of(successor_relation)))),second(ordered_pair(u,regular(symmetrization_of(successor_relation))))),ordered_pair(u,regular(symmetrization_of(successor_relation))))**.
% 299.89/300.47  185687[10:Rew:113504.0,185454.1] || equal(symmetric_difference(u,v),successor_relation) -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),union(complement(intersection(u,v)),union(u,v)))**.
% 299.89/300.47  6012[0:Rew:1005.0,6009.2] || equal(compose(u,singleton(v)),v) member(singleton(singleton(singleton(v))),cross_product(universal_class,universal_class))* -> member(singleton(singleton(singleton(v))),compose_class(u))*.
% 299.89/300.47  132302[0:Res:137.1,9647.0] || member(restrict(u,v,w),ordinal_numbers) -> subclass(sum_class(restrict(u,v,w)),x) member(not_subclass_element(sum_class(restrict(u,v,w)),x),u)*.
% 299.89/300.47  162023[10:Rew:160202.0,146566.3] || member(u,ordinal_numbers) well_ordering(v,u) subclass(sum_class(u),w) -> equal(sum_class(u),successor_relation) member(least(v,sum_class(u)),w)*.
% 299.89/300.47  108622[2:Obv:108617.3] || well_ordering(u,not_well_ordering(u,v)) connected(u,v) member(least(u,not_well_ordering(u,v)),not_well_ordering(u,v))* -> well_ordering(u,v).
% 299.89/300.47  108803[2:Res:31076.2,594.0] inductive(restrict(u,v,w)) || well_ordering(x,restrict(u,v,w)) -> member(least(x,restrict(u,v,w)),cross_product(v,w))*.
% 299.89/300.47  155755[6:Rew:155722.0,154242.2] inductive(symmetric_difference(universal_class,image(element_relation,identity_relation))) || well_ordering(u,power_class(universal_class)) -> member(least(u,intersection(power_class(universal_class),universal_class)),intersection(power_class(universal_class),universal_class))*.
% 299.89/300.47  163652[10:Rew:160202.0,161004.1] inductive(symmetric_difference(universal_class,image(element_relation,universal_class))) || well_ordering(u,power_class(successor_relation)) -> member(least(u,intersection(power_class(successor_relation),universal_class)),intersection(power_class(successor_relation),universal_class))*.
% 299.89/300.47  108823[2:Res:31076.2,307.0] inductive(image(element_relation,complement(u))) || well_ordering(v,image(element_relation,complement(u))) member(least(v,image(element_relation,complement(u))),power_class(u))* -> .
% 299.89/300.47  42958[0:Res:314.0,5839.2] || member(u,v)* member(u,w)* well_ordering(x,intersection(w,v)) -> member(least(x,intersection(w,v)),intersection(w,v))*.
% 299.89/300.47  42841[0:Res:314.0,5853.2] || member(u,v)* member(w,x)* well_ordering(y,cross_product(x,v)) -> member(least(y,cross_product(x,v)),cross_product(x,v))*.
% 299.89/300.47  162321[10:Rew:160202.0,147067.2] || well_ordering(u,image(element_relation,complement(v))) member(least(u,image(element_relation,complement(v))),power_class(v))* -> equal(image(element_relation,complement(v)),successor_relation).
% 299.89/300.47  162171[10:Rew:160202.0,146993.1] || well_ordering(u,restrict(v,w,x)) -> equal(restrict(v,w,x),successor_relation) member(least(u,restrict(v,w,x)),cross_product(w,x))*.
% 299.89/300.47  108257[2:Res:31069.2,10.0] inductive(unordered_pair(u,v)) || well_ordering(w,universal_class) -> equal(least(w,unordered_pair(u,v)),v)** equal(least(w,unordered_pair(u,v)),u)**.
% 299.89/300.47  108248[2:Res:31069.2,513.0] inductive(intersection(complement(u),complement(v))) || well_ordering(w,universal_class) member(least(w,intersection(complement(u),complement(v))),union(u,v))* -> .
% 299.89/300.47  162468[10:Rew:160202.0,147569.2] || member(least(u,complement(complement(intersection(v,w)))),symmetric_difference(v,w))* well_ordering(u,universal_class) -> equal(complement(complement(intersection(v,w))),successor_relation).
% 299.89/300.47  162454[10:Rew:160202.0,147108.1] || well_ordering(u,universal_class) -> equal(unordered_pair(v,w),successor_relation) equal(least(u,unordered_pair(v,w)),w)** equal(least(u,unordered_pair(v,w)),v)**.
% 299.89/300.47  162452[10:Rew:160202.0,147106.2] || well_ordering(u,universal_class) member(least(u,intersection(complement(v),complement(w))),union(v,w))* -> equal(intersection(complement(v),complement(w)),successor_relation).
% 299.89/300.47  181438[10:Rew:181437.2,181436.0] || member(ordinal_numbers,universal_class) well_ordering(element_relation,image(u,successor_relation)) subclass(apply(u,universal_class),image(u,successor_relation))* -> member(image(u,successor_relation),ordinal_numbers).
% 299.89/300.47  162531[10:Rew:160202.0,153502.0] || equal(apply(u,v),successor_relation) member(ordinal_numbers,universal_class) well_ordering(element_relation,image(u,singleton(v)))* -> member(image(u,singleton(v)),ordinal_numbers).
% 299.89/300.47  41327[0:Res:8.1,5841.1] || equal(u,unordered_pair(v,w))* member(w,universal_class) well_ordering(x,u)* -> member(least(x,unordered_pair(v,w)),unordered_pair(v,w))*.
% 299.89/300.47  41071[0:Res:8.1,5838.1] || equal(u,complement(v))* member(w,universal_class)* well_ordering(x,u)* -> member(w,v)* member(least(x,complement(v)),complement(v))*.
% 299.89/300.47  160057[3:Res:159952.1,5841.1] || subclass(unordered_pair(u,v),ordinal_numbers) member(v,universal_class) well_ordering(w,kind_1_ordinals) -> member(least(w,unordered_pair(u,v)),unordered_pair(u,v))*.
% 299.89/300.47  41468[0:Res:8.1,5842.1] || equal(u,unordered_pair(v,w))* member(v,universal_class) well_ordering(x,u)* -> member(least(x,unordered_pair(v,w)),unordered_pair(v,w))*.
% 299.89/300.47  160061[3:Res:159952.1,5838.1] || subclass(complement(u),ordinal_numbers) member(v,universal_class)* well_ordering(w,kind_1_ordinals) -> member(v,u)* member(least(w,complement(u)),complement(u))*.
% 299.89/300.47  107666[0:Res:6010.3,6045.0] || member(u,universal_class)* member(v,universal_class) equal(compose(w,v),u)* subclass(compose_class(w),x)* well_ordering(universal_class,x) -> .
% 299.89/300.47  163656[10:Rew:160202.0,161102.2,160202.0,161102.1] || member(u,universal_class) well_ordering(v,complement(inverse(successor_relation))) -> member(u,symmetrization_of(successor_relation))* member(least(v,complement(symmetrization_of(successor_relation))),complement(symmetrization_of(successor_relation)))*.
% 299.89/300.47  160059[3:Res:159952.1,5842.1] || subclass(unordered_pair(u,v),ordinal_numbers) member(u,universal_class) well_ordering(w,kind_1_ordinals) -> member(least(w,unordered_pair(u,v)),unordered_pair(u,v))*.
% 299.89/300.47  181121[10:SpL:181056.0,61.0] || member(u,image(v,image(w,successor_relation))) member(ordered_pair(universal_class,u),cross_product(universal_class,universal_class)) -> member(ordered_pair(universal_class,u),compose(v,w))*.
% 299.89/300.47  39593[0:Res:5768.2,144.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,rest_of(w)) -> equal(restrict(w,u,universal_class),ordered_pair(v,compose(u,v)))*.
% 299.89/300.47  163139[10:MRR:39597.3,160227.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,cross_product(universal_class,universal_class)) equal(ordered_pair(v,compose(u,v)),successor(u))** -> .
% 299.89/300.47  155803[3:Res:5768.2,141576.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,complement(kind_1_ordinals)) member(ordered_pair(u,ordered_pair(v,compose(u,v))),ordinal_numbers)* -> .
% 299.89/300.47  39566[0:Res:5768.2,26.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,complement(w)) member(ordered_pair(u,ordered_pair(v,compose(u,v))),w)* -> .
% 299.89/300.47  39571[0:Res:5768.2,24.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,intersection(w,x))* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),x)*.
% 299.89/300.47  39570[0:Res:5768.2,23.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,intersection(w,x))* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),w)*.
% 299.89/300.47  192556[10:Res:1006.0,162356.0] || subclass(ordered_pair(u,v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(unordered_pair(u,singleton(v)),least(omega,ordered_pair(u,v)))),successor_relation)**.
% 299.89/300.47  192541[10:Res:148.1,162356.0] || member(u,universal_class) subclass(rest_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(u,rest_of(u)),least(omega,rest_relation))),successor_relation)**.
% 299.89/300.47  192497[10:Res:3907.1,162356.0] || equal(complement(complement(u)),universal_class) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(w),least(omega,u))),successor_relation)**.
% 299.89/300.47  193545[2:Res:141787.0,127.0] || subclass(inverse(singleton(u)),v)* well_ordering(w,v)* -> asymmetric(singleton(u),x)* member(least(w,inverse(singleton(u))),inverse(singleton(u)))*.
% 299.89/300.47  194026[10:Res:5768.2,183622.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,successor(successor_relation)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),singleton(successor_relation))*.
% 299.89/300.47  194020[10:Res:5768.2,183723.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,symmetrization_of(successor_relation)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),inverse(successor_relation))*.
% 299.89/300.47  194091[10:Res:5768.2,193819.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,cantor(complement(cross_product(singleton(ordered_pair(u,ordered_pair(v,compose(u,v)))),universal_class))))* -> .
% 299.89/300.47  194537[0:Res:5768.2,183398.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,complement(complement(w))) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),w)*.
% 299.89/300.47  195414[0:SpR:194805.1,1943.0] || subclass(union(cross_product(u,v),w),complement(restrict(w,u,v)))* -> equal(symmetric_difference(cross_product(u,v),w),union(cross_product(u,v),w)).
% 299.89/300.47  195413[0:SpR:194805.1,1938.0] || subclass(union(u,cross_product(v,w)),complement(restrict(u,v,w)))* -> equal(symmetric_difference(u,cross_product(v,w)),union(u,cross_product(v,w))).
% 299.89/300.47  196341[6:Res:195720.1,5842.1] || equal(sum_class(u),universal_class) member(v,universal_class) well_ordering(w,sum_class(u))* -> member(least(w,unordered_pair(v,x)),unordered_pair(v,x))*.
% 299.89/300.47  196340[6:Res:195710.1,5842.1] || equal(inverse(u),universal_class) member(v,universal_class) well_ordering(w,inverse(u))* -> member(least(w,unordered_pair(v,x)),unordered_pair(v,x))*.
% 299.89/300.47  196383[6:Res:195720.1,5841.1] || equal(sum_class(u),universal_class) member(v,universal_class) well_ordering(w,sum_class(u))* -> member(least(w,unordered_pair(x,v)),unordered_pair(x,v))*.
% 299.89/300.47  196382[6:Res:195710.1,5841.1] || equal(inverse(u),universal_class) member(v,universal_class) well_ordering(w,inverse(u))* -> member(least(w,unordered_pair(x,v)),unordered_pair(x,v))*.
% 299.89/300.47  196444[10:Res:160848.0,160373.0] || well_ordering(u,image(element_relation,power_class(universal_class))) -> equal(segment(u,complement(power_class(image(element_relation,successor_relation))),least(u,complement(power_class(image(element_relation,successor_relation))))),successor_relation)**.
% 299.89/300.47  196496[10:Res:161138.0,160373.0] || well_ordering(u,image(element_relation,symmetrization_of(successor_relation))) -> equal(segment(u,complement(power_class(complement(inverse(successor_relation)))),least(u,complement(power_class(complement(inverse(successor_relation)))))),successor_relation)**.
% 299.89/300.47  196636[10:Res:160971.0,160373.0] || well_ordering(u,image(element_relation,power_class(successor_relation))) -> equal(segment(u,complement(power_class(image(element_relation,universal_class))),least(u,complement(power_class(image(element_relation,universal_class))))),successor_relation)**.
% 299.89/300.47  196804[10:Res:162888.0,160373.0] || well_ordering(u,image(element_relation,successor(successor_relation))) -> equal(segment(u,complement(power_class(complement(singleton(successor_relation)))),least(u,complement(power_class(complement(singleton(successor_relation)))))),successor_relation)**.
% 299.89/300.47  197068[10:Res:197034.0,162356.0] || subclass(complement(singleton(successor_relation)),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(complement(successor(successor_relation))),least(omega,complement(singleton(successor_relation))))),successor_relation)**.
% 299.89/300.47  200310[6:MRR:200309.1,199831.0] || member(u,universal_class) member(ordered_pair(ordered_pair(second(regular(rest_relation)),first(regular(rest_relation))),u),v)* -> member(ordered_pair(regular(rest_relation),u),flip(v)).
% 299.89/300.47  200312[6:MRR:200311.1,199831.0] || member(u,universal_class) member(ordered_pair(ordered_pair(second(regular(rest_relation)),u),first(regular(rest_relation))),v)* -> member(ordered_pair(regular(rest_relation),u),rotate(v)).
% 299.89/300.47  200718[10:Res:161493.2,129.3] inductive(u) || member(v,w) subclass(w,x)* well_ordering(u,x)* -> equal(integer_of(ordered_pair(v,least(u,w))),successor_relation)**.
% 299.89/300.47  200654[10:Res:161493.2,162356.0] inductive(u) || subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(w),successor_relation) equal(integer_of(ordered_pair(w,least(omega,u))),successor_relation)**.
% 299.89/300.47  201057[10:Res:51387.0,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> subclass(w,complement(u)) equal(integer_of(ordered_pair(not_subclass_element(w,complement(u)),least(omega,u))),successor_relation)**.
% 299.89/300.47  201147[10:Res:200239.1,162356.0] || equal(cross_product(universal_class,universal_class),ordinal_numbers) subclass(kind_1_ordinals,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(rest_relation),least(omega,kind_1_ordinals))),successor_relation)**.
% 299.89/300.47  201554[6:MRR:201553.1,201221.0] || member(u,universal_class) member(ordered_pair(ordered_pair(second(regular(domain_relation)),first(regular(domain_relation))),u),v)* -> member(ordered_pair(regular(domain_relation),u),flip(v)).
% 299.89/300.47  201556[6:MRR:201555.1,201221.0] || member(u,universal_class) member(ordered_pair(ordered_pair(second(regular(domain_relation)),u),first(regular(domain_relation))),v)* -> member(ordered_pair(regular(domain_relation),u),rotate(v)).
% 299.89/300.47  201847[10:Res:201474.1,162356.0] || equal(cross_product(universal_class,universal_class),ordinal_numbers) subclass(kind_1_ordinals,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(domain_relation),least(omega,kind_1_ordinals))),successor_relation)**.
% 299.89/300.47  202768[10:Rew:161194.0,202707.1,161194.0,202707.0] || member(symmetric_difference(complement(u),universal_class),universal_class) -> equal(symmetric_difference(complement(u),universal_class),successor_relation) member(apply(choice,symmetric_difference(complement(u),universal_class)),union(u,successor_relation))*.
% 299.89/300.47  203567[10:Rew:203192.0,162461.2] || section(universal_class,u,v) well_ordering(w,u) -> equal(segment(w,cantor(cross_product(v,u)),least(w,cantor(cross_product(v,u)))),successor_relation)**.
% 299.89/300.47  203586[6:Rew:203192.0,41911.2] || member(not_subclass_element(cross_product(u,v),w),rest_of(x)) -> subclass(cross_product(u,v),w) member(first(not_subclass_element(cross_product(u,v),w)),cantor(x))*.
% 299.89/300.47  203975[6:Rew:203192.0,200249.0] || member(first(regular(rest_relation)),cantor(u)) equal(restrict(u,first(regular(rest_relation)),universal_class),second(regular(rest_relation)))** -> member(regular(rest_relation),rest_of(u)).
% 299.89/300.47  203982[6:Rew:203192.0,201493.0] || member(first(regular(domain_relation)),cantor(u)) equal(restrict(u,first(regular(domain_relation)),universal_class),second(regular(domain_relation)))** -> member(regular(domain_relation),rest_of(u)).
% 299.89/300.47  204082[6:Rew:203285.0,108779.2] inductive(intersection(u,cantor(inverse(v)))) || well_ordering(w,range_of(v)) -> member(least(w,intersection(u,range_of(v))),intersection(u,range_of(v)))*.
% 299.89/300.47  204132[6:Rew:203285.0,108304.2] inductive(complement(complement(cantor(inverse(u))))) || well_ordering(v,range_of(u)) -> member(least(v,complement(complement(range_of(u)))),complement(complement(range_of(u))))*.
% 299.89/300.47  204835[6:Rew:204042.0,204139.2] inductive(symmetric_difference(range_of(u),universal_class)) || well_ordering(v,complement(range_of(u))) -> member(least(v,symmetric_difference(universal_class,range_of(u))),symmetric_difference(universal_class,range_of(u)))*.
% 299.89/300.47  204160[6:Rew:203285.0,108761.2] inductive(intersection(cantor(inverse(u)),v)) || well_ordering(w,range_of(u)) -> member(least(w,intersection(range_of(u),v)),intersection(range_of(u),v))*.
% 299.89/300.47  204473[6:Rew:203335.0,131349.2] inductive(cantor(restrict(u,v,singleton(w)))) || well_ordering(x,universal_class) -> member(least(x,segment(u,v,w)),segment(u,v,w))*.
% 299.89/300.47  204488[6:Rew:204482.0,149967.2] inductive(cantor(inverse(restrict(u,v,universal_class)))) || well_ordering(w,image(u,v)) -> member(least(w,image(u,v)),image(u,v))*.
% 299.89/300.47  206253[10:Res:206224.1,2078.1] || member(successor_relation,not_well_ordering(u,successor(successor_relation)))* connected(u,successor(successor_relation)) -> well_ordering(u,successor(successor_relation)) equal(not_well_ordering(u,successor(successor_relation)),successor(successor_relation)).
% 299.89/300.47  192617[10:Res:163188.1,162356.0] || equal(symmetrization_of(successor_relation),universal_class) subclass(inverse(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(omega,least(omega,inverse(successor_relation)))),successor_relation)**.
% 299.89/300.47  209514[12:SpR:209433.0,203278.2] || member(first(regular(element_relation)),cantor(u)) equal(restrict(u,first(regular(element_relation)),universal_class),second(regular(element_relation)))** -> member(regular(element_relation),rest_of(u)).
% 299.89/300.47  209574[12:MRR:209573.1,209313.0] || member(u,universal_class) member(ordered_pair(ordered_pair(second(regular(element_relation)),first(regular(element_relation))),u),v)* -> member(ordered_pair(regular(element_relation),u),flip(v)).
% 299.89/300.47  209576[12:MRR:209575.1,209313.0] || member(u,universal_class) member(ordered_pair(ordered_pair(second(regular(element_relation)),u),first(regular(element_relation))),v)* -> member(ordered_pair(regular(element_relation),u),rotate(v)).
% 299.89/300.47  210328[12:Res:209505.1,162356.0] || equal(cross_product(universal_class,universal_class),ordinal_numbers) subclass(kind_1_ordinals,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(regular(element_relation),least(omega,kind_1_ordinals))),successor_relation)**.
% 299.89/300.47  210396[15:Res:189563.1,96.1] || subclass(domain_relation,flip(cross_product(universal_class,universal_class))) equal(compose(u,ordered_pair(v,w)),successor_relation) -> member(ordered_pair(ordered_pair(v,w),successor_relation),compose_class(u))*.
% 299.89/300.47  210891[15:Res:210104.1,162356.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(power_class(successor_relation),successor_relation),least(omega,rest_relation))),successor_relation)**.
% 299.89/300.47  210927[15:Res:210139.1,162356.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(regular(rest_relation),successor_relation),least(omega,rest_relation))),successor_relation)**.
% 299.89/300.47  210935[15:Res:210174.1,162356.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(regular(domain_relation),successor_relation),least(omega,rest_relation))),successor_relation)**.
% 299.89/300.47  210943[15:Res:210209.1,162356.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(regular(element_relation),successor_relation),least(omega,rest_relation))),successor_relation)**.
% 299.89/300.47  211029[15:Res:210293.1,162356.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(ordered_pair(singleton(v),successor_relation),least(omega,rest_relation))),successor_relation)**.
% 299.89/300.47  211047[15:Res:211028.1,162356.0] || subclass(rest_relation,domain_relation) subclass(rest_relation,u) well_ordering(omega,u)* -> equal(integer_of(ordered_pair(singleton(singleton(singleton(successor_relation))),least(omega,rest_relation))),successor_relation)**.
% 299.89/300.47  211637[10:Res:211579.1,162356.0] || subclass(complement(u),v)* well_ordering(omega,v) -> member(singleton(successor_relation),u) equal(integer_of(ordered_pair(singleton(successor_relation),least(omega,complement(u)))),successor_relation)**.
% 299.89/300.47  211667[10:Res:181213.1,162356.0] || equal(u,singleton(singleton(successor_relation))) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(successor_relation),least(omega,u))),successor_relation)**.
% 299.89/300.47  211972[11:Res:183759.1,3874.1] || subclass(inverse(successor_relation),complement(intersection(u,v)))* member(regular(symmetrization_of(successor_relation)),union(u,v)) -> member(regular(symmetrization_of(successor_relation)),symmetric_difference(u,v)).
% 299.89/300.47  211965[11:Res:183759.1,162356.0] || subclass(inverse(successor_relation),u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(symmetrization_of(successor_relation)),least(omega,u))),successor_relation)**.
% 299.89/300.47  212545[13:Res:212515.0,162356.0] || subclass(image(element_relation,successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(complement(power_class(universal_class))),least(omega,image(element_relation,successor_relation)))),successor_relation)**.
% 299.89/300.47  212649[10:Res:212518.0,162356.0] || subclass(image(element_relation,universal_class),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(complement(power_class(successor_relation))),least(omega,image(element_relation,universal_class)))),successor_relation)**.
% 299.89/300.47  212812[15:Res:5768.2,203931.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,cross_product(universal_class,universal_class)) member(ordered_pair(v,compose(u,v)),cantor(u))* -> .
% 299.89/300.47  213196[15:Res:189485.1,162356.0] || subclass(domain_relation,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(singleton(singleton(singleton(successor_relation))),least(omega,u))),successor_relation)**.
% 299.89/300.47  215859[10:Res:197082.1,162356.0] || subclass(universal_class,u) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(complement(successor(successor_relation))),least(omega,u))),successor_relation)**.
% 299.89/300.47  216100[10:Res:199830.1,162356.0] || equal(u,cross_product(universal_class,universal_class)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(rest_relation),least(omega,u))),successor_relation)**.
% 299.89/300.47  216708[10:Res:201220.1,162356.0] || equal(u,cross_product(universal_class,universal_class)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(regular(domain_relation),least(omega,u))),successor_relation)**.
% 299.89/300.47  217255[10:Res:217225.1,129.3] || equal(singleton(ordered_pair(u,least(singleton(successor_relation),v))),kind_1_ordinals)** member(u,v) subclass(v,w)* well_ordering(singleton(successor_relation),w)* -> .
% 299.89/300.47  217245[10:Res:217225.1,162356.0] || equal(singleton(u),kind_1_ordinals) subclass(singleton(successor_relation),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(u,least(omega,singleton(successor_relation)))),successor_relation)**.
% 299.89/300.47  217418[20:Res:217226.1,129.3] || equal(singleton(ordered_pair(u,least(singleton(successor_relation),v))),omega)** member(u,v) subclass(v,w)* well_ordering(singleton(successor_relation),w)* -> .
% 299.89/300.47  217408[20:Res:217226.1,162356.0] || equal(singleton(u),omega) subclass(singleton(successor_relation),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(u,least(omega,singleton(successor_relation)))),successor_relation)**.
% 299.89/300.47  217597[10:MRR:217548.0,13.0] || subclass(universal_class,regular(intersection(complement(u),complement(v))))* -> member(unordered_pair(w,x),union(u,v))* equal(intersection(complement(u),complement(v)),successor_relation).
% 299.89/300.47  217939[3:Obv:217922.2] || subclass(unordered_pair(u,v),complement(kind_1_ordinals))* member(v,ordinal_numbers) -> equal(not_subclass_element(unordered_pair(u,v),w),u)** subclass(unordered_pair(u,v),w).
% 299.89/300.47  217940[3:Obv:217921.2] || subclass(unordered_pair(u,v),complement(kind_1_ordinals))* member(u,ordinal_numbers) -> equal(not_subclass_element(unordered_pair(u,v),w),v)** subclass(unordered_pair(u,v),w).
% 299.89/300.47  218325[10:MRR:218282.0,34189.1] ||  -> member(not_subclass_element(regular(image(element_relation,complement(u))),v),power_class(u))* subclass(regular(image(element_relation,complement(u))),v) equal(image(element_relation,complement(u)),successor_relation).
% 299.89/300.47  219216[3:Res:5768.2,218628.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,complement(kind_1_ordinals)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),complement(ordinal_numbers))*.
% 299.89/300.47  163649[10:Rew:160202.0,160673.2,160202.0,160673.1] || member(ordered_pair(u,regular(range_of(successor_relation))),cross_product(universal_class,universal_class)) -> equal(range_of(successor_relation),successor_relation) member(ordered_pair(u,regular(range_of(successor_relation))),compose(successor_relation,v))*.
% 299.89/300.47  195924[10:Rew:193730.0,195912.1] || member(ordered_pair(u,not_subclass_element(v,image(w,range_of(successor_relation)))),compose(w,complement(cross_product(singleton(u),universal_class))))* -> subclass(v,image(w,range_of(successor_relation))).
% 299.89/300.47  166961[10:Res:3872.2,163256.1] || member(successor_relation,cross_product(u,v)) member(successor_relation,w) equal(restrict(w,u,v),range_of(successor_relation)) -> inductive(restrict(w,u,v))*.
% 299.89/300.47  216971[10:MRR:216970.3,160227.0] || equal(compose_class(u),domain_relation) member(ordered_pair(v,regular(image(u,range_of(successor_relation)))),cross_product(universal_class,universal_class))* -> equal(image(u,range_of(successor_relation)),successor_relation).
% 299.89/300.47  206171[10:Res:203330.1,163335.1] inductive(cantor(restrict(u,v,range_of(successor_relation)))) || section(u,range_of(successor_relation),v) -> equal(cantor(restrict(u,v,range_of(successor_relation))),range_of(successor_relation))**.
% 299.89/300.47  204008[10:Rew:203192.0,164293.2] inductive(domain_of(restrict(u,v,range_of(successor_relation)))) || section(u,range_of(successor_relation),v) -> equal(cantor(restrict(u,v,range_of(successor_relation))),range_of(successor_relation))**.
% 299.89/300.47  163696[10:Rew:160305.0,162837.1,160305.0,162837.0,160202.0,162837.0] ||  -> equal(intersection(intersection(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u),v),successor_relation) member(regular(intersection(intersection(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u),v)),kind_1_ordinals)*.
% 299.89/300.47  163695[10:Rew:160305.0,162833.1,160305.0,162833.0,160202.0,162833.0] ||  -> equal(intersection(intersection(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),v),successor_relation) member(regular(intersection(intersection(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),v)),kind_1_ordinals)*.
% 299.89/300.47  163697[10:Rew:160305.0,162845.1,160305.0,162845.0,160202.0,162845.0] ||  -> equal(intersection(u,intersection(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),v)),successor_relation) member(regular(intersection(u,intersection(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),v))),kind_1_ordinals)*.
% 299.89/300.47  163698[10:Rew:160305.0,162846.1,160305.0,162846.0,160202.0,162846.0] ||  -> equal(intersection(u,intersection(v,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),successor_relation) member(regular(intersection(u,intersection(v,symmetric_difference(singleton(successor_relation),range_of(successor_relation))))),kind_1_ordinals)*.
% 299.89/300.47  221493[10:Res:218373.0,5553.2] || member(u,v) member(w,x) -> equal(singleton(cross_product(x,v)),successor_relation) member(ordered_pair(w,u),complement(singleton(cross_product(x,v))))*.
% 299.89/300.47  221635[10:Res:28321.1,185698.1] inductive(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u)))) || subclass(rest_relation,flip(ordinal_numbers)) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  221633[10:Res:28320.1,185698.1] inductive(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v)) || subclass(rest_relation,rotate(ordinal_numbers)) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  221858[10:Res:137.1,160703.0] || member(complement(compose(element_relation,universal_class)),ordinal_numbers) member(regular(sum_class(complement(compose(element_relation,universal_class)))),element_relation)* -> equal(sum_class(complement(compose(element_relation,universal_class))),successor_relation).
% 299.89/300.47  221881[10:MRR:221865.3,160371.1] || connected(u,complement(compose(element_relation,universal_class))) member(regular(not_well_ordering(u,complement(compose(element_relation,universal_class)))),element_relation)* -> well_ordering(u,complement(compose(element_relation,universal_class))).
% 299.89/300.47  222247[15:Res:25.2,189380.2] || member(ordered_pair(u,successor_relation),v)* member(ordered_pair(u,successor_relation),w)* member(u,universal_class) subclass(domain_relation,complement(intersection(w,v)))* -> .
% 299.89/300.47  222469[24:SpL:222326.0,61.0] || member(u,image(v,image(w,successor_relation))) member(ordered_pair(kind_1_ordinals,u),cross_product(universal_class,universal_class)) -> member(ordered_pair(kind_1_ordinals,u),compose(v,w))*.
% 299.89/300.47  223147[24:Res:223096.0,5838.1] || member(u,universal_class) well_ordering(v,symmetric_difference(universal_class,kind_1_ordinals)) -> member(u,successor(kind_1_ordinals))* member(least(v,complement(successor(kind_1_ordinals))),complement(successor(kind_1_ordinals)))*.
% 299.89/300.47  224326[25:Rew:224236.1,204854.3] function(u) function(v) || subclass(range_of(v),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(v,w,apply(u,x))*.
% 299.89/300.47  224348[25:Rew:224236.1,221108.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> compatible(u,v,regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation))))*.
% 299.89/300.47  224355[25:Rew:224236.1,204857.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> subclass(w,x) compatible(u,v,not_subclass_element(w,x))*.
% 299.89/300.47  224356[25:Rew:224236.1,204856.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> equal(singleton(cantor(w)),successor_relation) compatible(u,v,w)*.
% 299.89/300.47  224357[25:Rew:224236.1,204855.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> equal(integer_of(cantor(w)),successor_relation) compatible(u,v,w)*.
% 299.89/300.47  224389[25:Rew:224236.1,204853.3] function(u) || equal(successor_relation,v) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,power_class(v))*.
% 299.89/300.47  224390[25:Rew:224236.1,204852.3] function(u) || member(v,universal_class) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,power_class(v))*.
% 299.89/300.47  224391[25:Rew:224236.1,204851.3] function(u) || member(v,universal_class) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,sum_class(v))*.
% 299.89/300.47  224392[25:Rew:224236.1,204850.3] function(u) || member(v,universal_class) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,rest_of(v))*.
% 299.89/300.47  224393[25:Rew:224236.1,204849.3] function(u) || equal(cantor(v),successor_relation) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,v)*.
% 299.89/300.47  224394[25:Rew:224236.1,204848.3] function(u) || equal(rest_of(v),successor_relation) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,v)*.
% 299.89/300.47  224665[25:SpR:224236.1,203332.2] function(restrict(u,v,w)) || section(u,w,v)* well_ordering(x,w)* -> equal(segment(x,universal_class,least(x,universal_class)),successor_relation)**.
% 299.89/300.47  226011[15:SpL:1931.0,189381.1] || member(u,universal_class) subclass(domain_relation,symmetric_difference(complement(intersection(v,w)),union(v,w)))* -> member(ordered_pair(u,successor_relation),complement(symmetric_difference(v,w)))*.
% 299.89/300.47  226360[25:Rew:226350.1,224769.1] one_to_one(restrict(element_relation,universal_class,u)) || subclass(universal_class,cantor(sum_class(u))) equal(cross_product(cantor(sum_class(u)),cantor(sum_class(u))),sum_class(u))** -> .
% 299.89/300.47  226405[25:SpL:226350.1,224318.1] one_to_one(u) function(v) || subclass(range_of(v),cantor(universal_class)) equal(cantor(cantor(w)),universal_class) -> compatible(v,w,inverse(u))*.
% 299.89/300.47  226608[10:Res:161880.1,185698.1] inductive(regular(intersection(intersection(ordinal_numbers,u),v))) ||  -> equal(intersection(intersection(ordinal_numbers,u),v),successor_relation)** equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  227199[10:Res:161881.1,185698.1] inductive(regular(intersection(intersection(u,ordinal_numbers),v))) ||  -> equal(intersection(intersection(u,ordinal_numbers),v),successor_relation)** equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  227324[25:Res:224913.1,162356.0] function(u) || subclass(ordered_pair(u,v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(successor_relation,least(omega,ordered_pair(u,v)))),successor_relation)**.
% 299.89/300.47  227495[10:Res:161874.1,185698.1] inductive(regular(intersection(u,intersection(ordinal_numbers,v)))) ||  -> equal(intersection(u,intersection(ordinal_numbers,v)),successor_relation)** equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  228101[10:Res:161875.1,185698.1] inductive(regular(intersection(u,intersection(v,ordinal_numbers)))) ||  -> equal(intersection(u,intersection(v,ordinal_numbers)),successor_relation)** equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  228397[10:Res:161722.2,185698.1] inductive(regular(intersection(u,v))) || subclass(u,ordinal_numbers) -> equal(intersection(u,v),successor_relation)** equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  228618[10:Res:161711.2,185698.1] inductive(regular(intersection(u,v))) || subclass(v,ordinal_numbers) -> equal(intersection(u,v),successor_relation)** equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  228982[10:Res:163219.0,160788.0] || subclass(kind_1_ordinals,u) -> equal(symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation))),successor_relation) member(regular(symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation)))),u)*.
% 299.89/300.47  230545[10:Res:5768.2,229800.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,singleton(omega)) -> equal(integer_of(ordered_pair(u,ordered_pair(v,compose(u,v)))),successor_relation)**.
% 299.89/300.47  230993[0:SpR:194805.1,10028.0] || subclass(complement(inverse(image(element_relation,complement(u)))),power_class(u))* -> equal(complement(complement(inverse(image(element_relation,complement(u))))),symmetrization_of(image(element_relation,complement(u)))).
% 299.89/300.47  230909[0:SpR:10028.0,139600.0] ||  -> equal(intersection(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),complement(symmetrization_of(image(element_relation,complement(u))))),complement(symmetrization_of(image(element_relation,complement(u)))))**.
% 299.89/300.47  231317[0:SpR:194805.1,10029.0] || subclass(complement(singleton(image(element_relation,complement(u)))),power_class(u))* -> equal(complement(complement(singleton(image(element_relation,complement(u))))),successor(image(element_relation,complement(u)))).
% 299.89/300.47  231231[0:SpR:10029.0,139600.0] ||  -> equal(intersection(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),complement(successor(image(element_relation,complement(u))))),complement(successor(image(element_relation,complement(u)))))**.
% 299.89/300.47  231820[10:Res:1495.2,161035.0] || member(u,universal_class) subclass(rest_relation,intersection(power_class(successor_relation),complement(v))) member(ordered_pair(u,rest_of(u)),union(image(element_relation,universal_class),v))* -> .
% 299.89/300.47  10498[0:Res:25.2,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),u) member(least(element_relation,intersection(y__dfg,ordinal_numbers)),v) subclass(intersection(v,u),intersection(y__dfg,ordinal_numbers))* -> .
% 299.89/300.47  29192[0:SpR:506.0,161.0] ||  -> equal(intersection(complement(intersection(intersection(complement(u),complement(v)),w)),complement(intersection(union(u,v),complement(w)))),symmetric_difference(intersection(complement(u),complement(v)),w))**.
% 299.89/300.47  29276[0:SpR:507.0,161.0] ||  -> equal(intersection(complement(intersection(u,intersection(complement(v),complement(w)))),complement(intersection(complement(u),union(v,w)))),symmetric_difference(u,intersection(complement(v),complement(w))))**.
% 299.89/300.47  6324[0:Res:131.2,3926.1] single_valued_class(not_well_ordering(u,cross_product(universal_class,universal_class))) || connected(u,cross_product(universal_class,universal_class)) -> well_ordering(u,cross_product(universal_class,universal_class)) function(not_well_ordering(u,cross_product(universal_class,universal_class)))*.
% 299.89/300.47  43989[0:Res:999.0,6036.0] || member(ordered_pair(u,least(intersection(v,universal_class),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,universal_class),x)* -> .
% 299.89/300.47  6034[0:SpL:1005.0,129.3] || member(singleton(least(u,v)),v)* subclass(v,w)* well_ordering(u,w)* member(singleton(singleton(singleton(least(u,v)))),u)* -> .
% 299.89/300.47  39654[0:SpL:41.0,5919.0] || member(u,range_of(v))* subclass(rest_of(inverse(v)),w)* well_ordering(x,w)* -> member(least(x,rest_of(inverse(v))),rest_of(inverse(v)))*.
% 299.89/300.47  35709[0:Res:1478.2,3874.1] || member(u,universal_class) subclass(universal_class,complement(intersection(v,w)))* member(power_class(u),union(v,w)) -> member(power_class(u),symmetric_difference(v,w))*.
% 299.89/300.47  39959[0:Res:58.1,5554.0] || member(u,universal_class) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,power_class(u))),second(ordered_pair(v,power_class(u)))),ordered_pair(v,power_class(u)))**.
% 299.89/300.47  38398[0:Res:6010.3,3.0] || member(u,universal_class) member(v,universal_class) equal(compose(w,v),u)* subclass(compose_class(w),x)* -> member(ordered_pair(v,u),x)*.
% 299.89/300.47  112494[0:MRR:112459.0,999.0] || member(u,v) subclass(v,w)* well_ordering(union(x,y),w)* -> member(ordered_pair(u,least(union(x,y),v)),complement(y))*.
% 299.89/300.47  112655[0:MRR:112626.0,999.0] || member(u,v) subclass(v,w)* well_ordering(union(x,y),w)* -> member(ordered_pair(u,least(union(x,y),v)),complement(x))*.
% 299.89/300.47  125974[0:Res:28320.1,129.3] || subclass(rest_relation,rotate(u)) member(ordered_pair(v,rest_of(ordered_pair(least(u,w),v))),w)* subclass(w,x)* well_ordering(u,x)* -> .
% 299.89/300.47  149602[6:Rew:148462.0,42844.2] || connected(u,v)* member(w,v)* well_ordering(x,complement(complement(symmetrization_of(u))))* -> member(least(x,cross_product(v,v)),cross_product(v,v))*.
% 299.89/300.47  155786[2:MRR:155785.0,34067.1] || member(u,complement(v))* subclass(symmetric_difference(universal_class,v),w)* well_ordering(x,w)* -> member(least(x,symmetric_difference(universal_class,v)),symmetric_difference(universal_class,v))*.
% 299.89/300.47  6261[0:Res:1499.1,39.1] || subclass(universal_class,cross_product(cross_product(universal_class,universal_class),universal_class)) member(ordered_pair(ordered_pair(u,v),w),x) -> member(ordered_pair(ordered_pair(v,u),w),flip(x))*.
% 299.89/300.47  6270[0:Res:1499.1,36.1] || subclass(universal_class,cross_product(cross_product(universal_class,universal_class),universal_class)) member(ordered_pair(ordered_pair(u,v),w),x) -> member(ordered_pair(ordered_pair(w,u),v),rotate(x))*.
% 299.89/300.47  130413[0:Res:3595.3,9300.0] function(u) || member(v,universal_class) subclass(universal_class,symmetric_difference(w,cross_product(x,y))) -> member(image(u,v),complement(restrict(w,x,y)))*.
% 299.89/300.47  130506[0:Res:3595.3,9306.0] function(u) || member(v,universal_class) subclass(universal_class,symmetric_difference(cross_product(w,x),y)) -> member(image(u,v),complement(restrict(y,w,x)))*.
% 299.89/300.47  122746[0:Res:120366.1,5554.0] || member(u,universal_class) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,rest_of(u))),second(ordered_pair(v,rest_of(u)))),ordered_pair(v,rest_of(u)))**.
% 299.89/300.47  123507[0:Res:978.1,9322.0] ||  -> subclass(restrict(symmetric_difference(complement(u),complement(v)),w,x),y) member(not_subclass_element(restrict(symmetric_difference(complement(u),complement(v)),w,x),y),union(u,v))*.
% 299.89/300.47  130498[0:Res:340.1,9306.0] ||  -> subclass(intersection(symmetric_difference(cross_product(u,v),w),x),y) member(not_subclass_element(intersection(symmetric_difference(cross_product(u,v),w),x),y),complement(restrict(w,u,v)))*.
% 299.89/300.47  130405[0:Res:340.1,9300.0] ||  -> subclass(intersection(symmetric_difference(u,cross_product(v,w)),x),y) member(not_subclass_element(intersection(symmetric_difference(u,cross_product(v,w)),x),y),complement(restrict(u,v,w)))*.
% 299.89/300.47  130500[0:Res:322.1,9306.0] ||  -> subclass(intersection(u,symmetric_difference(cross_product(v,w),x)),y) member(not_subclass_element(intersection(u,symmetric_difference(cross_product(v,w),x)),y),complement(restrict(x,v,w)))*.
% 299.89/300.47  130407[0:Res:322.1,9300.0] ||  -> subclass(intersection(u,symmetric_difference(v,cross_product(w,x))),y) member(not_subclass_element(intersection(u,symmetric_difference(v,cross_product(w,x))),y),complement(restrict(v,w,x)))*.
% 299.89/300.47  130497[0:Res:34429.0,9306.0] ||  -> subclass(complement(complement(symmetric_difference(cross_product(u,v),w))),x) member(not_subclass_element(complement(complement(symmetric_difference(cross_product(u,v),w))),x),complement(restrict(w,u,v)))*.
% 299.89/300.47  130404[0:Res:34429.0,9300.0] ||  -> subclass(complement(complement(symmetric_difference(u,cross_product(v,w)))),x) member(not_subclass_element(complement(complement(symmetric_difference(u,cross_product(v,w)))),x),complement(restrict(u,v,w)))*.
% 299.89/300.47  3880[0:Res:25.2,309.0] || member(not_subclass_element(complement(intersection(u,v)),w),v)* member(not_subclass_element(complement(intersection(u,v)),w),u)* -> subclass(complement(intersection(u,v)),w).
% 299.89/300.47  108479[0:Res:1504.1,2142.0] || subclass(ordered_pair(u,v),ordered_pair(w,x))* -> equal(unordered_pair(u,singleton(v)),unordered_pair(w,singleton(x))) equal(unordered_pair(u,singleton(v)),singleton(w)).
% 299.89/300.47  40268[0:Rew:2143.2,40267.1] || member(u,v) member(u,w) -> equal(not_subclass_element(unordered_pair(u,x),intersection(w,v)),x)** subclass(unordered_pair(u,x),intersection(w,v)).
% 299.89/300.47  113263[0:Obv:113186.1] || member(u,v) -> equal(not_subclass_element(unordered_pair(u,w),intersection(v,unordered_pair(u,w))),w)** subclass(unordered_pair(u,w),intersection(v,unordered_pair(u,w))).
% 299.89/300.47  40266[0:Rew:2143.1,40265.1] || member(u,v) member(u,w) -> equal(not_subclass_element(unordered_pair(x,u),intersection(w,v)),x)** subclass(unordered_pair(x,u),intersection(w,v)).
% 299.89/300.47  113262[0:Obv:113187.1] || member(u,v) -> equal(not_subclass_element(unordered_pair(w,u),intersection(v,unordered_pair(w,u))),w)** subclass(unordered_pair(w,u),intersection(v,unordered_pair(w,u))).
% 299.89/300.47  108445[0:Res:1504.1,19.0] || subclass(ordered_pair(u,v),cross_product(w,x))* -> equal(ordered_pair(first(unordered_pair(u,singleton(v))),second(unordered_pair(u,singleton(v)))),unordered_pair(u,singleton(v)))**.
% 299.89/300.47  112451[0:Res:30985.1,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class) subclass(union(u,v),intersection(y__dfg,ordinal_numbers))* -> member(least(element_relation,intersection(y__dfg,ordinal_numbers)),complement(v))*.
% 299.89/300.47  112618[0:Res:30984.1,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class) subclass(union(u,v),intersection(y__dfg,ordinal_numbers))* -> member(least(element_relation,intersection(y__dfg,ordinal_numbers)),complement(u))*.
% 299.89/300.47  28086[0:SpR:124.0,1496.2] || member(restrict(u,v,singleton(w)),universal_class) subclass(domain_relation,x) -> member(ordered_pair(restrict(u,v,singleton(w)),segment(u,v,w)),x)*.
% 299.89/300.47  35708[0:Res:1479.2,3874.1] || member(u,universal_class) subclass(universal_class,complement(intersection(v,w)))* member(sum_class(u),union(v,w)) -> member(sum_class(u),symmetric_difference(v,w))*.
% 299.89/300.47  39961[0:Res:56.1,5554.0] || member(u,universal_class) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,sum_class(u))),second(ordered_pair(v,sum_class(u)))),ordered_pair(v,sum_class(u)))**.
% 299.89/300.47  139693[0:SpR:982.0,509.0] ||  -> equal(complement(intersection(complement(u),power_class(intersection(power_class(image(element_relation,complement(v))),complement(w))))),union(u,image(element_relation,union(image(element_relation,power_class(v)),w))))**.
% 299.89/300.47  139649[0:SpR:982.0,511.0] ||  -> equal(complement(intersection(power_class(intersection(power_class(image(element_relation,complement(u))),complement(v))),complement(w))),union(image(element_relation,union(image(element_relation,power_class(u)),v)),w))**.
% 299.89/300.47  30958[0:SpR:505.0,1032.1] || member(u,universal_class) -> member(u,intersection(complement(v),power_class(intersection(complement(w),complement(x)))))* member(u,union(v,image(element_relation,union(w,x)))).
% 299.89/300.47  140154[0:SpR:984.0,509.0] ||  -> equal(complement(intersection(complement(u),power_class(intersection(complement(v),power_class(image(element_relation,complement(w))))))),union(u,image(element_relation,union(v,image(element_relation,power_class(w))))))**.
% 299.89/300.47  140185[0:SpR:505.0,984.0] ||  -> equal(complement(intersection(complement(u),power_class(image(element_relation,power_class(intersection(complement(v),complement(w))))))),union(u,image(element_relation,power_class(image(element_relation,union(v,w))))))**.
% 299.89/300.47  30971[0:SpR:505.0,1032.1] || member(u,universal_class) -> member(u,intersection(power_class(intersection(complement(v),complement(w))),complement(x)))* member(u,union(image(element_relation,union(v,w)),x)).
% 299.89/300.47  139724[0:SpR:505.0,982.0] ||  -> equal(complement(intersection(power_class(image(element_relation,complement(u))),power_class(intersection(complement(v),complement(w))))),union(image(element_relation,power_class(u)),image(element_relation,union(v,w))))**.
% 299.89/300.47  140109[0:SpR:984.0,511.0] ||  -> equal(complement(intersection(power_class(intersection(complement(u),power_class(image(element_relation,complement(v))))),complement(w))),union(image(element_relation,union(u,image(element_relation,power_class(v)))),w))**.
% 299.89/300.47  139744[0:SpR:505.0,982.0] ||  -> equal(complement(intersection(power_class(image(element_relation,power_class(intersection(complement(u),complement(v))))),complement(w))),union(image(element_relation,power_class(image(element_relation,union(u,v)))),w))**.
% 299.89/300.47  107260[0:Rew:505.0,107163.1] ||  -> member(not_subclass_element(complement(power_class(intersection(complement(u),complement(v)))),w),image(element_relation,union(u,v)))* subclass(complement(power_class(intersection(complement(u),complement(v)))),w).
% 299.89/300.47  140206[0:SpR:505.0,984.0] ||  -> equal(complement(intersection(power_class(intersection(complement(u),complement(v))),power_class(image(element_relation,complement(w))))),union(image(element_relation,union(u,v)),image(element_relation,power_class(w))))**.
% 299.89/300.47  124297[0:Res:3595.3,986.1] function(u) || member(v,universal_class) subclass(universal_class,power_class(image(element_relation,complement(w)))) member(image(u,v),image(element_relation,power_class(w)))* -> .
% 299.89/300.47  125149[0:Rew:208.0,125106.1] ||  -> member(not_subclass_element(u,image(element_relation,power_class(image(element_relation,complement(v))))),power_class(image(element_relation,power_class(v))))* subclass(u,image(element_relation,power_class(image(element_relation,complement(v))))).
% 299.89/300.47  29356[0:SpR:208.0,1948.0] ||  -> equal(intersection(union(u,image(element_relation,power_class(v))),union(complement(u),power_class(image(element_relation,complement(v))))),symmetric_difference(complement(u),power_class(image(element_relation,complement(v)))))**.
% 299.89/300.47  124291[0:Res:322.1,986.1] || member(not_subclass_element(intersection(u,power_class(image(element_relation,complement(v)))),w),image(element_relation,power_class(v)))* -> subclass(intersection(u,power_class(image(element_relation,complement(v)))),w).
% 299.89/300.47  29368[0:SpR:208.0,1948.0] ||  -> equal(intersection(union(image(element_relation,power_class(u)),v),union(power_class(image(element_relation,complement(u))),complement(v))),symmetric_difference(power_class(image(element_relation,complement(u))),complement(v)))**.
% 299.89/300.47  124289[0:Res:340.1,986.1] || member(not_subclass_element(intersection(power_class(image(element_relation,complement(u))),v),w),image(element_relation,power_class(u)))* -> subclass(intersection(power_class(image(element_relation,complement(u))),v),w).
% 299.89/300.47  124288[0:Res:34429.0,986.1] || member(not_subclass_element(complement(complement(power_class(image(element_relation,complement(u))))),v),image(element_relation,power_class(u)))* -> subclass(complement(complement(power_class(image(element_relation,complement(u))))),v).
% 299.89/300.47  40064[0:Rew:57.0,40055.3] || member(u,v) subclass(v,w)* well_ordering(power_class(x),w)* -> member(ordered_pair(u,least(power_class(x),v)),image(element_relation,complement(x)))*.
% 299.89/300.47  137249[0:Rew:10029.0,137095.1] ||  -> member(not_subclass_element(u,successor(image(element_relation,complement(v)))),intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))* subclass(u,successor(image(element_relation,complement(v)))).
% 299.89/300.47  137865[0:Rew:10028.0,137714.1] ||  -> member(not_subclass_element(u,symmetrization_of(image(element_relation,complement(v)))),intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))* subclass(u,symmetrization_of(image(element_relation,complement(v)))).
% 299.89/300.47  124650[0:MRR:124631.0,191.0] || member(image(element_relation,complement(u)),universal_class) -> member(singleton(image(element_relation,complement(u))),power_class(u))* member(singleton(singleton(singleton(image(element_relation,complement(u))))),element_relation)*.
% 299.89/300.47  163671[10:Rew:160202.0,160918.1] || member(regular(power_class(intersection(power_class(successor_relation),complement(u)))),image(element_relation,union(image(element_relation,universal_class),u)))* -> equal(power_class(intersection(power_class(successor_relation),complement(u))),successor_relation).
% 299.89/300.47  160924[10:Rew:160202.0,151183.0] ||  -> equal(power_class(intersection(union(image(element_relation,universal_class),u),complement(singleton(intersection(power_class(successor_relation),complement(u)))))),complement(image(element_relation,successor(intersection(power_class(successor_relation),complement(u))))))**.
% 299.89/300.47  160926[10:Rew:160202.0,151184.0] ||  -> equal(power_class(intersection(union(image(element_relation,universal_class),u),complement(inverse(intersection(power_class(successor_relation),complement(u)))))),complement(image(element_relation,symmetrization_of(intersection(power_class(successor_relation),complement(u))))))**.
% 299.89/300.47  163672[10:Rew:160202.0,160936.1] || member(regular(intersection(union(image(element_relation,universal_class),u),v)),intersection(power_class(successor_relation),complement(u)))* -> equal(intersection(union(image(element_relation,universal_class),u),v),successor_relation).
% 299.89/300.47  163673[10:Rew:160202.0,160949.1] || member(regular(power_class(intersection(complement(u),power_class(successor_relation)))),image(element_relation,union(u,image(element_relation,universal_class))))* -> equal(power_class(intersection(complement(u),power_class(successor_relation))),successor_relation).
% 299.89/300.47  160955[10:Rew:160202.0,151179.0] ||  -> equal(power_class(intersection(union(u,image(element_relation,universal_class)),complement(singleton(intersection(complement(u),power_class(successor_relation)))))),complement(image(element_relation,successor(intersection(complement(u),power_class(successor_relation))))))**.
% 299.89/300.47  160957[10:Rew:160202.0,151180.0] ||  -> equal(power_class(intersection(union(u,image(element_relation,universal_class)),complement(inverse(intersection(complement(u),power_class(successor_relation)))))),complement(image(element_relation,symmetrization_of(intersection(complement(u),power_class(successor_relation))))))**.
% 299.89/300.47  163674[10:Rew:160202.0,160967.1] || member(regular(intersection(union(u,image(element_relation,universal_class)),v)),intersection(complement(u),power_class(successor_relation)))* -> equal(intersection(union(u,image(element_relation,universal_class)),v),successor_relation).
% 299.89/300.47  163675[10:Rew:160202.0,161028.1] || member(regular(intersection(u,union(v,image(element_relation,universal_class)))),intersection(complement(v),power_class(successor_relation)))* -> equal(intersection(u,union(v,image(element_relation,universal_class))),successor_relation).
% 299.89/300.47  163676[10:Rew:160202.0,161049.1] || member(regular(intersection(u,union(image(element_relation,universal_class),v))),intersection(power_class(successor_relation),complement(v)))* -> equal(intersection(u,union(image(element_relation,universal_class),v)),successor_relation).
% 299.89/300.47  163677[10:Rew:160202.0,161077.2,160202.0,161077.1] || member(intersection(u,power_class(successor_relation)),universal_class) member(apply(choice,intersection(u,power_class(successor_relation))),image(element_relation,universal_class))* -> equal(intersection(u,power_class(successor_relation)),successor_relation).
% 299.89/300.47  163678[10:Rew:160202.0,161081.2,160202.0,161081.1] || member(intersection(power_class(successor_relation),u),universal_class) member(apply(choice,intersection(power_class(successor_relation),u)),image(element_relation,universal_class))* -> equal(intersection(power_class(successor_relation),u),successor_relation).
% 299.89/300.47  160724[10:Rew:160202.0,146449.2] || subclass(u,union(v,image(element_relation,power_class(w)))) member(regular(u),intersection(complement(v),power_class(image(element_relation,complement(w)))))* -> equal(u,successor_relation).
% 299.89/300.47  160723[10:Rew:160202.0,146450.2] || subclass(u,union(image(element_relation,power_class(v)),w)) member(regular(u),intersection(power_class(image(element_relation,complement(v))),complement(w)))* -> equal(u,successor_relation).
% 299.89/300.47  160722[10:Rew:160202.0,146452.2] || subclass(u,symmetrization_of(image(element_relation,complement(v)))) member(regular(u),intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))* -> equal(u,successor_relation).
% 299.89/300.47  160721[10:Rew:160202.0,146453.2] || subclass(u,successor(image(element_relation,complement(v)))) member(regular(u),intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))* -> equal(u,successor_relation).
% 299.89/300.47  160718[10:Rew:160202.0,146456.2] || member(u,universal_class) subclass(u,symmetric_difference(cross_product(v,w),x)) -> equal(u,successor_relation) member(apply(choice,u),complement(restrict(x,v,w)))*.
% 299.89/300.47  160717[10:Rew:160202.0,146457.2] || member(u,universal_class) subclass(u,symmetric_difference(v,cross_product(w,x))) -> equal(u,successor_relation) member(apply(choice,u),complement(restrict(v,w,x)))*.
% 299.89/300.47  160715[10:Rew:160202.0,146469.3] || member(u,universal_class) subclass(u,power_class(image(element_relation,complement(v)))) member(apply(choice,u),image(element_relation,power_class(v)))* -> equal(u,successor_relation).
% 299.89/300.47  161578[10:Rew:160202.0,146795.1] || member(cross_product(u,v),universal_class) -> equal(cross_product(u,v),successor_relation) member(singleton(first(apply(choice,cross_product(u,v)))),apply(choice,cross_product(u,v)))*.
% 299.89/300.47  161576[10:Rew:160202.0,146819.1] || member(regular(cross_product(u,v)),rest_relation) -> equal(cross_product(u,v),successor_relation) equal(rest_of(first(regular(cross_product(u,v)))),second(regular(cross_product(u,v))))**.
% 299.89/300.47  161682[10:Rew:160202.0,146726.2] || subclass(union(u,v),w)* well_ordering(x,w)* -> equal(symmetric_difference(u,v),successor_relation) member(least(x,union(u,v)),union(u,v))*.
% 299.89/300.47  161769[10:Rew:160202.0,146689.2] || subclass(unordered_pair(u,v),symmetric_difference(w,x))* -> equal(regular(unordered_pair(u,v)),v) equal(unordered_pair(u,v),successor_relation) member(u,union(w,x)).
% 299.89/300.47  161768[10:Rew:160202.0,146690.2] || subclass(unordered_pair(u,v),symmetric_difference(w,x))* -> equal(regular(unordered_pair(u,v)),u) equal(unordered_pair(u,v),successor_relation) member(v,union(w,x)).
% 299.89/300.47  161872[10:Rew:160202.0,146886.1] || member(intersection(u,intersection(v,w)),universal_class) -> equal(intersection(u,intersection(v,w)),successor_relation) member(apply(choice,intersection(u,intersection(v,w))),v)*.
% 299.89/300.47  161871[10:Rew:160202.0,146887.1] || member(intersection(u,intersection(v,w)),universal_class) -> equal(intersection(u,intersection(v,w)),successor_relation) member(apply(choice,intersection(u,intersection(v,w))),w)*.
% 299.89/300.47  161878[10:Rew:160202.0,146907.1] || member(intersection(intersection(u,v),w),universal_class) -> equal(intersection(intersection(u,v),w),successor_relation) member(apply(choice,intersection(intersection(u,v),w)),u)*.
% 299.89/300.47  161877[10:Rew:160202.0,146908.1] || member(intersection(intersection(u,v),w),universal_class) -> equal(intersection(intersection(u,v),w),successor_relation) member(apply(choice,intersection(intersection(u,v),w)),v)*.
% 299.89/300.47  162485[10:Rew:160202.0,147897.1] || member(regular(successor(image(element_relation,complement(u)))),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* -> equal(successor(image(element_relation,complement(u))),successor_relation).
% 299.89/300.47  162489[10:Rew:160202.0,147917.1] || member(regular(symmetrization_of(image(element_relation,complement(u)))),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* -> equal(symmetrization_of(image(element_relation,complement(u))),successor_relation).
% 299.89/300.47  162494[10:Rew:160202.0,147111.1] || member(ordered_pair(u,regular(complement(image(v,image(w,singleton(u)))))),compose(v,w))* -> equal(complement(image(v,image(w,singleton(u)))),successor_relation).
% 299.89/300.47  162498[10:Rew:160202.0,147113.1] || member(regular(symmetric_difference(complement(intersection(u,v)),union(u,v))),symmetric_difference(u,v))* -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),successor_relation).
% 299.89/300.47  162497[10:Rew:160202.0,147115.0] ||  -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),successor_relation) member(regular(symmetric_difference(complement(intersection(u,v)),union(u,v))),complement(symmetric_difference(u,v)))*.
% 299.89/300.47  162508[10:Rew:160202.0,147440.1] || member(regular(restrict(intersection(complement(u),complement(v)),w,x)),union(u,v))* -> equal(restrict(intersection(complement(u),complement(v)),w,x),successor_relation).
% 299.89/300.47  162509[10:Rew:160202.0,147554.1] || member(regular(image(element_relation,power_class(image(element_relation,complement(u))))),power_class(image(element_relation,power_class(u))))* -> equal(image(element_relation,power_class(image(element_relation,complement(u)))),successor_relation).
% 299.89/300.47  162524[10:Rew:160202.0,147956.1] || subclass(union(image(element_relation,power_class(u)),v),intersection(power_class(image(element_relation,complement(u))),complement(v)))* -> equal(union(image(element_relation,power_class(u)),v),successor_relation).
% 299.89/300.47  162523[10:Rew:160202.0,147957.1] || equal(intersection(power_class(image(element_relation,complement(u))),complement(v)),union(image(element_relation,power_class(u)),v))** -> equal(union(image(element_relation,power_class(u)),v),successor_relation).
% 299.89/300.47  162528[10:Rew:160202.0,147976.1] || subclass(union(u,image(element_relation,power_class(v))),intersection(complement(u),power_class(image(element_relation,complement(v)))))* -> equal(union(u,image(element_relation,power_class(v))),successor_relation).
% 299.89/300.47  162527[10:Rew:160202.0,147977.1] || equal(intersection(complement(u),power_class(image(element_relation,complement(v)))),union(u,image(element_relation,power_class(v))))** -> equal(union(u,image(element_relation,power_class(v))),successor_relation).
% 299.89/300.47  182939[6:Res:157922.1,129.3] || member(ordered_pair(u,least(compose(element_relation,universal_class),v)),element_relation)* member(u,v) subclass(v,w)* well_ordering(compose(element_relation,universal_class),w)* -> .
% 299.89/300.47  183179[10:SpL:181044.1,5646.1] || member(u,universal_class) member(ordered_pair(successor(u),v),compose(w,x))* subclass(image(w,image(x,successor_relation)),y)* -> member(v,y)*.
% 299.89/300.47  187482[10:Res:186499.1,5554.0] || equal(successor_relation,u) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,power_class(u))),second(ordered_pair(v,power_class(u)))),ordered_pair(v,power_class(u)))**.
% 299.89/300.47  10121[0:Rew:70.0,10111.2] || member(image(u,singleton(v)),ordinal_numbers) subclass(image(u,singleton(v)),apply(u,v))* -> equal(image(u,singleton(v)),apply(u,v)).
% 299.89/300.47  39110[2:Res:5714.3,3.0] || connected(u,v) well_ordering(w,v) subclass(not_well_ordering(u,v),x) -> well_ordering(u,v) member(least(w,not_well_ordering(u,v)),x)*.
% 299.89/300.47  162089[10:Rew:160202.0,147223.2] || well_ordering(u,cross_product(universal_class,universal_class)) subclass(compose(v,w),x) -> equal(compose(v,w),successor_relation) member(least(u,compose(v,w)),x)*.
% 299.89/300.47  92637[2:MRR:92613.2,2450.0] || well_ordering(u,cross_product(universal_class,universal_class)) subclass(singleton(least(u,rest_of(v))),rest_of(v)) -> section(u,singleton(least(u,rest_of(v))),rest_of(v))*.
% 299.89/300.47  92636[2:MRR:92614.2,2450.0] || well_ordering(u,cross_product(universal_class,universal_class)) subclass(singleton(least(u,compose_class(v))),compose_class(v)) -> section(u,singleton(least(u,compose_class(v))),compose_class(v))*.
% 299.89/300.47  145042[2:MRR:108717.1,145036.0] || well_ordering(u,ordered_pair(v,w)) -> equal(least(u,ordered_pair(v,w)),unordered_pair(v,singleton(w)))** equal(least(u,ordered_pair(v,w)),singleton(v)).
% 299.89/300.47  181437[10:SpL:181082.0,139.1] || well_ordering(element_relation,image(u,successor_relation)) subclass(apply(u,universal_class),image(u,successor_relation))* -> equal(image(u,successor_relation),ordinal_numbers) member(image(u,successor_relation),ordinal_numbers).
% 299.89/300.47  184608[10:Res:184599.1,6041.0] || well_ordering(cross_product(u,universal_class),kind_1_ordinals)* member(v,u)* member(v,ordinal_numbers)* subclass(ordinal_numbers,w) well_ordering(cross_product(u,universal_class),w)* -> .
% 299.89/300.47  184602[10:Res:184565.1,6041.0] || well_ordering(cross_product(u,ordinal_numbers),kind_1_ordinals)* member(v,u)* member(v,ordinal_numbers)* subclass(ordinal_numbers,w) well_ordering(cross_product(u,ordinal_numbers),w)* -> .
% 299.89/300.47  110385[0:Res:110370.1,6041.0] || well_ordering(cross_product(u,rest_relation),universal_class)* member(v,u)* member(v,rest_relation)* subclass(rest_relation,w) well_ordering(cross_product(u,rest_relation),w)* -> .
% 299.89/300.47  110397[0:Res:110382.1,6041.0] || well_ordering(cross_product(u,universal_class),universal_class)* member(v,u)* member(v,rest_relation)* subclass(rest_relation,w) well_ordering(cross_product(u,universal_class),w)* -> .
% 299.89/300.47  130370[2:Res:31069.2,9300.0] inductive(symmetric_difference(u,cross_product(v,w))) || well_ordering(x,universal_class) -> member(least(x,symmetric_difference(u,cross_product(v,w))),complement(restrict(u,v,w)))*.
% 299.89/300.47  130463[2:Res:31069.2,9306.0] inductive(symmetric_difference(cross_product(u,v),w)) || well_ordering(x,universal_class) -> member(least(x,symmetric_difference(cross_product(u,v),w)),complement(restrict(w,u,v)))*.
% 299.89/300.47  124262[2:Res:31069.2,986.1] inductive(power_class(image(element_relation,complement(u)))) || well_ordering(v,universal_class) member(least(v,power_class(image(element_relation,complement(u)))),image(element_relation,power_class(u)))* -> .
% 299.89/300.47  162519[10:Rew:160202.0,147840.1] || well_ordering(u,universal_class) -> equal(symmetric_difference(cross_product(v,w),x),successor_relation) member(least(u,symmetric_difference(cross_product(v,w),x)),complement(restrict(x,v,w)))*.
% 299.89/300.47  162517[10:Rew:160202.0,147832.1] || well_ordering(u,universal_class) -> equal(symmetric_difference(v,cross_product(w,x)),successor_relation) member(least(u,symmetric_difference(v,cross_product(w,x))),complement(restrict(v,w,x)))*.
% 299.89/300.47  162511[10:Rew:160202.0,147562.2] || well_ordering(u,universal_class) member(least(u,power_class(image(element_relation,complement(v)))),image(element_relation,power_class(v)))* -> equal(power_class(image(element_relation,complement(v))),successor_relation).
% 299.89/300.47  110391[0:Res:110376.1,6041.0] || well_ordering(cross_product(u,rest_relation),rest_relation)* member(v,u)* member(v,rest_relation)* subclass(rest_relation,w) well_ordering(cross_product(u,rest_relation),w)* -> .
% 299.89/300.47  110411[0:Res:110388.1,6041.0] || well_ordering(cross_product(u,universal_class),rest_relation)* member(v,u)* member(v,rest_relation)* subclass(rest_relation,w) well_ordering(cross_product(u,universal_class),w)* -> .
% 299.89/300.47  34094[0:MRR:33511.1,34067.1] || member(least(element_relation,u),universal_class)* member(v,least(element_relation,u))* member(v,u) subclass(u,w)* well_ordering(element_relation,w)* -> .
% 299.89/300.47  41073[0:Res:64.1,5838.1] function(complement(u)) || member(v,universal_class)* well_ordering(w,cross_product(universal_class,universal_class)) -> member(v,u)* member(least(w,complement(u)),complement(u))*.
% 299.89/300.47  108233[0:Res:107289.0,5838.1] || member(u,universal_class) well_ordering(v,image(element_relation,complement(w))) -> member(u,power_class(w))* member(least(v,complement(power_class(w))),complement(power_class(w)))*.
% 299.89/300.47  152931[0:Res:1506.1,61.0] || equal(image(u,image(v,singleton(w))),universal_class) member(ordered_pair(w,omega),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,omega),compose(u,v))*.
% 299.89/300.47  163679[10:Rew:160202.0,162441.2] || equal(image(u,image(v,singleton(w))),universal_class) member(ordered_pair(w,successor_relation),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,successor_relation),compose(u,v))*.
% 299.89/300.47  162998[10:Rew:160202.0,156355.3] function(u) || member(ordered_pair(u,inverse(u)),cross_product(universal_class,universal_class)) subclass(composition_function,v) -> member(ordered_pair(u,ordered_pair(inverse(u),successor_relation)),v)*.
% 299.89/300.47  162999[10:Rew:160202.0,156320.3] single_valued_class(u) || member(ordered_pair(u,inverse(u)),cross_product(universal_class,universal_class)) subclass(composition_function,v) -> member(ordered_pair(u,ordered_pair(inverse(u),successor_relation)),v)*.
% 299.89/300.47  184014[14:MRR:183993.3,160227.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,cross_product(universal_class,universal_class)) equal(ordered_pair(v,compose(u,v)),sum_class(range_of(u)))** -> .
% 299.89/300.47  39576[0:Res:5768.2,595.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,restrict(w,x,y))* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),w)*.
% 299.89/300.47  48358[0:Res:5768.2,47888.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,rest_of(ordered_pair(u,ordered_pair(v,compose(u,v)))))* subclass(universal_class,complement(element_relation)) -> .
% 299.89/300.47  188733[17:Res:188716.1,6041.0] || well_ordering(cross_product(u,omega),universal_class)* member(v,u)* member(v,omega)* subclass(omega,w) well_ordering(cross_product(u,omega),w)* -> .
% 299.89/300.47  188741[17:Res:188721.1,6041.0] || well_ordering(cross_product(u,omega),omega)* member(v,u)* member(v,omega)* subclass(omega,w) well_ordering(cross_product(u,omega),w)* -> .
% 299.89/300.47  188748[17:Res:188729.1,6041.0] || well_ordering(cross_product(u,universal_class),universal_class)* member(v,u)* member(v,omega)* subclass(omega,w) well_ordering(cross_product(u,universal_class),w)* -> .
% 299.89/300.47  188760[17:Res:188737.1,6041.0] || well_ordering(cross_product(u,universal_class),omega)* member(v,u)* member(v,omega)* subclass(omega,w) well_ordering(cross_product(u,universal_class),w)* -> .
% 299.89/300.47  189467[15:Rew:189339.1,189405.3] || member(u,universal_class) subclass(domain_relation,ordered_pair(v,w))* -> equal(ordered_pair(u,successor_relation),unordered_pair(v,singleton(w)))* equal(ordered_pair(u,successor_relation),singleton(v)).
% 299.89/300.47  189702[15:Rew:189513.0,189579.2] || subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) member(ordered_pair(ordered_pair(u,successor_relation),v),w) -> member(ordered_pair(ordered_pair(v,u),successor_relation),rotate(w))*.
% 299.89/300.47  189703[15:Rew:189513.0,189580.1] || subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) member(ordered_pair(ordered_pair(u,v),successor_relation),w) -> member(ordered_pair(ordered_pair(v,u),successor_relation),flip(w))*.
% 299.89/300.47  191122[20:Res:191074.1,61.0] || equal(image(u,image(v,singleton(w))),omega) member(ordered_pair(w,successor_relation),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,successor_relation),compose(u,v))*.
% 299.89/300.47  191467[10:SpR:181082.0,162148.2] || member(image(u,successor_relation),ordinal_numbers) well_ordering(v,image(u,successor_relation)) -> equal(segment(v,apply(u,universal_class),least(v,apply(u,universal_class))),successor_relation)**.
% 299.89/300.47  192170[15:SpL:190721.0,5646.1] || member(ordered_pair(inverse(u),v),compose(w,x))* subclass(image(w,image(x,successor_relation)),y)* -> equal(range_of(u),successor_relation) member(v,y)*.
% 299.89/300.47  192560[10:Res:1009.0,162356.0] || subclass(singleton(singleton(singleton(u))),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(singleton(singleton(u)),least(omega,singleton(singleton(singleton(u)))))),successor_relation)**.
% 299.89/300.47  192525[10:Res:160290.2,162356.0] || subclass(u,v) subclass(v,w)* well_ordering(omega,w)* -> equal(u,successor_relation) equal(integer_of(ordered_pair(regular(u),least(omega,v))),successor_relation)**.
% 299.89/300.47  192524[10:Res:160465.1,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(intersection(w,u),successor_relation) equal(integer_of(ordered_pair(regular(intersection(w,u)),least(omega,u))),successor_relation)**.
% 299.89/300.47  192520[10:Res:157922.1,162356.0] || member(u,element_relation) subclass(compose(element_relation,universal_class),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(u,least(omega,compose(element_relation,universal_class)))),successor_relation)**.
% 299.89/300.47  192518[10:Res:12.1,162356.0] || member(u,universal_class) subclass(unordered_pair(v,u),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(u,least(omega,unordered_pair(v,u)))),successor_relation)**.
% 299.89/300.47  192517[10:Res:11.1,162356.0] || member(u,universal_class) subclass(unordered_pair(u,v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(u,least(omega,unordered_pair(u,v)))),successor_relation)**.
% 299.89/300.47  192500[10:Res:160466.1,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(intersection(u,w),successor_relation) equal(integer_of(ordered_pair(regular(intersection(u,w)),least(omega,u))),successor_relation)**.
% 299.89/300.47  193541[10:Res:141787.0,162356.0] || subclass(inverse(singleton(u)),v)* well_ordering(omega,v) -> asymmetric(singleton(u),w)* equal(integer_of(ordered_pair(u,least(omega,inverse(singleton(u))))),successor_relation)**.
% 299.89/300.47  194529[10:Res:161312.2,183398.0] || member(intersection(u,complement(complement(v))),universal_class) -> equal(intersection(u,complement(complement(v))),successor_relation) member(apply(choice,intersection(u,complement(complement(v)))),v)*.
% 299.89/300.47  194518[10:Res:161311.2,183398.0] || member(intersection(complement(complement(u)),v),universal_class) -> equal(intersection(complement(complement(u)),v),successor_relation) member(apply(choice,intersection(complement(complement(u)),v)),u)*.
% 299.89/300.47  195812[6:Res:195710.1,5838.1] || equal(inverse(u),universal_class) member(v,universal_class)* well_ordering(w,inverse(u))* -> member(v,x)* member(least(w,complement(x)),complement(x))*.
% 299.89/300.47  195871[6:Res:195720.1,5838.1] || equal(sum_class(u),universal_class) member(v,universal_class)* well_ordering(w,sum_class(u))* -> member(v,x)* member(least(w,complement(x)),complement(x))*.
% 299.89/300.47  197017[10:Res:186026.1,162356.0] || equal(complement(symmetrization_of(successor_relation)),successor_relation) subclass(inverse(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(omega,least(omega,inverse(successor_relation)))),successor_relation)**.
% 299.89/300.47  197571[10:Res:187784.1,162356.0] || subclass(universal_class,symmetrization_of(successor_relation)) subclass(inverse(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(power_class(successor_relation),least(omega,inverse(successor_relation)))),successor_relation)**.
% 299.89/300.47  199696[10:Res:183720.1,162356.0] || subclass(universal_class,symmetrization_of(successor_relation)) subclass(inverse(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(singleton(v),least(omega,inverse(successor_relation)))),successor_relation)**.
% 299.89/300.47  200133[14:SpL:200028.1,5646.1] || member(u,universal_class) member(ordered_pair(range_of(u),v),compose(w,x))* subclass(image(w,image(x,successor_relation)),y)* -> member(v,y)*.
% 299.89/300.47  200767[10:Res:161493.2,3886.0] inductive(u) || member(not_subclass_element(v,intersection(w,u)),w)* -> equal(integer_of(not_subclass_element(v,intersection(w,u))),successor_relation) subclass(v,intersection(w,u)).
% 299.89/300.47  201033[10:Res:200000.1,162356.0] || subclass(universal_class,symmetrization_of(successor_relation)) subclass(inverse(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(rest_relation),least(omega,inverse(successor_relation)))),successor_relation)**.
% 299.89/300.47  201713[10:Res:161419.0,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(complement(complement(u)),successor_relation) equal(integer_of(ordered_pair(regular(complement(complement(u))),least(omega,u))),successor_relation)**.
% 299.89/300.47  201804[10:Res:201390.1,162356.0] || subclass(universal_class,symmetrization_of(successor_relation)) subclass(inverse(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(domain_relation),least(omega,inverse(successor_relation)))),successor_relation)**.
% 299.89/300.47  201855[14:SpL:10417.0,184006.1] || member(restrict(cross_product(u,universal_class),v,w),universal_class)* equal(rest_of(restrict(cross_product(u,universal_class),v,w)),sum_class(image(cross_product(v,w),u))) -> .
% 299.89/300.47  201983[10:Res:161492.2,129.3] || equal(u,omega) member(v,w) subclass(w,x)* well_ordering(u,x)* -> equal(integer_of(ordered_pair(v,least(u,w))),successor_relation)**.
% 299.89/300.47  201918[10:Res:161492.2,162356.0] || equal(u,omega) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(w),successor_relation) equal(integer_of(ordered_pair(w,least(omega,u))),successor_relation)**.
% 299.89/300.47  202191[10:Res:34085.1,162356.0] || member(u,rest_of(u)) subclass(element_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(u,rest_of(u)),least(omega,element_relation))),successor_relation)**.
% 299.89/300.47  202421[10:Res:163225.0,127.0] || subclass(symmetric_difference(universal_class,u),v)* well_ordering(w,v)* -> member(successor_relation,union(u,successor_relation)) member(least(w,symmetric_difference(universal_class,u)),symmetric_difference(universal_class,u))*.
% 299.89/300.47  203379[10:Rew:203192.0,161577.2] || member(regular(cross_product(u,v)),domain_relation) -> equal(cross_product(u,v),successor_relation) equal(cantor(first(regular(cross_product(u,v)))),second(regular(cross_product(u,v))))**.
% 299.89/300.47  204859[10:Rew:203192.0,203854.0] || member(u,cantor(u)) subclass(element_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(u,cantor(u)),least(omega,element_relation))),successor_relation)**.
% 299.89/300.47  204861[10:Rew:203192.0,203998.2] || section(u,complement(v),w) member(regular(cantor(restrict(u,w,complement(v)))),v)* -> equal(cantor(restrict(u,w,complement(v))),successor_relation).
% 299.89/300.47  204862[10:Rew:203192.0,204005.3] || section(u,v,w) subclass(v,x) -> equal(cantor(restrict(u,w,v)),successor_relation) member(regular(cantor(restrict(u,w,v))),x)*.
% 299.89/300.47  204024[6:Rew:203192.0,6325.2] single_valued_class(domain_of(restrict(u,v,cross_product(universal_class,universal_class)))) || section(u,cross_product(universal_class,universal_class),v) -> function(cantor(restrict(u,v,cross_product(universal_class,universal_class))))*.
% 299.89/300.47  204230[6:Rew:204206.0,184168.2] inductive(intersection(u,intersection(inverse(v),universal_class))) || well_ordering(w,inverse(v)) -> member(least(w,intersection(u,inverse(v))),intersection(u,inverse(v)))*.
% 299.89/300.47  204244[6:Rew:204206.0,159620.2] inductive(complement(complement(intersection(inverse(u),universal_class)))) || well_ordering(v,inverse(u)) -> member(least(v,complement(complement(inverse(u)))),complement(complement(inverse(u))))*.
% 299.89/300.47  204269[6:Rew:204206.0,184187.2] inductive(intersection(intersection(inverse(u),universal_class),v)) || well_ordering(w,inverse(u)) -> member(least(w,intersection(inverse(u),v)),intersection(inverse(u),v))*.
% 299.89/300.47  204304[6:Rew:204278.0,188576.2] inductive(intersection(u,intersection(sum_class(v),universal_class))) || well_ordering(w,sum_class(v)) -> member(least(w,intersection(u,sum_class(v))),intersection(u,sum_class(v)))*.
% 299.89/300.47  204316[6:Rew:204278.0,159648.2] inductive(complement(complement(intersection(sum_class(u),universal_class)))) || well_ordering(v,sum_class(u)) -> member(least(v,complement(complement(sum_class(u)))),complement(complement(sum_class(u))))*.
% 299.89/300.47  204343[6:Rew:204278.0,188533.2] inductive(intersection(intersection(sum_class(u),universal_class),v)) || well_ordering(w,sum_class(u)) -> member(least(w,intersection(sum_class(u),v)),intersection(sum_class(u),v))*.
% 299.89/300.47  206172[6:Res:203330.1,3926.1] single_valued_class(cantor(restrict(u,v,cross_product(universal_class,universal_class)))) || section(u,cross_product(universal_class,universal_class),v) -> function(cantor(restrict(u,v,cross_product(universal_class,universal_class))))*.
% 299.89/300.47  206984[10:Res:206947.1,61.0] || equal(image(u,image(v,singleton(w))),kind_1_ordinals) member(ordered_pair(w,successor_relation),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,successor_relation),compose(u,v))*.
% 299.89/300.47  208443[10:Res:206224.1,204754.1] || member(successor_relation,cantor(restrict(u,v,successor(successor_relation))))* section(u,successor(successor_relation),v) -> equal(cantor(restrict(u,v,successor(successor_relation))),successor(successor_relation)).
% 299.89/300.47  199684[10:Res:183719.1,162356.0] || equal(symmetrization_of(successor_relation),universal_class) subclass(inverse(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(singleton(v),least(omega,inverse(successor_relation)))),successor_relation)**.
% 299.89/300.47  210308[12:Res:209468.1,162356.0] || subclass(universal_class,symmetrization_of(successor_relation)) subclass(inverse(successor_relation),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(regular(element_relation),least(omega,inverse(successor_relation)))),successor_relation)**.
% 299.89/300.47  211610[10:Res:203330.1,160705.0] || section(u,complement(kind_1_ordinals),v) member(regular(cantor(restrict(u,v,complement(kind_1_ordinals)))),ordinal_numbers)* -> equal(cantor(restrict(u,v,complement(kind_1_ordinals))),successor_relation).
% 299.89/300.47  212052[10:Res:184090.1,162356.0] || equal(symmetric_difference(universal_class,u),universal_class) subclass(complement(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(omega,least(omega,complement(u)))),successor_relation)**.
% 299.89/300.47  212083[10:Res:1951.1,163312.0] || member(regular(regular(complement(intersection(u,v)))),symmetric_difference(u,v))* -> equal(regular(complement(intersection(u,v))),successor_relation) equal(complement(intersection(u,v)),successor_relation).
% 299.89/300.47  212111[10:MRR:212092.2,186160.1] || member(ordered_pair(u,regular(regular(image(v,image(w,singleton(u)))))),compose(v,w))* -> equal(regular(image(v,image(w,singleton(u)))),successor_relation).
% 299.89/300.47  213109[10:Res:188444.1,162356.0] || equal(symmetric_difference(universal_class,u),universal_class) subclass(complement(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(successor_relation,least(omega,complement(u)))),successor_relation)**.
% 299.89/300.47  213203[15:Res:189485.1,3874.1] || subclass(domain_relation,complement(intersection(u,v))) member(singleton(singleton(singleton(successor_relation))),union(u,v)) -> member(singleton(singleton(singleton(successor_relation))),symmetric_difference(u,v))*.
% 299.89/300.47  214143[20:Res:193270.1,162356.0] || equal(symmetric_difference(universal_class,u),omega) subclass(complement(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(successor_relation,least(omega,complement(u)))),successor_relation)**.
% 299.89/300.47  215866[10:Res:197082.1,3874.1] || subclass(universal_class,complement(intersection(u,v))) member(regular(complement(successor(successor_relation))),union(u,v)) -> member(regular(complement(successor(successor_relation))),symmetric_difference(u,v))*.
% 299.89/300.47  216150[10:Res:199833.1,162356.0] || equal(inverse(u),universal_class) subclass(inverse(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(regular(rest_relation),least(omega,inverse(u)))),successor_relation)**.
% 299.89/300.47  216165[10:Res:199834.1,162356.0] || equal(sum_class(u),universal_class) subclass(sum_class(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(regular(rest_relation),least(omega,sum_class(u)))),successor_relation)**.
% 299.89/300.47  216774[10:Res:201223.1,162356.0] || equal(inverse(u),universal_class) subclass(inverse(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(regular(domain_relation),least(omega,inverse(u)))),successor_relation)**.
% 299.89/300.47  216789[10:Res:201224.1,162356.0] || equal(sum_class(u),universal_class) subclass(sum_class(u),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(regular(domain_relation),least(omega,sum_class(u)))),successor_relation)**.
% 299.89/300.47  216885[10:MRR:216863.3,214403.1] || member(apply(choice,regular(union(u,v))),universal_class) -> member(apply(choice,regular(union(u,v))),complement(v))* equal(regular(union(u,v)),successor_relation).
% 299.89/300.47  216886[10:MRR:216862.3,214550.1] || member(apply(choice,regular(union(u,v))),universal_class) -> member(apply(choice,regular(union(u,v))),complement(u))* equal(regular(union(u,v)),successor_relation).
% 299.89/300.47  216887[10:MRR:216859.3,186121.2] || member(apply(choice,regular(intersection(u,v))),v)* member(apply(choice,regular(intersection(u,v))),u)* -> equal(regular(intersection(u,v)),successor_relation).
% 299.89/300.47  216957[10:SpR:202307.1,5768.2] || equal(compose_class(u),domain_relation) member(ordered_pair(u,successor_relation),cross_product(universal_class,universal_class)) subclass(composition_function,v) -> member(ordered_pair(u,ordered_pair(successor_relation,successor_relation)),v)*.
% 299.89/300.47  218319[10:MRR:218275.3,186121.2] || member(not_subclass_element(regular(intersection(u,v)),w),v)* member(not_subclass_element(regular(intersection(u,v)),w),u)* -> subclass(regular(intersection(u,v)),w).
% 299.89/300.47  163704[10:Rew:160305.0,162950.1] || well_ordering(u,kind_1_ordinals) -> equal(segment(u,symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation))),least(u,symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation))))),successor_relation)**.
% 299.89/300.47  216219[10:SpR:163369.0,143766.2] || member(intersection(complement(singleton(successor_relation)),complement(range_of(successor_relation))),universal_class)* subclass(universal_class,omega) -> equal(integer_of(complement(image(element_relation,kind_1_ordinals))),complement(image(element_relation,kind_1_ordinals))).
% 299.89/300.47  163668[10:Rew:160202.0,160624.1] || member(ordered_pair(u,v),compose(w,regular(cross_product(singleton(u),universal_class))))* -> equal(cross_product(singleton(u),universal_class),successor_relation) member(v,image(w,range_of(successor_relation))).
% 299.89/300.47  163669[10:Rew:160202.0,160648.3,160202.0,160648.0] || member(ordered_pair(u,v),compose(successor_relation,w))* subclass(range_of(successor_relation),x)* well_ordering(y,x)* -> member(least(y,range_of(successor_relation)),range_of(successor_relation))*.
% 299.89/300.47  216973[10:MRR:216972.3,160227.0] || equal(compose_class(u),domain_relation) member(ordered_pair(v,not_subclass_element(image(u,range_of(successor_relation)),w)),cross_product(universal_class,universal_class))* -> subclass(image(u,range_of(successor_relation)),w).
% 299.89/300.47  163713[10:Rew:160305.0,162862.0] ||  -> equal(intersection(complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),union(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals)),symmetric_difference(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals))**.
% 299.89/300.47  163702[10:Rew:160305.0,162848.2,160202.0,162848.1,160305.0,162848.1] || member(u,kind_1_ordinals) member(u,complement(intersection(singleton(successor_relation),range_of(successor_relation))))* subclass(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),v)* -> member(u,v)*.
% 299.89/300.47  221647[10:Res:3595.3,185698.1] function(u) inductive(image(u,v)) || member(v,universal_class)* subclass(universal_class,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  221625[10:Res:160784.3,185698.1] inductive(apply(choice,u)) || member(u,universal_class) subclass(u,ordinal_numbers)* -> equal(u,successor_relation) equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  221777[10:Res:221522.0,162356.0] || subclass(complement(singleton(ordered_pair(universal_class,u))),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(successor_relation,least(omega,complement(singleton(ordered_pair(universal_class,u)))))),successor_relation)**.
% 299.89/300.47  222286[15:Res:60.1,189380.2] || member(ordered_pair(u,ordered_pair(v,successor_relation)),compose(w,x))* member(v,universal_class) subclass(domain_relation,complement(image(w,image(x,singleton(u)))))* -> .
% 299.89/300.47  223154[24:Res:222372.0,162356.0] || subclass(complement(singleton(ordered_pair(kind_1_ordinals,u))),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(successor_relation,least(omega,complement(singleton(ordered_pair(kind_1_ordinals,u)))))),successor_relation)**.
% 299.89/300.47  224353[25:Rew:224236.1,204887.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> equal(integer_of(range_of(w)),successor_relation) compatible(u,v,inverse(w))*.
% 299.89/300.47  224354[25:Rew:224236.1,204886.2] function(u) || subclass(range_of(u),successor_relation) equal(cantor(cantor(v)),universal_class) -> equal(singleton(range_of(w)),successor_relation) compatible(u,v,inverse(w))*.
% 299.89/300.47  224377[25:Rew:224236.1,214123.3] function(u) || well_ordering(v,universal_class) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,least(v,omega))*.
% 299.89/300.47  224378[25:Rew:224236.1,214077.3] function(u) || well_ordering(v,omega) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,least(v,omega))*.
% 299.89/300.47  224379[25:Rew:224236.1,214032.3] function(u) || well_ordering(v,universal_class) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,least(v,rest_relation))*.
% 299.89/300.47  224380[25:Rew:224236.1,213981.3] function(u) || well_ordering(v,rest_relation) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,least(v,rest_relation))*.
% 299.89/300.47  224381[25:Rew:224236.1,213936.3] function(u) || well_ordering(v,universal_class) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,least(v,universal_class))*.
% 299.89/300.47  224382[25:Rew:224236.1,213891.3] function(u) || well_ordering(v,kind_1_ordinals) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,least(v,ordinal_numbers))*.
% 299.89/300.47  224385[25:Rew:224236.1,204884.3] function(u) || equal(cantor(cantor(v)),successor_relation) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,v)*.
% 299.89/300.47  224386[25:Rew:224236.1,204883.3] function(u) || equal(rest_of(cantor(v)),successor_relation) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,v)*.
% 299.89/300.47  224387[25:Rew:224236.1,204879.3] function(u) || equal(cantor(v),universal_class) subclass(range_of(u),cantor(universal_class))* equal(cantor(cantor(w)),universal_class) -> compatible(u,w,v)*.
% 299.89/300.47  224388[25:Rew:224236.1,204878.2] function(u) || subclass(range_of(u),cantor(image(universal_class,v))) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,inverse(cross_product(v,universal_class)))*.
% 299.89/300.47  225490[25:Rew:224739.1,225082.2] function(u) || member(ordered_pair(u,not_subclass_element(v,image(w,image(x,successor_relation)))),compose(w,x))* -> subclass(v,image(w,image(x,successor_relation))).
% 299.89/300.47  226309[10:MRR:226225.3,226247.1] || member(apply(choice,regular(cantor(u))),universal_class) -> equal(apply(u,apply(choice,regular(cantor(u)))),sum_class(range_of(successor_relation)))** equal(regular(cantor(u)),successor_relation).
% 299.89/300.47  229807[10:Res:221521.1,129.3] || member(u,v) subclass(v,w)* well_ordering(complement(singleton(omega)),w)* -> equal(integer_of(ordered_pair(u,least(complement(singleton(omega)),v))),successor_relation)**.
% 299.89/300.47  229794[10:Res:221521.1,162356.0] || subclass(complement(singleton(omega)),u)* well_ordering(omega,u) -> equal(integer_of(v),successor_relation) equal(integer_of(ordered_pair(v,least(omega,complement(singleton(omega))))),successor_relation)**.
% 299.89/300.47  230872[10:MRR:230845.0,160295.1] ||  -> member(regular(regular(image(element_relation,power_class(successor_relation)))),power_class(image(element_relation,universal_class)))* equal(regular(image(element_relation,power_class(successor_relation))),successor_relation) equal(image(element_relation,power_class(successor_relation)),successor_relation).
% 299.89/300.47  231862[10:Res:161711.2,161035.0] || subclass(u,intersection(power_class(successor_relation),complement(v))) member(regular(intersection(w,u)),union(image(element_relation,universal_class),v))* -> equal(intersection(w,u),successor_relation).
% 299.89/300.47  231860[10:Res:161722.2,161035.0] || subclass(u,intersection(power_class(successor_relation),complement(v))) member(regular(intersection(u,w)),union(image(element_relation,universal_class),v))* -> equal(intersection(u,w),successor_relation).
% 299.89/300.47  231823[10:Res:28321.1,161035.0] || subclass(rest_relation,flip(intersection(power_class(successor_relation),complement(u)))) member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),union(image(element_relation,universal_class),u))* -> .
% 299.89/300.47  231821[10:Res:28320.1,161035.0] || subclass(rest_relation,rotate(intersection(power_class(successor_relation),complement(u)))) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),union(image(element_relation,universal_class),u))* -> .
% 299.89/300.47  231810[10:Res:160465.1,161035.0] || member(regular(intersection(u,intersection(power_class(successor_relation),complement(v)))),union(image(element_relation,universal_class),v))* -> equal(intersection(u,intersection(power_class(successor_relation),complement(v))),successor_relation).
% 299.89/300.47  231794[10:Res:160466.1,161035.0] || member(regular(intersection(intersection(power_class(successor_relation),complement(u)),v)),union(image(element_relation,universal_class),u))* -> equal(intersection(intersection(power_class(successor_relation),complement(u)),v),successor_relation).
% 299.89/300.47  231776[10:SpL:505.0,161035.0] || member(u,intersection(power_class(successor_relation),power_class(intersection(complement(v),complement(w)))))* member(u,union(image(element_relation,universal_class),image(element_relation,union(v,w)))) -> .
% 299.89/300.47  34058[0:SpL:1948.0,3883.2] || member(u,union(complement(v),complement(w)))* member(u,union(v,w)) subclass(symmetric_difference(complement(v),complement(w)),x)* -> member(u,x)*.
% 299.89/300.47  39952[0:Res:60.1,5554.0] || member(ordered_pair(u,v),compose(w,x))* member(y,z)* -> equal(ordered_pair(first(ordered_pair(y,v)),second(ordered_pair(y,v))),ordered_pair(y,v))**.
% 299.89/300.47  131011[0:Rew:10422.0,130984.2] || section(cross_product(u,singleton(v)),w,x) subclass(w,segment(cross_product(x,w),u,v))* -> equal(segment(cross_product(x,w),u,v),w).
% 299.89/300.47  123499[0:Res:978.1,513.0] || member(not_subclass_element(restrict(intersection(complement(u),complement(v)),w,x),y),union(u,v))* -> subclass(restrict(intersection(complement(u),complement(v)),w,x),y).
% 299.89/300.47  5643[0:Res:60.1,309.0] || member(ordered_pair(u,not_subclass_element(complement(image(v,image(w,singleton(u)))),x)),compose(v,w))* -> subclass(complement(image(v,image(w,singleton(u)))),x).
% 299.89/300.47  40716[0:Rew:1931.0,40552.0] ||  -> subclass(symmetric_difference(complement(intersection(u,v)),union(u,v)),w) member(not_subclass_element(symmetric_difference(complement(intersection(u,v)),union(u,v)),w),complement(symmetric_difference(u,v)))*.
% 299.89/300.47  126800[0:Rew:1931.0,126702.1] || member(not_subclass_element(symmetric_difference(complement(intersection(u,v)),union(u,v)),w),symmetric_difference(u,v))* -> subclass(symmetric_difference(complement(intersection(u,v)),union(u,v)),w).
% 299.89/300.47  35707[0:Res:1481.2,3874.1] || subclass(u,complement(intersection(v,w))) member(not_subclass_element(u,x),union(v,w)) -> subclass(u,x) member(not_subclass_element(u,x),symmetric_difference(v,w))*.
% 299.89/300.47  122499[0:Res:3872.2,9636.1] || member(not_subclass_element(u,v),cross_product(w,x))* member(not_subclass_element(u,v),y)* subclass(u,complement(restrict(y,w,x)))* -> subclass(u,v).
% 299.89/300.47  41891[0:SpR:2330.1,1006.0] ||  -> subclass(cross_product(u,v),w) member(unordered_pair(first(not_subclass_element(cross_product(u,v),w)),singleton(second(not_subclass_element(cross_product(u,v),w)))),not_subclass_element(cross_product(u,v),w))*.
% 299.89/300.47  9379[0:Res:322.1,10.0] ||  -> subclass(intersection(u,unordered_pair(v,w)),x) equal(not_subclass_element(intersection(u,unordered_pair(v,w)),x),w)** equal(not_subclass_element(intersection(u,unordered_pair(v,w)),x),v)**.
% 299.89/300.47  107189[0:Res:34429.0,10.0] ||  -> subclass(complement(complement(unordered_pair(u,v))),w) equal(not_subclass_element(complement(complement(unordered_pair(u,v))),w),v)** equal(not_subclass_element(complement(complement(unordered_pair(u,v))),w),u)**.
% 299.89/300.47  9493[0:Res:340.1,10.0] ||  -> subclass(intersection(unordered_pair(u,v),w),x) equal(not_subclass_element(intersection(unordered_pair(u,v),w),x),v)** equal(not_subclass_element(intersection(unordered_pair(u,v),w),x),u)**.
% 299.89/300.47  158730[0:SpR:10417.0,474.1] || member(inverse(restrict(cross_product(u,universal_class),v,w)),universal_class) -> member(ordered_pair(inverse(restrict(cross_product(u,universal_class),v,w)),image(cross_product(v,w),u)),domain_relation)*.
% 299.89/300.47  109343[0:SpR:505.0,9948.0] ||  -> equal(power_class(intersection(power_class(intersection(complement(u),complement(v))),complement(inverse(image(element_relation,union(u,v)))))),complement(image(element_relation,symmetrization_of(image(element_relation,union(u,v))))))**.
% 299.89/300.47  109286[0:SpR:505.0,9949.0] ||  -> equal(power_class(intersection(power_class(intersection(complement(u),complement(v))),complement(singleton(image(element_relation,union(u,v)))))),complement(image(element_relation,successor(image(element_relation,union(u,v))))))**.
% 299.89/300.47  139692[0:SpR:982.0,1028.1] || member(u,universal_class) -> member(u,image(element_relation,union(image(element_relation,power_class(v)),w))) member(u,power_class(intersection(power_class(image(element_relation,complement(v))),complement(w))))*.
% 299.89/300.47  139762[0:SpL:982.0,9069.0] || subclass(universal_class,image(element_relation,union(image(element_relation,power_class(u)),v))) member(unordered_pair(w,x),power_class(intersection(power_class(image(element_relation,complement(u))),complement(v))))* -> .
% 299.89/300.47  140153[0:SpR:984.0,1028.1] || member(u,universal_class) -> member(u,image(element_relation,union(v,image(element_relation,power_class(w))))) member(u,power_class(intersection(complement(v),power_class(image(element_relation,complement(w))))))*.
% 299.89/300.47  140224[0:SpL:984.0,9069.0] || subclass(universal_class,image(element_relation,union(u,image(element_relation,power_class(v))))) member(unordered_pair(w,x),power_class(intersection(complement(u),power_class(image(element_relation,complement(v))))))* -> .
% 299.89/300.47  140343[0:Rew:984.0,140157.1] ||  -> member(not_subclass_element(u,union(v,image(element_relation,power_class(w)))),intersection(complement(v),power_class(image(element_relation,complement(w)))))* subclass(u,union(v,image(element_relation,power_class(w)))).
% 299.89/300.47  140267[0:SpL:984.0,9118.1] || member(u,universal_class) subclass(universal_class,union(v,image(element_relation,power_class(w)))) member(sum_class(u),intersection(complement(v),power_class(image(element_relation,complement(w)))))* -> .
% 299.89/300.47  140268[0:SpL:984.0,9146.1] || member(u,universal_class) subclass(universal_class,union(v,image(element_relation,power_class(w)))) member(power_class(u),intersection(complement(v),power_class(image(element_relation,complement(w)))))* -> .
% 299.89/300.47  137116[0:SpR:208.0,10029.0] ||  -> equal(complement(intersection(power_class(image(element_relation,power_class(u))),complement(singleton(image(element_relation,power_class(image(element_relation,complement(u)))))))),successor(image(element_relation,power_class(image(element_relation,complement(u))))))**.
% 299.89/300.47  137736[0:SpR:208.0,10028.0] ||  -> equal(complement(intersection(power_class(image(element_relation,power_class(u))),complement(inverse(image(element_relation,power_class(image(element_relation,complement(u)))))))),symmetrization_of(image(element_relation,power_class(image(element_relation,complement(u))))))**.
% 299.89/300.47  139879[0:Rew:982.0,139695.1] ||  -> member(not_subclass_element(u,union(image(element_relation,power_class(v)),w)),intersection(power_class(image(element_relation,complement(v))),complement(w)))* subclass(u,union(image(element_relation,power_class(v)),w)).
% 299.89/300.47  139805[0:SpL:982.0,9118.1] || member(u,universal_class) subclass(universal_class,union(image(element_relation,power_class(v)),w)) member(sum_class(u),intersection(power_class(image(element_relation,complement(v))),complement(w)))* -> .
% 299.89/300.47  139806[0:SpL:982.0,9146.1] || member(u,universal_class) subclass(universal_class,union(image(element_relation,power_class(v)),w)) member(power_class(u),intersection(power_class(image(element_relation,complement(v))),complement(w)))* -> .
% 299.89/300.47  137179[0:SpL:10029.0,9146.1] || member(u,universal_class) subclass(universal_class,successor(image(element_relation,complement(v)))) member(power_class(u),intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))* -> .
% 299.89/300.47  137178[0:SpL:10029.0,9118.1] || member(u,universal_class) subclass(universal_class,successor(image(element_relation,complement(v)))) member(sum_class(u),intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))* -> .
% 299.89/300.47  137797[0:SpL:10028.0,9146.1] || member(u,universal_class) subclass(universal_class,symmetrization_of(image(element_relation,complement(v)))) member(power_class(u),intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))* -> .
% 299.89/300.47  137796[0:SpL:10028.0,9118.1] || member(u,universal_class) subclass(universal_class,symmetrization_of(image(element_relation,complement(v)))) member(sum_class(u),intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))* -> .
% 299.89/300.47  137252[0:Rew:10029.0,137142.1] || member(not_subclass_element(successor(image(element_relation,complement(u))),v),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* -> subclass(successor(image(element_relation,complement(u))),v).
% 299.89/300.47  137098[0:SpR:10029.0,161.0] ||  -> equal(intersection(successor(image(element_relation,complement(u))),union(power_class(u),complement(singleton(image(element_relation,complement(u)))))),symmetric_difference(power_class(u),complement(singleton(image(element_relation,complement(u))))))**.
% 299.89/300.47  137868[0:Rew:10028.0,137760.1] || member(not_subclass_element(symmetrization_of(image(element_relation,complement(u))),v),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* -> subclass(symmetrization_of(image(element_relation,complement(u))),v).
% 299.89/300.47  137717[0:SpR:10028.0,161.0] ||  -> equal(intersection(symmetrization_of(image(element_relation,complement(u))),union(power_class(u),complement(inverse(image(element_relation,complement(u)))))),symmetric_difference(power_class(u),complement(inverse(image(element_relation,complement(u))))))**.
% 299.89/300.47  28533[0:Res:1028.1,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class) subclass(image(element_relation,complement(u)),intersection(y__dfg,ordinal_numbers))* -> member(least(element_relation,intersection(y__dfg,ordinal_numbers)),power_class(u)).
% 299.89/300.47  163683[10:Rew:160202.0,160916.1] || member(regular(image(element_relation,union(image(element_relation,universal_class),u))),power_class(intersection(power_class(successor_relation),complement(u))))* -> equal(image(element_relation,union(image(element_relation,universal_class),u)),successor_relation).
% 299.89/300.47  163684[10:Rew:160202.0,160917.1] || member(not_subclass_element(power_class(intersection(power_class(successor_relation),complement(u))),v),image(element_relation,union(image(element_relation,universal_class),u)))* -> subclass(power_class(intersection(power_class(successor_relation),complement(u))),v).
% 299.89/300.47  160935[10:Rew:160202.0,151226.0] || member(not_subclass_element(intersection(union(image(element_relation,universal_class),u),v),w),intersection(power_class(successor_relation),complement(u)))* -> subclass(intersection(union(image(element_relation,universal_class),u),v),w).
% 299.89/300.47  163685[10:Rew:160202.0,160947.1] || member(regular(image(element_relation,union(u,image(element_relation,universal_class)))),power_class(intersection(complement(u),power_class(successor_relation))))* -> equal(image(element_relation,union(u,image(element_relation,universal_class))),successor_relation).
% 299.89/300.47  163686[10:Rew:160202.0,160948.1] || member(not_subclass_element(power_class(intersection(complement(u),power_class(successor_relation))),v),image(element_relation,union(u,image(element_relation,universal_class))))* -> subclass(power_class(intersection(complement(u),power_class(successor_relation))),v).
% 299.89/300.47  160966[10:Rew:160202.0,151220.0] || member(not_subclass_element(intersection(union(u,image(element_relation,universal_class)),v),w),intersection(complement(u),power_class(successor_relation)))* -> subclass(intersection(union(u,image(element_relation,universal_class)),v),w).
% 299.89/300.47  161022[10:Rew:160202.0,151215.0] ||  -> member(not_subclass_element(u,image(element_relation,union(v,image(element_relation,universal_class)))),power_class(intersection(complement(v),power_class(successor_relation))))* subclass(u,image(element_relation,union(v,image(element_relation,universal_class)))).
% 299.89/300.47  161027[10:Rew:160202.0,151216.0] || member(not_subclass_element(intersection(u,union(v,image(element_relation,universal_class))),w),intersection(complement(v),power_class(successor_relation)))* -> subclass(intersection(u,union(v,image(element_relation,universal_class))),w).
% 299.89/300.47  161043[10:Rew:160202.0,151221.0] ||  -> member(not_subclass_element(u,image(element_relation,union(image(element_relation,universal_class),v))),power_class(intersection(power_class(successor_relation),complement(v))))* subclass(u,image(element_relation,union(image(element_relation,universal_class),v))).
% 299.89/300.47  161048[10:Rew:160202.0,151222.0] || member(not_subclass_element(intersection(u,union(image(element_relation,universal_class),v)),w),intersection(power_class(successor_relation),complement(v)))* -> subclass(intersection(u,union(image(element_relation,universal_class),v)),w).
% 299.89/300.47  161693[10:Rew:160202.0,146712.0] ||  -> equal(restrict(u,v,w),successor_relation) equal(ordered_pair(first(regular(restrict(u,v,w))),second(regular(restrict(u,v,w)))),regular(restrict(u,v,w)))**.
% 299.89/300.47  162409[10:Rew:160202.0,151081.2] || member(complement(complement(symmetrization_of(u))),ordinal_numbers)* connected(u,v)* -> equal(cross_product(v,v),successor_relation) member(least(element_relation,cross_product(v,v)),cross_product(v,v))*.
% 299.89/300.47  162399[10:Rew:160202.0,147091.1] || member(regular(complement(intersection(u,v))),union(u,v)) -> equal(complement(intersection(u,v)),successor_relation) member(regular(complement(intersection(u,v))),symmetric_difference(u,v))*.
% 299.89/300.47  162522[10:Rew:160202.0,147955.1] || member(regular(union(image(element_relation,power_class(u)),v)),intersection(power_class(image(element_relation,complement(u))),complement(v)))* -> equal(union(image(element_relation,power_class(u)),v),successor_relation).
% 299.89/300.47  162526[10:Rew:160202.0,147975.1] || member(regular(union(u,image(element_relation,power_class(v)))),intersection(complement(u),power_class(image(element_relation,complement(v)))))* -> equal(union(u,image(element_relation,power_class(v))),successor_relation).
% 299.89/300.47  162540[10:Rew:160202.0,147356.1] || member(regular(power_class(image(element_relation,union(u,v)))),image(element_relation,power_class(intersection(complement(u),complement(v)))))* -> equal(power_class(image(element_relation,union(u,v))),successor_relation).
% 299.89/300.47  162543[10:Rew:160202.0,147399.0] ||  -> equal(symmetric_difference(intersection(complement(u),complement(v)),w),successor_relation) member(regular(symmetric_difference(intersection(complement(u),complement(v)),w)),complement(intersection(union(u,v),complement(w))))*.
% 299.89/300.47  162544[10:Rew:160202.0,147400.0] ||  -> equal(symmetric_difference(u,intersection(complement(v),complement(w))),successor_relation) member(regular(symmetric_difference(u,intersection(complement(v),complement(w)))),complement(intersection(complement(u),union(v,w))))*.
% 299.89/300.47  162545[10:Rew:160202.0,147526.0] ||  -> equal(symmetric_difference(complement(intersection(u,singleton(u))),successor(u)),successor_relation) member(regular(symmetric_difference(complement(intersection(u,singleton(u))),successor(u))),complement(symmetric_difference(u,singleton(u))))*.
% 299.89/300.47  162546[10:Rew:160202.0,147527.0] ||  -> equal(symmetric_difference(complement(intersection(u,inverse(u))),symmetrization_of(u)),successor_relation) member(regular(symmetric_difference(complement(intersection(u,inverse(u))),symmetrization_of(u))),complement(symmetric_difference(u,inverse(u))))*.
% 299.89/300.47  162547[10:Rew:160202.0,147563.1] || member(regular(restrict(power_class(image(element_relation,complement(u))),v,w)),image(element_relation,power_class(u)))* -> equal(restrict(power_class(image(element_relation,complement(u))),v,w),successor_relation).
% 299.89/300.47  162548[10:Rew:160202.0,147623.0] ||  -> equal(intersection(u,intersection(symmetric_difference(complement(v),complement(w)),x)),successor_relation) member(regular(intersection(u,intersection(symmetric_difference(complement(v),complement(w)),x))),union(v,w))*.
% 299.89/300.47  162549[10:Rew:160202.0,147681.0] ||  -> equal(intersection(u,intersection(v,symmetric_difference(complement(w),complement(x)))),successor_relation) member(regular(intersection(u,intersection(v,symmetric_difference(complement(w),complement(x))))),union(w,x))*.
% 299.89/300.47  162550[10:Rew:160202.0,147721.0] ||  -> equal(intersection(intersection(symmetric_difference(complement(u),complement(v)),w),x),successor_relation) member(regular(intersection(intersection(symmetric_difference(complement(u),complement(v)),w),x)),union(u,v))*.
% 299.89/300.47  162551[10:Rew:160202.0,147794.0] ||  -> equal(intersection(intersection(u,symmetric_difference(complement(v),complement(w))),x),successor_relation) member(regular(intersection(intersection(u,symmetric_difference(complement(v),complement(w))),x)),union(v,w))*.
% 299.89/300.47  162552[10:Rew:160202.0,147833.0] ||  -> equal(restrict(symmetric_difference(u,cross_product(v,w)),x,y),successor_relation) member(regular(restrict(symmetric_difference(u,cross_product(v,w)),x,y)),complement(restrict(u,v,w)))*.
% 299.89/300.47  162553[10:Rew:160202.0,147841.0] ||  -> equal(restrict(symmetric_difference(cross_product(u,v),w),x,y),successor_relation) member(regular(restrict(symmetric_difference(cross_product(u,v),w),x,y)),complement(restrict(w,u,v)))*.
% 299.89/300.47  162556[10:Rew:160202.0,147871.2] || subclass(cross_product(u,v),w)* well_ordering(x,w)* -> equal(restrict(y,u,v),successor_relation)** member(least(x,cross_product(u,v)),cross_product(u,v))*.
% 299.89/300.47  162557[10:Rew:160202.0,147900.1] ||  -> member(regular(complement(successor(image(element_relation,complement(u))))),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* equal(complement(successor(image(element_relation,complement(u)))),successor_relation).
% 299.89/300.47  162558[10:Rew:160202.0,147920.1] ||  -> member(regular(complement(symmetrization_of(image(element_relation,complement(u))))),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* equal(complement(symmetrization_of(image(element_relation,complement(u)))),successor_relation).
% 299.89/300.47  162763[10:Rew:160202.0,153498.0] || equal(restrict(u,v,v),successor_relation) transitive(u,v) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),restrict(u,v,v))**.
% 299.89/300.47  163699[10:Rew:160202.0,162971.3] || member(u,v) subclass(v,w)* well_ordering(union(x,successor_relation),w)* -> member(ordered_pair(u,least(union(x,successor_relation),v)),symmetric_difference(universal_class,x))*.
% 299.89/300.47  183797[10:Rew:183387.0,183796.0] ||  -> equal(symmetric_difference(complement(complement(power_class(universal_class))),union(image(element_relation,successor_relation),complement(power_class(universal_class)))),union(complement(complement(power_class(universal_class))),union(image(element_relation,successor_relation),complement(power_class(universal_class)))))**.
% 299.89/300.47  183804[10:Rew:183388.0,183803.0] ||  -> equal(symmetric_difference(complement(complement(power_class(successor_relation))),union(image(element_relation,universal_class),complement(power_class(successor_relation)))),union(complement(complement(power_class(successor_relation))),union(image(element_relation,universal_class),complement(power_class(successor_relation)))))**.
% 299.89/300.47  162533[10:Rew:160202.0,146834.2] || member(image(u,singleton(v)),ordinal_numbers) subclass(image(u,singleton(v)),w)* -> equal(apply(u,v),successor_relation) member(regular(apply(u,v)),w).
% 299.89/300.47  162535[10:Rew:160202.0,147318.3] || equal(cantor(restrict(u,v,w)),universal_class)** section(u,w,v) well_ordering(x,w)* -> equal(segment(x,universal_class,least(x,universal_class)),successor_relation)**.
% 299.89/300.47  108811[2:Res:31076.2,10.0] inductive(unordered_pair(u,v)) || well_ordering(w,unordered_pair(u,v)) -> equal(least(w,unordered_pair(u,v)),v)** equal(least(w,unordered_pair(u,v)),u)**.
% 299.89/300.47  162530[10:Rew:160202.0,153501.0] || equal(apply(u,v),successor_relation) well_ordering(element_relation,image(u,singleton(v)))* -> equal(image(u,singleton(v)),ordinal_numbers) member(image(u,singleton(v)),ordinal_numbers).
% 299.89/300.47  162534[10:Rew:160202.0,147116.2] || section(u,singleton(v),w) well_ordering(x,singleton(v)) -> equal(segment(x,segment(u,w,v),least(x,segment(u,w,v))),successor_relation)**.
% 299.89/300.47  162453[10:Rew:160202.0,147107.1] || well_ordering(u,unordered_pair(v,w)) -> equal(unordered_pair(v,w),successor_relation) equal(least(u,unordered_pair(v,w)),w)** equal(least(u,unordered_pair(v,w)),v)**.
% 299.89/300.47  163688[10:Rew:160202.0,161050.2] || well_ordering(u,universal_class) member(least(u,union(image(element_relation,universal_class),v)),intersection(power_class(successor_relation),complement(v)))* -> equal(union(image(element_relation,universal_class),v),successor_relation).
% 299.89/300.47  163687[10:Rew:160202.0,161029.2] || well_ordering(u,universal_class) member(least(u,union(v,image(element_relation,universal_class))),intersection(complement(v),power_class(successor_relation)))* -> equal(union(v,image(element_relation,universal_class)),successor_relation).
% 299.89/300.47  34965[0:MRR:34960.1,34067.1] || member(least(successor_relation,u),universal_class)* equal(successor(v),least(successor_relation,u))* member(v,u)* subclass(u,w)* well_ordering(successor_relation,w)* -> .
% 299.89/300.47  160825[10:Rew:160202.0,152648.3] || member(u,universal_class) subclass(power_class(universal_class),v)* well_ordering(w,v)* -> member(u,image(element_relation,successor_relation))* member(least(w,power_class(universal_class)),power_class(universal_class))*.
% 299.89/300.47  163689[10:Rew:160202.0,161059.4] || member(u,universal_class) subclass(power_class(successor_relation),v)* well_ordering(w,v)* -> member(u,image(element_relation,universal_class))* member(least(w,power_class(successor_relation)),power_class(successor_relation))*.
% 299.89/300.47  186038[10:Res:185647.1,61.0] || equal(complement(image(u,image(v,singleton(w)))),successor_relation)** member(ordered_pair(w,omega),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,omega),compose(u,v)).
% 299.89/300.47  185964[10:Res:185646.1,61.0] || equal(complement(image(u,image(v,singleton(w)))),successor_relation)** member(ordered_pair(w,successor_relation),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,successor_relation),compose(u,v)).
% 299.89/300.47  180018[11:Res:179843.1,61.0] || equal(image(u,image(v,singleton(w))),inverse(successor_relation)) member(ordered_pair(w,successor_relation),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,successor_relation),compose(u,v))*.
% 299.89/300.47  168555[11:Res:168384.1,61.0] || equal(image(u,image(v,singleton(w))),symmetrization_of(successor_relation)) member(ordered_pair(w,successor_relation),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,successor_relation),compose(u,v))*.
% 299.89/300.47  163692[10:Rew:160202.0,162439.2,160202.0,162439.0] || equal(image(u,image(v,singleton(w))),successor(successor_relation)) member(ordered_pair(w,successor_relation),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,successor_relation),compose(u,v))*.
% 299.89/300.47  163693[10:Rew:160202.0,162440.2,160202.0,162440.0] || equal(image(u,image(v,singleton(w))),singleton(successor_relation)) member(ordered_pair(w,successor_relation),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,successor_relation),compose(u,v))*.
% 299.89/300.47  39565[0:Res:5768.2,3.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,w)* subclass(w,x)* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),x)*.
% 299.89/300.47  39564[0:Res:5768.2,127.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,w) subclass(w,x)* well_ordering(y,x)* -> member(least(y,w),w)*.
% 299.89/300.47  48615[0:Res:5768.2,10254.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,symmetric_difference(w,singleton(w)))* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),successor(w))*.
% 299.89/300.47  48513[0:Res:5768.2,10191.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,symmetric_difference(w,inverse(w)))* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),symmetrization_of(w))*.
% 299.89/300.47  39588[0:Res:5768.2,1952.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,symmetric_difference(w,x)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),union(w,x))*.
% 299.89/300.47  157909[6:Res:5768.2,148657.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,complement(compose(element_relation,universal_class))) member(ordered_pair(u,ordered_pair(v,compose(u,v))),element_relation)* -> .
% 299.89/300.47  161089[10:Rew:160202.0,151178.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,power_class(successor_relation)) member(ordered_pair(u,ordered_pair(v,compose(u,v))),image(element_relation,universal_class))* -> .
% 299.89/300.47  191232[10:Res:161311.2,160481.0] || member(intersection(regular(u),v),universal_class) member(apply(choice,intersection(regular(u),v)),u)* -> equal(intersection(regular(u),v),successor_relation) equal(u,successor_relation).
% 299.89/300.47  191359[10:Res:161312.2,160481.0] || member(intersection(u,regular(v)),universal_class) member(apply(choice,intersection(u,regular(v))),v)* -> equal(intersection(u,regular(v)),successor_relation) equal(v,successor_relation).
% 299.89/300.47  192575[10:Res:67.2,162356.0] function(u) || member(v,universal_class) subclass(universal_class,w) well_ordering(omega,w)* -> equal(integer_of(ordered_pair(image(u,v),least(omega,universal_class))),successor_relation)**.
% 299.89/300.47  192530[10:Res:160482.2,162356.0] || well_ordering(u,universal_class) subclass(v,w)* well_ordering(omega,w)* -> equal(v,successor_relation) equal(integer_of(ordered_pair(least(u,v),least(omega,v))),successor_relation)**.
% 299.89/300.47  192526[10:Res:1479.2,162356.0] || member(u,universal_class) subclass(universal_class,v) subclass(v,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(sum_class(u),least(omega,v))),successor_relation)**.
% 299.89/300.47  192523[10:Res:322.1,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> subclass(intersection(w,u),x) equal(integer_of(ordered_pair(not_subclass_element(intersection(w,u),x),least(omega,u))),successor_relation)**.
% 299.89/300.47  192522[10:Res:1481.2,162356.0] || subclass(u,v) subclass(v,w)* well_ordering(omega,w)* -> subclass(u,x) equal(integer_of(ordered_pair(not_subclass_element(u,x),least(omega,v))),successor_relation)**.
% 299.89/300.47  192521[10:Res:1478.2,162356.0] || member(u,universal_class) subclass(universal_class,v) subclass(v,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(power_class(u),least(omega,v))),successor_relation)**.
% 299.89/300.47  192509[10:Res:27.2,162356.0] || member(u,universal_class) subclass(complement(v),w)* well_ordering(omega,w) -> member(u,v) equal(integer_of(ordered_pair(u,least(omega,complement(v)))),successor_relation)**.
% 299.89/300.47  192505[10:Res:160296.2,162356.0] || member(u,universal_class) subclass(u,v)* well_ordering(omega,v)* -> equal(u,successor_relation) equal(integer_of(ordered_pair(apply(choice,u),least(omega,u))),successor_relation)**.
% 299.89/300.47  192504[10:Res:340.1,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> subclass(intersection(u,w),x) equal(integer_of(ordered_pair(not_subclass_element(intersection(u,w),x),least(omega,u))),successor_relation)**.
% 299.89/300.47  196591[10:Rew:161137.0,196569.2,161137.0,196569.0] || member(power_class(complement(inverse(successor_relation))),universal_class) member(apply(choice,power_class(complement(inverse(successor_relation)))),image(element_relation,symmetrization_of(successor_relation)))* -> equal(power_class(complement(inverse(successor_relation))),successor_relation).
% 299.89/300.47  196796[10:Rew:162889.0,196775.2,162889.0,196775.0] || member(power_class(complement(singleton(successor_relation))),universal_class) member(apply(choice,power_class(complement(singleton(successor_relation)))),image(element_relation,successor(successor_relation)))* -> equal(power_class(complement(singleton(successor_relation))),successor_relation).
% 299.89/300.47  197155[10:Res:6269.3,185639.1] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,u),v),x)* equal(rotate(x),successor_relation) -> .
% 299.89/300.47  197231[10:Res:6260.3,185639.1] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,v),u),x)* equal(flip(x),successor_relation) -> .
% 299.89/300.47  202037[10:Res:161492.2,3886.0] || equal(u,omega) member(not_subclass_element(v,intersection(w,u)),w)* -> equal(integer_of(not_subclass_element(v,intersection(w,u))),successor_relation) subclass(v,intersection(w,u)).
% 299.89/300.47  202417[10:Res:163225.0,162356.0] || subclass(symmetric_difference(universal_class,u),v)* well_ordering(omega,v) -> member(successor_relation,union(u,successor_relation)) equal(integer_of(ordered_pair(successor_relation,least(omega,symmetric_difference(universal_class,u)))),successor_relation)**.
% 299.89/300.47  203364[10:Rew:203192.0,193755.0] || member(u,cantor(complement(cross_product(u,universal_class))))* equal(successor_relation,v) subclass(rest_of(complement(cross_product(u,universal_class))),w)* -> member(ordered_pair(u,v),w)*.
% 299.89/300.47  204881[6:Rew:203192.0,203587.2] || member(u,universal_class) member(v,universal_class) -> member(u,cantor(w)) member(v,cantor(x)) equal(range__dfg(w,u,universal_class),range__dfg(x,v,universal_class))*.
% 299.89/300.47  204889[10:Rew:203192.0,204004.3] || section(u,v,w) well_ordering(x,v) -> equal(cantor(restrict(u,w,v)),successor_relation) member(least(x,cantor(restrict(u,w,v))),universal_class)*.
% 299.89/300.47  204243[6:Rew:204206.0,149771.2] inductive(complement(complement(cantor(flip(cross_product(u,universal_class)))))) || well_ordering(v,inverse(u)) -> member(least(v,complement(complement(inverse(u)))),complement(complement(inverse(u))))*.
% 299.89/300.47  204315[6:Rew:204278.0,149816.2] inductive(complement(complement(cantor(restrict(element_relation,universal_class,u))))) || well_ordering(v,sum_class(u)) -> member(least(v,complement(complement(sum_class(u)))),complement(complement(sum_class(u))))*.
% 299.89/300.47  210395[15:Res:189563.1,36.1] || subclass(domain_relation,flip(cross_product(cross_product(universal_class,universal_class),universal_class)))* member(ordered_pair(ordered_pair(u,successor_relation),v),w) -> member(ordered_pair(ordered_pair(v,u),successor_relation),rotate(w))*.
% 299.89/300.47  210394[15:Res:189563.1,39.1] || subclass(domain_relation,flip(cross_product(cross_product(universal_class,universal_class),universal_class)))* member(ordered_pair(ordered_pair(u,v),successor_relation),w) -> member(ordered_pair(ordered_pair(v,u),successor_relation),flip(w))*.
% 299.89/300.47  210378[15:Res:189563.1,2142.0] || subclass(domain_relation,flip(ordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,x),successor_relation),unordered_pair(u,singleton(v)))* equal(ordered_pair(ordered_pair(w,x),successor_relation),singleton(u)).
% 299.89/300.47  210343[15:Res:189563.1,162356.0] || subclass(domain_relation,flip(u)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(ordered_pair(w,x),successor_relation),least(omega,u))),successor_relation)**.
% 299.89/300.47  210340[15:SpR:161565.2,189563.1] || member(cross_product(u,v),universal_class) subclass(domain_relation,flip(w)) -> equal(cross_product(u,v),successor_relation) member(ordered_pair(apply(choice,cross_product(u,v)),successor_relation),w)*.
% 299.89/300.47  210472[15:Res:189564.1,36.1] || subclass(domain_relation,rotate(cross_product(cross_product(universal_class,universal_class),universal_class)))* member(ordered_pair(ordered_pair(successor_relation,u),v),w) -> member(ordered_pair(ordered_pair(v,successor_relation),u),rotate(w))*.
% 299.89/300.47  210471[15:Res:189564.1,39.1] || subclass(domain_relation,rotate(cross_product(cross_product(universal_class,universal_class),universal_class)))* member(ordered_pair(ordered_pair(successor_relation,u),v),w) -> member(ordered_pair(ordered_pair(u,successor_relation),v),flip(w))*.
% 299.89/300.47  210451[15:Res:189564.1,2142.0] || subclass(domain_relation,rotate(ordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,successor_relation),x),unordered_pair(u,singleton(v)))* equal(ordered_pair(ordered_pair(w,successor_relation),x),singleton(u)).
% 299.89/300.47  210416[15:Res:189564.1,162356.0] || subclass(domain_relation,rotate(u)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(ordered_pair(w,successor_relation),x),least(omega,u))),successor_relation)**.
% 299.89/300.47  210550[10:Res:161312.2,149475.0] || member(intersection(u,cantor(v)),universal_class) subclass(universal_class,w) -> equal(intersection(u,cantor(v)),successor_relation) member(apply(choice,intersection(u,cantor(v))),w)*.
% 299.89/300.47  210539[10:Res:161311.2,149475.0] || member(intersection(cantor(u),v),universal_class) subclass(universal_class,w) -> equal(intersection(cantor(u),v),successor_relation) member(apply(choice,intersection(cantor(u),v)),w)*.
% 299.89/300.47  210662[10:Res:34429.0,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> subclass(complement(complement(u)),w) equal(integer_of(ordered_pair(not_subclass_element(complement(complement(u)),w),least(omega,u))),successor_relation)**.
% 299.89/300.47  210764[10:Res:31069.2,162356.0] inductive(u) || well_ordering(v,universal_class) subclass(u,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(least(v,u),least(omega,u))),successor_relation)**.
% 299.89/300.47  210957[10:Res:1504.1,162356.0] || subclass(ordered_pair(u,v),w) subclass(w,x)* well_ordering(omega,x)* -> equal(integer_of(ordered_pair(unordered_pair(u,singleton(v)),least(omega,w))),successor_relation)**.
% 299.89/300.47  211122[10:Res:161445.2,162356.0] || well_ordering(u,v) subclass(v,w)* well_ordering(omega,w)* -> equal(v,successor_relation) equal(integer_of(ordered_pair(least(u,v),least(omega,v))),successor_relation)**.
% 299.89/300.47  211176[10:Res:31076.2,162356.0] inductive(u) || well_ordering(v,u) subclass(u,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(least(v,u),least(omega,u))),successor_relation)**.
% 299.89/300.47  215554[10:Rew:195811.1,215458.4] || equal(inverse(u),universal_class) member(v,w) subclass(w,x)* well_ordering(successor_relation,x)* -> member(ordered_pair(v,least(successor_relation,w)),inverse(u))*.
% 299.89/300.47  215829[10:Rew:195870.1,215746.4] || equal(sum_class(u),universal_class) member(v,w) subclass(w,x)* well_ordering(successor_relation,x)* -> member(ordered_pair(v,least(successor_relation,w)),sum_class(u))*.
% 299.89/300.47  216218[0:SpR:9948.0,143766.2] || member(intersection(complement(u),complement(inverse(u))),universal_class)* subclass(universal_class,omega) -> equal(integer_of(complement(image(element_relation,symmetrization_of(u)))),complement(image(element_relation,symmetrization_of(u)))).
% 299.89/300.47  216217[0:SpR:9949.0,143766.2] || member(intersection(complement(u),complement(singleton(u))),universal_class)* subclass(universal_class,omega) -> equal(integer_of(complement(image(element_relation,successor(u)))),complement(image(element_relation,successor(u)))).
% 299.89/300.47  216311[14:SpL:199971.1,5646.1] || member(u,universal_class) member(ordered_pair(sum_class(range_of(u)),v),compose(w,x))* subclass(image(w,image(x,successor_relation)),y)* -> member(v,y)*.
% 299.89/300.47  216858[10:Res:1951.1,163343.0] || member(apply(choice,regular(complement(intersection(u,v)))),symmetric_difference(u,v))* -> equal(regular(complement(intersection(u,v))),successor_relation) equal(complement(intersection(u,v)),successor_relation).
% 299.89/300.47  216892[10:MRR:216869.2,186160.1] || member(ordered_pair(u,apply(choice,regular(image(v,image(w,singleton(u)))))),compose(v,w))* -> equal(regular(image(v,image(w,singleton(u)))),successor_relation).
% 299.89/300.47  217425[20:Res:217226.1,3886.0] || equal(singleton(not_subclass_element(u,intersection(v,singleton(successor_relation)))),omega) member(not_subclass_element(u,intersection(v,singleton(successor_relation))),v)* -> subclass(u,intersection(v,singleton(successor_relation))).
% 299.89/300.47  218274[10:Res:1951.1,160698.0] || member(not_subclass_element(regular(complement(intersection(u,v))),w),symmetric_difference(u,v))* -> subclass(regular(complement(intersection(u,v))),w) equal(complement(intersection(u,v)),successor_relation).
% 299.89/300.47  218324[10:MRR:218288.2,186160.1] || member(ordered_pair(u,not_subclass_element(regular(image(v,image(w,singleton(u)))),x)),compose(v,w))* -> subclass(regular(image(v,image(w,singleton(u)))),x).
% 299.89/300.47  218533[3:Res:218494.0,5838.1] || member(u,universal_class) well_ordering(v,complement(ordinal_numbers)) -> member(u,complement(complement(kind_1_ordinals)))* member(least(v,complement(complement(complement(kind_1_ordinals)))),complement(complement(complement(kind_1_ordinals))))*.
% 299.89/300.47  218623[3:Res:218475.0,5839.2] || member(u,v)* member(u,complement(kind_1_ordinals))* well_ordering(w,complement(ordinal_numbers)) -> member(least(w,intersection(complement(kind_1_ordinals),v)),intersection(complement(kind_1_ordinals),v))*.
% 299.89/300.47  218657[3:Res:218485.0,5839.2] || member(u,complement(kind_1_ordinals))* member(u,v)* well_ordering(w,complement(ordinal_numbers)) -> member(least(w,intersection(v,complement(kind_1_ordinals))),intersection(v,complement(kind_1_ordinals)))*.
% 299.89/300.47  218757[3:Res:218481.0,5832.1] inductive(restrict(complement(kind_1_ordinals),u,v)) || well_ordering(w,complement(ordinal_numbers)) -> member(least(w,restrict(complement(kind_1_ordinals),u,v)),restrict(complement(kind_1_ordinals),u,v))*.
% 299.89/300.47  218754[10:Res:218481.0,160292.0] || well_ordering(u,complement(ordinal_numbers)) -> equal(restrict(complement(kind_1_ordinals),v,w),successor_relation) member(least(u,restrict(complement(kind_1_ordinals),v,w)),restrict(complement(kind_1_ordinals),v,w))*.
% 299.89/300.47  219157[3:Res:218473.1,5838.1] || equal(complement(kind_1_ordinals),complement(u)) member(v,universal_class)* well_ordering(w,complement(ordinal_numbers)) -> member(v,u)* member(least(w,complement(u)),complement(u))*.
% 299.89/300.47  219131[3:Res:218473.1,5841.1] || equal(unordered_pair(u,v),complement(kind_1_ordinals)) member(v,universal_class) well_ordering(w,complement(ordinal_numbers)) -> member(least(w,unordered_pair(u,v)),unordered_pair(u,v))*.
% 299.89/300.47  219129[3:Res:218473.1,5842.1] || equal(unordered_pair(u,v),complement(kind_1_ordinals)) member(u,universal_class) well_ordering(w,complement(ordinal_numbers)) -> member(least(w,unordered_pair(u,v)),unordered_pair(u,v))*.
% 299.89/300.47  160604[10:Rew:160202.0,146320.2] || member(u,universal_class) -> member(u,segment(cross_product(v,w),x,y)) equal(apply(restrict(cross_product(x,singleton(y)),v,w),u),sum_class(range_of(successor_relation)))**.
% 299.89/300.47  204882[10:Rew:203192.0,203588.3] || member(u,v) subclass(v,w)* well_ordering(cantor(x),w)* -> equal(apply(x,ordered_pair(u,least(cantor(x),v))),sum_class(range_of(successor_relation)))**.
% 299.89/300.47  163682[10:Rew:160202.0,160676.2,160202.0,160676.1] || member(ordered_pair(u,not_subclass_element(range_of(successor_relation),v)),cross_product(universal_class,universal_class)) -> subclass(range_of(successor_relation),v) member(ordered_pair(u,not_subclass_element(range_of(successor_relation),v)),compose(successor_relation,w))*.
% 299.89/300.47  166972[10:Res:60.1,163256.1] || member(ordered_pair(u,successor_relation),compose(v,w)) equal(image(v,image(w,singleton(u))),range_of(successor_relation)) -> inductive(image(v,image(w,singleton(u))))*.
% 299.89/300.47  163714[10:Rew:160305.0,163160.3] inductive(u) || well_ordering(v,u)* subclass(singleton(least(v,range_of(successor_relation))),range_of(successor_relation)) -> section(v,singleton(least(v,range_of(successor_relation))),range_of(successor_relation))*.
% 299.89/300.47  163703[10:Rew:160305.0,162849.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,symmetric_difference(singleton(successor_relation),range_of(successor_relation))) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),kind_1_ordinals)*.
% 299.89/300.47  221738[6:Res:221565.0,5838.1] || member(u,universal_class) well_ordering(v,complement(element_relation)) -> member(u,compose(element_relation,universal_class))* member(least(v,complement(compose(element_relation,universal_class))),complement(compose(element_relation,universal_class)))*.
% 299.89/300.47  221889[10:Res:221523.0,127.0] || subclass(complement(singleton(singleton(singleton(successor_relation)))),u)* well_ordering(v,u)* -> member(least(v,complement(singleton(singleton(singleton(successor_relation))))),complement(singleton(singleton(singleton(successor_relation)))))*.
% 299.89/300.47  221885[10:Res:221523.0,162356.0] || subclass(complement(singleton(singleton(singleton(successor_relation)))),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(singleton(successor_relation),least(omega,complement(singleton(singleton(singleton(successor_relation))))))),successor_relation)**.
% 299.89/300.47  222145[10:Res:221525.0,127.0] || subclass(complement(singleton(ordered_pair(u,v))),w)* well_ordering(x,w)* -> member(least(x,complement(singleton(ordered_pair(u,v)))),complement(singleton(ordered_pair(u,v))))*.
% 299.89/300.47  222141[10:Res:221525.0,162356.0] || subclass(complement(singleton(ordered_pair(u,v))),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(singleton(u),least(omega,complement(singleton(ordered_pair(u,v)))))),successor_relation)**.
% 299.89/300.47  224325[25:Rew:224236.1,204937.2] function(cross_product(u,universal_class)) || subclass(image(universal_class,u),cantor(cantor(v)))* equal(cantor(cantor(w)),universal_class) -> compatible(cross_product(u,universal_class),w,v)*.
% 299.89/300.47  224383[25:Rew:224236.1,204906.3] function(u) || equal(cantor(range_of(v)),successor_relation) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,inverse(v))*.
% 299.89/300.47  224384[25:Rew:224236.1,204905.3] function(u) || equal(rest_of(range_of(v)),successor_relation) subclass(range_of(u),successor_relation) equal(cantor(cantor(w)),universal_class) -> compatible(u,w,inverse(v))*.
% 299.89/300.47  224398[25:Rew:224236.1,204902.2] function(u) || subclass(range_of(u),cantor(image(v,w))) equal(cantor(cantor(x)),universal_class) -> compatible(u,x,inverse(restrict(v,w,universal_class)))*.
% 299.89/300.47  224399[25:Rew:224236.1,204901.2] function(u) || subclass(range_of(u),cantor(segment(universal_class,v,w)))* equal(cantor(cantor(x)),universal_class) -> compatible(u,x,cross_product(v,singleton(w)))*.
% 299.89/300.47  224400[25:Rew:224236.1,204900.2] function(u) || subclass(range_of(u),cantor(segment(v,w,universal_class)))* equal(cantor(cantor(x)),universal_class) -> compatible(u,x,restrict(v,w,successor_relation))*.
% 299.89/300.47  228253[10:Res:222126.0,162356.0] || subclass(complement(singleton(regular(rest_relation))),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(singleton(first(regular(rest_relation))),least(omega,complement(singleton(regular(rest_relation)))))),successor_relation)**.
% 299.89/300.47  228457[10:Res:222127.0,162356.0] || subclass(complement(singleton(regular(domain_relation))),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(singleton(first(regular(domain_relation))),least(omega,complement(singleton(regular(domain_relation)))))),successor_relation)**.
% 299.89/300.47  228474[12:Res:222128.0,162356.0] || subclass(complement(singleton(regular(element_relation))),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(singleton(first(regular(element_relation))),least(omega,complement(singleton(regular(element_relation)))))),successor_relation)**.
% 299.89/300.47  230878[10:MRR:230813.0,34189.1] ||  -> member(not_subclass_element(regular(image(element_relation,power_class(successor_relation))),u),power_class(image(element_relation,universal_class)))* subclass(regular(image(element_relation,power_class(successor_relation))),u) equal(image(element_relation,power_class(successor_relation)),successor_relation).
% 299.89/300.47  231833[10:Res:3595.3,161035.0] function(u) || member(v,universal_class) subclass(universal_class,intersection(power_class(successor_relation),complement(w))) member(image(u,v),union(image(element_relation,universal_class),w))* -> .
% 299.89/300.47  231818[10:Res:31069.2,161035.0] inductive(intersection(power_class(successor_relation),complement(u))) || well_ordering(v,universal_class) member(least(v,intersection(power_class(successor_relation),complement(u))),union(image(element_relation,universal_class),u))* -> .
% 299.89/300.47  231816[10:Res:160482.2,161035.0] || well_ordering(u,universal_class) member(least(u,intersection(power_class(successor_relation),complement(v))),union(image(element_relation,universal_class),v))* -> equal(intersection(power_class(successor_relation),complement(v)),successor_relation).
% 299.89/300.47  231813[10:Res:160784.3,161035.0] || member(u,universal_class) subclass(u,intersection(power_class(successor_relation),complement(v))) member(apply(choice,u),union(image(element_relation,universal_class),v))* -> equal(u,successor_relation).
% 299.89/300.47  231809[10:Res:322.1,161035.0] || member(not_subclass_element(intersection(u,intersection(power_class(successor_relation),complement(v))),w),union(image(element_relation,universal_class),v))* -> subclass(intersection(u,intersection(power_class(successor_relation),complement(v))),w).
% 299.89/300.47  231799[10:Res:340.1,161035.0] || member(not_subclass_element(intersection(intersection(power_class(successor_relation),complement(u)),v),w),union(image(element_relation,universal_class),u))* -> subclass(intersection(intersection(power_class(successor_relation),complement(u)),v),w).
% 299.89/300.47  10454[0:SpL:955.0,121.0] || subclass(compose(restrict(cross_product(u,u),v,w),restrict(cross_product(u,u),v,w)),restrict(cross_product(u,u),v,w))* -> transitive(cross_product(v,w),u).
% 299.89/300.47  10432[0:SpR:955.0,120.1] || transitive(cross_product(u,v),w) -> subclass(compose(restrict(cross_product(w,w),u,v),restrict(cross_product(w,w),u,v)),restrict(cross_product(w,w),u,v))*.
% 299.89/300.47  29337[0:SpR:1948.0,161.0] ||  -> equal(intersection(complement(symmetric_difference(complement(u),complement(v))),union(union(u,v),union(complement(u),complement(v)))),symmetric_difference(union(u,v),union(complement(u),complement(v))))**.
% 299.89/300.47  36023[0:SpL:955.0,5971.0] || equal(compose(restrict(cross_product(u,u),v,w),restrict(cross_product(u,u),v,w)),restrict(cross_product(u,u),v,w))** -> transitive(cross_product(v,w),u).
% 299.89/300.47  31110[2:Res:9898.0,5832.1] inductive(symmetric_difference(complement(u),complement(v))) || well_ordering(w,union(u,v)) -> member(least(w,symmetric_difference(complement(u),complement(v))),symmetric_difference(complement(u),complement(v)))*.
% 299.89/300.47  38695[0:SpR:955.0,1348.1] || member(restrict(cross_product(u,v),w,singleton(x)),universal_class) -> member(ordered_pair(restrict(cross_product(w,singleton(x)),u,v),segment(cross_product(u,v),w,x)),domain_relation)*.
% 299.89/300.47  92639[2:MRR:92616.2,2450.0] || well_ordering(u,cross_product(cross_product(universal_class,universal_class),universal_class)) subclass(singleton(least(u,flip(v))),flip(v)) -> section(u,singleton(least(u,flip(v))),flip(v))*.
% 299.89/300.47  92640[2:MRR:92615.2,2450.0] || well_ordering(u,cross_product(cross_product(universal_class,universal_class),universal_class)) subclass(singleton(least(u,rotate(v))),rotate(v)) -> section(u,singleton(least(u,rotate(v))),rotate(v))*.
% 299.89/300.47  155825[3:Res:155815.1,6041.0] || member(least(cross_product(u,kind_1_ordinals),v),ordinal_numbers)* member(w,u)* member(w,v)* subclass(v,x)* well_ordering(cross_product(u,kind_1_ordinals),x)* -> .
% 299.89/300.47  28283[0:Res:1495.2,19.0] || member(u,universal_class) subclass(rest_relation,cross_product(v,w))* -> equal(ordered_pair(first(ordered_pair(u,rest_of(u))),second(ordered_pair(u,rest_of(u)))),ordered_pair(u,rest_of(u)))**.
% 299.89/300.47  130499[0:Res:978.1,9306.0] ||  -> subclass(restrict(symmetric_difference(cross_product(u,v),w),x,y),z) member(not_subclass_element(restrict(symmetric_difference(cross_product(u,v),w),x,y),z),complement(restrict(w,u,v)))*.
% 299.89/300.47  130406[0:Res:978.1,9300.0] ||  -> subclass(restrict(symmetric_difference(u,cross_product(v,w)),x,y),z) member(not_subclass_element(restrict(symmetric_difference(u,cross_product(v,w)),x,y),z),complement(restrict(u,v,w)))*.
% 299.89/300.47  39966[0:Res:34189.1,5554.0] || member(u,v)* -> subclass(w,x) equal(ordered_pair(first(ordered_pair(u,not_subclass_element(w,x))),second(ordered_pair(u,not_subclass_element(w,x)))),ordered_pair(u,not_subclass_element(w,x)))**.
% 299.89/300.47  122637[0:SpR:507.0,6832.1] ||  -> subclass(symmetric_difference(u,intersection(complement(v),complement(w))),x) member(not_subclass_element(symmetric_difference(u,intersection(complement(v),complement(w))),x),complement(intersection(complement(u),union(v,w))))*.
% 299.89/300.47  122644[0:SpR:506.0,6832.1] ||  -> subclass(symmetric_difference(intersection(complement(u),complement(v)),w),x) member(not_subclass_element(symmetric_difference(intersection(complement(u),complement(v)),w),x),complement(intersection(union(u,v),complement(w))))*.
% 299.89/300.47  131771[0:SpR:1933.0,9529.1] ||  -> subclass(symmetric_difference(complement(intersection(u,inverse(u))),symmetrization_of(u)),v) member(not_subclass_element(symmetric_difference(complement(intersection(u,inverse(u))),symmetrization_of(u)),v),complement(symmetric_difference(u,inverse(u))))*.
% 299.89/300.47  131772[0:SpR:1934.0,9529.1] ||  -> subclass(symmetric_difference(complement(intersection(u,singleton(u))),successor(u)),v) member(not_subclass_element(symmetric_difference(complement(intersection(u,singleton(u))),successor(u)),v),complement(symmetric_difference(u,singleton(u))))*.
% 299.89/300.47  31212[0:Res:3872.2,5.0] || member(not_subclass_element(u,restrict(v,w,x)),cross_product(w,x))* member(not_subclass_element(u,restrict(v,w,x)),v)* -> subclass(u,restrict(v,w,x)).
% 299.89/300.47  40264[0:Rew:161.0,40181.2,161.0,40181.1] || member(not_subclass_element(u,symmetric_difference(v,w)),union(v,w)) member(not_subclass_element(u,symmetric_difference(v,w)),complement(intersection(v,w)))* -> subclass(u,symmetric_difference(v,w)).
% 299.89/300.47  31051[0:Res:1495.2,2142.0] || member(u,universal_class) subclass(rest_relation,ordered_pair(v,w))* -> equal(ordered_pair(u,rest_of(u)),unordered_pair(v,singleton(w)))* equal(ordered_pair(u,rest_of(u)),singleton(v)).
% 299.89/300.47  89767[0:Res:51387.0,2142.0] ||  -> subclass(u,complement(ordered_pair(v,w))) equal(not_subclass_element(u,complement(ordered_pair(v,w))),unordered_pair(v,singleton(w)))** equal(not_subclass_element(u,complement(ordered_pair(v,w))),singleton(v)).
% 299.89/300.47  108436[0:Res:1504.1,3874.1] || subclass(ordered_pair(u,v),complement(intersection(w,x)))* member(unordered_pair(u,singleton(v)),union(w,x)) -> member(unordered_pair(u,singleton(v)),symmetric_difference(w,x)).
% 299.89/300.47  30758[0:Res:3595.3,19.0] function(u) || member(v,universal_class) subclass(universal_class,cross_product(w,x))* -> equal(ordered_pair(first(image(u,v)),second(image(u,v))),image(u,v))**.
% 299.89/300.47  144398[0:SpR:10422.0,102.1] || member(restrict(cross_product(u,singleton(v)),w,x),universal_class) -> member(ordered_pair(restrict(cross_product(u,singleton(v)),w,x),segment(cross_product(w,x),u,v)),domain_relation)*.
% 299.89/300.47  39964[0:Res:9089.1,5554.0] function(u) || member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,apply(u,x))),second(ordered_pair(v,apply(u,x)))),ordered_pair(v,apply(u,x)))**.
% 299.89/300.47  139800[0:SpL:982.0,986.1] || member(u,image(element_relation,power_class(intersection(power_class(image(element_relation,complement(v))),complement(w)))))* member(u,power_class(image(element_relation,union(image(element_relation,power_class(v)),w)))) -> .
% 299.89/300.47  140262[0:SpL:984.0,986.1] || member(u,image(element_relation,power_class(intersection(complement(v),power_class(image(element_relation,complement(w)))))))* member(u,power_class(image(element_relation,union(v,image(element_relation,power_class(w)))))) -> .
% 299.89/300.47  118920[0:SpL:505.0,1089.0] || member(not_subclass_element(power_class(image(element_relation,union(u,v))),w),image(element_relation,power_class(intersection(complement(u),complement(v)))))* -> subclass(power_class(image(element_relation,union(u,v))),w).
% 299.89/300.47  140272[0:SpL:984.0,29643.0] || equal(u,union(v,image(element_relation,power_class(w))))* member(x,universal_class) -> member(x,intersection(complement(v),power_class(image(element_relation,complement(w)))))* member(x,u)*.
% 299.89/300.47  140264[0:SpL:984.0,1487.1] || member(u,universal_class) subclass(union(v,image(element_relation,power_class(w))),x)* -> member(u,intersection(complement(v),power_class(image(element_relation,complement(w)))))* member(u,x)*.
% 299.89/300.47  140254[0:SpL:984.0,122532.0] || subclass(intersection(complement(u),power_class(image(element_relation,complement(v)))),union(u,image(element_relation,power_class(v))))* -> subclass(intersection(complement(u),power_class(image(element_relation,complement(v)))),w)*.
% 299.89/300.47  140344[0:Rew:984.0,140227.1] || member(not_subclass_element(union(u,image(element_relation,power_class(v))),w),intersection(complement(u),power_class(image(element_relation,complement(v)))))* -> subclass(union(u,image(element_relation,power_class(v))),w).
% 299.89/300.47  156808[6:SpL:984.0,153140.1] inductive(intersection(complement(u),power_class(image(element_relation,complement(v))))) || equal(intersection(complement(u),power_class(image(element_relation,complement(v)))),union(u,image(element_relation,power_class(v))))** -> .
% 299.89/300.47  139810[0:SpL:982.0,29643.0] || equal(u,union(image(element_relation,power_class(v)),w))* member(x,universal_class) -> member(x,intersection(power_class(image(element_relation,complement(v))),complement(w)))* member(x,u)*.
% 299.89/300.47  139802[0:SpL:982.0,1487.1] || member(u,universal_class) subclass(union(image(element_relation,power_class(v)),w),x)* -> member(u,intersection(power_class(image(element_relation,complement(v))),complement(w)))* member(u,x)*.
% 299.89/300.47  139792[0:SpL:982.0,122532.0] || subclass(intersection(power_class(image(element_relation,complement(u))),complement(v)),union(image(element_relation,power_class(u)),v))* -> subclass(intersection(power_class(image(element_relation,complement(u))),complement(v)),w)*.
% 299.89/300.47  139880[0:Rew:982.0,139765.1] || member(not_subclass_element(union(image(element_relation,power_class(u)),v),w),intersection(power_class(image(element_relation,complement(u))),complement(v)))* -> subclass(union(image(element_relation,power_class(u)),v),w).
% 299.89/300.47  156809[6:SpL:982.0,153140.1] inductive(intersection(power_class(image(element_relation,complement(u))),complement(v))) || equal(intersection(power_class(image(element_relation,complement(u))),complement(v)),union(image(element_relation,power_class(u)),v))** -> .
% 299.89/300.47  124290[0:Res:978.1,986.1] || member(not_subclass_element(restrict(power_class(image(element_relation,complement(u))),v,w),x),image(element_relation,power_class(u)))* -> subclass(restrict(power_class(image(element_relation,complement(u))),v,w),x).
% 299.89/300.47  28541[0:MRR:28534.0,999.0] || member(u,v) subclass(v,w)* well_ordering(image(element_relation,complement(x)),w)* -> member(ordered_pair(u,least(image(element_relation,complement(x)),v)),power_class(x))*.
% 299.89/300.47  137175[0:SpL:10029.0,1487.1] || member(u,universal_class) subclass(successor(image(element_relation,complement(v))),w)* -> member(u,intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))* member(u,w)*.
% 299.89/300.47  137183[0:SpL:10029.0,29643.0] || equal(u,successor(image(element_relation,complement(v))))* member(w,universal_class) -> member(w,intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))* member(w,u)*.
% 299.89/300.47  137793[0:SpL:10028.0,1487.1] || member(u,universal_class) subclass(symmetrization_of(image(element_relation,complement(v))),w)* -> member(u,intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))* member(u,w)*.
% 299.89/300.47  137801[0:SpL:10028.0,29643.0] || equal(u,symmetrization_of(image(element_relation,complement(v))))* member(w,universal_class) -> member(w,intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))* member(w,u)*.
% 299.89/300.47  137258[0:Rew:10029.0,137060.1] ||  -> member(not_subclass_element(complement(successor(image(element_relation,complement(u)))),v),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* subclass(complement(successor(image(element_relation,complement(u)))),v).
% 299.89/300.47  137878[0:Rew:10028.0,137679.1] ||  -> member(not_subclass_element(complement(symmetrization_of(image(element_relation,complement(u)))),v),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* subclass(complement(symmetrization_of(image(element_relation,complement(u)))),v).
% 299.89/300.47  33821[0:SpR:511.0,1938.0] ||  -> equal(intersection(complement(restrict(image(element_relation,complement(u)),v,w)),complement(intersection(power_class(u),complement(cross_product(v,w))))),symmetric_difference(image(element_relation,complement(u)),cross_product(v,w)))**.
% 299.89/300.47  33894[0:SpR:509.0,1943.0] ||  -> equal(intersection(complement(restrict(image(element_relation,complement(u)),v,w)),complement(intersection(complement(cross_product(v,w)),power_class(u)))),symmetric_difference(cross_product(v,w),image(element_relation,complement(u))))**.
% 299.89/300.47  124618[0:Res:1951.1,33515.1] || member(singleton(complement(intersection(u,v))),symmetric_difference(u,v))* member(complement(intersection(u,v)),universal_class) -> member(singleton(singleton(singleton(complement(intersection(u,v))))),element_relation)*.
% 299.89/300.47  41924[0:SpL:2330.1,21.0] || member(not_subclass_element(cross_product(u,v),w),element_relation) -> subclass(cross_product(u,v),w) member(first(not_subclass_element(cross_product(u,v),w)),second(not_subclass_element(cross_product(u,v),w)))*.
% 299.89/300.47  160714[10:Rew:160202.0,146508.2] || member(u,universal_class) subclass(u,cross_product(v,w))* -> equal(u,successor_relation) equal(ordered_pair(first(apply(choice,u)),second(apply(choice,u))),apply(choice,u))**.
% 299.89/300.47  161573[10:Rew:160202.0,146817.1] || member(regular(cross_product(u,v)),compose_class(w)) -> equal(cross_product(u,v),successor_relation) equal(compose(w,first(regular(cross_product(u,v)))),second(regular(cross_product(u,v))))**.
% 299.89/300.47  162030[10:Rew:160202.0,146939.1] || member(symmetric_difference(complement(u),complement(v)),universal_class) -> equal(symmetric_difference(complement(u),complement(v)),successor_relation) member(apply(choice,symmetric_difference(complement(u),complement(v))),union(u,v))*.
% 299.89/300.47  162047[10:Rew:160202.0,146962.1] || member(intersection(symmetric_difference(u,v),w),universal_class) -> equal(intersection(symmetric_difference(u,v),w),successor_relation) member(apply(choice,intersection(symmetric_difference(u,v),w)),union(u,v))*.
% 299.89/300.47  162050[10:Rew:160202.0,146965.1] || member(intersection(u,symmetric_difference(v,w)),universal_class) -> equal(intersection(u,symmetric_difference(v,w)),successor_relation) member(apply(choice,intersection(u,symmetric_difference(v,w))),union(v,w))*.
% 299.89/300.47  162406[10:Rew:160202.0,147126.1] || well_ordering(u,union(v,w)) -> equal(symmetric_difference(complement(v),complement(w)),successor_relation) member(least(u,symmetric_difference(complement(v),complement(w))),symmetric_difference(complement(v),complement(w)))*.
% 299.89/300.47  162420[10:Rew:160202.0,147537.1] || equal(sum_class(restrict(u,v,w)),restrict(u,v,w)) -> equal(sum_class(restrict(u,v,w)),successor_relation) member(regular(sum_class(restrict(u,v,w))),u)*.
% 299.89/300.47  162563[10:Rew:160202.0,147127.4] || member(u,v)* member(u,w)* subclass(w,x)* well_ordering(cross_product(v,universal_class),x)* -> equal(singleton(least(cross_product(v,universal_class),w)),successor_relation)**.
% 299.89/300.47  162566[10:Rew:160202.0,147441.0] ||  -> equal(restrict(unordered_pair(u,v),w,x),successor_relation) equal(regular(restrict(unordered_pair(u,v),w,x)),v)** equal(regular(restrict(unordered_pair(u,v),w,x)),u)**.
% 299.89/300.47  162568[10:Rew:160202.0,147482.1] || member(regular(intersection(u,power_class(intersection(complement(v),complement(w))))),image(element_relation,union(v,w)))* -> equal(intersection(u,power_class(intersection(complement(v),complement(w)))),successor_relation).
% 299.89/300.47  162569[10:Rew:160202.0,147509.1] || member(regular(intersection(power_class(intersection(complement(u),complement(v))),w)),image(element_relation,union(u,v)))* -> equal(intersection(power_class(intersection(complement(u),complement(v))),w),successor_relation).
% 299.89/300.47  162572[10:Rew:160202.0,147624.1] || member(regular(intersection(u,intersection(intersection(complement(v),complement(w)),x))),union(v,w))* -> equal(intersection(u,intersection(intersection(complement(v),complement(w)),x)),successor_relation).
% 299.89/300.47  162573[10:Rew:160202.0,147682.1] || member(regular(intersection(u,intersection(v,intersection(complement(w),complement(x))))),union(w,x))* -> equal(intersection(u,intersection(v,intersection(complement(w),complement(x)))),successor_relation).
% 299.89/300.47  162574[10:Rew:160202.0,147722.1] || member(regular(intersection(intersection(intersection(complement(u),complement(v)),w),x)),union(u,v))* -> equal(intersection(intersection(intersection(complement(u),complement(v)),w),x),successor_relation).
% 299.89/300.47  162575[10:Rew:160202.0,147795.1] || member(regular(intersection(intersection(u,intersection(complement(v),complement(w))),x)),union(v,w))* -> equal(intersection(intersection(u,intersection(complement(v),complement(w))),x),successor_relation).
% 299.89/300.47  162578[10:Rew:160202.0,147952.1] || equal(intersection(power_class(image(element_relation,complement(u))),complement(v)),union(image(element_relation,power_class(u)),v))** -> equal(intersection(power_class(image(element_relation,complement(u))),complement(v)),successor_relation).
% 299.89/300.47  162579[10:Rew:160202.0,147953.0] ||  -> equal(symmetric_difference(power_class(image(element_relation,complement(u))),complement(v)),successor_relation) member(regular(symmetric_difference(power_class(image(element_relation,complement(u))),complement(v))),union(image(element_relation,power_class(u)),v))*.
% 299.89/300.47  162580[10:Rew:160202.0,147958.1] ||  -> member(regular(complement(union(image(element_relation,power_class(u)),v))),intersection(power_class(image(element_relation,complement(u))),complement(v)))* equal(complement(union(image(element_relation,power_class(u)),v)),successor_relation).
% 299.89/300.47  162581[10:Rew:160202.0,147972.1] || equal(intersection(complement(u),power_class(image(element_relation,complement(v)))),union(u,image(element_relation,power_class(v))))** -> equal(intersection(complement(u),power_class(image(element_relation,complement(v)))),successor_relation).
% 299.89/300.47  162582[10:Rew:160202.0,147973.0] ||  -> equal(symmetric_difference(complement(u),power_class(image(element_relation,complement(v)))),successor_relation) member(regular(symmetric_difference(complement(u),power_class(image(element_relation,complement(v))))),union(u,image(element_relation,power_class(v))))*.
% 299.89/300.47  162583[10:Rew:160202.0,147978.1] ||  -> member(regular(complement(union(u,image(element_relation,power_class(v))))),intersection(complement(u),power_class(image(element_relation,complement(v)))))* equal(complement(union(u,image(element_relation,power_class(v)))),successor_relation).
% 299.89/300.47  162585[10:Rew:160202.0,148486.4] || member(u,v)* member(u,w)* subclass(w,x)* well_ordering(cross_product(v,omega),x)* -> equal(integer_of(least(cross_product(v,omega),w)),successor_relation)**.
% 299.89/300.47  162759[10:Rew:160202.0,153072.4] || member(u,v)* member(u,w)* subclass(w,x)* well_ordering(cross_product(v,universal_class),x)* -> equal(integer_of(least(cross_product(v,universal_class),w)),successor_relation)**.
% 299.89/300.47  126096[0:Res:28321.1,22.1] || subclass(rest_relation,flip(cross_product(universal_class,universal_class))) member(ordered_pair(u,v),rest_of(ordered_pair(v,u))) -> member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),element_relation)*.
% 299.89/300.47  125966[0:Res:28320.1,22.1] || subclass(rest_relation,rotate(cross_product(universal_class,universal_class))) member(ordered_pair(u,rest_of(ordered_pair(v,u))),v) -> member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),element_relation)*.
% 299.89/300.47  92638[2:MRR:92621.3,2450.0] || member(u,ordinal_numbers) well_ordering(v,u) subclass(singleton(least(v,sum_class(u))),sum_class(u)) -> section(v,singleton(least(v,sum_class(u))),sum_class(u))*.
% 299.89/300.47  111817[2:Res:31076.2,9322.0] inductive(symmetric_difference(complement(u),complement(v))) || well_ordering(w,symmetric_difference(complement(u),complement(v))) -> member(least(w,symmetric_difference(complement(u),complement(v))),union(u,v))*.
% 299.89/300.47  162562[10:Rew:160202.0,147123.2] || member(image(u,singleton(v)),ordinal_numbers) well_ordering(w,image(u,singleton(v))) -> equal(segment(w,apply(u,v),least(w,apply(u,v))),successor_relation)**.
% 299.89/300.47  162407[10:Rew:160202.0,147124.1] || well_ordering(u,symmetric_difference(complement(v),complement(w))) -> equal(symmetric_difference(complement(v),complement(w)),successor_relation) member(least(u,symmetric_difference(complement(v),complement(w))),union(v,w))*.
% 299.89/300.47  42452[0:Res:8.1,5565.2] || equal(image(u,singleton(v)),apply(u,v)) member(ordinal_numbers,universal_class) well_ordering(element_relation,image(u,singleton(v)))* -> member(image(u,singleton(v)),ordinal_numbers).
% 299.89/300.47  163705[10:Rew:160202.0,162970.3] || member(u,universal_class) well_ordering(v,symmetric_difference(universal_class,w)) -> member(u,union(w,successor_relation))* member(least(v,complement(union(w,successor_relation))),complement(union(w,successor_relation)))*.
% 299.89/300.47  41079[0:Rew:57.0,41062.4] || member(u,universal_class) subclass(power_class(v),w)* well_ordering(x,w)* -> member(u,image(element_relation,complement(v)))* member(least(x,power_class(v)),power_class(v))*.
% 299.89/300.47  6189[0:Res:1477.1,61.0] || subclass(universal_class,image(u,image(v,singleton(w))))* member(ordered_pair(w,singleton(x)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,singleton(x)),compose(u,v))*.
% 299.89/300.47  119701[0:Res:114897.1,61.0] || equal(image(u,image(v,singleton(w))),universal_class) member(ordered_pair(w,singleton(x)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,singleton(x)),compose(u,v))*.
% 299.89/300.47  43130[0:Res:6269.3,3514.1] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,u),v),x)* subclass(universal_class,complement(rotate(x))) -> .
% 299.89/300.47  43165[0:Res:6260.3,3514.1] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,v),u),x)* subclass(universal_class,complement(flip(x))) -> .
% 299.89/300.47  108396[0:Res:5768.2,9332.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,intersection(w,x)) member(ordered_pair(u,ordered_pair(v,compose(u,v))),symmetric_difference(w,x))* -> .
% 299.89/300.47  39575[0:Res:5768.2,594.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,restrict(w,x,y))* -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),cross_product(x,y))*.
% 299.89/300.47  39584[0:Res:5768.2,307.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,image(element_relation,complement(w))) member(ordered_pair(u,ordered_pair(v,compose(u,v))),power_class(w))* -> .
% 299.89/300.47  161724[10:Rew:160202.0,159710.3] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,regular(w)) member(ordered_pair(u,ordered_pair(v,compose(u,v))),w)* -> equal(w,successor_relation).
% 299.89/300.47  187826[10:Res:187500.1,61.0] || subclass(universal_class,image(u,image(v,singleton(w))))* member(ordered_pair(w,power_class(successor_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,power_class(successor_relation)),compose(u,v)).
% 299.89/300.47  189468[15:Rew:189339.1,189390.3] || member(u,universal_class) subclass(domain_relation,complement(intersection(v,w))) member(ordered_pair(u,successor_relation),union(v,w)) -> member(ordered_pair(u,successor_relation),symmetric_difference(v,w))*.
% 299.89/300.47  192094[10:Rew:181082.0,192081.2] || member(image(u,successor_relation),ordinal_numbers) well_ordering(v,image(u,successor_relation)) -> equal(apply(u,universal_class),successor_relation) member(least(v,apply(u,universal_class)),apply(u,universal_class))*.
% 299.89/300.47  192548[10:Res:34070.2,162356.0] || member(u,universal_class) member(v,u) subclass(element_relation,w) well_ordering(omega,w)* -> equal(integer_of(ordered_pair(ordered_pair(v,u),least(omega,element_relation))),successor_relation)**.
% 299.89/300.47  192539[15:Res:189374.2,162356.0] || member(u,universal_class) subclass(domain_relation,v) subclass(v,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(ordered_pair(u,successor_relation),least(omega,v))),successor_relation)**.
% 299.89/300.47  195922[15:Rew:190721.0,195909.2] || member(ordered_pair(inverse(u),not_subclass_element(v,image(w,image(x,successor_relation)))),compose(w,x))* -> equal(range_of(u),successor_relation) subclass(v,image(w,image(x,successor_relation))).
% 299.89/300.47  195923[10:Rew:181044.1,195908.2] || member(u,universal_class) member(ordered_pair(successor(u),not_subclass_element(v,image(w,image(x,successor_relation)))),compose(w,x))* -> subclass(v,image(w,image(x,successor_relation))).
% 299.89/300.47  197070[10:Res:197034.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,regular(complement(successor(successor_relation))))),second(ordered_pair(u,regular(complement(successor(successor_relation)))))),ordered_pair(u,regular(complement(successor(successor_relation)))))**.
% 299.89/300.47  200012[6:Res:199848.1,61.0] || subclass(universal_class,image(u,image(v,singleton(w))))* member(ordered_pair(w,regular(rest_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,regular(rest_relation)),compose(u,v)).
% 299.89/300.47  200218[14:Rew:200028.1,200135.2] || member(u,universal_class) member(ordered_pair(range_of(u),not_subclass_element(v,image(w,image(x,successor_relation)))),compose(w,x))* -> subclass(v,image(w,image(x,successor_relation))).
% 299.89/300.47  200721[10:Res:161493.2,5647.0] inductive(compose(u,v)) ||  -> equal(integer_of(ordered_pair(w,not_subclass_element(x,image(u,image(v,singleton(w)))))),successor_relation)** subclass(x,image(u,image(v,singleton(w)))).
% 299.89/300.47  201402[6:Res:201231.1,61.0] || subclass(universal_class,image(u,image(v,singleton(w))))* member(ordered_pair(w,regular(domain_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,regular(domain_relation)),compose(u,v)).
% 299.89/300.47  202468[10:Res:163217.0,127.0] || subclass(image(element_relation,complement(u)),v)* well_ordering(w,v)* -> member(successor_relation,power_class(u)) member(least(w,image(element_relation,complement(u))),image(element_relation,complement(u)))*.
% 299.89/300.47  202464[10:Res:163217.0,162356.0] || subclass(image(element_relation,complement(u)),v)* well_ordering(omega,v) -> member(successor_relation,power_class(u)) equal(integer_of(ordered_pair(successor_relation,least(omega,image(element_relation,complement(u))))),successor_relation)**.
% 299.89/300.47  204904[10:Rew:203192.0,203568.3] || section(universal_class,u,v) well_ordering(w,u) -> equal(cantor(cross_product(v,u)),successor_relation) member(least(w,cantor(cross_product(v,u))),cantor(cross_product(v,u)))*.
% 299.89/300.47  204910[10:Rew:203192.0,203994.2] || section(u,intersection(v,w),x) -> equal(cantor(restrict(u,x,intersection(v,w))),successor_relation) member(regular(cantor(restrict(u,x,intersection(v,w)))),v)*.
% 299.89/300.47  204911[10:Rew:203192.0,203995.2] || section(u,intersection(v,w),x) -> equal(cantor(restrict(u,x,intersection(v,w))),successor_relation) member(regular(cantor(restrict(u,x,intersection(v,w)))),w)*.
% 299.89/300.47  204912[6:Rew:203192.0,204016.1] || section(cross_product(u,v),w,x) subclass(w,cantor(restrict(cross_product(x,w),u,v)))* -> equal(cantor(restrict(cross_product(u,v),x,w)),w).
% 299.89/300.47  204172[6:Rew:203285.0,110180.2] inductive(restrict(cantor(inverse(u)),v,w)) || well_ordering(x,range_of(u)) -> member(least(x,restrict(range_of(u),v,w)),restrict(range_of(u),v,w))*.
% 299.89/300.47  204941[6:Rew:203335.0,204472.1] inductive(cantor(restrict(u,v,singleton(w)))) || well_ordering(x,segment(u,v,w)) -> member(least(x,segment(u,v,w)),segment(u,v,w))*.
% 299.89/300.47  209476[12:Res:209377.1,61.0] || subclass(universal_class,image(u,image(v,singleton(w))))* member(ordered_pair(w,regular(element_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,regular(element_relation)),compose(u,v)).
% 299.89/300.47  210360[15:Res:189563.1,19.0] || subclass(domain_relation,flip(cross_product(u,v)))* -> equal(ordered_pair(first(ordered_pair(ordered_pair(w,x),successor_relation)),second(ordered_pair(ordered_pair(w,x),successor_relation))),ordered_pair(ordered_pair(w,x),successor_relation))**.
% 299.89/300.47  210466[15:Res:189564.1,6044.0] || subclass(domain_relation,rotate(compose(u,v))) member(w,x)* subclass(x,y)* well_ordering(image(u,image(v,singleton(ordered_pair(z,successor_relation)))),y)* -> .
% 299.89/300.47  210433[15:Res:189564.1,19.0] || subclass(domain_relation,rotate(cross_product(u,v)))* -> equal(ordered_pair(first(ordered_pair(ordered_pair(w,successor_relation),x)),second(ordered_pair(ordered_pair(w,successor_relation),x))),ordered_pair(ordered_pair(w,successor_relation),x))**.
% 299.89/300.47  212113[10:MRR:212085.0,160295.1] ||  -> member(regular(regular(intersection(complement(u),complement(v)))),union(u,v))* equal(regular(intersection(complement(u),complement(v))),successor_relation) equal(intersection(complement(u),complement(v)),successor_relation).
% 299.89/300.47  212547[13:Res:212515.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,regular(complement(power_class(universal_class))))),second(ordered_pair(u,regular(complement(power_class(universal_class)))))),ordered_pair(u,regular(complement(power_class(universal_class)))))**.
% 299.89/300.47  212651[10:Res:212518.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,regular(complement(power_class(successor_relation))))),second(ordered_pair(u,regular(complement(power_class(successor_relation)))))),ordered_pair(u,regular(complement(power_class(successor_relation)))))**.
% 299.89/300.47  214746[10:Res:161697.1,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(restrict(u,w,x),successor_relation) equal(integer_of(ordered_pair(regular(restrict(u,w,x)),least(omega,u))),successor_relation)**.
% 299.89/300.47  218907[22:Res:218867.1,61.0] || subclass(kind_1_ordinals,image(u,image(v,singleton(w))))* member(ordered_pair(w,singleton(successor_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,singleton(successor_relation)),compose(u,v)).
% 299.89/300.47  203956[10:Rew:203192.0,160605.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class) subclass(cantor(u),intersection(y__dfg,ordinal_numbers)) -> equal(apply(u,least(element_relation,intersection(y__dfg,ordinal_numbers))),sum_class(range_of(successor_relation)))**.
% 299.89/300.47  163700[10:Rew:160202.0,160619.1] || member(ordered_pair(u,v),compose(regular(cross_product(image(w,singleton(u)),universal_class)),w))* -> equal(cross_product(image(w,singleton(u)),universal_class),successor_relation) member(v,range_of(successor_relation)).
% 299.89/300.47  193795[10:SpL:193730.0,61.0] || member(u,range_of(successor_relation)) member(ordered_pair(v,u),cross_product(universal_class,universal_class)) -> member(ordered_pair(v,u),compose(complement(cross_product(image(w,singleton(v)),universal_class)),w))*.
% 299.89/300.47  203582[10:Rew:203192.0,160635.3] || member(u,universal_class) member(ordered_pair(u,v),compose(w,x))* subclass(image(w,range_of(successor_relation)),y)* -> member(u,cantor(x)) member(v,y)*.
% 299.89/300.47  163701[10:Rew:160202.0,160678.0] || member(ordered_pair(u,ordered_pair(v,least(range_of(successor_relation),w))),compose(successor_relation,x))* member(v,w) subclass(w,y)* well_ordering(range_of(successor_relation),y)* -> .
% 299.89/300.47  203593[10:Rew:203192.0,160662.2] || member(u,image(v,range_of(successor_relation))) member(ordered_pair(w,u),cross_product(universal_class,universal_class)) -> member(w,cantor(x)) member(ordered_pair(w,u),compose(v,x))*.
% 299.89/300.47  193791[10:SpL:193730.0,61.0] || member(u,image(v,range_of(successor_relation))) member(ordered_pair(w,u),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,u),compose(v,complement(cross_product(singleton(w),universal_class))))*.
% 299.89/300.47  163724[10:Rew:160305.0,162860.1,160305.0,162860.0,160202.0,162860.0] ||  -> equal(symmetric_difference(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals),successor_relation) member(regular(symmetric_difference(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals)),complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation))))*.
% 299.89/300.47  221506[10:Res:218373.0,5838.1] || member(u,universal_class)* well_ordering(v,complement(singleton(complement(w)))) -> equal(singleton(complement(w)),successor_relation) member(u,w)* member(least(v,complement(w)),complement(w))*.
% 299.89/300.47  221626[10:Res:161312.2,185698.1] inductive(apply(choice,intersection(u,ordinal_numbers))) || member(intersection(u,ordinal_numbers),universal_class)* -> equal(intersection(u,ordinal_numbers),successor_relation) equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  221614[10:Res:161311.2,185698.1] inductive(apply(choice,intersection(ordinal_numbers,u))) || member(intersection(ordinal_numbers,u),universal_class)* -> equal(intersection(ordinal_numbers,u),successor_relation) equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation)**.
% 299.89/300.47  222130[10:SpR:161565.2,221525.0] || member(cross_product(u,v),universal_class) -> equal(cross_product(u,v),successor_relation) member(singleton(first(apply(choice,cross_product(u,v)))),complement(singleton(apply(choice,cross_product(u,v)))))*.
% 299.89/300.47  222227[10:SpL:161565.2,222147.0] || member(cross_product(u,v),universal_class) member(singleton(first(apply(choice,cross_product(u,v)))),singleton(apply(choice,cross_product(u,v))))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  222249[15:Res:3872.2,189380.2] || member(ordered_pair(u,successor_relation),cross_product(v,w))* member(ordered_pair(u,successor_relation),x)* member(u,universal_class) subclass(domain_relation,complement(restrict(x,v,w)))* -> .
% 299.89/300.47  224324[25:Rew:224236.1,204943.2] function(cross_product(u,universal_class)) || subclass(image(universal_class,u),cantor(range_of(v))) equal(cantor(cantor(w)),universal_class) -> compatible(cross_product(u,universal_class),w,inverse(v))*.
% 299.89/300.47  225209[25:SpL:224739.1,61.0] function(u) || member(v,image(w,image(x,successor_relation))) member(ordered_pair(u,v),cross_product(universal_class,universal_class)) -> member(ordered_pair(u,v),compose(w,x))*.
% 299.89/300.47  225491[25:Rew:224739.1,225120.4,224739.1,225120.2] function(u) || member(ordinal_numbers,universal_class) well_ordering(element_relation,image(v,successor_relation)) subclass(apply(v,u),image(v,successor_relation))* -> member(image(v,successor_relation),ordinal_numbers).
% 299.89/300.47  227321[25:SpR:161565.2,224913.1] function(first(apply(choice,cross_product(u,v)))) || member(cross_product(u,v),universal_class) -> equal(cross_product(u,v),successor_relation) member(successor_relation,apply(choice,cross_product(u,v)))*.
% 299.89/300.47  229044[10:Res:228991.1,61.0] || subclass(kind_1_ordinals,image(u,image(v,singleton(w))))* member(ordered_pair(w,regular(ordinal_numbers)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,regular(ordinal_numbers)),compose(u,v)).
% 299.89/300.47  229272[10:Res:229228.1,61.0] || subclass(universal_class,image(u,image(v,singleton(w))))* member(ordered_pair(w,regular(ordinal_numbers)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,regular(ordinal_numbers)),compose(u,v)).
% 299.89/300.47  230874[10:MRR:230833.0,191.0] || member(image(element_relation,power_class(successor_relation)),universal_class) -> member(singleton(image(element_relation,power_class(successor_relation))),power_class(image(element_relation,universal_class)))* member(singleton(singleton(singleton(image(element_relation,power_class(successor_relation))))),element_relation).
% 299.89/300.47  231855[10:Res:161697.1,161035.0] || member(regular(restrict(intersection(power_class(successor_relation),complement(u)),v,w)),union(image(element_relation,universal_class),u))* -> equal(restrict(intersection(power_class(successor_relation),complement(u)),v,w),successor_relation).
% 299.89/300.47  34035[0:SpL:1943.0,3883.2] || member(u,union(cross_product(v,w),x))* member(u,complement(restrict(x,v,w))) subclass(symmetric_difference(cross_product(v,w),x),y)* -> member(u,y)*.
% 299.89/300.47  34034[0:SpL:1938.0,3883.2] || member(u,union(v,cross_product(w,x)))* member(u,complement(restrict(v,w,x))) subclass(symmetric_difference(v,cross_product(w,x)),y)* -> member(u,y)*.
% 299.89/300.47  40560[0:SpR:1931.0,1951.1] || member(u,symmetric_difference(complement(symmetric_difference(v,w)),union(complement(intersection(v,w)),union(v,w))))* -> member(u,complement(symmetric_difference(complement(intersection(v,w)),union(v,w)))).
% 299.89/300.47  42840[0:Res:8.1,5853.2] || equal(u,cross_product(v,w))* member(x,w)* member(y,v)* well_ordering(z,u)* -> member(least(z,cross_product(v,w)),cross_product(v,w))*.
% 299.89/300.47  42957[0:Res:8.1,5839.2] || equal(u,intersection(v,w))* member(x,w)* member(x,v)* well_ordering(y,u)* -> member(least(y,intersection(v,w)),intersection(v,w))*.
% 299.89/300.47  40070[0:Rew:28.0,40048.3] || member(u,v) subclass(v,w)* well_ordering(union(x,y),w)* -> member(ordered_pair(u,least(union(x,y),v)),intersection(complement(x),complement(y)))*.
% 299.89/300.47  108326[0:SpL:1931.0,9332.1] || member(u,symmetric_difference(complement(symmetric_difference(v,w)),union(complement(intersection(v,w)),union(v,w))))* member(u,symmetric_difference(complement(intersection(v,w)),union(v,w))) -> .
% 299.89/300.47  120038[0:Rew:114854.0,120003.2] || transitive(universal_class,u) subclass(cross_product(u,u),compose(cross_product(u,u),cross_product(u,u)))* -> equal(compose(cross_product(u,u),cross_product(u,u)),cross_product(u,u)).
% 299.89/300.47  151303[6:Rew:149379.0,149480.4] || member(least(cross_product(u,universal_class),v),cantor(w))* member(x,u)* member(x,v)* subclass(v,y)* well_ordering(cross_product(u,universal_class),y)* -> .
% 299.89/300.47  31213[0:Res:3872.2,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),cross_product(u,v))* member(least(element_relation,intersection(y__dfg,ordinal_numbers)),w) subclass(restrict(w,u,v),intersection(y__dfg,ordinal_numbers))* -> .
% 299.89/300.47  113261[0:Rew:1948.0,113178.1] || member(not_subclass_element(union(complement(u),complement(v)),symmetric_difference(complement(u),complement(v))),union(u,v))* -> subclass(union(complement(u),complement(v)),symmetric_difference(complement(u),complement(v))).
% 299.89/300.47  113215[0:Res:60.1,40234.0] || member(ordered_pair(u,not_subclass_element(v,intersection(image(w,image(x,singleton(u))),v))),compose(w,x))* -> subclass(v,intersection(image(w,image(x,singleton(u))),v)).
% 299.89/300.47  122864[0:Res:131.2,9640.0] || connected(u,intersection(v,w)) -> well_ordering(u,intersection(v,w)) subclass(not_well_ordering(u,intersection(v,w)),x) member(not_subclass_element(not_well_ordering(u,intersection(v,w)),x),w)*.
% 299.89/300.47  123455[0:Res:131.2,9639.0] || connected(u,intersection(v,w)) -> well_ordering(u,intersection(v,w)) subclass(not_well_ordering(u,intersection(v,w)),x) member(not_subclass_element(not_well_ordering(u,intersection(v,w)),x),v)*.
% 299.89/300.47  112656[0:MRR:112628.0,34189.1] || member(not_subclass_element(u,intersection(v,union(w,x))),v)* -> member(not_subclass_element(u,intersection(v,union(w,x))),complement(w))* subclass(u,intersection(v,union(w,x))).
% 299.89/300.47  112495[0:MRR:112461.0,34189.1] || member(not_subclass_element(u,intersection(v,union(w,x))),v)* -> member(not_subclass_element(u,intersection(v,union(w,x))),complement(x))* subclass(u,intersection(v,union(w,x))).
% 299.89/300.47  113191[0:Res:25.2,40234.0] || member(not_subclass_element(u,intersection(intersection(v,w),u)),w)* member(not_subclass_element(u,intersection(intersection(v,w),u)),v)* -> subclass(u,intersection(intersection(v,w),u)).
% 299.89/300.47  35688[0:Res:4.1,3874.1] || member(not_subclass_element(complement(intersection(u,v)),w),union(u,v)) -> subclass(complement(intersection(u,v)),w) member(not_subclass_element(complement(intersection(u,v)),w),symmetric_difference(u,v))*.
% 299.89/300.47  41921[0:SpL:2330.1,147.0] || member(not_subclass_element(cross_product(u,v),w),rest_relation) -> subclass(cross_product(u,v),w) equal(rest_of(first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w)))**.
% 299.89/300.47  125928[0:Res:28320.1,10.0] || subclass(rest_relation,rotate(unordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),v)* equal(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),u)*.
% 299.89/300.47  126058[0:Res:28321.1,10.0] || subclass(rest_relation,flip(unordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),v)* equal(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),u)*.
% 299.89/300.47  30988[0:Res:1032.1,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class) subclass(intersection(complement(u),complement(v)),intersection(y__dfg,ordinal_numbers))* -> member(least(element_relation,intersection(y__dfg,ordinal_numbers)),union(u,v)).
% 299.89/300.47  132303[0:Res:5771.1,9647.0] || equal(sum_class(restrict(u,v,w)),restrict(u,v,w)) -> subclass(sum_class(restrict(u,v,w)),x) member(not_subclass_element(sum_class(restrict(u,v,w)),x),u)*.
% 299.89/300.47  140171[0:SpR:982.0,984.0] ||  -> equal(union(u,image(element_relation,power_class(intersection(power_class(image(element_relation,complement(v))),complement(w))))),complement(intersection(complement(u),power_class(image(element_relation,union(image(element_relation,power_class(v)),w))))))**.
% 299.89/300.47  139648[0:SpR:982.0,982.0] ||  -> equal(union(image(element_relation,power_class(intersection(power_class(image(element_relation,complement(u))),complement(v)))),w),complement(intersection(power_class(image(element_relation,union(image(element_relation,power_class(u)),v))),complement(w))))**.
% 299.89/300.47  140155[0:SpR:984.0,984.0] ||  -> equal(union(u,image(element_relation,power_class(intersection(complement(v),power_class(image(element_relation,complement(w))))))),complement(intersection(complement(u),power_class(image(element_relation,union(v,image(element_relation,power_class(w))))))))**.
% 299.89/300.47  29357[0:SpR:505.0,1948.0] ||  -> equal(intersection(union(u,image(element_relation,union(v,w))),union(complement(u),power_class(intersection(complement(v),complement(w))))),symmetric_difference(complement(u),power_class(intersection(complement(v),complement(w)))))**.
% 299.89/300.47  125152[0:Rew:505.0,125108.1] ||  -> member(not_subclass_element(u,image(element_relation,power_class(intersection(complement(v),complement(w))))),power_class(image(element_relation,union(v,w))))* subclass(u,image(element_relation,power_class(intersection(complement(v),complement(w))))).
% 299.89/300.47  126569[0:Rew:505.0,126478.1] || member(not_subclass_element(intersection(u,power_class(intersection(complement(v),complement(w)))),x),image(element_relation,union(v,w)))* -> subclass(intersection(u,power_class(intersection(complement(v),complement(w)))),x).
% 299.89/300.47  140108[0:SpR:984.0,982.0] ||  -> equal(union(image(element_relation,power_class(intersection(complement(u),power_class(image(element_relation,complement(v)))))),w),complement(intersection(power_class(image(element_relation,union(u,image(element_relation,power_class(v))))),complement(w))))**.
% 299.89/300.47  29369[0:SpR:505.0,1948.0] ||  -> equal(intersection(union(image(element_relation,union(u,v)),w),union(power_class(intersection(complement(u),complement(v))),complement(w))),symmetric_difference(power_class(intersection(complement(u),complement(v))),complement(w)))**.
% 299.89/300.47  126795[0:Rew:505.0,126686.1] || member(not_subclass_element(intersection(power_class(intersection(complement(u),complement(v))),w),x),image(element_relation,union(u,v)))* -> subclass(intersection(power_class(intersection(complement(u),complement(v))),w),x).
% 299.89/300.47  140347[0:Rew:984.0,140119.1] ||  -> member(not_subclass_element(complement(union(u,image(element_relation,power_class(v)))),w),intersection(complement(u),power_class(image(element_relation,complement(v)))))* subclass(complement(union(u,image(element_relation,power_class(v)))),w).
% 299.89/300.47  140166[0:SpR:984.0,9529.1] ||  -> subclass(symmetric_difference(complement(u),power_class(image(element_relation,complement(v)))),w) member(not_subclass_element(symmetric_difference(complement(u),power_class(image(element_relation,complement(v)))),w),union(u,image(element_relation,power_class(v))))*.
% 299.89/300.47  140117[0:SpR:984.0,10293.0] ||  -> subclass(symmetric_difference(union(u,image(element_relation,power_class(v))),complement(singleton(intersection(complement(u),power_class(image(element_relation,complement(v))))))),successor(intersection(complement(u),power_class(image(element_relation,complement(v))))))*.
% 299.89/300.47  140105[0:SpR:984.0,10292.0] ||  -> subclass(symmetric_difference(union(u,image(element_relation,power_class(v))),complement(inverse(intersection(complement(u),power_class(image(element_relation,complement(v))))))),symmetrization_of(intersection(complement(u),power_class(image(element_relation,complement(v))))))*.
% 299.89/300.47  139883[0:Rew:982.0,139659.1] ||  -> member(not_subclass_element(complement(union(image(element_relation,power_class(u)),v)),w),intersection(power_class(image(element_relation,complement(u))),complement(v)))* subclass(complement(union(image(element_relation,power_class(u)),v)),w).
% 299.89/300.47  139703[0:SpR:982.0,9529.1] ||  -> subclass(symmetric_difference(power_class(image(element_relation,complement(u))),complement(v)),w) member(not_subclass_element(symmetric_difference(power_class(image(element_relation,complement(u))),complement(v)),w),union(image(element_relation,power_class(u)),v))*.
% 299.89/300.47  139657[0:SpR:982.0,10293.0] ||  -> subclass(symmetric_difference(union(image(element_relation,power_class(u)),v),complement(singleton(intersection(power_class(image(element_relation,complement(u))),complement(v))))),successor(intersection(power_class(image(element_relation,complement(u))),complement(v))))*.
% 299.89/300.47  139645[0:SpR:982.0,10292.0] ||  -> subclass(symmetric_difference(union(image(element_relation,power_class(u)),v),complement(inverse(intersection(power_class(image(element_relation,complement(u))),complement(v))))),symmetrization_of(intersection(power_class(image(element_relation,complement(u))),complement(v))))*.
% 299.89/300.47  160713[10:Rew:160202.0,146505.2] || member(u,universal_class) subclass(u,ordered_pair(v,w))* -> equal(u,successor_relation) equal(apply(choice,u),unordered_pair(v,singleton(w))) equal(apply(choice,u),singleton(v)).
% 299.89/300.47  163734[10:MRR:161554.3,160227.0] || equal(successor(first(regular(cross_product(u,v)))),second(regular(cross_product(u,v)))) member(regular(cross_product(u,v)),cross_product(universal_class,universal_class))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  161572[10:Rew:160202.0,146816.1] || member(regular(cross_product(u,v)),rest_of(w)) -> equal(cross_product(u,v),successor_relation) equal(restrict(w,first(regular(cross_product(u,v))),universal_class),second(regular(cross_product(u,v))))**.
% 299.89/300.47  161681[10:Rew:160202.0,146723.2] || subclass(complement(intersection(u,v)),w)* well_ordering(x,w)* -> equal(symmetric_difference(u,v),successor_relation) member(least(x,complement(intersection(u,v))),complement(intersection(u,v)))*.
% 299.89/300.47  161870[10:Rew:160202.0,146884.2] || member(intersection(u,intersection(v,w)),universal_class) member(apply(choice,intersection(u,intersection(v,w))),symmetric_difference(v,w))* -> equal(intersection(u,intersection(v,w)),successor_relation).
% 299.89/300.47  161876[10:Rew:160202.0,146905.2] || member(intersection(intersection(u,v),w),universal_class) member(apply(choice,intersection(intersection(u,v),w)),symmetric_difference(u,v))* -> equal(intersection(intersection(u,v),w),successor_relation).
% 299.89/300.47  161889[10:Rew:160202.0,146978.2] || member(apply(choice,complement(complement(intersection(u,v)))),symmetric_difference(u,v))* member(complement(complement(intersection(u,v))),universal_class) -> equal(complement(complement(intersection(u,v))),successor_relation).
% 299.89/300.47  162593[10:Rew:160202.0,146858.1] || transitive(u,v) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),successor_relation) member(regular(compose(restrict(u,v,v),restrict(u,v,v))),u)*.
% 299.89/300.47  162039[10:Rew:160202.0,146953.1] || member(intersection(u,restrict(v,w,x)),universal_class) -> equal(intersection(u,restrict(v,w,x)),successor_relation) member(apply(choice,intersection(u,restrict(v,w,x))),v)*.
% 299.89/300.47  162044[10:Rew:160202.0,146958.1] || member(intersection(restrict(u,v,w),x),universal_class) -> equal(intersection(restrict(u,v,w),x),successor_relation) member(apply(choice,intersection(restrict(u,v,w),x)),u)*.
% 299.89/300.47  162054[10:Rew:160202.0,146981.2] || member(intersection(complement(u),complement(v)),universal_class) member(apply(choice,intersection(complement(u),complement(v))),union(u,v))* -> equal(intersection(complement(u),complement(v)),successor_relation).
% 299.89/300.47  162059[10:Rew:160202.0,147006.1] || subclass(u,cross_product(v,w))* -> equal(intersection(x,u),successor_relation) equal(ordered_pair(first(regular(intersection(x,u))),second(regular(intersection(x,u)))),regular(intersection(x,u)))**.
% 299.89/300.47  162058[10:Rew:160202.0,147007.1] || subclass(u,ordered_pair(v,w))* -> equal(intersection(x,u),successor_relation) equal(regular(intersection(x,u)),unordered_pair(v,singleton(w)))* equal(regular(intersection(x,u)),singleton(v)).
% 299.89/300.47  162073[10:Rew:160202.0,147021.1] || subclass(u,cross_product(v,w))* -> equal(intersection(u,x),successor_relation) equal(ordered_pair(first(regular(intersection(u,x))),second(regular(intersection(u,x)))),regular(intersection(u,x)))**.
% 299.89/300.47  162072[10:Rew:160202.0,147022.1] || subclass(u,ordered_pair(v,w))* -> equal(intersection(u,x),successor_relation) equal(regular(intersection(u,x)),unordered_pair(v,singleton(w)))* equal(regular(intersection(u,x)),singleton(v)).
% 299.89/300.47  162595[10:Rew:160202.0,147129.2] || member(regular(complement(restrict(u,v,w))),cross_product(v,w))* member(regular(complement(restrict(u,v,w))),u)* -> equal(complement(restrict(u,v,w)),successor_relation).
% 299.89/300.47  162597[10:Rew:160202.0,147131.0] ||  -> equal(intersection(u,ordered_pair(v,w)),successor_relation) equal(regular(intersection(u,ordered_pair(v,w))),unordered_pair(v,singleton(w)))** equal(regular(intersection(u,ordered_pair(v,w))),singleton(v)).
% 299.89/300.47  162599[10:Rew:160202.0,147133.0] ||  -> equal(intersection(ordered_pair(u,v),w),successor_relation) equal(regular(intersection(ordered_pair(u,v),w)),unordered_pair(u,singleton(v)))** equal(regular(intersection(ordered_pair(u,v),w)),singleton(u)).
% 299.89/300.47  162601[10:Rew:160202.0,147556.1] || member(regular(image(element_relation,power_class(intersection(complement(u),complement(v))))),power_class(image(element_relation,union(u,v))))* -> equal(image(element_relation,power_class(intersection(complement(u),complement(v)))),successor_relation).
% 299.89/300.47  162603[10:Rew:160202.0,147626.1] || member(regular(intersection(u,intersection(power_class(image(element_relation,complement(v))),w))),image(element_relation,power_class(v)))* -> equal(intersection(u,intersection(power_class(image(element_relation,complement(v))),w)),successor_relation).
% 299.89/300.47  162605[10:Rew:160202.0,147684.1] || member(regular(intersection(u,intersection(v,power_class(image(element_relation,complement(w)))))),image(element_relation,power_class(w)))* -> equal(intersection(u,intersection(v,power_class(image(element_relation,complement(w))))),successor_relation).
% 299.89/300.47  162606[10:Rew:160202.0,147724.1] || member(regular(intersection(intersection(power_class(image(element_relation,complement(u))),v),w)),image(element_relation,power_class(u)))* -> equal(intersection(intersection(power_class(image(element_relation,complement(u))),v),w),successor_relation).
% 299.89/300.47  162608[10:Rew:160202.0,147797.1] || member(regular(intersection(intersection(u,power_class(image(element_relation,complement(v)))),w)),image(element_relation,power_class(v)))* -> equal(intersection(intersection(u,power_class(image(element_relation,complement(v)))),w),successor_relation).
% 299.89/300.47  162609[10:Rew:160202.0,147834.0] ||  -> equal(intersection(u,intersection(v,symmetric_difference(w,cross_product(x,y)))),successor_relation) member(regular(intersection(u,intersection(v,symmetric_difference(w,cross_product(x,y))))),complement(restrict(w,x,y)))*.
% 299.89/300.47  162610[10:Rew:160202.0,147835.0] ||  -> equal(intersection(intersection(u,symmetric_difference(v,cross_product(w,x))),y),successor_relation) member(regular(intersection(intersection(u,symmetric_difference(v,cross_product(w,x))),y)),complement(restrict(v,w,x)))*.
% 299.89/300.47  162611[10:Rew:160202.0,147836.0] ||  -> equal(intersection(u,intersection(symmetric_difference(v,cross_product(w,x)),y)),successor_relation) member(regular(intersection(u,intersection(symmetric_difference(v,cross_product(w,x)),y))),complement(restrict(v,w,x)))*.
% 299.89/300.47  162612[10:Rew:160202.0,147837.0] ||  -> equal(intersection(intersection(symmetric_difference(u,cross_product(v,w)),x),y),successor_relation) member(regular(intersection(intersection(symmetric_difference(u,cross_product(v,w)),x),y)),complement(restrict(u,v,w)))*.
% 299.89/300.47  162613[10:Rew:160202.0,147842.0] ||  -> equal(intersection(u,intersection(v,symmetric_difference(cross_product(w,x),y))),successor_relation) member(regular(intersection(u,intersection(v,symmetric_difference(cross_product(w,x),y)))),complement(restrict(y,w,x)))*.
% 299.89/300.47  162614[10:Rew:160202.0,147843.0] ||  -> equal(intersection(intersection(u,symmetric_difference(cross_product(v,w),x)),y),successor_relation) member(regular(intersection(intersection(u,symmetric_difference(cross_product(v,w),x)),y)),complement(restrict(x,v,w)))*.
% 299.89/300.47  162615[10:Rew:160202.0,147844.0] ||  -> equal(intersection(u,intersection(symmetric_difference(cross_product(v,w),x),y)),successor_relation) member(regular(intersection(u,intersection(symmetric_difference(cross_product(v,w),x),y))),complement(restrict(x,v,w)))*.
% 299.89/300.47  162616[10:Rew:160202.0,147845.0] ||  -> equal(intersection(intersection(symmetric_difference(cross_product(u,v),w),x),y),successor_relation) member(regular(intersection(intersection(symmetric_difference(cross_product(u,v),w),x),y)),complement(restrict(w,u,v)))*.
% 299.89/300.47  162619[10:Rew:160202.0,147895.0] ||  -> equal(symmetric_difference(power_class(u),complement(singleton(image(element_relation,complement(u))))),successor_relation) member(regular(symmetric_difference(power_class(u),complement(singleton(image(element_relation,complement(u)))))),successor(image(element_relation,complement(u))))*.
% 299.89/300.47  162621[10:Rew:160202.0,147915.0] ||  -> equal(symmetric_difference(power_class(u),complement(inverse(image(element_relation,complement(u))))),successor_relation) member(regular(symmetric_difference(power_class(u),complement(inverse(image(element_relation,complement(u)))))),symmetrization_of(image(element_relation,complement(u))))*.
% 299.89/300.47  183772[10:Rew:113504.0,183767.0,160223.0,183767.0,28.0,183767.0] ||  -> equal(symmetric_difference(union(singleton(successor_relation),successor(successor_relation)),union(complement(singleton(successor_relation)),complement(successor(successor_relation)))),union(union(singleton(successor_relation),successor(successor_relation)),union(complement(singleton(successor_relation)),complement(successor(successor_relation)))))**.
% 299.89/300.47  183780[10:Rew:113504.0,183775.0,160223.0,183775.0,28.0,183775.0] ||  -> equal(symmetric_difference(union(inverse(successor_relation),symmetrization_of(successor_relation)),union(complement(inverse(successor_relation)),complement(symmetrization_of(successor_relation)))),union(union(inverse(successor_relation),symmetrization_of(successor_relation)),union(complement(inverse(successor_relation)),complement(symmetrization_of(successor_relation)))))**.
% 299.89/300.47  108837[2:Res:31076.2,6041.0] inductive(u) || well_ordering(cross_product(v,u),u)* member(w,v)* member(w,u)* subclass(u,x) well_ordering(cross_product(v,u),x)* -> .
% 299.89/300.47  108802[2:Res:31076.2,513.0] inductive(intersection(complement(u),complement(v))) || well_ordering(w,intersection(complement(u),complement(v))) member(least(w,intersection(complement(u),complement(v))),union(u,v))* -> .
% 299.89/300.47  161436[10:Rew:160202.0,146630.5] || well_ordering(cross_product(u,v),v)* member(w,u)* member(w,v)* subclass(v,x) well_ordering(cross_product(u,v),x)* -> equal(v,successor_relation).
% 299.89/300.47  162451[10:Rew:160202.0,147105.2] || well_ordering(u,intersection(complement(v),complement(w))) member(least(u,intersection(complement(v),complement(w))),union(v,w))* -> equal(intersection(complement(v),complement(w)),successor_relation).
% 299.89/300.47  160066[3:Res:159952.1,5853.2] || subclass(cross_product(u,v),ordinal_numbers) member(w,v)* member(x,u)* well_ordering(y,kind_1_ordinals) -> member(least(y,cross_product(u,v)),cross_product(u,v))*.
% 299.89/300.47  160068[3:Res:159952.1,5839.2] || subclass(intersection(u,v),ordinal_numbers) member(w,v)* member(w,u)* well_ordering(x,kind_1_ordinals) -> member(least(x,intersection(u,v)),intersection(u,v))*.
% 299.89/300.47  184598[10:Res:184565.1,5554.0] || well_ordering(u,kind_1_ordinals) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,least(u,ordinal_numbers))),second(ordered_pair(v,least(u,ordinal_numbers)))),ordered_pair(v,least(u,ordinal_numbers)))**.
% 299.89/300.47  108285[2:Res:31069.2,6041.0] inductive(u) || well_ordering(cross_product(v,u),universal_class)* member(w,v)* member(w,u)* subclass(u,x) well_ordering(cross_product(v,u),x)* -> .
% 299.89/300.47  161435[10:Rew:160202.0,146634.5] || well_ordering(cross_product(u,v),universal_class)* member(w,u)* member(w,v)* subclass(v,x) well_ordering(cross_product(u,v),x)* -> equal(v,successor_relation).
% 299.89/300.47  44804[0:Res:6.0,5857.1] || member(ordered_pair(u,v),compose(w,x))* well_ordering(y,universal_class) -> member(least(y,image(w,image(x,singleton(u)))),image(w,image(x,singleton(u))))*.
% 299.89/300.47  162699[10:Rew:160202.0,151346.1] || well_ordering(u,universal_class) -> equal(restrict(cross_product(v,w),x,x),successor_relation) member(least(u,restrict(cross_product(x,x),v,w)),restrict(cross_product(x,x),v,w))*.
% 299.89/300.47  162602[10:Rew:160202.0,147574.2] || well_ordering(u,universal_class) member(least(u,power_class(intersection(complement(v),complement(w)))),image(element_relation,union(v,w)))* -> equal(power_class(intersection(complement(v),complement(w))),successor_relation).
% 299.89/300.47  110381[0:Res:110370.1,5554.0] || well_ordering(u,universal_class) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,least(u,rest_relation))),second(ordered_pair(v,least(u,rest_relation)))),ordered_pair(v,least(u,rest_relation)))**.
% 299.89/300.47  110636[0:Res:110623.1,5554.0] || well_ordering(u,universal_class) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,least(u,universal_class))),second(ordered_pair(v,least(u,universal_class)))),ordered_pair(v,least(u,universal_class)))**.
% 299.89/300.47  110387[0:Res:110376.1,5554.0] || well_ordering(u,rest_relation) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,least(u,rest_relation))),second(ordered_pair(v,least(u,rest_relation)))),ordered_pair(v,least(u,rest_relation)))**.
% 299.89/300.47  112448[0:Res:30985.1,127.0] || member(u,universal_class) subclass(union(v,w),x)* well_ordering(y,x)* -> member(u,complement(w))* member(least(y,union(v,w)),union(v,w))*.
% 299.89/300.47  112615[0:Res:30984.1,127.0] || member(u,universal_class) subclass(union(v,w),x)* well_ordering(y,x)* -> member(u,complement(v))* member(least(y,union(v,w)),union(v,w))*.
% 299.89/300.47  111834[0:Res:5768.2,9322.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,symmetric_difference(complement(w),complement(x))) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),union(w,x))*.
% 299.89/300.47  161914[10:Rew:160202.0,147155.1] || member(ordered_pair(u,regular(cross_product(v,w))),composition_function)* -> equal(cross_product(v,w),successor_relation) equal(compose(u,first(regular(cross_product(v,w)))),second(regular(cross_product(v,w)))).
% 299.89/300.47  188728[17:Res:188716.1,5554.0] || well_ordering(u,universal_class) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,least(u,omega))),second(ordered_pair(v,least(u,omega)))),ordered_pair(v,least(u,omega)))**.
% 299.89/300.47  188736[17:Res:188721.1,5554.0] || well_ordering(u,omega) member(v,w)* -> equal(ordered_pair(first(ordered_pair(v,least(u,omega))),second(ordered_pair(v,least(u,omega)))),ordered_pair(v,least(u,omega)))**.
% 299.89/300.47  192542[10:Res:1495.2,162356.0] || member(u,universal_class) subclass(rest_relation,v) subclass(v,w)* well_ordering(omega,w)* -> equal(integer_of(ordered_pair(ordered_pair(u,rest_of(u)),least(omega,v))),successor_relation)**.
% 299.89/300.47  193423[10:Res:192947.1,61.0] || equal(complement(image(u,image(v,singleton(w)))),successor_relation) member(ordered_pair(w,singleton(x)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,singleton(x)),compose(u,v))*.
% 299.89/300.47  194180[6:Res:157922.1,3886.0] || member(not_subclass_element(u,intersection(v,compose(element_relation,universal_class))),element_relation)* member(not_subclass_element(u,intersection(v,compose(element_relation,universal_class))),v)* -> subclass(u,intersection(v,compose(element_relation,universal_class))).
% 299.89/300.47  195807[6:Res:195710.1,5839.2] || equal(inverse(u),universal_class) member(v,w)* member(v,x)* well_ordering(y,inverse(u))* -> member(least(y,intersection(x,w)),intersection(x,w))*.
% 299.89/300.47  195804[6:Res:195710.1,5853.2] || equal(inverse(u),universal_class) member(v,w)* member(x,y)* well_ordering(z,inverse(u))* -> member(least(z,cross_product(y,w)),cross_product(y,w))*.
% 299.89/300.47  195866[6:Res:195720.1,5839.2] || equal(sum_class(u),universal_class) member(v,w)* member(v,x)* well_ordering(y,sum_class(u))* -> member(least(y,intersection(x,w)),intersection(x,w))*.
% 299.89/300.47  195863[6:Res:195720.1,5853.2] || equal(sum_class(u),universal_class) member(v,w)* member(x,y)* well_ordering(z,sum_class(u))* -> member(least(z,cross_product(y,w)),cross_product(y,w))*.
% 299.89/300.47  196446[10:Res:160848.0,5832.1] inductive(complement(power_class(image(element_relation,successor_relation)))) || well_ordering(u,image(element_relation,power_class(universal_class))) -> member(least(u,complement(power_class(image(element_relation,successor_relation)))),complement(power_class(image(element_relation,successor_relation))))*.
% 299.89/300.47  196443[10:Res:160848.0,160292.0] || well_ordering(u,image(element_relation,power_class(universal_class))) -> equal(complement(power_class(image(element_relation,successor_relation))),successor_relation) member(least(u,complement(power_class(image(element_relation,successor_relation)))),complement(power_class(image(element_relation,successor_relation))))*.
% 299.89/300.47  196498[10:Res:161138.0,5832.1] inductive(complement(power_class(complement(inverse(successor_relation))))) || well_ordering(u,image(element_relation,symmetrization_of(successor_relation))) -> member(least(u,complement(power_class(complement(inverse(successor_relation))))),complement(power_class(complement(inverse(successor_relation)))))*.
% 299.89/300.47  196495[10:Res:161138.0,160292.0] || well_ordering(u,image(element_relation,symmetrization_of(successor_relation))) -> equal(complement(power_class(complement(inverse(successor_relation)))),successor_relation) member(least(u,complement(power_class(complement(inverse(successor_relation))))),complement(power_class(complement(inverse(successor_relation)))))*.
% 299.89/300.47  196638[10:Res:160971.0,5832.1] inductive(complement(power_class(image(element_relation,universal_class)))) || well_ordering(u,image(element_relation,power_class(successor_relation))) -> member(least(u,complement(power_class(image(element_relation,universal_class)))),complement(power_class(image(element_relation,universal_class))))*.
% 299.89/300.47  196635[10:Res:160971.0,160292.0] || well_ordering(u,image(element_relation,power_class(successor_relation))) -> equal(complement(power_class(image(element_relation,universal_class))),successor_relation) member(least(u,complement(power_class(image(element_relation,universal_class)))),complement(power_class(image(element_relation,universal_class))))*.
% 299.89/300.47  196806[10:Res:162888.0,5832.1] inductive(complement(power_class(complement(singleton(successor_relation))))) || well_ordering(u,image(element_relation,successor(successor_relation))) -> member(least(u,complement(power_class(complement(singleton(successor_relation))))),complement(power_class(complement(singleton(successor_relation)))))*.
% 299.89/300.47  196803[10:Res:162888.0,160292.0] || well_ordering(u,image(element_relation,successor(successor_relation))) -> equal(complement(power_class(complement(singleton(successor_relation)))),successor_relation) member(least(u,complement(power_class(complement(singleton(successor_relation))))),complement(power_class(complement(singleton(successor_relation)))))*.
% 299.89/300.47  197813[10:MRR:197794.3,160227.0] function(u) || member(ordered_pair(v,regular(image(u,image(inverse(u),singleton(v))))),cross_product(universal_class,universal_class))* -> equal(image(u,image(inverse(u),singleton(v))),successor_relation).
% 299.89/300.47  197814[10:MRR:197793.3,160227.0] single_valued_class(u) || member(ordered_pair(v,regular(image(u,image(inverse(u),singleton(v))))),cross_product(universal_class,universal_class))* -> equal(image(u,image(inverse(u),singleton(v))),successor_relation).
% 299.89/300.47  200690[10:Res:161493.2,61.0] inductive(image(u,image(v,singleton(w)))) || member(ordered_pair(w,x),cross_product(universal_class,universal_class)) -> equal(integer_of(x),successor_relation) member(ordered_pair(w,x),compose(u,v))*.
% 299.89/300.47  201986[10:Res:161492.2,5647.0] || equal(compose(u,v),omega) -> equal(integer_of(ordered_pair(w,not_subclass_element(x,image(u,image(v,singleton(w)))))),successor_relation)** subclass(x,image(u,image(v,singleton(w)))).
% 299.89/300.47  203376[6:Rew:203192.0,41909.2] || member(not_subclass_element(cross_product(u,v),w),domain_relation) -> subclass(cross_product(u,v),w) equal(cantor(first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w)))**.
% 299.89/300.47  203521[6:Rew:203192.0,120011.0] || member(u,cantor(universal_class))* equal(cross_product(u,universal_class),least(rest_of(universal_class),v))* member(u,v)* subclass(v,w)* well_ordering(rest_of(universal_class),w)* -> .
% 299.89/300.47  203638[15:Rew:203192.0,193971.0] || member(first(regular(cross_product(u,v))),cantor(w)) member(ordered_pair(w,regular(cross_product(u,v))),cross_product(universal_class,cross_product(universal_class,universal_class)))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  204929[6:Rew:203192.0,203996.2] || section(u,intersection(v,w),x) -> subclass(cantor(restrict(u,x,intersection(v,w))),y) member(not_subclass_element(cantor(restrict(u,x,intersection(v,w))),y),v)*.
% 299.89/300.47  204930[6:Rew:203192.0,203997.2] || section(u,intersection(v,w),x) -> subclass(cantor(restrict(u,x,intersection(v,w))),y) member(not_subclass_element(cantor(restrict(u,x,intersection(v,w))),y),w)*.
% 299.89/300.47  210350[15:Res:189563.1,3874.1] || subclass(domain_relation,flip(complement(intersection(u,v)))) member(ordered_pair(ordered_pair(w,x),successor_relation),union(u,v)) -> member(ordered_pair(ordered_pair(w,x),successor_relation),symmetric_difference(u,v))*.
% 299.89/300.47  210423[15:Res:189564.1,3874.1] || subclass(domain_relation,rotate(complement(intersection(u,v)))) member(ordered_pair(ordered_pair(w,successor_relation),x),union(u,v)) -> member(ordered_pair(ordered_pair(w,successor_relation),x),symmetric_difference(u,v))*.
% 299.89/300.47  212112[10:MRR:212086.3,188688.2] || member(regular(regular(restrict(u,v,w))),cross_product(v,w))* member(regular(regular(restrict(u,v,w))),u)* -> equal(regular(restrict(u,v,w)),successor_relation).
% 299.89/300.47  212792[15:SpL:161592.1,203931.0] || member(regular(cross_product(u,v)),cross_product(universal_class,universal_class)) member(second(regular(cross_product(u,v))),cantor(first(regular(cross_product(u,v)))))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  214314[10:Res:214277.1,61.0] || equal(complement(image(u,image(v,singleton(w)))),successor_relation) member(ordered_pair(w,power_class(successor_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,power_class(successor_relation)),compose(u,v))*.
% 299.89/300.47  216410[14:Rew:199971.1,216313.2] || member(u,universal_class) member(ordered_pair(sum_class(range_of(u)),not_subclass_element(v,image(w,image(x,successor_relation)))),compose(w,x))* -> subclass(v,image(w,image(x,successor_relation))).
% 299.89/300.47  216500[10:Res:216465.1,61.0] || equal(complement(image(u,image(v,singleton(w)))),successor_relation) member(ordered_pair(w,regular(rest_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,regular(rest_relation)),compose(u,v))*.
% 299.89/300.47  216928[10:Res:216847.1,61.0] || equal(complement(image(u,image(v,singleton(w)))),successor_relation) member(ordered_pair(w,regular(domain_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,regular(domain_relation)),compose(u,v))*.
% 299.89/300.47  218327[10:MRR:218276.0,34189.1] ||  -> member(not_subclass_element(regular(intersection(complement(u),complement(v))),w),union(u,v))* subclass(regular(intersection(complement(u),complement(v))),w) equal(intersection(complement(u),complement(v)),successor_relation).
% 299.89/300.47  219571[10:Res:978.1,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> subclass(restrict(u,w,x),y) equal(integer_of(ordered_pair(not_subclass_element(restrict(u,w,x),y),least(omega,u))),successor_relation)**.
% 299.89/300.47  204927[10:Rew:203192.0,203747.4] || member(u,universal_class) subclass(cantor(v),w)* well_ordering(x,w)* -> equal(apply(v,u),sum_class(range_of(successor_relation)))** member(least(x,cantor(v)),cantor(v))*.
% 299.89/300.47  204926[10:Rew:203192.0,203617.2,203192.0,203617.1] || member(not_subclass_element(u,intersection(v,cantor(w))),v)* -> equal(apply(w,not_subclass_element(u,intersection(v,cantor(w)))),sum_class(range_of(successor_relation)))** subclass(u,intersection(v,cantor(w))).
% 299.89/300.47  203581[10:Rew:203192.0,163706.2] || member(u,universal_class) member(ordered_pair(u,not_subclass_element(v,image(w,range_of(successor_relation)))),compose(w,x))* -> member(u,cantor(x)) subclass(v,image(w,range_of(successor_relation))).
% 299.89/300.47  163730[10:Rew:160202.0,162861.1,160305.0,162861.1,160305.0,162861.0] ||  -> subclass(symmetric_difference(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals),u) member(not_subclass_element(symmetric_difference(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals),u),complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation))))*.
% 299.89/300.47  221505[10:Res:218373.0,5646.1] || member(ordered_pair(u,v),compose(w,x)) -> equal(singleton(image(w,image(x,singleton(u)))),successor_relation) member(v,complement(singleton(image(w,image(x,singleton(u))))))*.
% 299.89/300.47  221857[10:Res:5771.1,160703.0] || equal(sum_class(complement(compose(element_relation,universal_class))),complement(compose(element_relation,universal_class))) member(regular(sum_class(complement(compose(element_relation,universal_class)))),element_relation)* -> equal(sum_class(complement(compose(element_relation,universal_class))),successor_relation).
% 299.89/300.47  225492[25:Rew:224739.1,225119.4,224739.1,225119.3,224739.1,225119.1] function(u) || well_ordering(element_relation,image(v,successor_relation)) subclass(apply(v,u),image(v,successor_relation))* -> equal(image(v,successor_relation),ordinal_numbers) member(image(v,successor_relation),ordinal_numbers).
% 299.89/300.47  228885[24:MRR:228884.0,34067.1] || member(u,successor(kind_1_ordinals))* subclass(symmetric_difference(complement(kind_1_ordinals),universal_class),v)* well_ordering(w,v)* -> member(least(w,symmetric_difference(complement(kind_1_ordinals),universal_class)),symmetric_difference(complement(kind_1_ordinals),universal_class))*.
% 299.89/300.47  229813[10:Res:221521.1,3886.0] || member(not_subclass_element(u,intersection(v,complement(singleton(omega)))),v)* -> equal(integer_of(not_subclass_element(u,intersection(v,complement(singleton(omega))))),successor_relation) subclass(u,intersection(v,complement(singleton(omega)))).
% 299.89/300.47  230827[10:Res:160972.1,179.1] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class) subclass(image(element_relation,power_class(successor_relation)),intersection(y__dfg,ordinal_numbers)) -> member(least(element_relation,intersection(y__dfg,ordinal_numbers)),power_class(image(element_relation,universal_class)))*.
% 299.89/300.47  231026[10:SpL:10028.0,195436.0] || subclass(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),symmetrization_of(image(element_relation,complement(u))))* -> equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),successor_relation).
% 299.89/300.47  230945[10:SpR:10028.0,218298.0] ||  -> subclass(regular(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))),symmetrization_of(image(element_relation,complement(u))))* equal(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))),successor_relation).
% 299.89/300.47  231350[10:SpL:10029.0,195436.0] || subclass(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),successor(image(element_relation,complement(u))))* -> equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),successor_relation).
% 299.89/300.47  231268[10:SpR:10029.0,218298.0] ||  -> subclass(regular(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))),successor(image(element_relation,complement(u))))* equal(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))),successor_relation).
% 299.89/300.47  231864[10:Res:978.1,161035.0] || member(not_subclass_element(restrict(intersection(power_class(successor_relation),complement(u)),v,w),x),union(image(element_relation,universal_class),u))* -> subclass(restrict(intersection(power_class(successor_relation),complement(u)),v,w),x).
% 299.89/300.47  35653[0:SpL:161.0,3874.1] || member(u,union(complement(intersection(v,w)),union(v,w))) member(u,complement(symmetric_difference(v,w))) -> member(u,symmetric_difference(complement(intersection(v,w)),union(v,w)))*.
% 299.89/300.47  9334[0:Res:1951.1,129.3] || member(ordered_pair(u,least(complement(intersection(v,w)),x)),symmetric_difference(v,w))* member(u,x) subclass(x,y)* well_ordering(complement(intersection(v,w)),y)* -> .
% 299.89/300.47  43982[0:Res:1499.1,6036.0] || subclass(universal_class,u) member(ordered_pair(v,least(intersection(w,u),x)),w)* member(v,x) subclass(x,y)* well_ordering(intersection(w,u),y)* -> .
% 299.89/300.47  31112[2:Res:10293.0,5832.1] inductive(symmetric_difference(complement(u),complement(singleton(u)))) || well_ordering(v,successor(u)) -> member(least(v,symmetric_difference(complement(u),complement(singleton(u)))),symmetric_difference(complement(u),complement(singleton(u))))*.
% 299.89/300.47  31111[2:Res:10292.0,5832.1] inductive(symmetric_difference(complement(u),complement(inverse(u)))) || well_ordering(v,symmetrization_of(u)) -> member(least(v,symmetric_difference(complement(u),complement(inverse(u)))),symmetric_difference(complement(u),complement(inverse(u))))*.
% 299.89/300.47  91290[2:Obv:91289.4] function(not_well_ordering(u,v)) || well_ordering(u,cross_product(universal_class,universal_class)) connected(u,v) member(least(u,not_well_ordering(u,v)),not_well_ordering(u,v))* -> well_ordering(u,v).
% 299.89/300.47  151439[6:MRR:151438.0,34067.1] || member(ordered_pair(u,least(symmetric_difference(universal_class,cantor(v)),w)),complement(cantor(v)))* member(u,w) subclass(w,x)* well_ordering(symmetric_difference(universal_class,cantor(v)),x)* -> .
% 299.89/300.47  42961[0:Res:64.1,5839.2] function(intersection(u,v)) || member(w,v)* member(w,u)* well_ordering(x,cross_product(universal_class,universal_class)) -> member(least(x,intersection(u,v)),intersection(u,v))*.
% 299.89/300.47  35716[0:Res:1495.2,3874.1] || member(u,universal_class) subclass(rest_relation,complement(intersection(v,w))) member(ordered_pair(u,rest_of(u)),union(v,w)) -> member(ordered_pair(u,rest_of(u)),symmetric_difference(v,w))*.
% 299.89/300.47  9416[0:Rew:30.0,9382.1,30.0,9382.0] ||  -> subclass(restrict(u,v,w),x) equal(ordered_pair(first(not_subclass_element(restrict(u,v,w),x)),second(not_subclass_element(restrict(u,v,w),x))),not_subclass_element(restrict(u,v,w),x))**.
% 299.89/300.47  132312[0:Res:120.1,9647.0] || transitive(u,v) -> subclass(compose(restrict(u,v,v),restrict(u,v,v)),w) member(not_subclass_element(compose(restrict(u,v,v),restrict(u,v,v)),w),u)*.
% 299.89/300.47  89249[0:Res:51387.0,19.0] ||  -> subclass(u,complement(cross_product(v,w))) equal(ordered_pair(first(not_subclass_element(u,complement(cross_product(v,w)))),second(not_subclass_element(u,complement(cross_product(v,w))))),not_subclass_element(u,complement(cross_product(v,w))))**.
% 299.89/300.47  123509[0:Res:978.1,10.0] ||  -> subclass(restrict(unordered_pair(u,v),w,x),y) equal(not_subclass_element(restrict(unordered_pair(u,v),w,x),y),v)** equal(not_subclass_element(restrict(unordered_pair(u,v),w,x),y),u)**.
% 299.89/300.47  137118[0:SpR:505.0,10029.0] ||  -> equal(complement(intersection(power_class(image(element_relation,union(u,v))),complement(singleton(image(element_relation,power_class(intersection(complement(u),complement(v)))))))),successor(image(element_relation,power_class(intersection(complement(u),complement(v))))))**.
% 299.89/300.47  137738[0:SpR:505.0,10028.0] ||  -> equal(complement(intersection(power_class(image(element_relation,union(u,v))),complement(inverse(image(element_relation,power_class(intersection(complement(u),complement(v)))))))),symmetrization_of(image(element_relation,power_class(intersection(complement(u),complement(v))))))**.
% 299.89/300.47  137102[0:SpR:10029.0,9529.1] ||  -> subclass(symmetric_difference(power_class(u),complement(singleton(image(element_relation,complement(u))))),v) member(not_subclass_element(symmetric_difference(power_class(u),complement(singleton(image(element_relation,complement(u))))),v),successor(image(element_relation,complement(u))))*.
% 299.89/300.47  137058[0:SpR:10029.0,10293.0] ||  -> subclass(symmetric_difference(successor(image(element_relation,complement(u))),complement(singleton(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))))),successor(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))))*.
% 299.89/300.47  137048[0:SpR:10029.0,10292.0] ||  -> subclass(symmetric_difference(successor(image(element_relation,complement(u))),complement(inverse(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))))),symmetrization_of(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))))*.
% 299.89/300.47  137721[0:SpR:10028.0,9529.1] ||  -> subclass(symmetric_difference(power_class(u),complement(inverse(image(element_relation,complement(u))))),v) member(not_subclass_element(symmetric_difference(power_class(u),complement(inverse(image(element_relation,complement(u))))),v),symmetrization_of(image(element_relation,complement(u))))*.
% 299.89/300.47  137677[0:SpR:10028.0,10293.0] ||  -> subclass(symmetric_difference(symmetrization_of(image(element_relation,complement(u))),complement(singleton(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))))),successor(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))))*.
% 299.89/300.47  137666[0:SpR:10028.0,10292.0] ||  -> subclass(symmetric_difference(symmetrization_of(image(element_relation,complement(u))),complement(inverse(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))))),symmetrization_of(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))))*.
% 299.89/300.47  124619[0:Res:25.2,33515.1] || member(singleton(intersection(u,v)),v)* member(singleton(intersection(u,v)),u)* member(intersection(u,v),universal_class) -> member(singleton(singleton(singleton(intersection(u,v)))),element_relation)*.
% 299.89/300.47  124652[0:MRR:124620.0,191.0] || member(intersection(complement(u),complement(v)),universal_class) -> member(singleton(intersection(complement(u),complement(v))),union(u,v))* member(singleton(singleton(singleton(intersection(complement(u),complement(v))))),element_relation)*.
% 299.89/300.47  161571[10:Rew:160202.0,146793.2] || member(cross_product(u,v),universal_class) subclass(apply(choice,cross_product(u,v)),w) -> equal(cross_product(u,v),successor_relation) member(singleton(first(apply(choice,cross_product(u,v)))),w)*.
% 299.89/300.47  161570[10:Rew:160202.0,146794.2] || member(cross_product(u,v),universal_class) equal(w,apply(choice,cross_product(u,v))) -> equal(cross_product(u,v),successor_relation) member(singleton(first(apply(choice,cross_product(u,v)))),w)*.
% 299.89/300.47  162157[10:Rew:160202.0,146968.1] || member(intersection(symmetric_difference(u,singleton(u)),v),universal_class) -> equal(intersection(symmetric_difference(u,singleton(u)),v),successor_relation) member(apply(choice,intersection(symmetric_difference(u,singleton(u)),v)),successor(u))*.
% 299.89/300.47  162159[10:Rew:160202.0,146970.1] || member(intersection(symmetric_difference(u,inverse(u)),v),universal_class) -> equal(intersection(symmetric_difference(u,inverse(u)),v),successor_relation) member(apply(choice,intersection(symmetric_difference(u,inverse(u)),v)),symmetrization_of(u))*.
% 299.89/300.47  162161[10:Rew:160202.0,146972.1] || member(intersection(u,symmetric_difference(v,singleton(v))),universal_class) -> equal(intersection(u,symmetric_difference(v,singleton(v))),successor_relation) member(apply(choice,intersection(u,symmetric_difference(v,singleton(v)))),successor(v))*.
% 299.89/300.47  162163[10:Rew:160202.0,146974.1] || member(intersection(u,symmetric_difference(v,inverse(v))),universal_class) -> equal(intersection(u,symmetric_difference(v,inverse(v))),successor_relation) member(apply(choice,intersection(u,symmetric_difference(v,inverse(v)))),symmetrization_of(v))*.
% 299.89/300.47  162165[10:Rew:160202.0,146983.2] || member(power_class(image(element_relation,complement(u))),universal_class) member(apply(choice,power_class(image(element_relation,complement(u)))),image(element_relation,power_class(u)))* -> equal(power_class(image(element_relation,complement(u))),successor_relation).
% 299.89/300.47  162236[10:Rew:160202.0,147044.1] || member(symmetric_difference(u,cross_product(v,w)),universal_class) -> equal(symmetric_difference(u,cross_product(v,w)),successor_relation) member(apply(choice,symmetric_difference(u,cross_product(v,w))),complement(restrict(u,v,w)))*.
% 299.89/300.47  162240[10:Rew:160202.0,147047.1] || member(symmetric_difference(cross_product(u,v),w),universal_class) -> equal(symmetric_difference(cross_product(u,v),w),successor_relation) member(apply(choice,symmetric_difference(cross_product(u,v),w)),complement(restrict(w,u,v)))*.
% 299.89/300.47  162496[10:Rew:160202.0,147112.1] || subclass(complement(symmetric_difference(u,v)),w) -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),successor_relation) member(regular(symmetric_difference(complement(intersection(u,v)),union(u,v))),w)*.
% 299.89/300.47  162627[10:Rew:160202.0,147137.1] || well_ordering(u,symmetrization_of(v)) -> equal(symmetric_difference(complement(v),complement(inverse(v))),successor_relation) member(least(u,symmetric_difference(complement(v),complement(inverse(v)))),symmetric_difference(complement(v),complement(inverse(v))))*.
% 299.89/300.47  162628[10:Rew:160202.0,147138.1] || well_ordering(u,successor(v)) -> equal(symmetric_difference(complement(v),complement(singleton(v))),successor_relation) member(least(u,symmetric_difference(complement(v),complement(singleton(v)))),symmetric_difference(complement(v),complement(singleton(v))))*.
% 299.89/300.47  162631[10:Rew:160202.0,147162.2] || member(regular(intersection(u,complement(intersection(v,w)))),w)* member(regular(intersection(u,complement(intersection(v,w)))),v)* -> equal(intersection(u,complement(intersection(v,w))),successor_relation).
% 299.89/300.47  162634[10:Rew:160202.0,147165.2] || member(regular(intersection(complement(intersection(u,v)),w)),v)* member(regular(intersection(complement(intersection(u,v)),w)),u)* -> equal(intersection(complement(intersection(u,v)),w),successor_relation).
% 299.89/300.47  162639[10:Rew:160202.0,147483.1] || member(ordered_pair(u,regular(intersection(v,complement(image(w,image(x,singleton(u))))))),compose(w,x))* -> equal(intersection(v,complement(image(w,image(x,singleton(u))))),successor_relation).
% 299.89/300.47  162640[10:Rew:160202.0,147510.1] || member(ordered_pair(u,regular(intersection(complement(image(v,image(w,singleton(u)))),x))),compose(v,w))* -> equal(intersection(complement(image(v,image(w,singleton(u)))),x),successor_relation).
% 299.89/300.47  162641[10:Rew:160202.0,147529.0] ||  -> equal(symmetric_difference(union(u,v),union(complement(u),complement(v))),successor_relation) member(regular(symmetric_difference(union(u,v),union(complement(u),complement(v)))),complement(symmetric_difference(complement(u),complement(v))))*.
% 299.89/300.47  162642[10:Rew:160202.0,147637.0] ||  -> equal(intersection(u,symmetric_difference(complement(intersection(v,w)),union(v,w))),successor_relation) member(regular(intersection(u,symmetric_difference(complement(intersection(v,w)),union(v,w)))),complement(symmetric_difference(v,w)))*.
% 299.89/300.47  162643[10:Rew:160202.0,147735.0] ||  -> equal(intersection(symmetric_difference(complement(intersection(u,v)),union(u,v)),w),successor_relation) member(regular(intersection(symmetric_difference(complement(intersection(u,v)),union(u,v)),w)),complement(symmetric_difference(u,v)))*.
% 299.89/300.47  162648[10:Rew:160202.0,147901.1] || member(regular(intersection(u,successor(image(element_relation,complement(v))))),intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))* -> equal(intersection(u,successor(image(element_relation,complement(v)))),successor_relation).
% 299.89/300.47  162649[10:Rew:160202.0,147902.1] || member(regular(intersection(successor(image(element_relation,complement(u))),v)),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* -> equal(intersection(successor(image(element_relation,complement(u))),v),successor_relation).
% 299.89/300.47  162650[10:Rew:160202.0,147921.1] || member(regular(intersection(u,symmetrization_of(image(element_relation,complement(v))))),intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))* -> equal(intersection(u,symmetrization_of(image(element_relation,complement(v)))),successor_relation).
% 299.89/300.47  162651[10:Rew:160202.0,147922.1] || member(regular(intersection(symmetrization_of(image(element_relation,complement(u))),v)),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* -> equal(intersection(symmetrization_of(image(element_relation,complement(u))),v),successor_relation).
% 299.89/300.47  181225[10:Rew:181067.0,181217.2] || member(ordered_pair(ordered_pair(universal_class,successor_relation),u),v) member(ordered_pair(singleton(singleton(successor_relation)),u),cross_product(cross_product(universal_class,universal_class),universal_class))* -> member(ordered_pair(singleton(singleton(successor_relation)),u),flip(v))*.
% 299.89/300.47  181226[10:Rew:181067.0,181216.2] || member(ordered_pair(ordered_pair(universal_class,u),successor_relation),v) member(ordered_pair(singleton(singleton(successor_relation)),u),cross_product(cross_product(universal_class,universal_class),universal_class))* -> member(ordered_pair(singleton(singleton(successor_relation)),u),rotate(v))*.
% 299.89/300.47  92641[2:MRR:92617.2,2450.0] || well_ordering(u,cross_product(universal_class,universal_class)) subclass(singleton(least(u,compose(v,w))),compose(v,w)) -> section(u,singleton(least(u,compose(v,w))),compose(v,w))*.
% 299.89/300.47  130462[2:Res:31076.2,9306.0] inductive(symmetric_difference(cross_product(u,v),w)) || well_ordering(x,symmetric_difference(cross_product(u,v),w)) -> member(least(x,symmetric_difference(cross_product(u,v),w)),complement(restrict(w,u,v)))*.
% 299.89/300.47  130369[2:Res:31076.2,9300.0] inductive(symmetric_difference(u,cross_product(v,w))) || well_ordering(x,symmetric_difference(u,cross_product(v,w))) -> member(least(x,symmetric_difference(u,cross_product(v,w))),complement(restrict(u,v,w)))*.
% 299.89/300.47  124261[2:Res:31076.2,986.1] inductive(power_class(image(element_relation,complement(u)))) || well_ordering(v,power_class(image(element_relation,complement(u)))) member(least(v,power_class(image(element_relation,complement(u)))),image(element_relation,power_class(u)))* -> .
% 299.89/300.47  162532[10:Rew:160202.0,146835.2] || member(image(u,singleton(v)),ordinal_numbers) well_ordering(w,image(u,singleton(v))) -> equal(apply(u,v),successor_relation) member(least(w,apply(u,v)),apply(u,v))*.
% 299.89/300.47  31149[2:Res:303.1,5832.1] inductive(apply(u,v)) || member(image(u,singleton(v)),ordinal_numbers) well_ordering(w,image(u,singleton(v))) -> member(least(w,apply(u,v)),apply(u,v))*.
% 299.89/300.47  43070[0:Res:8.1,5536.1] || equal(image(u,singleton(v)),apply(u,v)) well_ordering(element_relation,image(u,singleton(v)))* -> equal(image(u,singleton(v)),ordinal_numbers) member(image(u,singleton(v)),ordinal_numbers).
% 299.89/300.47  162255[10:Rew:160202.0,147136.2] || section(u,singleton(v),w) well_ordering(x,singleton(v)) -> equal(segment(u,w,v),successor_relation) member(least(x,segment(u,w,v)),segment(u,w,v))*.
% 299.89/300.47  31148[2:Res:2126.1,5832.1] inductive(segment(u,v,w)) || section(u,singleton(w),v) well_ordering(x,singleton(w)) -> member(least(x,segment(u,v,w)),segment(u,v,w))*.
% 299.89/300.47  162518[10:Rew:160202.0,147839.1] || well_ordering(u,symmetric_difference(cross_product(v,w),x)) -> equal(symmetric_difference(cross_product(v,w),x),successor_relation) member(least(u,symmetric_difference(cross_product(v,w),x)),complement(restrict(x,v,w)))*.
% 299.89/300.47  162516[10:Rew:160202.0,147831.1] || well_ordering(u,symmetric_difference(v,cross_product(w,x))) -> equal(symmetric_difference(v,cross_product(w,x)),successor_relation) member(least(u,symmetric_difference(v,cross_product(w,x))),complement(restrict(v,w,x)))*.
% 299.89/300.47  162510[10:Rew:160202.0,147561.2] || well_ordering(u,power_class(image(element_relation,complement(v)))) member(least(u,power_class(image(element_relation,complement(v)))),image(element_relation,power_class(v)))* -> equal(power_class(image(element_relation,complement(v))),successor_relation).
% 299.89/300.47  162637[10:Rew:160202.0,147168.3] || member(least(u,complement(intersection(v,w))),w)* member(least(u,complement(intersection(v,w))),v)* well_ordering(u,universal_class) -> equal(complement(intersection(v,w)),successor_relation).
% 299.89/300.47  161913[10:Rew:160202.0,147159.1] || well_ordering(u,universal_class) -> equal(cross_product(v,w),successor_relation) equal(ordered_pair(first(least(u,cross_product(v,w))),second(least(u,cross_product(v,w)))),least(u,cross_product(v,w)))**.
% 299.89/300.47  161895[10:Rew:160202.0,147085.5] || well_ordering(u,universal_class) member(v,singleton(w)) subclass(singleton(w),x)* well_ordering(u,x)* member(ordered_pair(v,w),u)* -> equal(singleton(w),successor_relation).
% 299.89/300.47  163716[10:Rew:160202.0,161667.4] || member(u,universal_class) subclass(union(v,successor_relation),w)* well_ordering(x,w)* -> member(u,symmetric_difference(universal_class,v))* member(least(x,union(v,successor_relation)),union(v,successor_relation))*.
% 299.89/300.47  42843[0:Res:64.1,5853.2] function(cross_product(u,v)) || member(w,v)* member(x,u)* well_ordering(y,cross_product(universal_class,universal_class)) -> member(least(y,cross_product(u,v)),cross_product(u,v))*.
% 299.89/300.47  183940[11:Res:183764.1,61.0] || subclass(universal_class,image(u,image(v,singleton(w)))) member(ordered_pair(w,regular(symmetrization_of(successor_relation))),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,regular(symmetrization_of(successor_relation))),compose(u,v))*.
% 299.89/300.47  6196[0:Res:1476.1,61.0] || subclass(universal_class,image(u,image(v,singleton(w)))) member(ordered_pair(w,unordered_pair(x,y)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,unordered_pair(x,y)),compose(u,v))*.
% 299.89/300.47  163717[10:Rew:160202.0,163106.2] || subclass(domain_relation,image(u,image(v,singleton(w)))) member(ordered_pair(w,ordered_pair(successor_relation,successor_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,ordered_pair(successor_relation,successor_relation)),compose(u,v))*.
% 299.89/300.47  6197[0:Res:1499.1,61.0] || subclass(universal_class,image(u,image(v,singleton(w)))) member(ordered_pair(w,ordered_pair(x,y)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,ordered_pair(x,y)),compose(u,v))*.
% 299.89/300.47  6188[0:Res:3907.1,61.0] || equal(complement(complement(image(u,image(v,singleton(w))))),universal_class)** member(ordered_pair(w,singleton(x)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,singleton(x)),compose(u,v))*.
% 299.89/300.47  156334[6:MRR:156324.3,146185.0] single_valued_class(u) || member(ordered_pair(v,not_subclass_element(image(u,image(inverse(u),singleton(v))),w)),cross_product(universal_class,universal_class))* -> subclass(image(u,image(inverse(u),singleton(v))),w).
% 299.89/300.47  156370[6:MRR:156360.3,146185.0] function(u) || member(ordered_pair(v,not_subclass_element(image(u,image(inverse(u),singleton(v))),w)),cross_product(universal_class,universal_class))* -> subclass(image(u,image(inverse(u),singleton(v))),w).
% 299.89/300.47  143784[0:Res:5768.2,159.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,omega) -> equal(integer_of(ordered_pair(u,ordered_pair(v,compose(u,v)))),ordered_pair(u,ordered_pair(v,compose(u,v))))**.
% 299.89/300.47  39572[0:Res:5768.2,513.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,intersection(complement(w),complement(x))) member(ordered_pair(u,ordered_pair(v,compose(u,v))),union(w,x))* -> .
% 299.89/300.47  39607[0:Res:5768.2,38.0] || member(ordered_pair(ordered_pair(u,v),w),cross_product(universal_class,universal_class)) subclass(composition_function,flip(x)) -> member(ordered_pair(ordered_pair(v,u),ordered_pair(w,compose(ordered_pair(u,v),w))),x)*.
% 299.89/300.47  39608[0:Res:5768.2,35.0] || member(ordered_pair(ordered_pair(u,v),w),cross_product(universal_class,universal_class)) subclass(composition_function,rotate(x)) -> member(ordered_pair(ordered_pair(v,ordered_pair(w,compose(ordered_pair(u,v),w))),u),x)*.
% 299.89/300.47  191207[10:Res:161311.2,148657.1] || member(intersection(complement(compose(element_relation,universal_class)),u),universal_class) member(apply(choice,intersection(complement(compose(element_relation,universal_class)),u)),element_relation)* -> equal(intersection(complement(compose(element_relation,universal_class)),u),successor_relation).
% 299.89/300.47  191334[10:Res:161312.2,148657.1] || member(intersection(u,complement(compose(element_relation,universal_class))),universal_class) member(apply(choice,intersection(u,complement(compose(element_relation,universal_class)))),element_relation)* -> equal(intersection(u,complement(compose(element_relation,universal_class))),successor_relation).
% 299.89/300.47  192545[10:Res:28321.1,162356.0] || subclass(rest_relation,flip(u)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),least(omega,u))),successor_relation)**.
% 299.89/300.47  192544[10:Res:28320.1,162356.0] || subclass(rest_relation,rotate(u)) subclass(u,v)* well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),least(omega,u))),successor_relation)**.
% 299.89/300.47  192511[10:Res:25.2,162356.0] || member(u,v) member(u,w) subclass(intersection(w,v),x)* well_ordering(omega,x) -> equal(integer_of(ordered_pair(u,least(omega,intersection(w,v)))),successor_relation)**.
% 299.89/300.47  192510[10:Res:1951.1,162356.0] || member(u,symmetric_difference(v,w)) subclass(complement(intersection(v,w)),x)* well_ordering(omega,x) -> equal(integer_of(ordered_pair(u,least(omega,complement(intersection(v,w))))),successor_relation)**.
% 299.89/300.47  193263[10:SoR:5564.0,160511.2] single_valued_class(sum_class(cross_product(universal_class,universal_class))) || member(ordinal_numbers,universal_class) well_ordering(element_relation,cross_product(universal_class,universal_class))* equal(sum_class(cross_product(universal_class,universal_class)),successor_relation) -> member(cross_product(universal_class,universal_class),ordinal_numbers).
% 299.89/300.47  193955[14:SpL:161592.1,184007.1] || equal(sum_class(range_of(first(regular(cross_product(u,v))))),second(regular(cross_product(u,v)))) member(regular(cross_product(u,v)),cross_product(universal_class,universal_class))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  195931[0:SpR:195152.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(u,intersection(u,v))),union(complement(intersection(u,v)),union(u,intersection(u,v)))),symmetric_difference(complement(intersection(u,v)),union(u,intersection(u,v))))**.
% 299.89/300.47  196073[0:SpR:195339.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(u,intersection(v,u))),union(complement(intersection(v,u)),union(u,intersection(v,u)))),symmetric_difference(complement(intersection(v,u)),union(u,intersection(v,u))))**.
% 299.89/300.47  196592[10:Rew:161137.0,196584.3] || member(u,v) subclass(v,w)* well_ordering(power_class(complement(inverse(successor_relation))),w)* -> member(ordered_pair(u,least(power_class(complement(inverse(successor_relation))),v)),image(element_relation,symmetrization_of(successor_relation)))*.
% 299.89/300.47  196797[10:Rew:162889.0,196790.3] || member(u,v) subclass(v,w)* well_ordering(power_class(complement(singleton(successor_relation))),w)* -> member(ordered_pair(u,least(power_class(complement(singleton(successor_relation))),v)),image(element_relation,successor(successor_relation)))*.
% 299.89/300.47  197157[10:Rew:181067.0,197146.1] || member(u,universal_class) member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(universal_class,u),successor_relation),v) -> member(ordered_pair(singleton(singleton(successor_relation)),u),rotate(v))*.
% 299.89/300.47  197233[10:Rew:181067.0,197222.1] || member(u,universal_class) member(singleton(singleton(successor_relation)),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(universal_class,successor_relation),u),v) -> member(ordered_pair(singleton(singleton(successor_relation)),u),flip(v))*.
% 299.89/300.47  197809[10:Res:162685.2,185639.1] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(universal_class,universal_class))* equal(compose(v,w),successor_relation) -> equal(image(v,image(w,singleton(u))),successor_relation).
% 299.89/300.47  201955[10:Res:161492.2,61.0] || equal(image(u,image(v,singleton(w))),omega) member(ordered_pair(w,x),cross_product(universal_class,universal_class)) -> equal(integer_of(x),successor_relation) member(ordered_pair(w,x),compose(u,v))*.
% 299.89/300.47  202771[10:MRR:202770.0,34067.1] || member(u,union(v,successor_relation))* subclass(symmetric_difference(complement(v),universal_class),w)* well_ordering(x,w)* -> member(least(x,symmetric_difference(complement(v),universal_class)),symmetric_difference(complement(v),universal_class))*.
% 299.89/300.47  203572[6:Rew:203192.0,40947.0] || member(u,cantor(cross_product(v,w))) equal(restrict(cross_product(u,universal_class),v,w),x)* subclass(rest_of(cross_product(v,w)),y)* -> member(ordered_pair(u,x),y)*.
% 299.89/300.47  207860[10:Res:206688.0,162356.0] || subclass(complement(intersection(complement(singleton(successor_relation)),power_class(u))),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(successor_relation,least(omega,complement(intersection(complement(singleton(successor_relation)),power_class(u)))))),successor_relation)**.
% 299.89/300.47  208140[10:Res:207196.0,162356.0] || subclass(complement(intersection(power_class(u),complement(singleton(successor_relation)))),v)* well_ordering(omega,v) -> equal(integer_of(ordered_pair(successor_relation,least(omega,complement(intersection(power_class(u),complement(singleton(successor_relation))))))),successor_relation)**.
% 299.89/300.47  211701[10:Res:181213.1,61.0] || equal(image(u,image(v,singleton(w))),singleton(singleton(successor_relation))) member(ordered_pair(w,singleton(successor_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,singleton(successor_relation)),compose(u,v))*.
% 299.89/300.47  213407[10:Res:161691.1,162356.0] || subclass(union(u,v),w)* well_ordering(omega,w) -> equal(symmetric_difference(u,v),successor_relation) equal(integer_of(ordered_pair(regular(symmetric_difference(u,v)),least(omega,union(u,v)))),successor_relation)**.
% 299.89/300.47  214204[10:Res:6842.1,162356.0] || subclass(universal_class,symmetric_difference(u,v)) subclass(union(u,v),w)* well_ordering(omega,w) -> equal(integer_of(ordered_pair(unordered_pair(x,y),least(omega,union(u,v)))),successor_relation)**.
% 299.89/300.47  214393[10:Res:30985.1,162356.0] || member(u,universal_class) subclass(union(v,w),x)* well_ordering(omega,x) -> member(u,complement(w)) equal(integer_of(ordered_pair(u,least(omega,union(v,w)))),successor_relation)**.
% 299.89/300.47  214540[10:Res:30984.1,162356.0] || member(u,universal_class) subclass(union(v,w),x)* well_ordering(omega,x) -> member(u,complement(v)) equal(integer_of(ordered_pair(u,least(omega,union(v,w)))),successor_relation)**.
% 299.89/300.47  216134[6:Res:199830.1,61.0] || equal(image(u,image(v,singleton(w))),cross_product(universal_class,universal_class)) member(ordered_pair(w,regular(rest_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,regular(rest_relation)),compose(u,v))*.
% 299.89/300.47  216742[6:Res:201220.1,61.0] || equal(image(u,image(v,singleton(w))),cross_product(universal_class,universal_class)) member(ordered_pair(w,regular(domain_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,regular(domain_relation)),compose(u,v))*.
% 299.89/300.47  163715[10:Rew:160202.0,160629.2] || member(ordered_pair(u,v),compose(w,regular(cross_product(singleton(u),universal_class))))* subclass(image(w,range_of(successor_relation)),x)* -> equal(cross_product(singleton(u),universal_class),successor_relation) member(v,x)*.
% 299.89/300.47  223372[24:Rew:222479.0,223338.2] || member(ordered_pair(ordered_pair(kind_1_ordinals,u),v),w) member(ordered_pair(ordered_pair(u,universal_class),v),cross_product(cross_product(universal_class,universal_class),universal_class))* -> member(ordered_pair(ordered_pair(u,universal_class),v),flip(w))*.
% 299.89/300.47  223373[24:Rew:222479.0,223337.2] || member(ordered_pair(ordered_pair(kind_1_ordinals,u),v),w) member(ordered_pair(ordered_pair(v,universal_class),u),cross_product(cross_product(universal_class,universal_class),universal_class))* -> member(ordered_pair(ordered_pair(v,universal_class),u),rotate(w))*.
% 299.89/300.47  223375[24:Rew:222479.0,223263.1] || member(u,universal_class) member(ordered_pair(v,universal_class),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(kind_1_ordinals,v),u),w) -> member(ordered_pair(ordered_pair(v,universal_class),u),flip(w))*.
% 299.89/300.47  223376[24:Rew:222479.0,223262.1] || member(u,universal_class) member(ordered_pair(v,universal_class),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(kind_1_ordinals,u),v),w) -> member(ordered_pair(ordered_pair(v,universal_class),u),rotate(w))*.
% 299.89/300.47  224328[25:Rew:224236.1,204973.2] function(restrict(u,v,universal_class)) || subclass(image(u,v),cantor(range_of(w))) equal(cantor(cantor(x)),universal_class) -> compatible(restrict(u,v,universal_class),x,inverse(w))*.
% 299.89/300.47  224995[25:SpR:224739.1,224321.3] function(u) function(v) || subclass(range_of(v),cantor(segment(w,x,u)))* equal(cantor(cantor(y)),universal_class) -> compatible(v,y,restrict(w,x,successor_relation))*.
% 299.89/300.47  226569[10:Res:161880.1,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(intersection(intersection(u,w),x),successor_relation) equal(integer_of(ordered_pair(regular(intersection(intersection(u,w),x)),least(omega,u))),successor_relation)**.
% 299.89/300.47  227160[10:Res:161881.1,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(intersection(intersection(w,u),x),successor_relation) equal(integer_of(ordered_pair(regular(intersection(intersection(w,u),x)),least(omega,u))),successor_relation)**.
% 299.89/300.47  227456[10:Res:161874.1,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(intersection(w,intersection(u,x)),successor_relation) equal(integer_of(ordered_pair(regular(intersection(w,intersection(u,x))),least(omega,u))),successor_relation)**.
% 299.89/300.47  228062[10:Res:161875.1,162356.0] || subclass(u,v)* well_ordering(omega,v)* -> equal(intersection(w,intersection(x,u)),successor_relation) equal(integer_of(ordered_pair(regular(intersection(w,intersection(x,u))),least(omega,u))),successor_relation)**.
% 299.89/300.47  228355[10:Res:161722.2,162356.0] || subclass(u,v) subclass(v,w)* well_ordering(omega,w)* -> equal(intersection(u,x),successor_relation) equal(integer_of(ordered_pair(regular(intersection(u,x)),least(omega,v))),successor_relation)**.
% 299.89/300.47  228576[10:Res:161711.2,162356.0] || subclass(u,v) subclass(v,w)* well_ordering(omega,w)* -> equal(intersection(x,u),successor_relation) equal(integer_of(ordered_pair(regular(intersection(x,u)),least(omega,v))),successor_relation)**.
% 299.89/300.47  230880[10:MRR:230830.0,999.0] || member(u,v) subclass(v,w)* well_ordering(image(element_relation,power_class(successor_relation)),w)* -> member(ordered_pair(u,least(image(element_relation,power_class(successor_relation)),v)),power_class(image(element_relation,universal_class)))*.
% 299.89/300.47  231863[10:Res:161875.1,161035.0] || member(regular(intersection(u,intersection(v,intersection(power_class(successor_relation),complement(w))))),union(image(element_relation,universal_class),w))* -> equal(intersection(u,intersection(v,intersection(power_class(successor_relation),complement(w)))),successor_relation).
% 299.89/300.47  231861[10:Res:161881.1,161035.0] || member(regular(intersection(intersection(u,intersection(power_class(successor_relation),complement(v))),w)),union(image(element_relation,universal_class),v))* -> equal(intersection(intersection(u,intersection(power_class(successor_relation),complement(v))),w),successor_relation).
% 299.89/300.47  231859[10:Res:161874.1,161035.0] || member(regular(intersection(u,intersection(intersection(power_class(successor_relation),complement(v)),w))),union(image(element_relation,universal_class),v))* -> equal(intersection(u,intersection(intersection(power_class(successor_relation),complement(v)),w)),successor_relation).
% 299.89/300.47  231858[10:Res:161880.1,161035.0] || member(regular(intersection(intersection(intersection(power_class(successor_relation),complement(u)),v),w)),union(image(element_relation,universal_class),u))* -> equal(intersection(intersection(intersection(power_class(successor_relation),complement(u)),v),w),successor_relation).
% 299.89/300.47  33818[0:SpR:506.0,1938.0] ||  -> equal(intersection(complement(restrict(intersection(complement(u),complement(v)),w,x)),complement(intersection(union(u,v),complement(cross_product(w,x))))),symmetric_difference(intersection(complement(u),complement(v)),cross_product(w,x)))**.
% 299.89/300.47  33895[0:SpR:507.0,1943.0] ||  -> equal(intersection(complement(restrict(intersection(complement(u),complement(v)),w,x)),complement(intersection(complement(cross_product(w,x)),union(u,v)))),symmetric_difference(cross_product(w,x),intersection(complement(u),complement(v))))**.
% 299.89/300.47  35654[0:SpL:1933.0,3874.1] || member(u,union(complement(intersection(v,inverse(v))),symmetrization_of(v))) member(u,complement(symmetric_difference(v,inverse(v)))) -> member(u,symmetric_difference(complement(intersection(v,inverse(v))),symmetrization_of(v)))*.
% 299.89/300.47  35655[0:SpL:1934.0,3874.1] || member(u,union(complement(intersection(v,singleton(v))),successor(v))) member(u,complement(symmetric_difference(v,singleton(v)))) -> member(u,symmetric_difference(complement(intersection(v,singleton(v))),successor(v)))*.
% 299.89/300.47  31008[0:MRR:30989.0,999.0] || member(u,v) subclass(v,w)* well_ordering(intersection(complement(x),complement(y)),w)* -> member(ordered_pair(u,least(intersection(complement(x),complement(y)),v)),union(x,y))*.
% 299.89/300.47  142664[2:Rew:113504.0,142538.1] || asymmetric(cross_product(u,v),w) -> equal(symmetric_difference(restrict(inverse(cross_product(u,v)),u,v),cross_product(w,w)),union(restrict(inverse(cross_product(u,v)),u,v),cross_product(w,w)))**.
% 299.89/300.47  142665[2:Rew:113504.0,142539.1] || asymmetric(cross_product(u,v),w) -> equal(symmetric_difference(cross_product(w,w),restrict(inverse(cross_product(u,v)),u,v)),union(cross_product(w,w),restrict(inverse(cross_product(u,v)),u,v)))**.
% 299.89/300.47  35726[0:Res:3595.3,3874.1] function(u) || member(v,universal_class) subclass(universal_class,complement(intersection(w,x))) member(image(u,v),union(w,x)) -> member(image(u,v),symmetric_difference(w,x))*.
% 299.89/300.47  113266[0:Rew:1938.0,113153.1] || member(not_subclass_element(union(u,cross_product(v,w)),symmetric_difference(u,cross_product(v,w))),complement(restrict(u,v,w)))* -> subclass(union(u,cross_product(v,w)),symmetric_difference(u,cross_product(v,w))).
% 299.89/300.47  113265[0:Rew:1943.0,113154.1] || member(not_subclass_element(union(cross_product(u,v),w),symmetric_difference(cross_product(u,v),w)),complement(restrict(w,u,v)))* -> subclass(union(cross_product(u,v),w),symmetric_difference(cross_product(u,v),w)).
% 299.89/300.47  126520[0:Res:60.1,9368.0] || member(ordered_pair(u,not_subclass_element(intersection(v,complement(image(w,image(x,singleton(u))))),y)),compose(w,x))* -> subclass(intersection(v,complement(image(w,image(x,singleton(u))))),y).
% 299.89/300.47  126738[0:Res:60.1,9482.0] || member(ordered_pair(u,not_subclass_element(intersection(complement(image(v,image(w,singleton(u)))),x),y)),compose(v,w))* -> subclass(intersection(complement(image(v,image(w,singleton(u)))),x),y).
% 299.89/300.47  31201[0:Res:3872.2,309.0] || member(not_subclass_element(complement(restrict(u,v,w)),x),cross_product(v,w))* member(not_subclass_element(complement(restrict(u,v,w)),x),u)* -> subclass(complement(restrict(u,v,w)),x).
% 299.89/300.47  41914[0:SpL:2330.1,95.0] || member(not_subclass_element(cross_product(u,v),w),compose_class(x)) -> subclass(cross_product(u,v),w) equal(compose(x,first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w)))**.
% 299.89/300.47  131806[0:SpR:1948.0,9529.1] ||  -> subclass(symmetric_difference(union(u,v),union(complement(u),complement(v))),w) member(not_subclass_element(symmetric_difference(union(u,v),union(complement(u),complement(v))),w),complement(symmetric_difference(complement(u),complement(v))))*.
% 299.89/300.47  40269[0:Rew:1934.0,40183.2,1934.0,40183.1] || member(not_subclass_element(u,symmetric_difference(v,singleton(v))),successor(v)) member(not_subclass_element(u,symmetric_difference(v,singleton(v))),complement(intersection(v,singleton(v))))* -> subclass(u,symmetric_difference(v,singleton(v))).
% 299.89/300.47  40270[0:Rew:1933.0,40182.2,1933.0,40182.1] || member(not_subclass_element(u,symmetric_difference(v,inverse(v))),symmetrization_of(v)) member(not_subclass_element(u,symmetric_difference(v,inverse(v))),complement(intersection(v,inverse(v))))* -> subclass(u,symmetric_difference(v,inverse(v))).
% 299.89/300.47  31043[0:Res:322.1,2142.0] ||  -> subclass(intersection(u,ordered_pair(v,w)),x) equal(not_subclass_element(intersection(u,ordered_pair(v,w)),x),unordered_pair(v,singleton(w)))** equal(not_subclass_element(intersection(u,ordered_pair(v,w)),x),singleton(v)).
% 299.89/300.47  31032[0:Res:340.1,2142.0] ||  -> subclass(intersection(ordered_pair(u,v),w),x) equal(not_subclass_element(intersection(ordered_pair(u,v),w),x),unordered_pair(u,singleton(v)))** equal(not_subclass_element(intersection(ordered_pair(u,v),w),x),singleton(u)).
% 299.89/300.47  107214[0:Res:34429.0,2142.0] ||  -> subclass(complement(complement(ordered_pair(u,v))),w) equal(not_subclass_element(complement(complement(ordered_pair(u,v))),w),unordered_pair(u,singleton(v)))** equal(not_subclass_element(complement(complement(ordered_pair(u,v))),w),singleton(u)).
% 299.89/300.47  137265[0:Rew:10029.0,137181.1] || member(not_subclass_element(intersection(u,successor(image(element_relation,complement(v)))),w),intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))* -> subclass(intersection(u,successor(image(element_relation,complement(v)))),w).
% 299.89/300.47  137885[0:Rew:10028.0,137799.1] || member(not_subclass_element(intersection(u,symmetrization_of(image(element_relation,complement(v)))),w),intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))* -> subclass(intersection(u,symmetrization_of(image(element_relation,complement(v)))),w).
% 299.89/300.47  137266[0:Rew:10029.0,137167.1] || member(not_subclass_element(intersection(successor(image(element_relation,complement(u))),v),w),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* -> subclass(intersection(successor(image(element_relation,complement(u))),v),w).
% 299.89/300.47  137886[0:Rew:10028.0,137785.1] || member(not_subclass_element(intersection(symmetrization_of(image(element_relation,complement(u))),v),w),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* -> subclass(intersection(symmetrization_of(image(element_relation,complement(u))),v),w).
% 299.89/300.47  163722[10:Rew:160202.0,160937.2] || member(union(image(element_relation,universal_class),u),universal_class) member(apply(choice,union(image(element_relation,universal_class),u)),intersection(power_class(successor_relation),complement(u)))* -> equal(union(image(element_relation,universal_class),u),successor_relation).
% 299.89/300.47  163723[10:Rew:160202.0,160968.2] || member(union(u,image(element_relation,universal_class)),universal_class) member(apply(choice,union(u,image(element_relation,universal_class))),intersection(complement(u),power_class(successor_relation)))* -> equal(union(u,image(element_relation,universal_class)),successor_relation).
% 299.89/300.47  160712[10:Rew:160202.0,146507.3] || member(u,universal_class) subclass(u,complement(intersection(v,w))) member(apply(choice,u),union(v,w)) -> equal(u,successor_relation) member(apply(choice,u),symmetric_difference(v,w))*.
% 299.89/300.47  161568[10:Rew:160202.0,146791.2] || member(cross_product(u,v),universal_class) member(apply(choice,cross_product(u,v)),cross_product(w,x))* -> equal(cross_product(u,v),successor_relation) member(first(apply(choice,cross_product(u,v))),w).
% 299.89/300.47  161567[10:Rew:160202.0,146792.2] || member(cross_product(u,v),universal_class) member(apply(choice,cross_product(u,v)),cross_product(w,x))* -> equal(cross_product(u,v),successor_relation) member(second(apply(choice,cross_product(u,v))),x).
% 299.89/300.47  161566[10:Rew:160202.0,146815.2] || member(second(regular(cross_product(u,v))),w) member(first(regular(cross_product(u,v))),x) -> equal(cross_product(u,v),successor_relation) member(regular(cross_product(u,v)),cross_product(x,w))*.
% 299.89/300.47  161912[10:Rew:160202.0,147147.1] || subclass(rest_relation,flip(u)) -> equal(cross_product(v,w),successor_relation) member(ordered_pair(ordered_pair(second(regular(cross_product(v,w))),first(regular(cross_product(v,w)))),rest_of(regular(cross_product(v,w)))),u)*.
% 299.89/300.47  161911[10:Rew:160202.0,147148.1] || subclass(rest_relation,flip(u)) -> equal(cross_product(v,w),successor_relation) member(ordered_pair(regular(cross_product(v,w)),rest_of(ordered_pair(second(regular(cross_product(v,w))),first(regular(cross_product(v,w)))))),u)*.
% 299.89/300.47  161910[10:Rew:160202.0,147149.1] || subclass(rest_relation,rotate(u)) -> equal(cross_product(v,w),successor_relation) member(ordered_pair(ordered_pair(second(regular(cross_product(v,w))),rest_of(regular(cross_product(v,w)))),first(regular(cross_product(v,w)))),u)*.
% 299.89/300.47  162038[10:Rew:160202.0,146952.1] || member(intersection(u,restrict(v,w,x)),universal_class) -> equal(intersection(u,restrict(v,w,x)),successor_relation) member(apply(choice,intersection(u,restrict(v,w,x))),cross_product(w,x))*.
% 299.89/300.47  162043[10:Rew:160202.0,146957.1] || member(intersection(restrict(u,v,w),x),universal_class) -> equal(intersection(restrict(u,v,w),x),successor_relation) member(apply(choice,intersection(restrict(u,v,w),x)),cross_product(v,w))*.
% 299.89/300.47  162057[10:Rew:160202.0,147005.2] || subclass(u,complement(intersection(v,w))) member(regular(intersection(x,u)),union(v,w)) -> equal(intersection(x,u),successor_relation) member(regular(intersection(x,u)),symmetric_difference(v,w))*.
% 299.89/300.47  162071[10:Rew:160202.0,147020.2] || subclass(u,complement(intersection(v,w))) member(regular(intersection(u,x)),union(v,w)) -> equal(intersection(u,x),successor_relation) member(regular(intersection(u,x)),symmetric_difference(v,w))*.
% 299.89/300.47  162243[10:Rew:160202.0,147049.2] || member(intersection(image(element_relation,complement(u)),v),universal_class) member(apply(choice,intersection(image(element_relation,complement(u)),v)),power_class(u))* -> equal(intersection(image(element_relation,complement(u)),v),successor_relation).
% 299.89/300.47  162245[10:Rew:160202.0,147051.2] || member(intersection(u,image(element_relation,complement(v))),universal_class) member(apply(choice,intersection(u,image(element_relation,complement(v)))),power_class(v))* -> equal(intersection(u,image(element_relation,complement(v))),successor_relation).
% 299.89/300.47  162654[10:Rew:160202.0,147287.0] ||  -> equal(complement(complement(cross_product(u,v))),successor_relation) equal(ordered_pair(first(regular(complement(complement(cross_product(u,v))))),second(regular(complement(complement(cross_product(u,v)))))),regular(complement(complement(cross_product(u,v)))))**.
% 299.89/300.47  162657[10:Rew:160202.0,147628.0] ||  -> equal(intersection(u,intersection(unordered_pair(v,w),x)),successor_relation) equal(regular(intersection(u,intersection(unordered_pair(v,w),x))),w)** equal(regular(intersection(u,intersection(unordered_pair(v,w),x))),v)**.
% 299.89/300.47  162658[10:Rew:160202.0,147686.0] ||  -> equal(intersection(u,intersection(v,unordered_pair(w,x))),successor_relation) equal(regular(intersection(u,intersection(v,unordered_pair(w,x)))),x)** equal(regular(intersection(u,intersection(v,unordered_pair(w,x)))),w)**.
% 299.89/300.47  162659[10:Rew:160202.0,147726.0] ||  -> equal(intersection(intersection(unordered_pair(u,v),w),x),successor_relation) equal(regular(intersection(intersection(unordered_pair(u,v),w),x)),v)** equal(regular(intersection(intersection(unordered_pair(u,v),w),x)),u)**.
% 299.89/300.47  162660[10:Rew:160202.0,147799.0] ||  -> equal(intersection(intersection(u,unordered_pair(v,w)),x),successor_relation) equal(regular(intersection(intersection(u,unordered_pair(v,w)),x)),w)** equal(regular(intersection(intersection(u,unordered_pair(v,w)),x)),v)**.
% 299.89/300.47  162663[10:Rew:160202.0,147960.1] || member(regular(intersection(u,union(image(element_relation,power_class(v)),w))),intersection(power_class(image(element_relation,complement(v))),complement(w)))* -> equal(intersection(u,union(image(element_relation,power_class(v)),w)),successor_relation).
% 299.89/300.47  162664[10:Rew:160202.0,147961.1] || member(regular(intersection(union(image(element_relation,power_class(u)),v),w)),intersection(power_class(image(element_relation,complement(u))),complement(v)))* -> equal(intersection(union(image(element_relation,power_class(u)),v),w),successor_relation).
% 299.89/300.47  162665[10:Rew:160202.0,147980.1] || member(regular(intersection(u,union(v,image(element_relation,power_class(w))))),intersection(complement(v),power_class(image(element_relation,complement(w)))))* -> equal(intersection(u,union(v,image(element_relation,power_class(w)))),successor_relation).
% 299.89/300.47  162666[10:Rew:160202.0,147981.1] || member(regular(intersection(union(u,image(element_relation,power_class(v))),w)),intersection(complement(u),power_class(image(element_relation,complement(v)))))* -> equal(intersection(union(u,image(element_relation,power_class(v))),w),successor_relation).
% 299.89/300.47  126108[0:Res:28321.1,96.1] || subclass(rest_relation,flip(cross_product(universal_class,universal_class))) equal(compose(u,ordered_pair(v,w)),rest_of(ordered_pair(w,v))) -> member(ordered_pair(ordered_pair(v,w),rest_of(ordered_pair(w,v))),compose_class(u))*.
% 299.89/300.47  125982[0:Res:28320.1,96.1] || subclass(rest_relation,rotate(cross_product(universal_class,universal_class))) equal(compose(u,ordered_pair(v,rest_of(ordered_pair(w,v)))),w) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(w,v))),w),compose_class(u))*.
% 299.89/300.47  161767[10:Rew:160202.0,146697.1] || member(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers) -> equal(unordered_pair(u,v),successor_relation) equal(apply(choice,unordered_pair(u,v)),u) subclass(v,image(choice,singleton(unordered_pair(u,v))))*.
% 299.89/300.47  161766[10:Rew:160202.0,146698.1] || member(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers) -> equal(unordered_pair(u,v),successor_relation) equal(apply(choice,unordered_pair(u,v)),v) subclass(u,image(choice,singleton(unordered_pair(u,v))))*.
% 299.89/300.47  162656[10:Rew:160202.0,147577.2] || member(ordered_pair(u,least(v,complement(image(w,image(x,singleton(u)))))),compose(w,x))* well_ordering(v,universal_class) -> equal(complement(image(w,image(x,singleton(u)))),successor_relation).
% 299.89/300.47  162662[10:Rew:160202.0,147923.2] || well_ordering(u,universal_class) member(least(u,symmetrization_of(image(element_relation,complement(v)))),intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))* -> equal(symmetrization_of(image(element_relation,complement(v))),successor_relation).
% 299.89/300.47  162661[10:Rew:160202.0,147903.2] || well_ordering(u,universal_class) member(least(u,successor(image(element_relation,complement(v)))),intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))* -> equal(successor(image(element_relation,complement(v))),successor_relation).
% 299.89/300.47  38406[0:MRR:38400.1,34067.1] || member(least(compose_class(u),v),universal_class)* equal(compose(u,w),least(compose_class(u),v))* member(w,v)* subclass(v,x)* well_ordering(compose_class(u),x)* -> .
% 299.89/300.47  107660[0:Res:6260.3,6045.0] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,v),u),x)* subclass(flip(x),y)* well_ordering(universal_class,y) -> .
% 299.89/300.47  107659[0:Res:6269.3,6045.0] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,u),v),x)* subclass(rotate(x),y)* well_ordering(universal_class,y) -> .
% 299.89/300.47  183203[10:SpL:181044.1,61.0] || member(u,universal_class) member(v,image(w,image(x,successor_relation))) member(ordered_pair(successor(u),v),cross_product(universal_class,universal_class)) -> member(ordered_pair(successor(u),v),compose(w,x))*.
% 299.89/300.47  160711[10:Rew:160202.0,146526.2] || subclass(u,image(v,image(w,singleton(x))))* member(ordered_pair(x,regular(u)),cross_product(universal_class,universal_class)) -> equal(u,successor_relation) member(ordered_pair(x,regular(u)),compose(v,w)).
% 299.89/300.47  130489[0:Res:5768.2,9306.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,symmetric_difference(cross_product(w,x),y)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),complement(restrict(y,w,x)))*.
% 299.89/300.47  130396[0:Res:5768.2,9300.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,symmetric_difference(w,cross_product(x,y))) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),complement(restrict(w,x,y)))*.
% 299.89/300.47  124282[0:Res:5768.2,986.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,power_class(image(element_relation,complement(w)))) member(ordered_pair(u,ordered_pair(v,compose(u,v))),image(element_relation,power_class(w)))* -> .
% 299.89/300.47  192207[15:SpL:190721.0,61.0] || member(u,image(v,image(w,successor_relation))) member(ordered_pair(inverse(x),u),cross_product(universal_class,universal_class)) -> equal(range_of(x),successor_relation) member(ordered_pair(inverse(x),u),compose(v,w))*.
% 299.89/300.47  192587[10:Res:3595.3,162356.0] function(u) || member(v,universal_class) subclass(universal_class,w) subclass(w,x)* well_ordering(omega,x)* -> equal(integer_of(ordered_pair(image(u,v),least(omega,w))),successor_relation)**.
% 299.89/300.47  192553[10:Res:476.1,162356.0] || member(flip(cross_product(u,universal_class)),universal_class) subclass(domain_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(flip(cross_product(u,universal_class)),inverse(u)),least(omega,domain_relation))),successor_relation)**.
% 299.89/300.47  192552[10:Res:475.1,162356.0] || member(restrict(element_relation,universal_class,u),universal_class) subclass(domain_relation,v) well_ordering(omega,v)* -> equal(integer_of(ordered_pair(ordered_pair(restrict(element_relation,universal_class,u),sum_class(u)),least(omega,domain_relation))),successor_relation)**.
% 299.89/300.47  192527[10:Res:160784.3,162356.0] || member(u,universal_class) subclass(u,v) subclass(v,w)* well_ordering(omega,w)* -> equal(u,successor_relation) equal(integer_of(ordered_pair(apply(choice,u),least(omega,v))),successor_relation)**.
% 299.89/300.47  194554[10:SoR:3846.0,160511.2] single_valued_class(flip(cross_product(u,universal_class))) || subclass(range_of(flip(cross_product(u,universal_class))),v) equal(flip(cross_product(u,universal_class)),successor_relation) -> maps(flip(cross_product(u,universal_class)),inverse(u),v)*.
% 299.89/300.47  194874[10:SoR:3844.0,160511.2] single_valued_class(restrict(element_relation,universal_class,u)) || subclass(range_of(restrict(element_relation,universal_class,u)),v) equal(restrict(element_relation,universal_class,u),successor_relation) -> maps(restrict(element_relation,universal_class,u),sum_class(u),v)*.
% 299.89/300.47  197966[10:Res:6187.2,185639.1] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(universal_class,universal_class))* equal(compose(v,w),successor_relation) -> subclass(image(v,image(w,singleton(u))),x).
% 299.89/300.47  200176[14:SpL:200028.1,61.0] || member(u,universal_class) member(v,image(w,image(x,successor_relation))) member(ordered_pair(range_of(u),v),cross_product(universal_class,universal_class)) -> member(ordered_pair(range_of(u),v),compose(w,x))*.
% 299.89/300.47  200700[10:Res:161493.2,6041.0] inductive(u) || member(v,w)* member(v,x)* subclass(x,y)* well_ordering(cross_product(w,u),y)* -> equal(integer_of(least(cross_product(w,u),x)),successor_relation)**.
% 299.89/300.47  203584[15:Rew:203192.0,186280.0] || member(first(not_subclass_element(cross_product(u,v),w)),cantor(x)) member(ordered_pair(x,not_subclass_element(cross_product(u,v),w)),cross_product(universal_class,cross_product(universal_class,universal_class)))* -> subclass(cross_product(u,v),w).
% 299.89/300.47  203643[10:Rew:203192.0,161569.3] || member(cross_product(u,v),universal_class) member(apply(choice,cross_product(u,v)),rest_of(w)) -> equal(cross_product(u,v),successor_relation) member(first(apply(choice,cross_product(u,v))),cantor(w))*.
% 299.89/300.47  204944[10:Rew:203192.0,203655.1] || member(u,universal_class) member(singleton(u),cantor(v))* equal(successor_relation,w) subclass(rest_of(v),x)* -> member(u,cantor(v)) member(ordered_pair(singleton(u),w),x)*.
% 299.89/300.47  203775[10:Rew:203192.0,161401.1] || asymmetric(u,universal_class) member(universal_class,cantor(intersection(u,inverse(u)))) equal(successor_relation,v) subclass(rest_of(intersection(u,inverse(u))),w)* -> member(ordered_pair(universal_class,v),w)*.
% 299.89/300.47  204946[10:Rew:203192.0,203992.2] || section(u,restrict(v,w,x),y) -> equal(cantor(restrict(u,y,restrict(v,w,x))),successor_relation) member(regular(cantor(restrict(u,y,restrict(v,w,x)))),v)*.
% 299.89/300.47  204026[6:Rew:203192.0,31084.3] inductive(domain_of(restrict(u,v,w))) || section(u,w,v) well_ordering(x,w) -> member(least(x,cantor(restrict(u,v,w))),cantor(restrict(u,v,w)))*.
% 299.89/300.47  206168[6:Res:203330.1,5832.1] inductive(cantor(restrict(u,v,w))) || section(u,w,v) well_ordering(x,w) -> member(least(x,cantor(restrict(u,v,w))),cantor(restrict(u,v,w)))*.
% 299.89/300.47  210552[10:Res:204942.3,149475.0] || section(u,v,w) well_ordering(x,v) subclass(universal_class,y) -> equal(cantor(restrict(u,w,v)),successor_relation) member(least(x,cantor(restrict(u,w,v))),y)*.
% 299.89/300.47  211929[10:Rew:183383.0,211928.0] ||  -> equal(symmetric_difference(complement(complement(union(u,successor_relation))),union(symmetric_difference(universal_class,u),complement(union(u,successor_relation)))),union(complement(complement(union(u,successor_relation))),union(symmetric_difference(universal_class,u),complement(union(u,successor_relation)))))**.
% 299.89/300.47  211999[11:Res:183759.1,61.0] || subclass(inverse(successor_relation),image(u,image(v,singleton(w))))* member(ordered_pair(w,regular(symmetrization_of(successor_relation))),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,regular(symmetrization_of(successor_relation))),compose(u,v)).
% 299.89/300.47  214432[21:Res:214356.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,regular(complement(complement(symmetrization_of(successor_relation)))))),second(ordered_pair(u,regular(complement(complement(symmetrization_of(successor_relation))))))),ordered_pair(u,regular(complement(complement(symmetrization_of(successor_relation))))))**.
% 299.89/300.47  216893[10:MRR:216861.3,188688.2] || member(apply(choice,regular(restrict(u,v,w))),cross_product(v,w))* member(apply(choice,regular(restrict(u,v,w))),u)* -> equal(regular(restrict(u,v,w)),successor_relation).
% 299.89/300.47  217254[10:Res:217225.1,6041.0] || equal(singleton(least(cross_product(u,singleton(successor_relation)),v)),kind_1_ordinals)** member(w,u)* member(w,v)* subclass(v,x)* well_ordering(cross_product(u,singleton(successor_relation)),x)* -> .
% 299.89/300.47  217417[20:Res:217226.1,6041.0] || equal(singleton(least(cross_product(u,singleton(successor_relation)),v)),omega)** member(w,u)* member(w,v)* subclass(v,x)* well_ordering(cross_product(u,singleton(successor_relation)),x)* -> .
% 299.89/300.47  218326[10:MRR:218277.3,188688.2] || member(not_subclass_element(regular(restrict(u,v,w)),x),cross_product(v,w))* member(not_subclass_element(regular(restrict(u,v,w)),x),u)* -> subclass(regular(restrict(u,v,w)),x).
% 299.89/300.47  219151[3:Res:218473.1,5839.2] || equal(intersection(u,v),complement(kind_1_ordinals)) member(w,v)* member(w,u)* well_ordering(x,complement(ordinal_numbers)) -> member(least(x,intersection(u,v)),intersection(u,v))*.
% 299.89/300.47  219141[3:Res:218473.1,5853.2] || equal(cross_product(u,v),complement(kind_1_ordinals)) member(w,v)* member(x,u)* well_ordering(y,complement(ordinal_numbers)) -> member(least(y,cross_product(u,v)),cross_product(u,v))*.
% 299.89/300.47  219469[10:Res:6832.1,162356.0] || subclass(union(u,v),w)* well_ordering(omega,w) -> subclass(symmetric_difference(u,v),x) equal(integer_of(ordered_pair(not_subclass_element(symmetric_difference(u,v),x),least(omega,union(u,v)))),successor_relation)**.
% 299.89/300.47  197819[10:Rew:193730.0,197802.1,193730.0,197802.0] || member(ordered_pair(u,regular(range_of(successor_relation))),cross_product(universal_class,universal_class)) -> equal(range_of(successor_relation),successor_relation) member(ordered_pair(u,regular(range_of(successor_relation))),compose(complement(cross_product(image(v,singleton(u)),universal_class)),v))*.
% 299.89/300.47  163719[10:Rew:160202.0,160632.2,160202.0,160632.1] || member(ordered_pair(u,not_subclass_element(v,image(w,range_of(successor_relation)))),compose(w,regular(cross_product(singleton(u),universal_class))))* -> equal(cross_product(singleton(u),universal_class),successor_relation) subclass(v,image(w,range_of(successor_relation))).
% 299.89/300.47  163720[10:Rew:160202.0,160640.2,160202.0,160640.1] || member(ordered_pair(u,not_subclass_element(v,range_of(successor_relation))),compose(regular(cross_product(image(w,singleton(u)),universal_class)),w))* -> equal(cross_product(image(w,singleton(u)),universal_class),successor_relation) subclass(v,range_of(successor_relation)).
% 299.89/300.47  163721[10:Rew:160202.0,160666.2,160202.0,160666.1] || member(ordered_pair(u,regular(image(v,range_of(successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(v,range_of(successor_relation)),successor_relation) member(ordered_pair(u,regular(image(v,range_of(successor_relation)))),compose(v,successor_relation))*.
% 299.89/300.47  221646[10:Res:5768.2,185698.1] inductive(ordered_pair(u,ordered_pair(v,compose(u,v)))) || member(ordered_pair(u,v),cross_product(universal_class,universal_class))* subclass(composition_function,ordinal_numbers) -> equal(segment(element_relation,omega,least(element_relation,omega)),successor_relation).
% 299.89/300.47  224001[10:Res:34427.0,162356.0] || subclass(power_class(u),v)* well_ordering(omega,v) -> subclass(w,image(element_relation,complement(u))) equal(integer_of(ordered_pair(not_subclass_element(w,image(element_relation,complement(u))),least(omega,power_class(u)))),successor_relation)**.
% 299.89/300.47  224401[25:Rew:224236.1,204956.2] function(u) || subclass(range_of(u),cantor(image(cross_product(v,w),x))) equal(cantor(cantor(y)),universal_class) -> compatible(u,y,inverse(restrict(cross_product(x,universal_class),v,w)))*.
% 299.89/300.47  226228[10:Res:203658.1,162356.0] || member(u,universal_class) subclass(cantor(v),w)* well_ordering(omega,w) -> equal(apply(v,u),sum_class(range_of(successor_relation))) equal(integer_of(ordered_pair(u,least(omega,cantor(v)))),successor_relation)**.
% 299.89/300.47  226429[25:Rew:226382.1,204965.1] one_to_one(restrict(u,v,universal_class)) || subclass(universal_class,cantor(cantor(w))) equal(cantor(cantor(x)),cantor(restrict(u,v,universal_class))) -> compatible(restrict(u,v,universal_class),x,w)*.
% 299.89/300.47  229191[10:Res:10258.1,162356.0] || subclass(successor(u),v)* well_ordering(omega,v) -> subclass(symmetric_difference(u,singleton(u)),w) equal(integer_of(ordered_pair(not_subclass_element(symmetric_difference(u,singleton(u)),w),least(omega,successor(u)))),successor_relation)**.
% 299.89/300.47  229298[10:Res:10194.1,162356.0] || subclass(symmetrization_of(u),v)* well_ordering(omega,v) -> subclass(symmetric_difference(u,inverse(u)),w) equal(integer_of(ordered_pair(not_subclass_element(symmetric_difference(u,inverse(u)),w),least(omega,symmetrization_of(u)))),successor_relation)**.
% 299.89/300.47  230744[10:Res:163539.1,162356.0] || subclass(kind_1_ordinals,u) well_ordering(omega,u)* -> subclass(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),v) equal(integer_of(ordered_pair(not_subclass_element(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),v),least(omega,kind_1_ordinals))),successor_relation)**.
% 299.89/300.47  230877[10:MRR:230815.3,230832.1] || member(apply(choice,regular(image(element_relation,power_class(successor_relation)))),universal_class) -> member(apply(choice,regular(image(element_relation,power_class(successor_relation)))),power_class(image(element_relation,universal_class)))* equal(regular(image(element_relation,power_class(successor_relation))),successor_relation).
% 299.89/300.47  231817[10:Res:31076.2,161035.0] inductive(intersection(power_class(successor_relation),complement(u))) || well_ordering(v,intersection(power_class(successor_relation),complement(u))) member(least(v,intersection(power_class(successor_relation),complement(u))),union(image(element_relation,universal_class),u))* -> .
% 299.89/300.47  231815[10:Res:161445.2,161035.0] || well_ordering(u,intersection(power_class(successor_relation),complement(v))) member(least(u,intersection(power_class(successor_relation),complement(v))),union(image(element_relation,universal_class),v))* -> equal(intersection(power_class(successor_relation),complement(v)),successor_relation).
% 299.89/300.47  231800[10:Res:160296.2,161035.0] || member(intersection(power_class(successor_relation),complement(u)),universal_class) member(apply(choice,intersection(power_class(successor_relation),complement(u))),union(image(element_relation,universal_class),u))* -> equal(intersection(power_class(successor_relation),complement(u)),successor_relation).
% 299.89/300.47  33805[0:SpR:1938.0,161.0] ||  -> equal(intersection(complement(symmetric_difference(u,cross_product(v,w))),union(complement(restrict(u,v,w)),union(u,cross_product(v,w)))),symmetric_difference(complement(restrict(u,v,w)),union(u,cross_product(v,w))))**.
% 299.89/300.47  33877[0:SpR:1943.0,161.0] ||  -> equal(intersection(complement(symmetric_difference(cross_product(u,v),w)),union(complement(restrict(w,u,v)),union(cross_product(u,v),w))),symmetric_difference(complement(restrict(w,u,v)),union(cross_product(u,v),w)))**.
% 299.89/300.47  28326[0:MRR:28317.0,999.0] || subclass(rest_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(v,u))),v),w) -> member(ordered_pair(ordered_pair(v,u),rest_of(ordered_pair(v,u))),rotate(w))*.
% 299.89/300.47  28327[0:MRR:28315.0,999.0] || subclass(rest_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(v,u))),w) -> member(ordered_pair(ordered_pair(v,u),rest_of(ordered_pair(v,u))),flip(w))*.
% 299.89/300.47  39657[0:SpL:40.0,5919.0] || member(u,inverse(v))* subclass(rest_of(flip(cross_product(v,universal_class))),w)* well_ordering(x,w)* -> member(least(x,rest_of(flip(cross_product(v,universal_class)))),rest_of(flip(cross_product(v,universal_class))))*.
% 299.89/300.47  39963[0:Res:67.2,5554.0] function(u) || member(v,universal_class) member(w,x)* -> equal(ordered_pair(first(ordered_pair(w,image(u,v))),second(ordered_pair(w,image(u,v)))),ordered_pair(w,image(u,v)))**.
% 299.89/300.47  126717[0:Res:25.2,9482.0] || member(not_subclass_element(intersection(complement(intersection(u,v)),w),x),v)* member(not_subclass_element(intersection(complement(intersection(u,v)),w),x),u)* -> subclass(intersection(complement(intersection(u,v)),w),x).
% 299.89/300.47  126499[0:Res:25.2,9368.0] || member(not_subclass_element(intersection(u,complement(intersection(v,w))),x),w)* member(not_subclass_element(intersection(u,complement(intersection(v,w))),x),v)* -> subclass(intersection(u,complement(intersection(v,w))),x).
% 299.89/300.47  41910[0:SpL:2330.1,144.0] || member(not_subclass_element(cross_product(u,v),w),rest_of(x)) -> subclass(cross_product(u,v),w) equal(restrict(x,first(not_subclass_element(cross_product(u,v),w)),universal_class),second(not_subclass_element(cross_product(u,v),w)))**.
% 299.89/300.47  163144[10:MRR:41951.3,160227.0] || equal(successor(first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w))) member(not_subclass_element(cross_product(u,v),w),cross_product(universal_class,universal_class))* -> subclass(cross_product(u,v),w).
% 299.89/300.47  89241[0:Res:51387.0,3874.1] || member(not_subclass_element(u,complement(complement(intersection(v,w)))),union(v,w)) -> subclass(u,complement(complement(intersection(v,w)))) member(not_subclass_element(u,complement(complement(intersection(v,w)))),symmetric_difference(v,w))*.
% 299.89/300.47  41277[0:Obv:41261.1] || member(ordered_pair(u,v),compose(w,x)) -> equal(not_subclass_element(unordered_pair(y,v),image(w,image(x,singleton(u)))),y)** subclass(unordered_pair(y,v),image(w,image(x,singleton(u)))).
% 299.89/300.47  41278[0:Obv:41260.1] || member(ordered_pair(u,v),compose(w,x)) -> equal(not_subclass_element(unordered_pair(v,y),image(w,image(x,singleton(u)))),y)** subclass(unordered_pair(v,y),image(w,image(x,singleton(u)))).
% 299.89/300.47  39655[0:SpL:55.0,5919.0] || member(u,sum_class(v))* subclass(rest_of(restrict(element_relation,universal_class,v)),w)* well_ordering(x,w)* -> member(least(x,rest_of(restrict(element_relation,universal_class,v))),rest_of(restrict(element_relation,universal_class,v)))*.
% 299.89/300.47  139893[0:Rew:982.0,139694.1] ||  -> member(not_subclass_element(u,image(element_relation,union(image(element_relation,power_class(v)),w))),power_class(intersection(power_class(image(element_relation,complement(v))),complement(w))))* subclass(u,image(element_relation,union(image(element_relation,power_class(v)),w))).
% 299.89/300.47  140357[0:Rew:984.0,140156.1] ||  -> member(not_subclass_element(u,image(element_relation,union(v,image(element_relation,power_class(w))))),power_class(intersection(complement(v),power_class(image(element_relation,complement(w))))))* subclass(u,image(element_relation,union(v,image(element_relation,power_class(w))))).
% 299.89/300.47  40069[0:Rew:208.0,40056.3] || member(u,v) subclass(v,w)* well_ordering(power_class(image(element_relation,complement(x))),w)* -> member(ordered_pair(u,least(power_class(image(element_relation,complement(x))),v)),image(element_relation,power_class(x)))*.
% 299.89/300.47  140273[0:SpL:984.0,3874.1] || member(u,union(complement(v),power_class(image(element_relation,complement(w))))) member(u,union(v,image(element_relation,power_class(w)))) -> member(u,symmetric_difference(complement(v),power_class(image(element_relation,complement(w)))))*.
% 299.89/300.47  140354[0:Rew:984.0,140270.1] || member(not_subclass_element(intersection(u,union(v,image(element_relation,power_class(w)))),x),intersection(complement(v),power_class(image(element_relation,complement(w)))))* -> subclass(intersection(u,union(v,image(element_relation,power_class(w)))),x).
% 299.89/300.47  140355[0:Rew:984.0,140253.1] || member(not_subclass_element(intersection(union(u,image(element_relation,power_class(v))),w),x),intersection(complement(u),power_class(image(element_relation,complement(v)))))* -> subclass(intersection(union(u,image(element_relation,power_class(v))),w),x).
% 299.89/300.47  139811[0:SpL:982.0,3874.1] || member(u,union(power_class(image(element_relation,complement(v))),complement(w))) member(u,union(image(element_relation,power_class(v)),w)) -> member(u,symmetric_difference(power_class(image(element_relation,complement(v))),complement(w)))*.
% 299.89/300.47  139890[0:Rew:982.0,139808.1] || member(not_subclass_element(intersection(u,union(image(element_relation,power_class(v)),w)),x),intersection(power_class(image(element_relation,complement(v))),complement(w)))* -> subclass(intersection(u,union(image(element_relation,power_class(v)),w)),x).
% 299.89/300.47  139891[0:Rew:982.0,139791.1] || member(not_subclass_element(intersection(union(image(element_relation,power_class(u)),v),w),x),intersection(power_class(image(element_relation,complement(u))),complement(v)))* -> subclass(intersection(union(image(element_relation,power_class(u)),v),w),x).
% 299.89/300.47  40273[0:MRR:40225.0,34189.1] || member(not_subclass_element(u,intersection(v,image(element_relation,complement(w)))),v)* -> member(not_subclass_element(u,intersection(v,image(element_relation,complement(w)))),power_class(w))* subclass(u,intersection(v,image(element_relation,complement(w)))).
% 299.89/300.47  161063[10:Rew:160202.0,151370.0] ||  -> equal(intersection(complement(symmetric_difference(complement(u),power_class(successor_relation))),union(union(u,image(element_relation,universal_class)),union(complement(u),power_class(successor_relation)))),symmetric_difference(union(u,image(element_relation,universal_class)),union(complement(u),power_class(successor_relation))))**.
% 299.89/300.47  161067[10:Rew:160202.0,151371.0] ||  -> equal(intersection(complement(symmetric_difference(power_class(successor_relation),complement(u))),union(union(image(element_relation,universal_class),u),union(power_class(successor_relation),complement(u)))),symmetric_difference(union(image(element_relation,universal_class),u),union(power_class(successor_relation),complement(u))))**.
% 299.89/300.47  160710[10:Rew:160202.0,146525.2] || member(u,universal_class) member(v,w)* -> equal(u,successor_relation) equal(ordered_pair(first(ordered_pair(v,apply(choice,u))),second(ordered_pair(v,apply(choice,u)))),ordered_pair(v,apply(choice,u)))**.
% 299.89/300.47  161563[10:Rew:160202.0,146813.1] || member(ordered_pair(regular(cross_product(u,v)),w),rotate(x)) -> equal(cross_product(u,v),successor_relation) member(ordered_pair(ordered_pair(second(regular(cross_product(u,v))),w),first(regular(cross_product(u,v)))),x)*.
% 299.89/300.47  161562[10:Rew:160202.0,146814.1] || member(ordered_pair(regular(cross_product(u,v)),w),flip(x)) -> equal(cross_product(u,v),successor_relation) member(ordered_pair(ordered_pair(second(regular(cross_product(u,v))),first(regular(cross_product(u,v)))),w),x)*.
% 299.89/300.47  162667[10:Rew:160202.0,147442.0] ||  -> equal(restrict(ordered_pair(u,v),w,x),successor_relation) equal(regular(restrict(ordered_pair(u,v),w,x)),unordered_pair(u,singleton(v)))** equal(regular(restrict(ordered_pair(u,v),w,x)),singleton(u)).
% 299.89/300.47  162669[10:Rew:160202.0,147855.2] || section(cross_product(u,singleton(v)),w,x) well_ordering(y,w) -> equal(segment(y,segment(cross_product(x,w),u,v),least(y,segment(cross_product(x,w),u,v))),successor_relation)**.
% 299.89/300.47  162671[10:Rew:160202.0,147963.1] || member(regular(image(element_relation,union(image(element_relation,power_class(u)),v))),power_class(intersection(power_class(image(element_relation,complement(u))),complement(v))))* -> equal(image(element_relation,union(image(element_relation,power_class(u)),v)),successor_relation).
% 299.89/300.47  162673[10:Rew:160202.0,147983.1] || member(regular(image(element_relation,union(u,image(element_relation,power_class(v))))),power_class(intersection(complement(u),power_class(image(element_relation,complement(v))))))* -> equal(image(element_relation,union(u,image(element_relation,power_class(v)))),successor_relation).
% 299.89/300.47  182938[6:Res:157922.1,6041.0] || member(least(cross_product(u,compose(element_relation,universal_class)),v),element_relation)* member(w,u)* member(w,v)* subclass(v,x)* well_ordering(cross_product(u,compose(element_relation,universal_class)),x)* -> .
% 299.89/300.47  184822[0:SpR:10422.0,1496.2] || member(restrict(cross_product(u,singleton(v)),w,x),universal_class) subclass(domain_relation,y) -> member(ordered_pair(restrict(cross_product(u,singleton(v)),w,x),segment(cross_product(w,x),u,v)),y)*.
% 299.89/300.47  39109[2:Res:5714.3,127.0] || connected(u,v) well_ordering(w,v)* subclass(not_well_ordering(u,v),x)* well_ordering(y,x)* -> well_ordering(u,v) member(least(y,not_well_ordering(u,v)),not_well_ordering(u,v))*.
% 299.89/300.47  108791[2:Res:31076.2,5554.0] inductive(u) || well_ordering(v,u) member(w,x)* -> equal(ordered_pair(first(ordered_pair(w,least(v,u))),second(ordered_pair(w,least(v,u)))),ordered_pair(w,least(v,u)))**.
% 299.89/300.47  162668[10:Rew:160202.0,147466.2] || transitive(universal_class,u) well_ordering(v,cross_product(u,u)) -> equal(segment(v,compose(cross_product(u,u),cross_product(u,u)),least(v,compose(cross_product(u,u),cross_product(u,u)))),successor_relation)**.
% 299.89/300.47  161909[10:Rew:160202.0,147150.1] || well_ordering(u,cross_product(v,w)) -> equal(cross_product(v,w),successor_relation) equal(ordered_pair(first(least(u,cross_product(v,w))),second(least(u,cross_product(v,w)))),least(u,cross_product(v,w)))**.
% 299.89/300.47  161434[10:Rew:160202.0,146629.2] || well_ordering(u,v) member(w,x)* -> equal(v,successor_relation) equal(ordered_pair(first(ordered_pair(w,least(u,v))),second(ordered_pair(w,least(u,v)))),ordered_pair(w,least(u,v)))**.
% 299.89/300.47  108238[2:Res:31069.2,5554.0] inductive(u) || well_ordering(v,universal_class) member(w,x)* -> equal(ordered_pair(first(ordered_pair(w,least(v,u))),second(ordered_pair(w,least(v,u)))),ordered_pair(w,least(v,u)))**.
% 299.89/300.47  162672[10:Rew:160202.0,147982.2] || well_ordering(u,universal_class) member(least(u,union(v,image(element_relation,power_class(w)))),intersection(complement(v),power_class(image(element_relation,complement(w)))))* -> equal(union(v,image(element_relation,power_class(w))),successor_relation).
% 299.89/300.47  162670[10:Rew:160202.0,147962.2] || well_ordering(u,universal_class) member(least(u,union(image(element_relation,power_class(v)),w)),intersection(power_class(image(element_relation,complement(v))),complement(w)))* -> equal(union(image(element_relation,power_class(v)),w),successor_relation).
% 299.89/300.47  161812[10:Rew:160202.0,147161.2] || well_ordering(u,universal_class) member(v,w)* -> equal(x,successor_relation) equal(ordered_pair(first(ordered_pair(v,least(u,x))),second(ordered_pair(v,least(u,x)))),ordered_pair(v,least(u,x)))**.
% 299.89/300.47  39285[0:SoR:5564.0,6317.2] single_valued_class(sum_class(cross_product(universal_class,universal_class))) || member(ordinal_numbers,universal_class) well_ordering(element_relation,cross_product(universal_class,universal_class))* equal(sum_class(cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class)) -> member(cross_product(universal_class,universal_class),ordinal_numbers).
% 299.89/300.47  34659[0:Res:173.1,127.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class) subclass(complement(intersection(y__dfg,ordinal_numbers)),u)* well_ordering(v,u)* -> member(least(v,complement(intersection(y__dfg,ordinal_numbers))),complement(intersection(y__dfg,ordinal_numbers)))*.
% 299.89/300.47  38397[0:Res:6010.3,127.0] || member(u,universal_class)* member(v,universal_class) equal(compose(w,v),u)* subclass(compose_class(w),x)* well_ordering(y,x)* -> member(least(y,compose_class(w)),compose_class(w))*.
% 299.89/300.47  28529[0:Res:1028.1,127.0] || member(u,universal_class) subclass(image(element_relation,complement(v)),w)* well_ordering(x,w)* -> member(u,power_class(v))* member(least(x,image(element_relation,complement(v))),image(element_relation,complement(v)))*.
% 299.89/300.47  41084[0:Rew:28.0,41055.4] || member(u,universal_class) subclass(union(v,w),x)* well_ordering(y,x)* -> member(u,intersection(complement(v),complement(w)))* member(least(y,union(v,w)),union(v,w))*.
% 299.89/300.47  9133[0:Res:1479.2,61.0] || member(u,universal_class) subclass(universal_class,image(v,image(w,singleton(x))))* member(ordered_pair(x,sum_class(u)),cross_product(universal_class,universal_class)) -> member(ordered_pair(x,sum_class(u)),compose(v,w))*.
% 299.89/300.47  9161[0:Res:1478.2,61.0] || member(u,universal_class) subclass(universal_class,image(v,image(w,singleton(x))))* member(ordered_pair(x,power_class(u)),cross_product(universal_class,universal_class)) -> member(ordered_pair(x,power_class(u)),compose(v,w))*.
% 299.89/300.47  44931[0:Res:6187.2,3514.1] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(universal_class,universal_class))* subclass(universal_class,complement(compose(v,w))) -> subclass(image(v,image(w,singleton(u))),x).
% 299.89/300.47  41938[0:SpL:2330.1,98.0] || member(ordered_pair(u,not_subclass_element(cross_product(v,w),x)),composition_function)* -> subclass(cross_product(v,w),x) equal(compose(u,first(not_subclass_element(cross_product(v,w),x))),second(not_subclass_element(cross_product(v,w),x))).
% 299.89/300.47  192543[10:Res:18.2,162356.0] || member(u,v) member(w,x) subclass(cross_product(x,v),y)* well_ordering(omega,y) -> equal(integer_of(ordered_pair(ordered_pair(w,u),least(omega,cross_product(x,v)))),successor_relation)**.
% 299.89/300.47  192540[10:Res:99.1,162356.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,w) well_ordering(omega,w)* -> equal(integer_of(ordered_pair(ordered_pair(u,ordered_pair(v,compose(u,v))),least(omega,composition_function))),successor_relation)**.
% 299.89/300.47  192519[10:Res:1028.1,162356.0] || member(u,universal_class) subclass(image(element_relation,complement(v)),w)* well_ordering(omega,w) -> member(u,power_class(v)) equal(integer_of(ordered_pair(u,least(omega,image(element_relation,complement(v))))),successor_relation)**.
% 299.89/300.47  196448[10:Res:160848.0,5838.1] || member(u,universal_class) well_ordering(v,image(element_relation,power_class(universal_class))) -> member(u,power_class(image(element_relation,successor_relation)))* member(least(v,complement(power_class(image(element_relation,successor_relation)))),complement(power_class(image(element_relation,successor_relation))))*.
% 299.89/300.47  196500[10:Res:161138.0,5838.1] || member(u,universal_class) well_ordering(v,image(element_relation,symmetrization_of(successor_relation))) -> member(u,power_class(complement(inverse(successor_relation))))* member(least(v,complement(power_class(complement(inverse(successor_relation))))),complement(power_class(complement(inverse(successor_relation)))))*.
% 299.89/300.47  196640[10:Res:160971.0,5838.1] || member(u,universal_class) well_ordering(v,image(element_relation,power_class(successor_relation))) -> member(u,power_class(image(element_relation,universal_class)))* member(least(v,complement(power_class(image(element_relation,universal_class)))),complement(power_class(image(element_relation,universal_class))))*.
% 299.89/300.47  196808[10:Res:162888.0,5838.1] || member(u,universal_class) well_ordering(v,image(element_relation,successor(successor_relation))) -> member(u,power_class(complement(singleton(successor_relation))))* member(least(v,complement(power_class(complement(singleton(successor_relation))))),complement(power_class(complement(singleton(successor_relation)))))*.
% 299.89/300.47  200307[6:Rew:199964.0,200300.2] || member(ordered_pair(ordered_pair(second(regular(rest_relation)),first(regular(rest_relation))),u),v)* member(ordered_pair(regular(rest_relation),u),cross_product(cross_product(universal_class,universal_class),universal_class)) -> member(ordered_pair(regular(rest_relation),u),flip(v)).
% 299.89/300.47  200308[6:Rew:199964.0,200299.2] || member(ordered_pair(ordered_pair(second(regular(rest_relation)),u),first(regular(rest_relation))),v)* member(ordered_pair(regular(rest_relation),u),cross_product(cross_product(universal_class,universal_class),universal_class)) -> member(ordered_pair(regular(rest_relation),u),rotate(v)).
% 299.89/300.47  201551[6:Rew:201355.0,201544.2] || member(ordered_pair(ordered_pair(second(regular(domain_relation)),first(regular(domain_relation))),u),v)* member(ordered_pair(regular(domain_relation),u),cross_product(cross_product(universal_class,universal_class),universal_class)) -> member(ordered_pair(regular(domain_relation),u),flip(v)).
% 299.89/300.47  201552[6:Rew:201355.0,201543.2] || member(ordered_pair(ordered_pair(second(regular(domain_relation)),u),first(regular(domain_relation))),v)* member(ordered_pair(regular(domain_relation),u),cross_product(cross_product(universal_class,universal_class),universal_class)) -> member(ordered_pair(regular(domain_relation),u),rotate(v)).
% 299.89/300.47  201965[10:Res:161492.2,6041.0] || equal(u,omega) member(v,w)* member(v,x)* subclass(x,y)* well_ordering(cross_product(w,u),y)* -> equal(integer_of(least(cross_product(w,u),x)),successor_relation)**.
% 299.89/300.47  204957[6:Rew:203192.0,203993.2] || section(u,restrict(v,w,x),y) -> subclass(cantor(restrict(u,y,restrict(v,w,x))),z) member(not_subclass_element(cantor(restrict(u,y,restrict(v,w,x))),z),v)*.
% 299.89/300.47  209571[12:Rew:209433.0,209564.2] || member(ordered_pair(ordered_pair(second(regular(element_relation)),first(regular(element_relation))),u),v)* member(ordered_pair(regular(element_relation),u),cross_product(cross_product(universal_class,universal_class),universal_class)) -> member(ordered_pair(regular(element_relation),u),flip(v)).
% 299.89/300.47  209572[12:Rew:209433.0,209563.2] || member(ordered_pair(ordered_pair(second(regular(element_relation)),u),first(regular(element_relation))),v)* member(ordered_pair(regular(element_relation),u),cross_product(cross_product(universal_class,universal_class),universal_class)) -> member(ordered_pair(regular(element_relation),u),rotate(v)).
% 299.89/300.47  212796[15:SpL:2330.1,203931.0] || member(not_subclass_element(cross_product(u,v),w),cross_product(universal_class,universal_class)) member(second(not_subclass_element(cross_product(u,v),w)),cantor(first(not_subclass_element(cross_product(u,v),w))))* -> subclass(cross_product(u,v),w).
% 299.89/300.47  213230[15:Res:189485.1,61.0] || subclass(domain_relation,image(u,image(v,singleton(w)))) member(ordered_pair(w,singleton(singleton(singleton(successor_relation)))),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,singleton(singleton(singleton(successor_relation)))),compose(u,v))*.
% 299.89/300.47  215893[10:Res:197082.1,61.0] || subclass(universal_class,image(u,image(v,singleton(w)))) member(ordered_pair(w,regular(complement(successor(successor_relation)))),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,regular(complement(successor(successor_relation)))),compose(u,v))*.
% 299.89/300.47  218135[10:Res:161690.1,162356.0] || subclass(complement(intersection(u,v)),w)* well_ordering(omega,w) -> equal(symmetric_difference(u,v),successor_relation) equal(integer_of(ordered_pair(regular(symmetric_difference(u,v)),least(omega,complement(intersection(u,v))))),successor_relation)**.
% 299.89/300.47  163725[10:Rew:160202.0,160614.3,160202.0,160614.2,160202.0,160614.1] || member(range_of(successor_relation),universal_class) member(ordered_pair(u,apply(choice,range_of(successor_relation))),cross_product(universal_class,universal_class)) -> equal(range_of(successor_relation),successor_relation) member(ordered_pair(u,apply(choice,range_of(successor_relation))),compose(successor_relation,v))*.
% 299.89/300.47  163737[10:Rew:160305.0,162783.2,160305.0,162783.1,160202.0,162783.1] || well_ordering(u,kind_1_ordinals) -> equal(symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation))),successor_relation) member(least(u,symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation)))),symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation))))*.
% 299.89/300.47  180640[10:Res:163219.0,5832.1] inductive(symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation)))) || well_ordering(u,kind_1_ordinals) -> member(least(u,symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation)))),symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation))))*.
% 299.89/300.47  163726[10:Rew:160202.0,160628.3,160202.0,160628.0] || member(ordered_pair(u,v),compose(w,successor_relation))* subclass(image(w,range_of(successor_relation)),x)* well_ordering(y,x)* -> member(least(y,image(w,range_of(successor_relation))),image(w,range_of(successor_relation)))*.
% 299.89/300.47  163727[10:Rew:160202.0,160638.0] || member(ordered_pair(u,ordered_pair(v,least(image(w,range_of(successor_relation)),x))),compose(w,successor_relation))* member(v,x) subclass(x,y)* well_ordering(image(w,range_of(successor_relation)),y)* -> .
% 299.89/300.47  193802[10:Rew:193730.0,193792.3] || member(ordered_pair(u,v),compose(complement(cross_product(image(w,singleton(u)),universal_class)),w))* subclass(range_of(successor_relation),x)* well_ordering(y,x)* -> member(least(y,range_of(successor_relation)),range_of(successor_relation))*.
% 299.89/300.47  163728[10:Rew:160202.0,160647.2] || member(ordered_pair(u,v),compose(regular(cross_product(image(w,singleton(u)),universal_class)),w))* subclass(range_of(successor_relation),x)* -> equal(cross_product(image(w,singleton(u)),universal_class),successor_relation) member(v,x)*.
% 299.89/300.47  163738[10:Rew:160202.0,162818.2,160305.0,162818.2,160305.0,162818.1,160202.0,162818.0,160305.0,162818.0] || member(u,union(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals)) member(u,complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))) -> member(u,symmetric_difference(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals))*.
% 299.89/300.47  163740[10:Rew:160202.0,162838.2,160305.0,162838.2,160305.0,162838.1,160202.0,162838.1,160305.0,162838.0] || member(intersection(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u),universal_class) -> equal(intersection(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u),successor_relation) member(apply(choice,intersection(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),u)),kind_1_ordinals)*.
% 299.89/300.47  163739[10:Rew:160202.0,162834.2,160305.0,162834.2,160305.0,162834.1,160202.0,162834.1,160305.0,162834.0] || member(intersection(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),universal_class) -> equal(intersection(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),successor_relation) member(apply(choice,intersection(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation)))),kind_1_ordinals)*.
% 299.89/300.47  221870[10:Res:203330.1,160703.0] || section(u,complement(compose(element_relation,universal_class)),v) member(regular(cantor(restrict(u,v,complement(compose(element_relation,universal_class))))),element_relation)* -> equal(cantor(restrict(u,v,complement(compose(element_relation,universal_class)))),successor_relation).
% 299.89/300.47  224402[25:Rew:224236.1,204962.2] function(u) || subclass(range_of(u),cantor(segment(cross_product(v,w),x,y))) equal(cantor(cantor(z)),universal_class) -> compatible(u,z,restrict(cross_product(x,singleton(y)),v,w))*.
% 299.89/300.47  229134[10:Res:160789.2,162356.0] || subclass(u,symmetric_difference(v,w)) subclass(union(v,w),x)* well_ordering(omega,x) -> equal(u,successor_relation) equal(integer_of(ordered_pair(regular(u),least(omega,union(v,w)))),successor_relation)**.
% 299.89/300.47  229773[10:Res:161696.1,162356.0] || subclass(cross_product(u,v),w)* well_ordering(omega,w) -> equal(restrict(x,u,v),successor_relation) equal(integer_of(ordered_pair(regular(restrict(x,u,v)),least(omega,cross_product(u,v)))),successor_relation)**.
% 299.89/300.47  229805[10:Res:221521.1,6041.0] || member(u,v)* member(u,w)* subclass(w,x)* well_ordering(cross_product(v,complement(singleton(omega))),x)* -> equal(integer_of(least(cross_product(v,complement(singleton(omega))),w)),successor_relation)**.
% 299.89/300.47  231832[10:Res:5768.2,161035.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,intersection(power_class(successor_relation),complement(w))) member(ordered_pair(u,ordered_pair(v,compose(u,v))),union(image(element_relation,universal_class),w))* -> .
% 299.89/300.47  125981[0:Res:28320.1,39.1] || subclass(rest_relation,rotate(cross_product(cross_product(universal_class,universal_class),universal_class))) member(ordered_pair(ordered_pair(rest_of(ordered_pair(u,v)),v),u),w) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(u,v))),u),flip(w))*.
% 299.89/300.47  125980[0:Res:28320.1,36.1] || subclass(rest_relation,rotate(cross_product(cross_product(universal_class,universal_class),universal_class))) member(ordered_pair(ordered_pair(rest_of(ordered_pair(u,v)),u),v),w) -> member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(u,v))),u),rotate(w))*.
% 299.89/300.47  126107[0:Res:28321.1,39.1] || subclass(rest_relation,flip(cross_product(cross_product(universal_class,universal_class),universal_class))) member(ordered_pair(ordered_pair(u,v),rest_of(ordered_pair(u,v))),w) -> member(ordered_pair(ordered_pair(v,u),rest_of(ordered_pair(u,v))),flip(w))*.
% 299.89/300.47  126106[0:Res:28321.1,36.1] || subclass(rest_relation,flip(cross_product(cross_product(universal_class,universal_class),universal_class))) member(ordered_pair(ordered_pair(u,rest_of(ordered_pair(u,v))),v),w) -> member(ordered_pair(ordered_pair(v,u),rest_of(ordered_pair(u,v))),rotate(w))*.
% 299.89/300.47  40346[0:SoR:3846.0,6317.2] single_valued_class(flip(cross_product(u,universal_class))) || subclass(range_of(flip(cross_product(u,universal_class))),v) equal(flip(cross_product(u,universal_class)),cross_product(universal_class,universal_class)) -> maps(flip(cross_product(u,universal_class)),inverse(u),v)*.
% 299.89/300.47  6271[0:Rew:1005.0,6268.2] || member(ordered_pair(ordered_pair(u,v),singleton(u)),w)* member(ordered_pair(singleton(singleton(singleton(u))),v),cross_product(cross_product(universal_class,universal_class),universal_class))* -> member(ordered_pair(singleton(singleton(singleton(u))),v),rotate(w))*.
% 299.89/300.47  6262[0:Rew:1005.0,6259.2] || member(ordered_pair(ordered_pair(u,singleton(u)),v),w)* member(ordered_pair(singleton(singleton(singleton(u))),v),cross_product(cross_product(universal_class,universal_class),universal_class))* -> member(ordered_pair(singleton(singleton(singleton(u))),v),flip(w))*.
% 299.89/300.47  132311[0:Res:131.2,9647.0] || connected(u,restrict(v,w,x)) -> well_ordering(u,restrict(v,w,x)) subclass(not_well_ordering(u,restrict(v,w,x)),y) member(not_subclass_element(not_well_ordering(u,restrict(v,w,x)),y),v)*.
% 299.89/300.47  125957[0:Res:28320.1,2142.0] || subclass(rest_relation,rotate(ordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),unordered_pair(u,singleton(v)))* equal(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),singleton(u)).
% 299.89/300.47  126087[0:Res:28321.1,2142.0] || subclass(rest_relation,flip(ordered_pair(u,v)))* -> equal(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),unordered_pair(u,singleton(v)))* equal(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),singleton(u)).
% 299.89/300.47  40435[0:SoR:3844.0,6317.2] single_valued_class(restrict(element_relation,universal_class,u)) || subclass(range_of(restrict(element_relation,universal_class,u)),v) equal(restrict(element_relation,universal_class,u),cross_product(universal_class,universal_class)) -> maps(restrict(element_relation,universal_class,u),sum_class(u),v)*.
% 299.89/300.47  140131[0:SpR:984.0,9948.0] ||  -> equal(power_class(intersection(union(u,image(element_relation,power_class(v))),complement(inverse(intersection(complement(u),power_class(image(element_relation,complement(v)))))))),complement(image(element_relation,symmetrization_of(intersection(complement(u),power_class(image(element_relation,complement(v))))))))**.
% 299.89/300.47  139671[0:SpR:982.0,9948.0] ||  -> equal(power_class(intersection(union(image(element_relation,power_class(u)),v),complement(inverse(intersection(power_class(image(element_relation,complement(u))),complement(v)))))),complement(image(element_relation,symmetrization_of(intersection(power_class(image(element_relation,complement(u))),complement(v))))))**.
% 299.89/300.47  140130[0:SpR:984.0,9949.0] ||  -> equal(power_class(intersection(union(u,image(element_relation,power_class(v))),complement(singleton(intersection(complement(u),power_class(image(element_relation,complement(v)))))))),complement(image(element_relation,successor(intersection(complement(u),power_class(image(element_relation,complement(v))))))))**.
% 299.89/300.47  139670[0:SpR:982.0,9949.0] ||  -> equal(power_class(intersection(union(image(element_relation,power_class(u)),v),complement(singleton(intersection(power_class(image(element_relation,complement(u))),complement(v)))))),complement(image(element_relation,successor(intersection(power_class(image(element_relation,complement(u))),complement(v))))))**.
% 299.89/300.47  137184[0:SpL:10029.0,3874.1] || member(u,union(power_class(v),complement(singleton(image(element_relation,complement(v)))))) member(u,successor(image(element_relation,complement(v)))) -> member(u,symmetric_difference(power_class(v),complement(singleton(image(element_relation,complement(v))))))*.
% 299.89/300.47  137802[0:SpL:10028.0,3874.1] || member(u,union(power_class(v),complement(inverse(image(element_relation,complement(v)))))) member(u,symmetrization_of(image(element_relation,complement(v)))) -> member(u,symmetric_difference(power_class(v),complement(inverse(image(element_relation,complement(v))))))*.
% 299.89/300.47  131015[0:Rew:10422.0,130956.0] || member(restrict(cross_product(u,singleton(v)),w,x),segment(cross_product(w,x),u,v)) -> member(ordered_pair(restrict(cross_product(u,singleton(v)),w,x),segment(cross_product(w,x),u,v)),element_relation)*.
% 299.89/300.47  161092[10:Rew:160202.0,151352.3] || member(u,v) subclass(v,w)* well_ordering(union(x,image(element_relation,universal_class)),w)* -> member(ordered_pair(u,least(union(x,image(element_relation,universal_class)),v)),intersection(complement(x),power_class(successor_relation)))*.
% 299.89/300.47  161093[10:Rew:160202.0,151353.3] || member(u,v) subclass(v,w)* well_ordering(union(image(element_relation,universal_class),x),w)* -> member(ordered_pair(u,least(union(image(element_relation,universal_class),x),v)),intersection(power_class(successor_relation),complement(x)))*.
% 299.89/300.47  161561[10:Rew:160202.0,146789.1] || member(cross_product(u,v),universal_class) -> equal(cross_product(u,v),successor_relation) member(unordered_pair(first(apply(choice,cross_product(u,v))),singleton(second(apply(choice,cross_product(u,v))))),apply(choice,cross_product(u,v)))*.
% 299.89/300.47  161560[10:Rew:160202.0,146812.2] || member(second(regular(cross_product(u,v))),universal_class) member(first(regular(cross_product(u,v))),second(regular(cross_product(u,v))))* -> equal(cross_product(u,v),successor_relation) member(regular(cross_product(u,v)),element_relation).
% 299.89/300.47  162398[10:Rew:160202.0,147089.3] || member(apply(choice,complement(intersection(u,v))),v)* member(apply(choice,complement(intersection(u,v))),u)* member(complement(intersection(u,v)),universal_class) -> equal(complement(intersection(u,v)),successor_relation).
% 299.89/300.47  162630[10:Rew:160202.0,147164.1] || member(regular(intersection(u,complement(intersection(v,w)))),union(v,w)) -> equal(intersection(u,complement(intersection(v,w))),successor_relation) member(regular(intersection(u,complement(intersection(v,w)))),symmetric_difference(v,w))*.
% 299.89/300.47  162633[10:Rew:160202.0,147167.1] || member(regular(intersection(complement(intersection(u,v)),w)),union(u,v)) -> equal(intersection(complement(intersection(u,v)),w),successor_relation) member(regular(intersection(complement(intersection(u,v)),w)),symmetric_difference(u,v))*.
% 299.89/300.47  162676[10:Rew:160202.0,147288.1] || member(regular(complement(complement(complement(intersection(u,v))))),union(u,v)) -> equal(complement(complement(complement(intersection(u,v)))),successor_relation) member(regular(complement(complement(complement(intersection(u,v))))),symmetric_difference(u,v))*.
% 299.89/300.47  162679[10:Rew:160202.0,147959.1] || member(regular(power_class(intersection(power_class(image(element_relation,complement(u))),complement(v)))),image(element_relation,union(image(element_relation,power_class(u)),v)))* -> equal(power_class(intersection(power_class(image(element_relation,complement(u))),complement(v))),successor_relation).
% 299.89/300.47  162680[10:Rew:160202.0,147979.1] || member(regular(power_class(intersection(complement(u),power_class(image(element_relation,complement(v)))))),image(element_relation,union(u,image(element_relation,power_class(v)))))* -> equal(power_class(intersection(complement(u),power_class(image(element_relation,complement(v))))),successor_relation).
% 299.89/300.47  184016[14:MRR:183991.3,160227.0] || equal(sum_class(range_of(first(not_subclass_element(cross_product(u,v),w)))),second(not_subclass_element(cross_product(u,v),w))) member(not_subclass_element(cross_product(u,v),w),cross_product(universal_class,universal_class))* -> subclass(cross_product(u,v),w).
% 299.89/300.47  43133[0:Rew:1005.0,43120.1] || member(u,universal_class) member(singleton(singleton(singleton(v))),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(v,u),singleton(v)),w)* -> member(ordered_pair(singleton(singleton(singleton(v))),u),rotate(w))*.
% 299.89/300.47  43168[0:Rew:1005.0,43155.1] || member(u,universal_class) member(singleton(singleton(singleton(v))),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(v,singleton(v)),u),w)* -> member(ordered_pair(singleton(singleton(singleton(v))),u),flip(w))*.
% 299.89/300.47  108243[2:Res:31069.2,3874.1] inductive(complement(intersection(u,v))) || well_ordering(w,universal_class) member(least(w,complement(intersection(u,v))),union(u,v)) -> member(least(w,complement(intersection(u,v))),symmetric_difference(u,v))*.
% 299.89/300.47  162636[10:Rew:160202.0,147170.2] || well_ordering(u,universal_class) member(least(u,complement(intersection(v,w))),union(v,w)) -> equal(complement(intersection(v,w)),successor_relation) member(least(u,complement(intersection(v,w))),symmetric_difference(v,w))*.
% 299.89/300.47  160814[10:Rew:160202.0,146398.3] || member(ordinal_numbers,universal_class) well_ordering(element_relation,image(choice,singleton(singleton(u))))* subclass(u,image(choice,singleton(singleton(u))))* -> equal(singleton(u),successor_relation) member(image(choice,singleton(singleton(u))),ordinal_numbers).
% 299.89/300.47  9652[0:Res:1481.2,61.0] || subclass(u,image(v,image(w,singleton(x)))) member(ordered_pair(x,not_subclass_element(u,y)),cross_product(universal_class,universal_class)) -> subclass(u,y) member(ordered_pair(x,not_subclass_element(u,y)),compose(v,w))*.
% 299.89/300.47  39598[0:Res:5768.2,22.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,cross_product(universal_class,universal_class)) member(u,ordered_pair(v,compose(u,v))) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),element_relation)*.
% 299.89/300.47  192536[10:Res:161922.2,162356.0] || well_ordering(u,cross_product(universal_class,universal_class)) subclass(rest_of(v),w)* well_ordering(omega,w) -> equal(rest_of(v),successor_relation) equal(integer_of(ordered_pair(least(u,rest_of(v)),least(omega,rest_of(v)))),successor_relation)**.
% 299.89/300.47  192535[10:Res:161927.2,162356.0] || well_ordering(u,cross_product(universal_class,universal_class)) subclass(compose_class(v),w)* well_ordering(omega,w) -> equal(compose_class(v),successor_relation) equal(integer_of(ordered_pair(least(u,compose_class(v)),least(omega,compose_class(v)))),successor_relation)**.
% 299.89/300.47  192528[10:Res:161312.2,162356.0] || member(intersection(u,v),universal_class) subclass(v,w)* well_ordering(omega,w)* -> equal(intersection(u,v),successor_relation) equal(integer_of(ordered_pair(apply(choice,intersection(u,v)),least(omega,v))),successor_relation)**.
% 299.89/300.47  192506[10:Res:161311.2,162356.0] || member(intersection(u,v),universal_class) subclass(u,w)* well_ordering(omega,w)* -> equal(intersection(u,v),successor_relation) equal(integer_of(ordered_pair(apply(choice,intersection(u,v)),least(omega,u))),successor_relation)**.
% 299.89/300.47  195415[0:SpR:194805.1,1931.0] || subclass(union(complement(intersection(u,v)),union(u,v)),complement(symmetric_difference(u,v)))* -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),union(complement(intersection(u,v)),union(u,v))).
% 299.89/300.47  204023[10:Rew:203192.0,162675.2] || section(cross_product(u,v),w,x) well_ordering(y,w) -> equal(segment(y,cantor(restrict(cross_product(x,w),u,v)),least(y,cantor(restrict(cross_product(x,w),u,v)))),successor_relation)**.
% 299.89/300.47  207864[10:Res:206688.0,127.0] || subclass(complement(intersection(complement(singleton(successor_relation)),power_class(u))),v)* well_ordering(w,v)* -> member(least(w,complement(intersection(complement(singleton(successor_relation)),power_class(u)))),complement(intersection(complement(singleton(successor_relation)),power_class(u))))*.
% 299.89/300.47  208144[10:Res:207196.0,127.0] || subclass(complement(intersection(power_class(u),complement(singleton(successor_relation)))),v)* well_ordering(w,v)* -> member(least(w,complement(intersection(power_class(u),complement(singleton(successor_relation))))),complement(intersection(power_class(u),complement(singleton(successor_relation)))))*.
% 299.89/300.47  216361[14:SpL:199971.1,61.0] || member(u,universal_class) member(v,image(w,image(x,successor_relation))) member(ordered_pair(sum_class(range_of(u)),v),cross_product(universal_class,universal_class)) -> member(ordered_pair(sum_class(range_of(u)),v),compose(w,x))*.
% 299.89/300.47  163736[10:Rew:160305.0,162782.2] inductive(symmetric_difference(complement(singleton(singleton_relation)),complement(image(successor_relation,ordinal_numbers)))) || well_ordering(u,kind_1_ordinals) -> member(least(u,symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation)))),symmetric_difference(complement(singleton(successor_relation)),complement(range_of(successor_relation))))*.
% 299.89/300.47  197975[10:Rew:193730.0,197958.1,193730.0,197958.0] || member(ordered_pair(u,not_subclass_element(range_of(successor_relation),v)),cross_product(universal_class,universal_class)) -> subclass(range_of(successor_relation),v) member(ordered_pair(u,not_subclass_element(range_of(successor_relation),v)),compose(complement(cross_product(image(w,singleton(u)),universal_class)),w))*.
% 299.89/300.47  163731[10:Rew:160202.0,160669.2,160202.0,160669.1] || member(ordered_pair(u,not_subclass_element(image(v,range_of(successor_relation)),w)),cross_product(universal_class,universal_class)) -> subclass(image(v,range_of(successor_relation)),w) member(ordered_pair(u,not_subclass_element(image(v,range_of(successor_relation)),w)),compose(v,successor_relation))*.
% 299.89/300.47  216975[10:MRR:216974.4,160227.0] || equal(compose_class(u),domain_relation) member(image(u,range_of(successor_relation)),universal_class) member(ordered_pair(v,apply(choice,image(u,range_of(successor_relation)))),cross_product(universal_class,universal_class))* -> equal(image(u,range_of(successor_relation)),successor_relation).
% 299.89/300.47  221502[10:Res:218373.0,5839.2] || member(u,v)* member(u,w)* well_ordering(x,complement(singleton(intersection(w,v)))) -> equal(singleton(intersection(w,v)),successor_relation) member(least(x,intersection(w,v)),intersection(w,v))*.
% 299.89/300.47  221492[10:Res:218373.0,5853.2] || member(u,v)* member(w,x)* well_ordering(y,complement(singleton(cross_product(x,v)))) -> equal(singleton(cross_product(x,v)),successor_relation) member(least(y,cross_product(x,v)),cross_product(x,v))*.
% 299.89/300.47  224764[25:MRR:197245.4,224753.0] single_valued_class(flip(cross_product(u,universal_class))) || subclass(range_of(flip(cross_product(u,universal_class))),range_of(u))* equal(cross_product(range_of(u),range_of(u)),inverse(u)) equal(flip(cross_product(u,universal_class)),successor_relation) -> .
% 299.89/300.47  229998[10:Res:9529.1,162356.0] || subclass(complement(intersection(u,v)),w)* well_ordering(omega,w) -> subclass(symmetric_difference(u,v),x) equal(integer_of(ordered_pair(not_subclass_element(symmetric_difference(u,v),x),least(omega,complement(intersection(u,v))))),successor_relation)**.
% 299.89/300.47  35683[0:SpL:1948.0,3874.1] || member(u,union(union(v,w),union(complement(v),complement(w)))) member(u,complement(symmetric_difference(complement(v),complement(w)))) -> member(u,symmetric_difference(union(v,w),union(complement(v),complement(w))))*.
% 299.89/300.47  40654[0:SpL:1931.0,3883.2] || member(u,union(complement(intersection(v,w)),union(v,w)))* member(u,complement(symmetric_difference(v,w))) subclass(symmetric_difference(complement(intersection(v,w)),union(v,w)),x)* -> member(u,x)*.
% 299.89/300.47  42997[0:Rew:161.0,42921.4] || member(u,union(v,w)) member(u,complement(intersection(v,w)))* subclass(symmetric_difference(v,w),x)* well_ordering(y,x)* -> member(least(y,symmetric_difference(v,w)),symmetric_difference(v,w))*.
% 299.89/300.47  31208[0:Res:3872.2,127.0] || member(u,cross_product(v,w))* member(u,x)* subclass(restrict(x,v,w),y)* well_ordering(z,y)* -> member(least(z,restrict(x,v,w)),restrict(x,v,w))*.
% 299.89/300.47  125894[0:SpR:2330.1,28320.1] || subclass(rest_relation,rotate(u)) -> subclass(cross_product(v,w),x) member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(v,w),x)),rest_of(not_subclass_element(cross_product(v,w),x))),first(not_subclass_element(cross_product(v,w),x))),u)*.
% 299.89/300.47  126019[0:SpR:2330.1,28321.1] || subclass(rest_relation,flip(u)) -> subclass(cross_product(v,w),x) member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(v,w),x)),first(not_subclass_element(cross_product(v,w),x))),rest_of(not_subclass_element(cross_product(v,w),x))),u)*.
% 299.89/300.47  126029[0:SpR:2330.1,28321.1] || subclass(rest_relation,flip(u)) -> subclass(cross_product(v,w),x) member(ordered_pair(not_subclass_element(cross_product(v,w),x),rest_of(ordered_pair(second(not_subclass_element(cross_product(v,w),x)),first(not_subclass_element(cross_product(v,w),x))))),u)*.
% 299.89/300.47  113193[0:Res:3872.2,40234.0] || member(not_subclass_element(u,intersection(restrict(v,w,x),u)),cross_product(w,x))* member(not_subclass_element(u,intersection(restrict(v,w,x),u)),v)* -> subclass(u,intersection(restrict(v,w,x),u)).
% 299.89/300.47  40218[0:Res:1951.1,3886.0] || member(not_subclass_element(u,intersection(v,complement(intersection(w,x)))),symmetric_difference(w,x))* member(not_subclass_element(u,intersection(v,complement(intersection(w,x)))),v)* -> subclass(u,intersection(v,complement(intersection(w,x)))).
% 299.89/300.47  107183[0:Res:34429.0,19.0] ||  -> subclass(complement(complement(cross_product(u,v))),w) equal(ordered_pair(first(not_subclass_element(complement(complement(cross_product(u,v))),w)),second(not_subclass_element(complement(complement(cross_product(u,v))),w))),not_subclass_element(complement(complement(cross_product(u,v))),w))**.
% 299.89/300.47  41897[0:SpR:2330.1,18.2] || member(second(not_subclass_element(cross_product(u,v),w)),x) member(first(not_subclass_element(cross_product(u,v),w)),y) -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),cross_product(y,x))*.
% 299.89/300.47  123533[0:Res:978.1,2142.0] ||  -> subclass(restrict(ordered_pair(u,v),w,x),y) equal(not_subclass_element(restrict(ordered_pair(u,v),w,x),y),unordered_pair(u,singleton(v)))** equal(not_subclass_element(restrict(ordered_pair(u,v),w,x),y),singleton(u)).
% 299.89/300.47  137690[0:SpR:10028.0,9948.0] ||  -> equal(power_class(intersection(symmetrization_of(image(element_relation,complement(u))),complement(inverse(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))))),complement(image(element_relation,symmetrization_of(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))))))**.
% 299.89/300.47  137071[0:SpR:10029.0,9948.0] ||  -> equal(power_class(intersection(successor(image(element_relation,complement(u))),complement(inverse(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))))),complement(image(element_relation,symmetrization_of(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))))))**.
% 299.89/300.47  137689[0:SpR:10028.0,9949.0] ||  -> equal(power_class(intersection(symmetrization_of(image(element_relation,complement(u))),complement(singleton(intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))))),complement(image(element_relation,successor(intersection(power_class(u),complement(inverse(image(element_relation,complement(u)))))))))**.
% 299.89/300.47  137070[0:SpR:10029.0,9949.0] ||  -> equal(power_class(intersection(successor(image(element_relation,complement(u))),complement(singleton(intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))))),complement(image(element_relation,successor(intersection(power_class(u),complement(singleton(image(element_relation,complement(u)))))))))**.
% 299.89/300.47  139763[0:SpL:982.0,1089.0] || member(not_subclass_element(power_class(intersection(power_class(image(element_relation,complement(u))),complement(v))),w),image(element_relation,union(image(element_relation,power_class(u)),v)))* -> subclass(power_class(intersection(power_class(image(element_relation,complement(u))),complement(v))),w).
% 299.89/300.47  140225[0:SpL:984.0,1089.0] || member(not_subclass_element(power_class(intersection(complement(u),power_class(image(element_relation,complement(v))))),w),image(element_relation,union(u,image(element_relation,power_class(v)))))* -> subclass(power_class(intersection(complement(u),power_class(image(element_relation,complement(v))))),w).
% 299.89/300.47  161559[10:Rew:160202.0,146788.2] || member(cross_product(u,v),universal_class) member(apply(choice,cross_product(u,v)),element_relation) -> equal(cross_product(u,v),successor_relation) member(first(apply(choice,cross_product(u,v))),second(apply(choice,cross_product(u,v))))*.
% 299.89/300.47  161558[10:Rew:160202.0,146810.2] || member(first(regular(cross_product(u,v))),second(regular(cross_product(u,v))))* member(regular(cross_product(u,v)),cross_product(universal_class,universal_class)) -> equal(cross_product(u,v),successor_relation) member(regular(cross_product(u,v)),element_relation).
% 299.89/300.47  162359[10:Rew:160202.0,147076.2] || member(power_class(intersection(complement(u),complement(v))),universal_class) member(apply(choice,power_class(intersection(complement(u),complement(v)))),image(element_relation,union(u,v)))* -> equal(power_class(intersection(complement(u),complement(v))),successor_relation).
% 299.89/300.47  162371[10:Rew:160202.0,147378.1] || member(intersection(u,symmetric_difference(complement(v),complement(w))),universal_class) -> equal(intersection(u,symmetric_difference(complement(v),complement(w))),successor_relation) member(apply(choice,intersection(u,symmetric_difference(complement(v),complement(w)))),union(v,w))*.
% 299.89/300.47  162373[10:Rew:160202.0,147380.1] || member(intersection(symmetric_difference(complement(u),complement(v)),w),universal_class) -> equal(intersection(symmetric_difference(complement(u),complement(v)),w),successor_relation) member(apply(choice,intersection(symmetric_difference(complement(u),complement(v)),w)),union(u,v))*.
% 299.89/300.47  162687[10:Rew:160202.0,147532.0] ||  -> equal(symmetric_difference(complement(restrict(u,v,w)),union(cross_product(v,w),u)),successor_relation) member(regular(symmetric_difference(complement(restrict(u,v,w)),union(cross_product(v,w),u))),complement(symmetric_difference(cross_product(v,w),u)))*.
% 299.89/300.47  162688[10:Rew:160202.0,147533.0] ||  -> equal(symmetric_difference(complement(restrict(u,v,w)),union(u,cross_product(v,w))),successor_relation) member(regular(symmetric_difference(complement(restrict(u,v,w)),union(u,cross_product(v,w)))),complement(symmetric_difference(u,cross_product(v,w))))*.
% 299.89/300.47  181140[10:Rew:181056.0,181103.3] || member(ordered_pair(universal_class,ordered_pair(u,least(image(v,image(w,successor_relation)),x))),compose(v,w))* member(u,x) subclass(x,y)* well_ordering(image(v,image(w,successor_relation)),y)* -> .
% 299.89/300.47  182940[6:Res:157922.1,6044.0] || member(ordered_pair(u,ordered_pair(v,least(image(element_relation,image(universal_class,singleton(u))),w))),element_relation)* member(v,w) subclass(w,x)* well_ordering(image(element_relation,image(universal_class,singleton(u))),x)* -> .
% 299.89/300.47  44809[0:Res:314.0,5857.1] || member(ordered_pair(u,v),compose(w,x))* well_ordering(y,image(w,image(x,singleton(u)))) -> member(least(y,image(w,image(x,singleton(u)))),image(w,image(x,singleton(u))))*.
% 299.89/300.47  43127[0:Res:6269.3,3.0] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,u),v),x)* subclass(rotate(x),y)* -> member(ordered_pair(ordered_pair(v,w),u),y)*.
% 299.89/300.47  43162[0:Res:6260.3,3.0] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,v),u),x)* subclass(flip(x),y)* -> member(ordered_pair(ordered_pair(v,w),u),y)*.
% 299.89/300.47  108469[0:Res:1504.1,61.0] || subclass(ordered_pair(u,v),image(w,image(x,singleton(y))))* member(ordered_pair(y,unordered_pair(u,singleton(v))),cross_product(universal_class,universal_class)) -> member(ordered_pair(y,unordered_pair(u,singleton(v))),compose(w,x)).
% 299.89/300.47  162686[10:Rew:160202.0,147255.3] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(universal_class,universal_class))* subclass(compose(v,w),x)* well_ordering(universal_class,x) -> equal(image(v,image(w,singleton(u))),successor_relation).
% 299.89/300.47  39577[0:Res:5768.2,10.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,unordered_pair(w,x))* -> equal(ordered_pair(u,ordered_pair(v,compose(u,v))),x)* equal(ordered_pair(u,ordered_pair(v,compose(u,v))),w)*.
% 299.89/300.47  189469[15:Rew:189339.1,189415.3] || member(u,universal_class) subclass(domain_relation,image(v,image(w,singleton(x)))) member(ordered_pair(x,ordered_pair(u,successor_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(x,ordered_pair(u,successor_relation)),compose(v,w))*.
% 299.89/300.47  192513[10:Res:3872.2,162356.0] || member(u,cross_product(v,w)) member(u,x) subclass(restrict(x,v,w),y)* well_ordering(omega,y) -> equal(integer_of(ordered_pair(u,least(omega,restrict(x,v,w)))),successor_relation)**.
% 299.89/300.47  196593[10:Rew:161137.0,196579.4] || member(u,universal_class) subclass(power_class(complement(inverse(successor_relation))),v)* well_ordering(w,v)* -> member(u,image(element_relation,symmetrization_of(successor_relation)))* member(least(w,power_class(complement(inverse(successor_relation)))),power_class(complement(inverse(successor_relation))))*.
% 299.89/300.47  196798[10:Rew:162889.0,196785.4] || member(u,universal_class) subclass(power_class(complement(singleton(successor_relation))),v)* well_ordering(w,v)* -> member(u,image(element_relation,successor(successor_relation)))* member(least(w,power_class(complement(singleton(successor_relation)))),power_class(complement(singleton(successor_relation))))*.
% 299.89/300.47  197812[10:Rew:181056.0,197795.1,181056.0,197795.0] || member(ordered_pair(universal_class,regular(image(u,image(v,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(u,image(v,successor_relation)),successor_relation) member(ordered_pair(universal_class,regular(image(u,image(v,successor_relation)))),compose(u,v))*.
% 299.89/300.47  203651[10:Rew:203192.0,192538.0] || member(u,cantor(v)) equal(restrict(v,u,universal_class),w) subclass(rest_of(v),x)* well_ordering(omega,x) -> equal(integer_of(ordered_pair(ordered_pair(u,w),least(omega,rest_of(v)))),successor_relation)**.
% 299.89/300.47  219379[22:Rew:219376.1,217261.1] || equal(singleton(ordered_pair(u,least(intersection(v,singleton(successor_relation)),w))),kind_1_ordinals)** member(singleton(successor_relation),v) member(u,w) subclass(w,x)* well_ordering(intersection(v,singleton(successor_relation)),x)* -> .
% 299.89/300.47  193800[10:Rew:193730.0,193794.3] || member(ordered_pair(u,ordered_pair(v,least(range_of(successor_relation),w))),compose(complement(cross_product(image(x,singleton(u)),universal_class)),x))* member(v,w) subclass(w,y)* well_ordering(range_of(successor_relation),y)* -> .
% 299.89/300.47  163732[10:Rew:160202.0,160661.2] || member(u,image(v,range_of(successor_relation))) member(ordered_pair(w,u),cross_product(universal_class,universal_class)) -> equal(cross_product(singleton(w),universal_class),successor_relation) member(ordered_pair(w,u),compose(v,regular(cross_product(singleton(w),universal_class))))*.
% 299.89/300.47  163744[10:Rew:160305.0,162820.2,160202.0,162820.1,160305.0,162820.1,160202.0,162820.0,160305.0,162820.0] || member(not_subclass_element(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals) member(not_subclass_element(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),complement(intersection(singleton(successor_relation),range_of(successor_relation))))* -> subclass(u,symmetric_difference(singleton(successor_relation),range_of(successor_relation))).
% 299.89/300.47  220416[23:Res:220406.0,5554.0] || member(u,v)* -> equal(ordered_pair(first(ordered_pair(u,regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation))))),second(ordered_pair(u,regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))))),ordered_pair(u,regular(symmetric_difference(singleton(successor_relation),range_of(successor_relation)))))**.
% 299.89/300.47  222524[24:Rew:222326.0,222420.3] || member(ordered_pair(kind_1_ordinals,ordered_pair(u,least(image(v,image(w,successor_relation)),x))),compose(v,w))* member(u,x) subclass(x,y)* well_ordering(image(v,image(w,successor_relation)),y)* -> .
% 299.89/300.47  222525[24:Rew:222326.0,222357.1,222326.0,222357.0] || member(ordered_pair(kind_1_ordinals,regular(image(u,image(v,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(u,image(v,successor_relation)),successor_relation) member(ordered_pair(kind_1_ordinals,regular(image(u,image(v,successor_relation)))),compose(u,v))*.
% 299.89/300.47  226362[25:Rew:226350.1,224765.1] one_to_one(restrict(u,v,singleton(w))) || subclass(universal_class,cantor(segment(u,v,w))) equal(cross_product(cantor(segment(u,v,w)),cantor(segment(u,v,w))),segment(u,v,w))** -> .
% 299.89/300.47  230822[10:Res:160972.1,127.0] || member(u,universal_class) subclass(image(element_relation,power_class(successor_relation)),v)* well_ordering(w,v)* -> member(u,power_class(image(element_relation,universal_class)))* member(least(w,image(element_relation,power_class(successor_relation))),image(element_relation,power_class(successor_relation)))*.
% 299.89/300.47  230818[10:Res:160972.1,162356.0] || member(u,universal_class) subclass(image(element_relation,power_class(successor_relation)),v)* well_ordering(omega,v) -> member(u,power_class(image(element_relation,universal_class))) equal(integer_of(ordered_pair(u,least(omega,image(element_relation,power_class(successor_relation))))),successor_relation)**.
% 299.89/300.47  230881[10:MRR:230836.0,34189.1] || member(not_subclass_element(u,intersection(v,image(element_relation,power_class(successor_relation)))),v)* -> member(not_subclass_element(u,intersection(v,image(element_relation,power_class(successor_relation)))),power_class(image(element_relation,universal_class)))* subclass(u,intersection(v,image(element_relation,power_class(successor_relation)))).
% 299.89/300.47  125911[0:Res:28320.1,3874.1] || subclass(rest_relation,rotate(complement(intersection(u,v)))) member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),union(u,v)) -> member(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x),symmetric_difference(u,v))*.
% 299.89/300.47  126041[0:Res:28321.1,3874.1] || subclass(rest_relation,flip(complement(intersection(u,v)))) member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),union(u,v)) -> member(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))),symmetric_difference(u,v))*.
% 299.89/300.47  131774[0:SpR:1938.0,9529.1] ||  -> subclass(symmetric_difference(complement(restrict(u,v,w)),union(u,cross_product(v,w))),x) member(not_subclass_element(symmetric_difference(complement(restrict(u,v,w)),union(u,cross_product(v,w))),x),complement(symmetric_difference(u,cross_product(v,w))))*.
% 299.89/300.47  131775[0:SpR:1943.0,9529.1] ||  -> subclass(symmetric_difference(complement(restrict(u,v,w)),union(cross_product(v,w),u)),x) member(not_subclass_element(symmetric_difference(complement(restrict(u,v,w)),union(cross_product(v,w),u)),x),complement(symmetric_difference(cross_product(v,w),u)))*.
% 299.89/300.47  35689[0:Res:340.1,3874.1] || member(not_subclass_element(intersection(complement(intersection(u,v)),w),x),union(u,v)) -> subclass(intersection(complement(intersection(u,v)),w),x) member(not_subclass_element(intersection(complement(intersection(u,v)),w),x),symmetric_difference(u,v))*.
% 299.89/300.47  35706[0:Res:322.1,3874.1] || member(not_subclass_element(intersection(u,complement(intersection(v,w))),x),union(v,w)) -> subclass(intersection(u,complement(intersection(v,w))),x) member(not_subclass_element(intersection(u,complement(intersection(v,w))),x),symmetric_difference(v,w))*.
% 299.89/300.47  107175[0:Res:34429.0,3874.1] || member(not_subclass_element(complement(complement(complement(intersection(u,v)))),w),union(u,v)) -> subclass(complement(complement(complement(intersection(u,v)))),w) member(not_subclass_element(complement(complement(complement(intersection(u,v)))),w),symmetric_difference(u,v))*.
% 299.89/300.47  41917[0:SpL:2330.1,38.0] || member(ordered_pair(not_subclass_element(cross_product(u,v),w),x),flip(y)) -> subclass(cross_product(u,v),w) member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(u,v),w)),first(not_subclass_element(cross_product(u,v),w))),x),y)*.
% 299.89/300.47  41918[0:SpL:2330.1,35.0] || member(ordered_pair(not_subclass_element(cross_product(u,v),w),x),rotate(y)) -> subclass(cross_product(u,v),w) member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(u,v),w)),x),first(not_subclass_element(cross_product(u,v),w))),y)*.
% 299.89/300.47  40274[0:Rew:1948.0,40211.2,1948.0,40211.1] || member(not_subclass_element(u,symmetric_difference(complement(v),complement(w))),union(complement(v),complement(w)))* member(not_subclass_element(u,symmetric_difference(complement(v),complement(w))),union(v,w)) -> subclass(u,symmetric_difference(complement(v),complement(w))).
% 299.89/300.47  40071[0:Rew:505.0,40057.3] || member(u,v) subclass(v,w)* well_ordering(power_class(intersection(complement(x),complement(y))),w)* -> member(ordered_pair(u,least(power_class(intersection(complement(x),complement(y))),v)),image(element_relation,union(x,y)))*.
% 299.89/300.47  161556[10:Rew:160202.0,146786.2] || member(cross_product(u,v),universal_class) member(apply(choice,cross_product(u,v)),rest_relation) -> equal(cross_product(u,v),successor_relation) equal(rest_of(first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))**.
% 299.89/300.47  162037[10:Rew:160202.0,146951.0] ||  -> equal(intersection(u,restrict(v,w,x)),successor_relation) equal(ordered_pair(first(regular(intersection(u,restrict(v,w,x)))),second(regular(intersection(u,restrict(v,w,x))))),regular(intersection(u,restrict(v,w,x))))**.
% 299.89/300.47  162042[10:Rew:160202.0,146956.0] ||  -> equal(intersection(restrict(u,v,w),x),successor_relation) equal(ordered_pair(first(regular(intersection(restrict(u,v,w),x))),second(regular(intersection(restrict(u,v,w),x)))),regular(intersection(restrict(u,v,w),x)))**.
% 299.89/300.47  162401[10:Rew:160202.0,147093.2] || member(intersection(u,intersection(complement(v),complement(w))),universal_class) member(apply(choice,intersection(u,intersection(complement(v),complement(w)))),union(v,w))* -> equal(intersection(u,intersection(complement(v),complement(w))),successor_relation).
% 299.89/300.47  162403[10:Rew:160202.0,147095.2] || member(intersection(intersection(complement(u),complement(v)),w),universal_class) member(apply(choice,intersection(intersection(complement(u),complement(v)),w)),union(u,v))* -> equal(intersection(intersection(complement(u),complement(v)),w),successor_relation).
% 299.89/300.47  162445[10:Rew:160202.0,147099.1] || member(intersection(u,unordered_pair(v,w)),universal_class) -> equal(intersection(u,unordered_pair(v,w)),successor_relation) equal(apply(choice,intersection(u,unordered_pair(v,w))),w)** equal(apply(choice,intersection(u,unordered_pair(v,w))),v)**.
% 299.89/300.47  162447[10:Rew:160202.0,147101.1] || member(intersection(unordered_pair(u,v),w),universal_class) -> equal(intersection(unordered_pair(u,v),w),successor_relation) equal(apply(choice,intersection(unordered_pair(u,v),w)),v)** equal(apply(choice,intersection(unordered_pair(u,v),w)),u)**.
% 299.89/300.47  162484[10:Rew:160202.0,147896.2] || member(successor(image(element_relation,complement(u))),universal_class) member(apply(choice,successor(image(element_relation,complement(u)))),intersection(power_class(u),complement(singleton(image(element_relation,complement(u))))))* -> equal(successor(image(element_relation,complement(u))),successor_relation).
% 299.89/300.47  162488[10:Rew:160202.0,147916.2] || member(symmetrization_of(image(element_relation,complement(u))),universal_class) member(apply(choice,symmetrization_of(image(element_relation,complement(u)))),intersection(power_class(u),complement(inverse(image(element_relation,complement(u))))))* -> equal(symmetrization_of(image(element_relation,complement(u))),successor_relation).
% 299.89/300.47  162689[10:Rew:160202.0,147487.2] || member(regular(intersection(u,complement(restrict(v,w,x)))),cross_product(w,x))* member(regular(intersection(u,complement(restrict(v,w,x)))),v)* -> equal(intersection(u,complement(restrict(v,w,x))),successor_relation).
% 299.89/300.47  162690[10:Rew:160202.0,147514.2] || member(regular(intersection(complement(restrict(u,v,w)),x)),cross_product(v,w))* member(regular(intersection(complement(restrict(u,v,w)),x)),u)* -> equal(intersection(complement(restrict(u,v,w)),x),successor_relation).
% 299.89/300.47  162692[10:Rew:160202.0,147636.0] ||  -> equal(intersection(u,intersection(ordered_pair(v,w),x)),successor_relation) equal(regular(intersection(u,intersection(ordered_pair(v,w),x))),unordered_pair(v,singleton(w)))** equal(regular(intersection(u,intersection(ordered_pair(v,w),x))),singleton(v)).
% 299.89/300.47  162693[10:Rew:160202.0,147687.0] ||  -> equal(intersection(u,intersection(v,ordered_pair(w,x))),successor_relation) equal(regular(intersection(u,intersection(v,ordered_pair(w,x)))),unordered_pair(w,singleton(x)))** equal(regular(intersection(u,intersection(v,ordered_pair(w,x)))),singleton(w)).
% 299.89/300.47  162694[10:Rew:160202.0,147734.0] ||  -> equal(intersection(intersection(ordered_pair(u,v),w),x),successor_relation) equal(regular(intersection(intersection(ordered_pair(u,v),w),x)),unordered_pair(u,singleton(v)))** equal(regular(intersection(intersection(ordered_pair(u,v),w),x)),singleton(u)).
% 299.89/300.47  162695[10:Rew:160202.0,147800.0] ||  -> equal(intersection(intersection(u,ordered_pair(v,w)),x),successor_relation) equal(regular(intersection(intersection(u,ordered_pair(v,w)),x)),unordered_pair(v,singleton(w)))** equal(regular(intersection(intersection(u,ordered_pair(v,w)),x)),singleton(v)).
% 299.89/300.47  181141[10:Rew:181056.0,181101.3] || member(ordered_pair(universal_class,u),compose(v,w))* subclass(image(v,image(w,successor_relation)),x)* well_ordering(y,x)* -> member(least(y,image(v,image(w,successor_relation))),image(v,image(w,successor_relation)))*.
% 299.89/300.47  96155[2:MRR:96153.3,2450.0] || connected(u,v) well_ordering(w,v) subclass(singleton(least(w,not_well_ordering(u,v))),not_well_ordering(u,v)) -> well_ordering(u,v) section(w,singleton(least(w,not_well_ordering(u,v))),not_well_ordering(u,v))*.
% 299.89/300.47  162691[10:Rew:160202.0,147578.3] || member(least(u,complement(restrict(v,w,x))),cross_product(w,x))* member(least(u,complement(restrict(v,w,x))),v)* well_ordering(u,universal_class) -> equal(complement(restrict(v,w,x)),successor_relation).
% 299.89/300.47  107655[0:Res:6187.2,6045.0] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(universal_class,universal_class))* subclass(compose(v,w),y)* well_ordering(universal_class,y) -> subclass(image(v,image(w,singleton(u))),x).
% 299.89/300.47  192537[10:Res:162026.3,162356.0] || member(u,ordinal_numbers) well_ordering(v,u) subclass(sum_class(u),w)* well_ordering(omega,w) -> equal(sum_class(u),successor_relation) equal(integer_of(ordered_pair(least(v,sum_class(u)),least(omega,sum_class(u)))),successor_relation)**.
% 299.89/300.47  192512[10:Res:1032.1,162356.0] || member(u,universal_class) subclass(intersection(complement(v),complement(w)),x)* well_ordering(omega,x) -> member(u,union(v,w)) equal(integer_of(ordered_pair(u,least(omega,intersection(complement(v),complement(w))))),successor_relation)**.
% 299.89/300.47  192976[10:Res:1348.1,162356.0] || member(restrict(u,v,singleton(w)),universal_class) subclass(domain_relation,x) well_ordering(omega,x)* -> equal(integer_of(ordered_pair(ordered_pair(restrict(u,v,singleton(w)),segment(u,v,w)),least(omega,domain_relation))),successor_relation)**.
% 299.89/300.47  195809[6:Res:195710.1,5857.1] || equal(inverse(u),universal_class) member(ordered_pair(v,w),compose(x,y))* well_ordering(z,inverse(u))* -> member(least(z,image(x,image(y,singleton(v)))),image(x,image(y,singleton(v))))*.
% 299.89/300.47  195868[6:Res:195720.1,5857.1] || equal(sum_class(u),universal_class) member(ordered_pair(v,w),compose(x,y))* well_ordering(z,sum_class(u))* -> member(least(z,image(x,image(y,singleton(v)))),image(x,image(y,singleton(v))))*.
% 299.89/300.47  203375[10:Rew:203192.0,161557.3] || member(cross_product(u,v),universal_class) member(apply(choice,cross_product(u,v)),domain_relation) -> equal(cross_product(u,v),successor_relation) equal(cantor(first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))**.
% 299.89/300.47  204976[10:Rew:203192.0,204003.4,203192.0,204003.2] || section(u,v,w) well_ordering(x,v) subclass(cantor(restrict(u,w,v)),y) -> equal(cantor(restrict(u,w,v)),successor_relation) member(least(x,cantor(restrict(u,w,v))),y)*.
% 299.89/300.47  210376[15:Res:189563.1,61.0] || subclass(domain_relation,flip(image(u,image(v,singleton(w))))) member(ordered_pair(w,ordered_pair(ordered_pair(x,y),successor_relation)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,ordered_pair(ordered_pair(x,y),successor_relation)),compose(u,v))*.
% 299.89/300.47  210487[15:Res:189564.1,6036.0] || subclass(domain_relation,rotate(u)) member(ordered_pair(ordered_pair(v,successor_relation),least(intersection(w,u),x)),w)* member(ordered_pair(v,successor_relation),x) subclass(x,y)* well_ordering(intersection(w,u),y)* -> .
% 299.89/300.47  210449[15:Res:189564.1,61.0] || subclass(domain_relation,rotate(image(u,image(v,singleton(w))))) member(ordered_pair(w,ordered_pair(ordered_pair(x,successor_relation),y)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,ordered_pair(ordered_pair(x,successor_relation),y)),compose(u,v))*.
% 299.89/300.47  216866[10:Res:1028.1,163343.0] || member(apply(choice,regular(image(element_relation,complement(u)))),universal_class) -> member(apply(choice,regular(image(element_relation,complement(u)))),power_class(u))* equal(regular(image(element_relation,complement(u))),successor_relation) equal(image(element_relation,complement(u)),successor_relation).
% 299.89/300.47  203632[10:Rew:203192.0,163733.1] || member(ordered_pair(u,regular(image(v,range_of(successor_relation)))),cross_product(universal_class,universal_class)) -> member(u,cantor(w)) equal(image(v,range_of(successor_relation)),successor_relation) member(ordered_pair(u,regular(image(v,range_of(successor_relation)))),compose(v,w))*.
% 299.89/300.47  197818[10:Rew:193730.0,197800.1,193730.0,197800.0] || member(ordered_pair(u,regular(image(v,range_of(successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(v,range_of(successor_relation)),successor_relation) member(ordered_pair(u,regular(image(v,range_of(successor_relation)))),compose(v,complement(cross_product(singleton(u),universal_class))))*.
% 299.89/300.47  222526[24:Rew:222326.0,222418.3] || member(ordered_pair(kind_1_ordinals,u),compose(v,w))* subclass(image(v,image(w,successor_relation)),x)* well_ordering(y,x)* -> member(least(y,image(v,image(w,successor_relation))),image(v,image(w,successor_relation)))*.
% 299.89/300.47  224330[25:Rew:224236.1,204993.2] function(restrict(cross_product(u,universal_class),v,w)) || subclass(image(cross_product(v,w),u),cantor(cantor(x))) equal(cantor(cantor(y)),universal_class) -> compatible(restrict(cross_product(u,universal_class),v,w),y,x)*.
% 299.89/300.47  224763[25:MRR:43230.4,224753.0] single_valued_class(flip(cross_product(u,universal_class))) || subclass(range_of(flip(cross_product(u,universal_class))),range_of(u))* equal(cross_product(range_of(u),range_of(u)),inverse(u)) equal(flip(cross_product(u,universal_class)),cross_product(universal_class,universal_class)) -> .
% 299.89/300.47  228783[24:Rew:113504.0,228768.0,160223.0,228768.0] ||  -> equal(symmetric_difference(complement(intersection(symmetric_difference(universal_class,kind_1_ordinals),complement(successor(kind_1_ordinals)))),union(symmetric_difference(universal_class,kind_1_ordinals),complement(successor(kind_1_ordinals)))),union(complement(intersection(symmetric_difference(universal_class,kind_1_ordinals),complement(successor(kind_1_ordinals)))),union(symmetric_difference(universal_class,kind_1_ordinals),complement(successor(kind_1_ordinals)))))**.
% 299.89/300.47  42470[0:Res:1951.1,6041.0] || member(least(cross_product(u,complement(intersection(v,w))),x),symmetric_difference(v,w))* member(y,u)* member(y,x)* subclass(x,z)* well_ordering(cross_product(u,complement(intersection(v,w))),z)* -> .
% 299.89/300.47  40276[0:MRR:40220.0,34189.1] || member(not_subclass_element(u,intersection(v,intersection(complement(w),complement(x)))),v)* -> member(not_subclass_element(u,intersection(v,intersection(complement(w),complement(x)))),union(w,x))* subclass(u,intersection(v,intersection(complement(w),complement(x)))).
% 299.89/300.47  124634[0:Res:60.1,33515.1] || member(ordered_pair(u,singleton(image(v,image(w,singleton(u))))),compose(v,w))* member(image(v,image(w,singleton(u))),universal_class) -> member(singleton(singleton(singleton(image(v,image(w,singleton(u)))))),element_relation).
% 299.89/300.47  124621[0:Res:3872.2,33515.1] || member(singleton(restrict(u,v,w)),cross_product(v,w))* member(singleton(restrict(u,v,w)),u)* member(restrict(u,v,w),universal_class) -> member(singleton(singleton(singleton(restrict(u,v,w)))),element_relation)*.
% 299.89/300.47  161908[10:Rew:160202.0,147154.1] || member(u,regular(cross_product(v,w)))* -> equal(cross_product(v,w),successor_relation) equal(u,unordered_pair(first(regular(cross_product(v,w))),singleton(second(regular(cross_product(v,w))))))* equal(u,singleton(first(regular(cross_product(v,w))))).
% 299.89/300.47  162592[10:Rew:160202.0,146857.2] || transitive(u,v) subclass(restrict(u,v,v),w) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),successor_relation) member(regular(compose(restrict(u,v,v),restrict(u,v,v))),w)*.
% 299.89/300.47  162397[10:Rew:160202.0,147090.2] || member(complement(intersection(u,v)),universal_class) member(apply(choice,complement(intersection(u,v))),union(u,v)) -> equal(complement(intersection(u,v)),successor_relation) member(apply(choice,complement(intersection(u,v))),symmetric_difference(u,v))*.
% 299.89/300.47  162462[10:Rew:160202.0,147477.2] || member(intersection(u,power_class(image(element_relation,complement(v)))),universal_class) member(apply(choice,intersection(u,power_class(image(element_relation,complement(v))))),image(element_relation,power_class(v)))* -> equal(intersection(u,power_class(image(element_relation,complement(v)))),successor_relation).
% 299.89/300.47  162464[10:Rew:160202.0,147504.2] || member(intersection(power_class(image(element_relation,complement(u))),v),universal_class) member(apply(choice,intersection(power_class(image(element_relation,complement(u))),v)),image(element_relation,power_class(u)))* -> equal(intersection(power_class(image(element_relation,complement(u))),v),successor_relation).
% 299.89/300.47  162470[10:Rew:160202.0,147629.1] || member(intersection(u,symmetric_difference(cross_product(v,w),x)),universal_class) -> equal(intersection(u,symmetric_difference(cross_product(v,w),x)),successor_relation) member(apply(choice,intersection(u,symmetric_difference(cross_product(v,w),x))),complement(restrict(x,v,w)))*.
% 299.89/300.47  162472[10:Rew:160202.0,147631.1] || member(intersection(u,symmetric_difference(v,cross_product(w,x))),universal_class) -> equal(intersection(u,symmetric_difference(v,cross_product(w,x))),successor_relation) member(apply(choice,intersection(u,symmetric_difference(v,cross_product(w,x)))),complement(restrict(v,w,x)))*.
% 299.89/300.47  162477[10:Rew:160202.0,147727.1] || member(intersection(symmetric_difference(cross_product(u,v),w),x),universal_class) -> equal(intersection(symmetric_difference(cross_product(u,v),w),x),successor_relation) member(apply(choice,intersection(symmetric_difference(cross_product(u,v),w),x)),complement(restrict(w,u,v)))*.
% 299.89/300.47  162479[10:Rew:160202.0,147729.1] || member(intersection(symmetric_difference(u,cross_product(v,w)),x),universal_class) -> equal(intersection(symmetric_difference(u,cross_product(v,w)),x),successor_relation) member(apply(choice,intersection(symmetric_difference(u,cross_product(v,w)),x)),complement(restrict(u,v,w)))*.
% 299.89/300.47  162700[10:Rew:160202.0,147443.1] || member(regular(restrict(complement(intersection(u,v)),w,x)),union(u,v)) -> equal(restrict(complement(intersection(u,v)),w,x),successor_relation) member(regular(restrict(complement(intersection(u,v)),w,x)),symmetric_difference(u,v))*.
% 299.89/300.47  162701[10:Rew:160202.0,148487.4] || member(ordered_pair(u,least(intersection(v,omega),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,omega),x)* -> equal(integer_of(ordered_pair(u,least(intersection(v,omega),w))),successor_relation).
% 299.89/300.47  155834[3:Res:155815.1,6036.0] || member(ordered_pair(u,least(intersection(v,kind_1_ordinals),w)),ordinal_numbers)* member(ordered_pair(u,least(intersection(v,kind_1_ordinals),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,kind_1_ordinals),x)* -> .
% 299.89/300.47  161920[10:Rew:160202.0,147192.5] || well_ordering(cross_product(u,rest_of(v)),cross_product(universal_class,universal_class))* member(w,u)* member(w,rest_of(v))* subclass(rest_of(v),x) well_ordering(cross_product(u,rest_of(v)),x)* -> equal(rest_of(v),successor_relation).
% 299.89/300.47  161925[10:Rew:160202.0,147196.5] || well_ordering(cross_product(u,compose_class(v)),cross_product(universal_class,universal_class))* member(w,u)* member(w,compose_class(v))* subclass(compose_class(v),x) well_ordering(cross_product(u,compose_class(v)),x)* -> equal(compose_class(v),successor_relation).
% 299.89/300.47  160813[10:Rew:160202.0,146397.2] || well_ordering(element_relation,image(choice,singleton(singleton(u))))* subclass(u,image(choice,singleton(singleton(u))))* -> equal(singleton(u),successor_relation) equal(image(choice,singleton(singleton(u))),ordinal_numbers) member(image(choice,singleton(singleton(u))),ordinal_numbers).
% 299.89/300.47  108796[2:Res:31076.2,3874.1] inductive(complement(intersection(u,v))) || well_ordering(w,complement(intersection(u,v))) member(least(w,complement(intersection(u,v))),union(u,v)) -> member(least(w,complement(intersection(u,v))),symmetric_difference(u,v))*.
% 299.89/300.47  162635[10:Rew:160202.0,147169.2] || well_ordering(u,complement(intersection(v,w))) member(least(u,complement(intersection(v,w))),union(v,w)) -> equal(complement(intersection(v,w)),successor_relation) member(least(u,complement(intersection(v,w))),symmetric_difference(v,w))*.
% 299.89/300.47  161894[10:Rew:160202.0,147084.6] || well_ordering(cross_product(u,v),universal_class)* member(w,v)* member(x,u)* member(x,singleton(w))* subclass(singleton(w),y)* well_ordering(cross_product(u,v),y)* -> equal(singleton(w),successor_relation).
% 299.89/300.47  30982[0:Res:1032.1,127.0] || member(u,universal_class) subclass(intersection(complement(v),complement(w)),x)* well_ordering(y,x)* -> member(u,union(v,w))* member(least(y,intersection(complement(v),complement(w))),intersection(complement(v),complement(w)))*.
% 299.89/300.47  28284[0:Res:1495.2,61.0] || member(u,universal_class) subclass(rest_relation,image(v,image(w,singleton(x)))) member(ordered_pair(x,ordered_pair(u,rest_of(u))),cross_product(universal_class,universal_class)) -> member(ordered_pair(x,ordered_pair(u,rest_of(u))),compose(v,w))*.
% 299.89/300.47  39613[0:Res:5768.2,96.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,cross_product(universal_class,universal_class)) equal(compose(w,u),ordered_pair(v,compose(u,v))) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),compose_class(w))*.
% 299.89/300.47  192561[10:Res:60.1,162356.0] || member(ordered_pair(u,v),compose(w,x)) subclass(image(w,image(x,singleton(u))),y)* well_ordering(omega,y) -> equal(integer_of(ordered_pair(v,least(omega,image(w,image(x,singleton(u)))))),successor_relation)**.
% 299.89/300.47  192547[10:Res:6010.3,162356.0] || member(u,universal_class) member(v,universal_class) equal(compose(w,v),u) subclass(compose_class(w),x)* well_ordering(omega,x) -> equal(integer_of(ordered_pair(ordered_pair(v,u),least(omega,compose_class(w)))),successor_relation)**.
% 299.89/300.47  192529[10:Res:173.1,162356.0] || member(least(element_relation,intersection(y__dfg,ordinal_numbers)),universal_class) subclass(complement(intersection(y__dfg,ordinal_numbers)),u)* well_ordering(omega,u) -> equal(integer_of(ordered_pair(least(element_relation,intersection(y__dfg,ordinal_numbers)),least(omega,complement(intersection(y__dfg,ordinal_numbers))))),successor_relation)**.
% 299.89/300.47  193997[10:Res:5768.2,162356.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,w) subclass(w,x)* well_ordering(omega,x)* -> equal(integer_of(ordered_pair(ordered_pair(u,ordered_pair(v,compose(u,v))),least(omega,w))),successor_relation)**.
% 299.89/300.47  197969[10:Rew:181056.0,197951.1,181056.0,197951.0] || member(ordered_pair(universal_class,not_subclass_element(image(u,image(v,successor_relation)),w)),cross_product(universal_class,universal_class)) -> subclass(image(u,image(v,successor_relation)),w) member(ordered_pair(universal_class,not_subclass_element(image(u,image(v,successor_relation)),w)),compose(u,v))*.
% 299.89/300.47  203363[10:Rew:203192.0,193756.0] || member(u,cantor(complement(cross_product(u,universal_class))))* equal(least(rest_of(complement(cross_product(u,universal_class))),v),successor_relation)** member(u,v) subclass(v,w)* well_ordering(rest_of(complement(cross_product(u,universal_class))),w)* -> .
% 299.89/300.47  163741[10:Rew:160202.0,160656.2] || member(u,range_of(successor_relation)) member(ordered_pair(v,u),cross_product(universal_class,universal_class)) -> equal(cross_product(image(w,singleton(v)),universal_class),successor_relation) member(ordered_pair(v,u),compose(regular(cross_product(image(w,singleton(v)),universal_class)),w))*.
% 299.89/300.47  193801[10:Rew:193730.0,193787.3] || member(ordered_pair(u,v),compose(w,complement(cross_product(singleton(u),universal_class))))* subclass(image(w,range_of(successor_relation)),x)* well_ordering(y,x)* -> member(least(y,image(w,range_of(successor_relation))),image(w,range_of(successor_relation)))*.
% 299.89/300.47  193799[10:Rew:193730.0,193789.3] || member(ordered_pair(u,ordered_pair(v,least(image(w,range_of(successor_relation)),x))),compose(w,complement(cross_product(singleton(u),universal_class))))* member(v,x) subclass(x,y)* well_ordering(image(w,range_of(successor_relation)),y)* -> .
% 299.89/300.47  222527[24:Rew:222326.0,222358.1,222326.0,222358.0] || member(ordered_pair(kind_1_ordinals,not_subclass_element(image(u,image(v,successor_relation)),w)),cross_product(universal_class,universal_class)) -> subclass(image(u,image(v,successor_relation)),w) member(ordered_pair(kind_1_ordinals,not_subclass_element(image(u,image(v,successor_relation)),w)),compose(u,v))*.
% 299.89/300.47  224329[25:Rew:224236.1,204995.2] function(restrict(cross_product(u,universal_class),v,w)) || subclass(image(cross_product(v,w),u),cantor(range_of(x))) equal(cantor(cantor(y)),universal_class) -> compatible(restrict(cross_product(u,universal_class),v,w),y,inverse(x))*.
% 299.89/300.47  224770[25:MRR:204992.4,224753.0] single_valued_class(restrict(element_relation,universal_class,u)) || subclass(range_of(restrict(element_relation,universal_class,u)),cantor(sum_class(u)))* equal(cross_product(cantor(sum_class(u)),cantor(sum_class(u))),sum_class(u)) equal(restrict(element_relation,universal_class,u),successor_relation) -> .
% 299.89/300.47  224904[25:SoR:224312.0,160511.2] single_valued_class(restrict(u,v,universal_class)) || subclass(image(u,v),cantor(cantor(w))) equal(cantor(cantor(x)),universal_class) equal(restrict(u,v,universal_class),successor_relation) -> compatible(restrict(u,v,universal_class),x,w)*.
% 299.89/300.47  39656[0:SpL:124.0,5919.0] || member(u,segment(v,w,x))* subclass(rest_of(restrict(v,w,singleton(x))),y)* well_ordering(z,y)* -> member(least(z,rest_of(restrict(v,w,singleton(x)))),rest_of(restrict(v,w,singleton(x))))*.
% 299.89/300.47  42998[0:Rew:1934.0,42923.4] || member(u,successor(v)) member(u,complement(intersection(v,singleton(v))))* subclass(symmetric_difference(v,singleton(v)),w)* well_ordering(x,w)* -> member(least(x,symmetric_difference(v,singleton(v))),symmetric_difference(v,singleton(v)))*.
% 299.89/300.47  42999[0:Rew:1933.0,42922.4] || member(u,symmetrization_of(v)) member(u,complement(intersection(v,inverse(v))))* subclass(symmetric_difference(v,inverse(v)),w)* well_ordering(x,w)* -> member(least(x,symmetric_difference(v,inverse(v))),symmetric_difference(v,inverse(v)))*.
% 299.89/300.47  125921[0:Res:28320.1,19.0] || subclass(rest_relation,rotate(cross_product(u,v)))* -> equal(ordered_pair(first(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x)),second(ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x))),ordered_pair(ordered_pair(w,rest_of(ordered_pair(x,w))),x))**.
% 299.89/300.47  126051[0:Res:28321.1,19.0] || subclass(rest_relation,flip(cross_product(u,v)))* -> equal(ordered_pair(first(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w)))),second(ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))))),ordered_pair(ordered_pair(w,x),rest_of(ordered_pair(x,w))))**.
% 299.89/300.47  126719[0:Res:3872.2,9482.0] || member(not_subclass_element(intersection(complement(restrict(u,v,w)),x),y),cross_product(v,w))* member(not_subclass_element(intersection(complement(restrict(u,v,w)),x),y),u)* -> subclass(intersection(complement(restrict(u,v,w)),x),y).
% 299.89/300.47  126501[0:Res:3872.2,9368.0] || member(not_subclass_element(intersection(u,complement(restrict(v,w,x))),y),cross_product(w,x))* member(not_subclass_element(intersection(u,complement(restrict(v,w,x))),y),v)* -> subclass(intersection(u,complement(restrict(v,w,x))),y).
% 299.89/300.47  40277[0:Rew:1943.0,40188.2,1943.0,40188.1] || member(not_subclass_element(u,symmetric_difference(cross_product(v,w),x)),union(cross_product(v,w),x))* member(not_subclass_element(u,symmetric_difference(cross_product(v,w),x)),complement(restrict(x,v,w))) -> subclass(u,symmetric_difference(cross_product(v,w),x)).
% 299.89/300.47  40278[0:Rew:1938.0,40187.2,1938.0,40187.1] || member(not_subclass_element(u,symmetric_difference(v,cross_product(w,x))),union(v,cross_product(w,x)))* member(not_subclass_element(u,symmetric_difference(v,cross_product(w,x))),complement(restrict(v,w,x))) -> subclass(u,symmetric_difference(v,cross_product(w,x))).
% 299.89/300.47  137271[0:Rew:10029.0,137187.3] || member(u,v) subclass(v,w)* well_ordering(successor(image(element_relation,complement(x))),w)* -> member(ordered_pair(u,least(successor(image(element_relation,complement(x))),v)),intersection(power_class(x),complement(singleton(image(element_relation,complement(x))))))*.
% 299.89/300.47  137891[0:Rew:10028.0,137805.3] || member(u,v) subclass(v,w)* well_ordering(symmetrization_of(image(element_relation,complement(x))),w)* -> member(ordered_pair(u,least(symmetrization_of(image(element_relation,complement(x))),v)),intersection(power_class(x),complement(inverse(image(element_relation,complement(x))))))*.
% 299.89/300.47  41898[0:SpR:2330.1,34070.2] || member(second(not_subclass_element(cross_product(u,v),w)),universal_class) member(first(not_subclass_element(cross_product(u,v),w)),second(not_subclass_element(cross_product(u,v),w)))* -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),element_relation).
% 299.89/300.47  161552[10:Rew:160202.0,146784.2] || member(cross_product(u,v),universal_class) member(apply(choice,cross_product(u,v)),compose_class(w)) -> equal(cross_product(u,v),successor_relation) equal(compose(w,first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))**.
% 299.89/300.47  161692[10:Rew:160202.0,146711.1] || member(restrict(u,v,w),universal_class) -> equal(restrict(u,v,w),successor_relation) equal(ordered_pair(first(apply(choice,restrict(u,v,w))),second(apply(choice,restrict(u,v,w)))),apply(choice,restrict(u,v,w)))**.
% 299.89/300.47  161907[10:Rew:160202.0,147153.2] || equal(compose(u,first(regular(cross_product(v,w)))),second(regular(cross_product(v,w))))** member(regular(cross_product(v,w)),cross_product(universal_class,universal_class))* -> equal(cross_product(v,w),successor_relation) member(regular(cross_product(v,w)),compose_class(u)).
% 299.89/300.47  162493[10:Rew:160202.0,147110.2] || member(ordered_pair(u,apply(choice,complement(image(v,image(w,singleton(u)))))),compose(v,w))* member(complement(image(v,image(w,singleton(u)))),universal_class) -> equal(complement(image(v,image(w,singleton(u)))),successor_relation).
% 299.89/300.47  162521[10:Rew:160202.0,147954.2] || member(union(image(element_relation,power_class(u)),v),universal_class) member(apply(choice,union(image(element_relation,power_class(u)),v)),intersection(power_class(image(element_relation,complement(u))),complement(v)))* -> equal(union(image(element_relation,power_class(u)),v),successor_relation).
% 299.89/300.47  162525[10:Rew:160202.0,147974.2] || member(union(u,image(element_relation,power_class(v))),universal_class) member(apply(choice,union(u,image(element_relation,power_class(v)))),intersection(complement(u),power_class(image(element_relation,complement(v)))))* -> equal(union(u,image(element_relation,power_class(v))),successor_relation).
% 299.89/300.47  162707[10:Rew:160202.0,147856.2] || section(cross_product(u,singleton(v)),w,x) well_ordering(y,w) -> equal(segment(cross_product(x,w),u,v),successor_relation) member(least(y,segment(cross_product(x,w),u,v)),segment(cross_product(x,w),u,v))*.
% 299.89/300.47  162591[10:Rew:160202.0,146862.2] || transitive(u,v) well_ordering(w,restrict(u,v,v)) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),successor_relation) member(least(w,compose(restrict(u,v,v),restrict(u,v,v))),universal_class)*.
% 299.89/300.47  184015[14:Rew:183958.0,183974.2,183958.0,183974.1] || member(ordinal_numbers,universal_class) well_ordering(element_relation,image(recursion(u,successor_relation,successor_relation),singleton(v))) subclass(ordinal_add(u,v),image(recursion(u,successor_relation,successor_relation),singleton(v)))* -> member(image(recursion(u,successor_relation,successor_relation),singleton(v)),ordinal_numbers).
% 299.89/300.47  41083[0:Rew:208.0,41063.4] || member(u,universal_class) subclass(power_class(image(element_relation,complement(v))),w)* well_ordering(x,w)* -> member(u,image(element_relation,power_class(v)))* member(least(x,power_class(image(element_relation,complement(v)))),power_class(image(element_relation,complement(v))))*.
% 299.89/300.47  30762[0:Res:3595.3,61.0] function(u) || member(v,universal_class) subclass(universal_class,image(w,image(x,singleton(y)))) member(ordered_pair(y,image(u,v)),cross_product(universal_class,universal_class)) -> member(ordered_pair(y,image(u,v)),compose(w,x))*.
% 299.89/300.47  160709[10:Rew:160202.0,146506.3] || member(u,universal_class) subclass(u,image(v,image(w,singleton(x)))) member(ordered_pair(x,apply(choice,u)),cross_product(universal_class,universal_class)) -> equal(u,successor_relation) member(ordered_pair(x,apply(choice,u)),compose(v,w))*.
% 299.89/300.47  162214[10:Rew:160202.0,147694.2] || subclass(u,image(v,image(w,singleton(x)))) member(ordered_pair(x,regular(intersection(u,y))),cross_product(universal_class,universal_class)) -> equal(intersection(u,y),successor_relation) member(ordered_pair(x,regular(intersection(u,y))),compose(v,w))*.
% 299.89/300.47  162205[10:Rew:160202.0,147595.2] || subclass(u,image(v,image(w,singleton(x)))) member(ordered_pair(x,regular(intersection(y,u))),cross_product(universal_class,universal_class)) -> equal(intersection(y,u),successor_relation) member(ordered_pair(x,regular(intersection(y,u))),compose(v,w))*.
% 299.89/300.47  192904[10:Res:162090.2,162356.0] || well_ordering(u,cross_product(universal_class,universal_class)) subclass(compose(v,w),x)* well_ordering(omega,x) -> equal(compose(v,w),successor_relation) equal(integer_of(ordered_pair(least(u,compose(v,w)),least(omega,compose(v,w)))),successor_relation)**.
% 299.89/300.47  193245[10:Res:5714.3,162356.0] || connected(u,v) well_ordering(w,v) subclass(not_well_ordering(u,v),x)* well_ordering(omega,x) -> well_ordering(u,v) equal(integer_of(ordered_pair(least(w,not_well_ordering(u,v)),least(omega,not_well_ordering(u,v)))),successor_relation)**.
% 299.89/300.47  197012[10:SoR:3845.0,160511.2] single_valued_class(restrict(u,v,singleton(w))) || subclass(range_of(restrict(u,v,singleton(w))),x) equal(restrict(u,v,singleton(w)),successor_relation) -> maps(restrict(u,v,singleton(w)),segment(u,v,w),x)*.
% 299.89/300.47  203641[15:Rew:203192.0,197462.1] || member(cross_product(u,v),universal_class) member(first(apply(choice,cross_product(u,v))),cantor(w)) member(ordered_pair(w,apply(choice,cross_product(u,v))),cross_product(universal_class,cross_product(universal_class,universal_class)))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  204984[10:Rew:203192.0,203653.1] || member(u,universal_class) member(singleton(u),cantor(v))* equal(least(rest_of(v),w),successor_relation)** member(singleton(u),w)* subclass(w,x)* well_ordering(rest_of(v),x)* -> member(u,cantor(v)).
% 299.89/300.47  163758[10:Rew:160305.0,162152.6,160305.0,162152.5,160305.0,162152.4,160305.0,162152.3,160305.0,162152.1] inductive(u) || well_ordering(cross_product(v,range_of(successor_relation)),u)* member(w,v)* member(w,range_of(successor_relation))* subclass(range_of(successor_relation),x) well_ordering(cross_product(v,range_of(successor_relation)),x)* -> equal(range_of(successor_relation),successor_relation).
% 299.89/300.47  203580[10:Rew:203192.0,163742.1] || member(ordered_pair(u,not_subclass_element(image(v,range_of(successor_relation)),w)),cross_product(universal_class,universal_class)) -> member(u,cantor(x)) subclass(image(v,range_of(successor_relation)),w) member(ordered_pair(u,not_subclass_element(image(v,range_of(successor_relation)),w)),compose(v,x))*.
% 299.89/300.47  197974[10:Rew:193730.0,197956.1,193730.0,197956.0] || member(ordered_pair(u,not_subclass_element(image(v,range_of(successor_relation)),w)),cross_product(universal_class,universal_class)) -> subclass(image(v,range_of(successor_relation)),w) member(ordered_pair(u,not_subclass_element(image(v,range_of(successor_relation)),w)),compose(v,complement(cross_product(singleton(u),universal_class))))*.
% 299.89/300.47  225493[25:Rew:224739.1,225081.4] function(u) || member(ordered_pair(u,ordered_pair(v,least(image(w,image(x,successor_relation)),y))),compose(w,x))* member(v,y) subclass(y,z)* well_ordering(image(w,image(x,successor_relation)),z)* -> .
% 299.89/300.47  225494[25:Rew:224739.1,224939.2,224739.1,224939.1] function(u) || member(ordered_pair(u,regular(image(v,image(w,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(v,image(w,successor_relation)),successor_relation) member(ordered_pair(u,regular(image(v,image(w,successor_relation)))),compose(v,w))*.
% 299.89/300.47  231814[10:Res:161312.2,161035.0] || member(intersection(u,intersection(power_class(successor_relation),complement(v))),universal_class) member(apply(choice,intersection(u,intersection(power_class(successor_relation),complement(v)))),union(image(element_relation,universal_class),v))* -> equal(intersection(u,intersection(power_class(successor_relation),complement(v))),successor_relation).
% 299.89/300.47  231801[10:Res:161311.2,161035.0] || member(intersection(intersection(power_class(successor_relation),complement(u)),v),universal_class) member(apply(choice,intersection(intersection(power_class(successor_relation),complement(u)),v)),union(image(element_relation,universal_class),u))* -> equal(intersection(intersection(power_class(successor_relation),complement(u)),v),successor_relation).
% 299.89/300.47  35660[0:SpL:1943.0,3874.1] || member(u,union(complement(restrict(v,w,x)),union(cross_product(w,x),v))) member(u,complement(symmetric_difference(cross_product(w,x),v))) -> member(u,symmetric_difference(complement(restrict(v,w,x)),union(cross_product(w,x),v)))*.
% 299.89/300.47  35659[0:SpL:1938.0,3874.1] || member(u,union(complement(restrict(v,w,x)),union(v,cross_product(w,x)))) member(u,complement(symmetric_difference(v,cross_product(w,x)))) -> member(u,symmetric_difference(complement(restrict(v,w,x)),union(v,cross_product(w,x))))*.
% 299.89/300.47  44013[0:MRR:43961.0,999.0] || member(ordered_pair(u,least(intersection(v,complement(w)),x)),v)* member(u,x) subclass(x,y)* well_ordering(intersection(v,complement(w)),y)* -> member(ordered_pair(u,least(intersection(v,complement(w)),x)),w)*.
% 299.89/300.47  44808[0:Res:8.1,5857.1] || equal(u,image(v,image(w,singleton(x))))* member(ordered_pair(x,y),compose(v,w))* well_ordering(z,u)* -> member(least(z,image(v,image(w,singleton(x)))),image(v,image(w,singleton(x))))*.
% 299.89/300.47  123493[0:Res:978.1,3874.1] || member(not_subclass_element(restrict(complement(intersection(u,v)),w,x),y),union(u,v)) -> subclass(restrict(complement(intersection(u,v)),w,x),y) member(not_subclass_element(restrict(complement(intersection(u,v)),w,x),y),symmetric_difference(u,v))*.
% 299.89/300.47  140358[0:Rew:984.0,140276.3] || member(u,v) subclass(v,w)* well_ordering(union(x,image(element_relation,power_class(y))),w)* -> member(ordered_pair(u,least(union(x,image(element_relation,power_class(y))),v)),intersection(complement(x),power_class(image(element_relation,complement(y)))))*.
% 299.89/300.47  139894[0:Rew:982.0,139814.3] || member(u,v) subclass(v,w)* well_ordering(union(image(element_relation,power_class(x)),y),w)* -> member(ordered_pair(u,least(union(image(element_relation,power_class(x)),y),v)),intersection(power_class(image(element_relation,complement(x))),complement(y)))*.
% 299.89/300.47  41950[0:Rew:2330.1,41927.3] || member(first(not_subclass_element(cross_product(u,v),w)),second(not_subclass_element(cross_product(u,v),w)))* member(not_subclass_element(cross_product(u,v),w),cross_product(universal_class,universal_class)) -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),element_relation).
% 299.89/300.47  163763[10:MRR:161537.4,160227.0] || member(cross_product(u,v),universal_class) equal(successor(first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v)))) member(apply(choice,cross_product(u,v)),cross_product(universal_class,universal_class))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  161550[10:Rew:160202.0,146782.2] || member(cross_product(u,v),universal_class) member(apply(choice,cross_product(u,v)),rest_of(w)) -> equal(cross_product(u,v),successor_relation) equal(restrict(w,first(apply(choice,cross_product(u,v))),universal_class),second(apply(choice,cross_product(u,v))))**.
% 299.89/300.47  162495[10:Rew:160202.0,147114.1] || member(symmetric_difference(complement(intersection(u,v)),union(u,v)),universal_class) -> equal(symmetric_difference(complement(intersection(u,v)),union(u,v)),successor_relation) member(apply(choice,symmetric_difference(complement(intersection(u,v)),union(u,v))),complement(symmetric_difference(u,v)))*.
% 299.89/300.47  162022[10:Rew:160202.0,146564.6] || member(u,ordinal_numbers) well_ordering(cross_product(v,sum_class(u)),u)* member(w,v)* member(w,sum_class(u))* subclass(sum_class(u),x) well_ordering(cross_product(v,sum_class(u)),x)* -> equal(sum_class(u),successor_relation).
% 299.89/300.47  162710[10:Rew:160202.0,147233.2] || well_ordering(u,cross_product(universal_class,universal_class)) member(v,w)* -> equal(rest_of(x),successor_relation) equal(ordered_pair(first(ordered_pair(v,least(u,rest_of(x)))),second(ordered_pair(v,least(u,rest_of(x))))),ordered_pair(v,least(u,rest_of(x))))**.
% 299.89/300.47  162709[10:Rew:160202.0,147232.2] || well_ordering(u,cross_product(universal_class,universal_class)) member(v,w)* -> equal(compose_class(x),successor_relation) equal(ordered_pair(first(ordered_pair(v,least(u,compose_class(x)))),second(ordered_pair(v,least(u,compose_class(x))))),ordered_pair(v,least(u,compose_class(x))))**.
% 299.89/300.47  162711[10:Rew:160202.0,147467.2] || transitive(universal_class,u) well_ordering(v,cross_product(u,u)) -> equal(compose(cross_product(u,u),cross_product(u,u)),successor_relation) member(least(v,compose(cross_product(u,u),cross_product(u,u))),compose(cross_product(u,u),cross_product(u,u)))*.
% 299.89/300.47  160070[3:Res:159952.1,5857.1] || subclass(image(u,image(v,singleton(w))),ordinal_numbers) member(ordered_pair(w,x),compose(u,v))* well_ordering(y,kind_1_ordinals) -> member(least(y,image(u,image(v,singleton(w)))),image(u,image(v,singleton(w))))*.
% 299.89/300.47  42469[0:Res:27.2,6041.0] || member(least(cross_product(u,complement(v)),w),universal_class)* member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,complement(v)),y)* -> member(least(cross_product(u,complement(v)),w),v)*.
% 299.89/300.47  161032[10:Rew:160202.0,151411.3] || member(u,universal_class) subclass(union(image(element_relation,universal_class),v),w)* well_ordering(x,w)* -> member(u,intersection(power_class(successor_relation),complement(v)))* member(least(x,union(image(element_relation,universal_class),v)),union(image(element_relation,universal_class),v))*.
% 299.89/300.47  161011[10:Rew:160202.0,151410.3] || member(u,universal_class) subclass(union(v,image(element_relation,universal_class)),w)* well_ordering(x,w)* -> member(u,intersection(complement(v),power_class(successor_relation)))* member(least(x,union(v,image(element_relation,universal_class))),union(v,image(element_relation,universal_class)))*.
% 299.89/300.47  43126[0:Res:6269.3,127.0] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,u),v),x)* subclass(rotate(x),y)* well_ordering(z,y)* -> member(least(z,rotate(x)),rotate(x))*.
% 299.89/300.47  43161[0:Res:6260.3,127.0] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,v),u),x)* subclass(flip(x),y)* well_ordering(z,y)* -> member(least(z,flip(x)),flip(x))*.
% 299.89/300.47  39591[0:Res:5768.2,2142.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,ordered_pair(w,x))* -> equal(ordered_pair(u,ordered_pair(v,compose(u,v))),unordered_pair(w,singleton(x)))* equal(ordered_pair(u,ordered_pair(v,compose(u,v))),singleton(w)).
% 299.89/300.47  161549[10:Rew:160202.0,146783.2] || member(cross_product(u,v),universal_class) member(ordered_pair(w,apply(choice,cross_product(u,v))),composition_function)* -> equal(cross_product(u,v),successor_relation) equal(compose(w,first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v)))).
% 299.89/300.47  203571[6:Rew:203192.0,43187.0] || member(u,cantor(cross_product(v,w))) equal(restrict(cross_product(u,universal_class),v,w),least(rest_of(cross_product(v,w)),x))* member(u,x)* subclass(x,y)* well_ordering(rest_of(cross_product(v,w)),y)* -> .
% 299.89/300.47  203639[10:Rew:203192.0,161548.0] || member(first(regular(cross_product(u,v))),cantor(w)) equal(restrict(w,first(regular(cross_product(u,v))),universal_class),second(regular(cross_product(u,v))))** -> equal(cross_product(u,v),successor_relation) member(regular(cross_product(u,v)),rest_of(w)).
% 299.89/300.47  203930[10:Rew:203192.0,161893.1] || well_ordering(rest_of(u),universal_class) member(v,cantor(u)) equal(restrict(u,v,universal_class),w)* member(v,singleton(w))* subclass(singleton(w),x)* well_ordering(rest_of(u),x)* -> equal(singleton(w),successor_relation).
% 299.89/300.47  212797[15:SpL:161565.2,203931.0] || member(cross_product(u,v),universal_class) member(apply(choice,cross_product(u,v)),cross_product(universal_class,universal_class)) member(second(apply(choice,cross_product(u,v))),cantor(first(apply(choice,cross_product(u,v)))))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  198545[10:Rew:193730.0,198528.2,193730.0,198528.1,193730.0,198528.0] || member(range_of(successor_relation),universal_class) member(ordered_pair(u,apply(choice,range_of(successor_relation))),cross_product(universal_class,universal_class)) -> equal(range_of(successor_relation),successor_relation) member(ordered_pair(u,apply(choice,range_of(successor_relation))),compose(complement(cross_product(image(v,singleton(u)),universal_class)),v))*.
% 299.89/300.47  224771[25:MRR:205000.4,224753.0] single_valued_class(restrict(element_relation,universal_class,u)) || subclass(range_of(restrict(element_relation,universal_class,u)),cantor(sum_class(u)))* equal(cross_product(cantor(sum_class(u)),cantor(sum_class(u))),sum_class(u)) equal(restrict(element_relation,universal_class,u),cross_product(universal_class,universal_class)) -> .
% 299.89/300.47  224903[25:SoR:224312.0,6317.2] single_valued_class(restrict(u,v,universal_class)) || subclass(image(u,v),cantor(cantor(w))) equal(cantor(cantor(x)),universal_class) equal(restrict(u,v,universal_class),cross_product(universal_class,universal_class)) -> compatible(restrict(u,v,universal_class),x,w)*.
% 299.89/300.47  225495[25:Rew:224739.1,225079.4] function(u) || member(ordered_pair(u,v),compose(w,x))* subclass(image(w,image(x,successor_relation)),y)* well_ordering(z,y)* -> member(least(z,image(w,image(x,successor_relation))),image(w,image(x,successor_relation)))*.
% 299.89/300.47  40586[0:SpR:161.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(complement(intersection(u,v)),union(u,v))),union(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v)))),symmetric_difference(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v))))**.
% 299.89/300.47  42812[0:SoR:3845.0,6317.2] single_valued_class(restrict(u,v,singleton(w))) || subclass(range_of(restrict(u,v,singleton(w))),x) equal(restrict(u,v,singleton(w)),cross_product(universal_class,universal_class)) -> maps(restrict(u,v,singleton(w)),segment(u,v,w),x)*.
% 299.89/300.47  40219[0:Res:25.2,3886.0] || member(not_subclass_element(u,intersection(v,intersection(w,x))),x)* member(not_subclass_element(u,intersection(v,intersection(w,x))),w)* member(not_subclass_element(u,intersection(v,intersection(w,x))),v)* -> subclass(u,intersection(v,intersection(w,x))).
% 299.89/300.47  40566[0:SpR:509.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(u,image(element_relation,complement(v)))),union(complement(intersection(u,image(element_relation,complement(v)))),complement(intersection(complement(u),power_class(v))))),symmetric_difference(complement(intersection(u,image(element_relation,complement(v)))),complement(intersection(complement(u),power_class(v)))))**.
% 299.89/300.47  40582[0:SpR:511.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(image(element_relation,complement(u)),v)),union(complement(intersection(image(element_relation,complement(u)),v)),complement(intersection(power_class(u),complement(v))))),symmetric_difference(complement(intersection(image(element_relation,complement(u)),v)),complement(intersection(power_class(u),complement(v)))))**.
% 299.89/300.47  162594[10:Rew:160202.0,147128.3] || member(apply(choice,complement(restrict(u,v,w))),cross_product(v,w))* member(apply(choice,complement(restrict(u,v,w))),u)* member(complement(restrict(u,v,w)),universal_class) -> equal(complement(restrict(u,v,w)),successor_relation).
% 299.89/300.47  162596[10:Rew:160202.0,147130.1] || member(intersection(u,ordered_pair(v,w)),universal_class) -> equal(intersection(u,ordered_pair(v,w)),successor_relation) equal(apply(choice,intersection(u,ordered_pair(v,w))),unordered_pair(v,singleton(w)))** equal(apply(choice,intersection(u,ordered_pair(v,w))),singleton(v)).
% 299.89/300.47  162598[10:Rew:160202.0,147132.1] || member(intersection(ordered_pair(u,v),w),universal_class) -> equal(intersection(ordered_pair(u,v),w),successor_relation) equal(apply(choice,intersection(ordered_pair(u,v),w)),unordered_pair(u,singleton(v)))** equal(apply(choice,intersection(ordered_pair(u,v),w)),singleton(u)).
% 299.89/300.47  162715[10:Rew:160202.0,147638.1] || member(regular(intersection(u,intersection(complement(intersection(v,w)),x))),union(v,w)) -> equal(intersection(u,intersection(complement(intersection(v,w)),x)),successor_relation) member(regular(intersection(u,intersection(complement(intersection(v,w)),x))),symmetric_difference(v,w))*.
% 299.89/300.47  162716[10:Rew:160202.0,147688.1] || member(regular(intersection(u,intersection(v,complement(intersection(w,x))))),union(w,x)) -> equal(intersection(u,intersection(v,complement(intersection(w,x)))),successor_relation) member(regular(intersection(u,intersection(v,complement(intersection(w,x))))),symmetric_difference(w,x))*.
% 299.89/300.47  162717[10:Rew:160202.0,147736.1] || member(regular(intersection(intersection(complement(intersection(u,v)),w),x)),union(u,v)) -> equal(intersection(intersection(complement(intersection(u,v)),w),x),successor_relation) member(regular(intersection(intersection(complement(intersection(u,v)),w),x)),symmetric_difference(u,v))*.
% 299.89/300.47  162718[10:Rew:160202.0,147801.1] || member(regular(intersection(intersection(u,complement(intersection(v,w))),x)),union(v,w)) -> equal(intersection(intersection(u,complement(intersection(v,w))),x),successor_relation) member(regular(intersection(intersection(u,complement(intersection(v,w))),x)),symmetric_difference(v,w))*.
% 299.89/300.47  44810[0:Res:64.1,5857.1] function(image(u,image(v,singleton(w)))) || member(ordered_pair(w,x),compose(u,v))* well_ordering(y,cross_product(universal_class,universal_class)) -> member(least(y,image(u,image(v,singleton(w)))),image(u,image(v,singleton(w))))*.
% 299.89/300.47  183234[10:Rew:181044.1,183180.4] || member(u,universal_class) member(ordered_pair(successor(u),ordered_pair(v,least(image(w,image(x,successor_relation)),y))),compose(w,x))* member(v,y) subclass(y,z)* well_ordering(image(w,image(x,successor_relation)),z)* -> .
% 299.89/300.47  192248[15:Rew:190721.0,192171.3] || member(ordered_pair(inverse(u),ordered_pair(v,least(image(w,image(x,successor_relation)),y))),compose(w,x))* member(v,y) subclass(y,z)* well_ordering(image(w,image(x,successor_relation)),z)* -> equal(range_of(u),successor_relation).
% 299.89/300.47  197446[14:SpL:161565.2,184007.1] || member(cross_product(u,v),universal_class) equal(sum_class(range_of(first(apply(choice,cross_product(u,v))))),second(apply(choice,cross_product(u,v)))) member(apply(choice,cross_product(u,v)),cross_product(universal_class,universal_class))* -> equal(cross_product(u,v),successor_relation).
% 299.89/300.47  200225[14:Rew:200028.1,200134.4] || member(u,universal_class) member(ordered_pair(range_of(u),ordered_pair(v,least(image(w,image(x,successor_relation)),y))),compose(w,x))* member(v,y) subclass(y,z)* well_ordering(image(w,image(x,successor_relation)),z)* -> .
% 299.89/300.47  200766[10:Res:161493.2,6036.0] inductive(u) || member(ordered_pair(v,least(intersection(w,u),x)),w)* member(v,x) subclass(x,y)* well_ordering(intersection(w,u),y)* -> equal(integer_of(ordered_pair(v,least(intersection(w,u),x))),successor_relation).
% 299.89/300.47  200719[10:Res:161493.2,6044.0] inductive(compose(u,v)) || member(w,x) subclass(x,y)* well_ordering(image(u,image(v,singleton(z))),y)* -> equal(integer_of(ordered_pair(z,ordered_pair(w,least(image(u,image(v,singleton(z))),x)))),successor_relation)**.
% 299.89/300.47  204987[10:Rew:203192.0,204017.3] || section(cross_product(u,v),w,x) well_ordering(y,w) -> equal(cantor(restrict(cross_product(u,v),x,w)),successor_relation) member(least(y,cantor(restrict(cross_product(x,w),u,v))),cantor(restrict(cross_product(x,w),u,v)))*.
% 299.89/300.47  204021[10:Rew:203192.0,162652.1] || asymmetric(cross_product(u,v),universal_class) member(universal_class,cantor(restrict(inverse(cross_product(u,v)),u,v))) equal(successor_relation,w) subclass(rest_of(restrict(inverse(cross_product(u,v)),u,v)),x)* -> member(ordered_pair(universal_class,w),x)*.
% 299.89/300.47  163746[10:Rew:160202.0,160672.3,160202.0,160672.2,160202.0,160672.1] || member(ordered_pair(u,regular(range_of(successor_relation))),cross_product(universal_class,universal_class)) -> equal(cross_product(image(v,singleton(u)),universal_class),successor_relation) equal(range_of(successor_relation),successor_relation) member(ordered_pair(u,regular(range_of(successor_relation))),compose(regular(cross_product(image(v,singleton(u)),universal_class)),v))*.
% 299.89/300.47  163760[10:Rew:160305.0,162151.4,160305.0,162151.3] inductive(u) || well_ordering(v,u)* member(w,x)* -> equal(range_of(successor_relation),successor_relation) equal(ordered_pair(first(ordered_pair(w,least(v,range_of(successor_relation)))),second(ordered_pair(w,least(v,range_of(successor_relation))))),ordered_pair(w,least(v,range_of(successor_relation))))**.
% 299.89/300.47  225496[25:Rew:224739.1,224940.2,224739.1,224940.1] function(u) || member(ordered_pair(u,not_subclass_element(image(v,image(w,successor_relation)),x)),cross_product(universal_class,universal_class)) -> subclass(image(v,image(w,successor_relation)),x) member(ordered_pair(u,not_subclass_element(image(v,image(w,successor_relation)),x)),compose(v,w))*.
% 299.89/300.47  41946[0:SpL:2330.1,2142.0] || member(u,not_subclass_element(cross_product(v,w),x))* -> subclass(cross_product(v,w),x) equal(u,unordered_pair(first(not_subclass_element(cross_product(v,w),x)),singleton(second(not_subclass_element(cross_product(v,w),x)))))* equal(u,singleton(first(not_subclass_element(cross_product(v,w),x)))).
% 299.89/300.47  161547[10:Rew:160202.0,146764.2] || member(cross_product(u,v),universal_class) subclass(rest_relation,flip(w)) -> equal(cross_product(u,v),successor_relation) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),first(apply(choice,cross_product(u,v)))),rest_of(apply(choice,cross_product(u,v)))),w)*.
% 299.89/300.47  161546[10:Rew:160202.0,146765.2] || member(cross_product(u,v),universal_class) subclass(rest_relation,flip(w)) -> equal(cross_product(u,v),successor_relation) member(ordered_pair(apply(choice,cross_product(u,v)),rest_of(ordered_pair(second(apply(choice,cross_product(u,v))),first(apply(choice,cross_product(u,v)))))),w)*.
% 299.89/300.47  161545[10:Rew:160202.0,146766.2] || member(cross_product(u,v),universal_class) subclass(rest_relation,rotate(w)) -> equal(cross_product(u,v),successor_relation) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),rest_of(apply(choice,cross_product(u,v)))),first(apply(choice,cross_product(u,v)))),w)*.
% 299.89/300.47  161544[10:Rew:160202.0,146781.3] || member(cross_product(u,v),universal_class) member(second(apply(choice,cross_product(u,v))),w) member(first(apply(choice,cross_product(u,v))),x) -> equal(cross_product(u,v),successor_relation) member(apply(choice,cross_product(u,v)),cross_product(x,w))*.
% 299.89/300.47  162021[10:Rew:160202.0,146565.3] || member(u,ordinal_numbers) well_ordering(v,u) member(w,x)* -> equal(sum_class(u),successor_relation) equal(ordered_pair(first(ordered_pair(w,least(v,sum_class(u)))),second(ordered_pair(w,least(v,sum_class(u))))),ordered_pair(w,least(v,sum_class(u))))**.
% 299.89/300.47  162721[10:Rew:160202.0,147522.6] || well_ordering(intersection(u,v),universal_class)* member(ordered_pair(w,x),v)* member(ordered_pair(w,x),u)* member(w,singleton(x)) subclass(singleton(x),y)* well_ordering(intersection(u,v),y)* -> equal(singleton(x),successor_relation).
% 299.89/300.47  183235[10:Rew:181044.1,183178.4] || member(u,universal_class) member(ordered_pair(successor(u),v),compose(w,x))* subclass(image(w,image(x,successor_relation)),y)* well_ordering(z,y)* -> member(least(z,image(w,image(x,successor_relation))),image(w,image(x,successor_relation)))*.
% 299.89/300.47  39568[0:Res:5768.2,3874.1] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,complement(intersection(w,x))) member(ordered_pair(u,ordered_pair(v,compose(u,v))),union(w,x)) -> member(ordered_pair(u,ordered_pair(v,compose(u,v))),symmetric_difference(w,x))*.
% 299.89/300.47  192249[15:Rew:190721.0,192169.4] || member(ordered_pair(inverse(u),v),compose(w,x))* subclass(image(w,image(x,successor_relation)),y)* well_ordering(z,y)* -> equal(range_of(u),successor_relation) member(least(z,image(w,image(x,successor_relation))),image(w,image(x,successor_relation)))*.
% 299.89/300.47  197816[15:Rew:190721.0,197797.2,190721.0,197797.0] || member(ordered_pair(inverse(u),regular(image(v,image(w,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(range_of(u),successor_relation) equal(image(v,image(w,successor_relation)),successor_relation) member(ordered_pair(inverse(u),regular(image(v,image(w,successor_relation)))),compose(v,w))*.
% 299.89/300.47  197817[10:Rew:181044.1,197796.2,181044.1,197796.1] || member(u,universal_class) member(ordered_pair(successor(u),regular(image(v,image(w,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(v,image(w,successor_relation)),successor_relation) member(ordered_pair(successor(u),regular(image(v,image(w,successor_relation)))),compose(v,w))*.
% 299.89/300.47  198535[10:Res:162736.3,185639.1] || member(image(u,image(v,singleton(w))),universal_class) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(universal_class,universal_class))* equal(compose(u,v),successor_relation) -> equal(image(u,image(v,singleton(w))),successor_relation).
% 299.89/300.47  198539[10:MRR:198520.4,160227.0] function(u) || member(image(u,image(inverse(u),singleton(v))),universal_class) member(ordered_pair(v,apply(choice,image(u,image(inverse(u),singleton(v))))),cross_product(universal_class,universal_class))* -> equal(image(u,image(inverse(u),singleton(v))),successor_relation).
% 299.89/300.47  198540[10:MRR:198519.4,160227.0] single_valued_class(u) || member(image(u,image(inverse(u),singleton(v))),universal_class) member(ordered_pair(v,apply(choice,image(u,image(inverse(u),singleton(v))))),cross_product(universal_class,universal_class))* -> equal(image(u,image(inverse(u),singleton(v))),successor_relation).
% 299.89/300.47  200226[14:Rew:200028.1,200132.4] || member(u,universal_class) member(ordered_pair(range_of(u),v),compose(w,x))* subclass(image(w,image(x,successor_relation)),y)* well_ordering(z,y)* -> member(least(z,image(w,image(x,successor_relation))),image(w,image(x,successor_relation)))*.
% 299.89/300.47  200227[14:Rew:200028.1,200082.2,200028.1,200082.1] || member(u,universal_class) member(ordered_pair(range_of(u),regular(image(v,image(w,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(v,image(w,successor_relation)),successor_relation) member(ordered_pair(range_of(u),regular(image(v,image(w,successor_relation)))),compose(v,w))*.
% 299.89/300.47  202036[10:Res:161492.2,6036.0] || equal(u,omega) member(ordered_pair(v,least(intersection(w,u),x)),w)* member(v,x) subclass(x,y)* well_ordering(intersection(w,u),y)* -> equal(integer_of(ordered_pair(v,least(intersection(w,u),x))),successor_relation).
% 299.89/300.47  201984[10:Res:161492.2,6044.0] || equal(compose(u,v),omega) member(w,x) subclass(x,y)* well_ordering(image(u,image(v,singleton(z))),y)* -> equal(integer_of(ordered_pair(z,ordered_pair(w,least(image(u,image(v,singleton(z))),x)))),successor_relation)**.
% 299.89/300.47  204990[10:Rew:203192.0,203573.2,203192.0,203573.2,203192.0,203573.1,203192.0,203573.1] single_valued_class(restrict(u,v,universal_class)) || subclass(image(u,v),cantor(cantor(w))) equal(cantor(cantor(x)),cantor(restrict(u,v,universal_class))) equal(restrict(u,v,universal_class),successor_relation) -> compatible(restrict(u,v,universal_class),x,w)*.
% 299.89/300.47  203774[10:Rew:203192.0,162720.1] || asymmetric(u,universal_class) member(universal_class,cantor(intersection(u,inverse(u)))) equal(least(rest_of(intersection(u,inverse(u))),v),successor_relation)** member(universal_class,v) subclass(v,w)* well_ordering(rest_of(intersection(u,inverse(u))),w)* -> .
% 299.89/300.47  216417[14:Rew:199971.1,216312.4] || member(u,universal_class) member(ordered_pair(sum_class(range_of(u)),ordered_pair(v,least(image(w,image(x,successor_relation)),y))),compose(w,x))* member(v,y) subclass(y,z)* well_ordering(image(w,image(x,successor_relation)),z)* -> .
% 299.89/300.47  216860[10:Res:1032.1,163343.0] || member(apply(choice,regular(intersection(complement(u),complement(v)))),universal_class) -> member(apply(choice,regular(intersection(complement(u),complement(v)))),union(u,v))* equal(regular(intersection(complement(u),complement(v))),successor_relation) equal(intersection(complement(u),complement(v)),successor_relation).
% 299.89/300.47  217424[20:Res:217226.1,6036.0] || equal(singleton(ordered_pair(u,least(intersection(v,singleton(successor_relation)),w))),omega) member(ordered_pair(u,least(intersection(v,singleton(successor_relation)),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,singleton(successor_relation)),x)* -> .
% 299.89/300.47  219154[3:Res:218473.1,5857.1] || equal(image(u,image(v,singleton(w))),complement(kind_1_ordinals)) member(ordered_pair(w,x),compose(u,v))* well_ordering(y,complement(ordinal_numbers)) -> member(least(y,image(u,image(v,singleton(w)))),image(u,image(v,singleton(w))))*.
% 299.89/300.47  163768[10:Rew:160305.0,162751.4,160305.0,162751.3,160305.0,162751.2] inductive(image(u,singleton(v))) || well_ordering(w,image(u,singleton(v))) member(ordered_pair(v,least(w,range_of(successor_relation))),cross_product(universal_class,universal_class)) -> equal(range_of(successor_relation),successor_relation) member(ordered_pair(v,least(w,range_of(successor_relation))),compose(successor_relation,u))*.
% 299.89/300.47  203559[10:Rew:203192.0,163748.5] || member(u,universal_class) member(ordered_pair(u,ordered_pair(v,least(image(w,range_of(successor_relation)),x))),compose(w,y))* member(v,x) subclass(x,z)* well_ordering(image(w,range_of(successor_relation)),z)* -> member(u,cantor(y)).
% 299.89/300.47  203579[10:Rew:203192.0,163747.4] || member(u,universal_class) member(ordered_pair(u,v),compose(w,x))* subclass(image(w,range_of(successor_relation)),y)* well_ordering(z,y)* -> member(u,cantor(x)) member(least(z,image(w,range_of(successor_relation))),image(w,range_of(successor_relation)))*.
% 299.89/300.47  163749[10:Rew:160202.0,160646.4,160202.0,160646.3] || member(ordered_pair(u,v),compose(regular(cross_product(image(w,singleton(u)),universal_class)),w))* subclass(range_of(successor_relation),x)* well_ordering(y,x)* -> equal(cross_product(image(w,singleton(u)),universal_class),successor_relation) member(least(y,range_of(successor_relation)),range_of(successor_relation))*.
% 299.89/300.47  163750[10:Rew:160202.0,160681.3,160202.0,160681.2,160202.0,160681.1] || member(image(u,range_of(successor_relation)),universal_class) member(ordered_pair(v,apply(choice,image(u,range_of(successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(u,range_of(successor_relation)),successor_relation) member(ordered_pair(v,apply(choice,image(u,range_of(successor_relation)))),compose(u,successor_relation))*.
% 299.89/300.47  163762[10:Rew:160202.0,162847.4,160305.0,162847.4,160305.0,162847.2,160202.0,162847.1,160305.0,162847.1] || member(u,kind_1_ordinals) member(u,complement(intersection(singleton(successor_relation),range_of(successor_relation))))* subclass(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),v)* well_ordering(w,v)* -> member(least(w,symmetric_difference(singleton(successor_relation),range_of(successor_relation))),symmetric_difference(singleton(successor_relation),range_of(successor_relation)))*.
% 299.89/300.47  40587[0:SpR:1933.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(complement(intersection(u,inverse(u))),symmetrization_of(u))),union(complement(symmetric_difference(u,inverse(u))),union(complement(intersection(u,inverse(u))),symmetrization_of(u)))),symmetric_difference(complement(symmetric_difference(u,inverse(u))),union(complement(intersection(u,inverse(u))),symmetrization_of(u))))**.
% 299.89/300.47  40588[0:SpR:1934.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(complement(intersection(u,singleton(u))),successor(u))),union(complement(symmetric_difference(u,singleton(u))),union(complement(intersection(u,singleton(u))),successor(u)))),symmetric_difference(complement(symmetric_difference(u,singleton(u))),union(complement(intersection(u,singleton(u))),successor(u))))**.
% 299.89/300.47  44008[0:Rew:30.0,43975.5,30.0,43975.2,30.0,43975.0] || member(least(restrict(u,v,w),x),w)* member(y,v) member(ordered_pair(y,least(restrict(u,v,w),x)),u)* member(y,x) subclass(x,z)* well_ordering(restrict(u,v,w),z)* -> .
% 299.89/300.47  44016[0:Rew:161.0,43925.4,161.0,43925.1] || member(ordered_pair(u,least(symmetric_difference(v,w),x)),union(v,w)) member(ordered_pair(u,least(symmetric_difference(v,w),x)),complement(intersection(v,w)))* member(u,x) subclass(x,y)* well_ordering(symmetric_difference(v,w),y)* -> .
% 299.89/300.47  43002[0:Rew:1948.0,42952.4] || member(u,union(complement(v),complement(w)))* member(u,union(v,w)) subclass(symmetric_difference(complement(v),complement(w)),x)* well_ordering(y,x)* -> member(least(y,symmetric_difference(complement(v),complement(w))),symmetric_difference(complement(v),complement(w)))*.
% 299.89/300.47  31214[0:Res:3872.2,129.3] || member(ordered_pair(u,least(restrict(v,w,x),y)),cross_product(w,x))* member(ordered_pair(u,least(restrict(v,w,x),y)),v)* member(u,y) subclass(y,z)* well_ordering(restrict(v,w,x),z)* -> .
% 299.89/300.47  41952[0:Rew:2330.1,41943.3] || equal(compose(u,first(not_subclass_element(cross_product(v,w),x))),second(not_subclass_element(cross_product(v,w),x)))** member(not_subclass_element(cross_product(v,w),x),cross_product(universal_class,universal_class))* -> subclass(cross_product(v,w),x) member(not_subclass_element(cross_product(v,w),x),compose_class(u)).
% 299.89/300.47  161543[10:Rew:160202.0,146779.2] || member(cross_product(u,v),universal_class) member(ordered_pair(apply(choice,cross_product(u,v)),w),rotate(x)) -> equal(cross_product(u,v),successor_relation) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),w),first(apply(choice,cross_product(u,v)))),x)*.
% 299.89/300.47  161542[10:Rew:160202.0,146780.2] || member(cross_product(u,v),universal_class) member(ordered_pair(apply(choice,cross_product(u,v)),w),flip(x)) -> equal(cross_product(u,v),successor_relation) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),first(apply(choice,cross_product(u,v)))),w),x)*.
% 299.89/300.47  162723[10:Rew:160202.0,147536.0] ||  -> equal(symmetric_difference(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v))),successor_relation) member(regular(symmetric_difference(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v)))),complement(symmetric_difference(complement(intersection(u,v)),union(u,v))))*.
% 299.89/300.47  42485[2:Res:5714.3,6041.0] || connected(u,v) well_ordering(cross_product(w,not_well_ordering(u,v)),v)* member(x,w)* member(x,not_well_ordering(u,v))* subclass(not_well_ordering(u,v),y) well_ordering(cross_product(w,not_well_ordering(u,v)),y)* -> well_ordering(u,v).
% 299.89/300.47  162088[10:Rew:160202.0,147222.5] || well_ordering(cross_product(u,compose(v,w)),cross_product(universal_class,universal_class))* member(x,u)* member(x,compose(v,w))* subclass(compose(v,w),y) well_ordering(cross_product(u,compose(v,w)),y)* -> equal(compose(v,w),successor_relation).
% 299.89/300.47  41085[0:Rew:505.0,41064.4] || member(u,universal_class) subclass(power_class(intersection(complement(v),complement(w))),x)* well_ordering(y,x)* -> member(u,image(element_relation,union(v,w)))* member(least(y,power_class(intersection(complement(v),complement(w)))),power_class(intersection(complement(v),complement(w))))*.
% 299.89/300.47  125944[0:Res:28320.1,61.0] || subclass(rest_relation,rotate(image(u,image(v,singleton(w))))) member(ordered_pair(w,ordered_pair(ordered_pair(x,rest_of(ordered_pair(y,x))),y)),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,ordered_pair(ordered_pair(x,rest_of(ordered_pair(y,x))),y)),compose(u,v))*.
% 299.89/300.47  126074[0:Res:28321.1,61.0] || subclass(rest_relation,flip(image(u,image(v,singleton(w))))) member(ordered_pair(w,ordered_pair(ordered_pair(x,y),rest_of(ordered_pair(y,x)))),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,ordered_pair(ordered_pair(x,y),rest_of(ordered_pair(y,x)))),compose(u,v))*.
% 299.89/300.47  162684[10:Rew:160202.0,147257.2] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(universal_class,universal_class))* subclass(compose(v,w),x) -> equal(image(v,image(w,singleton(u))),successor_relation) member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),x)*.
% 299.89/300.47  39583[0:Res:5768.2,19.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,cross_product(w,x))* -> equal(ordered_pair(first(ordered_pair(u,ordered_pair(v,compose(u,v)))),second(ordered_pair(u,ordered_pair(v,compose(u,v))))),ordered_pair(u,ordered_pair(v,compose(u,v))))**.
% 299.89/300.47  204994[6:Rew:203192.0,204007.3] || section(u,v,w) well_ordering(x,v) subclass(singleton(least(x,cantor(restrict(u,w,v)))),cantor(restrict(u,w,v))) -> section(x,singleton(least(x,cantor(restrict(u,w,v)))),cantor(restrict(u,w,v)))*.
% 299.89/300.47  216418[14:Rew:199971.1,216310.4] || member(u,universal_class) member(ordered_pair(sum_class(range_of(u)),v),compose(w,x))* subclass(image(w,image(x,successor_relation)),y)* well_ordering(z,y)* -> member(least(z,image(w,image(x,successor_relation))),image(w,image(x,successor_relation)))*.
% 299.89/300.47  163752[10:Rew:160202.0,160675.3,160202.0,160675.2,160202.0,160675.1] || member(ordered_pair(u,not_subclass_element(range_of(successor_relation),v)),cross_product(universal_class,universal_class)) -> equal(cross_product(image(w,singleton(u)),universal_class),successor_relation) subclass(range_of(successor_relation),v) member(ordered_pair(u,not_subclass_element(range_of(successor_relation),v)),compose(regular(cross_product(image(w,singleton(u)),universal_class)),w))*.
% 299.89/300.47  163751[10:Rew:160202.0,160664.3,160202.0,160664.2,160202.0,160664.1] || member(ordered_pair(u,regular(image(v,range_of(successor_relation)))),cross_product(universal_class,universal_class)) -> equal(cross_product(singleton(u),universal_class),successor_relation) equal(image(v,range_of(successor_relation)),successor_relation) member(ordered_pair(u,regular(image(v,range_of(successor_relation)))),compose(v,regular(cross_product(singleton(u),universal_class))))*.
% 299.89/300.47  42471[0:Res:25.2,6041.0] || member(least(cross_product(u,intersection(v,w)),x),w)* member(least(cross_product(u,intersection(v,w)),x),v)* member(y,u)* member(y,x)* subclass(x,z)* well_ordering(cross_product(u,intersection(v,w)),z)* -> .
% 299.89/300.47  42488[0:Res:60.1,6041.0] || member(ordered_pair(u,least(cross_product(v,image(w,image(x,singleton(u)))),y)),compose(w,x))* member(z,v)* member(z,y)* subclass(y,x1)* well_ordering(cross_product(v,image(w,image(x,singleton(u)))),x1)* -> .
% 299.89/300.47  112496[0:MRR:112463.0,34067.1] || member(ordered_pair(u,least(intersection(v,union(w,x)),y)),v)* member(u,y) subclass(y,z)* well_ordering(intersection(v,union(w,x)),z)* -> member(ordered_pair(u,least(intersection(v,union(w,x)),y)),complement(x))*.
% 299.89/300.47  112657[0:MRR:112630.0,34067.1] || member(ordered_pair(u,least(intersection(v,union(w,x)),y)),v)* member(u,y) subclass(y,z)* well_ordering(intersection(v,union(w,x)),z)* -> member(ordered_pair(u,least(intersection(v,union(w,x)),y)),complement(w))*.
% 299.89/300.47  113270[0:Rew:1931.0,113155.1] || member(not_subclass_element(union(complement(intersection(u,v)),union(u,v)),symmetric_difference(complement(intersection(u,v)),union(u,v))),complement(symmetric_difference(u,v)))* -> subclass(union(complement(intersection(u,v)),union(u,v)),symmetric_difference(complement(intersection(u,v)),union(u,v))).
% 299.89/300.47  40230[0:Res:60.1,3886.0] || member(ordered_pair(u,not_subclass_element(v,intersection(w,image(x,image(y,singleton(u)))))),compose(x,y))* member(not_subclass_element(v,intersection(w,image(x,image(y,singleton(u))))),w)* -> subclass(v,intersection(w,image(x,image(y,singleton(u))))).
% 299.89/300.47  131776[0:SpR:1931.0,9529.1] ||  -> subclass(symmetric_difference(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v))),w) member(not_subclass_element(symmetric_difference(complement(symmetric_difference(u,v)),union(complement(intersection(u,v)),union(u,v))),w),complement(symmetric_difference(complement(intersection(u,v)),union(u,v))))*.
% 299.89/300.47  182941[6:Res:157922.1,6036.0] || member(ordered_pair(u,least(intersection(v,compose(element_relation,universal_class)),w)),element_relation)* member(ordered_pair(u,least(intersection(v,compose(element_relation,universal_class)),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,compose(element_relation,universal_class)),x)* -> .
% 299.89/300.47  39919[2:Res:5714.3,5554.0] || connected(u,v) well_ordering(w,v) member(x,y)* -> well_ordering(u,v) equal(ordered_pair(first(ordered_pair(x,least(w,not_well_ordering(u,v)))),second(ordered_pair(x,least(w,not_well_ordering(u,v))))),ordered_pair(x,least(w,not_well_ordering(u,v))))**.
% 299.89/300.47  162724[10:Rew:160202.0,147234.2] || well_ordering(u,cross_product(universal_class,universal_class)) member(v,w)* -> equal(compose(x,y),successor_relation) equal(ordered_pair(first(ordered_pair(v,least(u,compose(x,y)))),second(ordered_pair(v,least(u,compose(x,y))))),ordered_pair(v,least(u,compose(x,y))))**.
% 299.89/300.47  184017[14:Rew:183958.0,183973.2,183958.0,183973.1,183958.0,183973.0] || well_ordering(element_relation,image(recursion(u,successor_relation,successor_relation),singleton(v))) subclass(ordinal_add(u,v),image(recursion(u,successor_relation,successor_relation),singleton(v)))* -> equal(image(recursion(u,successor_relation,successor_relation),singleton(v)),ordinal_numbers) member(image(recursion(u,successor_relation,successor_relation),singleton(v)),ordinal_numbers).
% 299.89/300.47  112619[0:Res:30984.1,6041.0] || member(least(cross_product(u,union(v,w)),x),universal_class) member(y,u)* member(y,x)* subclass(x,z)* well_ordering(cross_product(u,union(v,w)),z)* -> member(least(cross_product(u,union(v,w)),x),complement(v))*.
% 299.89/300.47  112452[0:Res:30985.1,6041.0] || member(least(cross_product(u,union(v,w)),x),universal_class) member(y,u)* member(y,x)* subclass(x,z)* well_ordering(cross_product(u,union(v,w)),z)* -> member(least(cross_product(u,union(v,w)),x),complement(w))*.
% 299.89/300.47  43978[0:Res:34070.2,6036.0] || member(least(intersection(u,element_relation),v),universal_class) member(w,least(intersection(u,element_relation),v)) member(ordered_pair(w,least(intersection(u,element_relation),v)),u)* member(w,v) subclass(v,x)* well_ordering(intersection(u,element_relation),x)* -> .
% 299.89/300.47  137893[0:Rew:10028.0,137792.4] || member(u,universal_class) subclass(symmetrization_of(image(element_relation,complement(v))),w)* well_ordering(x,w)* -> member(u,intersection(power_class(v),complement(inverse(image(element_relation,complement(v))))))* member(least(x,symmetrization_of(image(element_relation,complement(v)))),symmetrization_of(image(element_relation,complement(v))))*.
% 299.89/300.47  137273[0:Rew:10029.0,137174.4] || member(u,universal_class) subclass(successor(image(element_relation,complement(v))),w)* well_ordering(x,w)* -> member(u,intersection(power_class(v),complement(singleton(image(element_relation,complement(v))))))* member(least(x,successor(image(element_relation,complement(v)))),successor(image(element_relation,complement(v))))*.
% 299.89/300.47  89260[0:Res:51387.0,61.0] || member(ordered_pair(u,not_subclass_element(v,complement(image(w,image(x,singleton(u)))))),cross_product(universal_class,universal_class)) -> subclass(v,complement(image(w,image(x,singleton(u))))) member(ordered_pair(u,not_subclass_element(v,complement(image(w,image(x,singleton(u)))))),compose(w,x))*.
% 299.89/300.47  197971[15:Rew:190721.0,197953.2,190721.0,197953.0] || member(ordered_pair(inverse(u),not_subclass_element(image(v,image(w,successor_relation)),x)),cross_product(universal_class,universal_class)) -> equal(range_of(u),successor_relation) subclass(image(v,image(w,successor_relation)),x) member(ordered_pair(inverse(u),not_subclass_element(image(v,image(w,successor_relation)),x)),compose(v,w))*.
% 299.89/300.47  197972[10:Rew:181044.1,197952.2,181044.1,197952.1] || member(u,universal_class) member(ordered_pair(successor(u),not_subclass_element(image(v,image(w,successor_relation)),x)),cross_product(universal_class,universal_class)) -> subclass(image(v,image(w,successor_relation)),x) member(ordered_pair(successor(u),not_subclass_element(image(v,image(w,successor_relation)),x)),compose(v,w))*.
% 299.89/300.47  200228[14:Rew:200028.1,200083.2,200028.1,200083.1] || member(u,universal_class) member(ordered_pair(range_of(u),not_subclass_element(image(v,image(w,successor_relation)),x)),cross_product(universal_class,universal_class)) -> subclass(image(v,image(w,successor_relation)),x) member(ordered_pair(range_of(u),not_subclass_element(image(v,image(w,successor_relation)),x)),compose(v,w))*.
% 299.89/300.47  204996[6:Rew:203192.0,203575.2,203192.0,203575.2,203192.0,203575.1,203192.0,203575.1] single_valued_class(restrict(u,v,universal_class)) || subclass(image(u,v),cantor(cantor(w))) equal(cantor(cantor(x)),cantor(restrict(u,v,universal_class))) equal(restrict(u,v,universal_class),cross_product(universal_class,universal_class)) -> compatible(restrict(u,v,universal_class),x,w)*.
% 299.89/300.47  203585[6:Rew:203192.0,41904.0] || member(first(not_subclass_element(cross_product(u,v),w)),cantor(x)) equal(restrict(x,first(not_subclass_element(cross_product(u,v),w)),universal_class),second(not_subclass_element(cross_product(u,v),w)))** -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),rest_of(x)).
% 299.89/300.47  216419[14:Rew:199971.1,216246.2,199971.1,216246.1] || member(u,universal_class) member(ordered_pair(sum_class(range_of(u)),regular(image(v,image(w,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(v,image(w,successor_relation)),successor_relation) member(ordered_pair(sum_class(range_of(u)),regular(image(v,image(w,successor_relation)))),compose(v,w))*.
% 299.89/300.47  204997[10:Rew:203192.0,203615.4,203192.0,203615.3] || member(ordered_pair(u,least(intersection(v,cantor(w)),x)),v)* member(u,x) subclass(x,y)* well_ordering(intersection(v,cantor(w)),y)* -> equal(apply(w,ordered_pair(u,least(intersection(v,cantor(w)),x))),sum_class(range_of(successor_relation)))**.
% 299.89/300.47  204998[10:Rew:203192.0,203681.5,203192.0,203681.4] || member(least(cross_product(u,cantor(v)),w),universal_class) member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,cantor(v)),y)* -> equal(apply(v,least(cross_product(u,cantor(v)),w)),sum_class(range_of(successor_relation)))**.
% 299.89/300.47  163755[10:Rew:160202.0,160627.4,160202.0,160627.3] || member(ordered_pair(u,v),compose(w,regular(cross_product(singleton(u),universal_class))))* subclass(image(w,range_of(successor_relation)),x)* well_ordering(y,x)* -> equal(cross_product(singleton(u),universal_class),successor_relation) member(least(y,image(w,range_of(successor_relation))),image(w,range_of(successor_relation)))*.
% 299.89/300.47  163756[10:Rew:160202.0,160637.4,160202.0,160637.3] || member(ordered_pair(u,ordered_pair(v,least(image(w,range_of(successor_relation)),x))),compose(w,regular(cross_product(singleton(u),universal_class))))* member(v,x) subclass(x,y)* well_ordering(image(w,range_of(successor_relation)),y)* -> equal(cross_product(singleton(u),universal_class),successor_relation).
% 299.89/300.47  163757[10:Rew:160202.0,160677.4,160202.0,160677.3] || member(ordered_pair(u,ordered_pair(v,least(range_of(successor_relation),w))),compose(regular(cross_product(image(x,singleton(u)),universal_class)),x))* member(v,w) subclass(w,y)* well_ordering(range_of(successor_relation),y)* -> equal(cross_product(image(x,singleton(u)),universal_class),successor_relation).
% 299.89/300.47  229812[10:Res:221521.1,6036.0] || member(ordered_pair(u,least(intersection(v,complement(singleton(omega))),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,complement(singleton(omega))),x)* -> equal(integer_of(ordered_pair(u,least(intersection(v,complement(singleton(omega))),w))),successor_relation).
% 299.89/300.47  43004[0:Rew:1943.0,42928.4] || member(u,union(cross_product(v,w),x))* member(u,complement(restrict(x,v,w))) subclass(symmetric_difference(cross_product(v,w),x),y)* well_ordering(z,y)* -> member(least(z,symmetric_difference(cross_product(v,w),x)),symmetric_difference(cross_product(v,w),x))*.
% 299.89/300.47  43005[0:Rew:1938.0,42927.4] || member(u,union(v,cross_product(w,x)))* member(u,complement(restrict(v,w,x))) subclass(symmetric_difference(v,cross_product(w,x)),y)* well_ordering(z,y)* -> member(least(z,symmetric_difference(v,cross_product(w,x))),symmetric_difference(v,cross_product(w,x)))*.
% 299.89/300.47  44012[0:Rew:1005.0,43959.1] || member(singleton(singleton(singleton(least(intersection(u,v),w)))),v)* member(singleton(singleton(singleton(least(intersection(u,v),w)))),u)* member(singleton(least(intersection(u,v),w)),w)* subclass(w,x)* well_ordering(intersection(u,v),x)* -> .
% 299.89/300.47  140164[0:SpR:984.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(complement(u),power_class(image(element_relation,complement(v))))),union(union(u,image(element_relation,power_class(v))),union(complement(u),power_class(image(element_relation,complement(v)))))),symmetric_difference(union(u,image(element_relation,power_class(v))),union(complement(u),power_class(image(element_relation,complement(v))))))**.
% 299.89/300.47  139701[0:SpR:982.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(power_class(image(element_relation,complement(u))),complement(v))),union(union(image(element_relation,power_class(u)),v),union(power_class(image(element_relation,complement(u))),complement(v)))),symmetric_difference(union(image(element_relation,power_class(u)),v),union(power_class(image(element_relation,complement(u))),complement(v))))**.
% 299.89/300.47  161540[10:Rew:160202.0,146778.3] || member(cross_product(u,v),universal_class) member(second(apply(choice,cross_product(u,v))),universal_class) member(first(apply(choice,cross_product(u,v))),second(apply(choice,cross_product(u,v))))* -> equal(cross_product(u,v),successor_relation) member(apply(choice,cross_product(u,v)),element_relation).
% 299.89/300.47  43128[0:Res:6269.3,129.3] || member(least(rotate(u),v),universal_class) member(ordered_pair(w,x),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(x,least(rotate(u),v)),w),u)* member(ordered_pair(w,x),v) subclass(v,y)* well_ordering(rotate(u),y)* -> .
% 299.89/300.47  43163[0:Res:6260.3,129.3] || member(least(flip(u),v),universal_class) member(ordered_pair(w,x),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(x,w),least(flip(u),v)),u)* member(ordered_pair(w,x),v) subclass(v,y)* well_ordering(flip(u),y)* -> .
% 299.89/300.47  108274[2:Res:31069.2,61.0] inductive(image(u,image(v,singleton(w)))) || well_ordering(x,universal_class) member(ordered_pair(w,least(x,image(u,image(v,singleton(w))))),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,least(x,image(u,image(v,singleton(w))))),compose(u,v))*.
% 299.89/300.47  162728[10:Rew:160202.0,147173.2] || well_ordering(u,universal_class) member(ordered_pair(v,least(u,image(w,image(x,singleton(v))))),cross_product(universal_class,universal_class)) -> equal(image(w,image(x,singleton(v))),successor_relation) member(ordered_pair(v,least(u,image(w,image(x,singleton(v))))),compose(w,x))*.
% 299.89/300.47  44929[0:Res:6187.2,3.0] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(universal_class,universal_class))* subclass(compose(v,w),y) -> subclass(image(v,image(w,singleton(u))),x) member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),y)*.
% 299.89/300.47  162729[10:Rew:160202.0,147290.1] || member(ordered_pair(u,regular(complement(complement(image(v,image(w,singleton(u))))))),cross_product(universal_class,universal_class)) -> equal(complement(complement(image(v,image(w,singleton(u))))),successor_relation) member(ordered_pair(u,regular(complement(complement(image(v,image(w,singleton(u))))))),compose(v,w))*.
% 299.89/300.47  162727[10:Rew:160202.0,147172.1] || member(ordered_pair(u,regular(intersection(image(v,image(w,singleton(u))),x))),cross_product(universal_class,universal_class)) -> equal(intersection(image(v,image(w,singleton(u))),x),successor_relation) member(ordered_pair(u,regular(intersection(image(v,image(w,singleton(u))),x))),compose(v,w))*.
% 299.89/300.47  162726[10:Rew:160202.0,147171.1] || member(ordered_pair(u,regular(intersection(v,image(w,image(x,singleton(u)))))),cross_product(universal_class,universal_class)) -> equal(intersection(v,image(w,image(x,singleton(u)))),successor_relation) member(ordered_pair(u,regular(intersection(v,image(w,image(x,singleton(u)))))),compose(w,x))*.
% 299.89/300.47  162683[10:Rew:160202.0,147256.3] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(universal_class,universal_class))* subclass(compose(v,w),x)* well_ordering(y,x)* -> equal(image(v,image(w,singleton(u))),successor_relation) member(least(y,compose(v,w)),compose(v,w))*.
% 299.89/300.47  163759[10:Rew:160202.0,160667.3,160202.0,160667.2,160202.0,160667.1] || member(ordered_pair(u,not_subclass_element(image(v,range_of(successor_relation)),w)),cross_product(universal_class,universal_class)) -> equal(cross_product(singleton(u),universal_class),successor_relation) subclass(image(v,range_of(successor_relation)),w) member(ordered_pair(u,not_subclass_element(image(v,range_of(successor_relation)),w)),compose(v,regular(cross_product(singleton(u),universal_class))))*.
% 299.89/300.47  163765[10:Rew:160305.0,162863.0] ||  -> equal(intersection(complement(symmetric_difference(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals)),union(complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),union(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals))),symmetric_difference(complement(symmetric_difference(singleton(successor_relation),range_of(successor_relation))),union(complement(intersection(singleton(successor_relation),range_of(successor_relation))),kind_1_ordinals)))**.
% 299.89/300.47  40568[0:SpR:506.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(intersection(complement(u),complement(v)),w)),union(complement(intersection(intersection(complement(u),complement(v)),w)),complement(intersection(union(u,v),complement(w))))),symmetric_difference(complement(intersection(intersection(complement(u),complement(v)),w)),complement(intersection(union(u,v),complement(w)))))**.
% 299.89/300.47  40567[0:SpR:507.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(u,intersection(complement(v),complement(w)))),union(complement(intersection(u,intersection(complement(v),complement(w)))),complement(intersection(complement(u),union(v,w))))),symmetric_difference(complement(intersection(u,intersection(complement(v),complement(w)))),complement(intersection(complement(u),union(v,w)))))**.
% 299.89/300.47  44018[0:Rew:1934.0,43927.4,1934.0,43927.1] || member(ordered_pair(u,least(symmetric_difference(v,singleton(v)),w)),successor(v)) member(ordered_pair(u,least(symmetric_difference(v,singleton(v)),w)),complement(intersection(v,singleton(v))))* member(u,w) subclass(w,x)* well_ordering(symmetric_difference(v,singleton(v)),x)* -> .
% 299.89/300.47  44019[0:Rew:1933.0,43926.4,1933.0,43926.1] || member(ordered_pair(u,least(symmetric_difference(v,inverse(v)),w)),symmetrization_of(v)) member(ordered_pair(u,least(symmetric_difference(v,inverse(v)),w)),complement(intersection(v,inverse(v))))* member(u,w) subclass(w,x)* well_ordering(symmetric_difference(v,inverse(v)),x)* -> .
% 299.89/300.47  137100[0:SpR:10029.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(power_class(u),complement(singleton(image(element_relation,complement(u)))))),union(successor(image(element_relation,complement(u))),union(power_class(u),complement(singleton(image(element_relation,complement(u))))))),symmetric_difference(successor(image(element_relation,complement(u))),union(power_class(u),complement(singleton(image(element_relation,complement(u)))))))**.
% 299.89/300.47  137719[0:SpR:10028.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(power_class(u),complement(inverse(image(element_relation,complement(u)))))),union(symmetrization_of(image(element_relation,complement(u))),union(power_class(u),complement(inverse(image(element_relation,complement(u))))))),symmetric_difference(symmetrization_of(image(element_relation,complement(u))),union(power_class(u),complement(inverse(image(element_relation,complement(u)))))))**.
% 299.89/300.47  161539[10:Rew:160202.0,146775.3] || member(cross_product(u,v),universal_class) member(first(apply(choice,cross_product(u,v))),second(apply(choice,cross_product(u,v))))* member(apply(choice,cross_product(u,v)),cross_product(universal_class,universal_class)) -> equal(cross_product(u,v),successor_relation) member(apply(choice,cross_product(u,v)),element_relation).
% 299.89/300.47  161538[10:Rew:160202.0,146807.3] || member(second(regular(cross_product(u,v))),universal_class) member(first(regular(cross_product(u,v))),universal_class) equal(compose(w,first(regular(cross_product(u,v)))),second(regular(cross_product(u,v))))** -> equal(cross_product(u,v),successor_relation) member(regular(cross_product(u,v)),compose_class(w)).
% 299.89/300.47  162629[10:Rew:160202.0,147163.2] || member(intersection(u,complement(intersection(v,w))),universal_class) member(apply(choice,intersection(u,complement(intersection(v,w)))),union(v,w)) -> equal(intersection(u,complement(intersection(v,w))),successor_relation) member(apply(choice,intersection(u,complement(intersection(v,w)))),symmetric_difference(v,w))*.
% 299.89/300.47  162632[10:Rew:160202.0,147166.2] || member(intersection(complement(intersection(u,v)),w),universal_class) member(apply(choice,intersection(complement(intersection(u,v)),w)),union(u,v)) -> equal(intersection(complement(intersection(u,v)),w),successor_relation) member(apply(choice,intersection(complement(intersection(u,v)),w)),symmetric_difference(u,v))*.
% 299.89/300.47  162738[10:Rew:160202.0,147521.5] || well_ordering(image(u,image(v,singleton(w))),universal_class) member(ordered_pair(w,ordered_pair(x,y)),compose(u,v))* member(x,singleton(y)) subclass(singleton(y),z)* well_ordering(image(u,image(v,singleton(w))),z)* -> equal(singleton(y),successor_relation).
% 299.89/300.47  161764[10:Rew:160202.0,146694.3] || member(ordinal_numbers,universal_class) well_ordering(element_relation,image(choice,singleton(unordered_pair(u,v))))* subclass(v,image(choice,singleton(unordered_pair(u,v))))* -> equal(unordered_pair(u,v),successor_relation) equal(apply(choice,unordered_pair(u,v)),u) member(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers).
% 299.89/300.47  161765[10:Rew:160202.0,146693.3] || member(ordinal_numbers,universal_class) well_ordering(element_relation,image(choice,singleton(unordered_pair(u,v))))* subclass(u,image(choice,singleton(unordered_pair(u,v))))* -> equal(unordered_pair(u,v),successor_relation) equal(apply(choice,unordered_pair(u,v)),v) member(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers).
% 299.89/300.47  139896[0:Rew:982.0,139801.4] || member(u,universal_class) subclass(union(image(element_relation,power_class(v)),w),x)* well_ordering(y,x)* -> member(u,intersection(power_class(image(element_relation,complement(v))),complement(w)))* member(least(y,union(image(element_relation,power_class(v)),w)),union(image(element_relation,power_class(v)),w))*.
% 299.89/300.47  140360[0:Rew:984.0,140263.4] || member(u,universal_class) subclass(union(v,image(element_relation,power_class(w))),x)* well_ordering(y,x)* -> member(u,intersection(complement(v),power_class(image(element_relation,complement(w)))))* member(least(y,union(v,image(element_relation,power_class(w)))),union(v,image(element_relation,power_class(w))))*.
% 299.89/300.47  162737[10:Rew:160202.0,147064.4] || member(image(u,image(v,singleton(w))),universal_class) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(universal_class,universal_class))* subclass(compose(u,v),x)* well_ordering(universal_class,x) -> equal(image(u,image(v,singleton(w))),successor_relation).
% 299.89/300.47  44928[0:Res:6187.2,127.0] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(universal_class,universal_class))* subclass(compose(v,w),y)* well_ordering(z,y)* -> subclass(image(v,image(w,singleton(u))),x) member(least(z,compose(v,w)),compose(v,w))*.
% 299.89/300.47  197147[10:Res:6269.3,162356.0] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,u),v),x) subclass(rotate(x),y)* well_ordering(omega,y) -> equal(integer_of(ordered_pair(ordered_pair(ordered_pair(v,w),u),least(omega,rotate(x)))),successor_relation)**.
% 299.89/300.47  197223[10:Res:6260.3,162356.0] || member(u,universal_class) member(ordered_pair(v,w),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(w,v),u),x) subclass(flip(x),y)* well_ordering(omega,y) -> equal(integer_of(ordered_pair(ordered_pair(ordered_pair(v,w),u),least(omega,flip(x)))),successor_relation)**.
% 299.89/300.47  198538[10:Rew:181056.0,198521.2,181056.0,198521.1,181056.0,198521.0] || member(image(u,image(v,successor_relation)),universal_class) member(ordered_pair(universal_class,apply(choice,image(u,image(v,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(u,image(v,successor_relation)),successor_relation) member(ordered_pair(universal_class,apply(choice,image(u,image(v,successor_relation)))),compose(u,v))*.
% 299.89/300.47  216420[14:Rew:199971.1,216247.2,199971.1,216247.1] || member(u,universal_class) member(ordered_pair(sum_class(range_of(u)),not_subclass_element(image(v,image(w,successor_relation)),x)),cross_product(universal_class,universal_class)) -> subclass(image(v,image(w,successor_relation)),x) member(ordered_pair(sum_class(range_of(u)),not_subclass_element(image(v,image(w,successor_relation)),x)),compose(v,w))*.
% 299.89/300.47  203630[10:Rew:203192.0,163761.2] || member(image(u,range_of(successor_relation)),universal_class) member(ordered_pair(v,apply(choice,image(u,range_of(successor_relation)))),cross_product(universal_class,universal_class)) -> member(v,cantor(w)) equal(image(u,range_of(successor_relation)),successor_relation) member(ordered_pair(v,apply(choice,image(u,range_of(successor_relation)))),compose(u,w))*.
% 299.89/300.47  198544[10:Rew:193730.0,198526.2,193730.0,198526.1,193730.0,198526.0] || member(image(u,range_of(successor_relation)),universal_class) member(ordered_pair(v,apply(choice,image(u,range_of(successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(u,range_of(successor_relation)),successor_relation) member(ordered_pair(v,apply(choice,image(u,range_of(successor_relation)))),compose(u,complement(cross_product(singleton(v),universal_class))))*.
% 299.89/300.47  222528[24:Rew:222326.0,222394.2,222326.0,222394.1,222326.0,222394.0] || member(image(u,image(v,successor_relation)),universal_class) member(ordered_pair(kind_1_ordinals,apply(choice,image(u,image(v,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(u,image(v,successor_relation)),successor_relation) member(ordered_pair(kind_1_ordinals,apply(choice,image(u,image(v,successor_relation)))),compose(u,v))*.
% 299.89/300.47  40652[0:SpL:1931.0,3874.1] || member(u,union(complement(symmetric_difference(v,w)),union(complement(intersection(v,w)),union(v,w)))) member(u,complement(symmetric_difference(complement(intersection(v,w)),union(v,w)))) -> member(u,symmetric_difference(complement(symmetric_difference(v,w)),union(complement(intersection(v,w)),union(v,w))))*.
% 299.89/300.47  43883[0:SpL:1005.0,6044.0] || member(ordered_pair(u,singleton(singleton(singleton(least(image(v,image(w,singleton(u))),x))))),compose(v,w))* member(singleton(least(image(v,image(w,singleton(u))),x)),x)* subclass(x,y)* well_ordering(image(v,image(w,singleton(u))),y)* -> .
% 299.89/300.47  40222[0:Res:3872.2,3886.0] || member(not_subclass_element(u,intersection(v,restrict(w,x,y))),cross_product(x,y))* member(not_subclass_element(u,intersection(v,restrict(w,x,y))),w)* member(not_subclass_element(u,intersection(v,restrict(w,x,y))),v)* -> subclass(u,intersection(v,restrict(w,x,y))).
% 299.89/300.47  44024[0:MRR:43970.0,999.0] || member(ordered_pair(u,least(intersection(v,image(element_relation,complement(w))),x)),v)* member(u,x) subclass(x,y)* well_ordering(intersection(v,image(element_relation,complement(w))),y)* -> member(ordered_pair(u,least(intersection(v,image(element_relation,complement(w))),x)),power_class(w))*.
% 299.89/300.47  161536[10:Rew:160202.0,146805.2] || member(ordered_pair(ordered_pair(second(regular(cross_product(u,v))),w),first(regular(cross_product(u,v)))),x)* member(ordered_pair(regular(cross_product(u,v)),w),cross_product(cross_product(universal_class,universal_class),universal_class)) -> equal(cross_product(u,v),successor_relation) member(ordered_pair(regular(cross_product(u,v)),w),rotate(x)).
% 299.89/300.47  161535[10:Rew:160202.0,146806.2] || member(ordered_pair(ordered_pair(second(regular(cross_product(u,v))),first(regular(cross_product(u,v)))),w),x)* member(ordered_pair(regular(cross_product(u,v)),w),cross_product(cross_product(universal_class,universal_class),universal_class)) -> equal(cross_product(u,v),successor_relation) member(ordered_pair(regular(cross_product(u,v)),w),flip(x)).
% 299.89/300.47  161906[10:Rew:160202.0,147151.3] || member(u,universal_class) member(regular(cross_product(v,w)),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(second(regular(cross_product(v,w))),first(regular(cross_product(v,w)))),u),x)* -> equal(cross_product(v,w),successor_relation) member(ordered_pair(regular(cross_product(v,w)),u),flip(x)).
% 299.89/300.47  161905[10:Rew:160202.0,147152.3] || member(u,universal_class) member(regular(cross_product(v,w)),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(second(regular(cross_product(v,w))),u),first(regular(cross_product(v,w)))),x)* -> equal(cross_product(v,w),successor_relation) member(ordered_pair(regular(cross_product(v,w)),u),rotate(x)).
% 299.89/300.47  31102[2:Res:120.1,5832.1] inductive(compose(restrict(u,v,v),restrict(u,v,v))) || transitive(u,v) well_ordering(w,restrict(u,v,v)) -> member(least(w,compose(restrict(u,v,v),restrict(u,v,v))),compose(restrict(u,v,v),restrict(u,v,v)))*.
% 299.89/300.47  42478[0:Res:1028.1,6041.0] || member(least(cross_product(u,image(element_relation,complement(v))),w),universal_class) member(x,u)* member(x,w)* subclass(w,y)* well_ordering(cross_product(u,image(element_relation,complement(v))),y)* -> member(least(cross_product(u,image(element_relation,complement(v))),w),power_class(v))*.
% 299.89/300.47  107206[0:Res:34429.0,61.0] || member(ordered_pair(u,not_subclass_element(complement(complement(image(v,image(w,singleton(u))))),x)),cross_product(universal_class,universal_class)) -> subclass(complement(complement(image(v,image(w,singleton(u))))),x) member(ordered_pair(u,not_subclass_element(complement(complement(image(v,image(w,singleton(u))))),x)),compose(v,w))*.
% 299.89/300.47  9497[0:Res:340.1,61.0] || member(ordered_pair(u,not_subclass_element(intersection(image(v,image(w,singleton(u))),x),y)),cross_product(universal_class,universal_class)) -> subclass(intersection(image(v,image(w,singleton(u))),x),y) member(ordered_pair(u,not_subclass_element(intersection(image(v,image(w,singleton(u))),x),y)),compose(v,w))*.
% 299.89/300.47  9383[0:Res:322.1,61.0] || member(ordered_pair(u,not_subclass_element(intersection(v,image(w,image(x,singleton(u)))),y)),cross_product(universal_class,universal_class)) -> subclass(intersection(v,image(w,image(x,singleton(u)))),y) member(ordered_pair(u,not_subclass_element(intersection(v,image(w,image(x,singleton(u)))),y)),compose(w,x))*.
% 299.89/300.47  203665[6:Rew:203192.0,43984.0] || member(u,cantor(v)) equal(restrict(v,u,universal_class),least(intersection(w,rest_of(v)),x)) member(ordered_pair(u,least(intersection(w,rest_of(v)),x)),w)* member(u,x) subclass(x,y)* well_ordering(intersection(w,rest_of(v)),y)* -> .
% 299.89/300.47  221504[10:Res:218373.0,5857.1] || member(ordered_pair(u,v),compose(w,x))* well_ordering(y,complement(singleton(image(w,image(x,singleton(u)))))) -> equal(singleton(image(w,image(x,singleton(u)))),successor_relation) member(least(y,image(w,image(x,singleton(u)))),image(w,image(x,singleton(u))))*.
% 299.89/300.47  40616[0:SpR:1948.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(union(u,v),union(complement(u),complement(v)))),union(complement(symmetric_difference(complement(u),complement(v))),union(union(u,v),union(complement(u),complement(v))))),symmetric_difference(complement(symmetric_difference(complement(u),complement(v))),union(union(u,v),union(complement(u),complement(v)))))**.
% 299.89/300.47  161533[10:Rew:160202.0,146777.2] || member(cross_product(u,v),universal_class) member(w,apply(choice,cross_product(u,v)))* -> equal(cross_product(u,v),successor_relation) equal(w,unordered_pair(first(apply(choice,cross_product(u,v))),singleton(second(apply(choice,cross_product(u,v))))))* equal(w,singleton(first(apply(choice,cross_product(u,v))))).
% 299.89/300.47  162739[10:Rew:160202.0,147445.1] || member(ordered_pair(u,regular(restrict(image(v,image(w,singleton(u))),x,y))),cross_product(universal_class,universal_class)) -> equal(restrict(image(v,image(w,singleton(u))),x,y),successor_relation) member(ordered_pair(u,regular(restrict(image(v,image(w,singleton(u))),x,y))),compose(v,w))*.
% 299.89/300.47  39587[0:Res:5768.2,61.0] || member(ordered_pair(u,v),cross_product(universal_class,universal_class)) subclass(composition_function,image(w,image(x,singleton(y)))) member(ordered_pair(y,ordered_pair(u,ordered_pair(v,compose(u,v)))),cross_product(universal_class,universal_class)) -> member(ordered_pair(y,ordered_pair(u,ordered_pair(v,compose(u,v)))),compose(w,x))*.
% 299.89/300.47  163764[10:Rew:160202.0,160613.4,160202.0,160613.3,160202.0,160613.2,160202.0,160613.1] || member(range_of(successor_relation),universal_class) member(ordered_pair(u,apply(choice,range_of(successor_relation))),cross_product(universal_class,universal_class)) -> equal(cross_product(image(v,singleton(u)),universal_class),successor_relation) equal(range_of(successor_relation),successor_relation) member(ordered_pair(u,apply(choice,range_of(successor_relation))),compose(regular(cross_product(image(v,singleton(u)),universal_class)),v))*.
% 299.89/300.47  43962[0:Res:1951.1,6036.0] || member(ordered_pair(u,least(intersection(v,complement(intersection(w,x))),y)),symmetric_difference(w,x))* member(ordered_pair(u,least(intersection(v,complement(intersection(w,x))),y)),v)* member(u,y) subclass(y,z)* well_ordering(intersection(v,complement(intersection(w,x))),z)* -> .
% 299.89/300.47  42475[0:Res:3872.2,6041.0] || member(least(cross_product(u,restrict(v,w,x)),y),cross_product(w,x))* member(least(cross_product(u,restrict(v,w,x)),y),v)* member(z,u)* member(z,y)* subclass(y,x1)* well_ordering(cross_product(u,restrict(v,w,x)),x1)* -> .
% 299.89/300.47  161532[10:Rew:160202.0,146772.3] || member(cross_product(u,v),universal_class) equal(compose(w,first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))** member(apply(choice,cross_product(u,v)),cross_product(universal_class,universal_class))* -> equal(cross_product(u,v),successor_relation) member(apply(choice,cross_product(u,v)),compose_class(w)).
% 299.89/300.47  205017[10:MRR:205016.6,200894.0] || section(u,v,w) well_ordering(cross_product(x,cantor(restrict(u,w,v))),v)* member(y,x)* member(y,cantor(restrict(u,w,v)))* subclass(cantor(restrict(u,w,v)),z) well_ordering(cross_product(x,cantor(restrict(u,w,v))),z)* -> .
% 299.89/300.47  163767[10:Rew:160202.0,162854.4,160305.0,162854.4,160202.0,162854.1,160305.0,162854.1,160305.0,162854.0] || member(ordered_pair(u,least(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),v)),kind_1_ordinals) member(ordered_pair(u,least(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),v)),complement(intersection(singleton(successor_relation),range_of(successor_relation))))* member(u,v) subclass(v,w)* well_ordering(symmetric_difference(singleton(successor_relation),range_of(successor_relation)),w)* -> .
% 299.89/300.47  224766[25:MRR:205014.4,224753.0] single_valued_class(restrict(u,v,singleton(w))) || subclass(range_of(restrict(u,v,singleton(w))),cantor(segment(u,v,w)))* equal(cross_product(cantor(segment(u,v,w)),cantor(segment(u,v,w))),segment(u,v,w)) equal(restrict(u,v,singleton(w)),successor_relation) -> .
% 299.89/300.47  225497[25:Rew:224739.1,224993.3,224739.1,224993.2,224739.1,224993.1] function(u) || member(image(v,image(w,successor_relation)),universal_class) member(ordered_pair(u,apply(choice,image(v,image(w,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(v,image(w,successor_relation)),successor_relation) member(ordered_pair(u,apply(choice,image(v,image(w,successor_relation)))),compose(v,w))*.
% 299.89/300.47  230828[10:Res:160972.1,6041.0] || member(least(cross_product(u,image(element_relation,power_class(successor_relation))),v),universal_class) member(w,u)* member(w,v)* subclass(v,x)* well_ordering(cross_product(u,image(element_relation,power_class(successor_relation))),x)* -> member(least(cross_product(u,image(element_relation,power_class(successor_relation))),v),power_class(image(element_relation,universal_class)))*.
% 299.89/300.47  230882[10:MRR:230835.0,34067.1] || member(ordered_pair(u,least(intersection(v,image(element_relation,power_class(successor_relation))),w)),v)* member(u,w) subclass(w,x)* well_ordering(intersection(v,image(element_relation,power_class(successor_relation))),x)* -> member(ordered_pair(u,least(intersection(v,image(element_relation,power_class(successor_relation))),w)),power_class(image(element_relation,universal_class)))*.
% 299.89/300.47  44022[0:Rew:1948.0,43958.4,1948.0,43958.1] || member(ordered_pair(u,least(symmetric_difference(complement(v),complement(w)),x)),union(complement(v),complement(w)))* member(ordered_pair(u,least(symmetric_difference(complement(v),complement(w)),x)),union(v,w)) member(u,x) subclass(x,y)* well_ordering(symmetric_difference(complement(v),complement(w)),y)* -> .
% 299.89/300.47  40759[0:Rew:1931.0,40653.2,1931.0,40653.1] || member(not_subclass_element(u,symmetric_difference(complement(intersection(v,w)),union(v,w))),union(complement(intersection(v,w)),union(v,w)))* member(not_subclass_element(u,symmetric_difference(complement(intersection(v,w)),union(v,w))),complement(symmetric_difference(v,w))) -> subclass(u,symmetric_difference(complement(intersection(v,w)),union(v,w))).
% 299.89/300.47  161762[10:Rew:160202.0,146692.2] || well_ordering(element_relation,image(choice,singleton(unordered_pair(u,v))))* subclass(v,image(choice,singleton(unordered_pair(u,v))))* -> equal(unordered_pair(u,v),successor_relation) equal(apply(choice,unordered_pair(u,v)),u) equal(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers) member(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers).
% 299.89/300.47  161763[10:Rew:160202.0,146691.2] || well_ordering(element_relation,image(choice,singleton(unordered_pair(u,v))))* subclass(u,image(choice,singleton(unordered_pair(u,v))))* -> equal(unordered_pair(u,v),successor_relation) equal(apply(choice,unordered_pair(u,v)),v) equal(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers) member(image(choice,singleton(unordered_pair(u,v))),ordinal_numbers).
% 299.89/300.47  44017[0:MRR:43980.1,34067.1] || member(least(intersection(u,compose_class(v)),w),universal_class) equal(compose(v,x),least(intersection(u,compose_class(v)),w)) member(ordered_pair(x,least(intersection(u,compose_class(v)),w)),u)* member(x,w) subclass(w,y)* well_ordering(intersection(u,compose_class(v)),y)* -> .
% 299.89/300.47  108826[2:Res:31076.2,61.0] inductive(image(u,image(v,singleton(w)))) || well_ordering(x,image(u,image(v,singleton(w)))) member(ordered_pair(w,least(x,image(u,image(v,singleton(w))))),cross_product(universal_class,universal_class)) -> member(ordered_pair(w,least(x,image(u,image(v,singleton(w))))),compose(u,v))*.
% 299.89/300.47  162740[10:Rew:160202.0,147339.2] || well_ordering(u,image(v,image(w,singleton(x)))) member(ordered_pair(x,least(u,image(v,image(w,singleton(x))))),cross_product(universal_class,universal_class)) -> equal(image(v,image(w,singleton(x))),successor_relation) member(ordered_pair(x,least(u,image(v,image(w,singleton(x))))),compose(v,w))*.
% 299.89/300.47  123524[0:Res:978.1,61.0] || member(ordered_pair(u,not_subclass_element(restrict(image(v,image(w,singleton(u))),x,y),z)),cross_product(universal_class,universal_class)) -> subclass(restrict(image(v,image(w,singleton(u))),x,y),z) member(ordered_pair(u,not_subclass_element(restrict(image(v,image(w,singleton(u))),x,y),z)),compose(v,w))*.
% 299.89/300.47  39614[0:Res:5768.2,36.1] || member(ordered_pair(ordered_pair(u,v),w),cross_product(universal_class,universal_class)) subclass(composition_function,cross_product(cross_product(universal_class,universal_class),universal_class)) member(ordered_pair(ordered_pair(v,ordered_pair(w,compose(ordered_pair(u,v),w))),u),x) -> member(ordered_pair(ordered_pair(u,v),ordered_pair(w,compose(ordered_pair(u,v),w))),rotate(x))*.
% 299.89/300.47  39609[0:Res:5768.2,39.1] || member(ordered_pair(ordered_pair(u,v),w),cross_product(universal_class,universal_class)) subclass(composition_function,cross_product(cross_product(universal_class,universal_class),universal_class)) member(ordered_pair(ordered_pair(v,u),ordered_pair(w,compose(ordered_pair(u,v),w))),x) -> member(ordered_pair(ordered_pair(u,v),ordered_pair(w,compose(ordered_pair(u,v),w))),flip(x))*.
% 299.89/300.47  203642[10:Rew:203192.0,161530.1] || member(cross_product(u,v),universal_class) member(first(apply(choice,cross_product(u,v))),cantor(w)) equal(restrict(w,first(apply(choice,cross_product(u,v))),universal_class),second(apply(choice,cross_product(u,v))))** -> equal(cross_product(u,v),successor_relation) member(apply(choice,cross_product(u,v)),rest_of(w)).
% 299.89/300.47  205009[10:Rew:203192.0,203999.5,203192.0,203999.2] || section(u,v,w) well_ordering(x,v) subclass(cantor(restrict(u,w,v)),y)* well_ordering(omega,y) -> equal(cantor(restrict(u,w,v)),successor_relation) equal(integer_of(ordered_pair(least(x,cantor(restrict(u,w,v))),least(omega,cantor(restrict(u,w,v))))),successor_relation)**.
% 299.89/300.47  44027[0:MRR:43964.0,999.0] || member(ordered_pair(u,least(intersection(v,intersection(complement(w),complement(x))),y)),v)* member(u,y) subclass(y,z)* well_ordering(intersection(v,intersection(complement(w),complement(x))),z)* -> member(ordered_pair(u,least(intersection(v,intersection(complement(w),complement(x))),y)),union(w,x))*.
% 299.89/300.47  126000[0:Res:28320.1,6036.0] || subclass(rest_relation,rotate(u)) member(ordered_pair(ordered_pair(v,rest_of(ordered_pair(least(intersection(w,u),x),v))),least(intersection(w,u),x)),w)* member(ordered_pair(v,rest_of(ordered_pair(least(intersection(w,u),x),v))),x) subclass(x,y)* well_ordering(intersection(w,u),y)* -> .
% 299.89/300.47  43816[0:SpL:955.0,5932.1] || transitive(cross_product(u,v),w) subclass(restrict(cross_product(w,w),u,v),compose(restrict(cross_product(w,w),u,v),restrict(cross_product(w,w),u,v)))* -> equal(compose(restrict(cross_product(u,v),w,w),restrict(cross_product(u,v),w,w)),restrict(cross_product(u,v),w,w)).
% 299.89/300.47  43170[0:Rew:2330.1,43158.1] || member(u,universal_class) member(not_subclass_element(cross_product(v,w),x),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(v,w),x)),first(not_subclass_element(cross_product(v,w),x))),u),y)* -> subclass(cross_product(v,w),x) member(ordered_pair(not_subclass_element(cross_product(v,w),x),u),flip(y)).
% 299.89/300.48  43135[0:Rew:2330.1,43123.1] || member(u,universal_class) member(not_subclass_element(cross_product(v,w),x),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(v,w),x)),u),first(not_subclass_element(cross_product(v,w),x))),y)* -> subclass(cross_product(v,w),x) member(ordered_pair(not_subclass_element(cross_product(v,w),x),u),rotate(y)).
% 299.89/300.48  41953[0:Rew:2330.1,41937.3] || member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(u,v),w)),first(not_subclass_element(cross_product(u,v),w))),x),y)* member(ordered_pair(not_subclass_element(cross_product(u,v),w),x),cross_product(cross_product(universal_class,universal_class),universal_class)) -> subclass(cross_product(u,v),w) member(ordered_pair(not_subclass_element(cross_product(u,v),w),x),flip(y)).
% 299.89/300.48  41954[0:Rew:2330.1,41936.3] || member(ordered_pair(ordered_pair(second(not_subclass_element(cross_product(u,v),w)),x),first(not_subclass_element(cross_product(u,v),w))),y)* member(ordered_pair(not_subclass_element(cross_product(u,v),w),x),cross_product(cross_product(universal_class,universal_class),universal_class)) -> subclass(cross_product(u,v),w) member(ordered_pair(not_subclass_element(cross_product(u,v),w),x),rotate(y)).
% 299.89/300.48  41900[0:SpR:2330.1,6010.3] || member(second(not_subclass_element(cross_product(u,v),w)),universal_class) member(first(not_subclass_element(cross_product(u,v),w)),universal_class) equal(compose(x,first(not_subclass_element(cross_product(u,v),w))),second(not_subclass_element(cross_product(u,v),w)))** -> subclass(cross_product(u,v),w) member(not_subclass_element(cross_product(u,v),w),compose_class(x)).
% 299.89/300.48  162742[10:Rew:160202.0,147258.2] || transitive(cross_product(u,v),w) well_ordering(x,restrict(cross_product(u,v),w,w)) -> equal(segment(x,compose(restrict(cross_product(w,w),u,v),restrict(cross_product(w,w),u,v)),least(x,compose(restrict(cross_product(w,w),u,v),restrict(cross_product(w,w),u,v)))),successor_relation)**.
% 299.89/300.48  162589[10:Rew:160202.0,146861.3] || transitive(u,v) well_ordering(w,restrict(u,v,v)) subclass(compose(restrict(u,v,v),restrict(u,v,v)),x) -> equal(compose(restrict(u,v,v),restrict(u,v,v)),successor_relation) member(least(w,compose(restrict(u,v,v),restrict(u,v,v))),x)*.
% 299.89/300.48  42472[0:Res:1032.1,6041.0] || member(least(cross_product(u,intersection(complement(v),complement(w))),x),universal_class) member(y,u)* member(y,x)* subclass(x,z)* well_ordering(cross_product(u,intersection(complement(v),complement(w))),z)* -> member(least(cross_product(u,intersection(complement(v),complement(w))),x),union(v,w))*.
% 299.89/300.48  162746[10:Rew:160202.0,147803.1] || member(ordered_pair(u,regular(intersection(intersection(v,image(w,image(x,singleton(u)))),y))),cross_product(universal_class,universal_class)) -> equal(intersection(intersection(v,image(w,image(x,singleton(u)))),y),successor_relation) member(ordered_pair(u,regular(intersection(intersection(v,image(w,image(x,singleton(u)))),y))),compose(w,x))*.
% 299.89/300.48  162745[10:Rew:160202.0,147738.1] || member(ordered_pair(u,regular(intersection(intersection(image(v,image(w,singleton(u))),x),y))),cross_product(universal_class,universal_class)) -> equal(intersection(intersection(image(v,image(w,singleton(u))),x),y),successor_relation) member(ordered_pair(u,regular(intersection(intersection(image(v,image(w,singleton(u))),x),y))),compose(v,w))*.
% 299.89/300.48  162744[10:Rew:160202.0,147690.1] || member(ordered_pair(u,regular(intersection(v,intersection(w,image(x,image(y,singleton(u))))))),cross_product(universal_class,universal_class)) -> equal(intersection(v,intersection(w,image(x,image(y,singleton(u))))),successor_relation) member(ordered_pair(u,regular(intersection(v,intersection(w,image(x,image(y,singleton(u))))))),compose(x,y))*.
% 299.89/300.48  162743[10:Rew:160202.0,147640.1] || member(ordered_pair(u,regular(intersection(v,intersection(image(w,image(x,singleton(u))),y)))),cross_product(universal_class,universal_class)) -> equal(intersection(v,intersection(image(w,image(x,singleton(u))),y)),successor_relation) member(ordered_pair(u,regular(intersection(v,intersection(image(w,image(x,singleton(u))),y)))),compose(w,x))*.
% 299.89/300.48  224767[25:MRR:205019.4,224753.0] single_valued_class(restrict(u,v,singleton(w))) || subclass(range_of(restrict(u,v,singleton(w))),cantor(segment(u,v,w)))* equal(cross_product(cantor(segment(u,v,w)),cantor(segment(u,v,w))),segment(u,v,w)) equal(restrict(u,v,singleton(w)),cross_product(universal_class,universal_class)) -> .
% 299.89/300.48  44025[0:Rew:1943.0,43933.4,1943.0,43933.1] || member(ordered_pair(u,least(symmetric_difference(cross_product(v,w),x),y)),union(cross_product(v,w),x))* member(ordered_pair(u,least(symmetric_difference(cross_product(v,w),x),y)),complement(restrict(x,v,w))) member(u,y) subclass(y,z)* well_ordering(symmetric_difference(cross_product(v,w),x),z)* -> .
% 299.89/300.48  44026[0:Rew:1938.0,43932.4,1938.0,43932.1] || member(ordered_pair(u,least(symmetric_difference(v,cross_product(w,x)),y)),union(v,cross_product(w,x)))* member(ordered_pair(u,least(symmetric_difference(v,cross_product(w,x)),y)),complement(restrict(v,w,x))) member(u,y) subclass(y,z)* well_ordering(symmetric_difference(v,cross_product(w,x)),z)* -> .
% 299.89/300.48  198542[15:Rew:190721.0,198523.3,190721.0,198523.1,190721.0,198523.0] || member(image(u,image(v,successor_relation)),universal_class) member(ordered_pair(inverse(w),apply(choice,image(u,image(v,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(range_of(w),successor_relation) equal(image(u,image(v,successor_relation)),successor_relation) member(ordered_pair(inverse(w),apply(choice,image(u,image(v,successor_relation)))),compose(u,v))*.
% 299.89/300.48  198543[10:Rew:181044.1,198522.3,181044.1,198522.2,181044.1,198522.1] || member(u,universal_class) member(image(v,image(w,successor_relation)),universal_class) member(ordered_pair(successor(u),apply(choice,image(v,image(w,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(v,image(w,successor_relation)),successor_relation) member(ordered_pair(successor(u),apply(choice,image(v,image(w,successor_relation)))),compose(v,w))*.
% 299.89/300.48  200229[14:Rew:200028.1,200106.3,200028.1,200106.2,200028.1,200106.1] || member(u,universal_class) member(image(v,image(w,successor_relation)),universal_class) member(ordered_pair(range_of(u),apply(choice,image(v,image(w,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(v,image(w,successor_relation)),successor_relation) member(ordered_pair(range_of(u),apply(choice,image(v,image(w,successor_relation)))),compose(v,w))*.
% 299.89/300.48  163766[10:Rew:160202.0,160679.4,160202.0,160679.3,160202.0,160679.2,160202.0,160679.1] || member(image(u,range_of(successor_relation)),universal_class) member(ordered_pair(v,apply(choice,image(u,range_of(successor_relation)))),cross_product(universal_class,universal_class)) -> equal(cross_product(singleton(v),universal_class),successor_relation) equal(image(u,range_of(successor_relation)),successor_relation) member(ordered_pair(v,apply(choice,image(u,range_of(successor_relation)))),compose(u,regular(cross_product(singleton(v),universal_class))))*.
% 299.89/300.48  204020[10:Rew:203192.0,162748.1] || asymmetric(cross_product(u,v),universal_class) member(universal_class,cantor(restrict(inverse(cross_product(u,v)),u,v))) equal(least(rest_of(restrict(inverse(cross_product(u,v)),u,v)),w),successor_relation)** member(universal_class,w) subclass(w,x)* well_ordering(rest_of(restrict(inverse(cross_product(u,v)),u,v)),x)* -> .
% 299.89/300.48  40593[0:SpR:1943.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(complement(restrict(u,v,w)),union(cross_product(v,w),u))),union(complement(symmetric_difference(cross_product(v,w),u)),union(complement(restrict(u,v,w)),union(cross_product(v,w),u)))),symmetric_difference(complement(symmetric_difference(cross_product(v,w),u)),union(complement(restrict(u,v,w)),union(cross_product(v,w),u))))**.
% 299.89/300.48  40592[0:SpR:1938.0,1931.0] ||  -> equal(intersection(complement(symmetric_difference(complement(restrict(u,v,w)),union(u,cross_product(v,w)))),union(complement(symmetric_difference(u,cross_product(v,w))),union(complement(restrict(u,v,w)),union(u,cross_product(v,w))))),symmetric_difference(complement(symmetric_difference(u,cross_product(v,w))),union(complement(restrict(u,v,w)),union(u,cross_product(v,w)))))**.
% 299.89/300.48  162735[10:Rew:160202.0,147066.3] || member(image(u,image(v,singleton(w))),universal_class) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(universal_class,universal_class))* subclass(compose(u,v),x) -> equal(image(u,image(v,singleton(w))),successor_relation) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),x)*.
% 299.89/300.48  197803[10:Res:162685.2,162356.0] || member(ordered_pair(u,regular(image(v,image(w,singleton(u))))),cross_product(universal_class,universal_class)) subclass(compose(v,w),x)* well_ordering(omega,x) -> equal(image(v,image(w,singleton(u))),successor_relation) equal(integer_of(ordered_pair(ordered_pair(u,regular(image(v,image(w,singleton(u))))),least(omega,compose(v,w)))),successor_relation)**.
% 299.89/300.48  216421[14:Rew:199971.1,216280.3,199971.1,216280.2,199971.1,216280.1] || member(u,universal_class) member(image(v,image(w,successor_relation)),universal_class) member(ordered_pair(sum_class(range_of(u)),apply(choice,image(v,image(w,successor_relation)))),cross_product(universal_class,universal_class)) -> equal(image(v,image(w,successor_relation)),successor_relation) member(ordered_pair(sum_class(range_of(u)),apply(choice,image(v,image(w,successor_relation)))),compose(v,w))*.
% 299.89/300.48  162734[10:Rew:160202.0,147065.4] || member(image(u,image(v,singleton(w))),universal_class) member(ordered_pair(w,apply(choice,image(u,image(v,singleton(w))))),cross_product(universal_class,universal_class))* subclass(compose(u,v),x)* well_ordering(y,x)* -> equal(image(u,image(v,singleton(w))),successor_relation) member(least(y,compose(u,v)),compose(u,v))*.
% 299.89/300.48  205015[10:Rew:203192.0,204002.4] || section(u,v,w) well_ordering(x,v) member(y,z)* -> equal(cantor(restrict(u,w,v)),successor_relation) equal(ordered_pair(first(ordered_pair(y,least(x,cantor(restrict(u,w,v))))),second(ordered_pair(y,least(x,cantor(restrict(u,w,v)))))),ordered_pair(y,least(x,cantor(restrict(u,w,v)))))**.
% 299.89/300.48  43963[0:Res:25.2,6036.0] || member(ordered_pair(u,least(intersection(v,intersection(w,x)),y)),x)* member(ordered_pair(u,least(intersection(v,intersection(w,x)),y)),w)* member(ordered_pair(u,least(intersection(v,intersection(w,x)),y)),v)* member(u,y) subclass(y,z)* well_ordering(intersection(v,intersection(w,x)),z)* -> .
% 299.89/300.48  43006[0:Rew:1931.0,42929.4] || member(u,union(complement(intersection(v,w)),union(v,w)))* member(u,complement(symmetric_difference(v,w))) subclass(symmetric_difference(complement(intersection(v,w)),union(v,w)),x)* well_ordering(y,x)* -> member(least(y,symmetric_difference(complement(intersection(v,w)),union(v,w))),symmetric_difference(complement(intersection(v,w)),union(v,w)))*.
% 299.89/300.48  197959[10:Res:6187.2,162356.0] || member(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),cross_product(universal_class,universal_class)) subclass(compose(v,w),y)* well_ordering(omega,y) -> subclass(image(v,image(w,singleton(u))),x) equal(integer_of(ordered_pair(ordered_pair(u,not_subclass_element(image(v,image(w,singleton(u))),x)),least(omega,compose(v,w)))),successor_relation)**.
% 299.89/300.48  43986[0:Res:60.1,6036.0] || member(ordered_pair(u,ordered_pair(v,least(intersection(w,image(x,image(y,singleton(u)))),z))),compose(x,y))* member(ordered_pair(v,least(intersection(w,image(x,image(y,singleton(u)))),z)),w)* member(v,z) subclass(z,x1)* well_ordering(intersection(w,image(x,image(y,singleton(u)))),x1)* -> .
% 299.89/300.48  161528[10:Rew:160202.0,146767.4] || member(cross_product(u,v),universal_class) member(w,universal_class) member(apply(choice,cross_product(u,v)),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),w),first(apply(choice,cross_product(u,v)))),x)* -> equal(cross_product(u,v),successor_relation) member(ordered_pair(apply(choice,cross_product(u,v)),w),rotate(x)).
% 299.89/300.48  161527[10:Rew:160202.0,146768.4] || member(cross_product(u,v),universal_class) member(w,universal_class) member(apply(choice,cross_product(u,v)),cross_product(universal_class,universal_class)) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),first(apply(choice,cross_product(u,v)))),w),x)* -> equal(cross_product(u,v),successor_relation) member(ordered_pair(apply(choice,cross_product(u,v)),w),flip(x)).
% 299.89/300.48  161526[10:Rew:160202.0,146769.3] || member(cross_product(u,v),universal_class) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),w),first(apply(choice,cross_product(u,v)))),x)* member(ordered_pair(apply(choice,cross_product(u,v)),w),cross_product(cross_product(universal_class,universal_class),universal_class)) -> equal(cross_product(u,v),successor_relation) member(ordered_pair(apply(choice,cross_product(u,v)),w),rotate(x)).
% 299.89/300.48  161525[10:Rew:160202.0,146770.3] || member(cross_product(u,v),universal_class) member(ordered_pair(ordered_pair(second(apply(choice,cross_product(u,v))),first(apply(choice,cross_product(u,v)))),w),x)* member(ordered_pair(apply(choice,cross_product(u,v)),w),cross_product(cross_product(universal_class,universal_class),universal_class)) -> equal(cross_product(u,v),successor_relation) member(ordered_pair(apply(choice,cross_product(u,v)),w),flip(x)).
% 299.89/300.48  161524[10:Rew:160202.0,146771.4] || member(cross_product(u,v),universal_class) member(second(apply(choice,cross_product(u,v))),universal_class) member(first(apply(choice,cross_product(u,v))),universal_class) equal(compose(w,first(apply(choice,cross_product(u,v)))),second(apply(choice,cross_product(u,v))))** -> equal(cross_product(u,v),successor_relation) member(apply(choice,cross_product(u,v)),compose_class(w)).
% 299.89/300.48  162752[10:Rew:160202.0,147217.2] || member(intersection(image(u,image(v,singleton(w))),x),universal_class) member(ordered_pair(w,apply(choice,intersection(image(u,image(v,singleton(w))),x))),cross_product(universal_class,universal_class)) -> equal(intersection(image(u,image(v,singleton(w))),x),successor_relation) member(ordered_pair(w,apply(choice,intersection(image(u,image(v,singleton(w))),x))),compose(u,v))*.
% 299.89/300.48  162753[10:Rew:160202.0,147218.2] || member(intersection(u,image(v,image(w,singleton(x)))),universal_class) member(orderCputime limit exceeded (core dumped)
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